All categories

1 year ago

Solve for x. 7/8(−32−48x)+36 =2/3(−33x−18)−10x

Mathematics

2 answers:

Aleksandr [31]1 year ago

5 0

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

x = 2

emmainna [20.7K]1 year ago

5 0

Answer:

x=2

Step-by-step explanation:

7/8(-32)-7/8(48x)+36=2/3(-33x)-2/3(18)-10x

= -224/8-336x/8+36

=-66x/3-36/3-10x.

Simplifying the fractions

-28-42x+36=-22x-12-10x.

Combining like terms

-42x+8=-32x-12.

Add 32x to both sides:

-42x+8+32x=-32x-12+32x

-10x+8=-12.

Subtract 8 from both sides:

-10x+8-8=-12-8

-10x=-20.

Divide both sides by -10:

-10x/-10 = -20/-10

x=2.

You might be interested in

At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

Step-by-step explanation:

Let X = temperature increase.

The random variable X follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of X is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable X as follows:

$E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5$

Thus, the expected value of the temperature increase is 17.5°C.

7 0

2 years ago

At smith’s Mountain Lake Boat Rentals, it cost $25 per hour to rent a pontoon boat, plus a one-time

sergey [27]

Answer:

Jones family paid a total of $139

Step-by-step explanation:

Smith's Mountain Lake Boat provides Rental services that can be expressed as follows;

Total cost=cost per hour×number of hours rented+one time cleaning deal

For Benael's family;

Benael family total cost=Cost per hour×number of hours rented+one-time cleaning deal

where;

Benael family total cost=$226.50

Cost per hour=$25

Number of hours rented=11 am-6:30 pm=7 hours 30 minutes=7.5 hours

One time cleaning deal=x

Replacing;

226.50=(25×7.5)+x

187.5+x=226.50

x=226.50-187.5

x=39

One time cleaning deal=$39

For Jones family;

Jones family total cost=Cost per hour×number of hours rented+one-time cleaning deal

where;

Cost per hour=$25

Number of hours rented=9 am-1 pm=4 hours

One time cleaning deal=$39

Replacing;

Jones family total cost=(25×4)+39

Jones family total cost=$139

Jones family paid a total of $139

4 0

2 years ago

A store is advertising a sale with 15% off all prices in the store. Sales tax is 8%. Which equation will correctly determine the

ICE Princess25 [194]

Answer: 15%-8%=C

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town

Maksim231197 [3]

Answer:

2.1 miles

Step-by-step explanation:

you can see a drawing of the situation in the attached picture (you need to draw all the places mentioned and the distance between them),

this way we can form a right triangle between the school and the hospital with measures of sides: 1.7 and 1.2 miles

and the green line is the straight line between the school and the hospital, so you need pythagoras to find the value:

$\sqrt{1.7^2+1.2^2}\\=\sqrt{2.89+1.44}\\=\sqrt{4.33} \\ =2.081$

rounding to the nearest tenth:

2.1 miles

4 0

2 years ago

a rectangle on a coordinate plane is translated 5 units up and 3 units to the left. which rule describes the translation?

andre [41]

The correct answer is (x, y) → (x – 3, y + 5)

9 0

1 year ago

Read 2 more answers