AJ is the bisector of ∠HJI. Determine the value of x.
Question 2 options:

A)

12

B)

10

C)

2.5

D)

22.5

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:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4

Answer:

y > -4

Step-by-step explanation:

−2y<8

Divide each side by -2, remembering to flip the inequality since we are dividing by a negative

-2y/-2 > 8/-2

y > -4

Answer:

Last option

y > -4

Step-by-step explanation:

-2y < 8

Switch sides

-8 < 2y

-4 < y

Or

y > -4

Answer:

C. [tex]c = \frac{-7+-\sqrt{129} }{8}[/tex]

Step-by-step explanation:

Before we start, you can think of the variable "c," as x.

The quadratic formula/equation is:

[tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

The setup is:

[tex]ax^2+bx+c=0[/tex]

[tex]4c^2+7c-5=0[/tex]

Plug in the numbers accordingly to the letter associated, like so:

[tex]x = \frac{-7+-\sqrt{7^2-4(4)(-5)} }{2(4)}[/tex]

[tex]x = \frac{-7+-\sqrt{49+80} }{8}[/tex]

[tex]x = \frac{-7+-\sqrt{129} }{8}[/tex]

Answer:

26

Step-by-step explanation:

I subtracted DF and DE to find the missing difference for the segment EF. I'm not sure if this is correct though. I hope it helps.

The length of line segment EF is 26.

A line segment is a subset of a line which has two endpoints.

A ray has one end point and extends indefinitely on the other direction.

A line extends indefinitely on both of it's directions.

From the given data

Line segment DF has a length 38 and line segment DE has a length 12.

To find the length of line segment EF we have to subtract the length of line segment DE from length segment DF.

∴ EF = DF - DE

  EF = 38 - 12'

  EF = 26.

So, the line segment EF has a length of 26.

Learn more about Line segments here :

https://brainly.com/question/25727583

#SPJ6

Answer:

C. Fair Credit Billing Act

Step-by-step explanation:PLATO

Answer:if you double all of the dimensions of a rectangular prism, you create a similar prism with a scale factor of 2. The surface area of the similar prism will increase as the square of the scale factor (22 = 4) and the volume will increase as the cube of the scale factor (23 = 8).

Step-by-step explanation:

Scale factor are used to increase or diminish the original figrure. The new volume will be 8times larger than the initial volum

Scale factor are used to increase or diminish the original figrure.

Assume the original dimension of the figure is a, b and c, the volume of te figure will be expresed as:

A = length * width * heiht

A = abc

If the measure of the sides are doubled, hence;

New volume = 2a * 2b * 2c

New volume = 8abc

Ratio = 8abc/abc
Ratio = 8

Hence the new volume will be 8times larger than the initial volume

Learn more on volume of a figure here: https://brainly.com/question/511679

Answer:

$3,125

Step-by-step explanation:

Answer:

1440

Step-by-step explanation:

Answer:

54 sq in.

Step-by-step explanation:  9x12= 108   108 divided by 2 = 54

so yeah

Answer:

B. 90

Step-by-step explanation:

In a triangle if one of the angle is 90 deg the triangle is said to be a RIGHT ANGLED TRIANGLE.

Hope this helps, Pls Mark me as Brainliest!!!

Given triangle is a right-angle triangle. option B is correct.

The properties of the triangle are:

1. The sum of all the angles of a triangle (of all types) is equal to 180°.

2. The sum of the length of the two sides of a triangle is greater than the length of the third side.

3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

A triangle is said to have a right angle if one of its angles is precisely 90 degrees. There are several techniques to spot a right angle triangle, including:

Therefor, the given triangle is a right-angle triangle.

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ7

Answer:

1. 20 + 2x ≤ 60

2. Yes, see explanation

Step-by-step explanation:

Let x equal the amount of exercises Anna can perform.

The inequality will look like this:

20 + 2x ≤ 60

Let's go over each of the values and why there in the equation.

20: The amount of minutes Anna has already spent in the gym

2: The amount of minutes per exercise

x: The amount of exercises Anna can perform

≤: The amount of exercises must be less than or equal to the amount of time Anna is willing to spend in the gym.

60: The amount of minutes in an hour; the amount of time Anna is willing to spend at the gym.

Now, plug in 18 for x for question 2.

20 + 2(18) ≤ 60

Evaluating 2*18, the inequality becomes 20 + 36 ≤ 60.

Evaluating 20 + 36, the inequality becomes 56 ≤ 60.

Since 56 is less than 60, we can determine that Anna has time to do 18 more exercises.

Answer:

D.24

hope i helped :D

Answer:

16

Step-by-step explanation:

Answer:

It is D, and or 57

Step-by-step explanation:

So the right answer is 5/6.

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

[tex] \frac{5}{6} [/tex]

Step-by-step explanation:

[tex] \frac{1}{2} + \frac{2}{6} \\ \frac{6 + 4}{6 \times 2} \\ \frac{10}{12} \frac{ \div 2}{ \div 2} \\ = \frac{5}{6} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer: 1 i think is option b, 2 i think is option c, page 2, question 1 i think is option b, question 2 i think is option a, page 3, question 1 i think is option a or b, and the last one i think is option c

Step-by-step explanation: i cant figure out others

Step-by-step explanation:

I think 40 should be the first term in the sequence because it is given 40.. 6n - 1

Answer:

#3    1/2

Step-by-step explanation:

if you start where the line and the boxes in the graph line up like at (0,-2) and then you go up 1 and right 2 the line will be there again line up with the boxes and since slope is rise/run it is 1/2

Answer:

6550

Step-by-step explanation:

You can put this solution on YOUR website!

Call the number of hardcover and paperback books, h and p.

Thus  

h + p = 8 and the value equation is

4h + 2p = 26

Now multiply the top one by four and subtract from the second one...we get

4h + 2p = 26

-(4h + 4p = 32)

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

-2p = -6

p = 3 so that

h = 5   x +  y = 8,    (1)

4x + 2y = 26,   (2)

where x and y are the numbers of hardcover and softcover books respectively.

To solve, multiply the equation (1) by 2 (both sides) and then distract it from the equation (2). You will get

4x - 2x = 26 - 16,   or

2x = 10,   or   x = 5 - the number of hardcover books purchased.

Then from the equation (1) you get y = 3.

Check. 4*x + 2*3 = 4*5 + 2*3 = 26. OK.

Answer:

(1,2)

Step-by-step explanation:

I graphed the inequality on the graph below and found which answer was a solution.

If this answer is correct, please make me Brainliest!

Interest formula: A = Pe^rt

A = amount

P = principal amount

r = interest rate

t = time

We know that in the question we have:

P = 8,000

r = 0.019

t = 6

Now, solve with the given values:

A = 8000e^(0.019*6)

A = 8000e^(0.114)

A = 8966.016...

Round to the nearest hundredth:

8966.016... → 8,966.02

Therefore, the answer is [ $8,966.02 ]

Best of Luck!

Answer:

$8,966.02

Step-by-step explanation:

Amount = 8000 × e^(6 × 1.9/100)

Amount = 8000 × e^0.114

Amount = 8966.016999

Answer:

B

Step-by-step explanation:

Answer:

The difference between the number of expected outcomes and the number of actual outcomes = 5

Step-by-step explanation:

She tosses a two sided counter and spins a spinner with six equal sized sections numbered 1 to 6.

Probability of the counter landing on either of the two sides is exactly = (1/2)

Probability of the counter landing on the red side = (1/2)

Probability of the spinner landing in a region greater than 3 = Probability of the spinner landing in a region of 4, 5 or 6. = (3/6) = (1/2)

In one toss and spin, the probability of a toss landing on red and the spinner landing on a number greater than 3 = p = (1/2)×(1/2)

p = (1/4)

Expected number of times that a toss will land on a red and a spinner will land on a number greater than 3 in 80 trials

= np = 80 × (1/4) = 20

Number of actual times that the toss lands on a red and a spinner lands on a number greater than 3 in 80 trials = 25

The difference between the number of expected outcomes and the number of actual outcomes = 25 - 20 = 5

Hope this Helps!!!

Answer:

The sample proportion is 0.253.

Step-by-step explanation:

We are given that a 90% confidence interval for a proportion is found to be (0.22, 0.28).

Firstly, as we know that the confidence interval for sample proportion is calculated as;

90% confidence interval = Sample proportion [tex]\pm[/tex] Margin of Error

Here, let [tex]\hat p[/tex] = sample proportion

Also, the level of significance = 1 - 0.90 = 0.10 or 10%

And, the critical value of z at 5% (two-sided) level of significance is 1.645.

So, 90% confidence interval =  [tex]\hat p \pm 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

           (0.22 , 0.28)    =   [tex]\hat p \pm 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

This means;  

          0.22  =  [tex]\hat p - 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]  -------------- [Equation 1]

          0.28  =  [tex]\hat p + 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]  -------------- [Equation 2]

From equation 1 and 2, we get;

           [tex]0.22 + 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }= 0.28 - 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

           [tex]1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} } + 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }= 0.28 -0.22[/tex]

             [tex]2 \times 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} } =0.06[/tex]

                 [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} } =\frac{0.06}{2 \times 1.645}[/tex]

                  [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} } =0.02[/tex]

Now, squaring both sides, we get;

                    [tex]{\frac{\hat p(1-\hat p)}{n} } =0.0004[/tex]

                      [tex]n ={\frac{\hat p(1-\hat p)}{0.0004} }[/tex]

Now, putting value of n in equation 1, we get;

                    0.22  =  [tex]\hat p - 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]  

                    0.22  =  [tex]\hat p - 1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{\hat p(1-\hat p)}\times 0.0004 }[/tex]

                    0.22  =  [tex]\hat p - 1.645 \times \sqrt{ 0.0004 }[/tex]

                    0.22  =  [tex]\hat p -( 1.645 \times 0.02)[/tex]

                    0.22  =  [tex]\hat p -0.033[/tex]

                      [tex]\hat p = 0.22 + 0.033[/tex] = 0.253

Therefore, the sample proportion  [tex]\hat p[/tex] is 0.253.

Answer:

g(3)=9

Step-by-step explanation:

We want to find what g(x), or y is, when x is equal to 3.

Therefore, we can substitute 3 in for x in the equation

g(x)=x^2

g(3)=3^2

Evaluate the exponent

g(3)=3*3

g(3)=9

Answer:

49.3%

Step-by-step explanation:

37 / 75  = 49.3%

The answer is 49.3%.

Probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

How to find that at least 7 will be girls?

Given that 75 babies are born assume that boys and girls are equally probable.

Then the probability that at least 37 will be girls is

37 / 75  = 49.3%.

Learn more about probability on: https://brainly.com/question/12992041

#SPJ2

Answer:

x=5 and x=15

Step-by-step explanation:

3x^2-60x+225=0

3x^2-60x+225/3=0/3

x^2-20x+75=0

x^2-5x-15x+75=0

x(x-5)-15(x-5)=0

(x-5)(x-15)=0

x-5=0 x-15=0

x=5 x=15

Answer:

40°

Step-by-step explanation:

complementary angels makes the sum of two angles = 90°

so

<ABC + < CBD = 90°

if <ABC = 50°

then 90° - 50° = 40°

Answer:

a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1

Step-by-step explanation:

Let the price of 1 sq.m. of fence panel be x

Let the price of 1 m of wooden frame be y

In Fig 1

Length = 4 m

Breadth = 3 m

Area =[tex]Length \times breadth = 4 \times 3 = 12 sq.m.[/tex]

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(4+3)=14 m

Cost of 1 m of wooden frame = y

Cost of 14 m of wooden frame = 14y

We are given that total cost of framing and fencing is 38

So. 12x+14y=38 ----1

In Fig 2

Length = 6 m

Breadth = 2 m

Area =[tex]Length \times breadth = 6 \times 2 = 12 sq.m[/tex].

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(6+2)=16 m

Cost of 1 m of wooden frame = y

Cost of 16 m of wooden frame = 16y

We are given that total cost of framing and fencing is 40

So. 12x+16y=40---2

Substitute the value of 12x form 1 in 2

38-14y+16y=40

2y=2

y=1

Substitute the value of y in 2

12x+16=40

12x=24

x=2

So, cost of 1 sq.m. of fence panel is 2 and cost of 1 m of wooden frame is 1

In fig 3

To verify :

Length = 3 m

Breadth = 5 m

Area = [tex]Length \times breadth = 3 \times 5 = 15 sq.m.[/tex]

Cost of 1 sq.m. = 2

Cost of 12 sq.m. =[tex]15 \times 2 = 30[/tex]

Perimeter =2(l+b)=2(3+5)=16 m

Cost of 1 m of wooden frame = 1

Cost of 16 m of wooden frame = 16

So, Total cost = 30+16=46

We are given that cost of fencing and framing is 46

Thus verified

Hence

a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1

Answer:

steps

1) 14/28 to convert to a percent you have to first divide the numerator from the demoninator and then  you  multiply by 100 and you get get %50 (you could had known bc 14 is half of 28)

2) 5/28 do the same thing as the first step and get %17.85

-Feel free to ask for more help :)

Answer:

A

Step-by-step explanation:

Given

f(x) = - 9(x + 5)² + 4 ← expand parenthesis using FOIL

     = - 9(x² + 10x + 25) + 4 ← distribute parenthesis by - 9

     = - 9x² - 90x - 225 + 4 ← collect like terms

     = - 9x² - 90x - 221 ← in standard form

Answer: Bro write the question better

Step-by-step explanation: