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3 years ago

Solve for x. Show each step of the solution. 4(8-x)-32=98-5(3x+24)

Mathematics

1 answer:

Firlakuza [10]3 years ago

8 0

Answer: x=−2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(8−x)−32=98−5(3x+24)

Step 1: Simplify both sides of the equation.

4(8−x)−32=98−5(3x+24)

(4)(8)+(4)(−x)+−32=98+(−5)(3x)+(−5)(24)(Distribute)

32+−4x+−32=98+−15x+−120

(−4x)+(32+−32)=(−15x)+(98+−120)(Combine Like Terms)

−4x=−15x+−22

−4x=−15x−22

Step 2: Add 15x to both sides.

−4x+15x=−15x−22+15x

11x=−22

Step 3: Divide both sides by 11.

11x /11 = −22 /11

x=−2

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Three Texas drovers met on a highway and began to dicker as follows:

Alik [6]

Answer:

Jim's: 7
Duke's: 21
Hank's: 11

Step-by-step explanation:

Let J, D, and H represent the drove sizes of Jim, Duke, and Hank.

2(H -6 + 1) = (J +6 -1) . . . . . Hank's offer

3(D -14 +1) = (H +14 -1) . . . . Duke's offer

6(J -4 +1) = (D +4 -1) . . . . . . Jim's offer

These equations can be simplified to ...

2H - J = 15

3D - H = 52

6J - D = 21

<u>Solution</u>

Adding twice the second equation to the first gives ...

2(3D -H) +(2H -J) = 2(52) +(15)

6D -J = 119

Adding 6 times the third equation to this one gives ...

6(6J -D) +(6D -J) = 6(21) +(119)

35J = 245

J = 7

Using this value in the third equation gives ...

6(7) -D = 21

42 -21 = D = 21

Using the value of J in the first equation gives ...

2H -7 = 15

H = (15 +7)/2 = 11

Then the solution is (J, D, H) = (7, 21, 11).

Jim's drove had 7 animals; Duke's drove had 21 animals; Hank's drove had 11 animals.

5 0

3 years ago

3 + 2p - 4 = 11<br><br> algebra 1 solving equations

leonid [27]

Answer: the variable is p=6 .

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

8 0

3 years ago

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Laboratory experiment shows that the life of the average butterfly is normally distributed with a mean of 18.8 days and a standa

inessss [21]

Answer:

a) 0.4164

Step-by-step explanation:

Mean lifespan (μ) = 18.8 days

Standard deviation (σ) = 2 days

For any given lifespan 'X', the z-score is:

$z=\frac{X- \mu}{\sigma} \\z=\frac{X- 18.8}{2}$

For X=12.04 days:

$z=\frac{12.04 - 18.8}{2} \\z=-3.38$

A z-score of -3.38 falls in the 0.036-th percentile of a normal distribution.

For X=18.38 days:

$z=\frac{18.38 - 18.8}{2} \\z=-0.21$

A z-score of -3.38 falls in the 41.68th percentile of a normal distribution.

The probability that a butterfly lives between 12.04 and 18.38 days is

$P=41.68-0.036\\P=41.64\%\ or\ 0.4164$

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3 years ago

A corporate attorney has weekends off and has 30 paid vacation days per year, including holidays that fall on weekdays. If his s

snow_tiger [21]

It's slightly ambiguous because the year isn't an even number of weeks, so sometimes that extra day falls on a weekend and sometimes on a weekday. We'll assume a weekend; that makes the numbers come out nice.

Total working days, 52 five day weeks minus 30 days vacation

$d = 52 \times 5 - 30 = 230$

So his daily rate is

$119600/230 = 520$ dollars per day

Answer: A

It's closer to $518 when we count the extra day as a weekday.

3 0

3 years ago

What is the value of |−32|?

Vlad [161]

32. The absolute value of a number x (|x|) will always be positive. It just means how far the number is from 0 on the number line.

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3 years ago

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