If ΔFGH ≅ ΔIJK, which segment is congruent to segment GH?

segment HF
segment JK
segment IJ
segment FG

Answer:

2.8

Step-by-step explanation:

The given data set is;

6, 12, 10, 9, 8, 6, 2, 4, 8, 15

The mean of this set is;

[tex]\bar X=\frac{\sum x}{n}[/tex]

[tex]\bar X=\frac{6+12+10+9+8+6+2+4+8+15}{10}[/tex]

[tex]\bar X=\frac{80}{10}=8[/tex]

The mean absolute deviation is given by

[tex]M.A.D=\frac{\sum |x-\bar X|}{n}[/tex]

[tex]M.A.D=\frac{|6-8|+|12-8|+|10-8|+|9-8|+|8-8|+|6-8|+|2-8|+|4-8|+|8-8|+|15-8|}{10}[/tex]

[tex]M.A.D=\frac{2+4+2+1+0+2+6+4+0+7}{10}[/tex]

[tex]M.A.D=\frac{28}{10}[/tex]

[tex]M.A.D=2.8[/tex]

Answer:

y=6sin3(x+1)

Step-by-step explanation:

Answer:

28.8π ft² ≅ 90.48 ft²

Explanation:

Use the formula area of a sector.

Answer:

≈ 28.8π ft2 ≈ 90.48 ft2

Step-by-step explanation:

Answer:

1)  0.785 cubic units

2) 696.91 cu feet - see explanation.

3) π/12

Step-by-step explanation:

1) Volume of a cylinder with radius 1/2 and height of 1.

A cylinder is a circular prism. For any prism, to calculate its volume, we calculate the area of the shape of the prism, then multiply by its height. We all know how to calculate the area of a circle: A = π r², we have r (1/2). So...

A = π r² = π (1/2)² = π / 4 = 0.785 sq units

Now, we multiply this area by the height of the prism (h = 1):

V = A * h = 0.785 * 1 = 0.785 cubic units

2) Volume of a sphere, diameter of 11 ft

Since the diameter is 11 feet, that means the radius is 5.5 feet.

The sphere volume formula is:

V = (4/3)π r³, now that we have the radius, we can proceed:

V = (4/3)π r³ = V = (4/3)π (5.5)³ = V = (4/3)π * 166.375 =  221.833 π = 696.91 cu ft

However, that doesn't match any of your choices for answer.. so either you made an error in copying the answer choices or there was an error in the question... if we take a radius of 11 (instead of a diameter, we have 5575 cu ft, which is very close to one of your possible answers (5572).

3) Volume of a cone, radius of 1/2 and height of 1

The volume of a cone is found out with the formula:

V = (1/3)π r² h

We have all we need to calculate it:

V = (1/3)π (1/2)² (1) = (1/3) (1/4) π = (1/12) π = π/12

Prisms with a height of one are weird because it's basically like if they're a shape without height.

Answer:

5575.28

Step-by-step explanation:

Step-by-step Answer:

What is the solution to the system of equations?

y = –3x – 2 ..............(1)

5x + 2y = 15..............(2)

Substitute (1) in (2) to give

5x + 2(-3x-2) = 15

5x-6x-4 = 15

-x-4=15

solve for x:

-4-15 = x

x=-19

Now substitute x=-19 into equation (1)

y = -3x-2 = 57-2 = 55

Therefore the solution is (-19, 55)

The solution of system of equations are  (-19, 55)

The given system of equations are,

                        [tex]y=-3x-2..........(1)\\\\5x+2y=15........(2)[/tex]

Substituting the value of y from equation 1 into equation 2.

               [tex]5x+2(-3x-2)=15\\\\5x-6x-4=15\\\\x=-4-15=-19[/tex]

Substituting the value of x in equation 1

        [tex]y=-3(-19)-2\\\\y=57-2=55[/tex]

Thus, the solution of system of equations are  (-19, 55)

Learn more:

https://brainly.com/question/12526075

Your answer is D. 36 - 8i

I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!

Answer: D) 36 - 8i

Step-by-step explanation:

  (5 - 3i)(6 + 2i)

= 5(6 + 2i) -3i(6 + 2i)

= 30 + 10i  -18i - 6i²

= 30       - 8i     -6(-1)      reminder that i² = -1

= 30       - 8i     + 6

= 36 - 8i

Answer:

$59.27

Step-by-step explanation:

It is exponential decrease.

After each year goes by its worth 100 - 0.13 = 0.87 of the previous value.

The equation of decrease  is V = 90(0.87)^t   where t = the number of years.

So after 3 years it is worth  90(0.87)^3

= $59.27.

Answer:

88 times

Step-by-step explanation:

The two comes up 20 out of 50 times

We don't know how many times 2 will come up if the die is rolled 220 times. We can, however, set up a proportion

20/50 = x/220                    Cross multiply

50x = 20 * 220                   Combine the right

50x = 4400                         Divide by 50

50x/50 = 4400/50             Do the division

x = 88   times.

Answer:

88

Step-by-step explanation:

ANSWER

[tex]y ={x}^{2} + 2[/tex]

EXPLANATION

The equation of a parabola that has vertex at (h,k) is given by:

[tex]y = a {(x - h)}^{2} + k[/tex]

If the given parabola has vertex at (0,2), then h=0 and k=2.

Considering the possible answers, we must have a=1.

We substitute the values in to the formula to get:

[tex]y =1 {(x - 0)}^{2} + 2[/tex]

[tex]y ={x }^{2} + 2[/tex]

The first option is correct.

3x-14=58

3x-14+14= 58+14

3x= 72

Divide by 3 for 3x=72

x= 24

check answer by using substitution method

3x-14=58

3(24)-14=58

72-18=58

58=58

Answer is C.(x=24)

Answer:  The correct option is (A) 58.

Step-by-step explanation:  We are given to find the length of JK in the given figure.

From the figure, we note that

JKLM is a parallelogram. So, the opposite sides of JKLM will be parallel and congruent.

Also, JK = 3x - 14  and  LM = 58.

Since JK and LM are the opposite sides of the parallelogram JKLM , so we must have

[tex]JK=LM\\\\\Rightarrow 3x-14=58\\\\\Rightarrow 3x=58+14\\\\\Rightarrow 3x=72\\\\\Rightarrow x=\dfrac{72}{3}\\\\\Rightarrow x=24.[/tex]

Therefore, the length of JK is given by

[tex]JK=3x-14=3\times24-14=72-14=58.[/tex]

Thus, the length of JK is 58 units.

Option (A) is CORRECT.

Answer:

256 cm³

Step-by-step explanation:

Here, V = (1/3)(area of base)(height), and the numbers here are

          V = (1/3)(64 cm²)(12 cm) = 256 cm³

Answer: B.) an obtuse, C.) a right , C.) 4 or 6

Step-by-step explanation: i hope this helps :)

Answer:

3

Step-by-step explanation:

You have a 1 in 6 chance to roll a two. This means that every six times you roll a dice 1 of those should be a two (Obviously in the real world this wouldn't happen)

You roll the dice 18 TIMES and your chances are 1 in 6 so you take

[tex]18 \times \frac{1}{6} [/tex]

Answer:

the answer is 3

Answer:

34

Step-by-step explanation:

The sum of the 3rd and 5th square numbers is calculated by squaring 3 and 5, and then adding the results together, which gives us a total of 34.

The sum of the 3rd and 5th square numbers can be found by adding the squares of 3 and 5. A square number, or a perfect square, is a number that can be expressed as the product of an integer with itself. For example, to find the 3rd square number, we square 3 (3²), and for the 5th square number, we square 5 (5²).

So, calculating these we get:

Now, to find the sum of the squares, we just add these two results together:

9 + 25 = 34

Therefore, the sum of the 3rd and 5th square numbers is 34.

The question is:

What is the sum of the 3rd and 5th square numbers?

I need a more detailed question, but I think the answer is 6.

Answer:

x^4 + 4x^3 + 6x^2 + 7x +2

Step-by-step explanation:

Answer: Last option

(42÷2) +5

Step-by-step explanation:

We know that Mr. Roberts drove 42 miles on Monday.

On Tuesday Mr. Roberts drove half of what he drove on Monday plus 5 miles.

If we want to know how many miles Mr. Roberts drove on Tuesday then we should divide 42÷2 to find half of 42.

[tex]\frac{42}{2} = 21[/tex]

Then we know that in addition to the 21 miles he drove 5 more miles. Then we add 21 +5 = 26 miles.

So the expression that gives us the number of miles that Mr. Roberts drove on Tuesday is:

(42÷2) +5

The answer is D trust me

Plant with treatment A in general grow more than plants with treatment B.

Picture below.

Answer:

Treatment A:

Least value or minimum value= 6

Maximum value= 11.25

First quartile or lower quartile i.e. [tex]Q_1[/tex]= 8

Middle quartile or Median i.e. [tex]Q_2[/tex]= 8.5

Upper quartile or third quartile i.e. [tex]Q_3[/tex]= 9.5

Range= Maximum value-Minimum value

         =  11.25-6

        = 5.25

Interquartile range ( IQR)= [tex]Q_3-Q_1[/tex]

                                     =  9.5-8

                                    = 1.5

Treatment B:

Least value or minimum value= 2

Maximum value= 7.5

First quartile or  or lower quartile  i.e. [tex]Q_1[/tex] = 3.5

Middle quartile or Median  i.e. [tex]Q_2[/tex]= 4.75

Upper quartile or third quartile  i.e. [tex]Q_3[/tex]= 6

Range= Maximum value-Minimum value

         =  7.5-2

        = 5.5

Interquartile range ( IQR)= [tex]Q_3-Q_1[/tex]

                                     =  6-3.5

                                    = 2.5

The range in growth for treatment B is not much greater than the range in growth for treatment A.

( since there is a very less difference in range

5.5-5.25=0.25)

Since, the IQR as well range of treatment B is greater than treatment A.

Hence, Plants with treatment B in general grow more than plants with treatment A.

this is the answer, I guess.

1. Positive

2. Positive

3. Negative

4. Negative

5. Positive

6. Negative

When dividing, the only time you will get a negative answer is when only one of the numbers is negative

The identification of the rational numbers is as follows:

To identify whether the given rational numbers are positive or negative, we need to analyze each one based on the rules of sign with fractions. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers. In this context, if the numerator and denominator have the same sign, the fraction is positive. If they have different signs, the fraction is negative.

Let's evaluate each one:

+1/+7: Both the numerator (1) and the denominator (7) are positive, so this fraction is positive.
Result: Positive

+4/+4: Here too, both the numerator and denominator are positive, making this fraction positive.
Result: Positive

+4/-5: The numerator is positive (4) and the denominator is negative (-5), so this fraction is negative.
Result: Negative

+1/-7: Similar to the previous one, the numerator is positive (1) while the denominator is negative (-7), resulting in a negative fraction.
Result: Negative

-1/-7: Both the numerator (-1) and denominator (-7) are negative. Since a negative divided by a negative is positive, this fraction is positive.
Result: Positive

-4/+5: The numerator is negative (-4) and the denominator is positive (+5), making this fraction negative.
Result: Negative

the answer is........ B

For this case we must factor the following expression:

[tex]x^{12}y{18}+1[/tex]

We rewrite [tex]x^{12}y^{18}[/tex]as [tex](x ^ 4y ^ 6) ^ 3:[/tex]

[tex](x ^ 4y ^ 6) ^ 3 + 1[/tex]

Being both perfect cube terms, it is factored by applying the cube sum formula:

[tex]a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2)[/tex]

Where:

[tex]a = x ^ 4y ^ 6\\b = 1[/tex]

So:

[tex](x ^ 4y ^ 6 + 1) ((x ^ 4y ^ 6) ^ 2-x ^ 4y ^ 6 + 1 ^ 2) =\\(x ^ 4y ^ 6 + 1) (x ^ {8} y ^ {12} -x ^ 4y ^ 6 + 1)[/tex]

Answer:

Option B

Answer:

an area

Step-by-step explanation:

A two-dimensional (2D) figure is like drawing on a sheet of paper. It has some width and some length, but no height.

So, you cannot calculate its volume, since it has only 2 dimensions, a volume requires 3 dimensions.

The only spacial measure you can do on a two-dimensional figure is its area (basically length * width, if we talk about a rectangle, other forms have different calculation methods).

Answer:

A tree dimensional solid object bounded by six square faces

Answer:

<ACD = 35 degrees

Step-by-step explanation:

An intercepted angle is an arc segment of a circle whose endpoints connect at a point on the opposite side of the circle to create an angle. In this case arc AD is the intercepted arc of <ACD.

The measure of angle is half the measure of its intercepted arc.

AD measures 70 degrees, so divide this by 2.

70/2 = 35

<ACD = 35 degrees

Answer:

Both ladder reaches 18.1 m up the building ⇒ 3rd answer

Step-by-step explanation:

* Lets study the information to solve the problem

- There are two ladders

- The lengths of them are 22 m and 20 m

- The bottom of the longer was 4 m farther than the bottom of the

  shorter from the building

- Both of them reached the same distance up the building

* Lets solve the problem

- Let the distance between the bottom of the shorter ladder to the

 building is x

∵ The bottom of the longer ladder is farther by 4

∴ The distance between the bottom of the longer ladder and the

   building is x + 4

- Let the ladders reached the distance h up the building

* Now we have two right triangles

# Their hypotenuses are 22 and 20

# Their heights are h

# Their bases are x + 4 , x

- Lets find h in each triangle using the rule of Pythagoras

∵ (hypotenuse)² = (leg 1)² + (leg 2)²

# The longer ladder

∵ hypotenuse = 22

∵ leg 1 = x + 4

∵ leg 2 = h

∴ (22)² = (x + 4)² + h² ⇒ simplify

∴ 484 = (x + 4)² + h² ⇒ subtract (x + 4)² from both sides

∴ h² = 484 - (x + 4)² ⇒ (1)

# The shorter ladder

∵ hypotenuse = 20

∵ leg 1 = x

∵ leg 2 = h

∴ (20)² = (x )² + h² ⇒ simplify

∴ 400 = x² + h² ⇒ subtract x² from both sides

∴ h² = 400 - x² ⇒ (2)

- Equate (1) , (2) to find x

∴ 484 - (x + 4)² = 400 - x² ⇒ Add (x + 4)² and subtract 400 in both sides

∴ 84 = (x + 4)² - x² ⇒ open the bracket

∴ 84 = x² + 2(4)(x) + 4² - x² ⇒ simplify

∴ 84 = 8x + 14 ⇒ subtract 16 from both sides

∴ 68 = 8x ⇒ divide both sides by 8

∴ x = 8.5

- Substitute this value of x in (1) or (2) to find h

∵ h² = 400 - x²

∴ h² = 400 - (8.5)² = 327.75 ⇒ take √ for both sides

∴ h = 18.1

* Both ladder reaches 18.1 m up the building

Answer:

there is no relation between millimeters and liters

4000 milliliters = 4 liters

Step-by-step explanation:

"milli-" is a prefix meaning 1/1000. So 1 milliliter = (1/1000) liter. Thus it takes 1000 milliliters to make 1 liters, hence 4000 milliliters to make 4 liters.

_____

A meter, and a millimeter, is a measure of distance. A liter, and a milliliter, is a measure of volume. There is no sensible conversion between linear (one-dimensional) distance and 3-dimensional volume.

Converting liters to millimeters directly isn't typical because they represent different types of measurement: volume and length. However, in the context of a container's dimensions, it's needed to know that a 1-liter volume takes up a cube that is 10 cm (or 100 mm) on each side, and a 4-liter volume would be a cube of approximately 15.92 mm on each edge.

To convert liters to millimeters, it's important to understand that these are units of different quantities: liters are a measure of volume, while millimeters are a measure of length. Therefore, converting between the two directly isn't possible or meaningful. However, if you have a container with a certain liter capacity and want to know its dimensions in millimeters, you could potentially do this if the shape of the container is known.

As a reminder, when dealing with volume in the metric system, one cubic decimeter (dm³) is equivalent to one liter. A cube with edge lengths of exactly one decimeter, therefore, would contain a volume of one liter. This works out to a cube that is 10 cm (or 100 mm) on each side to equal 1 liter of volume. So, for a 4-liter volume, considering a perfect cubic, each side would be the cubic root of 4000 mm³ which is approximately 15.92 mm.

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Answer:

Option C. [tex]y+3=5(x+2)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

In this problem we have

[tex]m=5[/tex]

[tex](x1,y1)=(-2,-3)[/tex]

substitute the given values

[tex]y+3=5(x+2)[/tex]

Final answer:

The equation of the line with slope 5 that contains the point (-2, -3) is y + 3 = 5(x + 2), which corresponds to answer choice C.

Explanation:

To find the equation of the line with a given slope that contains a specific point, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). In this equation, m is the slope and (x1, y1) is the point the line passes through. Given the slope is 5 and the point is (
-2, -3), we substitute these values into the formula: y - (-3) = 5(x - (-2)), which simplifies to y + 3 = 5(x + 2). Therefore, the correct answer is C.

Answer:

3.1 ft

Step-by-step explanation:

The segment from the centre of the circle to the chord is a perpendicular bisector.

Thus the third side of the right triangle is half of x

let the third side be a then x = 2a

Applying Pythagoras' identity to the right triangle with hypotenuse 2.1 then

a² + 1.4² = 2.1²

a² + 1.96 = 4.41 ( subtract 1.96 from both sides )

a² = 2.45 ( take the square root of both sides )

a = [tex]\sqrt{2.45}[/tex]

Hence x = 2 × [tex]\sqrt{2.45}[/tex] ≈ 3.1 ft

Answer:

  second difference

Step-by-step explanation:

The differences of the y-values will differ by a common amount.

Example:

  y = x^2 for x = 2, 4, 6, 8

  y-values are 4, 16, 36, 64

  differences of these are 12, 20, 28

  differences of these differences are 8 and 8, a common value.

Answer:

For reference

Step-by-step explanation:

The Answer:

C. x=-1/2

Answer:  [tex]\bold{C)\quad -\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x+2}{15}=\dfrac{x+1}{5}\\\\\\\underline{\text{Multiply both sides by the LCD (15) to eliminate the denominator:}}\\x+2=3(x+1)\\x+2=3x+3\\.\quad \ 2=2x+3\\.\quad -1=2x\\\\.\quad \large\boxed{-\dfrac{1}{2}=x}[/tex]

Answer:

We have to determine the time it takes for carbon 14 to decay to 15% of its original amount.

The half life of carbon 14 is 5,730 years

elapsed time = half life * log (beginning amount / ending amount) / log 2

elapsed time = 5,730 * log (100 / 15) / log 2

elapsed time = 5,730 * 0.82390874094 / 0.30102999566

elapsed time = 5,730 * 2.7369655942

elapsed time = 15,683 years

= 15,700 years

Step-by-step explanation:

Solving the exponential equation, it is found that the painting is 15,679 years old.

The amount of carbon-14 after t years is modeled by the following equation:

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

It retains 15% of the original amount, thus:

[tex]A(t) = 0.15A(0)[/tex]

Solving for t, we find the age.

[tex]0.15A(0) = A(0)e^{-0.000121t}[/tex]

[tex]e^{-0.000121t} = 0.15[/tex]

[tex]\ln{e^{-0.000121t}} = \ln{0.15}[/tex]

[tex]-0.000121t = \ln{0.15}[/tex]

[tex]t = -\frac{\ln{0.15}}{0.000121}[/tex]

[tex]t = 15679[/tex]

The painting is 15,679 years old.

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