To solve the system of linear equations 3x - 2y - 4 and 9x-by= 12 by using the linear combination method, Henry decided that
he should first multiply the first equation by -3 and then add the two equations together to eliminate the x-terms. When he did
so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite
number of solutions. To check his answer, he graphed the equations 3x-2y = 4 and 9x-by= 12 with his graphing calculator,
but he could only see one line. Why is this?
because the system of equations actually has only one solution
because the system of equations actually has no solution
because the graphs of the two equations overlap each other
because the graph of one of the equations does not exist

Step-by-step explanation:

Step 1:  Solve using the first point

(2, 28)

[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]

[tex]28 = 8a + 4b + 2c + d[/tex]

Step 2:  Solve using the second point

(-1, -5)

[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]

[tex]-5 = -a + b - c + d[/tex]

Step 3:  Solve using the third point

(4, 220)

[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]

[tex]220 = 64a + 16b + 4c + d[/tex]

Step 4:  Solve using the fourth point

(-2, -20)

[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]

[tex]-20 = -8a + 4b - 2c + d[/tex]

Step 5:  Combine the first and fourth equations

[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]

[tex]8 = 8b + 2d[/tex]

[tex]8 - 8b = 8b - 8b + 2d[/tex]

[tex](8 -8b)/2 = 2d/2[/tex]

[tex]4 - 4b = d[/tex]

Step 6:  Solve for c in the second equation

[tex]-5 + 5 = -a + b - c + d + 5[/tex]

[tex]0 + c = -a + b - c + c + d + 5[/tex]

[tex]c = -a + b + d + 5[/tex]

Step 7:  Substitute d with the stuff we got in step 5

[tex]c = -a + b + (4 - 4b) + 5[/tex]

[tex]c = -a + b + 4 - 4b + 5[/tex]

[tex]c = -a - 3b + 9[/tex]

Step 8:  Substitute d and c into the first equation

[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]

[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]

[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]

[tex]6 / 6 = (6a - 6b) / 6[/tex]

[tex]1 + b = a - b + b[/tex]

[tex]1 + b = a[/tex]

Step 9:  Substitute a, b, and c into the third equation

[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]

[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]

[tex]220 - 100 = 60b + 100 - 100[/tex]

[tex]120 / 60 = 60b / 60[/tex]

[tex]2 = b[/tex]

Step 10:  Find a using b = 2

[tex]a = b + 1[/tex]

[tex]a = (2) + 1[/tex]

[tex]a = 3[/tex]

Step 11:  Find c using a = 3 and b = 2

[tex]c = -a - 3b + 9[/tex]

[tex]c = -(3) - 3(2) + 9[/tex]

[tex]c = -3 - 6 + 9[/tex]

[tex]c = 0[/tex]

Step 12:  Find d using b = 2

[tex]d = 4 - 4b[/tex]

[tex]d = 4 - 4(2)[/tex]

[tex]d = 4 - 8[/tex]

[tex]d = -4[/tex]

Answer:  [tex]a = 3, b = 2, c = 0,d = -4[/tex]

Answer:

43 paperback books

Step-by-step explanation:

7.50(15) + 1.25x = 166.25

112.50 + 1.25x = 166.25

Subtract 112.50 from both sides

(112.50 - 112.50) + 1.25x = (166.25 - 112.50)

1.25x = 53.75

Divide 1.25 from both sides

x = 43

Answer:

x=65

Step-by-step explanation:

145 and 2x+15 are vertical angles meaning that they are congruent to each other. Subtract 15 from both sides, and divide by 2 giving x=65.

Hope this helps!

Answer:

the factors of 63 are:

1,3,7, 9, 21, 63

D. 3, 7, 9, 21, 63

Step-by-step explanation:

Answer:

43.01m^2

Step-by-step explanation:

[tex]A=\frac{1}{4} \sqrt{5(5+2\sqrt{5}) } a^2\\[/tex]

This is the formula for a pentagon

Answer:52.2in

Step-by-step explanation:

Did it on a test and got it correct

We have been given that the distance from Pensacola, Florida to Tallahassee, Florida on a map is 8 inches, which represents 200 miles. We are asked to find the actual distance from Pensacola to Miami if the distance on the map measures 27 inches.

We will use proportions to solve our given problem as proportion states that ratio between two proportional quantities is similar.

[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{27 inches}}=\frac{200\text{ miles}}{\text{8 inches}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{27 inches}}\times \text{27 inches}=\frac{200\text{ miles}}{\text{8 inches}}\times \text{27 inches}[/tex]

[tex]\text{Actual distance}=\frac{25\text{ miles}}{1}\times 27[/tex]

[tex]\text{Actual distance}=675\text{ miles}[/tex]

Therefore, the actual distance from Pensacola to Miami is 675 miles.

Answer:

it’s 76 ft squared

Step-by-step explanation:

happy to help:)

Answer:

Quickly learn how to find the Area of Composite Figures in today's geometry lesson. With 19 worked examples, you'll have everything you need ...

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

the range is = maximum value given - the minimum value given

the data is spread from 0 -12. that means that someone either had 0 pencils or any other number of pencils to 12.

the range would then be 12 - 0.

Answer:

4x^2 -16

Step-by-step explanation:

(2x + 4)(2x - 4)

FOIL

first:2x*2x = 4x^2

outer: -4 *2x = -8x

inner:  4*2x = 8x

last: -4*4 = -16

Add them together

4x^2 -8x+8x =-16

4x^2 -16

The multiplication of the expression (2x + 4)(2x - 4) is 4x² - 16.

Given the expression in the question:
(2x + 4)(2x - 4)

We can multiply the expression (2x + 4)(2x - 4) using the distributive property and the FOIL method.

(2x + 4)(2x - 4)

Apply the FOIL method:

2x( 2x - 4 ) + 4( 2x - 4 )

Apply distributive property:

2x × 2x + 2x × - 4 + 4 × 2x 4 × - 4

Multiply the terms:

4x² - 8x + 8x - 16

Collect and add like terms:

4x² - 16

Therefore, the simplified form is 4x² - 16.

Learn more about the FOIL method here: https://brainly.com/question/27980306

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Answer:

4x+9, 1st degree binomial

Step-by-step explanation:

It's already in standard form

Answer:

can you show the planets. or do you want real planets volumes?

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of sector = angle/360 * pi * r^2

r is 19m

37/360 * 22/7 * 19 * 19

Area = 116.61 m^2

Answer: this is the right answer Both functions must be linear functions. And The y-intercept for one function must be positive, while the y-intercept for the other function must be negative.

Step-by-step explanation:

The true statements about the functions f(x) and g(x) are (a), (c) and (d)

The functions are given as:

h(x) = x + 1

j(x) = 3x - 6

From the question, we have:

h(x) = f(x) + g(x)

j(x) = f(x) * g(x)

Expand the function j(x)

j(x) = f(x) * g(x) = 3 * (x - 2)

By comparison, we have:

f(x) = 3

g(x) = x - 2

f(x) + g(x) = 3 + x - 2

f(x) + g(x) = x + 1

This gives

h(x) = x + 1

By analyzing the functions f(x) = 3 and g(x) = x - 2, we can see that:

Hence, the true statements are (a), (c) and (d)

Read more about linear functions at:

https://brainly.com/question/4025726

Answer:

5 sqrt(3)

Step-by-step explanation:

Since this is a right triangle

sin theta = opposite side/ hypotenuse

sin 60 = x /10

10 sin 60 = x

10 sqrt(3) /2 =x

5 sqrt(3) =x

Answer:

5√3

Step-by-step explanation:

The sine function ties together the information at hypotenuse = 10, opposite side = x and angle of elevation = 60 degrees:

sin 60 degrees = opp side / hypotenuse  =  x/10.

Therefore, x = 10 sin 60 degrees = √3/2, and so x = 10√3/2  =  5√3  (equal to the third answer choice).

Answer:

Im guessing this i might be wrong

54 ounces

3 ounces

Step-by-step explanation:

Answer:

To be honest i think 54 ounces and 3 ounces

Step-by-step explanation:

i was going to say 54 and 84 but i said to myself that didn't make any sense if it is 84 let me know plz

Answer:

(0,-21)

Step-by-step explanation:

The x value of a y intercept is always 0

So we can plug in 0 to the equation to solve for the y intercept

(2*0-3)(3*0+7)

-3*7= -21

y intercept: (0,-21)

Answer:

-21

Step-by-step explanation:

f(x)=(2x-3)(3x+7)

The y intercept is when x=0

f(0) = (0-3) (0+7)

     -3*7

    -21

The y intercept is -21

Answer:

11/12

Step-by-step explanation:

1

3

(

11

4

)

=(

1

3

)(

11

4

)

=

(1)(11)

(3)(4)

=

11

12

(Decimal: 0.916667)

PLease mark me brainllest!!!

The given equation in fraction should be [tex]\frac{5}{12}[/tex]

Since two fractions are given i.e. [tex]\frac{1}{3}[/tex] and [tex]1 \frac{1}{4}[/tex]

We have to multiply these two in fractions

So,

[tex]= \frac{1}{3} \times 1\frac{1}{4}\\\\ = = \frac{1}{3} \times \frac{5}{4} \\\\= \frac{5}{12}[/tex]

Therefore, we can concluded that The given equation in fraction should be [tex]\frac{5}{12}[/tex]

Learn more about fraction here: https://brainly.com/question/17748421

Answer:

f(x) will be 11

Step-by-step explanation:

since the first 1 is (0,5) the (0,8) so +3 so next would be 11

Answer:

5(8/5)^x

Step-by-step explanation:

Answer: A. 343.08

Step-by-step explanation:

with the property tax rate and monthly tax payment is what were looking for

Answer:

20.31%

Step-by-step explanation:

a) Construct a binomial distribution.

P = nCx* p%5Ex%2Aq%5E%28n-x%29 p= .8 and q = .2  and n = 8

b) Find the

mean = np = 8%2A.8+=+6.4

variance = npq = 6.4%2A.2+=+1.28

standard deviation of the probability distribution.sqrt%281.28%29

c) P(x = 6) = 28+%2A%28.8%29%5E6%28.2%29%5E2 =  .2936  or 29.36%

d) P(x < 6) = 1 - P(x = 8) - P(x = 7) - P(x = 6)

           =  1 - .1678 - .3355 - .2936  = .2031   or 20.31%

HOPE THIS HELPS PLZ MRK BRAINLIEST

Answer:

My sister is getting ready to prepare, I would say 1100 it means you are above.

Step-by-step explanation:

Answer:

V_rectangular_box = width x height x length

V = V_big_one + V_small_one

  =  (1/3)x(1/4)x(5/8) + (1/6)x(1/4)x(1/4) = 1/16 (ft3)

Answer:

fjdjdkhfidkfjsidmi

Step-by-step explanation:

irufusidjf9sodf8wpud8dkdhd8idhddh

The graph of the absolute value parent function will be V-shaped. Then the correct option is C.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x – h | + k

The graph of the absolute value parent function will be V-shaped.

Then the correct option is C.

More about the absolute function link is given below.

https://brainly.com/question/10664936

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Answer:

A,C,D

Step-by-step explanation:

just took the test

Answer:

2 6 10

Step-by-step explanation:

Answer:

21.24°

Step-by-step explanation:

I hope it helps :)

Your answer will be 10m.

We can picture this question as a right-angled triangle, where the pole is one leg, and the distance from the pole to the pigeon on the ground is another leg. Using this, the hypotenuse would be the distance that the pigeon would travel to get from the ground to the top of the pole, presuming it flies in a straight line, and so we can use Pythagoras’ Theorem to find the length of the hypotenuse.

a² + b² = c²

(6)² + (8)² = c²

36 + 64 = c²

100 = c²

10 = c

I hope this helps! Let me know if you have any questions :)