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3 years ago

What is the solution of the system of equations y=2/3x+5 7x-3y=15

Mathematics

1 answer:

alisha [4.7K]3 years ago

5 0

Answer:

(6, 9)

Step-by-step explanation:

Plug in 2/3x + 5 as y into 7x - 3y = 15

7x - 3(2/3x + 5) = 15

7x - 2x - 15 = 15

Add like terms:

5x - 15 = 15

5x = 30

x = 6

Then, plug in 6 as x into y = 2/3x + 5 to solve for y:

y = 2/3x + 5

y = 2/3(6) + 5

y = 9

So, the solution to the system of equations is (6, 9)

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Find the function y = f(t) passing through the point (0, 18) with the given first derivative.

monitta

Answer:

$\displaystyle y = \frac{t^2}{16} + 18$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

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Function Notation
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Calculus

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

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

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

Step-by-step explanation:

Step 1: Define

Identify

Point (0, 18)

$\displaystyle \frac{dy}{dt} = \frac{1}{8} t$

Step 2: Find General Solution

Use integration

[Derivative] Rewrite: $\displaystyle dy = \frac{1}{8} t\ dt$
[Equality Property] Integrate both sides: $\displaystyle \int dy = \int {\frac{1}{8} t} \, dt$
[Left Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle y = \int {\frac{1}{8} t} \, dt$
[Right Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle y = \frac{1}{8}\int {t} \, dt$
[Right Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C$
Multiply: $\displaystyle y = \frac{t^2}{16} + C$

Step 3: Find Particular Solution

Substitute in point [Function]: $\displaystyle 18 = \frac{0^2}{16} + C$
Simplify: $\displaystyle 18 = 0 + C$
Add: $\displaystyle 18 = C$
Rewrite: $\displaystyle C = 18$
Substitute in C [Function]: $\displaystyle y = \frac{t^2}{16} + 18$

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

Unit: Integration

Book: College Calculus 10e

4 0

3 years ago

Factor the quadratic expression t^2 + 4t - 7

zepelin [54]

Answer:

Not factorable.

Step-by-step explanation:

We have a trinomial (3 terms). We factor by splitting the middle term 4t into factors of -7 (the last term) which add to 4.

-7 = 1 * -7

4t= 1t+-7t doesn't work

4t=-1t+7t doesn't work

This is not factorable.

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3 years ago

If a customer wants to cover an area 20ft wide by 57ft long with rock, how many square feet does he have to cover?

uranmaximum [27]

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3 years ago

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Assume f is a one to one function of f(x)= 4-6x find f^-1(-32)

OleMash [197]

Answer:

f^-1(-32)=6

Step-by-step explanation:

Find the inverse of the function f(x)=4-6x:

f(x)=4-6x

y=4-6x

x=4-6y

x-4=-6y

(x-4)/-6=y

-1/6x+2/3=y

y=-1/6x+2/3

f^-1(x)=-1/6x+2/3

Plug in f^-1(-32) for f^-1(x) and simplify:

f^-1(-32)=-1/6(-32)+2/3

f^-1(-32)=16/3+2/3

f^-1(-32)=18/3

f^-1(-32)=6

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Sphinxa [80]

Answer:

Tyler is correct

Step-by-step explanation:

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4 years ago

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