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aksik [14]
3 years ago
8

Which property is used in the first step to solve this equation?

Mathematics
2 answers:
chubhunter [2.5K]3 years ago
6 0

Answer:

distributive property

Step-by-step explanation:

when you distribute the 4 to both the x and the 6, you get 4x-24 (because 4 times x is 4x and 4times 6 is 24)

Rudik [331]3 years ago
6 0

Answer:

distributive property

Step-by-step explanation:

When solving this equation, they used the distributive property to get from

4(x-6)=5 to 4x-24=5.

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Anarel [89]
-6 +8x = -38
8x = -32
x = -4
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3 years ago
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What; is; the; volume; of; 13; and; 4
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Answer: 13/4 or 3.25

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NemiM [27]

9514 1404 393

Answer:

  162 degrees

Step-by-step explanation:

Angles P and F are supplementary, so ...

  3x^2 +12x = 180

  x^2 +4x = 60

  x^2 +4x -60 = 0

  (x +10)(x -6) = 0

The useful value of x that makes this true is x=6.

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5 0
3 years ago
Complete the​ table, for the following​ investments, which shows the performance​ (interest and​ balance) over a​ 5-year period.
sergiy2304 [10]

Answer:

After 5 years of investment, Suzanne will have $ 4,400 in her account, while Derek will have $ 4,416.32 in his account.

Step-by-step explanation:

Since Suzanne deposits $ 4000 in an account that earns simple interest at an annual rate of 2%, and Derek deposits $ 4000 in an account that earns compound interest at an annual rate of 2% and is compounded annually., Both for a period of 5 years, to determine how much money each one will have in their account after 5 years, the following calculation must be made:

Suzanne:

((4,000 x 0.02) x 5) + 4,000 = X

(80 x 5) + 4,000 = X

400 + 4,000 = X

4,400 = X

Derek:

4,000 x (1 + 0.02 / 1) ^ 5x1 = X

4,000 x 1.02 ^ 5 = X

4,416.32 = X

Thus, after 5 years of investment, Suzanne will have $ 4,400 in her account, while Derek will have $ 4,416.32 in her account.

5 0
2 years ago
Find the measures of the three angles, in radians, of the triangle with the given vertices: d(1,1,1), e(1,−5,2), and f(−2,2,7).
Oduvanchick [21]

Consider triangle DEF with vertices D(1,1,1), E(1,-5,2) and F(-2,2,7).

1. Find

\overrightarrow{DE}=(1-1,-5-1,2-1)=(0,-6,1),\\ \\\overrightarrow{DF}=(-2-1,2-1,7-1)=(-3,1,6).

Then

\cos \angle D=\dfrac{0\cdot (-3)+(-6)\cdot 1+1\cdot 6}{\sqrt{0^2+(-6)^2+1^2}\cdot \sqrt{(-3)^2+1^2+6^2}}=\dfrac{0}{\sqrt{37} \cdot \sqrt{46} }=0.

2. Find

\overrightarrow{ED}=(1-1,1-(-5),1-2)=(0,6,-1),\\ \\\overrightarrow{EF}=(-2-1,2-(-5),7-2)=(-3,7,5).

Then

\cos \angle E=\dfrac{0\cdot (-2)+6\cdot 7+(-1)\cdot 5}{\sqrt{0^2+6^2+(-1)^2}\cdot \sqrt{(-3)^2+7^2+5^2}}=\dfrac{37}{\sqrt{37} \cdot \sqrt{83} }=\sqrt{\dfrac{37}{83}}.

3. Find

\overrightarrow{FE}=(1-(-2),-5-2,2-7)=(3,-7,-5),\\ \\\overrightarrow{FD}=(1-(-2),1-2,1-7)=(3,-1,-6).

Then

\cos \angle F=\dfrac{3\cdot 3+(-7)\cdot (-1)+(-5)\cdot (-6)}{\sqrt{3^2+(-7)^2+(-5)^2}\cdot \sqrt{3^2+(-1)^2+(-6)^2}}=\dfrac{46}{\sqrt{83} \cdot \sqrt{46} }=\sqrt{\dfrac{46}{83}}.

4.

\angle E=\arccos0=\dfrac{\pi}{2},\\ \\&#10;\angle D=\arccos\letf(\sqrt{\dfrac{37}{83}}\right)\approx 0.27\pi,\\ \\&#10;\angle F=\arccos\letf(\sqrt{\dfrac{46}{83}}\right)\approx 0.23\pi.

3 0
2 years ago
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