The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

Answer: no, no, no, yes

Step-by-step explanation:

Hello!

Just take each value of "u" and multiply it by 4. If the answer is smaller than 32, it is a solution. If not, it isn't a solution.

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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The simplest form of the expression (8x²y²) / (10x²y³) has 4 in the numerator and 5y in the denominator. The missing terms are 4 and 5y.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

The given expression,

(8x²y²) / (10x²y³)

In order to simplify the expression,

factor out the greatest common factor.

Here, GCF is 2x²y².

That means,

(8x²y²) / (10x²y³) = (2x²y²)4 / (2x²y²)(5y)

(8x²y²) / (10x²y³) = 4/(5y)

This is required, the simplest form of the expression.

And it has 4 in the numerator and 5y in the denominator.

Therefore, the simplest form of the expression has 4 in the numerator and 5y in the denominator.

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The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The average variable cost for producing 42 sneakers is $2.98 per unit.

Step-by-step explanation:

We have, for 42 sneakers, the following costs:

The total cost for 42 snickers is $243.

The average variable cost can be calculated dividing the total variable cost by the number of units.

This, for 42 snickers, is:

\(\bar{vc}=\dfrac{VC}{q}=\dfrac{125}{42}\approx2.98\)

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

\((3,0)\)

Step-by-step explanation:

Answer:

B. the weight of a dog and the amount of food it eats per day.

This is because dogs only eat around 1/3 of their body weight a day, hence the dogs weight having a positive comparison value to the weight of the food that it eats.

Hope this helps!

Answer: B

Answer:

Step-by-step explanation:

n = 3 => f(n) = -4*-3+8 = -44

n= 0 =>  f(n) = -4*0+8 = 8

n= 2 =>  f(n) = -4*2+8 = 0

n= 7 =>  f(n) = -4*7+8 = -20

Answer:

175

Step-by-step explanation:

Because why would i lie?

The number of square feet of their backyard will NOT be taken up by the pool should be 100 square feet.

Since 1  centimeter represents 5 feet. 4 cm 6 cm And, the area of the Hamiltons' backyard is 900 square feet.

So here it can be like

4cm (5) = 20ft

6cm (5) = 40ft

Now

20ft : 40ft pool

20(40) = 800 square ft

So,

= 900sq ft - 800sq ft

= 100 square feet

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Answer:

emily gets 21 marbles and the other child gets 7 marbles

Step-by-step explanation:

3+1=4

28/4=7

7*3=21

7*1=7

so the ratio between them is 21:7

Answer:

b

Step-by-step explanation:

Answer:

12$

Step-by-step explanation: 100/6 then multiply it by .72=12$

Answer

$12

Step-by-step explanation:

theres a picture on how I did it that I linked.

After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.

So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)

The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.

The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:

Midpoint of JK: (1, -4)

Midpoint of J'K': (4, 1)

The slope of the vector: 3/5

(x₁ + x₂)/2, (y₁ + y₂) /2

Point-slope formula: y - y₁ = m(x - x₁)

Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)

Applying simplification , we get: y = (- 3/5)x - 1.2

To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:

y - 1 = (7/3)( x - 4)

Apply simplification , we get: y = (7/3)x - 17/3

To evaluate the intersection point, we can solve the system of equations:

y =(- 3/5)x - 1.2 = (7/3)x - 17/3

Evaluating for x and y, we get x = -6 and y = -1.

Therefore, the center of rotation is (-6, -1).

√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)

Distance between image points and center of rotation

√( ( 6 - (-6))² + ( 3 - (-1))² = 13

The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).

The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':

Angle of vector: arctan(5/3) = 59.04 degrees

Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

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Answer: The answer is 2x + 7.

Explanation: First, we need to add the numbers:

9x + 3 – 7x + 4

9x + 7 - 7x

And finally, we combine like terms:

9x + 7 - 7x

2x + 7

Answer:

y=11x

Step-by-step explanation:

we use formula y2-y1/x2-x1 with 2 of the order pairs

22-11/2-1

11/1

11 is the slope

We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time

When x is zero y is zero so we write it like this

Y=11x

Hopes this helps please mark brainliest

The order of the graphs from largest to lowest correlation coefficients is:

Graph D, Graph A, graph C, graph B.

The correlation coefficient between two variables is a coefficient that tells us "how much" these variables relate.

So, in the case for linear correlation, as "more linear" the data appears to be, a large correlation is between the two variables.

With that in mind, we conclude that the order of the graphs (going for larger correlation coefficient to smaller correlation coefficient) is:

Graph D, Graph A, graph C, graph B.

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Answer:

35  5/9 cm total

Step-by-step explanation:

24 +   8   +  8/3  +    8 / 9   =  35  5/9 cm

The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

Assume that the total calling time is a linear function of the credit left on a phone card (measured in dollars) (in minutes).

m(call time) + b = credit

The function produces a line with a slope of -0.14 when graphed.

After 43 minutes of calls, the card's balance is $26.02 left.

After 32 minutes of calls, there was 26.02 = -0.14(43) + b b = 26.02+6.02 b = 32.04 C(x) = -0.14x+32.04

credit?

C(32) = -0.14(32) + 32.04\sC(32) = $27.56

After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.

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Answer:

A= 1.50x+75  B= 2.50x+45

Company A is cheaper than Company B when x > 30 miles.

Step-by-step explanation:

Company A charges$75 for the rental even when driving x=0 miles, and will charge and additional $1.50 per mile driven. Therefore the amount Company A would charge for xx miles is:

A=1.50x+75

Company B charges $45 for the rental even when driving x=0 miles, and will charge and additional $2.50 per mile driven. Therefore the amount Company B would charge for x miles is:

B=2.50x+45

When x takes less than 30 miles, Company A is cheaper than Company B. This is the equation of price that companies i.e. A = 1.50x+75 and B= 2.50x + 45.

A linear equation is defined as an equation in which the highest power of the variable is always one.

When driving x = 0 miles, Company A charges $75 for the rental and an additional $1.50 for each mile driven. Thus, the price that Company A would charge for x miles is as follows:

⇒ A = 1.50x + 75

When driving x = 0 miles, Company B charges $45 for the rental and an additional $2.50 for each mile driven. Thus, the price that Company B would charge for x miles is as follows:

⇒ B = 2.50x + 45

Hence, when x takes less than 30 miles, Company A is less expensive than Company B. This is the equation of price that companies i.e. A = 1.50x+75 and B= 2.50x + 45.

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The lottery game is an illustration of probability

Each of the three selections can be any of the 1o digits 0 - 9.

So, the total number of different selections is:

\(n = 10^3\)

\(n = 1000\)

Only one of the 1000 selections can win.

So, the probability of winning is:

\(p = \frac 1{1000}\)

\(p = 0.001\)

The stake amount is given as $1.42, and the earnings per game is given as $264.25.

So, the net profit is:

Net = $264.25 - $1.42

Net = $262.82

This is calculated as:

\(E(x) = \sum x P(x)\)

So, we have:

\(E(x) = 262.82 * 0.001 - 1.42 * (1 - 0.001)\)

\(E(x) = -1.156\)

Hence, the expected earning is -$1.156

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Answer:

8,111 Seconds

Step-by-step explanation:

Answer:

m<1 = 142°

m<3 = 142°

Step-by-step explanation:

We are given two vertical angles, which are <1 and <3.

We know that m<1 = 2x + 26°, and m<3 = 3x - 32°.

We want to find the measure of each angle.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <1 ≅ <3.

This also means that 2x + 26 = 3x - 32.

We can solve the above equation.

Subtract 2x from both sides.

2x + 26 = 3x - 32.

-2x           -2x

_________________

26 = x - 32

Add 32 to both sides.

58 = x

Now, substitute this value of x into the values given.

Substitute x as 58 in 2x+26 to find the value of <1.

m<1 = 2x + 26 =  2(58) + 26 = 116 + 26 = 142°

We can now substitute x as 58 in 3x - 32 to find the value of <3.

m<3 = 3x - 32  =  3(58) - 32 = 174 - 32 = 142°

The total amount that the person with base salary 42000; total sales 175000; commission 4% gets is $51000.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. In this case, the percentage of commission is given as 4%.

The commission will be:

= Percentage × Amount

= 4% × 175000

= 7000

Therefore, the total amount that the person gets will be:

= Salary + Commission

= 42000 + 7000

= $51000

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Answer:

Step-by-step explanation:

1. If a is the length of the side of the square, then a 2 is the area of the square. The rectangle’s side lengths will be (a − 1) and      (a + 1). That product, which represents the area of the rectangle, is a 2 − 1, or 1 square unit less than the area of the square.

2. Using the same logic as for Problem 1, the rectangle dimensions will be     (a + 2) and (a − 2) with an area of a 2 − 4. Therefore, the area of the rectangle is 4 square units less than the area of the original square

3. It is called the product-sum method because you look for the two numbers with a product equal to the constant term of the quadratic expression and a sum equal to the coefficient of the linear term

Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

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

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.