1. What is true about a function?

Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of

ollegr [7]

Question:

Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q?

Answer:

x-coordinate of Q is 5

Solution:

Given that,

Point R divides in the ratio 1 : 3

Which means,

Point R divides the line segment PQ internally

The x-coordinate of the point which divides the line segment in ration m:n internally is given as:

$x=(\frac{mx_{2}+nx_{1}}{m+n} )$

Where,

$x$ = x-coordinate of point dividing the segment R = -1

$x_1$ = x-coordinate of P = -3

$x_2$ = x-coordinate of Q = ?

m : n = 1 : 3

m = 1

n = 3

Therefore,

$-1 = \frac{1 \times x_2 + 3 \times -3}{1+3}\\\\-1 = \frac{x_2 -9}{4}\\\\x_2 - 9 = -4\\\\x_2 = 9 - 4\\\\x_2 = 5$

Thus x-coordinate of Q is 5

5 0

2 years ago

The cylinders are similar the volume of the larger cylinder is 1600 cubic centimeters what is the volume of the smaller cylinder

cestrela7 [59]

We are given Volume of the larger cylinder is = 1600 cubic centimeters.

Height of the larger cylinder = 16 cm.

We know formula of volume of a cylinder V= $\pi r^2h$ , where r is the radius of cylinder, h is the height of the cylinder.

Plugging value of V and h of larger cylinder, we get

$1600=\pi r^2(16).$

Dividing both sides by 16, we get

$\frac{1600}{16}=\frac{\pi r^2 (16)}{16}$

$r^2=100$

Taking square root on both sides, we get

r=10.

Therefore, radius of the larger cylinder is 10 cm.

We are given cylinders are similar .

Note: The radii and heights of similiar cylinders are in same ratio.

Therefore, we can setup a proportion:

Let us take radius of small cylinder is x.

$\frac{x}{10}=\frac{4}{16}$

$\frac{x}{10}=\frac{1}{4}$

Multiplying both sides by 10, we get

$10 \times \frac{x}{10}=10 \times\frac{1}{4}$

x=2.50.

Therefore, radius of the small cylinder = 2.5 cm.

Now, plugging radius =2.5 and height = 4 in the formula of volume the cylinder, we get

$V=\pi (2.5)^2(4)=\pi (6.25)(4) =25 \pi \ cm^3.$

Therefore, correct option is 25 pi cm^3.

8 0

2 years ago

What is the length of side AB of parallelogram ABCD? units 4g - 8 B q+4

Andrews [41]

Answer:

8 units

Step-by-step explanation:

» Concepts

Parallelogram Side Theorem states that the opposite sides of a parallelogram are congruent, meaning they have the same length.

» Application

In this case, we're asked to apply the theorem to find the value of q and then find the length of AB. Thus, we have to set up the equation 4q - 8 = q + 4.

» Solving

Step 1: Subtract q from both sides.

$4q-8-q=q+4-q$
$3q-8=4$

Step 2: Add 8 to both sides.

$3q-8+8=4+8$
$3q=12$

Step 3: Divide both sides by 3.

$3q/3 = 12/3$
$q=4$

Step 4: Plug in the value of q for side AB.

$4(4)-8$
$16-8$
$8$

Therefore, the answer is 8 units.

6 0

1 year ago

A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 26 mugs with coffee, how many total quarts of co

r-ruslan [8.4K]

First let's find how many total ounces it would be by multiplying 16 ounces by the number of mugs (26).

16 × 26 = 416

So she needs 416 ounces of coffee. Now we have to convert ounces to quarts. We need to know that there are 32 ounces per quart. So to find quarts we divide 416 ounces by 32...

416 ÷ 32 = 13 quarts

*FYI- since the mugs hold 16 ounces we can see that 16 is half of 32 so we could have just taken 1/2 of 26 mugs which is 13.

4 0

3 years ago

Which statement is true?

Taya2010 [7]

Answer:

The sum of 78 and -78 is zero.

Step-by-step explanation:

I used a calculator ;)

7 0

2 years ago

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