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#19<br> The distance between the points (4, 1) and (9, 1) is

kirill115 [55]

Hello!

Given the two points, $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ , and to find the distance between these two points is found by using the formula:

$d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$

$(x_{1}, y_{1})$ is assigned to one the points, in this case, is (4, 1).

$(x_{2}, y_{2})$ is assigned to other point, which is (9, 1).

Then, plug in these values into the formula and solve.

$d = \sqrt{(9-4)^{2}-(1-1)^{2}}$

$d = \sqrt{5^{2}-0^{2}}$

$d = \sqrt{25}$

$d = 5$

Therefore, the distance between the two points is 5.

4 0

3 years ago

Which of the following equations describes the line shown

Arisa [49]

(-4,4) , (2,1)
slope=(y2-y1)/(x2-x1)
slope=m =(4-1)/(-4-2)=-3/6=-1/2
(y-y1)=m(x2-x1)
y-4=-1/2(x+4)
y-1=-1/2(x-2)

A,F

5 0

3 years ago

A mother is 1 and 3/4 times as tall as her son. Her son is 3 feet tall. How tall is the mother?

Inga [223]

Answer:

The mom is 5 feet 3 inches

Step-by-step explanation:

<u>Step 1: Make an equation</u>

m = 1 3/4 * 3

<u>Step 2: Solve</u>

m = (4/4+3/4) * 3

m = 7/4 * 3

m = 21/4

m = 5.25

<em>m = 5 feet 3 inches</em>

<em />

Answer: The mom is 5 feet 3 inches

7 0

3 years ago

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A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

3 years ago

Select the correct answer.

Svetlanka [38]

Answer:

<h3> $\boxed{ \boxed{ \bold{ {x}^{2} + 4x - 21}}}$ </h3>

Step-by-step explanation:

$\sf{(x - 3)(x + 7)}$

Use the distributive property to multiply each term of the first binomial by each term of the second binomial.

⇒ $\sf{x(x + 7) - 3(x + 7)}$

⇒ $\sf{ {x}^{2} + 7x - 3x - 21}$

Collect like terms

⇒ $\sf{ {x}^{2} + 4x - 21}$

Hope I helped!

Best regards!!

3 0

3 years ago

Read 2 more answers