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zlopas [31]
3 years ago
7

Which equation demonstrates the distributive property? A) 2 (5 + 7) = 2 (7 + 5) B) 2 (5 + 7) = 2 × 5 + 2 × 7 C) (2 × 5) × 7 = 2

× (5 × 7) D) 7 × (2 × 5) = 7 × (5 × 2)
Mathematics
1 answer:
Sonbull [250]3 years ago
4 0

Answer:

B

Step-by-step explanation:

Distributive property is when you distribute the values in a parenthesis with the outside multiplying factor

2*(5+7)= 2*5 + 2*7

2*(12) = 10 +14

24 = 24

distributive property holds true

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Find the solution set to the inequality.<br><br> 4x - 1 &lt; 11
Lemur [1.5K]
4x - 1 < 11
Add 1 to both sides
4x < 12
Divide both sides by 4
x < 3
x is less than 3
4 0
3 years ago
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The vertices of ∆ABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of ∆ABC is units is? What is the area?
11111nata11111 [884]

we have

A(-2, 2),B(6, 2),C(0, 8)

see the attached figure to better understand the problem

we know that

The perimeter of the triangle is equal to

P=AB+BC+AC

and

the area of the triangle is equal to

A=\frac{1}{2}*base *heigth

in this problem

base=AB\\heigth=DC

we know that

The distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Step 1

<u>Find the distance AB</u>

A(-2, 2),B(6, 2)

Substitute the values in the formula

d=\sqrt{(2-2)^{2}+(6+2)^{2}}

d=\sqrt{(0)^{2}+(8)^{2}}

dAB=8\ units

Step 2

<u>Find the distance BC</u>

B(6, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-6)^{2}}

d=\sqrt{(6)^{2}+(-6)^{2}}

dBC=6\sqrt{2}\ units

Step 3

<u>Find the distance AC</u>

A(-2, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0+2)^{2}}

d=\sqrt{(6)^{2}+(2)^{2}}

dAC=2\sqrt{10}\ units

Step 4

<u>Find the distance DC</u>

D(0, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-0)^{2}}

d=\sqrt{(6)^{2}+(0)^{2}}

dDC=6\ units

Step 5

<u>Find the perimeter of the triangle</u>

P=AB+BC+AC

substitute the values

P=8\ units+6\sqrt{2}\ units+2\sqrt{10}\ units

P=22.81\ units

therefore

The perimeter of the triangle is equal to 22.81\ units

Step 6

<u>Find the area of the triangle</u>

A=\frac{1}{2}*base *heigth

in this problem

base=AB=8\ units\\heigth=DC=6\ units

substitute the values

A=\frac{1}{2}*8*6

A=24\ units^{2}

therefore

the area of the triangle is 24\ units^{2}

4 0
3 years ago
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Can someone please help me out?
jek_recluse [69]

Answer:

Ligh blue

Step-by-step explanation:

6 0
3 years ago
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if £500 is invested for 3 years at a rate of compound interest of 4% per annum how much will be in the account after three years
Hoochie [10]

Answer:

£562.43

Step-by-step explanation:

£500 is invested for 3 years at a rate of compound interest of 4% per annum how much will be in the account after three years

Given data

P= £500

t= 3 years

r= 4%

The expression for the compound interest is given as

A= P(1+r)^t

substitute

A= 500(1+0.04)^3

A= 500(1.04)^3

A= 500*1.124864

A= 562.432

Hence the final amount is £562.43

4 0
2 years ago
I need help with this one asap please and thank you
inna [77]

Answer:

C

Step-by-step explanation:

A

(m² - 3m + 2) / (m² - m)

we see due to a little bit of experience with expressions and multiplications of expressions that

(m² - 3m + 2) = (m - 2)(m - 1)

(m² - m) = m(m - 1)

so,

(m - 2)(m - 1) / (m(m - 1)) = (m - 2) / m

so, that's not it.

B

(m² - 2m + 1) / (m - 1)

we see again

(m² - 2m + 1) = (m - 1)(m - 1)

so,

(m - 1)(m - 1) / (m - 1) = m - 1

so, that's not it.

C

(m² - m - 2) / (m² - 1)

we see again

(m² - m - 2) = (m - 2)(m + 1)

and

(m² - 1) = (m + 1)(m - 1)

so,

(m - 2)(m + 1) / ((m + 1)(m - 1)) = (m - 2) / (m - 1)

yes, that is the solution.

D

(2m² - 4m) / (2(m - 2))

2m(m - 2) / (2(m - 2)) = 2m/2 = m

no, that is not a solution.

8 0
1 year ago
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