Grade 8 Pre-Algebra B
07.03
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected ove
the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

Using the  sinking fund formula, the monthly payment needed to accumulate 270,000 with 5% interest or combine did monthly for 28 years, the monthly invested payment is 369.65.

A sinking fund, also referred to as a sinking fund, is defined by its name. Fundamentally speaking, it is built to sink. Although there are some similarities between a sinking fund and a reserve fund, their purposes differ significantly. Unlike reserve funds, which typically serve no particular purpose, sinking funds have a designated purpose.

Simply put, a reserve fund is a company's method of saving its surplus funds. There are numerous uses for reserve funds. They can be applied to a variety of costs, including those related to emergency situations, asset purchases, business expansions, and capital expenditures.

Sinking fund (A) = P × [tex]\frac{(1+r/n)^{tn}-1}{r/n}[/tex]

Where

A – Money accumulated

P – Periodic contribution,

r – Interest rate

t – Number of years

n – Number of payments per year

So, periodic contribution P = A / (((1 + r / n) ^ (t * n) – 1) / (r / n))

Here given that,

A – 270,000

r – 5%

t – 28 years

n – 12

P – To find

Substituting the values we get

P = [tex]270000/(((1+0.05/12)^{\left(28\times 12\right)}-1)/(0.05/12))[/tex]

P = 369.649667

P = 369.65

Therefore, the monthly payment needed to accumulate 270,000 with 5% interest or combine did monthly for 28 years, the monthly invested payment is 369.65.

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The probability that the subject​ lied, given that the test yields a positive result is; 81.81%

From the given table, we see that;

Number of people with a positive result who did not lie = 10

Number of people with a positive result who lied = 45

Total number of people with positive results = (10 + 45) = 55

Number of people with a negative result who did not lie = 34

Number of people with a negative result who lied = 12

Total number of people with negative results = (34 + 12) = 46

The probability that the subject​ lied, given that the test yields a positive result is;

Probability = 45/55 = 0.818 = 81.81%

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Answer:

A = 28

B = 2

C = 29

Step-by-step explanation:

28×2+29 = 85

28+2×29 = 86

Step 1

Given;

Required; To find the dot product

Step 2

Find the dot product

The answer thus is;

Answer: $97.5

Step-by-step explanation:

15(4) + 7.5(5) = $97.5

Answer:

97.5

Step-by-step explanation:

got it right

Answer:

|-74| = 74

yw:)

hope it helps

do the sum

the number is 40 because 40 is 8 more than 32

Answer:-7\5 IS THE ANSWER TO THAT

Step-by-step explanation:

Bill's projected monthly payment under the Monthly Payments for Long-Term Loans using the Rule of Thumb is $870.00.

Bill's exact monthly payment using the Monthly Payments calculation is $933.36.

The real monthly payment is approximately $63.36 more than the predicted cost.

Simple procedures may be used to calculate the Monthly Payments for Long-Term Loans Rule of Thumb.

To begin, divide the annual percentage rate (APR) by 12 to obtain the monthly percentage rate (MPR).

Second, calculate the MPR on the principal amount. The product is the estimated monthly payment, which is similar to the real monthly payment and was computed using a financial calculator below.

Estimated Monthly Payment:

Home Mortgage = $116,000

Term of loan = 30 years

APR = 9%

Monthly interest rate = 0.0075 (0.09/12)

Estimated monthly payment based on the Monthly Payments for Long-Term Loans Rule of Thumb

($116,000 x 0.0075) = $870

Actual Monthly Payment Formula:

N (# of periods) = 360 months (30 x 12)

I/Y (Interest per year) = 9%

PV (Present Value) = $116,000

FV (Future Value) = $0

The outcome is given as:

PMT = $-933.36

Sum of all periodic payments = $-336,010.40

Total Interest = $220,010.40

Actual monthly payment =  $933.36

Estimated monthly payment 870.00

Difference = $63.36


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The option that is an appropriate procedure for this experiment is D. The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.

From the information illustrated, the doctor wants to determine if a new medication for cholesterol is more effective than the previous medication.

In this case, it should be noted that it's important to prevent bias. Therefore, it's important that the doctor randomly assign the 30 patients to the new medication

In conclusion, the correct option is D.

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Answer:

answer is A got it right

Step-by-step explanation:

The annual rate of change of the boat's value is $5334.

Given,

Chris bought a new boat in 2008.

The value of boat in 2008 (Initial value) = $35000

The value of boat in 2011 = $19000

Chris knows that the value of the boat depreciated linearly.

We have to find the annual rate of change of the boat's value, x.

Number of years, n = 2008 to 2011 = 3 years

Here, x be a constant.

So,

Value in 2011 = Initial value - nx

19000 = 35000 - 3x

3x = 35000 - 19000

3x = 16000

x = 16000/3

x = 5333.33

x = 5334

That is,

The annual rate of change of the boat's value is $5334.

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The equation that can be derived is [tex]4(x-3)=12[/tex]

Given

Four times the difference of some number and 3 amounts to the quotient of 144 and 12.

Let us say some number is x

Quotient of 144 and 12,

Quotient = [tex]\frac{144}{12}[/tex]

Quotient = 12

Four times the difference of x and 3 is as follows

[tex]4(x-3)[/tex]

Writing this in the form of an equation we get

[tex]4(x-3)=12[/tex]

Hence the equation is obtained, also solving the equation for x

[tex]4x-12=12[/tex]

[tex]4x = 24[/tex]

[tex]x=\frac{24}{4}[/tex]

[tex]x=6[/tex]

Hence the equation for given conditions is obtained.

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The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]

An exponent is a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

Here we have to determine the sign for exponential or radical expression

(-3m[tex]n^{5}[/tex])^4

Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]

Similarly

(-3m[tex]n^{5}[/tex])^4

= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]

Now using the exponent  power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get

= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]

Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].

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Answer:

  (a) ∠e +∠d = 180°  is false

Step-by-step explanation:

You want to know which angle expression is not true.

We can figure the measures of all of the unknown angles, then check the given expressions.

Angles 'a' and 130° are corresponding angles, so congruent:

  a = 130°

Angles 'a' and 'e' are vertical angles, so congruent:

  e = a = 130°

Angle 'd' and 62° are vertical angles, so congruent:

  d = 62°

Angles 'b' and 'd' are corresponding angles, so congruent:

  b = d = 62°

Angles 'f' and 62° are corresponding angles, so congruent:

  f = 62°

Angles 'c' and 130° are a linear pair, so supplementary:

  c + 130° = 180°

  c = 50° . . . . . . subtract 130°

(a) ∠e +∠d = 180°   ⇒   130° +62° = 180° . . . . false

(b) ∠d +∠b = 124°   ⇒   62° +62° = 124° . . . . true

(c) ∠a +∠c = 180°   ⇒   130° +50° = 180° . . . . true

(d) ∠ 180° -∠f = 118°   ⇒   180° -62° = 118° . . . . true

The matrix equation is given to be:

where A is the coefficient matrix of the system.

To get the value of X, we need to multiply both sides of the equation by the inverse of A, since:

Therefore, we have:

he TLAST OPTION is correct.

Answer:

to solve for x, you gotta make the two equations equal to each other then you can move the numbers to get the value of x

20x+10=30x-10

20x-30x=-10-10

-10x=-20

x=2

Answer:

x=2

Step-by-step explanation:

if m/A and m/B are equal, to find x, your equation would be 20x+10=30x-10. doing two step equations, you would substract 20x from both sides, making your equation look like 10=10x-10. then you would add 10 from both sides making your equation 20=10x. then you would divide 10x from both sides making x=2.

Answer:

no solution that's my answer

The valid solution to the problem is: The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.

Let's solve the problem step by step to determine the smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8. We'll express the answer as a reduced fraction.

We have 4 boxes arranged in a square as described:

 A  B

 C  D

The fraction can be represented as AB/CD.

To make the fraction as small as possible, we need to arrange the digits in a specific way. We want to minimize the numerator (AB) and maximize the denominator (CD).

For the numerator (AB), we want the smallest two-digit number. The smallest two-digit number that can be formed using the digits 3, 4, 5, and 8 is 34.

For the denominator (CD), we want the largest two-digit number. The largest two-digit number that can be formed using the digits 3, 4, 5, and 8 is 85.

Therefore, the smallest fraction that can be formed is 34/85.

To ensure that this fraction cannot be further reduced, we need to check if 34 and 85 share any common factors greater than 1. If they do not share any common factors other than 1, then the fraction is in its reduced form.

Checking for common factors:

Factors of 34: 1, 2, 17, 34

Factors of 85: 1, 5, 17, 85

The only common factor is 1, which means the fraction 34/85 is already in its reduced form.

Thus, the valid solution to the problem is:

The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.

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The correct option is d. No extrema, is obtained for the given function.

For the state question,

The function is defined as; f(x) = 2/(3x-5).

To estimated the extrema of the function, first find the critical points.

Differentiate the function with respect to x suing division rule.

f(x) = 2/(3x-5).

f'(x) = 3/(3x-5)²

Now, put the function equals to zero.

f'(x) = 3/(3x-5)² = 0.

3 = 0

But, 3 ≠ 0

Thus, there is no critical point found for the function.

The give function is independent of the value of the x, and thus called the constant function.

Therefore, there is no extrema obtained for the function.

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We are asked to solve for a number such that:

Twice that number plus 4 equals 6

Which can be written in math terms as:

2 x + 4 = 6

Now we proceed to isolate the unknown in steps.

First we subtract 4 from both sides:

2 x + 4 - 4 = 6 + 4

we combine like terms:

2 x = 10

Now we divide both sides by 2 so as to cancel the factor 2 that accompanies "x":

2 x / 2 = 10/ 2

perform the indicated operations:

x = 5

Lenght of a rectangle: L

Widht of the rectangle: W

Perimeter of the rectangle: P

length of a rectangle is four times it's width: L = 4W

Perimeter is at most 106: P <= 106

Perimeter is 2L + 2W: P = 2L + 2W

P <= 106

if we use the value of P = 2L + 2W, we can write:

2L + 2W <= 106

Since L = 4W, then we can write this equation:

2L + 2W <= 106

2(4W) + 2W <= 106

8W + 2W <= 106

10W <= 106

W <= 106/10 = 10.6

W <= 10.6

Therefore, the greatest possible value for the width is 10.6

Answer:

10.6

For every 4 liters of synthetic oil, there are 7 liters of natural oil. 671 liters of Petrolyn oil. 244 liters of synthetic oil is needed and 427 liters of natural oil is needed.

Given that,

Petrolyn motor oil is a blend of synthetic and natural oil. For every 4 liters of synthetic oil, there are 7 liters of natural oil. 671 liters of Petrolyn oil are needed to produce it.

We have to find how much synthetic oil, in liters, is required.

According to the given values;

The ratio of natural to synthetic oil

= 7:4

If 671 liters have to be made then,

By adding 7+4=11

So, 7/11 of 671 liters will be = 427 liters of natural oil

and, 4/11 of 671  liters will be = 244 liters of synthetic oil

Therefore,244 liters of synthetic oil is needed and 427 liters of natural oil is needed.

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On an average 9.043 [tex]\times10^{5}[/tex] beats more does the mouse heart beats in a day.

The average human heart beats = 1.037[tex]\times10^5[/tex] times per day.

The approximate average mouse heart beats = 1.008[tex]\times10^6[/tex] times per day.

We have to find the how many beats more does the mouse heart beats in a day.

Since we have to find the more heart beat of mouse comparing to the human heartbeats. So we subtract their heart beat.

The human heartbeats have [tex]10^5[/tex] while mouse heartbeats have [tex]10^6[/tex]. So we first equal the power of 10. After equal the power we can easily find the value of the more heart beat of mouse.

We can write,

The average human heart beats = 0.1037[tex]\times10^6[/tex]

Now,

The more heartbeats of mouse = average mouse heart beats − average human heart beats.

The more heartbeats of mouse [tex]= 1.008\times10^6-0.1037\times10^6[/tex]

The more heartbeats of mouse [tex]=(1.008-0.1037)\times10^{6}[/tex]

The more heartbeats of mouse = 0.9043[tex]\times10^{6}[/tex]

The more heartbeats of mouse = 9.043[tex]\times10^{5}[/tex]

Hence, on an average 9.043[tex]\times10^{5}[/tex] beats more does the mouse heart beats in a day.

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Answer: your welcome

Step-by-step explanation:

Let x = the certain number

"A certain number was tripled                       3x

"then decreased by 10":        3x - 10

"then doubled":           2*(3x-10)

"Then increased by 2":      2(3x-10)+2

"result was 5 times original number":

   2(3x-10)+2 = 5x

   6x - 20 + 2 = 5x

   6x - 5x = 20 - 2

      x = 18

Check (very important):

Is    2*(3*18 - 10) + 2:= 5*18        ?

     2*(54-10) + 2 = 90    ?

      2*(44) + 2 = 90    ?

         90 = 90    ?yes

The coordinates of RS are R(2, 3) and S(-5, 6)

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

Given:

Segment RS is rotated 90 counterclockwise about the origin

So, When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).

Also, the coordinates are reflected over y- axis.

So, The coordinates of RS before reflection over y- axis is

R(-3, 2) and S(-6, -5)

Now, the coordinates of RS before rotation is

R(2, 3) and S(-5, 6)

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The number of chips and drinks are 46 chips and 56 drinks respectively.

Let the number of drinks be d.

Let the number of chips be c.

From the information, he works at a football concession stand selling drinks for $2 and bags of chips for $3 and he makes a total of $246 and sells a total of 100 drinks and bags of chips.

This will be:

c + d = 100 ........ i

2d + 3c = 246 ........ ii

From equation i, c = 100 - d

Substitute this into equation ii

2d + 3c = 246

2d + 3(100 - d) = 246

2d + 300 - 3d = 246

Collect like terms

2d - 3d = 246 - 300

-d = -54

d = 54

Number of drinks = 54

Since c + d = 100

c + 54 = 100

c = 100 - 54 = 46

Chips = 46

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Complete question

Russell works at a football concession stand selling drinks for $2 and bags of chips for $3. At one football game, Russell makes a total of $246 and sells a total of 100 drinks and bags of chips. Calculate the number of drinks and chips sold.

Answer:

9, 9, 9900

Step-by-step explanation:

After evaluating the limit we have came to find that the limit of       [tex]\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}[/tex] as x approaches 1 is −0.0625

In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits are crucial to calculus and mathematical analysis and are necessary for the definitions of continuity, derivatives, and integrals.

The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network, in addition to sharing a connection with the category theory concepts of limit and direct limit.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit

⇒ [tex]\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}[/tex]

Evalúe 2 as x

⇒ [tex]\frac{1-2}{1^2-10(1) + 25}[/tex]

⇒ [tex]\frac{-1}{-9 + 25}[/tex]

⇒ [tex]\frac{-1}{16}[/tex]

⇒−0.0625

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