Bella plans to put $300 into a savings account. She can place her money into an account represented by p(x) = 3x+300, or into another account represented by
n(x) =300(1.04)^x. Which account has the highest value in 5 years? Which account has the highest in 12 years? Show your work!​

Answer: The first one

Answer:

(5,6) , (5,-2)

Step-by-step explanation:

Let the required point be P(5,y).

Its distance from (2,2) is 5 units.

So, [tex](5-2)^{2}[/tex] + [tex](y-2)^{2}[/tex] = 25.

So, [tex]3^{2}[/tex] +  [tex](y-2)^{2}[/tex] = 25.

  9 +  [tex](y-2)^{2}[/tex] = 25.

   [tex](y-2)^{2}[/tex] = 16

    Two cases are possible for now

case 1 : y-2 = 4 .

            y = 6

required point will be (5,6)

case 2 : y - 2 = -4.

              y = -2.

required point will be (5,-2).

Two points are possible : (5,6) , (5,-2).

Answer:

16 groups

Step-by-step explanation:

Add all the people up then divided it by 8 so now it will be 8 people in each group and there will be a total of 16 groups

30+32+29+28+9=128/8=16

The number of groups will be needed so everyone can see the exhibition is 16.

Given that, the fourth graders are going to the science museum.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

Total number of people

=30+32+29+28+9

= 128

Groups of 8 people can see a special exhibit on space travel.

Number of groups = Total number of people/Number of groups

= 128/8

= 16

Therefore, the number of groups will be needed so everyone can see the exhibition is 16.

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Harrison's prediction that the actual quotient for 57872 divided by 305 would be less than his estimate of 200 is correct. This is because the divisor (305) is larger than in the estimate (300), and also because the dividend (57872) is smaller than in the estimate (60000), leading to a smaller quotient.

Harrison predicted that the actual quotient for 57872 divided by 305 would be less than his estimate of 60,000 divided by 300 which equals 200. To understand Harrison's prediction, we have to look at the numbers involved. When you are dividing two numbers, the quotient decreases as the divisor (the number you are dividing by) increases, given that the dividend (the number being divided) remains the same. In this case, 305 is larger than 300, so if the dividend were the same, the quotient for our original problem would indeed be smaller. However, the dividend in our original problem (57872) is smaller than the dividend in the estimate (60000). So we have a smaller number being divided by a slightly larger one, and this will also lead to a smaller quotient. Therefore, Harrison's prediction is correct.

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Answer:

6.9 foot.

Step-by-step explanation:

Given: Length of lamp post= 12-foot.

           The angle of elevation of the sun is 60°.

∴ The length of Lamp post, which is opposite is 12-foot.

  Now, finding the length of shadow cast by foot lamp.

Length of shadow is adjacent.

∴ We know the formula for [tex]Tan\theta[/tex]= [tex]\frac{Opposite}{adjacent}[/tex]

Next, putting the value in the formula.

⇒ [tex]Tan 60° = \frac{12}{adjacent}[/tex]

Cross multiplying both side and using the value of Tan 60°

∴ Adjacent= [tex]\frac{12}{\sqrt{3} } = 6.92[/tex] ≅ 6.9 (nearest tenth value)

6.9 is the length of shadow cast by a 12-foot lamp post.

Answer:6.9

Step-by-step explanation:

usatestprep

Answer:

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side

The formula of a perimeter of a square:

[tex]P=4s[/tex]

s - side

We have a perimeter

[tex]P=60\ in[/tex]

Substitute:

[tex]4s=60[/tex]             divide both sides by 4

[tex]\dfrac{4s}{4}=\dfrac{60}{4}\\\\s=15\ in[/tex]

Put it to the formula of an area of a square:

[tex]A=15^2=225\ in^2[/tex]

Answer: 225 in.²

Step-by-step explanation: First, we want to find the length of one side. Since we know that a square has 4 sides and the perimeter is 60 inches, we can set up the following equation to find the length of one side.

Let's use l as our variable to represent length.

4l = 60

To get l by itself, we need to divide by 4 on the left side of the equation. Since we divided by 4 on the left side, we must also divide by 4 on the right side. On the left side, the 4's cancel and we are left with l. On the right side, we have 60 over 4 which simplifies to 15.

This means that a side of the square is 15 inches.

Now, we are asking ourselves what is the area of a square with a side length of 15 inches.

To find the area of a square, remember that a square is a type of rectangle so we can use the following formula.

Area = length × width

However, since the length and width of a square are always equal, we use a special version of this formula to find the area of a square.

Instead of area = length × width, we say that the area of a square equals side × side or S².

Since the sides of the square each have a length of 15 inches, the area of the square is equal to (15 in.)² or (15 in) (15 in) which equals 225 in.²

Therefore, the area of the square is 225 in.².

Answer:

Area of the surface area of the lower half made of exposed granite = 1/4 (Perimeter of the base * Slant length)

Step-by-step explanation:

1. Let's review the data provided to us for solving the question:

Lower half of a square pyramid is made of granite

Top half of a square pyramid is made of limestone

2. Let's explain how we could find the surface area of the exposed granite.

First of all, let's remember what is the area of a square pyramid:

Area of square pyramid = Base area + Surface area of the four sides

Normally, we need to know the length of the square base and the slant length. And now let's replace in the formula:

Area of square pyramid = Length of the side of the square² + 1/2 (4 * Length of the side of the square * Slant length)

For calculating the surface area of the lower half made of exposed granite, we need to don't consider the base area and just the half of the surface area of the four sides, so the formula is:

Area of the surface area of the lower half made of exposed granite = 1/2 [1/2 (4 * Length of the side of the square * Slant length)]

Area of the surface area of the lower half made of exposed granite = 1/4 (4 * Length of the side of the square * Slant length)

Area of the surface area of the lower half made of exposed granite = 1/4 (4 * Length of the side of the square * Slant length)

Area of the surface area of the lower half made of exposed granite = 1/4 (Perimeter of the base * Slant length)

If we want to know the surface area of the lower half made of limestone, we can use the same formula:

Area of the surface area of the lower half made of limestone = 1/4 (Perimeter of the base * Slant length)

Answer:

Find the surface area of the entire square pyramid. Find the surface area of the exposed sides of the square pyramid made from limestone. Subtract the surface area of the square pyramid made from limestone from the surface area of the entire square pyramid.

Step-by-step explanation:

edg.

Answer:

9 hours at 9 dollars an hour is 81 dollars so therefore he needs to work 9 weeks in order to raise the money.

Step-by-step explanation:

Without the total cost of the car and additional fees, we cannot accurately calculate the number of hours or weeks Ryan needs to work. However, the process involves dividing the total cost by his hourly or weekly wage and interpreting the results.

In order to answer these questions, we first need to know the total cost of the car including the taxes, title, and plates. We are given that Ryan earns $9 per hour and works about 9 hours a week. However, without the total cost of the car and other fees, we cannot accurately calculate how many hours or weeks Ryan needs to work to afford the car.

Part A: Once we have the total cost, we could draw a bar diagram partitioning it into units of $9 (one hour's wage). This would visually represent the number of hours Ryan needs to work.

Part B & C: For these parts, we would also need to know the total cost. Once we have it, we divide the total cost by Ryan's weekly wage ($9/hour x 9 hours = $81/week) to get the number of weeks he needs to work. If the result is a fraction, we would round it up to the next whole number for Part B, as Ryan cannot work a fraction of a week. This provides an estimate. For Part C, we would be more precise by exactly computing the number of weeks and explaining why our solution is reasonable.

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Answer:

65 feet.

Step-by-step explanation:

80 feet roll of the fence is there.

It fits in the backyard the width must be 15 feet long.

So, there will be remaining (80 - 15 ) = 65 feet of fence.

If he wants to use the entire roll to fence the other side of the area then he can do it for more 65 feet length. (Answer)

Answer:

y = -9x + 4 ?

Step-by-step explanation:

y-4 I=I -(x+9)

y-4 I=I -9x

+4 I I +4

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

y = -9x+4

Answer:

Step-by-step explanation:

1/7+1/13=1/t

multiply both sides by 7*13*t

13t+7t=7*13

21t=91

t=91/19

it will take 4 hours and 8 minutes

Answer:

$21.70-3.4n

Step-by-step explanation:

Decimal Decisions: 12.70-n+9

Ratio rage: n÷4

Expression: 12.70-n+9+n/4

Combine 12.70 and 9= 21.70

Bring down the rest of the expression.

21.70-n+n/4

Combine -n and n/4= -4n/4÷1n/4= 3/n

So, the answer is $21.70-3.4n

To determine the cost for n people to play Decimal Decisions and Ratio Rage, we need the cost per person for each game.

To find out how much it would cost n people to play Decimal Decisions and Ratio Rage, we need to know the cost per person for each game. However, the cost for these games is not provided in the question. Can you please provide the cost for each game so that I can help you calculate the total cost?

Answer:

x = 20

Step-by-step explanation:

To do this question, you can use the pythagorean theorem.  c is your hypotenuse, a is the unknown side length and b is the known side length.

a^2+b^2=c^2

x^2+15^2=25^2

x^2=225=625

x^2=400

(x^2)^(1/2)=400^(1/2)

x = 20

Answer:

10 hours

Step-by-step explanation:

you need to drop 36 degrees, so 36/4 = 9 hours

1 pm + 9 hours = 10 pm

Answer:

Step-by-step explanation:

Answer:

-x^3+2x^2+4x-8

Step-by-step explanation:

(2-x)(x^2-4)

2x^2-8-x^3+4x

-x^3+2x^2+4x-8

Answer:

y=x^2-10x+27

Step-by-step explanation:

y=x^2

Shifted 5 to the right: y = (x-5)^2

Shifted 2 up: y = (x-5)^2+2

Simplify. You can use "(a-b)^2 = a^2-2ab+b^2" formula.

y = (x-5)^2+2 becomes y=x^2-10x+25+2 = y=x^2-10x+27

Answer:

c. 106 million

Step-by-step explanation:

A = number of people in the sample that use public transportation 5 or more days per week

A = 2,067,153

B = number of people total in the sample

B = 4,295,280

C = proportion of those in the sample that use public transportation 5 or more days per week

C = A/B

C = (2,067,153)/(4,295,280)

C = 0.48126 approximately

Multiply this value by the figure 220 million to compute the estimated number of people who use public transportation 5 or more days per week

C*(220 million) = 0.48126*(220 million) = (0.48126*220) million = 105.8772 million = 106 million

Answer:

The equation for the statement is  ( x + 9 ) × 3 = 12 , and the value of         x is - 5   .

Step-by-step explanation:

Given as :

Let The number picked by Amy = x

Amy told to Stephanie

she add 9  to the number and multiply the sum by 3 it would be 12

So, According to statement

( x + 9 ) × 3 = 12

Or, 3 x + ( 9×3 ) = 12

Or, 3 x + 27 = 12

or, 3 x = 12 - 27

or, 3 x = - 15

∴  x = - [tex]\frac{15}{3}[/tex]

I.e x = - 5

Hence The equation for the statement is  ( x + 9 ) × 3 = 12 , and the value of x is - 5   .  Answer

Answer:

(0,5) and (10,0)

Step-by-step explanation:

The equation of the straight line is given by 2x + 4y = 20 .......... (1)

Now, point (0,5) satisfies the equation (1) as putting x = 0, we will get y = 5.

Now, point (0,10) does not satisfy the equation (1) as putiing x = 0, we get y = 5 ≠ 10

Again, point (1,2) does not satisfy the equation (1) as putiing x = 1, we get y = 4.5 ≠ 2

Now, point (1,4) does not satisfy the equation (1) as putiing x = 1, we get y = 4.5 ≠ 4

Again, point (5,0) does not satisfy the equation (1) as putiing y = 0, we get x = 10 ≠ 5

Finally, point (10,0) satisfies the equation (1) as putiing y = 0, we get x = 10 .

Therefore, only points (0,5) and (10,0) are on the graph of the line 2x + 4y = 20 (Answer)

Answer:

The points a. (0,5) and f. (10,0) will lie on the given line.

Step-by-step explanation:

The given equation of line is [tex]2x + 4y=20[/tex].

Now, it is required to check whether the given point lie on the line or not. To check it, put the points in the equation of line and if they satisfies, then the point will be on the line else not.

(a) The first point is (0,5). Put this point in the equation as,

[tex]2x + 4y=20\\2\times0+4\times 5=20\\20=20[/tex]

Thus, the point satisfies and it will lie on the line.

(b) The first point is (0,10). Put this point in the equation as,

[tex]2x + 4y=20\\2\times0+4\times 10=20\\40\neq20[/tex]

Thus, the point doesn't satisfy and hence, it will not lie on the line.

(c) The first point is (1,4). Put this point in the equation as,

[tex]2x + 4y=20\\2\times1+4\times 4=20\\18 \neq 20[/tex]

Thus, the point doesn't satisfy and hence, it will not lie on the line.

(d) The first point is (5,0). Put this point in the equation as,

[tex]2x + 4y=20\\2\times5+4\times 0=20\\10 \neq 20[/tex]

Thus, the point doesn't satisfy and hence, it will not lie on the line.

(f) The first point is (10,0). Put this point in the equation as,

[tex]2x + 4y=20\\2\times10+4\times 0=20\\20 =20[/tex]

Thus, the point satisfies and it will lie on the line.

Therefore, points (0,5) and (10,0) will lie on the given line.

Refer the graph of line and points.

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Answer:

equation: -23 x -1

Step-by-step explanation:

two negatives equal positive

two positive equal positive

one positive and one negative equals negative

Answer:

no

Step-by-step explanation:

it would not make a a circle

Answer:

No! :)

Step-by-step explanation:

It wouldn't create a circle, Hope this helps xx

To model the money spent on a cell phone plan each month, the equation Cost = $15 + $0.10 × minutes can be used. A table and graph can be created by choosing different values for minutes and calculating the corresponding cost. The slope of the line represents the rate of change and the y-intercept represents the fixed cost.

Cost = $15 + $0.10 imes minutes

Minutes Cost

0 $15

10 $16

20 $17

Answer:

-10

Step-by-step explanation:

y=6x+8

y=6(-3)+8

y=-18+8

y=-10

Answer:

In 4 hours, Brad will travel 220 miles.

Step-by-step explanation:

Create the direct variation model-

y = kx

y- represents the total miles

x- represents hours

660 = k12

660/12 = k

k = 55

Model:

y = 55x

Replace x with 4:

y = 55(4)

y = 220

In 4 hours, Brad will travel 220 miles.

The answer is 220 miles.

[tex]\text{Hello there!}\\\\\text{We know that Brad traveled 660 miles in 12 hours. However, we need to}\\\text{find how many miles he traveled in 4 hours}\\\\\text{First, we need to find how many miles he can travel per hour}\\\\\text{Do this by dividing 660 by 12}\\\\660\div12=55\\\\\text{Now multiply 55 by 4 in order to see how many miles he traveled in 4 hours}\\\\55*4=220\\\\\boxed{\text{Answer: 220 miles}}[/tex]

Answer:

The answers are 31, 46, 52

Step-by-step explanation:

The sequence is 4+6=10, 10+15= 25, 25+6=31, 31+15=46, 46+6=52

The cost to rent one chair is $1.5 and one table is $8.5

Step-by-step explanation:

Let,

x be the cost of one chair

y be the cost of one table

According to given statement;

2x+12y=105    Eqn 1

5x+3y=33    Eqn 2

Multiplying Eqn 2 by 4;

[tex]4(5x+3y=33)\\20x+12y=132\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 1 from Eqn 3;

[tex](20x+12y)-(2x+12y)=132-105\\20x+12y-2x-12y=27\\18x=27[/tex]

Dividing both sides by 18

[tex]\frac{18x}{18}=\frac{27}{18}\\x=1.5[/tex]

Putting x=1.5 in Eqn 1

[tex]2(1.5)+12y=105\\3+12y=105\\12y=105-3\\12y=102\\[/tex]

Dividing both sides by 12

[tex]\frac{12y}{12}=\frac{102}{12}\\y=8.5[/tex]

The cost to rent one chair is $1.5 and one table is $8.5

Keywords: linear equations, subtraction

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Final answer:

Using a system of linear equations, we determine that the cost to rent each chair is $3 and the cost to rent each table is $6 from the party rental company.

Explanation:

To determine the cost to rent each chair and each table from the party rental company, we need to solve a system of linear equations based on the information provided:

The total cost to rent 2 chairs and 12 tables is $105.

The total cost to rent 5 chairs and 3 tables is $33.

Let's let c represent the cost of renting one chair and t represent the cost of renting one table. We can write the following system of equations:

2c + 12t = $105

5c + 3t = $33

By solving this system, we find that the cost to rent each chair (c) is $3 and the cost to rent each table (t) is $6.

Answer:

2.48

Step-by-step explanation:

For each gallon she got she paid $2.48. I know this by doing 34.72 divided by 14 which got me the answer of $2.48.

Answer:

14 quarters and 28 nickels

Step-by-step explanation:

System of Equations where x = number of quarters and y = number of nickels

(1) equation with value of each coin

    0.25(x)+0.05(y) = 4.90

(2) total number of coins

    x + y = 42

Solve system of equations using either substitution or elimination

(elimination multiplying equation 2 by -0.5)

.25(x) + 0.05(y) = 4.90

-0.05(x) - 0.05(y) = 42 * (-0.05)

(3) Resulting equation

.20(x) = 2.8

x = 14

plug x into equation 2

14 + y = 42

y = 28

There are 14 quarters and 28 nickels in Mary's collection.

Answer:

The total cost of the bond is none of the given choices.

Step-by-step explanation:

The selling price of a $1000 bond  =   $99.875

The brokerage fee = 5.5 %

Now, 5.5%  of $99.875 =  [tex]\frac{5.5}{100}  \times 99.875 = 5.493[/tex]

So, the brokerage fee = $5.493

Now, to find out the total cost of the bond:

Total Cost  = The selling Price + Brokerage Price

                  = $99.875 + $5.493

                  =  $105.368

or, the total price of the $1000 bond is $ 105.368.

Hence,  the total cost of the bond is none of the given choices.

Answer:

24

Step-by-step explanation:

-3x^3*y^2=-3(-2)^3=(-3)(-8)*(-1)^2=24*1=24