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3 years ago

What is the measure of angle y in this figure?

Mathematics

2 answers:

prohojiy [21]3 years ago

6 0

The measure of angle y is 163 degrees because the two angles are vertical angles

sergiy2304 [10]3 years ago

6 0

The measure of angle y is 163 degrees because the two angles are vertical angles

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Which statements about the cylinder are true? Select two

Rus_ich [418]

Answer:

The radius of the cylinder is (1/2)x units

The area of the cylinder’s base is (1/4)πx2 square units

The height of the cylinder is 4x units

Step-by-step explanation:

The complete question is

A cylinder with a base diameter of x units has a volume of πx3 cubic units.

Which statements about the cylinder are true? Check all that apply.

(1) The radius of the cylinder is (1/2)x units.

(2) The radius of the cylinder is 2x units.

(3) The area of the cylinder’s base is (1/4)πx2 square units.

(4) The area of the cylinder’s base is (1/2)πx2 square units.

(5) The height of the cylinder is 2x units.

(6) The height of the cylinder is 4x units

we know that

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=\frac{x}{2}\ units$ ----> the radius is half the diameter

$V=\pi x^{3}\ units^3$

substitute the given values in the formula of volume

$\pi x^3=\pi (\frac{x}{2})^{2}h$

solve for h

simplify

$x=(\frac{1}{4})h$

$h=4x\ units$

Verify each statement

(1) The radius of the cylinder is (1/2)x units

The statement is true

see the explanation

(2) The radius of the cylinder is 2x units.

The statement is false

Because, the radius of the cylinder is x/2 units

(3) The area of the cylinder’s base is (1/4)πx2 square units

The statement is true

Because, the area of the cylinder's base is equal to

$A=\pi r^{2}$

$r=\frac{x}{2}\ units$

substitute

$A=\pi (\frac{x}{2})^{2}$

$A=\frac{\pi x^2}{4}\ units^2$

(4) The area of the cylinder’s base is (1/2)πx2 square units.

The statement is false

Because, the area of the cylinder's base is equal to

$A=\frac{\pi x^2}{4}\ units^2$

see the part (3)

(5) The height of the cylinder is 2x units.

The statement is false

Because, the height of the cylinder is 4x units (see the explanation)

(6) The height of the cylinder is 4x units

The statement is true

see the explanation

7 0

3 years ago

Prachi was 555 kilometers east of her home when she began driving farther east at 707070 kilometers per hour. Let f(n)f(n)f, lef

vladimir2022 [97]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Whenever she began to drive farther east, at 70 km per hour, Prachi was 5 km east of her home.

Let f(n) at the beginning of her nth hour drive be Prachi's distance to her home.

f is a sequence of arithmetic.

Write a series explicit form.

$\to f(n) = 70n + 5$

3 0

3 years ago

There are 3/4 as many boys as girls in class of fifth-grade. If there are 35 students in class, how many are girls?

Anuta_ua [19.1K]

Answer:

girls = 20

boys = 15

Step-by-step explanation:

boys = 3/4 x = .75x

girls = x

x + .75x = 35

1.75x = 35

x = 35/1.75

x = 20

girls = 20

boys = 3/4 * 20 = 15

boys = 15

4 0

3 years ago

Jessica is on a website that lets her build her own pizza for delivery. She has a budget of $14 (Not including tax or tip) to sp

nexus9112 [7]

Answer:

d. Jessica can have up to 7 toppings on her pizza

Step-by-step explanation:

We know that the inequality that gives us the number of toppings Jessica can put on her pizza is $0.75(t-1)+9.50\leq 14$ where $t\geq 1$ , so, to find the number of topics we just need to solve the inequality.

Let's do it step-by-step

Step 1. Subtract 9.50 from both sides of the inequality

$0.75(t-1)+9.50-9.50\leq 14-9.50$

$0.75(t-1)\leq 4.50$

Step 2. Distribute 0.75 to the two terms inside the parenthesis

$0.75t-0.75\leq 4.50$

Step 3. Add 0.75 to both sides of the inequality

$0.75t-0.75+0.75\leq 4.50+0.75$

$0.75t\leq 5.25$

Step 4. Divide both sides of the inequality bu 0.75

$\frac{0.75t}{0.75} \leq \frac{5.25}{0.75}$

$t\leq 7$

Jessica can put up to 7 topping on her pizza.

We can conclude that the correct answer is d. Jessica can have up to 7 toppings on her pizza

6 0

3 years ago

A collection of coins has value of 64 cents. There are two more nickels than dimes and three times as many pennies as dimes. How

Alborosie

Let d = number of dimes

Let n = number of nickels

Let p = number of pennies

As given, there are two more nickels than dimes and three times as many pennies as dimes:

$d+2=n$

$3d=p$

$0.10d+0.05n+0.01p=0.64$

Plug in the value to find d

$0.10d+0.05(d+2)+0.01(3d)=0.64$

$0.10d+0.05d+0.1+0.03d=0.64$

$0.18d=0.54$

$d=3$

As p=3d

p= $3\times3=9$

As n=d+2

$n=3+2=5$

Hence, there are 5 nickels, 3 dimes and 9 pennies.

5 0

3 years ago