The highest elevation in California is 14,494 feet at Mt. Whitney and the lowest elevation is –282 feet at Death Valley. What is the total difference in elevation between these two places

Answer:

  8 cm

Step-by-step explanation:

See the diagram below.

The triangle formed by the radius, half the chord length, and the distance (d) from the center to the water is a right triangle with hypotenuse 20 cm and one leg length 16 cm. Then the other leg (d) can be found using the Pythagorean theorem:

  d^2 + 16^2 = 20^2

  d = √(400 -256) = 12

The depth of the water is the difference between this distance and the radius, so is ...

  20 cm - 12 cm = 8 cm

The maximum depth of the water in the pipe is 8 cm.

Answer:

8 cm

Step-by-step explanation:

I think it is A because the numbers decreased

Answer:

The coordinate would be (-1, -1)

Step-by-step explanation:

Answer: x = 19.42, y = 18.47, z = 18°

Step-by-step explanation:

This is assumed to be a 90° triangle so you can use Soh Cah Toa to answer the questions. You must use a calculator for the last step.

[tex]cos\theta=\dfrac{adjacent}{hypotenuse}\implies cos72^o=\dfrac{6}{x}\implies x=\dfrac{6}{cos72^o}\implies x=19.42\\\\\\tan\theta=\dfrac{opposite}{adjacent}\implies tan72^o=\dfrac{y}{6}\implies y=6\ tan72^o}\implies y=18.47\\\\[/tex]

Use Triangle Sum Theorem to find the angle measure of z:

90° + 72° + z = 180°

   162°     + z = 180°

                  z = 18°

Answer:

Step-by-step explanation:

[tex]\text{If set of order pairs belongs to a linear function, then}\\\\(x_1,\ y_1),\ (x_2,\ y_2),\ (x_3,\ y_3)\\\\\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_3-y_2}{x_3-x_2}\\\\=========================[/tex]

[tex]A)\\(-5,\ 16),\ (-1,\ 4),\ (3,\ -8),\ (7,\ -20)\\\\\dfrac{4-16}{-1-(-5)}=\dfrac{-12}{4}=-3\\\\\dfrac{-8-4}{3-(-1)}=\dfrac{-12}{4}=-3\\\\\dfrac{-20-(-8)}{7-3}=\dfrac{-12}{4}=-3\\\\\bold{CORRECT}[/tex]

[tex]B)\\(5,\ 16),\ (1,\ -4),\ (-3,\ -8),\ (-7,\ -20)\\\\\dfrac{-4-16}{1-5}=\dfrac{-20}{-4}=5\\\\\dfrac{-8-(-4)}{-3-1}=\dfrac{-4}{-4}=1\\\\\bold{INCORRECT}[/tex]

[tex]C)\\(-4,\ 16),\ (-1,\ 4),\ (2,\ -8),\ (6,\ -20)\\\\\dfrac{4-16}{-1-(-4)}=\dfrac{-12}{3}=-4\\\\\dfrac{-8-4}{2-(-1)}=\dfrac{-12}{3}=-4\\\\\dfrac{-20-(-8)}{6-2}=\dfrac{-12}{4}=-3\\\\\bold{INCORRECT}[/tex]

[tex]D)\\(5,\ -16),\ (1,\ -4),\ (-3,\ 8),\ (-7,\ -20)\\\\\dfrac{-4-(-16)}{1-5}=\dfrac{12}{-4}=-3\\\\\dfrac{8-(-4)}{-3-1}=\dfrac{12}{-4}=-3\\\\\dfrac{-20-8}{-7-(-3)}=\dfrac{-28}{-4}=7\\\\\bold{INCORRECT}[/tex]

Coordinates are the group of a number used to indicate the position of a point in a graph or at a scale.the coordinate of Cristian's house are (11,0)

Given-

Jayda's house is located at (1, 5).

A fast-food restaurant is located at (9, 1).

Fast-food restaurant partitions the way from Jayda's house to Cristian's house by a ratio of 4:1

Coordinates are the group of a number used to indicate the position of a point in a graph or at a scale.

Let the coordinate of jadya's be A (1,5))

Let the coordinate of Cristian's be B ([tex]x_2,y_2[/tex])

Let the coordinate of fast food restaurant be R (9,1)

The ratio is 4:1. Thus m is 4 and n is 1.

The coordinate of the point B is,

[tex]x_R=\dfrac{nx_1+mx_2}{m+n}[/tex]

[tex]9=\dfrac{1\times1+4\times x_2}{1+4}[/tex]

[tex]9=\dfrac{1+4 x_2}{5}[/tex]

[tex]4 x_2=9\times 5-1[/tex]

[tex]x_2=\dfrac{44}{4} =11[/tex]

Find the other point of Critian's house,

[tex]y_R=\dfrac{ny_1+my_2}{m+n}[/tex]

[tex]1=\dfrac{1\times5+4\times y_2}{1+4}[/tex]

[tex]1=\dfrac{5+4 y_1}{5}[/tex]

[tex]4y_1=5-5[/tex]

[tex]y_1=0[/tex]

Thus the coordinate of Cristian's house are (11,0).

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Answer:

  ±1/5, ±1, ±11/5, ±11

Step-by-step explanation:

Potential rational roots of 5x² -7x +11 will be of the form ...

  (divisor of 11)/(divisor of 5)

so will include ...

  ±1/5, ±1, ±11/5, ±11

Answer:

The lines are parallel.

Step-by-step explanation:

They are parallel if their slopes are the same.

Slope of Line A =  rise / run = (7-5) / (0 - -3) = 2/3.

Slope of Line B = (4-2) / 9-6) = 2/3.

Therefore they are parallel.

The lines passing through points (-3,5) and (0,7) and through points (6,2) and (9,4) are parallel to each other. The equation of a line perpendicular to y=-4x that passes through the point (2,6) is y=1/4x+5.5.

To determine whether the lines are parallel, perpendicular, or neither, we first need to calculate the slope of both lines. The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line. It's given by the formula m = (y2 - y1) / (x2 - x1).

For line A passing through points (-3,5) and (0,7), the slope (m1) is (7-5) / (0 - (-3)) = 2/3. For line B passing through points (6,2) and (9,4), the slope (m2) is (4-2) / (9-6) = 2/3. Since m1 = m2, Line A and Line B are parallel.

To write an equation of a line in slope-intercept form that is perpendicular to the line y = -4x and passes through the point (2,6), we first note that the slope of lines that are perpendicular to each other multiply to -1. Since the slope of the given line is -4, the slope of the line perpendicular to it would be 1/4. Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute for m and a point on the line (2,6) to solve for b: 6 = 1/4*2 + b. Solving for b gives b = 5.5. So the equation of the line is y = 1/4x + 5.5.

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For this case we have that there are a total of 14 male students and a total of 16 female students. Thus, there is a total of 30 students distributed in the four categories.

On the other hand, we have a total of 8 Junior students.

Then, the probability of selecting a student Junior is [tex]\frac {8} {30} * 100 = 26.67[/tex]

Rounding off we have 27%

Answer:

27%

The probability that the student is junior to the nearest whole percent is 27%

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

The total outcome will be the total number of students (both male and female)

Total outcome = 4+6+2+2+3+4+6+3

Total outcome = 30

Since we are to find the probability that the student is a junior.

Total Juniors = 2 + 6 = 8

Expected outcome = 8

Probability that the student is junior = 8/30

Express as a percentage:

[tex]Pr(Juniors)=\dfrac{8}{30} \times 100\%\\ Pr(Juniors)=\dfrac{800}{30}\\ Pr(Juniors)=26.66\%\\[/tex]

Hence the probability that the student is a junior is 27%.

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Answer:

The common difference is 3

Step-by-step explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant called the common difference

we have

[tex]5,8,11,14[/tex]

so

[tex]a1=5[/tex]

[tex]a2=8[/tex]

[tex]a3=11[/tex]

[tex]a4=14[/tex]

[tex]a2-a1=8-5=3[/tex]

[tex]a3-a2=11-8=3[/tex]

[tex]a4-a3=14-11=3[/tex]

therefore

The common difference is 3

Answer:

159.12

Step-by-step explanation:

find the amount with taxe (Ax1.02)

add all of them up together

then divide by 5

Answer:

159.12

Step-by-step explanation:

find the amount with taxe (Ax1.02)

add all of them up together

then divide by 5

Answer:

Part A)

scientific notation ------> [tex]2.56*10^{11}\ bits[/tex]

standard notation ----->  [tex]256,000,000,000\ bits[/tex]

Part B)

scientific notation ------> [tex]5.12*10^{11}\ bits[/tex]

standard notation ----->  [tex]512,000,000,000\ bits[/tex]

Part C)

scientific notation ------> [tex]1.28*10^{11}\ bits[/tex]

standard notation ----->  [tex]128,000,000,000\ bits[/tex]

Part D)

scientific notation ------> [tex]6.4*10^{10}\ bits[/tex]

standard notation ----->  [tex]64,000,000,000\ bits[/tex]

Part E)

scientific notation ------> [tex]3.2*10^{11}\ bits[/tex]

standard notation ----->  [tex]320,000,000,000\ bits[/tex]

Step-by-step explanation:

we know that

[tex]1\ Gigabyte=1*10^{9}\ bytes[/tex]

[tex]1\ byte=8\ bits[/tex]

therefore

[tex]1\ Gigabyte=8*10^{9}\ bits[/tex]

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation

we know that

Each phone have 32 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{32}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=32*8*10^{9}\\ \\x=256*10^{9}\ bits\\ \\x=2.56*10^{11}\ bits[/tex]

scientific notation ------> [tex]2.56*10^{11}\ bits[/tex]

standard notation ----->  [tex]256,000,000,000\ bits[/tex]

Part B

Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

we know that

Each phone have 64 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{64}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=64*8*10^{9}\\ \\x=512*10^{9}\ bits\\ \\x=5.12*10^{11}\ bits[/tex]

scientific notation ------> [tex]5.12*10^{11}\ bits[/tex]

standard notation ----->  [tex]512,000,000,000\ bits[/tex]

Part C

Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

we know that

Each tablet have 16 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{16}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=16*8*10^{9}\\ \\x=128*10^{9}\ bits\\ \\x=1.28*10^{11}\ bits[/tex]

scientific notation ------> [tex]1.28*10^{11}\ bits[/tex]

standard notation ----->  [tex]128,000,000,000\ bits[/tex]

Part D

Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation

we know that

Each SD card have 8 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{8}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=8*8*10^{9}\\ \\x=64*10^{9}\ bits\\ \\x=6.4*10^{10}\ bits[/tex]

scientific notation ------> [tex]6.4*10^{10}\ bits[/tex]

standard notation ----->  [tex]64,000,000,000\ bits[/tex]

Part E

With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation

we know that

The cloud have 40 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{40}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=40*8*10^{9}\\ \\x=320*10^{9}\ bits\\ \\x=3.2*10^{11}\ bits[/tex]

scientific notation ------> [tex]3.2*10^{11}\ bits[/tex]

standard notation ----->  [tex]320,000,000,000\ bits[/tex]

Answer:

Part A)

scientific notation ------> 2.56*10^{11}\ bits2.56∗10

11

bits

standard notation -----> 256,000,000,000\ bits256,000,000,000 bits

Part B)

scientific notation ------> 5.12*10^{11}\ bits5.12∗10

11

bits

standard notation -----> 512,000,000,000\ bits512,000,000,000 bits

Part C)

scientific notation ------> 1.28*10^{11}\ bits1.28∗10

11

bits

standard notation -----> 128,000,000,000\ bits128,000,000,000 bits

Part D)

scientific notation ------> 6.4*10^{10}\ bits6.4∗10

10

bits

standard notation -----> 64,000,000,000\ bits64,000,000,000 bits

Part E)

scientific notation ------> 3.2*10^{11}\ bits3.2∗10

11

bits

standard notation -----> 320,000,000,000\ bits320,000,000,000 bits

Step-by-step explanation:

we know that

1\ Gigabyte=1*10^{9}\ bytes1 Gigabyte=1∗10

9

bytes

1\ byte=8\ bits1 byte=8 bits

therefore

1\ Gigabyte=8*10^{9}\ bits1 Gigabyte=8∗10

9

bits

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation

we know that

Each phone have 32 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{32}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=32*8*10^{9}\\ \\x=256*10^{9}\ bits\\ \\x=2.56*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

32

bits

Gigabytes

x=32∗8∗10

9

x=256∗10

9

bits

x=2.56∗10

11

bits

scientific notation ------> 2.56*10^{11}\ bits2.56∗10

11

bits

standard notation -----> 256,000,000,000\ bits256,000,000,000 bits

Part B

Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

we know that

Each phone have 64 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{64}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=64*8*10^{9}\\ \\x=512*10^{9}\ bits\\ \\x=5.12*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

64

bits

Gigabytes

x=64∗8∗10

9

x=512∗10

9

bits

x=5.12∗10

11

bits

scientific notation ------> 5.12*10^{11}\ bits5.12∗10

11

bits

standard notation -----> 512,000,000,000\ bits512,000,000,000 bits

Part C

Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

we know that

Each tablet have 16 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{16}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=16*8*10^{9}\\ \\x=128*10^{9}\ bits\\ \\x=1.28*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

16

bits

Gigabytes

x=16∗8∗10

9

x=128∗10

9

bits

x=1.28∗10

11

bits

scientific notation ------> 1.28*10^{11}\ bits1.28∗10

11

bits

standard notation -----> 128,000,000,000\ bits128,000,000,000 bits

Part D

Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation

we know that

Each SD card have 8 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{8}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=8*8*10^{9}\\ \\x=64*10^{9}\ bits\\ \\x=6.4*10^{10}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

8

bits

Gigabytes

x=8∗8∗10

9

x=64∗10

9

bits

x=6.4∗10

10

bits

scientific notation ------> 6.4*10^{10}\ bits6.4∗10

10

bits

standard notation -----> 64,000,000,000\ bits64,000,000,000 bits

Part E

With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation

we know that

The cloud have 40 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{40}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=40*8*10^{9}\\ \\x=320*10^{9}\ bits\\ \\x=3.2*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

40

bits

Gigabytes

x=40∗8∗10

9

x=320∗10

9

bits

x=3.2∗10

11

bits

scientific notation ------> 3.2*10^{11}\ bits3.2∗10

11

bits

standard notation -----> 320,000,000,000\ bits320,000,000,000 bits

Answer: Option A

[tex]tan(60\°) = \sqrt{3}[/tex]

Step-by-step explanation:

We know the sides and z. So since it is a straight triangle we use the Pythagorean theorem to pull the length of the x side.

[tex]z ^ 2 = x ^ 2 + y ^ 2\\\\x^2 = z^2 - y^2\\\\x=\sqrt{z^2 - y^2}\\\\x=\sqrt{2^2 - 1^2}\\\\x=\sqrt{4 - 1}\\\\x=\sqrt{3}[/tex]

By definition, the tangent of an angle is:

[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]

In this case:

[tex]adjacent = y=1\\\\opposite=x =\sqrt{3}\\\\\theta=60\°[/tex]

Then:

[tex]tan(60\°) = \frac{\sqrt{3}}{1}[/tex]

[tex]tan(60\°) = \sqrt{3}[/tex]

The answer is:

The correct option is:

A. [tex]\sqrt{3}[/tex]

Since we already know the hypothenuse and the opposite side of the triangle (y), we can calculate the value of "x" using the Pythagorean Theorem.

We have that:

[tex]Hypothenuse^{2}=Adjacent^{2}+Opposite^{2}[/tex]

We know that:

[tex]Hypothenuse=z=2\\Adjacent=x=1[/tex]

So, substituting and calculating we have:

[tex]2^{2}=1^{2}+Opposite^{2}[/tex]

[tex]4-1=Opposite^{2}[/tex]

[tex]Opposite^{2}=3\\Opposite=\sqrt{3}[/tex]

Then,using the following trigonometric relation:

[tex]Tan(\alpha)=\frac{Opposite}{Adjacent}\\\\Tan(60\°)=Tan(\frac{Opposite}{Adjacent})=Tan(\frac{\sqrt{3} }{1})^=\sqrt{3[/tex]

We have that the correct option is:

A. [tex]\sqrt{3}[/tex]

Have a nice day!

Answer:

15 units

Step-by-step explanation:

I just took this geometry test with the same question. Its 15

Answer:

B

Step-by-step explanation:

Answer:

All the real numbers.

Step-by-step explanation:

We have that x≥-1 or x<2.

The 'or' means that it can be one value or another: [-1, +∞) U (-∞, 2) = ℝ. Then, the solution to the compound inequality is All the real numbers. In set notation: ℝ.

Final answer:

The compound inequality x ≥ -1 or x < 2 is satisfied by all real numbers between -1 and 2, inclusive on the -1. The solution set can be expressed as -1 ≤ x < 2 and visualized on a number line, including all numbers from -1 to just below 2.

Explanation:

To solve the compound inequality x ≥ -1 or x < 2, we need to consider the two parts of the inequality separately and then find the union of their solutions. The first inequality, x ≥ -1, represents all real numbers greater than or equal to -1. The second inequality, x < 2, represents all real numbers less than 2. Since any real number that satisfies either condition is part of the solution set, we find that the entire set of real numbers between -1 and 2, inclusive on the -1, satisfies the compound inequality.

To visualize this, we can plot the solution on a number line. The number -1 will be included in the solution set (as indicated by a closed circle or bracket), and extend to the right, towards infinity. Simultaneously, we will plot the solution for the second inequality, which starts from negative infinity and continues to the number 2, not including 2 (indicated by an open circle or parenthesis). The overlap of these two ranges gives us the final solution set for the inequality.

The solution to the compound inequality is therefore all real numbers that are greater than or equal to -1 or less than 2, which can be expressed simply as -1 ≤ x < 2.

The value of x is 20.1036 given that x³=8125. This can be obtained by using prime factorization.

The number 8125 can be written as factors of primes as,

8125 = 5×5×5×5×13

x³ = 5×5×5×5×13

Take cube roots on both sides,

⇒ x = ∛5×5×5×5×13

x = 5∛5×13

x = 5 × 4.02072 ⇒ x = 20.1036

Hence the value of x is 20.1036 given that x³=8125.

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To solve the equation x^3 = 8125 for x, we need to take the cube root of both sides of the equation. The cube root of a number y, denoted as y^(1/3), is a number which, when raised to the power of 3, gives y.
So, let's calculate the cube root of 8125:
First, we can factor 8125 into its prime factors to help simplify the cube root:
8125 = 5 * 1625 = 5 * 5 * 325 = 5 * 5 * 5 * 65 = 5 * 5 * 5 * 5 * 13   (Since 65 = 5 * 13)
Now that we have the prime factorization of 8125, we can group the factors into triples:
8125 = (5 * 5 * 5) * 13
Notice that there are three 5s in one group and a leftover 13 that cannot form a triple.
The cube root of a product of factors is the product of the cube roots of those factors, so taking the cube root of both sides of the equation gives us:
x = (5 * 5 * 5)^(1/3) * 13^(1/3)
x = 5 * 13^(1/3)
Because 13 is a prime number and cannot be broken down any further, it does not have a rational cube root. As a result, 13^(1/3) is an irrational number and cannot be represented exactly as a fraction. However, we can write the exact answer as:
x = 5 * 13^(1/3)
To find an approximate rational representation, we can look for a fraction that is close to the cube root of 13. Since we cannot do this exactly without a calculator, we can only leave our final answer like this, with the understanding that the cube root of 13 remains irrational.
In conclusion, the exact result, in simplest form without using an irrational-to-rational conversion (which would not be exact), is:
x = 5 * 13^(1/3)

8 days ago is -8 and the time was 24 minutes

9 days ago is -9 and the time was 18 minutes.

The time 2 days ago was halfway in between.

Add the two times together and divide by 2:

24 + 18 = 42 / 2 = 21 minutes

The coordinate is at (-2,21)

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilation's) can be found that map one figure onto another.  

In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that

Circle 1 is centered at (5,8) and has a radius of 8 centimeters

Circle 2 is centered at (1,-2) and has a radius of 4 centimeters

step 1

Move the center of the circle 1 onto the center of the circle 2

the transformation has the following rule

(x,y)--------> (x-4,y-10)

so

(5,8)------> (5-4,8-10)-----> (1,-2)

center circle 1 is now equal to center circle 2  

The circles are now concentric (they have the same center)

step 2

A dilation is needed to decrease the size of circle 1 to coincide with circle 2

scale factor=radius circle 2/radius circle 1-----> 4/8----> 0.5

radius circle 1 will be=8*scale factor-----> 8*0.5-----> 4 cm

radius circle 1 is now equal to radius circle 2  

therefore

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

Answer:

Option A (48 yards).

Step-by-step explanation:

The perimeter of any shape other than the ellipse is given by:

Perimeter = Sum of all sides.

Since there are two pairs of lines and both lines in the pair are congruent in each other in a rectangle, the formula can be updated as:

Perimeter of a rectangle = 2L + 2W; where L is the length and W is the width.

The perimeter of the fence around the rectangular pool is 108 feet and the width of the pool is 6 feet. The length can be calculated by plugging in the values in the above equation:

108 = 2L + 2(6).

2L = 108 - 12.

L = 96/2.

L = 48 feet.

So Option A is the correct answer!!!

The length of the fence in yards, if he uses all 108 feet of material, is 48 feet if Mason has 108 feet of material to build a fence around a rectangular pool on his property.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

Mason has 108 feet of material to build a fence around a rectangular pool on his property.

As we know,

Perimeter = Sum of all sides.

The perimeter of a rectangle (P) = 2L + 2W

Here L is the length and W is the width.

P = 109 feet

W = 6 feet

108 = 2L + 2(6)

2L = 108 - 12

L = 96/2

L = 48 feet.

Thus, the length of the fence in yards, if he uses all 108 feet of material, is 48 feet if Mason has 108 feet of material to build a fence around a rectangular pool on his property.

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Answer: Radical conjugate.

Step-by-step explanation:

By definition  [tex]a+\sqrt{b}[/tex] and [tex]a-\sqrt{b}[/tex] are called "Conjugate radicals".

Therefore, by this definition, you can know the following:

1) [tex]a+\sqrt{b}[/tex] is the conjugate of [tex]a-\sqrt{b}[/tex]

2) [tex]a-\sqrt{b}[/tex] is the conjugate of [tex]a+\sqrt{b}[/tex].

Then, since you know that [tex]3+\sqrt{11}[/tex] is a root of a polynomial function, therefore you can conclude that the name given to the other root [tex]3-\sqrt{11}[/tex] of the same function is the following:

"Radical conjugate".

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf f(x)=\cfrac{20}{4+3e^{-0.2x}}\implies f(3)=\cfrac{20}{4+3e^{-0.2(\stackrel{\downarrow }{3})}}\implies f(3)=\cfrac{20}{4+3e^{-0.6}} \\\\\\ f(3)=\cfrac{20}{4+3\frac{1}{e^{0.6}}}\implies f(3)=\cfrac{20}{4+3\frac{1}{e^{\frac{3}{5}}}}\implies f(3)=\cfrac{20}{4+3\frac{1}{\sqrt[5]{e^3}}} \\\\\\ f(3)=\cfrac{20}{4+\frac{3}{\sqrt[5]{e^3}}}\implies f(3)\approx\cfrac{20}{4+5.6464}\implies f(3)\approx 3.5421[/tex]

you could also just use plug in 0.6 as the exponent for "e", Euler's constant, in your calculator, and that works the same.

Answer:

  eight more than a fifth of a number

Step-by-step explanation:

k/5 is one-fifth of a number. When 8 is added to it, the result is ...

  eight more than a fifth of a number

_____

There is no multiplication by 5, so any phrasing with "five times" is incorrect.

The one-fifth multiplier is applied only to k, not to any sum.

Answer:

The correct statements that are true to functions are :

These above two can be explained as : We write a function as y = f(x), where x is the independent variable, and y is dependent as it depends on x values.

Rest all options are incorrect.

Answer:

The correct options are:

Option A: All functions have a dependent variable.

Option B: All functions have an independent variable.

Option E: A horizontal line is an example of a functional relationship.

Step-by-step explanation:

Consider the provided information.

Function: A function is a relationship where each input has only one output.

Which is denoted by "y=f(x)" where x is input value, also the variable x is independent and y is dependent.

Each input value has exactly one output value vice versa is not true.

Vertical line test: A equation is said to be a function if all vertical lines intersect the graph at most once.

Now consider the provided options:

Option A: All functions have a dependent variable.

This option is true, by the above definition of function.

Option B: All functions have an independent variable.

This option is true, by the above definition of function.

Option C: The range of a function includes its domain.

This option is false.

Understand this with the help of an example:

Consider the function [tex]y=x^2[/tex]

The range of the function is [0,∞) and domain of the function (-∞,∞).

Here range doesn't contains the domain.

Thus this option is wrong.  

Option D: vertical line is an example of a functional relationship.

The equation of the vertical line is x=a where a can be any real number.  

We have different values of y for a unique x also the function fails the vertical line test.

Thus the option D is False.

Option E: A horizontal line is an example of a functional relationship.

The equation of horizontal line is y=a where a can be any real number.

For each input has only one output also it satisfy the vertical line test. We will have same value of y for any x.  Which satisfy the property of function.

Thus this option is true.

Option F: Each output value of a function can correspond to only one input value by definition of function.

Understand this with the help of an example:

Consider the function y=a

The function has same output value for each input value. Which is the contradictory to the option's statement.

Thus, this option is false.

The correct options are:

Option A: All functions have a dependent variable.

Option B: All functions have an independent variable.

Option E: A horizontal line is an example of a functional relationship.

Answer:

1.83×[tex]10^{-9}[/tex]

Step-by-step explanation:

The exponent on the base of ten is -9 for both.  The easiest way to do this when that is the case is to factor it out:

[tex]10^{-9}(6.33-4.5)[/tex]

and then perform the subtraction to give you

1.83×[tex]10^{-9}[/tex]

Answer:

  A.  x ≈ 9/8

Step-by-step explanation:

We can see that left side > right side at x=1 and left side < right side at x=2. So, the solution is between x=1 and x=2.

As a first approximation, we can choose x = 3/2. Left side ≈ 0.73, right = 3.5

The solution is between x=1 and x=3/2.

For the 2nd approximation, we choose x = 5/4. Left ≈ 1.28, right = 2.25

The solution is between x=1 and x=5/4.

For the 3rd approximation, we choose x = 9/8. Left ≈ 1.62, right ≈ 1.63

The solution is between x=1 and x=9/8. The next estimate will be 17/16.

Our third estimate of the solution is 9/8.

d = 25 ft

ω = (45º) ⁄ 2 = 22.5º

sin(ω) = R ⁄ d

                sin(22.5º) = R ⁄ 25

R = 9.57 feet

Diameter = 2R

Diameter = 2 • (9.57)

Diameter = 19.1 feet

Diameter = 19 feet (when rounded)

Answer:

20

Step-by-step explanation:

did it on study island

To find the arithmetic sequence, we can first find it's common difference by deducting the first term by the second term:

-7-(-15)

=-7+15

=8

Therefore the common difference is 8, and to find the remaining terms we can add 8 for the respective terms.

T(4) = 1+8 =9

Therefore the answer is c)9,17,25,33.

Hope it helps!

Answer: c) 9,17,25,33

Step-by-step explanation:

Use the equation [tex]a_n=a_1+d(n-1)[/tex]

Where "n" is the nth term,  [tex]a_1[/tex] is the first term, "d" is the common difference and "n" is a integer greater than zero.

Find the common diference "d":

[tex]d=(-7)-(-15)\\d=8[/tex]

Then we know that:

[tex]a_1=-15\\d=8\\[/tex]

Since we need to find the next four terms and we know three terms then:

 For [tex]n=4[/tex]:

[tex]a_4=-15+8(4-1))=9[/tex]

For [tex]n=5[/tex]:

[tex]a_5=-15+8(5-1))=17[/tex]

For [tex]n=6[/tex]:

[tex]a_6=-15+8(6-1))=25[/tex]

For [tex]n=7[/tex]:

[tex]a_7=-15+8(7-1))=33[/tex]

Percentage is related to 100 and tells us how much we have of a quantity compared to another one. Suppose you have 100 cars and want to know how much cars are in red color. If 70 cars are red, then 70 percent of the cars are red. In general, we can find the percentage of a number following the steps:

For this example, let's take number 200 and the percentage 20%:

STEP 1: Multiply the number by the percentage:

200 x 20 = 4000

STEP 2: Now divide the number by 100:

400/100 = 40

STEP 3: If necessary., round to the desired precision.

To calculate the percentage of a number, divide the part by the whole and multiply by 100.

The percentage of a number is a measure of the proportion that a given quantity represents in relation to a whole, expressed as a fraction of 100. It's commonly used to express portions, ratios, and comparisons. For example, 25% of 100 is 25.

To calculate the percentage of a number, you can use the formula: (part/whole) * 100. Start by dividing the part by the whole, then multiply the result by 100. For example, if you want to find 25% of 80, you would divide 25 by 100 to get 0.25, then multiply 0.25 by 80 to get 20. So, 25% of 80 is 20.

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Answer:

No, because 3(2)+3 not equal to 15

Step-by-step explanation:

let the goals of Skylar be x

goals of wyatt be y

y=2x

x+y=15

3x=15

x=5

y=10

An equation is formed of two equal expressions. The correct option is A.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the goal scored by Skylar and Wyatt be x and y respectively. Now, given Wyatt scored 2 times as many goals as Skylar. Therefore,

y = 2x

Also, Together they scored 15 goals. Therefore,

x + y = 15

x + 2x = 15

3x = 15

x = 5

Thus, Skylar and Wyatt have scored 5 and 10 goals respectively.

Hence, the correct option is A.

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