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3 years ago

Simplify 8 (y +1 ) - 2 (x + 3)

Mathematics

2 answers:

melomori [17]3 years ago

8 0

Answer:

8y - 2x + 2

Step-by-step explanation:

Distribute;

8y + 8 - 2x - 6

Combine like terms;

8y - 2x + 2

alexdok [17]3 years ago

4 0

Answer:

8y+2-2x

Step-by-step explanation:

Use the distributive property to multiply 8 by y+1.

8y+8−2(x+3)

Use the distributive property to multiply −2 by x+3.

8y+8−2x−6

Subtract 6 from 8 to get 2.

8y+2−2x

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What is the slope of the line y = 3?

CaHeK987 [17]

The slope would be 0. Because the line would be flat if all of the y values equal 3, that means the slope = 0. If now x=9 or anything like that, that would be undefined,

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3 years ago

Read 2 more answers

The Lopez family and the Russell family each used their sprinklers last summer. The water output rate for the Lopez family's spr

grin007 [14]

L = hours used by the Lopez's sprinkler

R = hours used by the Russell's sprinkler

so, we know the Lopez's sprinkler uses 15 Liters per hour, so say after 1 hour it has used 15(1), after 2 hours it has used 15(2), after 3 hours it has used 15(3) liters and after L hours it has used then 15(L) or 15L.

likewise, the Russell's sprinkler, after R hours it has used 40R, since it uses 40 Liters per hour.

we know that both sprinklers combined went on and on for 45 hours, therefore whatever L and R are, L + R = 45.

we also know that the output on those 45 hours was 1050 Liters, therefore, we know that 15L + 40R = 1050.

$\bf \begin{cases}
L+R=45\implies \boxed{L}=45-R\\
15L+40R=1050\\
----------\\
15\left(\boxed{45-R} \right)+40R=1050
\end{cases}
\\\\\\
675-15R+40R=1050\implies 25R=375\implies R=\cfrac{375}{25}\\\\\\ R=15$

how long was the Lopez's on for? well, L = 45 - R.

7 0

3 years ago

What is the probability that a number selected at random from the set {2,3,7,12,15,22,72,108} will be divisible by both 2 and 3?

enot [183]

Answer: 3/8
There are only three numbers in there that 2 and 3 can go into evenly.

The probability that you will randomly select one of those numbers is 3/8.

-Brainly Answerer

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3 years ago

What is the shortest board a man must buy in order to cut 3 sections from it, each 4 feet 8 inches long?

kakasveta [241]

Convert the mixed number to inches. 3 feet 8 inches = 44 inches (12 inches per foot x 3 feet= 36 inches + 8 inches= 44 inches). 44 inches (length each section needs to be) x 4 (number of sections needed)=176 inches (total molding needed). To determine the amount of molding needed in feet, convert 176 inches into feet by dividing 176 inches by 12 inches. You get 14 2/3 feet, so the shortest board length is 15 feet.

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3 years ago

Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

∴ we have used u-solve (u-substitution) to find the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

5 0

2 years ago