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elixir [45]
3 years ago
12

The rectangle shown below will undergo a single reflection through a line L. If the result of the reflection is a rectangle in t

he same position, which of the following could be a description of line L? Choose all that apply.
the y-axis

y = 4

the line through A and C

the line through B and D

Mathematics
2 answers:
labwork [276]3 years ago
4 0

Answer with explanation:

When the rectangle ABCD, is reflected through a single line, we get the Image of rectangle in same Position, having location of vertices interchanged.

The Word Reflection is mostly used in Physics, which means, that if you look something ,in a transparent objects,like water ,Mirror,the Preimage and Image are at same Distance,from the object through which you are Reflecting Something.

Rectangle, ABCD, is Symmetrical, when you draw four lines through it,that is through two diagonals, and two other from , middle of Rectangle that is one across middle of Length ,and other across the Middle of Breadth.

Out of four option ,given rectangle ABCD is , symmetrical that is preimage and Image appears same is:

Option A:→ the Y axis.  

B: Line, y=4.

C: The Line through A and C

D: The Line through ,B and D.

Xelga [282]3 years ago
3 0
I agree that it is the first two
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There are two mixtures. One mixture contains 5% alchol and the other mixture contains 12% alchol. How much of each should be mix
hichkok12 [17]

Answer:

to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture that contains 5% alcohol and 285,7 gallons of mixture that contains 12% alcohol.

Step-by-step explanation:

According to the statement, there are two mixtures. One mixture contains 5% alcohol and the other contains 12% alcohol.

We want to make 1000 gallons with 10% alcohol, so we have the following system of equations:

A + B = 1000 gallons. [1]

0.05A + 0.12B = 0.1(1000) ⇒ 0.05A + 0.12B = 100 [2]

(Where 'A' represents the mixture that contains 5% alcohol and 'B' the one that contains 12% alcohol).

Solving the system of equations:

A + B = 1000 ⇒ A = 1000 - B [3]

[3] → [2]

0.05(1000 - B) + 0.12B = 100 ⇒ 50 - 0.05B + 0.12B = 100

⇒ 0.07B = 50 ⇒ B = 714.28 ≈ B=714.3 [4]

[4] → [1]

A + B = 1000 ⇒ A + 714.3 = 1000 ⇒ A = 285,7

Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'

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
What does first difference mean?
Sunny_sXe [5.5K]

Answer:

In statistics and econometrics, the first-difference (FD) estimator is an estimator used to address the problem of omitted variables with panel data. It is consistent under the assumptions of the fixed effects model. In certain situations it can be more efficient than the standard fixed effects (or "within") estimator.

First differences are the differences between consecutive y-‐values in tables of values with evenly spaced x-‐values. If the first differences of a relation are constant, the relation is _______________________________ If the first differences of a relation are not constant, the relation is ___________________________

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Answer:

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Step-by-step explanation:

X- (-12)=25

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