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3 years ago

7x-5=8(x+3) solve for x

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

6 0

Answer:

The value of x is -29.

Step-by-step explanation:

We are given an algebraic equation and have one goal: solve for x. We can use simplifying techniques as well as addition and subtraction to solve this equation.

$\text{7x - 5 = 8(x + 3) \ \ \ Distribute the 8 throughout the parentheses.}\\\text{7x - 5 = 8x + 24 \ \ \ \ Subtract 7x from both sides.}\\\text{-5 = x + 24 \ \ \ \ \ \ \ \ \ \ Flip the equation.}\\\text{x + 24 = -5 \ \ \ \ \ \ \ \ \ \ Subtract 24 from both sides.}\\\small\boxed{\bold{{x = -29}}}$

Now that we have solved for x, we can plug in -29 to see if we get a true statement.

$\text{7(-29) - 5 = 8(-29 + 3)}\\\text{-203 - 5 = -232 + 24}\\\text{-208 = -208} \ \checkmark$

Because we ended up with a true statement, we have determined that the value of x is -29.

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NEED HELP ASAP!!!!!!!!!!

GenaCL600 [577]

Answer:

Hey there!

A is correct. The +2 means shifted up two units, 1/2 means compressed by a factor of 1/2, and the -3 means to the left of three units.

Let me know if this helps :)

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3 years ago

The base of a solid is the region in the first quadrant bounded above by the line y = 5, below by y = sin−1(x), and to the right

Arturiano [62]

Each cross section is a square with side length equal to the vertical distance between the curves $y=5$ and $y=\sin^{-1}x$ , with $0\le x\le1$ , or $5-\sin^{-1}x$ . Then each section has an area of $(5-\sin^{-1}x)^2$ , so the volume of this solid is

$\displaystyle\int_0^1(5-\sin^{-1}x)^2\,\mathrm dx=\boxed{33-5\pi+\frac{\pi^2}4}$

For computing the integral, consider the substitution

$u=5-\sin^{-1}x\implies x=\sin(5-u)\implies\mathrm dx=-\cos(5-u)\,\mathrm du$

Then the integral becomes

$\displaystyle\int_5^{5-\pi/2}u^2(-\cos(5-u))\,\mathrm du$

$=\displaystyle\int_{5-\pi/2}^5u^2\cos(u-5)\,\mathrm du$

Integrate by parts twice; for the first round, take

$f=u^2\implies\mathrm df=2u\,\mathrm du$

$\mathrm dg=\cos(u-5)\,\mathrm du\implies g=\sin(u-5)$

$\implies\displaystyle u^2\sin(u-5)\bigg|_{5-\pi/2}^5-2\int_{5-\pi/2}^5u\sin(u-5)\,\mathrm du$

For the second round, take

$f=u\implies\mathrm df=\mathrm du$

$\mathrm dg=-\sin(u-5)\,\mathrm du\implies g=\cos(u-5)$

$\implies\displaystyle\bigg(u^2\sin(u-5)+u\cos(u-5)\bigg)\bigg|_{5-\pi/2}^5-\int_{5-\pi/2}^5\cos(u-5)\,\mathrm du$

and the rest is trivial.

8 0

3 years ago

How much interest is earned on a principal of $2.58 invested at an interest rate of 5% for four years?

pochemuha

Answer:

Step-by-step explanation:

The formula for simple interest is

prt = I, where p is the initial investment, r is the interest rate in decimal form, t is the time it's invested for, and I is the interest earned. We multiply the p, the r, and the t together to get I. For us that looks like this:

(2.58)(.05)(4) = I and

I = .516 or 52 cents.

7 0

3 years ago

Read 2 more answers

alberto knows that all the lines and rays are congruent to each other . he reasons that all segments must therefore be congruent

saw5 [17]

Answer:

Step-by-step explanation:

Alberto is correct in reasoning that all lines and rays are congruent to each other but incorrect in his reasoning about the line segments.

Line segments are equal in measure only when they are equal in length. They can have any orientation on a plane.

Since, AB = 3 units

CD = 4 units

Therefore, AB ≠ CD

Error in AB ≅ CD

7 0

3 years ago

All right angles are congruent. Converse Inverse: Contrapositive

WITCHER [35]

Answer:

No not all right angles are congruent.

Step-by-step explanation:

7 0

3 years ago

7x-5=8(x+3) solve for x​

7x-5=8(x+3) solve for x