Formula: A=bh/2<br><br> if b=50 and h=20, then A=?<br><br> Can someone explain how to solve this?

The scale factor of two similar solids is 6:13 determine the ratio of their corresponding areas and the volume of the larger sol

maksim [4K]

1. If the scale factor is k=6:13, then the ratio of their corresponding area is $k^{2}=6^{2} :13^{2} =36:169$ ;
2. $\frac{V_{small\ solid}}{V_{big\ solid}} =k^3= \frac{6^{3}}{13^{3}} = \frac{216}{2197}$ .

6 0

3 years ago

Please help with the questions in the image

Pavel [41]

Answer: f(x) = (x - 3)²

<u>Step-by-step explanation:</u>

Use the vertex formula: y = a(x - h)² + k

and input the vertex (h, k) = (3, 0) and the given point (x, y) = (4, 2) to solve for a

2 = a(4 - 3)² + 0

2 = a(1)²

2 = a

Now, input (h, k) = (3, 0) and a = 1 into the vertex formula:

y = 1(x - 3)² + 0 → y = (x - 3)²

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Answer: g(x) = -(x + 1.25)² + 2.5625

<u>Step-by-step explanation:</u>

Use the vertex formula: y = a(x - h)² + k

and input the given points for (x, y) to create a system of equations, then solve for a, h, and k.

EQ1: 2 = a(-2 - h)² + k

2 = a(4 + 4h + h²) + k

2 - 4a - 4ah - ah² = k

EQ2: 1 = a(0 - h)² + k

1 = ah² + k

1 - ah² = k

EQ3: -2.5 = a(1 - h)² + k

-2.5 = a(1 - 2h + h²) + k

-2.5 -a + 2h + ah² = k

<u>Substitute</u> - set EQ1 = EQ2 and EQ2 = EQ3 to eliminate k

EQ1 = EQ2: 2 - 4a - 4ah - ah² = 1 - ah²

1 - 4a - 4ah = 0

EQ2 = EQ3: 1 - ah² = -2.5 - a + 2ah - ah²

3.5 + a - 2ah = 0

<u>Elimination:</u> - now solve the system for "a"

1 - 4a - 4ah = 0 → 1(1 - 4a - 4ah = 0) → 1 - 4a - 4ah = 0

3.5 + a - 2ah = 0 → -2(3.5 + a - 2ah = 0) → <u> -7 - 2a + 4ah = 0 </u>

-6 - 6a = 0

-6a = 6

Next, replace "a" with -1 into either of the equations to solve for "h"

1 - 4a - 4ah = 0

1 - 4(-1) - 4(-1)h = 0

1 + 4 + 4h = 0

5 + 4h = 0

4h = -5

Now, replace "a" with -1 and "h" with -1.25 into any of the original equations (EQ1, EQ2, or EQ3) to solve for k:

1 - ah² = k

1 - (-1)(-1.25)² = k

1 - (-1)(1.5625) = k

1 + 1.5625 = k

Now, input (h, k) = (-1.25, 2.5625) and a = -1 into the vertex formula:

y = -1(x - (-1.25))² + 2.5625 → y = -(x + 1.25)² + 2.5625

4 0

3 years ago

in 2009 , first baseman matt craig of jacksonville suns southern league double-A baseball team had 24 hits in 80 times at bat .

maw [93]

Divide 24 by 80: 24/80=.3 :)

6 0

3 years ago

A town is designing a rectangular park that will be 600 feet wide by 1000 feet long. On a scale drawing, the dimensions of the p

KonstantinChe [14]

Scale drawing takes scaled versions of original lengths. The actual length of the swing set area of the park is 25 ft long and 100 ft wide

<h3>How are scale drawings formed?</h3>

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

$\rm 1\: ft : \dfrac{s}{k}\: in.$

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

For the given case, it is given that

Real dimension of a rectangular park : 600 ft by 1000 ft

In drawing, it was of 12 inches by 20 inches.

Let the scale that the drawing is using be k feet to s inches, then

$\rm 1\: ft : \dfrac{s}{k}\: in.$

Since it is given that 600 ft : 12 inches and 1000 ft : 20 inches, thus, we get:

$\rm 1\: ft : \dfrac{s}{k}\: in.\\\\600 \: ft = \dfrac{600\times s}{k} \: in. = 12 \: in.\\\\\dfrac{600 \times s}{k} = 12\\\\\dfrac{s}{k} = \dfrac{12}{600} = 0.02$

Thus, every feet is reduced 0.02 times in drawing.

Now,

it is given that in drawing, the rectangular area for swing sets is 0.5 inch to 2 inch.

Let its real length was L and real width was W. Then we have:
$\rm L \times 0.02 = 0.5 \\\\L = \dfrac{0.5}{0.02} = 25 \:\\\\W \times 0.02 = 2 \\W = \dfrac{2}{0.02} = 100$

Since these are only magnitudes, and unit was converted from feet to inches, so we have L = 25 feet and W = 100 feet

Thus,

The actual length of the swing set area of the park is 25 ft long and 100 ft wide

Learn more about scaling here:
brainly.com/question/8765466

6 0

2 years ago

What is the slope of the equation Y=5/4x-7/4?

maksim [4K]

Answer:

Step-by-step explanation:

Compare the equation with y = mx + b where m is slope and b is y intercept

y = (5/4)x - (7/4)

Slope = m = 5/4

4 0

2 years ago

Formula: A=bh/2 if b=50 and h=20, then A=? Can someone explain how to solve this?