find the length of the side labled x

The piecewise function represented by the graph is:

A piecewise function is a function that has different definitions, depending on the input.

For x to the left of 0, inclusive, the function is constant at y = -3, hence the definition is:

f(x) = -3, x ≤ 0.

For x to the right of 0, with an open interval, the function is linear, with an intercept of 3(when x = 0, y = 3) and a slope of -3(the function fell from y = 3 to y = 0 when x moved from x = 0 to x = 1), hence:

f(x) = 3 - 3x, x > 0.

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Supplementary angles have a sum of 180°

Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.

( 7x - 15 ) + ( 2x - 3 ) = 180

Now we can combine like terms and use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x  = 198

9x/9 = 198/9

x = 22

Then Angle A will have a measure of 7x - 15 or 7• 22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle b will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

NOTE:  139 + 41 = 180

The value of the other angle will be 40°.

It should be noted that the value of the angle on a straight line equals to 180°.

In this case, the adjacent angles (two angles that share a common side and vertex) form a straight

angle and one of the angles measures 140°.

The value of the other angle will be:

= 180° - 140°

= 40°

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Answer:

give me one second brooo

Explanation:

The inequality that represents the possible area of the triangle is 2/7a < 10

The solution to the inequality is a < 35

From the question, we are to write and solve an inequality that represents the possible area, a, of the triangle

From the given information,

The base of the triangle is given by

b = 2/7a

Also, from the given information,

The base of the triangle is less than 10

That is,

b < 10

Then,

we can write that

2/7a < 10

This is the inequality that represents the possible area of the triangle

Now, solve the inequality

2/7a < 10

Multiply both sides of the equation by 7/2

7/2× 2/7a < 7/2× 10

a < 7 × 5

a < 35

Hence, the inequality that represents the possible area of the triangle is 2/7a < 10

The solution to the inequality is a < 35

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The answers to both the subparts are as follows:

So, the cycle's velocity-time graph:

Now,

Then,

Therefore, the answer to both the subparts are as follows:

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The coordinates of the given points are:

Refer to the diagram to know the coordinates of the given points.

Therefore, the coordinates of the given points are:

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Answer:

9

Step-by-step explanation:

Answer:

F is inversely proportional to d^2when F=9,d=

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Area equal LxWxH

2x2.5x3.5=17+5

The amount of material needed to make the box is 41.5 ft².

The surface area of a figure is the number of unit squares it takes to cover the entire surface without gaps or overlaps. If a three-dimensional figure has flat sides, the sides are called faces. The surface area is the total of the areas of the faces.

Given that, a rectangular storage box is to be made with length is 3.5 feet, the width is 2 feet, and the height is 2.5 feet.

For finding the same, we will find the surface area of the box,

Surface area of the box = 2(length·width + width·height + height·length)

Therefore,

SA = 2(3.5x2+2x2.5+3.5x2.5)

SA = 2 x 20.75

SA = 41.5

Hence, the amount of material needed to make the box is 41.5 ft².

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Answer:− 9/56

​

Step-by-step explanation: hope this helps you!!!!

The population that would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases is All 513 bolts that were randomly selected.

Generalizing the conclusions from a study can only be done with a sample that is well-represented. The question here says that all 513 bolts were chosen without bias. This means that a fair conclusion can be reached from the sample.

So, the results that occur from studying the 513 bolts can be sure to produce accurate results. Moreso, the population is large, thus, the population can be used to generalize conclusions.

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The measure of angle COD will be 85° and it will be an acute angle.

If an angles is less than 90°, it is known as an acute angle. If it is more than 90°, it will be an obtuse angle. And if it is equal to 90, then it is called a right angle.  

Here, we are given a a figure and we need to find the measure of ∠COD.

∠COD can be written as ∠AOB - ∠AOC - ∠DOB

Here, ∠AOB = 180° (straight line)

∠AOC = 30°

and ∠DOB = 65°

Thus, ∠COD = 180 - 30 - 65

∠COD = 180 - 95

∠COD = 85°

As ∠COD is less than 90°, it will be an acute angle.

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Answer:D

Step-by-step explanation:

√81 - √25 = 9 - 5 = 4

√64 + √25 = 8 + 5 = 13

√64 - 31 = 8 - 31 = -23

Using proportions, her commission would be of $3,700.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Her commissions are divided as follows:

Hence the total commission is:

0.15 x 5000 + 0.25 x 1000 + 0.3 x 9000 = $3,700.

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It will take 4 hours for both companies to equal the same price and it will cost $ 90 at that time.

There are two companies:

Company A-
It charges $ 50 to come and $ 10 per hour to work.

Let the number of hours worked be x

The equation will be:

Price of Company A = 50 + 10 x   …(1)

Company B-

It charges $ 30 to come and $ 15 per hour to work.

The equation will be:

Price of Company B = 30 + 15 x    …(2)

Now, for the same prices, we will equate (1) with (2):

50 + 10 x = 30 + 15 x

15 x - 10 x = 50 - 30

5 x = 20

x = 20 / 5

x = 4

At x = 4, price of the companies will be:

A = 50 + 10 (4) = 50 + 40

A = $ 90

B = 30 + 15(4)

B = 30 + 60

B = $ 90.

Therefore, it will take 4 hours for both companies to equal the same price and it will cost $ 90 at that time.

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The sum of the multiples of 9 till 81 is 405 by arithmetic progression.

We have to sum the multiples of 9 up to 81

= 9 + 18 + … +  45  + …+ 72 + 81

We will use arithmetic progression for this.

we get that:

initial term = a = 9

Common difference = d = 9

n = 9

Sum of terms = n / 2 ( 2 a + ( n - 1) d )

Sum = 9 / 2 (2( 9) + 8 ( 9))

sum = 9 / 2 (18 + 72)

Sum = 9 / 2 ( 90)

Sum = 810 / 2

Sum = 405

Therefore, we get that, the sum of the multiples of 9 till 81 is 405 by arithmetic progression.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\ax+by=c\\\\by=c-ax\\\\\frac{by}{b}=\frac{c-ax}{b} \\\\y=\frac{c-ax}{b}[/tex]

Answer: Basically, bottom is first. The top is second, and the middle one is last.

Step-by-step explanation:

1. Super Duper Easy, first, subtract ax, making it by = c - ax

2. Then, divide b , so by/b = c/b - ax/b

3. Becoming y = c/b - ax/b

Answer:

a bunch of gas money

Step-by-step explanation:

Answer:

Increased towing capacity

Step-by-step explanation:

?

50 books can be purchased with $ 350.

We have the data:

Books Cost (dollars)    Amount left (dollars)

            1                                    343

            2                                   336

            3                             336 - 7 = 329

            4                             329 - 7 = 322

            7                             322 - 21 = 301

           14                             301 - 49 = 252

Cost of 1 book = $ 7

Cost of b books = 7 × b = 7 b    

Amount of budget after b books = 350 - 7 b

We can buy = 350 / 7 = 50 books before spending the entire amount.

Therefore, we get that 50 books can be purchased with $ 350.

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The correct option is b. 16.67 acres would the lot next to it contain if it has a 900' frontage and is the same width as the first rectangular lot.

The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.). The quantity of unit squares that can fit inside a rectangle called its area. Blackboards, painting canvases, laptop monitors, and other flat surfaces are a few instances of rectangular shapes.

Area of a Rectangle = (Length × Breadth) square units.

We know that the Area = Length × Width.

For first lot:

43,560 (sq. ft. in acre) × 25 acres = 1,089,000 sq. ft.

We know that 1,089,000 sq. ft. = Width × 1,350 (length). Therefore width =1,089,000 / 1,350 = 806.67.

From the problem the lots were of the same width.

In second lot: Area =806.67 (width) × 900( length)= 726,000 sq. ft. Therefore:

⇒726,000 (area) / 43,560 = 16.67 acres.

The correct answer is:  b. 16.67 acres

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Answer:

32ft

Step-by-step explanation:

According to the question, let us consider the random variable for the discrete uniform distribution to be x.

What is the discrete uniform distribution?

Uniform distribution is another name for the rectangular distribution. And it is the family of the symmetric probability distribution. It has constant probability and the outcomes are equal in nature.

The standard formula for the mean and the variance of the distribution in terms of the lower bounds(L) and the upper bounds(U) is as follows:

Mean = (L+U)/2 ;

Variance = (L+U)/12

The value of the lower bound(L) is 1000 and the upper bound(U) is 1500.

The calculation is as follows:

Mean = (1000+1500)/2 = 1250

Variance =  (1000+1500)/12 = 208.3

Therefore, the values are: mean = 1250 and variance = 208.3

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Answer:its 180 cm

Step-by-step explanation:

Jason is incorrect, because inequality signs change when we multiply/divide by negative numbers, and we need to follow the signs to make sure we use the correct one.

Well, Jason says that you can solve an inequality by replacing the sign by an equal sign, solve the equation as you already have done a thousand times, and then put the inequality sign again.

Now, this is clearly incorrect, because inequalities have a really nice property. If you multiply or divide both sides of the inequality by a negative number, then the "direction" of the sign changes.

This means that if we have an inequality like:

-2x > 10

And we divide both sides by -2, we should get:

x < 10/-2

x < -5

Where the direction of the sign changed.

If you did what Jason said, the direction of that sign would not have changed, and thus, you would have got an incorrect solution for the inequality.

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The discount rate, as a percent is 20%

The given parameters are:

Cost of 1 T-shirt = $15.97

Also, we have

4 purchases gives 1 free item

So, the discount rate is

Discount = 1/(1 + 4) * 100%

Evaluate the sum

Discount = 1/5 * 100%

Evaluate the product

Discount = 20%

Hence, the discount rate, as a percent is 20%

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The equation of Leo's line is given by: 3 (y - G) = ( F - x)

Given: An equation of a line on a grid, about which another line is perpendicularly.

To find: Equation of the perpendicular line.

Finding:

=> m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{4-1}{2-1}=\frac{3}{1} = 3[/tex]

The equation of the line becomes:  [tex]y-y_0=3(x-x_0)[/tex]

    2. Since the line passes through (1,1), the final equation of the line can be given by:

=> y - 1 = 3 ( x - 1)

=> y = 3x - 3 + 1

=> y = 3x - 2

=> m' = -1/m

=> m' = -1/3

=> [tex]3(y-y_0)=(x_0-x)[/tex]

    2. Since the perpendicular line passes through the point (F,G), the equation of the line will be: 3 (y - G) = ( F - x).

Hence, The equation of Leo's line is given by: 3 (y - G) = ( F - x).

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The smallest n such that 1 can be written as a sum of n

special numbers is 8.

A number is a mathematical concept that is used for counting, measuring, and labeling. The natural numbers 1, 2, 3, 4, and so forth are the original examples. Number terms in language can be used to represent numbers. More commonly, individual numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five. Basic numerals are frequently arranged in a numeral system, which is an ordered manner to represent any number, as only a very small number of symbols can be learned. The most widely used numeral system is the Hindu-Arabic numeral system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."

Calculations:

Suppose 1 = x1 + x2 + · · · + xn where x1, x2, . . . , xn are special and

n ≤ 9. For k = 1, 2, 3, . . . , let ak be the number of elements of {x1, x2, . . . , xn}whose kth decimal digit is 7. Then

1 =7a1}/10 +7a2/10 +7a3/10 + ... ,

which yields

1/7 = 0.142857 =a1 /10 +a2/[tex]10^{2}[/tex] +a3/[tex]10^{3}[/tex] + ... ,

Hence a1 = 1, a2 = 4, a3 = 2, a4 = 8, etc. In particular, this implies that n ≥ 8. On

the other hand,

x1 = 0.700, x2 = x3 = 0.07, x4 = x5 = 0.077777, and x6 = x7 = x8 = 0.000777

are 8 special numbers whose sum is

(700700+2(70707)+2(77777)+3(777))/{999999} =1

Thus the smallest n is 8.

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Answer:

Since there are a total of six friends and they each use a $2 off coupon then what you first want to do is multiply:

2 times 6 = 12

Then you want to add:

42 + 12 = 54

So the total that they would have spent without the discount would be $54.

Step-by-step explanation:

Hope it helps! =D