2.1−2.7 on a number line

The present age of Paul is 52 years and the present age of Matt is 10 years.

We are given that two years ago, Paul =  7 times as Matt

Let the current age of Matt be x and of Paul be y

2 years ago, we will have that:

Age of Matt = x - 2

So, we get the equation as:

Age of Paul = 7 ( x - 2) = 7 x - 14

y - 2 = 7 x - 14

y = 7 x - 14 + 2

y = 7 x - 12

Also, we are given that to year from now, Paul = five times Matt

We get that:

y + 2 = 5 ( x + 2)

y + 2 = 5 x + 10

y = 5 x + 10 - 2

y = 5 x + 8

So, we get:

7 x - 12 = 5 x + 8

7 x - 5 x = 8 + 12

2 x = 20

x = 20 / 2

x = 10

y = 5 (10) + 2

y = 50 + 2

y = 52

Therefore, the present age of Paul is 52 years and the present age of Matt is 10 years.

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Answer:

6/5

Step-by-step explanation:

Rise

_____

Run

The slope of parallel line is -6/5

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

given:

Equation: 18x + 15y = 90.

Now, writing the given equation in slope intercept form

15y= 90- 18x

y= 90/15 - 18/15 x

y= 6 - 6/5x

So, the slope of given line is -6/5

Now, the slope of parallel and given is same.

Thus, the slope of parallel line is -6/5

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Answer:

3/8

change to an improper fraction

1 1/8=9/8

3/4 times 2 equals

6/8

9/8-6/8

3/8

Answer: I think the answer is 3/8 or it can be 5/8.

explanation: I hope this helps.

Answer: 8.4261

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3 } \times \sqrt{2 \times {5}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2 \times 5 \sqrt{5 \times 3 \times 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 10 \sqrt{30} [/tex]

This statement is false. when constructing a congruent line segment to cd the ray needed for the construction it must be not shorter.

Because when constituting a configured line segment to CD the ray never can be shorter. The reason is when we constitute a configured it's Ray line is always increase that mean it's go up Hight and it's must be longer . That's why this statement is false.

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments. The congruent segments continue to be congruent even after being turned, flipped, or rotated.

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Answer:

(-1, -4)

Step-by-step explanation:

To find the missing endpoint, we can multiply the midpoint coordinates by 2, so we can get 4 and 2. Then we can subtract the coordinates from the endpoint we have, which is A, to those numbers.

4-5 is -1

2-6 is -4

Put them together and we get (-1, -4) as our endpoint B.

Answer:

Step-by-step explanation:

(5+x)/2=2, (6+y)/2=1

for the x value

5+x=4

x=-1

then for the y value

6+y=2

y=-4

then your answer would be (-1,-4)

The addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power". option C

(1.38×10⁴) + (8×10³)

= (1.38 + 8) × 10^(4 + 3)

= 9.38 × 10^7

Options:

9.38×10⁴

2.18×10⁴

9.38×10^7

Therefore, the addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power".

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Answer:

169 squared I think,hope this helps

The combined number of widgets and gadgets that the packaging department can handle is 2300 per day that is x + y =2300

A manufacturer makes widgets and gadgets. At least 500 widgets(x) and 700 gadgets (y) are

[tex]x\geq 500\\\\y\geq 700[/tex]

The machinery can produce no more than 1200 widgets(x) and 1400 gadgets(y) per day

[tex]x\leq 1200\\\\y\leq 1400[/tex]

The combined number of widgets and gadgets that the packaging department can handle is 2300 per day

x+ y =2300

then the possible values of x and y are

( 1000, 1300)

(1100, 1200)

( 1200,1100) etc.

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The unit rate of the watermelons would tell us the cost of 1 of the watermelon. The last option is correct.

The question tells us that the melons are sold for 5 for $20.

Hence the price of 1 would be at: 20/5

= 4 dollars per watermelon.

The weight of one of the melons is 8 pounds and the unit rate for 1 is 4 dollars. The unit rate is the price per one of the fruits or the cost of the fruit.

Hence we can say that The unit rate of the watermelons would tell us the cost of 1 of the watermelon.

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Answer:

27%

Step-by-step explanation:

3000 + 3500 + 4000 + 4200 = 14700

4000 / 14700 ≈ 0.27

0.27 = 27%

Thus L.H.S = R.H.S that is [tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex]  = [tex]sec(\frac{\pi }{6-x} )[/tex] is proved

According to the question we have been given that

[tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex]  = [tex]sec(\frac{\pi }{6-x} )[/tex]

And we need to prove that left hand side is equal to the right hand side.

To prove this we will solve the right-hand side of the equation first with the help of trigonometry identity. The right hand side of the equation is :

R.H.S = [tex]sec(\frac{\pi }{6-x} )[/tex]

          = [tex]\frac{1}{cos(\frac{\pi }{6-x} )}[/tex]

[As secƟ = 1/cosƟ)

           = [tex]\frac{1}{\frac{cos\pi }{6cosx} + \frac{sin\pi }{6sinx} }[/tex]

[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]

                   [tex]=\frac{1}{\frac{\sqrt{3} }{2}cosx + \frac{1}{2}sinx } \\= \frac{1}{\frac{\sqrt{3}cosx + sinx }{2} }\\=\frac{2}{\sqrt{3}cosx + sinx}[/tex]          

    R.H.S = L.H.S

or L.H.S = R.H.S

Hence [tex]\frac{2}{\sqrt{3} cosx + sinx } = sec(\frac{\pi }{6-x})[/tex] is proved

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In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.

Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.

In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.

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Answer:B $20 an hour

Step-by-step explanation:

if you look at the graph, in one hour he made $20

The last digit of the product of numbers from 0 to 99 is 0.

Multiplication is a method of finding the product of two or more numbers.

We have,

1, 2, 3, .............till 99.

We know that any number multiplied by 10 will give us 0 as the last digit.

And there are 10, 20, 30, 40, 50, 60, 70, 80, and 90.

We also know that 5, 15, 25, 35, 45, 65, 75, 85, 95 if multiplied with an even number the last digit is zero.

So if all the numbers from 1 to 99 are multiplied together, the last digit of the product will be a zero.

Thus the last digit of the product of numbers from 0 to 99 is 0.

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The total earning of Whitney in may including her salary and commission is $70,400.

A sales commission is money given to an employee for completing a task, typically selling a specific amount of products or services.

Now, as per the given question;

The monthly salary of Whitney is $60000.

The sales he did in the month of the may is $13000.

He got 8% commission on his total sales.

8% of $13000 = 10,400.

Thus, the total earning of the may will be-

Total earning = Salary + commission

Total earning = $60000 + 10,400

Total earning = $70,400

Therefore, the total earning done by Whitney in the May is $70,400.

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The 4•x by 5•x inner dimensions of the 53 inches outer perimeter picture frame, the 1 inch wide frame and the 4 × 5 inch picture to be enlarged, gives;

a. The outer perimeter equation is presented as follows;

18•x + 8 = 53 inches

b. The scale factor required for the enlargement of the picture is 2.5

The dimensions of the photo = 4 × 5 inch

Width of the frame = 1 inch

Outer perimeter of the frame = 53 inches

The width of the inside of the picture frame = 4•x

The height of the inside of the picture frame = 5•x

a. The equation for the outer perimeter of the picture frame is therefore;

2 × (4•x + 1 + 1) + 2 × (5•x + 1 + 1) = 53

Which gives;

2 × (4•x + 2) + 2 × (5•x + 2) = 53

8•x + 4 + 10•x + 4 = 53

A simplified equation for the outer perimeter of the picture frame is therefore;

b. Solving the above equation, we have;

18•x + 8 = 53

18•x = 53 - 8 = 45

18•x = 45

Therefore;

x = 45 ÷ 18 = 2.5

x = 2.5

The width and height of the picture frame are therefore;

Width = 4•x = 4 × 2.5 = 10

Height = 5•x = 5 × 2.5 = 12.5

Which gives;

Width = 10 inches

Height = 12.5 inches

The enlargement factor, sf, is given by the ratio of a side of the picture frame to a side of the picture as follows;

sf = 12.5/5 = 2.5

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The equation representing the minimum and maximum scores |x-87| = 1.8

Given that the average score on a lab report is 87 points. All students score within 1.8 points of the average.

Let 'x' be the score of student. The maximum and minimum score of a student lies within 1.8 points of the average.

Then, maximum score of a student, x = 87+1.8

and minimum score of a student, x = 87-1.8

Combining these two equations, we get, x = 87 ±1.8

Or, more conveniently, |x-87| = 1.8 represents the minimum and maximum scores obtained by a student.

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The distance of the boat from its destination depends on

So with these factors, the distance of the boat from its distance can be calculated.

The distance of the boat from the destination currently is 63 miles

Speed of the boat is 10 miles / hr

Let c be the speed of the river current and

h be the number of hours to reach a particular destination

So, the formula to find the distance of the boat from destination is given by

D = 63 - h(10 - c)

We need to find the formula for boat's distance from its destination after 3 hours

Thus h = 3 hrs

Let us substitute h in above equation, Then

D = 63 - 3(10 - c)

D = 63 - 30 - 3c

D = 33 - 3c

which is the formula for the boat's distance from its destination after 3 hours.

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Based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.

The side-angle-side congruence theorem (SAS) means that two triangles have two pairs of sides that are congruent to each other with a pair of included congruent angles in between the two pairs of congruent sides of both triangles, and thus, both triangles must be congruent to one another.

The diagram shows two triangles that share a common side which is a pair of congruent sides. It also shows a pair of another congruent sides that is marked congruent.

Also, we have a pair of included congruent angles that both triangles have.

Therefore, based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.

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The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.

From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.

The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:

585.43 + x - 302.05 ≥ 300

Collect like terms

x ≥ 300 - 585.43 + 302.05

x ≥ $16.62

She's needs to deposit at least $16.62.

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The term or expression 12b represents the number of raffle tickets sold by the members of the band.

Expression: An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

There are b number of members in a jazz band. The jazz band wants to take a tour.

Each of the members sold 12 raffle tickets to raise money for the tour.

Therefore, the number of raffle tickets sold will be the product of the number of jazz members and the number of raffle tickets sold by each member.

So, the expression for the number of raffle tickets sold by the members of the jazz band will be:

= 12 × b

= 12b

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Using the monthly payment formula, it is found that the best plan is given by:

The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For the simple interest payment method, the parameters are given as follows:

r = 0.06, n = 3 x 12 = 36, P = 11000, r/12 = 0.06/12 = 0.005.

Hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 11000(0.005)\frac{(1.005)^{36}}{(1.005)^{36} - 1}[/tex]

A = 334.64.

For the credit card payment method, the parameters are given as follows:

r = 0.16, n = 6 x 12 = 72, P = 11000, r/12 = 0.16/12 = 0.0133.

Hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 11000(0.0133)\frac{(1.0133)^{72}}{(1.0133)^{72} - 1}[/tex]

A = 238.37.

The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.

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Answer:

Seconds and Minutes

Step-by-step explanation:

Randomly pick 55 students to run a lap around the track and measure their time.

This is the only option that avoids any type of bias.

Answer:

q = [tex]\frac{7}{5}[/tex]p + 7

Step-by-step explanation:

7p -5q = -35  Subtract 7p from both sides of the equation

-5q = -7p - 35  /Dive all the way through by -5

q = [tex]\frac{7}{5}[/tex]p + 7