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4 years ago

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A parallelogram with a height of 2x+3 has an area of 2x^2+13x+15. What is the length of the base of the parallelogram? Please sh

ow work.

2 answers:

OlgaM077 [116]4 years ago

8 0

(2x^2+13x+15)/2x+3=x+5

Use long or synthetic division to solve this problem.

rosijanka [135]4 years ago

8 0

Answer : The length of the base of the parallelogram is, $x+5$

Step-by-step explanation :

As we know that:

Area of parallelogram = Height × Base

Given:

Height of parallelogram = $2x+3$

Area of parallelogram = $2x^2+13x+15$

Now put all the given values in the above formula, we get:

Area of parallelogram = Height × Base

$2x^2+13x+15$ = $2x+3$ × Base

Base = $\frac{2x^2+13x+15}{2x+3}$

Now factorize this expression $2x^2+13x+15$ , we get:

Base = $\frac{2x^2+(10x+3x)+15}{2x+3}$

Base = $\frac{2x(x+5)+3(x+5)}{2x+3}$

Base = $\frac{(2x+3)(x+5)}{2x+3}$

Base = $x+5$

Therefore, the length of the base of the parallelogram is, $x+5$

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Choose the number sentence that shows the distributive property of multiplication over addition.

Anarel [89]

we know that

distributive property of multiplication over addition:

$a \times (b+c)=a \times b + a \times c$

now, we will verify each options

option-A:

3 × (4 + 5) = (3 × 4) + (3 × 5)

We can see that both sides match with property

so, this is TRUE

option-B:

3 × (4 + 5) = (3 + 4) × (3 + 5)

We can see that right side does not match with property

so, this is FALSE

option-C:

3 × (4 + 5) = (3 × 4) + 5

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so, this is FALSE

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4 years ago

Learning Task 1 4/625 11. 796 A. Simplify the radical expressions 1. V63 6. V24 2. 48 7. 781 3. 775 8. V128 4. 99 9. 340 5. 92 1

kompoz [17]

Question:

Simplify the radical expressions

$1.\ \sqrt{63$ $2.\ \sqrt{48$ $3.\ \sqrt{75$ $4.\ \sqrt{99$ $5.\ \sqrt{92$

$6.\ \sqrt[3]{24}$ $7.\ \sqrt[3]{81}$ $8.\ \sqrt{128}$ $9.\sqrt[3]{40}$ $10.\ \sqrt[3]{135}$

Answer:

$\sqrt{63}= 3 \sqrt7$

$\sqrt{48} = 4\sqrt{3}$

$\sqrt{75} = 5\sqrt{3}$

$\sqrt{99} = 3 \sqrt{11$

$\sqrt{92} = 2\sqrt{23$

$\sqrt[3]{24} = 2 \sqrt[3]{3}$

$\sqrt[3]{81} =3\sqrt[3]{3}$

$\sqrt{128} = 8 \sqrt{2}$

$\sqrt[3]{40} = 2 \sqrt[3]{5}$

$\sqrt[3]{135} =3\sqrt[3]{5}$

Step-by-step explanation:

$1.\ \sqrt{63$

Express 63 as 9 * 7

$\sqrt{63}= \sqrt{9 * 7$

Split:

$\sqrt{63}= \sqrt{9} * \sqrt7$

$\sqrt{63}= 3 * \sqrt7$

$\sqrt{63}= 3 \sqrt7$

$2.\ \sqrt{48$

Express 48 as 16 * 3

$\sqrt{48} = \sqrt{16*3}$

Split

$\sqrt{48} = \sqrt{16}*\sqrt{3}$

$\sqrt{48} = 4*\sqrt{3}$

$\sqrt{48} = 4\sqrt{3}$

$3.\ \sqrt{75$

Express 75 as 25 * 3

$\sqrt{75} = \sqrt{25*3}$

Split

$\sqrt{75} = \sqrt{25}*\sqrt{3}$

$\sqrt{75} = 5\sqrt{3}$

$4.\ \sqrt{99$

Express 99 as 9 * 11

$\sqrt{99} = \sqrt{9} * \sqrt{11}$

Split

$\sqrt{99} = 3 \sqrt{11$

$5.\ \sqrt{92$

Express 92 as 4 * 23

$\sqrt{92} = \sqrt{4} * \sqrt{23$

$\sqrt{92} = 2* \sqrt{23$

$\sqrt{92} = 2\sqrt{23$

$6.\ \sqrt[3]{24}$

Express 24 as 8 * 3

$\sqrt[3]{24} = \sqrt[3]{8} * \sqrt[3]{3}$

Express 8 as 2^3

$\sqrt[3]{24} = \sqrt[3]{2^3} * \sqrt[3]{3}$

$\sqrt[3]{24} = 2 \sqrt[3]{3}$

$7.\ \sqrt[3]{81}$

Express 81 as 27 * 3

$\sqrt[3]{81} =\sqrt[3]{27}*\sqrt[3]{3}$

Express 27 as 3^3

$\sqrt[3]{81} =\sqrt[3]{3^3}*\sqrt[3]{3}$

$\sqrt[3]{81} =3\sqrt[3]{3}$

$8.\ \sqrt{128}$

Express 128 as 64 * 2

$\sqrt{128} = \sqrt{64} * \sqrt{2}$

$\sqrt{128} = 8 \sqrt{2}$

$9.\sqrt[3]{40}$

Express 40 as 8 * 5

$\sqrt[3]{40} = \sqrt[3]{8} * \sqrt[3]{5}$

$\sqrt[3]{40} = \sqrt[3]{2^3} * \sqrt[3]{5}$

$\sqrt[3]{40} = 2 \sqrt[3]{5}$

$10.\ \sqrt[3]{135}$

Express 135 as 27 * 5

$\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}$

Express 27 as 3^3

$\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}$

$\sqrt[3]{135} =3\sqrt[3]{5}$

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