Solve the system using the method of you choice:
-x + 4y = 12

5x - 2y = -6

Answers

Answer 1

Answer:

(0, 3)

Step-by-step explanation:

Let's first eliminate x.  To do this, multiply all three terms of the first equation by 5:  

-5x + 20y = 60

5x -    2y  = -6

----------------------

         18y = 54, so that y = 3.

Substituting 3 for y in the first equation yields:

-x + 4(3) = 12, or -x = 0.  Thus, x = 0, and the solution is

(0, 3)


Related Questions

HELP


What is the longest line segment that can be drawn in a right rectangular prism that is 15cm long, 8 cm wide, and 7 cm talk

Answers

Answer:

=18.38cm

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment .

Look at the attached picture. The longest segment we can draw is AG (or any of its equivalent: BH, CE, DF). Let's focus on AG for example.

We can think of AG as the hypotenuse of triangle ACG. So, we need AC first. AC is itself the hypotenuse of triangle ABC,

so we have,

[tex]AC^2 = AB^2+BC^2=8^2+7^2=113[/tex]

Now we can resume where we stopped with triangle AGC, and we have

[tex]AG=\sqrt{AC^2+CG^2}=\sqrt{113+225}=\sqrt{338}[/tex]

=18.38cm

PLEASE!!!
A survey asks a random sample of 2500 adults in Ohio if they support an increase in the state sales tax from 5.25% to 5.50%, with the additional revenue going to education. Let X denote the number in the sample that say they support the increase. Suppose that 30% of all adults in Ohio support the increase.

9. The standard deviation of X is

a. 22.91.

b. 27.39.

c. 5255.

d. 750.


10. The probability that X is at least 800 is

a. less than 0.0001.

b. about 0.015.

c. 0.025.

d. 0.05.

Answers

Answer:

Step-by-step explanation:

a) Total number of people surveyed, n = 2500

Let X denote the number in the sample that say they support the increase. If 30% of all adults in Ohio support the increase, it means that the percentage of all adults in Ohio that did not support the increase is

100 - 30 = 70%

This is a binomial probability because there are only two possible outcomes. Therefore,

Probability of success, p = 30/100 = 0.3

Probability of failure, q = 1 - p = 1 - 0.3

q = 0.7

Standard deviation = √npq

Standard deviation = √(2500 × 0.3 × 0.7) = 22.91

b) The probability that x is at least 800 is expressed as

P(x ≥ 800)

We would determine the probability by using the binomial probability calculator. Therefore,

P(x ≥ 800) = 0.01577

b. about 0.015.

Can anyone help explain this to me lol-

-Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles. ​
7.4 cm, 8.1 cm, 9.8 cm​

A.unique triangle
B.many different triangles
C.no triangles
Thanks to anyone who helps-

Answers

Answer:

Since you are given ALL three sides, then you will ALWAYS be able to make ONLY unique triangles.   ^‿^

I'm in quite in a bit of a pickle... so, please? and I never forget to mark brainiest

Answers

The correct answer is a translation.

A rotation would change the direction, a reflection would change the direction, and a dilation would change the size.

I hope this helps :)

Answer:

translation

Step-by-step explanation:

An aquarium in the shape of a rectangular prism has a bottom, no top, two square sides, and two sides
the same height as the square sides but twice their length. The total area of the five sides 15 2,592 in?.
Find the volume of the aquarium. Complete the explanation of your reasoning.
Let x represent the length and height of the square sides. Then the longer sides and the bottom measure
2x by x. The total area of the five sides, in terms of x, is A =____
So, the total area of the five sides,
A, is 2,592 in2. Solving for x we get x =____
The tank's volume is ____
in squared?

Answers

Answer:

volume = 11,664 units cubed

Step-by-step explanation:

2[tex]x^{2}[/tex] times 3 = bottom and sides

[tex]x^{2}[/tex] times 2 = ends

A = 6[tex]x^{2}[/tex] + 2[tex]x^{2}[/tex] = 8[tex]x^{2}[/tex]

2592 = A

2592/8 = 8[tex]x^{2}[/tex]/8

324 = [tex]x^{2}[/tex]

take square root of both sides

18 = x

so volume = length times width times height

2(18) times 18 times 18 = 11664

11664 units cubed

What is “rate of change”? Hint: it’s NOT “y=mx+b.” What term (begins with an S!) is it very closely related to?

Answers

Answer:

Standard Form

Step-by-step explanation:

Answer:

Rate of change refers to the change in one variable (i.e. independent variable) as a result of a change in another (i.e. dependant variable). A very common example is speed as it refers to the change in distance per a change in time. Graphically representing the relationship between two variables, the rate of change will be the gradient or slope of the graph.

what is the quotient of the equation Below in simplest form? State any restrictions on the variable

Answers

Answer:

A

Step-by-step explanation:

Factor the numerators/ denominators where possible, that is

[tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] ÷ [tex]\frac{(x-5)(x+3)}{(x+4)(x+1)}[/tex]

Leave the first fraction, change division to multiplication and turn the second fraction upside down.

= [tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] × [tex]\frac{(x+4)(x+1)}{(x-5)(x+3)}[/tex]

Cancel the factors (x - 5) and (x + 4) from numerator/denominator

= [tex]\frac{-1}{(x-1)}[/tex] × [tex]\frac{(x+1)}{(x+3)}[/tex]

= [tex]\frac{-(x+1)}{(x-1)(x+3)}[/tex] , x ≠ 1, x ≠ - 3

30 points
In two or more complete sentences, discuss the advantages and disadvantages of investing in a CD versus investing in a basic savings account.

Answers

A savings account helps you save for retirement and college while a CD isn’t typically used for that. A savings account is much more beneficial because it is also an emergency fund when you need it.

What is the true solution to the logarithmic equation?
log2[log2 (4x)) - 1
x=-4
X-0
X-2
X=4

Answers

Answer:

x=4

Step-by-step explanation:

Answer:d

Step-by-step explanation:

caroline bought 6 pieces of gold ribbon. each piece was 3/5 of a yard long. How many yards of ribbon did she buy in all?

Answers

Answer:

= 3 3/5 yards

Step-by-step explanation:

If 1 piece = 3/5 yard

What about 6 pieces = ?

= (6 x 3/5) ÷ 1

= 18/5 ÷ 1

= 18/5

= 3 3/5 yards

what is the answer to -12= -2x-4x

Answers

Answer:

x = 2

Step-by-step explanation:

-12 = -2x - 4x

-12 = - 6x

x = -12/(-6) = 2

Answer:

Step-by-step explanation:

A 10-foot ladder is to be placed Against the side of the building. The base of the latter must be placed in an angle of 72° With the level ground for a secure footing. Find, to the nearest inch, how far the base of the latter should be from the side of the building and how far up the side of the building the latter will reach.

Answers

Answer:

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

Step-by-step explanation:

Please refer to the figure attached in the answer area.

A right angled triangle [tex]\triangle ABC[/tex] is formed by the ladder with the building where hypotenuse is the length of ladder.

Hypotenuse, AC = 10 foot

Also, we are given that angle made by the base of ladder with the ground is [tex]72^\circ[/tex].

We have to find AB and BC.

[tex]\angle BAC = 72^\circ[/tex]

Using trigonometric functions:

[tex]cos \theta= \dfrac{Base}{Hypotenuse}\\cos 72^\circ= \dfrac{AB}{AC}\\\Rightarrow 0.309 = \dfrac{AB}{AC}\\\Rightarrow AB = 10 \times 0.309\\$\approx$ 3.1 foot\\$\approx$ 37.2 inches[/tex]

[tex]sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin72^\circ = \dfrac{BC}{AC}\\\Rightarrow 0.95 = \dfrac{BC}{AC}\\\Rightarrow AB = 10 \times 0.95\\$\approx$ 9.5 foot\\$\approx$ 114 inches[/tex]

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

You are assigned a computer generated 4-digit password to access your new voice mail account. If the
digits can not be repeated, how many passwords are possible?
b
34 different passwords are possible
5,040 different passwords are possible
40 different passwords are possible
10,000 different passwords are possible
d

Answers

Answer:

5,040 different passwords are possible

Step-by-step explanation:

Assuming that 4-digit means using only numeric values.

This is a permutations problem.

n = number of values used with number values only this is 10

r = the number used in each case without repeating in this case 4

nPr = n! / (n - r)!

nPr = 10! / (10-4)!

nPr = 10! / 6!

The ! means factorial. For example 4! = 4 x 3 x 2 x 1 = 24

A quick hack for dividing factorials is to use cancelling.

10! / 6! = 10 x 9 x 8 x 7 (because 6 to 1 are cancelled by 6!)

= 5040

Read the lines from Langston Hughes's poem ", Too, Sing America."
Tomorrow,
I'll be at the table
When company comes.
The lines promoted social change in the United States in the first half of the twentieth century because they spoke about
Ob
equal rights for African Americans.
European Americans' views of African Americans.
parties hosted by European Americans.
African Americans working as servants.
Od

Answers

Maybe summarize next time!

Answer:

Answer: D) equal rights for African Americans

Step-by-step explanation:

A cube has an edge measuring 6 cm. Find its volume.

Answers

Answer:

216

Step-by-step explanation:

Hope this helps.

Answer:

Side of cube = 6 cm

Volume = side ^3 = 6^3 = 216 cm^2

From the moment the first car started how many hours will it take the second car to catch up to the first

Answers

Answer:

HELP

Step-by-step explanation:

PLEASE HELP WILL MARK BRAINIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Question 3 (5 points)


Look at the frequency table. Using the Addition Rule P(A and B) = P(A) + P(B) – P(A and B), what is the probability someone being a man said dog? P(dog|man)

Answers

Answer:

28/50

Step-by-step explanation:

You look at the total amount of men there are, (50)

then amount of dog in the column of men, (28)

So (dog|man) = 28/50

ask questions if u need anything else

The graph of the function f(x) is shown
Which graph represents the function 4(2x)?

Answers

Answer:

[tex]8x[/tex]

Step-by-step explanation:

[tex]4 \: time \: 2x = 8x[/tex]

A sector with a radius of 8 cm has an area of 56pi cm2. What is the central angle measure of the sector in radians?

Answers

Answer:

[tex]\frac{7\pi}{4}[/tex].

Step-by-step explanation:

Given information:

Radius of circle = 8 cm

Area of sector = [tex]56\pi\text{ cm}^2[/tex]

Formula for area of sector is

[tex]A=\dfrac{1}{2}\theta r^2[/tex]

where, r is radius and [tex]\theta[/tex] is central angle in radian.

Substitute [tex]A=56\pi[/tex] and r=8 in the above formula.

[tex]56\pi=\dfrac{1}{2}\theta (8)^2[/tex]

[tex]56\pi=\dfrac{64}{2}\theta[/tex]

[tex]56\pi=32\theta[/tex]

[tex]\dfrac{56\pi}{32}=\theta[/tex]

[tex]\dfrac{7\pi}{4}=\theta[/tex]

Therefore, the measure of the sector in radians is [tex]\frac{7\pi}{4}[/tex].

15)
Which expression is a PRODUCT?
A)
8(6+ 3)

B)
8
(6 + 3)

5(2) + 2(6 x 3)

D)
5(2 + 3) - 4(8 + 1)

Answers

Step-by-step explanation:

the answer is

A,72

B,739

D,-11

Assignment
Health Club Fees You are choosing between two health clubs Club A offers membership for a fee of $7 plus a monthly fee of $23. Club B offers membership for a
tee of $35 plus a monthly fee of $16. After how many months will the total cost of each health club be the same?
in month(s) the total cost of each health club will be the same

Answers

Answer: The solution is (4,99) which means for in 4 months the total cost of each health club will be the same.

Step-by-step explanation:

Club A can be represented by the equation    y = 23x + 7  where x is the number of months  and y is the cost.

Club B can be represented by the equation   y = 16x + 35  where x is the number of months and y is the cost.

23x + 7 = 16x + 35     set the equation equal each other to solve for x

        -7               -7

23x  = 16x + 28

-16x     -16x

7x= 28

x= 4   now we know the value of  x is 4 so we will put it into the equation and solve for y

y= 16(4) + 35

y= 99

Solve the quadratic equation.
2x2 − 11x − 21 = 0
A) −
3
2
and 7
B)
3
2
and −7
C) −
2
3
and
1
7
D)
2
3
and −
1
7

Answers

Answer:

A) -3/2 and 7

Step-by-step explanation:

this equation factors to (2x+3)(x-7)

the goal is to solve for 0

if 2x+3=0 then x=-3/2

if x-7=0 then x=7

In ΔIJK, the measure of ∠K=90°, the measure of ∠J=76°, and JK = 3.6 feet. Find the length of IJ to the nearest tenth of a foot.

Answers

This is my answer
Hope it help!

Which description of the graph of the linear inequality y ≥ 7x – 4 is correct????The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.

Answers

Answer:

It's the second description

Step-by-step explanation:

It's one of the inequality symbols for greater/less than or equal to, which means the line is solid. Then, y is greater than or equal to 7x-4 which means it will be shaded above the line.

Answer:

The correct answer is the 2nd option

Step-by-step explanation:


What is the inverse function of f(x) = 4x + 3?

Answers

Answer:

f(x)=(x-3)/4

Step-by-step explanation:

To find the inverse of a function, I like to flip the x and the y, and then try to isolate the y. In this case:

x=4y+3

x-3=4y

y=(x-3)/4

Hope this helps!

f-1(x)=x-3/4 that is the answer hope it helps

write an equation that represent the line. ASAP !!!!!! 40 POINTS + BRAINLIEST

Answers

Answer:

y = (3/2)x + 3

Step-by-step explanation:

slope is rise over run so 3 up and, 2 right

y-intercept is at (3,0)

How many 9’s are there between 1 and a 100?

Answers

Answer:

11

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

You've got 9

19

29

39

49

59

69

79

89

And then all of the numbers in the 90s

90, 91, 92, 93, 94, 95, 96, 97, 98, 99

99 counts as two

What is 3 1/2 times 2 4/5​

Answers

Answer:

9 4/5

Step-by-step explanation:

You can rewrite them into decimal. It would be 3.5 times 2.8 and you get 9.8 or 9 4/5

Answer:

49 /5  = 9.8

Step-by-step explanation:

please help im having trouble with these problems​

Answers

Answer:

B I think

Step-by-step explanation:

How is the distributive property used when multiplying two binomials

Answers

Answer:

Step-by-step explanation:

When multiplying a binomial times a binomial, each term of the first binomial must be multiplied by each term of the second binomial. Like terms are then combined.

When multiplying two binomials, four multiplications must take place. These multiplications can occur in any order, as long as each of the first two terms is multiplied by each of the second two terms.

There are numerous ways to set up the multiplication of two binomials. The two basic formats, horizontal line-up and vertical line-up, are similar to what we saw in adding and subtracting polynomials. Let's investigate the simple product (x + 2)(x + 4) with a variety of set-ups. Start with the first term of the first binomial (the blue x).

• Distribute (multiply) this term times EACH of the terms in the second binomial (x + 4).

• Then take the second term in the first binomial (including its sign: +2) and distribute (multiply) this term times EACH of the terms in the second binomial (x + 4).

• Add the results, combining like terms when needed.

• This method will work with all polynomials, not just binomials times binomials.

Answer:

Distributive.

Step-by-step explanation:

I did the quiz.

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