MATHEMATICS COLLEGE

You go to buy a new sofa and find that it is on sale.The original price is $459. The markdown is 25%.
What will you have to pay for your sofa?

Answers

Answer 1

Answer:

344.25

Step-by-step explanation:

Answer 2

Answer:

The Answer is: $344.25

7-3x4 subtract 3 from 7 means you need to take 3 out of 7 (7-3) then you need to multiply that by 4!

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Lydia has money in two savings accounts. One rate is 7% and the other is 13%. If she has $300 more in the 13% account and the total interest is $252, how much is invested in each savings account?

Answers

Answer:

7%: $1065
13%: $1365

Step-by-step explanation:

If x represents the amount invested at 7%, then the amount invested at 13% is x+300. Lydia's total interest is ...

0.07x +0.13(x +300) = 252

0.20x = 213 . . . . . subtract 39

x = 213/0.20 = 1065

Lydia has $1065 invested at 7% and $1365 invested at 13%.

Final answer:

Using the given conditions, we set up and solve an equation where x is the amount invested at a 7% rate and x + $300 is the amount at a 13% rate. After solving, we find that Lydia has $1065 in the 7% account and $1365 in the 13% account.

Explanation:

Let's assume Lydia's investment at 7% to be x and her investment at 13% to be x + $300. Since the total interest is $252, we can create an equation to solve for the values of x.

The equation will look like this:

0.07x + 0.13(x + 300) = 252

Let's solve the equation:

0.07x + 0.13x + 39 = 252

Combine like terms to get 0.2x + 39 = 252

Subtract 39 from both sides to get 0.2x = 213

Divide by 0.2 to solve for x, which gives x = 1065.

So, Lydia has $1065 in the 7% account and $1065 + $300 = $1365 in the 13% account.

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What is $45.79 multiplied by .50 equal

Answers

Answer:

$45.79 multiplied by .50 equals 22.895

Answer:

686.85

Step-by-step explanation:

What is the slope of a line segment with endpoints at (-1, 1) and (1, 5)

Answers

The slope(m) of the line segment whose endpoints are (-1, 1) and (1, 5) is: 2.

Recall:

Slope (m) = rate of change of y / rate of change of x
Slope (m) = $\mathbf{(y_2 - y_1)/(x_2 - x_1)}$

Given the endpoints of a line as:

(-1, 1) and (1, 5)

Let,

$(-1, 1) = (x_1, y_1)\n\n(1, 5) = (x_2, y_2)$

Plug in the values

Slope (m) = $(5-1)/(1-(-1))$

Slope (m) = $(4)/(2)$

Slope (m) = 2

In summary, the slope(m) of the line segment whose endpoints are (-1, 1) and (1, 5) is: 2.

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Answer:

Slope = 2

Step-by-step explanation:

(x,y) ->(-1,1)
(x,y) -> (1,5)

5 - 1 = 4

1 - (-1) = 2

4/2 = 2

a home has a triangular backyard. The second angle of the triangle is 6 more than the first angle. The third angle is 14 more than three times the first angle. Find the angles of the triangular yard

Answers

Answer: The first angle is 32 degrees

The second angle is 38 degrees

The third angle is 110 degrees.

Step-by-step explanation:

Let x represent the size of the first angle.

Let y represent the size of the second angle.

Let z represent the size of the third angle.

The second angle of the triangle is 6 more than the first angle. This means that

y = x + 6

The third angle is 14 more than three times the first angle. This means that.

z = 3x + 14

The sum of the angles in a triangle is 180 degrees. It means that

x + y + z = 180 - - - - - - - - - - - -2

Substituting y = x + 6 and z = 3x + 14 into equation 2, it becomes

x + x + 6 + 3x + 14 = 180

x + x + 3x = 180 - 14 - 6

5x = 160

x = 160/5 = 32

y = x + 6

y = 32 + 6 = 38

z = 3x + 14

z = 3×32 + 14 = 96 + 14

z = 110

Use induction to prove the following formula is true for all integers n where n greaterthanorequalto 1. 1 + 4 + 9 + .. + n^2 = n(n + 1)(2n + 1)/6

Answers

Answer with Step-by-step explanation:

Since we have given that

1+4+9+........................+n² = $(n(n+1)(2n+1))/(6)$

We will show it using induction on n:

Let n = 1

L.H.S. :1 = R.H.S. : $(1* 2* 3)/(6)=(6)/(6)=1$

So, P(n) is true for n = 1

Now, we suppose that P(n) is true for n = k.

$1+4+9+...................+k^2=(k(k+1)(2k+1))/(6)$

Now, we will show that P(n) is true for n = k+1.

So, it L.H.S. becomes,

$1+4+9+......................+(k+1)^2$

and R.H.S. becomes,

$((k+1)(k+2)(2k+3))/(6)$

Consider, L.H.S.,

$1+4+9+..+k^2+(k+1)^2\n\n=(k(k+1)(2k+1))/(6)+(k+1)^2\n\n=k+1[(k(2k+1))/(6)+(k+1)]\n\n=(k+1)[(2k^2+k+6k+6)/(6)]\n\n=(k+1)(2k^2+7k+6)/(6)]\n\n=(k+1)(2k^2+4k+3k+6)/(6)]\n\n=(k+1)[(2k(k+2)+3(k+2))/(6)]\n\n=((k+1)(2k+3)(k+2))/(6)$