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4 years ago

Please help me, I will give brainliest and 13 points!

Mathematics

1 answer:

mario62 [17]4 years ago

4 0

The solutions of the system of equations are (0 , 13) , (3 , 34)

Step-by-step explanation:

To solve an system of equations, one of them linear and the other is quadratic do that

Use the linear equation to find one variable in terms of the other variable
Substitute this variable in the quadratic equation
Solve the quadratic equation to find the values of the other variable
Substitute the values of the other variable in the linear equation to find the first variable

The system of equation is:

y = x² + 4x + 13 ⇒ (1)

y = 7x + 13 ⇒ (2)

Substitute y in equation (1) by equation (2)

x² + 4x + 13 = 7x + 13

Subtract 13 from both sides

∴ x² + 4x = 7x

Subtract 7x from both sides

x² - 3x = 0

Take x as a common factor

x(x - 3) = 0

Equate each factor by 0

x = 0

x - 3 = 0

Add 3 to both sides

x = 3

The values of x are 0 and 3

Substitute the values of x in equation (2) to find y

When x = 0

y = 7(0) + 13

y = 0 + 13

y = 13

When x = 3

y = 7(3) + 13

y = 21 + 13

y = 34

The values of y are 13 and 34

The solutions of the system of equations are (0 , 13) , (3 , 34)

Learn more:

You can learn more about the system of equations in brainly.com/question/3739260

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BigorU [14]

Zeros: x = 2, x = 4

Turning point: (halfway between the zeros) x = 3, y = -1

y-intercept: where x=0, at f(0) = 8.

Axis of symmetry: the vertical line through the turning point: x = 3.

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4 years ago

Molly had 1/8 of a bag of birdseed. She separated it equally into 2 bird feeders. What part of a bag did each feeder get?

Wewaii [24]

1/8 of a bag divided into two equal parts.
Each part gets 1/2 of 1/8, which is (1/2)*(1/8)=1/16 of a bag.
(hint: "of" frequently means multiply)

Answer: each feeder gets 1/16 of a bag of birdseed.

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3 years ago

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Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable.

Mashcka [7]

Answer:

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Step-by-step explanation:

Integration Rule:

$\int x^n dx= \frac{x^{n+1}}{n+1}+c$
$\int \frac1x dx= ln(x) +c$

Given differential equation is

$x^2 \frac{dw}{dx}= \sqrt{w}(2x+5)$

$\Rightarrow x^2 dw= \sqrt{w} (2x+5) dx$ [ multiplying dx both sides]

$\Rightarrow \frac{dw}{\sqrt w}= \frac{(2x+5)}{x^2} dx$ [ dividing $x^2\sqrt w$ both sides]

Integrating both sides

$\int \frac{dw}{\sqrt w}=\int \frac{(2x+5)}{x^2} dx$

$\Rightarrow \int w^{-\frac12} dw=\int (\frac{2x}{x^2}+\frac{5}{x^2} )dx$

$\Rightarrow \int w^{-\frac12} dw=\int \frac{2}{x}dx +\int\frac{5}{x^2} dx$

$\Rightarrow \frac{w^{-\frac12+1}}{-\frac12+1} =2ln x+5 \frac{x^{-2+1}}{-2+1}+c$ [ c is arbitrary constant]

$\Rightarrow 2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

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3 years ago

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ivann1987 [24]

Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

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