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4 years ago

11

Find all factors for the following numbers and classify each number as prime or composite explain the classification of each as

prime or composite

1 answer:

Kisachek [45]4 years ago

7 0

Prime numbers have only themselves and 1 as factors, like 7, and all other numbers are composite.

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The naturalist found 9 bright blue poisonous frogs in South America. Each frog weighed 3 grams. In all, how much did the 9 frogs

adell [148]

Answer: B) 27 grams in all

Step-by-step explanation:

Given: The weight of each bright blue poisonous frog = 3 grams

By using the multiplication operator (x)

Then, the weight of 9 such frogs = 9 x (Weight of each frog)

⇒ The weight of 9 frogs = 9 x 3 grams

⇒ The weight of 9 frogs = 7 grams

Therefore, the correct option is B) 27 grams in all

3 0

3 years ago

Solve 2x^2 − 8x = −7

kenny6666 [7]

Answer:

The answer to your question is below

Step-by-step explanation:

2x² - 8x = - 7

Divide by 2

$\frac{2}{2} x^{2} - \frac{8}{2} x = \frac{-7}{2}$

Complete the trinomial

$x^{2} - 4x + (2)^{2} = \frac{-7}{2} + (2)^{2}$

Simplify

$x^{2} - 4x + (2)^{2} = \frac{- 7 + 4}{2}$

$x^{2} - 4x + 4 = \frac{-3}{2}$

Factor

(x - 2)² = $\frac{-3}{2}$

Get the square root

$\sqrt{(x - 2)^{2}} = \sqrt{\frac{-3}{2}}$

Simplification

x - 2 =± $\sqrt{\frac{3}{2}} i$

x₁ = 2 + $\sqrt{\frac{3}{2}} i$

x₂ = 2 - $\sqrt{\frac{3}{2}}$

6 0

3 years ago

Solve 15x + 60 < 240

Alenkasestr [34]

Answer:

15x+60<240 is x<12

Step-by-step explanation:

Let's solve your inequality step-by-step.

15x+60<240

Step 1: Subtract 60 from both sides.

15x+60−60<240−60

15x<180

Step 2: Divide both sides by 15.

15x

15

<

180

15

x<12

8 0

3 years ago

An equilateral triangle is inscribed in a circle of radius 6r. Express the area A within the circle but outside the triangle as

Paul [167]

Answer:

$A(x)=\frac{100\pi x^2-75\sqrt{3}x^2}{12}$

Step-by-step explanation:

We have been given that an equilateral triangle is inscribed in a circle of radius 6r. We are asked to express the area A within the circle but outside the triangle as a function of the length 5x of the side of the triangle.

We know that the relation between radius (R) of circumscribing circle to the side (a) of inscribed equilateral triangle is $\frac{a}{\sqrt{3}}=R$ .

Upon substituting our given values, we will get:

$\frac{5x}{\sqrt{3}}=6r$

Let us solve for r.

$r=\frac{5x}{6\sqrt{3}}$

$\text{Area of circle}=\pi(6r)^2=\pi(6\cdot \frac{5x}{6\sqrt{3}})^2=\pi(\frac{5x}{\sqrt{3}})^2=\frac{25\pi x^2}{3}$

We know that area of an equilateral triangle is equal to $\frac{\sqrt{3}}{4}s^2$ , where s represents side length of triangle.

$\text{Area of equilateral triangle}=\frac{\sqrt{3}}{4}s^2=\frac{\sqrt{3}}{4}(5x)^2=\frac{25\sqrt{3}}{4}x^2$

The area within circle and outside the triangle would be difference of area of circle and triangle as:

$A(x)=\frac{25\pi x^2}{3}-\frac{25\sqrt{3}x^2}{4}$

We can make a common denominator as:

$A(x)=\frac{4\cdot 25\pi x^2}{12}-\frac{3\cdot 25\sqrt{3}x^2}{12}$

$A(x)=\frac{100\pi x^2-75\sqrt{3}x^2}{12}$

Therefore, our required expression would be $A(x)=\frac{100\pi x^2-75\sqrt{3}x^2}{12}$ .

7 0

3 years ago

For the data set below, calculate the variance to the nearest hundredth decimal place.

zhuklara [117]

The variance would be 1213.89

i hope this helps :)

8 0

3 years ago