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3 years ago

If Michael and Imani add an 18% tip to 27.32, what does their lunch cost in total?

1 answer:

3 0

.18 * 27.32 = 4.9176
18% of 27.32 = 4.91
4.91 + 27.32 = 32.23

If Michael and Imani add an 18% tip to 27.32, their lunch cost will be $32.23 in total.

Hope this helps you! (:
-Hamilton1757

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What is the slop of a line perpendicular to the line whose equation is 4x+6y=108. Reduce your answer

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I honestly don’t know so don’t pay attention to me pls I’m so sorry

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3 years ago

Solve the system by using a matrix equation

Sergeu [11.5K]

Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as $\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right]$

A= $\left[\begin{array}{cc}6&-9\\3&4\end{array}\right]$

X= $\left[\begin{array}{c}x\\y\end{array}\right]$

B= $\left[\begin{array}{c}3\\7\end{array}\right]$

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

= (-24)-(-27)

= (-24) + 27 = 3

so, |A| = 3

Adj A= $\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]$

A⁻¹ = $\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]$ /3

A⁻¹ = $\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right]$

X= A⁻¹ B

X= $\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right]$

X= $\left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right]$

X= $\left[\begin{array}{c}-4+21\\-3+14\end{array}\right]$

X= $\left[\begin{array}{c}17\\11\end{array}\right]$

x= 17, y= 11

solution set= (17,11).

6 0

3 years ago

Read 2 more answers

Find the slope of a line given the following two points: (4, 3) and (5, 2). 1 -1 2 -2

galben [10]

Given two points; (x₁,y₁) and (x₂,y₂) the slope is:

m=(y₁-y₂) / (x₁-x₂) or m=(y₂-y₁) / (x₂-x₁)

In this case:
(4,3)
(5,2)

m=(5-4)/(2-3)=1/-1=-1

Answer: the slope is -1

7 0

3 years ago

Use triple scalar products to find volume of the parallelepiped having adjacent edges

Mila [183]

Answer my question and I'll answer yours!!!

4 0

3 years ago

Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and

Vikentia [17]

Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

We lost out the important values given in the question as follows:

Amount of Mortgage - $675,250

Tenure - 30 Years

The Rate of interest without points = 7.25%

The number of points = 3 points

The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

Therefore, 3 discount points = 3% of mortgage value

The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

M = P[r(1+r)^n/((1+r)^n)-1)]

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

6 0

3 years ago