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2 years ago

Equations and Inequalities 2x-4=4x-5

Mathematics

2 answers:

ankoles [38]2 years ago

7 0

2x−4=4x−5
(2x−4)+(4−4x)=(4x−5)+(4−4x)
2x−4+4−4x=4x−5+4−4x
2x−4x−4+4=4x−4x−5+4
−2x=−1

Answer: x=1/2

Zina [86]2 years ago

3 0

Much easier way to do it:
2x-4=4x-5
-2x -2x
-4=2x-5
+5 +5
1=2x
2
x= 1/2
Step By Step in words:
Step1: In order to get the x's on both sides, subtract 2x from both sides
Step2 : Now to get the x by itself, do the opposite operation of -5 and add five to both sides
Step 3: Final Step to get the x by itself, do the opposite operation of 2 times x. Divide 2x by 2 and 1 by 2
Which gives you 1/2

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Ani was told to write the number four and eight hundredths. She wrote

JulsSmile [24]

Answer:

It would be 4.08, so Ani is wrong writing it as 4.8.

Step-by-step explanation:

So, with this, the number 4 is 4, a single-digit number. Anything below that has a decimal point before it. With the knowledge of there being 8 hundredths, first see this diagram explaining the terms for numbers after the decimal point:

0.1 --> 1 Tenth

0.01 --> 1 Hundredth

0.001 ---> 1 Thousandth

With this, we can see that it will be something of the likes of 4.01-4.09. Since there are 8 Hundredths, it would be 4.08, as 0.01 * 8 = 0.08.

Therefore, she is wrong because she wrote it as 4 and 8 tenths rather than 4 and 8 hundredths.

6 0

3 years ago

Need help with AP CAL

anzhelika [568]

Answer: Choice C

$\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)$

============================================================

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve $y = e^{-x}$

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is $e^{-x}$ where 0 < x < 1

Let's compute the area of each general cross section.

$\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\$

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

$\displaystyle \int_{0}^{1}e^{-2x}dx\\\\$

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

If x = 0, then u = -2x = -2(0) = 0
If x = 1, then u = -2x = -2(1) = -2

This means,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\$

I used the rule that $\displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx$ which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

$\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

In short,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

This points us to choice C as the final answer.

5 0

2 years ago

Wimming Pool On a certain hot summer's day, 528 people used the public swimming pool. The daily prices are $1.25 for children an

Lubov Fominskaja [6]

The answer is 2,770.3125 or you want me to check for a other answer

7 0

3 years ago

Read 2 more answers

3,857 rounded to the nearest thousand

alekssr [168]

3,857:

1. 3 is located in the thousands place

2. Since 8 is bigger than 3, it's telling it to go up a number (turning 3 into a 4)

Stays the Same: 1,2,3,4
Goes Up: 5,6,7,8, etc.

So 3,857 is now rounded into 4,000

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3 years ago

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PLEASE HELP ME!!!!!

Irina18 [472]

Answer:

f(6) = 1

Step-by-step explanation:

Function:

f(x) = -2/3x + 5

f(6) = -2/3(6) + 5

f(6) = -4 + 5

f(6) = 1

4 0

3 years ago

Read 2 more answers

Equations and Inequalities 2x-4=4x-5​

Equations and Inequalities 2x-4=4x-5