What is the simplified form of...

The length of Joseph’s rectangular poster is two times it’s width. If the perimeter is 24 inches, what is the area of the poster

leonid [27]

Let's assign the width to a variable, with that variable being x. the length is two times the width, so it would be 2x. the perimeter of a rectangle is length + length + width + width, so you would add 2x + 2x + x + x = 24 inches. combine like terms (x) to get 6x = 24. divide both sides by 6 to get x = 4. so the width (x) is 4, and the length (2x) is 8. the area of a rectangle is length times width, so multiply 4 * 8. that would get you 32 inches^2.

6 0

4 years ago

The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure

Novosadov [1.4K]

Hello!

The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure?

Use 3.14 to approximate π .

Enter your answer in the box. in.³

Data: (Cylinder)

h (height) = 7 in

r (radius) = 2.5 in (The diameter is 5 being twice the radius)

Adopting: $\pi \approx 3.14$

V (volume) = ?

Solving: (Cylinder volume)

$V = \pi *r^2*h$

$V = 3.14 *2.5^2*7$

$V = 3.14*6.25*7$

$V = 137.375 \to \boxed{V_{cylinder} \approx 137.38\:in^3}$

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

r (radius) = 2.5 in (The diameter is 5 being twice the radius)

Adopting: $\pi \approx 3.14$

If: We know that the volume of a sphere is $V = 4* \pi * \dfrac{r^3}{3}$ , but we have a hemisphere, so the formula will be half the volume of the hemisphere $V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}$

Formula: (Volume of the hemisphere)

$V = 2* \pi * \dfrac{r^3}{3}$

Solving:

$V = 2* \pi * \dfrac{r^3}{3}$

$V = 2*3.14 * \dfrac{2.5^3}{3}$

$V = 2*3.14 * \dfrac{15.625}{3}$

$V = \dfrac{98.125}{3}$

$\boxed{ V_{hemisphere} \approx 32.70\:in^3}$

Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)

Volume of the figure = cylinder volume + hemisphere volume

Volume of the figure = 137.38 in³ + 32.70 in³

$Volume\:of\:the\:figure =170.08 \to \boxed{\boxed{\boxed{Volume\:of\:the\:figure = 170\:in^3}}}\end{array}}\qquad\quad\checkmark$

_______________________

I Hope this helps, greetings ... Dexteright02! =)

5 0

3 years ago

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Please help! I'm terrible at these map questions!!

Luba_88 [7]

The answer is [c.]
Hope this helped

3 0

3 years ago

Which ordered pair is a solution of the equation? 6x+3y=15

kipiarov [429]

Y=2x+5 so order pair would be (1,7) and (2,9)

8 0

4 years ago

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You are given the equation \sqrt{76+n } and \sqrt{2n + 26}. What is the smallest value of n that will make each number rational?

Diano4ka-milaya [45]

Answer:

A proof that square root of 2 is irrational. ... An equation x² = a, and the principal square root ... The number under the radical sign is called the radicand. ... the given square numbers, each product of square numbers is equal to what square ... are relatively prime -- and it will be impossible to divide n· n into m· m and get 2.

Step-by-step explanation:

4 0

3 years ago