Which logarithmic graph can be used to approximate the value of y in the equation 3^y = 4?

The value of the natural logarithm when x = 0.5 is rounded to the nearest hundredth is -0.69. So option B is correct.

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Since x is lesser than 1, then the value of its natural logarithm must be negative.

The natural logarithm is a transcendental function and an irrational number, then it can be estimated by approximations.

ln ( 0.5) = -0.69

The value of the natural logarithm when x = 0.5 is rounded to the nearest hundredth is -0.69. So option B is correct.

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ten ways(10) i think so

The answer is 21 ways.

Hope this helps!

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=56 \end{cases}\implies 56=\cfrac{1}{2}bh\implies 112=bh \\\\\\ \boxed{112=2\cdot 2\cdot 2\cdot 2\cdot 7}\to \begin{cases} 16\cdot 7\\ 8\cdot 14\\ 4\cdot 28\\ 2\cdot 56 \end{cases}\qquad or\qquad \begin{cases} 7 \cdot 16\\ 14 \cdot 8\\ 28 \cdot 4\\ 56 \cdot 2 \end{cases}[/tex]

so their product is 112, so tis just a matter of doing some quick prime factoring and combining the factors about.

The triangle with an area of 56 m² can have the base-height pairs: (1, 112), (2, 56), (4, 28), (7, 16), (8, 14), (14, 8), (16, 7), (28, 4), (56, 2), and (112, 1). These pairs satisfy the equation base × height = 112.

The formula for the area of a triangle is 1/2 × base × height. Given that the area of a triangle is 56 m², we can write this as:

Area = 1/2 × base × height

Rearranging for whole number dimensions, we get:

base × height = 2 × Area

Therefore, base × height = 112 m².

Next, we find all pairs of whole numbers (base, height) whose product is 112:

These are all the possible sets of whole number dimensions for the base and height of the triangle with an area of 56 m².

For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.

So, we have to:

We look for the factors of 18 and 36:

18: 1,2,3,6,9,18

36: 1, 2,3,4, 6,9,18 ...

It is observed that the GFC of both numbers is 18.

Then, the GFC of [tex]18x ^ 2[/tex] and [tex]36x[/tex] is:

18x

Answer:

18x

The fourth vertex of a kite, given the vertices D(0, 3b), E(a, 0), and F(0, -5b), would be located at (-a, 0). This is based on the principles of symmetry inherent to a kite shape in geometry.

To identify the fourth vertex of the kite, we must consider the properties of the kite shape in geometry. A kite is defined by two pairs of adjacent sides that are equal in length. In a coordinate system, this corresponds to certain symmetries in the point coordinates.

Given the vertices D(0, 3b), E(a, 0), and F(0, -5b), we see that vertex D and F are both located on the y-axis, their y-coordinates being mirror images with respect to the x-axis. Thus, we can infer that vertex G is going to be a mirror image of point E with respect to y-axis, as we are dealing with a kite.

Hence, the coordinates for vertex G would be (-a, 0). This is because, the x-coordinate becomes the negative of 'a', while the 'y' coordinate remains the same, reflecting the symmetry of a kite's structure.

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The coordinates of point G in the kite are G(a, 3b)

To find the coordinates of point G, we can use the fact that the kite is a parallelogram.

Since the opposite sides of a parallelogram are congruent, we can find the coordinates of point G by using the coordinates of points D, E, and F.

Point G will have the same x-coordinate as point E and the same y-coordinate as point D.

Therefore, the coordinates of point G are G(a, 3b).

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Answer:

(x-5) (x+1)

Step-by-step explanation:

x^2-4x-5

We need to find what 2 numbers multiply to -5 and add to -4

-5*1 = -5

-5+1 = -4

(x-5) (x+1)

Answer:

6 miles per hour

Step-by-step explanation:

speed = distance/time

speed = 1/2÷1/12 which is the same as

1/2 x 12/1 = 6

6 miles per hour.

or ou could change the 1/2 to become 0.5

and the 1/12 to become 0.083333333

and divide 0.5 ÷ 0.083333333 = 6.000000024

rounded to one decima place become 6.0

6 miles per hour

Answer:

8 hour is the answer hope this help

Step-by-step explanation:

5) We want to find the union and the intersection of the given intervals.

A1(0,3] ; A2 [2,6)

From the diagram we can see that the intersection is

[2,3]

The union is from the lower boundary of the first interval to the upper boundary of the second interval.

The union is (0,6)

6) The second interval is

A1= (-∞, 6) A2 =(6,∞)

From the diagram, this interval has no intersection.

The intersection is a null set

[tex] \emptyset[/tex]

The union of this set is

(-∞,∞)

Answer:

the front part of a person's head from the forehead to the chin, or the corresponding part in an animal.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[8-6]^2+[5-(-3)]^2}\implies d=\sqrt{(8-6)^2+(5+3)^2} \\\\\\ d=\sqrt{2^2+8^2}\implies d=\sqrt{68}\implies d\approx 8.24[/tex]

Answer:

B. 8.24 units

Step-by-step explanation:

the distance between two points is given by

√(x₂₋x₁)²+ (y₂-y₁)²

x₂=8, x₁=6

y₂=5, y₁= -3

√(8-6)² + (5- (-3))²

√2²+ (5 + 3)²

√4 + 8²

√4 + 64

√68 = 8.24 units

Answer:

a. 9.5x + 6.5(x+c) < 8   when c>0

b. Must be one child more than the no. of adults.

Step-by-step explanation:

For Cinema 1:

for adult = $9.50

for child = $6.50

For Cinema 2:

Per person regardless of age = $8.00

First of all, we will find out the condition when per person rates in both cinema are equal.

Assume x = no. of adults

y = no. of children

Rate per person in Cinema I = Rate per person in Cinema II

(9.5x + 6.5y)/(x+y)   =   8

9.5x + 6.5y = 8(x+y)

9.5x + 6.5y = 8x + 8y

9.5x-8x = 8y-6.5y

=> x = y

So rates are equal when no. of adults equals no. of children

For Cinema I to have better rates, no. of children should be atleast 1 more than the no. of adult. In this way the rate per person of Cinema I will be less than 8

Hence we form an inequality when y = x+c and c > 0

9.5x + 6.5(x+c) < 8   when c>0

Hence there must be 1 more children than the no. of adults attending Cinema I for it to be a better deal.

Answer:

9.50a+6.50c < 8.00(a+c), 6 children

Step-by-step explanation:

Let the number of adults be a

the number of children be c

Part 1 :

Cinema 1:

Cost for adults = $9.50 x a = 9.50a

Cost of children = $6.50 x c = 6.50c

Total cost = 9.50a+6.50c

Cinema 2 :

Total cost = 8.00(a+c)

The inequality which shows that the cinema I is cheaper

9.50a+6.50c < 8.00(a+c)

9.50a+6.5c<8a+8c

9.5a-8a<8c-6.5c

1.5a<1.5c

a<c

Case 2:

6 adults goes to cinema , let they are accompanied by c number of children

Cinema 1

Total cost = 9.5 x 6 + 6.5 x c

for cinema 2 the total cost will be

8 ( 6+c)

for cinema 1 to be a better deal

9.5 x 6 + 6.5 x c  < 8(6+c)

57+6.5c<48+8c

57-48<8c-6.5c

9<1.5c

c>6

Hence for Cinema 1 to be a better deal , there must be 6 children accompanying them

Answer:

option C is correct.

Step-by-step explanation:

The area of triangle with sides a, b and c can be found by using formula

[tex]Area = \sqrt{s(s-a)(s-b)(s-c)} \\where \\s= \frac{1}{2}(a+b+c)[/tex]

We are given:

a= 20

b=30

c=40

Finding s:

Putting values in the formula and solving:

[tex]s= \frac{1}{2}(a+b+c)\\s=\frac{1}{2}(20+30+40)\\s=\frac{90}{2}\\s= 45[/tex]

Now, Finding the area:

Putting values in the formula and solving:

[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}\\Area =\sqrt{45(45-20)(45-30)(45-40)}\\Area =\sqrt{45(25)(15)(5)}\\Area = \sqrt{84,375}  \\Area = 290.5 units^2[/tex]

So, option C 290.5 units^2 is correct.

Answer:

option C 290.5 units^2 is correct.

Step-by-step explanation:

To solve the equation (j)/5 + 1 = -4, subtract 1 from both sides and then multiply by 5 to isolate j, which gives the solution j = -25.

To solve the equation (j)/5 + 1 = -4, you must first isolate the variable, j. Begin by subtracting 1 from both sides of the equation.

(j)/5 + 1 - 1 = -4 - 1

(j)/5 = -5

Next, multiply both sides by 5 to solve for j:

5 * (j)/5 = -5 * 5

j = -25

Therefore, the solution to the equation is j = -25.

Remember to always check your solution by substituting it back into the original equation to ensure it makes sense.

Answer:

The center is (8 , -9)

The vertices are (11 , -9) and (5 , -9)

The foci are (8 , -9 + √58) and (8 , -9 - √58)

The equations of the asymptotes are y = 3/7(x − 8) - 9 , y = -3/7 (x − 8) - 9

Step-by-step explanation:

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- The length of the transverse axis is 2 a  

- The coordinates of the vertices are ( h ± a , k )  

- The length of the conjugate axis is 2 b  

- The coordinates of the co-vertices are ( h , k ± b )

- The coordinates of the foci are (h , k ± c), where c² = a² + b²

- The equations of the asymptotes are y = ± a/b (x − h) + k

* Now lets solve the problem

∵ (y + 9)²/9 - (x - 8)²/49 = 1

∴ h = 8 and k = -9

∴ a² = 9 ⇒ a = ± 3

∴ b² = 49 ⇒ b = ± 7

∵ c² = a² + b²

∴ c² = 9 + 49 = 58

∴ c = ± √58

∵ The center is (h , k)

∴ The center is (8 , -9)

∵ The coordinates of the vertices are ( h ± a , k )

∴ The vertices are (8 + 3 , -9) and (8 - 3 , -9)

∴ The vertices are (11 , -9) and (5 , -9)

∵ The coordinates of the foci are (h , k ± c)

∴ The foci are (8 , -9 + √58) and (8 , -9 - √58)

∵ The equations of the asymptotes are y = ± a/b (x − h) + k

∴ The equations of the asymptotes are y  = 3/7 (x - 8) - 9 and  

   y  = -3/7 (x − 8) - 9

Answer:

Center = (-9,8)

Foci = (0,±7.6)

Vertices = (0,±3)

Asymptotes y = 8±(3/7)(x+9)

Step-by-step explanation:

We need to find the center, vertices, foci and asymptotes of hyperbola:

[tex]\frac{(y+9)^2}{9} - \frac{(x-8)^2}{49}=1[/tex]

The hyperbola has vertical transverse axis having standard equation:

[tex]\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2}=1[/tex]

The center is (h,k), foci (0,±c) , vertices = (0,±a) and

asymptotes = y= k±(a/b)(x-h)

Solving for the given equation by comparing with standard equation:

a^2 = 9 => a = 3

b^2 = 49 => b =7

h= -9

k= 8

c^2 - a^2 = b^2

c^2 = b^2 + a^2

c^2 = 49+9

c^2 = 58

c = 7.6

Now Center(h,k) = (-9,8)

Vertices (0, ±a) = (0,±3) or (0,+3), (0,-3)

Foci (0,±c) = (0, ±7.6) or (0+7.6), (0,-7.6)

Asymptotes = y= k±(a/b)(x-h)

Putting values:

y= 8±(3/7)(x-(-9)

y = 8±(3/7)(x+9)

or y = 8+(3/7)(x+9) and y= 8-(3/7)(x+9)

Check the picture below.

for "b", well, recall that the sum of all interior angles in a triangle is 180°.

for "a", "c" and "d", well, all those are just intercepted arcs.

Answer: mean = 3.6,  standard deviation = 3

Step-by-step explanation:

[tex]\text{Mean: }\dfrac{90\times 4}{100}=\dfrac{360}{100}=3.6\\\\\\\text{Standard Deviation: }\\\bullet n=100\qquad \rightarrow \text{number of students}\\\bullet p=0.9\qquad \rightarrow \text{probability of success}\\\bullet q=0.1\qquad \rightarrow \text{probability of failure}\\\\SD=\sqrt{n\times p\times q}\\.\quad =\sqrt{(100)(0.9)(0.1)}\\.\quad =\sqrt{9}\\.\quad =3[/tex]

Answer:

The first 4 are correct and the last one is incorrect

Step-by-step explanation:

1. The diameter of the circle is 30.8 m ( Correct )

Radius = 15.4 so diameter is 2 times the radius which is 30.8 m

2. The circumference in terms of π is 30.8 π ( Correct )

Circumference = π × Diameter

Circumference = π × 30.8

Circumference = 30.8 π

3 . The circumference of the circle can be found using 2 × π × 15 . 4 ( Correct )

Circumference = π × Diameter

Circumference = π × 30.8

Circumference = 30.8 π

4 . The approximate circumference of the circle rounded to the nearest tenth is 96.7 m ( Correct )

Circumference = 30.8 π = 96.7610537306

5 . A little more than 6 diameters could be wrapped around the circle

( False )

Circumference = 96.7610537306

Diameter = 30 . 8

96.7610537306 ÷ 30 . 8 = 3.14

P(7) = 1/8 = 0.125 out of 1

The value of P(7) = 1/8 = 0.125

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

There are 8 possibilities, all equally spaced

each one has a probability of 1/8

landing on a 7 is one options

so the P(7) is 1/8

P(7) = 1/8 = 0.125 out of 1

Toss a coin 100 times, how many Heads will come up, Probability says that heads have a ½ chance, so we can expect 50 Heads.

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Using the given inequality 16w≤ 40

Divide both sides by 16:

w ≤ 40/16

w ≤2.5

The answer would be: at most 2.5 ft wide.

The answer is A: at most 2.5 ft wide

Answer:

A. 10

Step-by-step explanation:

The two angles are vertical angles, thus they are equal. You solve once you set the two angles equal in an equation. See work for more.

Answer:

The correct answer is option B.  70

Step-by-step explanation:

From the figure we can see that a pair of vertically opposite angles.

Vertical opposite angles are equal.

To find the value of x

From figure we get,

<AEB = <CDE

2x + 50 = 7x

7x - 2x = 50

5x = 50

x = 10

To find m<AEB

m,<AEB =  2x + 50

 = 2*10 + 50

 = 20 + 50

 = 70°

Therefore the correct answer is option B.  70

Answer: C, the mean is most likely about 28 lbs.

Step-by-step explanation: The mean of a data set is the average value. When looking at this histogram, you can determine how many bags were checked in  total by adding up the frequencies for each weight.

Add the Weights

1+16(4)+20(5)+24(6)+28(5)+32(4)+36(3)+40+48+52+56+60

**16(4)=64. The number in parenthesis represents how many times each weight occurred in the data set. To make it easier, you can combine some of these instead of typing the extended equation into your calculator.

12+64+100+144+140+128+108+208= 904

Solve for the Mean

To do this, divide 904 by the number of bags checked (32).

Mean: 28.25

**The answer is MORE than 28, but it would round down because the decimal is less than half.

Hope this helps,

LaciaMelodii :)

The mean is most likely more than 28 pounds

The median is given as:

Median = 27.5 pounds

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{12+16(4)+20(5)+24(6)+28(5)+32(4)+36(3)+40+48(0)+52+56+60}{32}[/tex]

[tex]\bar x = \frac{904}{32}[/tex]

[tex]\bar x = 28.25[/tex]

28.25 is approximately 28, and it is more than 28

Hence, the mean is most likely more than 28 pounds

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ANSWER

reflection in the x-axis

shift 4 units right

shift 4 units down

EXPLANATION

The given function is

[tex]g(x) = - {2}^{x + 4} - 2[/tex]

The parent function is

[tex]f(x) = {2}^{x} [/tex]

The transformation applied to f(x) to obtain g(x) is of the form

g(x)=-f(x+c)-k

This will shift the graph to the left by c units and shift down by k units and reflected in the x-axis.

For

[tex]g(x) = - {2}^{x + 4} - 2[/tex]

The transformation are:

reflection in the x-axis

shift 4 units right

shift 4 units down

Answer: 325 feet per minute

Step-by-step explanation: If 65 feet is one minute, all you have to do is multiply 65 by 5.

Answer:

325 feet

Step-by-step explanation:

65 x 5 = 325

for every minute, she travels 65ft

Answer:

x<168

Step-by-step explanation:

The top left graph is the only one correct. It rises up slowly then faster, and then stays constant for an hour, then decreases.

The temperature starts at 50°, then it slowly increases. Next it increases quickly, then it stays the same temperature for an hour. And finally the temperature slowly decreases.

The 1st graph is your answer(top left)

It is not the 2nd graph (top right) because the temperature stays at 50° for 2 hours, than decreases, which does not match the description.

It is not graph 3 (bottom left) because it increases quickly, than stays the same for 4 hours.

It is not graph 4 (bottom right) because the graph is decreasing most of the time

Answer:

15 two-point questions and 5 four-point questions.

Step-by-step explanation:

Let x represent number of two-points questions and y represent number of four-points questions.

We have been given that Janice wants to create a test containing 20 questions. We can represent this information in an equation as:

[tex]x+y=20...(1)[/tex]

Since all questions are worth 50 points. We can represent this information in an equation as:

[tex]2x+4y=50...(2)[/tex]

From equation (1), we will get:

[tex]x=20-y[/tex]

Upon substituting this value in equation (2), we will get:

[tex]2(20-y)+4y=50[/tex]

[tex]40-2y+4y=50[/tex]

[tex]40+2y=50[/tex]

[tex]40-40+2y=50-40[/tex]

[tex]2y=10[/tex]

[tex]\frac{2y}{2}=\frac{10}{2}[/tex]

[tex]y=5[/tex]

Therefore, there are 5 questions that are worth 4 points each.

Now, we will substitute [tex]y=5[/tex] in equation (1) to solve for x.

[tex]x+5=20[/tex]

[tex]x+5-5=20-5[/tex]

[tex]x=15[/tex]

Therefore, there are 15 questions that are worth 2 points each.

Answer:

Step-by-step explanation:

I can give you an answer, but I'm afraid it will only be true on paper.

Area = L * W

(x^2- 6x - 7) = L * (x - 7)

(x - 7)(x + 1) = L * (x - 7)

(x - 7)(x + 1)

=========     = L

(x - 7)

(x + 1) = L

The expression representing the length of a rectangle could vary depending on context, such as using graph measurements (Δx = 41 m), significant figures (1.25 cm), or scaling factors (4 inches × 2 = 8 inches).

To determine the expression that represents the length of a rectangle, we generally use the formula for the perimeter or area, depending on what information is available. In this case, information provided suggests different scenarios involving measurements and area calculations. From one scenario, the length of a rectangle is calculated using graph paper measurements, resulting in Δx = 41 m. In another scenario, we're given information about a rectangle's width being 1.25 cm with three significant figures.

In physics-related contexts, references to frame of reference and speed c suggest considering displacement in spacetime, though this might not relate directly to the geometrical dimensions of a rectangle. Lastly, one mention involves the scaling up by a factor, such as a square with side length doubled, resulting in a side length expression of 4 inches × 2 = 8 inches. Without further context, it is not possible to provide a definitive expression for the length of a rectangle.

Answer: 82.26 yd^2

Step-by-step explanation:

Solve this question in steps.

Find the area of the rectangle.

9x6=54

Now, find the area of the circle.

The diameter is 6 so the radius must be 3.

3^2xpi=9pi=28.26

Add the values together.

54+28.26=82.26

Hope this helps!

Answer: 6300 cm 2

Step-by-step explanation: To find the volume of a 3d shape you have to use the formula L x W x H or (Length times Width Times Height).

So now we can see 15 x 15 x 28 = 6300

So you answer is 6300 cm 2

Btw if you did not know the 2 above cm means squared :)

Hope this helped have a nice day :)))))

the assumption here being that both lines JH and FH are tangent lines to the circle, if that's the case the external angle of 34° is the angle made by the equal tangents, meaning the triangle is an isosceles with twin sides.

In an isosceles triangle the twin sides make also twin angles, so the angles at J and F are twins, and they'd be 180° - 34° = 146° total, since they're twins, each one takes half, or 73°.

Answer:

n0

Step-by-step explanation: