Rewrite the function by completing the square.

h(x)= x^2+3x-18

Answer:

® 6(2x - 1); @ -6(-2x + 1)  

Step-by-step explanation:

12x - 6 = 6(2x- 1)  Factored out 6

12x - 6 = -6(-2x + 1)     Factored out -6

Answer:

[tex] \: \: \: \: \: \: \: \: 5h + ( - 6h) = 20 \\ = > 5h - 6h = 20 \\ = > - h = 20 \\ = > h = - 20[/tex]

Answer:

286

Step-by-step explanation:

If the three-digit number is xyz, then:

x + y + z = 16

y = z + 2

z = 3x

Substitute the third equation into the second:

y = 3x + 2

Substitute this and the third equation into the first:

x + (3x + 2) + (3x) = 16

7x + 2 = 16

7x = 14

x = 2

y = 3x + 2 = 8

z = 3x = 6

The number is 286.

The three-digit number where the sum of its digits equal 16, the tens digit is two more than the unit's digit, and the unit's digit is triple the hundreds digit is 286.

The question involves finding a three-digit number where the sum of the digits is 16, the tens digit is two more than the unit's digit, and the unit's digit is triple the hundreds digit. Let's represent the hundreds digit as 'h,' the tens digit as 't', and the units digit as 'u'. According to the problem, we have three equations:

Substituting the third equation into the first, we get h + (3h + 2) + 3h = 16, which simplifies to 7h + 2 = 16, leading to h = 2. Thus, u = 3h = 6, and t = u + 2 = 8. Therefore, the three-digit number is 286.

Answer:

Step-by-step explanation:

3,068 × 108

= 331344

Answer:

331,344

Step-by-step explanation:

Line up the numbers like how u would do it if adding or subtracting and multiply each digit in 108 by each digit in 3068 starting with 8*8. Then do the same with multiplying each digit in 3068 by each digit in 108 starting with 8*8

Answer:

E

Step-by-step explanation:

We will first find the percentage increase of 20 years. Then we will divide that by 20 to get the annual average percentage increase.

To get the percentage increase, we will find the increased amount and divide that by original population (2,000,000). Multiply that by 100 to get the percentage.

So,

Increased amount = 4,500,000 - 2,000,000 = 2,500,000

Now the percentage increase:

[tex]\frac{2,500,000}{2,000,000}*100=125[/tex]

So, in 20 years, the percentage increase is 125%

Per Year = 125/20 = 6.25% average per year

No correct answer in the answer choices from A through D, so E is the correct answer, None of These.

Answer:

The total of Charlie's be $7.

Step-by-step explanation:

Given:

Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.

The regular ticket price was $9.00.

And the tax is 6%.

Now, to find Charlie’s total.

So ,we deduct the 25% off first:

[tex]\$9.00-25\%\ of\ \$9.00[/tex]

[tex]=9-\frac{25}{100} \times 9[/tex]

[tex]=9-\frac{225}{100}[/tex]

[tex]=9-2.25[/tex]

[tex]=\$6.75.[/tex]

Now, including tax :

[tex]\$6.75+6\%\ of\ \$6.75[/tex]

[tex]=6.75+\frac{6}{100} \times 6.75[/tex]

[tex]=6.75+0.06\times 6.75[/tex]

[tex]=6.75+0.405[/tex]

[tex]=\$7.155.[/tex]

Approximately = $7.

Therefore, the total of Charlie's be $7.

Answer: OPTION B.

Step-by-step explanation:

When parallel lines are cut by a transversal several angles are formed.

There are pairs of angles called "Alternate Interior angles".

 These angles are not adjacent and they are located between the parallel lines, and on opposite sides of the transversal.

By definition, they are are congruent, or, in other words the measure of Alternate Interior angles are equal.

In this case, you can identify that the [tex]\angle 8[/tex] and the [tex]\angle 2[/tex] are Alternate Interior angles.

Based on the data given in the exercise, you know that the measure of the angle 8 is:

 [tex]\angle 8=115\°[/tex]

So, You can determine that the angle 2 have the same measure. This is:

 [tex]\angle 2=115\°[/tex]

The cost of adult and kid tickets, we set up two equations representing the total cost for separate groups and use the elimination method to solve the system of linear equations. Once we solve for one ticket type, we can use its value to find the cost of the other ticket type.

The problem presented is a system of linear equations where we have two unknowns: the cost of an adult ticket and the cost of a kid ticket. We can set up the two equations based on the given information:

40A + 26K = 486.70 (First group's total cost)

21A + 31K = 332.45 (Second group's total cost)

To solve this system, we can use either substitution or elimination methods. For simplification, let's use the elimination method:

Multiply the second equation by 2: (2 x 21A) + (2 x 31K) = 2 x 332.45, which gives us 42A + 62K = 664.90.

Now subtract the first equation from this new equation: (42A + 62K) - (40A + 26K) = 664.90 - 486.70, resulting in 2A + 36K = 178.20.

Divide the entire equation by 2: A + 18K = 89.10.

We now have an easier equation to work with along with our original first equation.

To find the value of one variable, we could substitute the value of A from the first equation (using the second simplified equation) into the second equation and solve for K.

Once we have the value of K, we can substitute it back into either original equation to solve for A.

These steps will give us the exact cost of an adult ticket (A) and a kid ticket (K).

Answer:

Step-by-step explanation:

10

Answer:

27

Step-by-step explanation:

To find the answer to this, you need to divide the 15 slices of pizza by 5/9. 15/(5/9) is 15*9/5 (multiply both the top and the bottom by 9 and you cancel out the 9 in the 5/9 fraction) and you get 135/5 = 27

1) 155.91 grams would be left after 10 years

2) The population would be 376,478 in 2040

Step-by-step explanation:

The form of the exponential function is [tex]y=a(b)^{x}[/tex] , where

1)

Scientists are studying a 500 grams sample of a radioactive element, which has an annual decay rate of 11%

∵ The initial amount is 500 grams

∴ a = 500

∵ The annual decay rate is 11%

∴ r = 11% = 11 ÷ 100 = 0.11

∵ b = 1 - r ⇒ decay

∴ b = 1 - 0.11 = 0.89

- We need to find how many grams of the sample would be left

  after 10 years

∴ x = 10

- Substitute all of these values in the form of the exponential function

∵ [tex]y=500(0.89)^{10}[/tex]

∴ y = 155.9085996

- Round it to 2 decimal places

∴ y = 155.91

155.91 grams would be left after 10 years

2)

In 2000, the population of an Ohio town was 140,212. The population is expected to grow at a rate of 2.5% each year

∵ The population of an Ohio town was 140,212

∴ a = 140.212

∵ The population is expected to grow at a rate of 2.5% each year

∴ r = 2.5% = 2.5 ÷ 100 = 0.025

∵ b = 1 + r ⇒ growth

∴ b = 1 + 0.025 = 1.025

- We need to find the population in 2040

∵ The number of years is 2040 - 2000 = 40 years

∴ x = 40

- Substitute all of these values in the form of the exponential function

∵ [tex]y=140212(1.025)^{40}[/tex]

∴ y = 376478.1709

- Round it to the nearest whole number

∴ y = 376,478

The population would be 376,478 in 2040

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Answer:

Hi here is your answer

an=5n-3

an-1= -3+5n

an-1= -3+5(n-1)

an-1= -3+5n-5

an-1= 5n-7

d= an- an-1

d=(5n-3)-(5n-7)

d=5n-3-5n+7

d=4

Answer: d = 4

Hope this helps you.

Answer:

d = 5

Step-by-step explanation:

an = 5n -3

a1 = 5 -3 = 2

a2 = 5*2 -3 = 10 - 3 = 7

d = a2 - a1 = 7 - 2 = 5

Answer:

C

Step-by-step explanation: As you can see, the correlation goes up and down, this does not represent positive nor negative.  Therefore, C would be your final answer.

Answer:

5

Step-by-step explanation:

Answer: the answer is 6

Step-by-step explanation: the hundredth place is 2 spaces behind the decimal.

Answer:

164 and one over two

Step-by-step explanation:

47 over 8 *28

=1316 over 8

=164 and four over eight

=164 and one over two

[tex] \frac{47}{8} \times 28 \\ = \frac{1316}{8} \\ = 164 \frac{4}{8} \\ = 164 \frac{1}{2} [/tex]

Hope that helps

68,246 inches of road had been repaved before today.

Step-by-step explanation:

Given,

Length of road repaved so far = 97338 inches

Length repaved today = 29092 inches

Length repaved before today = Total length repaved - Length repaved today

Length repaved before today = 97338 - 29092

Length repaved before today = 68246 inches

68,246 inches of road had been repaved before today.

Keywords: subtraction

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If f(4a) = 80, then the value of "a" is 4.2

Solution:

Given that cost for the olive oil used to fill the containers on the tables in an Italian restaurant is given by the function:

f(x) = 5x – 4

where "x" represents the number of quarts of olive oil

f(x) represents the quarts of oil used

To find: value of "a" when f(4a) = 80

Substitute x = 4a in given function

f(4a) = 5(4a) - 4

80 = 20a - 4

20a = 84

10a = 42

a = 4.2

Thus the value of "a" is 4.2

We want to know the value of a factor, given that we know f(4a) = 80 and the function f(x).

The value of a is 4.2

Here we start with the function f(x) = 5x - 4

Now we know that:

f(4a) = 5*(4a) - 4 = 80

Then we can just solve the above equation to find the value of a:

5*(4a) - 4 = 80

20*a - 4 = 80

20*a = 80 + 4 = 84

a = 84/20 = 4.2

The value of a is 4.2

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To find the calories in a 14 ounce drink, we first determine the calorie content per ounce from a 90 ounce drink. We find it to be about 9.89 calories per ounce. Multiplying this by 14 gives us approximately 138.46 calories in a 14 ounce drink.

To find the calories in a 14 ounce drink, we need to first determine the calorie content per ounce in the 90-ounce drink. This is found by dividing the total calories (890) by the total ounces (90). The number we get from this division (calories per ounce) can then be multiplied by the ounces in the smaller drink (14) to get the number of calories in that drink.

Therefore, a 14 ounce drink from this gas station would have approximately 138.46 calories.

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Answer:

non linear

Step-by-step explanation:

linear means a straight line graph. This type is quadratic since it has a parabola.

Answer:

Step-by-step explanation:

When we talk about linear and nolinear funciton, we can distinguish them by using their graphs.

A linear function has a linear behaviour, that means it's representes by a straight line.

A nonlinear function doesn't have a straight line behaviour.

That's the easiest way to distinguish wether is a linear function or nonlinear.

Therefore, in this case, you can observe that the graph is not a straight line, that means the function is nonlinear.

Answer:3x(45/5)-7)

(3x9)-7=27-7=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

3×[(12+33)]÷5-7 ​ = 3 * 45/5 -7

=3*9 - 7 = 27 - 7 = 20

Answer:

3(6y-11)+2y=7

18y-33+2y=7

20y-33=7

20y=40

y=40/20

y=2

Put equation 1 into equation 2.

3(6y - 11) + 2y = 7

18y - 33 + 2y = 7

18y + 2y = 40

20y = 40

y = 2

x = 6(2) - 11

x = 12 - 11

x = 1

The coordinate pair is (1, 2) (x = 1, y = 2.)

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You have purchased 5 weekday hours.

Step-by-step explanation:

Parking hours purchased = 26

Cost per hour on weekday = $2

Cost per hour on weekend = $10

Total spent = $220

Let,

Number of hours on weekdays = x

Number of hours on weekend = y

According to given statement;

x+y=26      Eqn 1

2x+10y=220    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=26)\\10x+10y=260\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](10x+10y)-(2x+10y)=260-220\\10x+10y-2x-10y=40\\8x=40[/tex]

Dividing both sides by 8

[tex]\frac{8x}{8}=\frac{40}{8}\\x=5[/tex]

You have purchased 5 weekday hours.

Keywords: linear equation, elimination method

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Answer:

The number of visit so that both plan cost same is 10 .

Both the plan has equivalent choice of benefit

Step-by-step explanation:

Given as :

A gym has two membership plans.

For Gold plan

The charge per month = $50  

The charge per visit = $3

For Platinum plan

The charge per month = $20  

The charge per visit = $6

Let The number of visit for which each plan be same = n visits

Now, According to question

∵ Each plan cost to be same

So,

The charge per month for gold plan+ The charge per visit × numbers of visit = The charge per month for platinum plan+ The charge per visit × numbers of visit

I.e $50 + $3 × n = $20 + $6 × n

Or, $50 - $20 =  $6 × n  -  $3 × n

Or, $30 = ($6 - $3) × n  

Or, $30 = $3 × n  

∴ n = [tex]\dfrac{30}{3}[/tex]

I.e n = 10

So, The number of visits = n = 10

Now, For Gold plan

The charge per month = $50  

The charge per visit = $3 × 10 = $30

So, Total charge for gold plan = $50 + $30 = $80

Similarly For Platinum plan

The charge per month = $20  

The charge per visit = $6×10 = $60

So, For Platinum plan ,total charge = $20 + $60 = $80

Hence, The number of visit so that both plan cost same is 10

and both the plan has equivalent benefit. Answer

Answer: x = -26

Step-by-step explanation:

3x-47

substitute x with 7: 3(7)-47

3(7) = 21 -47 = -26

Answer:

-26

Step-by-step explanation:

x=7

3 is being multiplied by X

replace X with 7 in your equation

Your equation should then look like this: 3(7)-47

The parentheses around the 7 indicate that the 7 is being multiplied by the 3 or in other words: (3*7)-47

multiply 3 and seven before subtracting 47

3*7= 21

Once you have your answer to that subtract 47, your answer should be a negative # because you are subtracting a larger # from a smaller #

21-47= -26

so if X equals 7.  3x-47= -26

The shortest possible height of the tower is 24 cm

They used 4 blue blocks and 3 green blocks

Step-by-step explanation:

Tim and his brother are building towers out of blocks

We need to find the shortest possible height of the tower and how many of each color block they used

∵ Tim is using blue blocks that are 6 cm tall

∴ The height of his tower is a number divisible by 6

∵ His brother is using green blocks that are 8 cm tall

∴ The height of his tower is a number divisible by 8

∵ The heights of their towers are equal

∴ The height of the towers must be a number divisible by 6 and 8

Let us write some multiples of 6 and 8 to find the first common multiple of them

∵ The multiples of 6 are 6 , 12 , 18 , 24 , 30 , 36 , .........

∵ The multiples of 8 are 8 , 16 , 24 , 32 , 40 , .............

∵ The first common multiple of them is 24

∴ The shortest possible height of the tower is 24 cm

∵ The height of each blue block is 6 cm

- Divide the height of the tower by the height of the block to

   find the number of blue blocks

∵ 24 ÷ 6 = 4

∴ Time is using 4 blue blocks

∵ The height of each green block is 8 cm

- Divide the height of the tower by the height of the block to

   find the number of green blocks

∵ 24 ÷ 8 = 3

∴ His brother is using 3 green blocks

The shortest possible height of the tower is 24 cm

They used 4 blue blocks and 3 green blocks

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Answer:

C

Step-by-step explanation:

The lower quartile is the value at the left side of the box, that is

LQ = 14

The upper quartile is the value at the right side of the box, that is

UQ = 28

The median is positioned at the vertical line inside the box. that is

Median = 21

Answer:

The rent owe by me is Rs 1435

The rent owe by roommate is Rs 1360

Step-by-step explanation:

Given as :

The total rent of the room = x = Rs 2795

Let The room rent pay by friend = Rs y

And The room rent pay by me = Rs z

Now, According to question

The room rent pay by me = Rs 75 + room rent pay by roommate

i,e Rs z = Rs 75 + Rs y

Now, Again

The total rent of the room = The room rent pay by me + room rent pay by roommate

Or, x = Rs z + Rs y

Or, Rs 2795 = (Rs 75 + Rs y) + Rs y

Or, 2795 = 75 + 2 y

Or, 2 y = 2795 - 75

Or, 2 y = 2720

∴  y = [tex]\dfrac{2720}{2}[/tex]

i.e y = Rs 1360

So, room rent pay by friend = y = Rs 1360

And,The room rent pay by me = Rs 75 + room rent pay by roommate

Or,The room rent pay by me = Rs 75 + Rs 1360

So,he room rent pay by me = Rs 1435

Hence,The rent owe by me is Rs 1435

And ,The rent owe by roommate is Rs 1360    Answer

Answer:

Ordered pairs are (0,7) , (1,8) , (-1,6) and (-7,0)

Step-by-step explanation:

Answer:

(7, -27)

Step-by-step explanation:

Given y=8-5x and x=7,

We substitute x=7 into the equation y=8-5x.

This would give us y= 8-5(7) and can be further sinplified to y= 8-35 = -27.

Ordered pair refers to 2 numbers that come in a pair to fulfil an equation in the form of (x, y).

Answer:

73155 is the required 3rd number that will complete the sequence as: 88511, 16351, 73155 , 10251.

Step-by-step explanation:

So, let us consider 88511 and determine the pattern to find the next number and so on to complete the sequence.

Adding the first 2 digits in the number 88511 i.e.  8 + 8 = 16

Subtracting the 3rd digit from the 2nd digit i.e. 8 - 5 = 3

Multiplying the 3rd digit and 4th digit i.e. 5 × 1 = 5

Dividing the 4th digit by the 5th digit i.e. 1 ÷ 1 = 1

Hence, using these steps would get us the number 16351.

So, the next number would be obtained using same steps:

Adding the first 2 digits in the number 16351 i.e.  1 + 6 = 7

Subtracting the 3rd digit from the 2nd digit i.e. 6 - 3 = 3

Multiplying the 3rd digit and 4th digit i.e. 3 × 5 = 15

Dividing the 4th digit by the 5th digit i.e. 5 ÷ 1 = 5

Hence, using these steps would get us the number 73155.

So, the next number would be obtained using same steps:

Adding the first 2 digits in the number 73155 i.e.  7 + 3 = 10

Subtracting the 3rd digit from the 2nd digit i.e. 3 - 1 = 2

Multiplying the 3rd digit and 4th digit i.e. 1 × 5 = 5

Dividing the 4th digit by the 5th digit i.e. 5 ÷ 5 = 1

Hence, using these steps would get us the final number 10251.

So, from this pattern method, we determine that 73155 will be the 3rd number in the sequence: 88511,16351,?,10251.

So, the complete sequence would be: 88511, 16351, 73155, 10251.

Keywords: sequence, number

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Answer:

[tex]g(x)=\frac{x}{4}-3[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4x+12[/tex]

Find the inverse

Let

y=f(x)

[tex]y=4x+12[/tex]

Exchange the variables (x for y and y for x)

[tex]x=4y+12[/tex]

Isolate he variable y

subtract 12 both sides

[tex]4y=x-12[/tex]

divide by 4 both sides

[tex]y=\frac{x}{4}-3[/tex]

Let

g(x)=y

[tex]g(x)=\frac{x}{4}-3[/tex] ---> inverse of the function f(x)