If you buy a home and make a relatively small down payment, what happens to the monthly payments and total payment for you loan?

The equation of the line in standard form is 3x - 5y = 26

Step-by-step explanation:

Let us revise the forms of the linear equation

∵ The line passes through point (2 , -4)

∵ The slope of the line is [tex]\frac{3}{5}[/tex]

- Let us using the point-slope form and then change it to the

  standard form

∵ [tex]x_{1}[/tex] = 2 and [tex]y_{1}[/tex] = -4

∵ m = [tex]\frac{3}{5}[/tex]

- Substitute these values in the form of the equation below

∵ [tex]y-y_{1}=m(x-x_{1})[/tex]

∴ [tex]y-(-4)=\frac{3}{5}(x - 2)[/tex]

∴ [tex]y+4=\frac{3}{5}(x - 2)[/tex]

Let us change it to standard form

- Multiply each side my 5 to cancel the denominator in the

   right hand side

∴ 5(y) + 5(4) = 3(x - 2)

- Simplify the two sides

∴ 5y + 20 = 3x - 6

- Add 6 to both sides

∴ 5y + 26 = 3x

- Subtract 5y from both sides

∴ 26 = 3x - 5y

- Switch the two sides

∴ 3x - 5y = 26

The equation of the line in standard form is 3x - 5y = 26

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Answer:

101/3 or 33 2/3

Step-by-step explanation:

7 2/15=107/15

9 13/15=138/15

107/15+52/3+138/15

107/15+138/15+52/3

245/15+52/3

245/15+260/15

505/15

simplify,

101/3

Answer:

y-4=4(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

m=4

y-4=4(x-(-1))

y-4=4(x+1)

Answer: equation = y=4x+8

Step-by-step explanation:

y=mx+b

4=4(-1)+b

b=8

equation = y=4x+8

Answer:

5

Step-by-step explanation:

take 0.5 divided by 5 and it gives you your next number on the chart:)

Answer:  5

Step-by-step explanation:

The growth factor of the exponential function is the ratio of the two consecutive terms (y-values).

i.e. Growth factor = [tex]b=\dfrac{y(x_2)}{y(x_1)}[/tex]

As per given , we have table

x         y

-2     0.004

-1       0.02

0       0.1

1        0.5

Then, for [tex]x_1=-2[/tex] and [tex]x_2=-1[/tex] the growth factor of the exponential function represented by the table would be :

[tex]b=\dfrac{y(-1)}{y(-2)}=\dfrac{0.02}{0.004} =5[/tex]

Hence, the growth factor of the exponential function represented by the table is 5 .

Answer:

[tex]a_{n}[/tex] = 2n - 3

Step-by-step explanation:

Note the difference in consecutive terms is constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2

This indicates that the terms are an arithmetic sequence with

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 2, thus

[tex]a_{n}[/tex] = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

Answer:

x=-5, y=-5. (-5, -5).

Step-by-step explanation:

-x-5y=30

10x+5y=-75

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

9x=-45

x=-45/9

x=-5

-(-5)-5y=30

5-5y=30

5y=5-30

5y=-25

y=-25/5

y=-5

Answer:

k=5

Step-by-step explanation:

7

k

−

12

=

13

+

2

k

Move all terms containing

k

to the left side of the equation.

Answer:

1260 words

Step-by-step explanation:

if you divide 840 by 2.4 you would get 350 then multiply by 3.6

With the same rate the number of words typed in 3.6 hour is 1260.

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.

Given that, a typewriter types 840 words in 2.4 hours.

Now, number of words typed in 1 hour is

840/2.4

= 350

Now, the number of words typed in 3.6 hour is

350×3.6

= 1260

Therefore, with the same rate the number of words typed in 3.6 hour is 1260.

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Answer:

[tex]x=0,x=-4,x=-3[/tex]

Step-by-step explanation:

The given equation is

[tex]x^3 + 7x^2 + 12x = 0[/tex]

Factoring by x:

[tex](x^2 + 7x + 12)x = 0[/tex]

One of the root is x=0. Let's solve the parentheses.

Expanding the trinomial

[tex]x^2 + 4x+3x + 12=0[/tex]

Factoring

[tex]x(x + 4)+3(x + 4)=0[/tex]

Factoring

[tex](x + 4)(x+3)=0[/tex]

This will give us the two remaining roots

[tex]x=-4,x=-3[/tex]

Answer:

The average rate of change = -10

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Step-by-step explanation:

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function [tex]f(x) =-x^2 + 20x + 100[/tex] models the crops in pounds per acre over x years.

The average rate of change can be calculated using formula

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

In your case,

[tex]a=10\\ \\b=20,[/tex]

then

[tex]f(a)=-10^2+20\cdot 10+100=-100+200+100=200\\ \\f(b)=-20^2+20\cdot 20+100=-400+400+100=100[/tex]

and the average rate of change is

[tex]\dfrac{100-200}{20-10}=\dfrac{-100}{10}=-10[/tex]

This means the crop yield decreased by 10 pounds per acre (negative rate of change) from year 10 to year 20.

Answer:

'The crop yield decreased by 10 pounds per acre from year 10 to year 20.'

Step-by-step explanation:

i got it right on the test =)

Answer: 53.2

Step-by-step explanation:

Answer:

0.01879

Step-by-step explanation:

Answer:

(x − 6i) (x + 6i)

Step-by-step explanation:

Using real numbers, x² + 36 is already simplified.

Using imaginary numbers:

x² + 36

x² − 36i²

(x − 6i) (x + 6i)

Answer:

b=22

Step-by-step explanation:

11/4 divided by 1/4 equals 11. 11*2 =22

Answer:

The answer is actually 10

Step-by-step explanation:

b = 10

Answer:

The sum of the age of pupils is 81

Step-by-step explanation:

Let sum of age of 18pupils = x

Average ages = 4.5

Average = total/no. of pupil

4.5 = x/18

x = 81

Answer:

The sum of the age of pupils is 81

The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]

Step-by-step explanation:

Given

Length of box = l = ab

Width of box = w = a+5b

Height of box = h = 2b^2

The volume of a box is given by:

[tex]V = Length*Width*Height\\V = l*w*h[/tex]

Putting the values

[tex]V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4[/tex]

Hence,

The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]

Keywords: Volume, Polynomials

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Answer:

(0, 5 )

Step-by-step explanation:

The y- intercept is the value of the y- coordinate where the function crosses the y- axis. At this point the x- coordinate is zero.

From the table when x = 0, y = 5

Thus (0, 5) is the y- intercept

Answer:

[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 6 and r = 30 ÷ 6 = 5, thus

[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]

Answer:

Step-by-step explanation:

$3.55 ÷ 5 = .71 each peach

To find out how much Tomas paid for each fruit, we set up the equation m = $3.55 / 5, which when solved gives m = $0.71. This means that Tomas paid $0.71 for each peach.

To find out how much Tomas paid for each peach, you can set up an equation. Because Tomas buys 5 peaches for $3.55 in total, you can express this as a simple division. To solve the equation, divide $3.55 (total cost) by 5 (total number of peaches).

So, the equation would be m = $3.55 / 5.

Solving this equation gives: m = $0.71. Therefore, Tomas paid $0.71 for each peach.

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Answer:

One pair of sunglasses is $70

Step-by-step explanation:

Answer:

6 papayas and 11 pineapples

Step-by-step explanation:

So, we need to find an answer of how many papayas and pineapples she bought, and we only spent $48.

So,  papayas are $2.50 each, and Pineapples are $3.00 each and we only bought 17 fruits total.

lets try 8 papayas, and 9 Pineapples.

$2.50 x 8 = $20.00 total on Papayas

$3.00 x 9 = $27.00 total on Pineapples.

That would only be $47 spent total.

Lets try 10 papayas and 7 pineapples.

$2.50 x 10 = $25.00

$3.00 x 7 = $21.00

That would only be a total of $26 spent.

Lets try 6 papayas and 11 pineapples.

$2.50 x 6 = $15.00

$3.00 x 11 = $33.00

This would be a total of $48 spent.

The solution is x = 6

Step-by-step explanation:

Let us revise some rules of the exponents

∵ [tex]9^{(x+15)}=3^{7x}[/tex]

∵ 9 = 3 × 3

∴ 9 = 3²

- Substitute 9 by 3² in the equation above

∴ [tex](3^{2})^{(x+15)}=3^{7x}[/tex]

- Use the second rule above for the left hand side

∵ [tex](3^{2})^{(x+15)}=3^{2(x+15)}[/tex]

∴ [tex](3^{2})^{(x+15)}=3^{2x+30}[/tex]

∴ [tex]3^{2x+30}=3^{7x}[/tex]

- By using the first rule above

∴ 2x + 30 = 7x

- Subtract 2x from both sides

∴ 30 = 5x

- Divide both sides by 5

∴ 6 = x

The solution is x = 6

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Answer:

yes.

Step-by-step explanation:

because I did the work and 10 times 3 equals 30 and 4 plus 6 times 3 equals 30.

Answer:

Yes because L.H.S = R.H.S

Step-by-step explanation:

4 + 6 = 10

(4 + 6) X 3

=> 10 X 3

=> 30

The right answer is Option D.

Step-by-step explanation:

Given,

Food and Drinks = $200

Game tokens = $100

Other = $60

Total amount = 200+100+60 = 360

Deposit = 10%

Deposit amount = 10% of total amount

[tex]Deposit\ amount=\frac{10}{100}*360\\Deposit\ amount=\frac{3600}{100}\\Deposit\ amount= \$36[/tex]

Amount left to be paid = Total amount - deposit amount

Amount left to be paid = [tex]360-36=\$324[/tex]

$324 is still owed for Molly's party.

The right answer is Option D.

Keywords: Percentage, subtraction

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Step-by-step explanation:

You have the equation of a line in the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

Convert the given equation to the slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept (0, b)

[tex]y+1=\dfrac{1}{3}(x-3)[/tex]         use the distributive property

[tex]y+1=\dfrac{1}{3}x-1[/tex]          subtract 1 from both sides

[tex]y=\dfrac{1}{3}x-2[/tex]

We only need two points to draw the line.

Choose two different x values. Put them in the line equation and calculate the y values:

for x = 0:

[tex]y=\dfrac{1}{3}(0)-2=0-2=-2\to(0,\ -2)[/tex]

for x = 3:

[tex]y=\dfrac{1}{3}(3)-2=1-2=-1\to(3,\ -1)[/tex]

Answer:

The age of the pottery bowl to the nearest year is 15606 years.

Step-by-step explanation:

Let the initial amount of C-14 in the bowl i.e. [tex]N_{0} = 100[/tex] and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.

Therefore, from the given equation we can write  

[tex]21 = 100 e^{- 0.0001t}[/tex] {Since, k is give to be 0.0001}

⇒ [tex]0.21 = e^{- 0.0001t}[/tex]

Now, taking ln on both sides we get

ln 0.21 = - 0.0001t (ln e) {Since, [tex]\ln a^{b} = b \ln a[/tex]}

⇒ - 1.560647 = - 0.0001t  {We have ln e = 1}

⇒ t = 15606.47 years ≈ 15606 years  

Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)

Answer:

4.8, 135, 0.2822, 0.024

Step-by-step explanation:

4*1.2=4.8

7.5*18=135

0.34*0.83=0.2822

0.04*0.6=0.024

It would take 13 buses to get everyone to the zoo

It would take 26 vans to get everyone to the zoo

It would be cheaper to rent buses

Step-by-step explanation:

The given is:

We need to find how many buses it would take to get everyone to the zoo, how many vans it would take to get everyone to the zoo, and would it be cheaper to rent

∵ The number of students is 388

∵ Each bus can hold 30 students

- Divide the number of students by 30 to find the number of buses

∴ The number of buses = 388 ÷ 30 = 12.92

- They must to rent 13 bus to hold all the students

∴ The number of buses is 13

It would take 13 buses to get everyone to the zoo

∵ The number of students is 388

∵ Each van can hold 15 students

- Divide the number of students by 15 to find the number of vans

∴ The number of vans = 388 ÷ 15 = 25.87

- They must to rent 26 vans to hold all the students

∴ The number of vans is 26

It would take 26 vans to get everyone to the zoo

Let us find the cost of rent of the buses and vans to find which of them is cheaper

∵ The cost of rent of each bus = $895

∵ The number of buses = 13

∴ The cost of rent the buses = 13 × 895 = $11635

∵ The cost of rent of each van = $450

∵ The number of vans = 26

∴ The cost of rent the buses = 26 × 450 = $11700

∵ $11635 < $11700

∴ The cost of rent the buses < the cost of rent the vans

∴ The buses is cheaper than the vans

It would be cheaper to rent buses

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Answer:

6-pack for 3.12

Step-by-step explanation:

Find unit price

2.24/4=0.56

3.00/3=1

4.24/8=0.53

3.12/6=0.52

Answer:

B.9

Step-by-step explanation:

9*1=9