The sum of three lengths of a fence rages from 31 to 40 inches. Two side lengths are 9 and 12 inches. If the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side

Given the piece-wise function, the output value of f(7) is 42.

A piece-wise function is simply a function built from pieces of different functions over different intervals

Given the piecewise function in the question;

                   x² - x,       x > 5      

                   2/(x-6),    x ≤ 5

To determine the output value of f(7), determine where 7 falls in the given domains of the pieces of the function.

7 falls in the domain of x > 5

Hence,

f(x) = x² - x

Relace all the occurrence of x with 7 and simplify

f(7) = (7)² - 7

f(7) = 49 - 7

f(7) = 42

Given the piece-wise function, the output value of f(7) is 42.

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The equation of the line containing the points ​(​-2,8) and (4,-1) is:

y = -3x/2 + 5

Given data

points ​(​-2,8) and (4,-1)

From the equation of the straight line y = mx + c

The slope of the line m is solved by

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

m = ( -1 - 8 ) / ( 4 - -2 )

m = (-9 ) / ( 6 )

m = -3/2

using the point ( 4, -1 ) we find the intercept as

y = mx + c

-1 = -3/2 * 4 + c

-1 = -3 * 2 + c

-1 = -6 + c

-1 + 6 = c

c = 5

Substituting the values of m = -3/2 and c = 5 to the equation y = mx + c gives the equation of the line. This is done as follows

y = mx + c

y = -3/2 * x + 5

y = -3x/2 + 5

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8000 is the population of village in 1970.

Given that:

The linear equation of the population, P, of a village t years after it was founded in 1970, is given by

P(t) = 8000 + 600t.

To find:

What is the population in 1970 ?

So, according the question

We have,

The population of a village after t years from 1970 in a form of linear equation is,

 P(t) = 8000 + 600t.

This linear equation was founded in 1970, so t years will be counted after 1970. If we need to find the population of a village in 1971, we can use t = 1971 - 1970, which is one year. But here we have to find the population of a village in 1970, so the value of time is 0.

Now, putting the value of t.

We will be get,

 P(t) = 8000 + 600t.

 P(0) = 8000 + 600 × 0.

 P = 8000

So, the population of a village in 1970 is 8000.

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Answer:

C. 6.39

its right behind 6.4, therefore it's 6.39.

24 pounds  of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given situation:

A coffee $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound

Now, Let x be the amount of coffee which is $10 per pound

So,

10x + 3(30) = 5(x+30)

10x + 30 = 5x+150

5x + 30 = 150

5x = 120

x = 24 pounds

Hence, 24 pounds  of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.

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Answer:$6.15

Step-by-step explanation: 80 dollars divided by 13 pounds will give us a answer and we need to round down     80/13=6.15

Hey there!

(4y + 9z)

= 4y + 9z

= 4(5) + 9(4)

= 20 + 36

= 56

Therefore, your answer should be: 56

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Your response's numerical variable is x=-13.

Variable, A symbol (often a letter) used in algebra to represent an unknowable numerical value in an equation. X and Y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are examples of frequently used variables (arc length).

Mathematical expressions are used to represent situations or problems in algebra, a branch of mathematics. We use integers with fixed or definite values in algebra, such 2, 7, 0.068, etc. In algebra, we mix variables like x, y, and z with numbers.

accordance with the data provided;

the equation is 9+x=-4

x+9=-4

(x+9)+(-9)=-4+(-9)

x+9-9=-4-9

x=-13

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Answer: I have no idea

Step-by-step explanation: can anyone else pls help me???

Answer:

30 cm

Step-by-step explanation:

The equation which equals to 20 can be x + y = 20.It can also be f(x) = 5x where x = 4 and many more.

A function behaves like an output or response to an input.The set of all inputs are known as independent variable and the set of all outputs are known as dependent variable.

According to the given question we need an equation that equals to 20.

As the type of equation is not defined we will construct a simple equation known as linear equation in two variables.

So, It can be formed by x + y = 20 this equation has an infinite no. of solutions.Some of them are (1,19), (2,18),.....(19,1).We can also go by negative number and a positive number.

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Answer: a=15/8

Step-by-step explanation:

a^2 = 225/64 ​

a=[tex]\frac{\sqrt{225}}{\sqrt{64}}[/tex]

a=15/8

Answer:

1.875 or 15/8

Step-by-step explanation:

a= square root of 224/64

=sqrt(225)/sqrt(64)

=15/8

Answer:

1 hour and 30 minutes

Step-by-step explanation:

I think this because it said his top speed was 20,000 and he flew 30,000 if you add another 20,000 to the 20,000 he flew in 30,000 you would get 40,000 which is 2 hours so 1 hour and 30 min. Hope it Helped!

Answer:

[tex]17[/tex] and [tex]20[/tex].

Step-by-step explanation:

Let [tex]x[/tex] denote the larger one of the two positive integers ([tex]x > 0[/tex].) The smaller integer would be [tex](x - 3)[/tex]. The square of the larger integer would be [tex]x^{2}[/tex].

The sum of the smaller integer and the square of the larger integer is [tex](x^{2} + (x - 3))[/tex]. If this sum is equal to [tex]417[/tex], then:

[tex]x^{2} + x - 3 = 417[/tex].

[tex]x^{2} + x - 420 = 0[/tex].

Solve this quadratic equation for [tex]x[/tex] through factorization. Since [tex]420 = 21 \times 20[/tex]:

[tex]x^{2} + x - (21 \times 20) = 0[/tex].

[tex]x^{2} + 21\, x - 20\, x + (21)\, (-20) = 0[/tex].

[tex](x + 21)\, (x - 20) = 0[/tex].

Thus, either [tex]x = 20[/tex] or [tex]x = (-21)[/tex] by the Factor Theorem. However, since [tex]x > 0[/tex] (the two integers are both positive,) only [tex]x = 20[/tex] is a valid solution.

Hence, the larger one of the two integers would be [tex]20[/tex]. The smaller one of the two integers would be [tex](x - 3) = (20 - 3) = 17[/tex].

Answer:

D

Step-by-step explanation:

My mom is a teacher lol

Based on the amount that the individual is paying monthly, the total amount that will be paid over the full term of the loan is $150,900

The amount that the individual will pay in total over the loan's full term can be found to be:

= Amount paid per month x Number of years x number of months per year

Solving gives:

= 503 x 25 x 12

= 503 x 300

= $150,900

In conclusion the total amount paid is $150,900.

The rest of the question is:

What is the total amount paid over the full term of the​ loan?

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The taxi ride was 7 miles

Mia took a taxi from her house to the airport

The taxi charged a pick up fee of $1.30

They also charged $4.25 per mile

The total fare was $31.05

The number of miles can be calculated as follows

31.05 - 1.30 = 4.25x

29.75= 4.25x

Divide both sides by the coefficient of x which is 4.25

29.75/4.25= 4.25x/4.25

x= 7

Hence the taxi ride was 7 miles

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One gallon of pure acid must be added to get a 40% acid solution.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

Given that

3 gallons of a 40% acid solution means you have (20%)×(3) = 0.6 gallons of acid already.

Let x of gallons of pure acid be added to get a 40% acid solution.

⇒ (0.6 +x)/(3+x) = 40%

⇒ (0.6 +x)/(3+x) = 4/10

Cross multiply, we get

⇒ 10(0.6+x) = 4(3+x)

⇒ 6 + 10x = 12 + 4x

⇒ 10x - 4x = 12 - 6

⇒ 6x = 6

⇒ x = 1

Therefore, one gallon of pure acid must be added to get a 40% acid solution.

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W.H. must spend $100 to fix his old water heater to reduce his overall cost

If he spends money to fix his old water heater.

Repair cost of his old water heater = $100

Electricity cost for three years as he sells his house 3 years from now = $125 * 3 = $375

Total cost If he spends money to fix his old water heater = $475

If he spends money to buy new water heater

Cost of purchasing new water heater= $ 350

Reduced yearly electricity bill = $125- 40%of $ 125 = $75

Electricity cost for three years as he sells his house 3 years from now = $75 * 3 = $225

Total cost If he spends money to buy new water heater = $575

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The measurement of the angle indicated for each trapezoid is m<B equal to 70.

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs.

Given :

In the trapezoid angle

m<B=11x+15

m<C=19x+15

According to the question,

The trapezoid is a quadrilateral.

The 4 angles of a quadrilateral all equal to 360 degrees.

The angles between parallel lines add up to 180degree due to adjacent angle.

So,

The equation is

m<B+m<C=180

11x+15+19x+15=180

30x+30=180

Subtract 30 from both sides we get,

30x=150

Divide by 30 on both sides we get,

x=5

∴m<B=11x+15=11*5+15

m<B=70

m<C=19x+15=19*5+15

m<C=110

Therefore, the measurement of the angle indicated for each trapezoid is m<B equal to 70.

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Answer:

Step-by-step explanation:

Cut out square on each corner has side of x.

When folded up the height of the box becomes same as the side of the cut-out square.

Sides  of the base of the box are:

The volume of the box which is the right square prism is:

Substitute the values and find the volume:

The graph of the resulting polygon is shown in the image attached below.

In this problem we find a polygon generated by four vertices, whose locations are shown in the picture and whose image must be found by using rigid transformation formulas.

Rigid transformations are transformations such that the form of a geometric loci is conserved, dilations are an example of rigid transformation. The general formula of a dilation is described below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]  

Where:

If we know that O(x, y) = (- 2, 4), k = 2 / 3, T(x, y) = (7, 1), U(x, y) = (4, 4), V(x, y) = (1, 13) and W(x, y) = (- 2, 4), then the coordinates of the polygon are now determined:

T'(x, y) = (- 2, 4) + (2 / 3) · [(7, 1) - (- 2, 4)]

T'(x, y) = (- 2, 4) + (2 / 3) · (9, - 3)

T'(x, y) = (- 2, 4) + (6, - 2)

T'(x, y) = (4, 2)

U'(x, y) = (- 2, 4) + (2 / 3) · [(4, 4) - (- 2, 4)]

U'(x, y) = (- 2, 4) + (2 / 3) · (6, 0)

U'(x, y) = (- 2, 4) + (4, 0)

U'(x, y) = (2, 4)

V'(x, y) = (- 2, 4) + (2 / 3) · [(1, 13) - (- 2, 4)]

V'(x, y) = (- 2, 4) + (2 / 3) · (3, 9)

V'(x, y) = (- 2, 4) + (2, 6)

V'(x, y) = (0, 10)

W'(x, y) = (- 2, 4) + (2 / 3) · [(- 2, 4) - (- 2, 4)]

W'(x, y) = (- 2, 4) + (2 / 3) · (0, 0)

W'(x, y) = (- 2, 4) + (0, 0)

W'(x, y) = (- 2, 4)

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Answer:

1/6

Step-by-step explanation:

I dunno, I put this into a calculator and that's the answer it gave me.

Given numbers in the form of the decimal number are:

Decimal numbers:

Therefore, given numbers in the decimal numbers form are:

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The coordinates are (-4,3).

Glad to help.

Mark me Brainliest. :)

The shifted point G when translated to left 4 units and up 3 units has coordinate ( -8, 6).

Rotation, translation, Reflection, and Dilation are the four types of translation.

Assuming the square boxes of the paper graph are 1 sq unit means each side is 1 unit.

Now by counting we can conclude that before shifting the point has an x coordinate of - 4 units and a y coordinate of 3 units.

∴ The coordinates of the points are (-4, 3).

Now it has been shifted left 4 units and up 3 units, We know going towards left is negative on the x coordinate and going towards up is positive on the y coordinate.

So, points after the translation is (-4 -4, 3+3) = (-8,6)

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The measures of angle ACB and angle ABC are 40° and 63° respectively

From the information given, we have that angle DAB is on a straight line

But angle D is 103°

Remember that angles on a straight line sum up to 180°

Then,

103° + Angle A = 180°

Angle A = 180 - 103

Angle A = 77°

It is important to note that sum of angles in a triangle is 180°

angle ACB + angle ABC + angle CAB = 180°

Where;

Substitute into the formula

3x - 14 + 3x + 9 + 77 = 180

collect like terms

3x + 3x = 180 - 72

6x = 108

Make 'x' the subject

x = 108/6

x = 18

But;

Angle ACB = 3x - 14 = 3(18) - 14 = 54 - 14 = 40°

Angle ABC = 3x + 9 = 3(14) + 9 = 54 + 9 = 63°

Thus, the measures of angle ACB and angle ABC are 40° and 63° respectively.

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The coordinates of Point T are (7,4)

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

The [tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

where,

([tex]x_m, y_m[/tex]) = coordinates of the midpoint

([tex]x_1, y_1[/tex]) = coordinates of the first point

([tex]x_2, y_2[/tex]) = coordinates of the second point

So, given that we have a line RT and M is the midpoint of the line RT means  M divides the line in two equal segments.

Let coordinates of M be ([tex]x_m, y_m[/tex]) and coordinates of point R be ([tex]x_1, y_1[/tex]) and coordinates of point T be ([tex]x_2, y_2[/tex]).

So,

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

[tex](3, 0) = (\frac{-1+x_2}{2}, \frac{-4+y_2}{2})[/tex]

on compairing both sides

[tex]3 = \frac{-1 + x_2}{2} \\x_2 - 1 = 6 \\ x_2 = 7[/tex]

Similarly,

[tex]0 = \frac{-4 + y_2}{2} \\y_2 - 4 = 0 \\ y_2 = 4[/tex]

So, the line RT having midpoint M has coordinates of R is (-1,-4) and

T is = (7,4).

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The coordinates of Point T are (7,4)

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

The [tex](x_m,y_m)=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})\\[/tex]

where,

([tex]x_m,y_m[/tex]) = coordinates of the midpoint

([tex]x_1,y_1[/tex]) = coordinates of the first point

([tex]x_2,y_2[/tex]) = coordinates of the second point

So, given that we have a line RT and M is the midpoint of the line RT means  M divides the line in two equal segments.

Let coordinates of M be ([tex]x_m,y_m[/tex]) and coordinates of point R be () and coordinates of point T be ([tex]x_2,y_2[/tex]).

[tex](x_m,y_m)=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})\\[/tex]

[tex](3,0)=(\frac{(-1+x_2)}{2},\frac{(-4+y_2)}{2})\\[/tex]

So, on compairing both sides

[tex]3=\frac{(-4+y_2)}{2}[/tex]

[tex]x_2-1=6\\x_2=7[/tex]

Similarly,

[tex]0=\frac{-4+y_2}{2}\\ y_2-4=0\\\\y_2=4[/tex]

So, the line RT having midpoint M has coordinates of R is (-1,-4) and coordinates of T is = (7,4).

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The angels of parallelogram is 162, 18, 162 and 18.

given that A parallelogram has one angle that measures 18° means one angle is 18°

we know that

A special variety of quadrilateral called a parallelogram has two sets of opposite sides that are parallel and equal.

The sum of all the angels of parallelogram is equal to 360°

so, the other means second angle of parallelogram is 18°

Let us assume the 3rd be x.

then the 4th also be x, because the opposite sides are equal.

now sum of all angles is 360°

then x + 18 + x + 18 = 360

2x + 36 = 360

2x = 360 - 36

x = 162.

so the 3rd and 4th angles are 162°.

Hence the angels of parallelogram is 162, 18, 162 and 18.

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The probability that a randomly selected tire will have a depth less than 0.31mm is 0.03.

From the information, the tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.99mm and a standard deviation of 0.35mm.

The probability that a randomly selected tire will have a depth less than 0.31mm will be:

P(X < 0.31) = P[(Z < (0.31 - 0.99)/0.35]

= P(Z < -1.943)

= 0.025

= 0.03

The probability that a randomly selected tire will have a depth less than 0.31mm is 0.03.

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Based on the amount invested into the two accounts and their interest rates, the amount invested at each rate is:

Assuming the amount invested at 2% is x, then the formula for this amount would be:

0.02x + 0.08 (6,000 - x ) = 360

Solving for x gives:

0.02x + 0.08 (6,000 - x ) = 360

2x + 48,000 - 8x = 36,000

6x = 12,000

x = 12,000 / 6

x = $2,000

The amount invested at 8% is:

= 6,000 - 2,000

= $4,000

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