RectangleA′B′C′D′ is the image of rectangleABCD after a dilation.



What is the scale factor of the dilation?


Enter your answer in the box.

Answer:

x = 13

Step-by-step explanation:

Let's simplify and solve for x:

4(x+56.5) = 30x - 112

First, we distribute the 4:

4x + 4(56.5) = 30x - 112

Simplifying the expression:

4x + 226 = 30x - 112

Now we move all the x terms to one side and all the constants to the other:

226 + 112 = 30x - 4x

338 = 26x

Finally, we solve for x by dividing both sides by 26:

x = 13

Therefore, the solution to the equation 4(x+56.5)=30x-112 is x = 13.

Answer:

x=9.94

Step-by-step explanation:

4x + 226 = 30x - 112
226+112 = 34x
338 = 34x
338/34=x
9.94=x

The probability that the next person will purchase no costume is 0.13.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of visitors to the website in a single day is:

38 + 239 + 12 = 289

Of these visitors, we know that 38 purchased no costume.

Therefore, the probability that the next person to visit the website will also purchase no costume is:

38/289 = 0.13

Hence, the probability that the next person will purchase no costume is approximately 0.13, or 13% to the nearest hundredth.

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(Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.

To find the height of an object in mathematics, you must first identify the shape of the object. Then, use the relevant formula for the shape to calculate the height. For example, if the object is a right triangle, the height can be found by using the Pythagorean Theorem. Additionally, if the object is a rectangle, you can use the formula for the area of a rectangle to calculate the height. Finally, if the object is a circle, you can use the formula for the circumference of a circle to find the height.

To solve this question, we will use the numerical approach. First, we need to subtract the number of saplings with a height greater than 27 1/4 inches from the total number of saplings. Then, we subtract the result from the total number of saplings. The result will be the number of saplings with a height of 27 1/4 inches or less.

Therefore, the equation is (Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.

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The choice in the blank to make the statement true will be D. between $17 and $30)

Revenue = Price per book × Number of books sold = (745 - 30P) b

Since the store needs to sell at least 235 books, we have:

Revenue ≥ 235 × Price per book = 235(745 - 30P)

Simplifying this inequality, we get:

745b - 30Pb ≥ 235 × 745

P ≤ (745/30) - (235/b)

Since we want to find the minimum profit per book sold, we need to maximize the value of (235/b). The maximum value of (235/b) occurs when b is minimized

If we assume that the cost per book is constant, then the profit per book sold will increase as the price per book increases. Therefore, we can say that the minimum profit per book sold that would enable the store to sell at least 235 books is greater than $17.

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Answer:

1/2

Step-by-step explanation:

42/84=1/2

Answer:

x = 20

Step-by-step explanation:

x² − 1 = 399

x² = 400

x = 20

In order to create a 28-pound blend that he can sell for $1.45 per pound, the grocer should combine approximately 17.73 pounds of the less costly coffee and 10.27 pounds of the more expensive coffee.

Let's designate the quantity of the less expensive coffee X and the more expensive coffee Y. Since we are aware that the grocer wishes to combine 28 pounds altogether, we can write:

x + y = 28

The total profit from selling the mixture would be: 28($1.45) = $40.60 because we also know that he intends to sell it for $1.45 per pound.

The costs and quantities of the two varieties of coffee can be used to create a new equation.

0.9x + 2.4y = $40.60

With two variables in each equation, we now have two equations that we can solve by substitution or elimination. Use of substitution

28 + y = x - 0.9x + 2.4y = 40.60

0.9x + 2.4(28 - x) = $40.60

0.9x + 67.2 - 2.4x = $40.60\s-1.5x = -$26.60\sx = 17.73

We can apply the first equation to determine y now that we know x: x + y = 28.

17.73 + y = 28 \sy = 10.27

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Answer: You have a probability of 1/2.

Step-by-step explanation: Since there are 12 marbles in total, and there are 6 green marbles, you have a 1 in 2 chance to draw a green marble.

We simplify the summation to get:

S₄ = 8*(3ⁿ⁻¹)

Remember that the large sigma means that we need to add from the lower number to the larger number.

The particular problem here is that "n" is not the index in the summation, so we can't evaluate that variable, we will just have 4 terms (for k = 1 to k = 4) but the variable k does not appear, so we will  have 4 times the same term:

S₄ = 2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹) +  2*(3ⁿ⁻¹)

S₄ = 4*2*(3ⁿ⁻¹)

S₄ = 8*(3ⁿ⁻¹)

That is the simplification we can do.

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The total surface area of the prism is equal to 74 m².

In Mathematics, the total surface area of a triangular prism can be calculated by using this mathematical expression:

Total surface area of triangular prism = (Perimeter of the base × Length of the prism) + (2 × Base area)

Total surface area of triangular prism = (S₁ + S₂ + S₃)L + bh

where:

By substituting the given parameters, we have:

Total surface area of triangular prism = 4 + (5 × 4)3.5

Total surface area of triangular prism = 4 + (20)3.5

Total surface area of triangular prism = 74 m².

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Answer:

False

Step-by-step explanation:

The absolute value of a number is defined as its distance from zero on the number line. Distance is always a non-negative quantity, so the absolute value of a number can never be negative.

Therefore, the absolute value of any number, whether positive or negative, is always a non-negative value.

The arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.

In mathematics, an equation is a statement that two expressions are equal. It typically involves one or more variables that can take on different values, and the goal is often to solve for the value(s) of the variable(s) that make the equation true.

The total circumference of the dartboard is given by:

C = 2πr

where r is the radius of the dartboard.

Substituting the given values, we get:

C = 2π(170 mm)

C = 1068.18 mm

Dividing the circumference by the number of sections, we get the arc length of a single section:

Arc length = C/20

Arc length = 1068.18 mm/20

Arc length ≈ 53.41 mm

Rounding this to the nearest millimeter, we get:

Arc length ≈ 53 mm

Therefore, the arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.

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Answer: 21

Step-by-step explanation:

A= b x h/2

6 x 7/2= 21

Answer: Let's call the portions that the second friend gets "x". Then, the third friend gets four times that amount, which is 4x. Finally, the first friend gets four times the third friend's portion, which is 4(4x) = 16x.

The sum of the portions is equal to the total prize money of $273,000, so:

x + 4x + 16x = 273000

21x = 273000

x = 13000

So, the second friend gets $13,000, the third friend gets four times that amount, which is $52,000, and the first friend gets four times the third friend's portion, which is $208,000.

Step-by-step explanation:

Answer:

180 degree

Step-by-step explanation:

The right triangle equals 180 degree. All three angles must add up to 180.

Answer:

180°

Step-by-step explanation:

right triangles equal 180°

The required equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.

The cosine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.

The graph of the cosine function is a wave-like curve that oscillates between -1 and 1, with a period of 2π radians or 360 degrees.

As we can see, the function's behavior repeats itself. In terms of the form of the function, we may select any interval of length 2π and the following interval of length 2π will be equal to the previous one.

Here, y = 2cos[(π/8)(x-2)-2]

Thus, the equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.

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Answer:

2

Step-by-step explanation:

you first follow the BODMAS law then you divide 1/3÷2/3 It will give you 1/2 so you 3/2-1/2 +1 it will give you 2

Answer: We can plot the given points on a coordinate plane where each unit represents 2 miles:

 y

 |    E(1,2)

 |      

 | M(-4,2)

 |      

 |      

 |H(-4,-1)   F(1,-1)

 |___________________

           x

Now we can see that the distance between the football field (F) and the high school (H) is 5 units in the x direction and 1 unit in the y direction, which corresponds to a distance of 5 x 2 = 10 miles in the x direction and 1 x 2 = 2 miles in the y direction. Using the Pythagorean theorem, we can find the distance between the two points:

distance = sqrt((10)^2 + (2)^2)

        = sqrt(104)

So the distance between the football field and the high school is approximately 10.198 miles. Therefore, the statement that is true is:

"The distance between the football field and the high school is approximately 10.198 miles."

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Let's assume that the customer ordered x burrito bowls.

The cost of x burrito bowls at $6.50 each is 6.50x.

The cost of the plate of corn tacos is $12.96.

The total cost of the order is $32.46.

So we can set up the equation:

6.50x + 12.96 = 32.46

Subtracting 12.96 from both sides, we get:

6.50x = 19.50

Dividing both sides by 6.50, we get:

x = 3

Therefore, the customer ordered 3 burrito bowls.

Answer:

Below

Step-by-step explanation:

A cube has SIX sides of equal area

  each side has area = L x W       and L and W are the same = 4.5 m

      so:   Area =   six   X   ( 4.5  X 4.5)  =   6 * 4.5 * 4.5 = 121.5 m^2

Answer:

Hope the picture will help you...

Answer:

the answer is d because 2.2 6+2 with a exponent of 3 = 14 and 14 is less than 20

Step-by-step explanation:

The probability that one client drives less than 10,000 miles a year and has an accident is 0.06.

Given is a table as shown in the image attached.

It is aske to find the probability that one client drives less than 10,000 miles a year and has an accident. Form the table, we can write the cell corresponding to driving less than 10,000 miles and having the accident as 0.06.

Therefore, the probability that one client drives less than 10,000 miles a year and has an accident is 0.06.

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Answer:

96in²

Step-by-step explanation:

64+((4*8/2)*2)=96in²

Answer:

68

Step-by-step explanation:

x = original number of marbles

x = 104 - 36

x = 68

Answer:

   1. Gross pay = hourly rate x hours worked

   Gross pay = $14 x 32 = $448

   2. Net pay = gross pay - deductions

   Federal taxes = 10% of gross pay = 0.1 x $448 = $44.80

   State taxes = 4.5% of gross pay = 0.045 x $448 = $20.16

   FICA = 6% of gross pay = 0.06 x $448 = $26.88

   Total deductions = $44.80 + $20.16 + $26.88 = $91.84

   Net pay = $448 - $91.84 = $356.16

   3. Gross pay = hourly rate x hours worked

   Gross pay = $17 x 40 = $680

   4. Regular pay = hourly rate x hours worked

   Regular pay = $20 x 40 = $800

   Overtime pay = (hourly rate x 1.5) x overtime hours

   Overtime pay = ($20 x 1.5) x 5 = $150

   Gross pay = regular pay + overtime pay

   Gross pay = $800 + $150 = $950

   5. Net pay = gross pay - deductions

   Federal taxes = 14% of gross pay = 0.14 x $950 = $133

   State taxes = 4.5% of gross pay = 0.045 x $950 = $42.75

   FICA = 6% of gross pay = 0.06 x $950 = $57

   Total deductions = $133 + $42.75 + $57 = $232.75

   Net pay = $950 - $232.75 = $717.25

Step-by-step explanation:

For function f(x)= -4x²-4x-1,   f(x+h)= -4x² - 8xh - 4h² - 4x - 4h - 1, (f(x+h) - f(x))/h= -8x - 4h - 4

The input values of a function are called the domain, and the output values are called the range. The domain can be any set of values, but each input value must have a unique corresponding output value. If there are multiple input values that produce the same output value, the function is not considered to be well-defined. Functions are used to model a wide range of phenomena in many different fields, including science, engineering, and economics. They are also used in calculus to study rates of change and slopes of curves.

To find f(x+h), we need to replace x with (x+h) in the given function:

f(x+h) = -4(x+h)² - 4(x+h) - 1

= -4(x² + 2xh + h²) - 4x - 4h - 1

= -4x² - 8xh - 4h² - 4x - 4h - 1

To find (f(x+h) - f(x))/h, we first need to find f(x):

f(x) = -4x² - 4x - 1

Then we can substitute f(x+h) and f(x) in the formula:

(f(x+h) - f(x))/h = (-4x² - 8xh - 4h² - 4x - 4h - 1 - (-4x² - 4x - 1))/h

= (-4x² - 8xh - 4h² - 4x - 4h - 1 + 4x^2 + 4x + 1)/h

= (-8xh - 4h² - 4h)/h

= -8x - 4h - 4

So, f(x+h) = -4x² - 8xh - 4h² - 4x - 4h - 1, and (f(x+h) - f(x))/h = -8x - 4h - 4.

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Answer:

Step-by-step explanation:

5/6 - 2/5 = 25/30 - 12/30 = 13/30

Answer:

Step-by-step explanation:

To subtract two fractions, we need a common denominator. The smallest number that 6 and 5 both divide into is 30.

Converting the fractions to have 30 as the denominator, we get:

5/6 = 25/30

2/5 = 12/30

Now we can subtract:

25/30 - 12/30 = 13/30

Therefore, 5/6 - 2/5 = 13/30 in simplest form.

Making linear equations for given scores, Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.

What is a linear equation, exactly?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable, with the degree of each variable being 1. In other words, a linear equation is an equation of a straight line, which can be expressed in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept of the line. Linear equations are used to model relationships between variables that have a constant rate of change, such as distance traveled over time or cost per item.

Now,

Let's assume that Grace's score is x.

Then, John's score will be x-4.

And, Julius's score will be x-4+5 = x+1.

The sum of their scores is given as 150. So, we can write an equation as:

x + (x-4) + (x+1) = 150

Simplifying the equation, we get:

3x - 3 = 150

Adding 3 to both sides, we get:

3x = 153

Dividing by 3 on both sides, we get:

x = 51

So, Grace's score is x = 51.

John's score is x-4 = 47.

And, Julius's score is x+1 = 52.

Therefore,

                      Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.

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Answer:

34 Foot

Step-by-step explanation:

You're basically just doing the pythagorean theory: a^2+b^2=c^2

You just are not directly being given a or b and instead you have to find them which you do by subtracting how big the garden is from the total length: 50-20=30(a) 30-14=16(b). After that you just do the normal theory getting 30^2+16^2=c^2 which leads to 900+256=c^2 then 1156=c^2 so you take the square root of both sides in order to turn c^2 into plain c or the length of the walk way which will get you 34 feet.