A collection of dimes and quarters is worth $10.45. There are 70 coins in all. Find how many of each there are

Answer:

2.5 x 13.7 = 34.25

4.9 + 1.6 = 6.5

Step-by-step explanation:

Here we are multiplying 2 decimals we can just write it as

[tex]25 * 10^{-1} * 137 * 10^{-1}[/tex]

= [tex]25*137*10^{-2}[/tex]

= [tex]3425 *10^{-2}[/tex]

= 34.25

Here we are just performing simple addition

4.9 + 1.6

= [tex]49 *10^{-1} +16*10^{-1}[/tex]

= [tex](49+16)*10^{-1}[/tex]

=[tex]65 * 10^{-1}[/tex]

= 6.5

Paying an extra $100 each month on a $60,000 loan with an 8% APR over 25 years will reduce the loan term and total interest paid. To calculate the effect, compute the total cost of the loan with and without the extra payments and subtract these two sums.

The subject at hand pertains to understanding the impact of additional payments on a loan, which falls under the domain of financial mathematics. Let's dissect the impact of paying an extra $100 per month on a $60,000 loan with an 8% annual interest rate over 25 years.

Firstly, we need to calculate the monthly payment for a 25-year loan of $60,000 at 8% interest. This can be calculated by using a loan calculator or the loan payment formula. Then, calculate the total cost of the loan by multiplying this monthly payment by the number of months in the loan term (25 years x 12 months).

You then do a similar calculation, but this time add an extra $100 to the monthly payment. The extra repayment will reduce the loan term and decrease the total interest paid. To see the effect, compare the total cost of the loan with and without the extra $100.

Therefore, the difference between these two sums will give you the saved amount due to the additional $100 monthly payment. This saving is the effect of making additional payments on the loan.

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Making additional monthly payments can shorten the loan term and save money on interest payments.

To calculate the effect of making additional monthly payments on the cost of the loan, we can compare the total interest paid and the duration of the loan with and without the additional payments. Without any additional payments, the monthly payment for a $60,000 loan with an 8% APR and a 25-year term would be $459.18. With an additional $100 each month, the monthly payment would increase to $559.18.

By making the additional $100 payments, the loan would be paid off faster, reducing the term from 25 years to approximately 17 years and saving the borrower 8 years of monthly payments. Additionally, the total interest paid over the course of the loan would also be significantly reduced compared to just paying the required monthly payments.

In summary, making extra monthly payments of $100 can shorten the loan term and save the borrower money on interest payments.

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Answer:

Option 1. Lynn, only

Step-by-step explanation:

The correct question is

Listen Lynn, Jude, and Anne were given the function f(x)=-2x^2+32, and they were asked to find f(3). Lynn's answer was 14, Jude's answer was 4, and Anne's answer was (+/-)4. Who is correct?

1. Lynn, only

2. Jude, only

3. Anne, only

4. Both Lynn and Jude

we have

[tex]f(x)=-2x^{2} +32[/tex]

This is a vertical parabola open downward (leading coefficient is negative)

The vertex is a maximum

we know that

f(3) means, the value of f(x) when the value of x is equal to 3

so

For x=3

substitute in the quadratic equation and solve for f(x)

[tex]f(3)=-2(3^{2}) +32[/tex]

[tex]f(3)=-18 +32[/tex]

[tex]f(3)=14[/tex]

therefore

Lynn's answer is correct

To determine the value of the function f(x) = 2x + 32 at x=3, we substitute x with 3, and solve to obtain f(3) = 38. Therefore, all students' answers were incorrect.

In the function f(x) = 2x + 32, to find the value of f(3), you first need to substitute 'x' with 3. The equation it becomes f(3) = 2 * 3 + 32

By solving the equation, you obtain is f(3) = 6 + 32 which equals to f(3) = 38.

Thus, all the students, Lynn, Jude, and Anne, unfortunately provided incorrect answers.

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Answer:

$215.94

Step-by-step explanation:

You do 20% × $179.95 to get $35.99

Since the 20% is being added to your bill, you add it to your base price

$179.95 + $35.99 = $215.94

Answer: 7 pizzas

Step-by-step explanation:

Answer:

60/8 = 7.5 = 7 pizzas (round down to the nearest integer)

Step-by-step explanation:

You can only buy a whole pizza, not slices of it.

Answer:

Linear

Step-by-step explanation:

Because it has no exponents

If it has no exponents than its always linear

Answer:

Linear

Step-by-step explanation:

It is in Slope-Intercept Form [y = mx + b], and this formula is ALWAYS a linear function [NO EXPONENTS].

I am joyous to assist you anytime.

Answer:

The Area of rectangle A is  576 feet²  .

Step-by-step explanation:

Given as :

The width of rectangle A = 16 feet

The Length of rectangle A = 8 feet + The length of rectangle B

The width of rectangle B = 14 feet

Let The length of rectangle B = L feet

So, The Length of rectangle A = 8 feet + L feet

The perimeter of rectangle A + The perimeter of rectangle B = 156 feet

So, 2 × ( Length A + width A ) +  2 × ( Length B + width B ) = 156 feet

Or,  2 × ( 8 + L + 16 ) +  2 × ( L + 14 ) = 156 feet

Or,  2 ×( 24 + L ) +  2 × ( L + 14 ) = 156 feet

Or, 48 + 2 L + 2 L + 28 = 156

Or, 76 L + 4 L = 156

So, 4 L = 156 - 76

Or, 4 L = 80

∴  L = [tex]\frac{80}{4}[/tex] = 20 feet

So , The Length of rectangle A = 8 feet + 28 feet = 36 feet

And The width of rectangle A = 16 feet

So, Area of rectangle A = Length of rectangle A × width of rectangle A

I.e  Area of rectangle A = 36 × 16 = 576 feet²

Hence The Area of rectangle A is  576 feet²  . Answer

Answer:

t = 1/2

Step-by-step explanation:

4(t+1/4)=3

First, distribute:

4(t)+4(1/4)=3

4t+1=3

Then isolate the variable:

4t+1-1=3-1

4t=2

4t/4=2/4

t=2/4

t=1/2

The equation is solved first by distributing the 4, then by subtracting 1 from both sides to isolate the variable term, and finally by dividing both sides by 4 to solve for 't', which gives the solution t = 0.5.

To solve the equation 4(t+1/4) = 3, we start by distributing the 4 inside the parentheses, so we get 4t + 1 = 3.

Then, we subtract 1 from both sides of the equation to isolate the variable term, and this gives us 4t = 2.

Finally, to solve for 't', we divide both sides of the equation by 4, and we find that t = 0.5.

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Answer:

[tex]\large\boxed{W=\dfrac{A}{L}}[/tex]

Step-by-step explanation:

[tex]A=LW\qquad\text{divide both sides by}\ L\neq0\\\\\dfrac{A}{L}=\dfrac{LW}{L}\\\\\dfrac{A}{L}=W[/tex]

Answer:− 1 x (small)2  y + 39 x(small)  2 + 30 x

Step-by-step explanation:

Answer:

the quotient is 4000 and the square is a perfect square

Step-by-step explanation:

120/0.03=4000

40 time 40 is 1600 so its perfectly square.

hope this helps

Answer:s

Step-by-step explanation:

Answer:

0.5 891 7,800

Step-by-step explanation:

is because least always go first

To order from least to greatest, convert all measurements to grams: 7,800 mg becomes 7.8 g, and 0.5 kg becomes 500 g. The order is 7.8 g, 500 g, and 891 g.

To order the weights 891 g, 7,800 mg, and 0.5 kg from least to greatest, we first convert them all to the same unit. Given that there are 1,000 mg in a gram (g) and 1,000 g in a kilogram (kg), we can convert as follows:

Now that we have all the weights in grams, we can easily compare them:

Ordering these from least to greatest, we get: 7.8 g < 500 g < 891 g.

Answer:

The time after which the rocket hit the ground is 5 seconds

Step-by-step explanation:

Given as :

The distance of the cover by rocket at the height h = - 16 t² + 160 t

Let the time after which rocket hit the ground = T seconds

Now, When the rocket hits the ground, then at that time, the velocity of the rocket becomes zero.

I.e velocity = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Or, v = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Now, v = [tex]\frac{\partial h}{\partial t}[/tex]

Or, v = [tex]\frac{\partial (-16t^{2}+160t)}{\partial t}[/tex]

or, v = - 32 t + 160

Now, ∵ velocity of rocket after reaching the ground becomes zero

So, v = - 32 t + 160 = 0

Or, 32 t = 160

Or, t = [tex]\frac{160}{32}[/tex]

∴ t = 5 sec

So, The time after which the rocket hit the ground = 5 sec

Hence The time after which the rocket hit the ground is 5 seconds answer

To find when the rocket will hit the ground using the quadratic equation h = -16t² + 160t, solve for t when h=0; the rocket will hit the ground after 10 seconds.

To determine when the rocket will hit the ground given the equation h = -16t² + 160t, we need to find the value of t at which the height h is zero. The equation represents a quadratic equation, where t is the time in seconds after the rocket was fired, and h is the height of the rocket at any time t.

To solve for the time when the rocket hits the ground, we set h to zero and solve for t:

We discard the t = 0 since it represents the initial time at launch. Thus, the rocket will hit the ground after 10 seconds.

During this entire period, while the rocket is ascending and descending, it is important to consider the horizontal motion if analyzing its trajectory in more detail, but for this problem, we are only concerned with the vertical motion.

Answer: 1/10

Step-by-step explanation:

There is  1 yellow marble out of the 10 marbles

Answer:

Step-by-step explanation:

1/9

Answer:

x ≤ 435

Step-by-step explanation:

Given is the following condition.

The sum of a number and 15 is less than and equal to 450.

So, if the number is x, then we have  

x + 15 ≤ 450

⇒ x + 15 - 15 ≤ 450 - 15

⇒ x ≤ 435

Therefore, the solutions of the number are either 435 or less than 435 up to negative infinity. ( Answer )

a) The total amount the Bells will pay for their house is $187,488. b) The interest paid, including the 3 points, is $97,488. c) The exact amount applied to the principal in the first payment is unknown without additional information.

a) To determine the total amount the Bells will pay for their house, we need to calculate the total amount paid over 20 years. The monthly mortgage payment is $781.20, so the annual payment would be $781.20 x 12 = $9374.40. Therefore, over 20 years, the Bells will pay $9374.40 x 20 = $187,488.

b) The interest paid over the 20-year mortgage period can be calculated by subtracting the total mortgage amount from the total amount paid. The total mortgage amount is $90,000, so the interest paid is $187,488 - $90,000 = $97,488, including the 3 points.

c) The first payment on the mortgage is typically applied mostly to the interest. However, to determine the exact amount applied to the principal, we need more information about the breakdown of the monthly mortgage payment between interest and principal.

Answer: -1, 0, and 1

Step-by-step explanation: -1 is an integer and all integers are rational numbers so -1 is rational.

0 is also an integer and all integers are rational numbers. Therefore, 0 is considered a rational number.

1 is a natural number and all natural numbers are rational numbers. Therefore, 1 would be a rational number.

Answer:

I am going to assume you mean the relationship between x and y.

If the y-intercept is 0, that means the point is on the origin.

So x and y are equal to each other. they are both zero

Answer:

For [tex]\left | x \right |[/tex] we will have positive values only.

[tex]\left | -2.7 |\right =2.7[/tex]

[tex]\left | -9 |\right =9[/tex]

Rest are positive so will give positive values out of the modulus function.

Step-by-step explanation:

The absolute value of any number is its positive value only.

As for example [tex](-2.7)[/tex] and [tex](2.7)[/tex] both are having equal distance from [tex]0[/tex] in a number line, one on the left other on the right side of the number line but are equidistant from [tex]0[/tex].

So absolute value of a number is its distance on number line from reference point [tex]0[/tex].

One by one we will work with all of our question.

[tex]\left | 10 |\right =10[/tex]

[tex]\left | 0.3 |\right =0.3[/tex]

[tex]\left | 0 |\right =0[/tex]

[tex]\left | -2.7 |\right =2.7[/tex]

[tex]\left | -9 |\right =9[/tex]

So we have to take the positive number out of the modulus function that is also called absolute value.

Answer:

17/4

Step-by-step explanation:

2 5/6=17/6

4/6=2/3

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

(17/6)/(2/3)=(17/6)(3/2)=51/12=17/4

Number line is the line in which the numbers are marked at the intervals to the show the inequality. The value of the x, is 2 which is shown on the number line by attached image below.

The equations given in the problem are,

[tex] 5 x + 4 = 14[/tex]

Number line is the line in which the numbers are marked at the intervals to the show the inequality.

Here in the problem the given equation is,

[tex] 5 x + 4 = 14[/tex]

Solve it for the x,

[tex]\begin{aligned}\\ 5 x &= 14-4\\ 5x&=10\\ x&=\dfrac{10}{5} \\ x&=2\\ \end[/tex]

The value of the x is 2. It can be shown on the number line graph by making a circle on the number 2.

As the inequality is shown with the equal sign in the given equation. Therefore the direction would be nigher side. The graph for the given equation number line shown in the attached image.

Hence the value of the x, is 2 which is shown on the number line by attached image below.

Learn more about the number line here;

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Final answer:

To solve the equation 5x + 4 = 14, subtract 4 from both sides, then divide by 5. This gives x = 2, which can be checked by substitution back into the equation and verifying it holds true.

Explanation:

To solve the equation 5x + 4 = 14, we need to isolate the variable x. First, we subtract 4 from both sides of the equation to get 5x = 10. Next, we divide both sides of the equation by 5 to find the value of x:

5x ÷ 5 = 10 ÷ 5

x = 2

This means that the value of x that satisfies the equation 5x + 4 = 14 is 2. We can check our answer by substituting 2 back into the original equation to see if it makes a true statement:

5(2) + 4 = 10 + 4 = 14

Since the left side of the equation equals the right side, x = 2 is indeed the solution.

Answer:

8

Step-by-step explanation:

AD is half of AB

1/2 * 16 = 8

Answer:

8

Step-by-step explanation:

CD is an altitude. It is perpendicular to AB, and it splits AB in half. If AB=16, and CD splits AB in half, to find AD you would do this:

1/2AB

1/2·16=8

8 is your answer.

Yu can also see that AD and DB are congruent, so their values must be the same.

~Stay golden~:)

Answer: The y-intercept represents what is the value of y when x=0.

425 g for the 15 ounce box of cereal?

Answer:

7 x + y = 9

Step-by-step explanation:

Answer:

$13.20

Step-by-step explanation:

so add the prices up 1.25+0.40 should be

$1.65 now multiply it by the 8 postcards he will send

so 1.65•8= $13.20

Answer:

f(3) = g(3)

Step-by-step explanation:

we know that

When solve a system of linear equations by graphing, the solution of the system is the intersection point both lines

The intersection point is common point for bot lines

In this problem

we have the system of equations

f(x)

g(x)

The intersection point is (3,6)

That means that the solution for the system is the point (3,6)

so

For x=3

The value of f(3)=6 and the value of g(3)=3

therefore

f(3)=g(3)

Verify the statements

Find the equation of the blue line f(x)

(0,-3) and (1,0)

the slope is

[tex]m=(0+3)/(1-0)=3[/tex]

The equation  in slope intercept form is equal to

[tex]f(x)=3x-3[/tex]

Find the equation of the red line g(x)

(-3,0) and (0,3)

the slope is

[tex]m=(3-0)/(0+3)=1[/tex]

The equation  in slope intercept form is equal to

[tex]g(x)=x+3[/tex]

case 1) f(6) = g(3)

The statement is false

Because

For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]

For x=3 ----> [tex]g(3)=3+3=6[/tex]

therefore

[tex]f(6) \neq g(3)[/tex]

case 2) f(3) = g(3)

The statement is true

Because

For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]

For x=3 ----> [tex]g(3)=3+3=6[/tex]

therefore

[tex]f(3)=g(3)[/tex]

case 3) f(3) = g(6)

The statement is false

Because

For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]

For x=6 ----> [tex]g(6)=6+3=9[/tex]

therefore

[tex]f(3) \neq g(6)[/tex]

case 4) f(6) = g(6)

The statement is false

Because

For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]

For x=6 ----> [tex]g(6)=6+3=9[/tex]

therefore

[tex]f(6) \neq g(6)[/tex]

Answer:

f(3)=g(3)

Step-by-step explanation:

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