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3 years ago

What is the solution of the equation 6x - 3 = -51?

Mathematics

2 answers:

Alexus [3.1K]3 years ago

4 0

The solution of the equation is
6x - 3 = -51
6x = -51 + 3
6x = -48
—————
X = -8
The solution is -8

Bad White [126]3 years ago

3 0

Answer:

x = -8

Step-by-step explanation:

$6x - 3 = -51?\\To - find-x- collect-like-terms.\\6x=-51+3\\6x =-48\\Divide-both-sides-of-the-equation-by-6\\\frac{6x}{6} = \frac{-48}{6} \\x = -8$

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hichkok12 [17]

$cos(4\theta) - cos(2\theta) = sin(\theta)$
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3 years ago

11. The coordinates of endpoint A are A(5, -15). The midpoint of AC is B(5, -8). Find the coordinate of endpoint C. (1 point wor

raketka [301]

12. The answer in its simplest form is $4\sqrt{34}$

5 0

3 years ago

Solve the following systems of equations 2a+4b+c=5 ; a-4b=-6 ; 2b+c=7.

SOVA2 [1]

Answer:

a = -2

b = 1

c = 5

Step-by-step explanation:

Given:

2a + 4b + c = 5 ............(1)

a - 4b = - 6

a = 4b - 6 .............(2)

2b + c = 7

c = 7 - 2b ...........(3)

substituting 2 and 3 in 1, we get

2(4b - 6 ) + 4b + (7 - 2b) = 5

8b - 12 + 4b + 7 - 2b = 5

10b - 5 = 5

b = 1

substituting b in 2, we get

a = 4(1) - 6

a = -2

substituting b in 3, we get

c = 7 - 2(1)

c = 5

thus,

a = -2

b = 1

c = 5

8 0

3 years ago

Water is being pumped into a 12-foot-tall cylindrical tank at a constant rate.

Stels [109]

Answer:

4 feet

Step-by-step explanation:

It is given that:

• At 2:30 p.m., the water depth was 2.6 feet.

• It is now 5:00 p.m., and the depth of the water is 3.6 feet.

So in 2.5 hours ( 5pm - 2:30pm) the water rose 1 feet (3.6 - 2.6).

Now <em><u>we can find how much water rises in 1 hour by setting up a ratio (let x be the depth increase of water in 1 hr):</u></em>

$\frac{2.5}{1}=\frac{1}{x}\\2.5x=1*1\\2.5x=1\\x=\frac{1}{2.5}\\x=0.4$

So, in 1 hour, the water level will rise 0.4 feet

So, at 6pm (1 hour from 5 pm) it will rise to 3.6 + 0.4 = 4 feet

8 0

3 years ago

A college job placement office collected data about students’ GPAs and the salaries they earned in their first jobs after gradua

frez [133]

Answer:

X is the GPA

Y is the Salary

Standard deviation of X is 0.4

Standard deviation of Y is 8500

E(X)=2.9

E(Y)=47200

We are given that The correlation between the two variables was r = 0.72

a) $y = a+bx$

$b = \frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sum(x_i-\bar{x})^2} = \frac{r \times \sqrt{var(X) \times Var(Y)}}{Var(X)} = \frac{0.72 \times \sqrt{0.4^2 \times 8500^2}}{0.4^2} = 15300$

$a=y-bx = 47200-(15300 \times 29) = 2830$

So, slope = 15300

Intercept = 2830

So, equation : $y = 2830+15300x$

b) Your brother just graduated from that college with a GPA of 3.30. He tells you that based on this model the residual for his pay is -$1880. What salary is he earning?

$y = 2830+15300 \times 3.3 = 53320$

Observed salary = Residual + predicted = -1860+53320 = 51440

c)) What proportion of the variation in salaries is explained by variation in GPA?

The proportion of the variation in salaries is explained by variation in GPA = $r^2 = (0.72)^2 =0.5184$

8 0

3 years ago