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Answer:

[tex]m = - \frac{1}{5} n + 2[/tex]

The two lines have only one intersection

[tex]\therefore[/tex] There are only one solution to the system of equation.

Answer:

Reflection over y- axis

Answer:

0.008 3repeating

Step-by-step explanation:

Answer:

-15/4 = x

Step-by-step explanation:

17 = -13 -8x

Solving for x

Add 13 to each side

17 +13 = -13+13-8x

30 = -8x

Divide each side by -8

30/-8 = -8x/-8

Simplify by dividing the top and bottom by 2

-15/4 = x

The number of minutes per day that Dominie practise the piano is 51 minutes per day.

The first step is to convert two weeks to days.

1 week = 7 days

2 weeks : 7 x 2 = 14 days

The second step is to divide the total minutes Dominie practices by the total number of days. Division is the mathematical operation that is used in grouping a number into equal parts using another number. The result of a division is known as the quotient. The sign used to represent division is ÷.

Number of minutes they practice per day : total practice / number of days in two weeks

714 / 14 = 51 minutes per day

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Number name = 22 million

Expanded form = 20,000,000 + 2,000,000

To write the number name and expanded form for the number of driver ants that could be in two colonies.

Given that Up to 22,000,000 driver of ants can live in a single colony

Now, from number expressions, we know that;

1, 000, 000 = 1 million

Thus number name is;

22,000,000= 22 million

Expanded form of 22,000,000 = 20,000,000 + 2,000,000

Thus, we conclude that;

Number name = 22 million

Expanded form = 20,000,000 + 2,000,000

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At the end of 3 years second account will earn the most interest, that is $148.38

Given,

The amount Cole has with him = $1750

Two types of account bank offered:

First account has simple interest rate = 2.75% annually

Second account has compound interest rate = 2.75% compounded annually.

Number of years = 3

We have to find the account which earn the most interest at the end of 3 years.

Simple interest = PRT/100

Compound interest = A - P

A is the amount

A [tex]=P(1+\frac{R}{N} )^{NT}[/tex]

Where,

P is the principal amount

R is the rate of interest

T is the time period

N is the number of times interest compounded yearly.

Here,

P = 1750

R = 2.75%

T = 3 years

N = 1

Now,

First account:

Simple interest = PRT/100

SI = (1750 × 2.75 × 3) / 100

SI = 14437.5/100

SI = 144.375

First account offers $144.375 as interest for 3 years.

Second account:

Compound interest = A - P

A  [tex]=P(1+\frac{R}{N} )^{NT}[/tex]

A = 1750 [tex](1+\frac{0.0275}{1} )^{1(3)}[/tex]

A = 1750 (1 + 0.0275)³

A = 1750 × 1.0275³

A = 1750 × 1.084789547

A = 1898.381707

A ≈ 1898.38

Compound interest = A - P

CI = 1898.38 - 1750

CI = 148.38

Second account offers $148.38 as interest for 3 years.

So, we can conclude that second account will earn the most interest at the end of 3 years.

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The transformed function can be seen in the image below, and the rule is:

g(x)= x/3 + 7

Here we have the parent function, and we want to apply a translation of 7 units up and stretch it vertically by a scale factor of 3

First, we need to apply the translation, remember that a vertical translation of N units is written as:

g(x) = f(x) + N

If we want the translation to be upwards, then we need to use a positive value of N, so in this case we wil have:

g(x) = f(x) + 7

And now we apply a stretch of scale factor 3, this means that we need to divide the variable inside of the function by 3, so we get:

g(x) = f(x/3) + 7

This will give:

g(x)= x/3 + 7

Where we use the fact that f(x) = x

The graph of this function can be seen below.

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The linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2

The given parameters are

Slope, m = -1/2

Point, (x1, y1) = (-2, 3)

The linear equation is calculated as:

y = m(x - x1) + y1

Substitute the known values in the above equation

y = -1/2(x + 2) + 3

Expand

y = -1/2x - 1 + 3

Evaluate the sum

y = -1/2x + 2

This means that the linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2

See attachment for the graph of the point and the three other points

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Answer:

B, J, C.

Collinear points means the points are on the same straight line, which means they have the same gradient. B, J, C are the only points on the sane straight line.

The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct

The graph given in the question shows the time worked on x axis and wages earned on y axis and a ray staring from the origin and moving upward

from the graph we can say that when time worked is zero then wages earned is zero. As the time worked is increasing the wages earned is also increasing .

Hence, it can be said that The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct

The correct question is -Determine the relationship between the quantities on the given graph.

Total Wages

Wages Earned ($)

Time Worked (hours)

OA. The hourly rate depends on the wages earned.

OB. The time worked depends on the wages earned.

OC. The wages earned depends on the time worked.

OD. The time worked depends on the hourly rate.

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Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. He is incorrect

From the information, Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends.

Let's add (-3) + (-4)

It should be noted that the addition is equal to -7.

It should be noted that this doesn't corelate with what Luciana said.

Therefore, she is incorrect. It's only correct for positive numbers.

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it will be 7:8

Step-by-step explanation:

28/4 32/4

7 8

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.

The area of each triangle is 200 square inches.

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.

We have,

The area of a right triangle is given by:

= 1/2 x base x height

We have from the figure,

Base = 20 inches

Height = 20 inches

Area = 1/2 x 20 x 20

Area = 10 x 20

Area = 200 square inches

Thus the area of each triangle is 200 square inches.

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The complete question is:

You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches?

A. 200 square inches

B. 400 square inches

C. 570 square inches

D. 2,800 square inches

E. 5,600 square inches

Answer:

2

Step-by-step explanation:

-3/3 + (7-2^2) = _

-1+3=2

Answer:

24/15

Step-by-step explanation:

120 : 75 =

120/5 : 75/5 =

24 : 15 =

24/15

Answer:

8 : 5 or 8/5

Step-by-step explanation:

starts as 120 : 75

divide both by 5

= 24 : 15

divide both by 3

= 8 : 5 or 8/5

you just need to get them down to the smallest they can. in this case it is 8 and 5. for every 8 $10 bills there are, you have 5 $20 bills.

Answer:

514 grams is equal to 0.514 kilograms

For x = -2,-6, and -10 the value of the polynomial will be satisfied.

Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

Given the polynomial,

x³ + 18x² + 92x + 120 = 0

By hit trial method let's put x = -2

-8 + 72 - 184 + 120 = 0

-192 + 192 = 0

0 = 0

Now,divide x³ + 18x² + 92x + 120 = 0 by x + 2

(x + 2)(x²+ 16x + 60) = 0

(x + 2)(x + 6)(x + 10) = 0

x = -2,-6 and -10.

Hence "For x = -2,-6, and -10 the value of the polynomial will be satisfied".

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The lateral area of the square pyramid that has a base of 10ft and height of 10 ft is calculated as: 200 ft²

A square pyramid is a solid that has a square base and four triangular lateral faces.

The lateral area of the square pyramid is therefore the total area of the four triangular lateral faces of the square pyramid.

Area of one triangular lateral face = 1/2(base)(height)

Lateral area of the square pyramid = Total area of the four triangular lateral faces = 4 × 1/2(base)(height) = 2(base)(height)

We know the following:

Base = 10 ft

Height = 10 ft

Therefore:

Lateral area of the square pyramid = 2(10)(10)

Lateral area of the square pyramid = 200 ft²

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The true statement is that (a) in approximately 50% of the months he sold less than 9 cars.

The given parameter is the box and whisker plot

As mentioned above, the box and whisker plot is a great tool to show the five-number summary.

The five-number summaries are:

On the box and whisker plot, we have the following five-number summaries:

The difference between the quartlles is

Difference = Upper quartile - Lower quartile

So, we have

Difference = 12 - 4

Evaluate

Difference = 8

This means that in approximately 50% of the months he sold 8 cars

8 is less than 9

This means that in approximately 50% of the months he sold less than 9 cars.

Hence, the true statement is that (a) in approximately 50% of the months he sold less than 9 cars.

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The value of the given expression when simplified is equal to 318.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified using the PEMDAS as shown below.

-7 + 5 - 40 × -8

As per the PEMDAS multiplication should be solved first,

= -7 + 5 + 320

Further, solve addition,

= -7 + 5 + 320

= -7 +325

= 318

Hence, the value of the given expression when simplified is equal to 318.

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Answer:
No solution

Step-by-step explanation:
Let's solve your system by elimination.−2x+14y=−29;x−7y=19Multiply the second equation by 2, then add the equations together.(−2x+14y=−29)2(x−7y=19)
Becomes

−2x+14y=−292x−14y=38Add these equations to eliminate x:0=9

The size of the file that has been downloaded is 50 megabytes.

Given total size of the file is 244 megabytes

The percentage that completed the download till now = 18.5%

We have to determine the size of the file downloaded till now can be written as

= 18.5 % of 244

= 18.5 / 100 * 244

= 45.14 megabytes

≈ 50 megabytes

The size of the file that has been downloaded is 50 megabytes.

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Answer:

==============================

Prime factors of 168 are:

In order to make 168n a square number we need to use each prime factor even number of times.

Add 2, 3 and 7 to the prime factors (as a minimum) to get:

To have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.

As given in the question,

Final amount 'A'= $600,000

Time 't' = 30years

Rate of interest 'r'= 6%

Month =12

Let 'P' be the amount deposit in the account each month

[tex]A = \frac{(P(1+\frac{r}{m})^{mt}-1 )}{\frac{r}{m} }\\\\\implies 600,000 = \frac{(P(1+\frac{6}{12\times 100})^{12\times 30}-1 )}{\frac{6}{12\times 100} }\\\\\implies 600,000 \times \frac{1}{200}= P (\frac{12.06}{12})^{360}-1 \\\\\implies 3000 +1 = P(1.005)^{360} \\\\\implies P = \frac{3001}{6.02258} \\\\\implies P = \$498.29[/tex]

Therefore, to have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.

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