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3 years ago

Solve the problem by entering and solving an equation.

Mathematics

1 answer:

geniusboy [140]3 years ago

5 0

Given : A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 12 inches.

To Find : The width of the frame .

Solution : Let us take the width of the frame be x . So , we know the formula to find the perimeter of rectangle as ;

$\boxed{\red{\bf Perimeter_{rectangle}=2(l+b)}}$

Where , l is the length of the rectangle and b is the breadth of the rectangle .

⇒ Perimeter = 2 ( l + b ) .

⇒ 52 in. = 2 ( 12 + x ) in.

⇒ 52 in.= 24in. + 2x .

⇒ 2x =( 52 - 24 ) in

⇒ 2x = 28 in.

⇒ x = 28/2 in.

⇒ x = 14 in.

Hence the width of the rectangle is 14 inches.

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The table shows the height of a plant as it grows. Which equation in point slope form gives the plant’s height at any time

vodka [1.7K]

Answer:

Option A is correct.

$y-16=8(x-2)$ is the equation represent the point slope form gives the plant's height at any time.

Step-by-step explanation:

Point slope intercept form: For any two points $(x_1, y_1)$ and $(x_2, y_2)$ then,

the general form

$y-y_1=m(x-x_1)$ for linear equations; where m is the slope given by:

$m =\frac{y_2-y_1}{x_2-x_1}$

Consider any two points from the table;

let A= (2 , 16) and B =(4, 32)

First calculate the slope of the line AB:

$m =\frac{y_2-y_1}{x_2-x_1}=\frac{32-16}{4-2}=\frac{16}{2}$ = 8

Therefore, slope of the line m = 8

Then,

the equation of line is:

$y-y_1=m(x-x_1)$

Substitute the value of m=8 and (2, 16) above we get;

$y-16=8(x-2)$

Therefore, the equation in point slope form which gives the plant's height at any time is; $y-16=8(x-2)$ , where x is the time(months) and y is the plant height (cm)

5 0

3 years ago

Read 2 more answers

Which are the solutions of x2 = –7x – 8?

vovangra [49]

Answer:

The solutions are:

$x_1=\frac{-7+\sqrt{17}}{2}$ $x_2=\frac{-7-\sqrt{17}}{2}$

Step-by-step explanation:

We have the following quadratic equation

$x^2 = -7x - 8$

We can rewrite the equation as follows

$x^2+7x + 8=0$

Now we use the quadratic formula to solve the equation

For an equation of the form $ax ^ 2 + bx + c = 0$ the quadratic formula is:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case:

$a=1,\ b=7,\ c=8$

Then:

$x=\frac{-7\±\sqrt{7^2-4(1)(8)}}{2(1)}$

$x=\frac{-7\±\sqrt{49-32}}{2}$

$x=\frac{-7\±\sqrt{17}}{2}$

$x_1=\frac{-7+\sqrt{17}}{2}$

$x_2=\frac{-7-\sqrt{17}}{2}$

7 0

3 years ago

Read 2 more answers

Pleaseeeee help, I need this now...

hoa [83]

Answer:

7/16.

Step-by-step explanation:

The first triangle has no shading.

The second triangle has 1/4 shaded.

The third has 3/9.

The fourth has 6/16.

Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.

The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.

So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.

Hope this helps!

3 0

3 years ago

In a test gender selection technique results consisted of 250 baby girls and 234 boys. Based on this result what is the probabil

Assoli18 [71]

Answer: 125/242

Step-by-step explanation: Probability is favorable outcomes over all outcome, since there were 250+234 total outcome, and 250 were favorable (girls), then the probability is 250/250+234=250/484=125/242

8 0

3 years ago

Ill give you brainliest

pentagon [3]

Answer:

376.8 ft²

Step-by-step explanation:

that is the correct answer for you friend

3 0

3 years ago