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3 years ago

In the figure above, are <3 and <7 alternate interior angles,

Mathematics

1 answer:

icang [17]3 years ago

7 0

Answer:

Corresponding angles

Step-by-step explanation:

<3 and <7 lie on the same side of the transversal line. Each angle also is located on the outside of each parallel lines cut across by the transversal.

Therefore, <3 and <7 are corresponding angles.

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If it takes 18 gallons of gas to go 400 miles how many gallons would it take to go 300 miles

ivanzaharov [21]

We will use the ratio and proportion method ( an equation formed with two ratios that are equal) to solve the question “if it takes 18 gallons of gas to go 400 miles, how many gallons would it take to go 300 miles?”

Let x= the number of gallons for the gas to go 300 miles

18:400=X:300

400x=300*18

400x=5400

X=5400/400

X=13.5 so the answer is B.

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3 years ago

The value of 4 less than the product of 0.25 and x is greater then 6

Karolina [17]

Answer:

0.25x - 4 > 6

Step-by-step explanation:

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3 years ago

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Quadrilateral A'B'C'D' is the image of quadrilateral ABC D under a dilation.

Semenov [28]

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Step-by-step explanation:

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3 years ago

Evaluate the integral, show all steps please!

zalisa [80]

Answer:

$\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x$

Take partial fractions of the given fraction by writing out the fraction as an identity:

$\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}$

Calculate the values of A and B using substitution:

$\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}$

$\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}$

Substitute the found values of A and B:

$\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}$

If the terms are multiplied by constants, take them outside the integral:

$\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}$