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4 years ago

What is -5x - 3y = 21 in slope-intercept form?

Mathematics

1 answer:

djyliett [7]4 years ago

7 0

Answer:

$\displaystyle y = -1\frac{2}{3}x -7$

Step-by-step explanation:

−5x - 3y = 21

+ 5x + 5x

__________

$\displaystyle \frac{-3y}{-3} = \frac{5x + 21}{-3} \\ \\ y = -1\frac{2}{3}x - 7$

I am joyous to assist you anytime.

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The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard de

Sergio [31]

To solve this problem, we use the formula:

z = (x – u) / s

where z is the z score value which can be obtained from the tables, x is the sample value, u is the mean = 6.3 min, and s is the std dev = 2.2 min

at P value = 0.90, the z = 1.28, finding for x:

x = z s + u

x = 1.28 * 2.2 + 6.3

x = 9.116

at P value = 1.0, the z = 3.49, finding for x:

x = z s + u

x = 3.49 * 2.2 + 6.3

x = 13.978 ~ 14

Therefore the longest 10% calls last about 9.1 minutes to 14 minutes

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4 years ago

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denis-greek [22]

Answer:

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Step-by-step explanation:

3 0

3 years ago

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If not able to awnser say it in the comments

olga_2 [115]

Answer:

Step-by-step explanation:

4y-9+4y simplified by combining like terms is 8y-9

6 0

3 years ago

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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

(a^(2)-4ac+3bc)/(a^(2)-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c)

Bingel [31]

Answer:

The answer is −a^4 + 5a^3b + 2a^3c − 4a^2b^2 − 10a^2bc − a^2c^2 + 8ab^2c + 5abc^2 − 4b^2c^2 / −a^4 + 2a^3b + 2a^3c − a^2b^2 − 4a^2bc − a^2c^2 + 2ab^2c + 2abc^2 − b^2c^2

Step-by-step explanation:

This the equation being simplified

4 0

3 years ago

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