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

The equivalent expressions from the list will be 8 + 32y and 8•1+8•4y. Then the correct options are B and C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 8(1 + 4y)

Simplify the expression, then we have

⇒ 8(1 + 4y)

⇒ 8 + 32y

The equivalent expressions from the list will be 8 + 32y and 8•1+8•4y. Then the correct options are B and C.

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Answer:If Rafael has saved $16, which is one-fourth of the total cost of the game, then the total cost of the game is 4 times the amount he has saved. So, the game costs:

$16 * 4 = $64

Therefore, the game costs $64.

Step-by-step explanation:

If Rafael has saved $16, which is one-fourth of the total cost of the game, then the total cost of the game is 4 times the amount he has saved. So, the game costs:

$16 * 4 = $64

Therefore, the game costs $64.

Theo used 2250 milliliters of water to water the garden.

Theo filled a watering can with 3 liters of water to water the garden. After using some of the water, he has 750 milliliters left in the can.

The amount of water used by Theo can be calculated by subtracting the remaining water from the total amount of water filled in the watering can.

For this, we first need to equate the unit of water present in the can initially with the amount of water left in the can.

We know, 1 liter = 1000 milliliters

Therefore, 3 liters = 3000 milliliters

This means that he used a total of 3000 milliliters - 750 milliliters = 2250 milliliters of water to water the garden.

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The value of b is 4.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

We can make the ordered pairs (x, y).

Where x is the number of quarters and y is the number of playable characters.

Now,

A video game was released with 4 playable characters.

This means,

(0, 4)

Now,

The video game company has a plan to add 6 new characters every quarter (every 3 months).

This means,

(1, 10)

(2, 16)

(3, 22)

Now,

y = mx + b

Now,

Take any two ordered pairs:

(1, 10)

(2, 16)

m = (16 - 10) / (2 - 1)

m = 6

Now,

(0, 4) = (x, y)

4 = 6 x 0 + b

b = 4

Thus,

4 is the value of b.

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First-principle differentiation of sec x results in ten times sec x.

Regarding the variable x, y = f(x). Wherever the limit occurs is defined to be the derivative of f at x if this limit exists and is finite. The first principle of derivative is another name for this definition.

Sec x tan x is, as far as we are aware, the derivative of sec x. Determining that sec x equals the integral of sec x tan x. Specifically, sec x tan x dx = sec x + C

On a graph, the first derivative shows the slope of the function at a particular position, while the second derivative shows how the slope changes as the independent variable is changed. The second derivative accounts for the curve in the above graph for a function with a variable slope.

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The minimum of y = f(x) occurs at (x,y) = (3,1). Hence y= f(x) >=1 for all other x in its domain of definition.

What is Quadratic equation ?

Quadratic equation can be defined as equation in which it is in the form of ax^2 + bx + c = 0

where c is a constant.

y = f(x) + 3 merely increases the value y by 3 for any x, or just raises its graph up 3. The x-value for its minimum remains at x=3 and y = f(3) + 3 = 1 + 3 = 4.  Hence, new minimum = (3,4)

y = f(x-2) just shifts or translates the graph of f to the right by 2.  So what occurred at x=3 (the minimum y) now occurs at x=5  without changing y = 1.  Hence, new minimum = (5,1).

y = f(1.5x) compresses the x-scale without changing y.  So what happened at x=3 before now happens at x'=2 on the new scale.

Therefore, the minimum point now becomes  (2,1).

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The probability that exactly 10 of the 20 women have dark eyes is 0.2051.

The theory used in this question is the binomial probability formula, which is used to calculate the probability of a certain number of successes in a given number of trials.

The steps for this process are as follows

Step 1: Calculate the binomial formula: (n!)/(x!(n-x)!) * p^x * (1-p)^(n-x),

where n is the number of trials (in this case, 20), x is the number of successes (10), p is the probability of a success (0.40 in this case), and n-x is the number of failures (10).

Step 2: Plug the values into the formula: (20!)/(10!(20-10)!) * 0.40^10 * (1-0.40)^(20-10)

Step 3: Simplify the formula: (20*19*18*17*16*15*14*13*12*11) / (10*9*8*7*6*5*4*3*2*1) * 0.40^10 * 0.60^10

Step 4: Calculate the result: 0.2051

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you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

What is meant by arithmetic ?

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Answer: 900 peaches

Step-by-step explanation:

cuz please thank

Slowest growing plant is plant A.

The Slope (also called Gradient) of a line shows how steep it is.

To calculate the Slope:

Divide the change in vertical distance by the change in horizontal distance

Given,

Amir grows three plants,

Graph of plant A is given with straight line,

Height is denoted on x axis,

Time is denoted on y axis

Slope of the line will represent growth rate.

Line passes through (1,2) and (2,4)

slope of the line

= y-y'/x-x'

= 2 - 4/1 - 2

= - 2 / - 1

= 2

Growth rate = 2 inches per month

For plant 2

by the table,

Height  is 15 inches in 6 months.

Growth rate = 15/6 = 2.5 inches per month

Equation for plant 3

h = 3.5t

Slope of the equation = 3.5

Growth rate = 3.5 inches per month

By the above calculation,

Growth rate of plant A is least.

Hence, Plant A is growing slowest.

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Answer:

see below

Step-by-step explanation:

let n = x-5

so 3n+8n = 22

n = 22/11 =2

so x-5=2

x=7

Answer:

A' (-2, -1.5)

B' (-2, 1.5)

C' (1, 1.5)

D' (1, -1.5)

Step-by-step explanation:

If you start at (0,0) and go to Point A, you go 4 to the left and down 2.  Half of that is left 3 and down 1.5.  That is where A' will go.  Do the same thing to the other 3 points.

Answer:

18.33 m/s

Step-by-step explanation:

Convert units.

1 km = 1000 m

1 h = 3600 s

66 km/h × (1000 m)/(1 h) × (1 h)/(3600 s) = 18.33 m/s

Answer:

10 years

Step-by-step explanation:

principal = 6000

int = 7.5% annual compounding CONTINUOUSLY = everyday

so every day of the year he gets 7.5% / 365

so annual effective rate =7.7876%

so to get to 12500 it'll take t years

12500 = 6000* (1+ 7.7876% )^t

2.0833=1.077876^t

solve for t

approximately 10 years

The initial valuation of each asset Samtech acquired in transactions:

Value capitalized  = $4,000,000 + $16,000 + $5,000 + $4,000

Value capitalized   = $4,025,000

Assets              Fair value       Total percentage      Proportional value

1.Land           $3,300,000             75%                        $2,475,000

2.Building       $1,100,000             25%                        $275,000

Total              $4,400,000           100 %                      $2,750,000

Working Notes :

Land =($3,300,000 ÷ $4,400,000) =75%

Building =($1,100,000 ÷ $4,400,000) = 25%

Land Improvement =$82,000 + $40,000 =$122,000

2) The initial valuation of each asset assumes that immediately after acquisition that Samtech demolished the building:

  Entries                                                               Amounts

1. Purchase cost                                                  $4,000,000

2. Add: Title insurance of                                     $16,000

3. Add: Legal fees for drawing the contract         $5,000

4. Add: State transfer fee of                                  $4,000

5. Add: Demolition cost                                        $250,000

6. Add: Cleaning and grading cost                     $86,000

7. Less: Salvage material                                     $6,000

    Total Cost of land                                          $4,355,000

Land Improvement = $82,000 + $40,000 = $122,000

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The complete question is:

Samtech Manufacturing purchased land and building for $4 million. In addition to the purchase price, Samtech made the following expenditures in connection with the purchase of the land and building: Title insurance $ 16,000 Legal fees for drawing the contract 5,000 Pro-rated property taxes for the period after acquisition 36,000 State transfer fees 4,000 An independent appraisal estimated the fair values of the land and building if purchased separately, at $3.3 and $1.1 million, respectively. Shortly after the acquisition, Samtech spent $82,000 to construct a parking lot and $40,000 for landscaping. Required: 1. Determine the initial valuation of each asset Samtech acquired in these transactions. 2. Determine the initial valuation of each asset, assuming that immediately after acquisition, Samtech demolished the building. Demolition costs were $250,000 and the salvaged materials were sold for $6,000. In addition, Samtech spent $86,000 clearing and grading the land in preparation for the construction of a new building.

Using the quadratic formula we will see that the solutions are:

u₊  = 2

u₋ = -1/3

Here we have the quadratic equation:

3u² -2 = 5u

We can rewrite that in the general form so we get:

3u² -2 - 5u = 0

Now we can use the quadratic formula to find the solutions, we will get:

[tex]u = \frac{5 \pm \sqrt{(-5)^2 - 4*-2*3} }{2*3} \\\\u = \frac{5 \pm 7 }{6}[/tex]

Then the two solutions are:

u₊ = (5 + 7)/6 = 2

u₋ = (5 - 7)/6 = -2/6 = -1/3

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Answer:

Step-by-step explanation:

After his football game malik drinks 1/2 Liter of water and the 1/3 liter of juice did malik drink more juice draw an estimate to partition explain your answer

After his football game, Malik drank 1/2 liter of water and 1/3 liter of juice. To compare the amounts, we can draw an estimate by partitioning the 1 liter unit into equal parts. For example, we can divide 1 liter into 6 parts, each representing 1/6 of a liter.

If 1/2 liter of water is represented by 3 parts, then 1/3 liter of juice is represented by 2 parts. We can see that Malik drank more water than juice. This is because the partition representing 1/2 liter of water is longer than the partition representing 1/3 liter of juice.

Therefore, the answer is that Malik drank more water than juice.

Answer:

see below

Step-by-step explanation:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The four properties of parallelogram are:

i) Opposite sides are parallel & equal.

ii) Sum of adjacent interior angles is 180°

iii) Opposite angles are equal.

iv) Diagonals bisect each other.

The quadrilateral with two pairs of parallel sides is known as a parallelogram. Equal in length and width on both sides is required. Four vertices make up a parallelogram, which also has four edges.

A parallelogram is a two-dimensional (2D) shape that has two matching pairs of opposite sides that are parallel and equal in length. The angles inside the two sides of the shape must add up to 180 degrees, which means that all of the angles must add up to 360 degrees.

A rectangle that has been pushed over slightly is all that a parallelogram really is. Because of this, finding the area of a parallelogram can be done using the same formula as finding the area of a rectangle.

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Using the concept of ratio in the similar triangles, the length scale factor is 1:25

Similar triangles are triangles that have the same shape but may be scaled differently. Two triangles are considered similar if and only if their corresponding angles are congruent (equal in measure) and the ratio of their corresponding sides is the same. This property is known as the "AA Similarity Postulate" or "Angle-Angle Similarity".

In other words, similar triangles have the same shape and proportional sides. This means that if two triangles are similar, corresponding sides are in proportion and corresponding angles are equal in measure.

In the given figures, the two triangles have areas of 3m² and 75m²

The formula of area of a triangle is given as ;

A = 1/2 (b * h)

Assuming the side lengths are equal, we can apply heron's formula which is given as;

S = [a + b + c / 2]

A = √s(s - a)(s - b)(s - c)

But a = b = c

Using the two triangles to find the ratio between the ratios;

Q : R = 3 : 75 = 1 : 25

The length will be given as;

Area = 1/2 b * h

b = h

75 = 1/2 * a * a

a² = 75 * 2

a² = 150

a = √150

In the second triangle;

3 = 1/2(b²)

6 = b²

b = √6

The ratio between Q to R = √6 : √150 = 1 : 25

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I redrawn the line in the picture. Hopefully this helps you

Answer:

2007 and beyond.

Step-by-step explanation:

y = 34  ==> y doesn't equal 34 billion as y is already measured in billions

Since y=10.5x:

34 = 10.5x  ==> solve for x

x = 34 / 10.5   ==> divide both sides by 10.5

x = 3.2  ==> x is approximately 3.2 years

2004 + 3.2 = 2007.2

2007.2 rounded to the nearest year is 2007

Hence, businesses will spend more than $34 billion in the year 2007 and beyond.

Based on the information provided, the two whose is 101 are 1010 and 1313.

?

The is the highest common factor or in other words, the highest by which two numbers can be divided. Let's start by listing the four digits that can be the related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these numbers, there are two numbers whose difference is

1313 - 1010 = 303

Based on this, the two numbers are and

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Find two numbers whose difference is 303, hcf is 101 and are 4 digits long.

Start by writing down two 4-digit numbers that have a difference of 303. The two numbers should be close together, but not the same number. For example, you could choose 9801 and 9498.

Next, find the factors of each number. For 9801, the factors are 3 x 3 x 11 x 101 and for 9498 the factors are 2 x 7 x 13 x 101.

Now, find the Highest Common Factor (HCF) of the two numbers. To do this, you can look at the factors of both numbers and find which ones are the same. In this case, the HCF is 101.

Finally, check if the difference between the two numbers is still 303. As 9801-9498 = 303, this is correct. Therefore, 9801 and 9498 are the smallest pair of 4-digit numbers with a difference of 303 and an HCF of 101.

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Percentage of sandwiches out of all lunch orders = 61%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Order of sandwich = 61%

Total lunch order = 100%

Percentage of sandwiches = 61%

Hence, There are 61% of sandwiches out of all lunch orders.

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True, when students are asked to list their age and the percentage of their college expenses that they pay for themselves, the type of data being collected is quantitative.

The data being collected is quantitative because both age and the percentage of college expenses paid for oneself are numerical values that can be quantified and measured. Age can be expressed in years and the percentage of college expenses can be expressed as a decimal or a percentage (e.g. 50%). This type of data can be analyzed using mathematical operations and statistical methods.

Hence, when students are asked to list their age and the percentage of their college expenses that they pay for themselves, the type of data being collected is quantitative.

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Answer:Let's call the distance of the boat trip "d".

Since the whole trip took 5 hours, and Maxwell was driving for part of it, we know that:

d/40 + x/60 = 5

where x is the number of hours Maxwell spent driving.

We also know that the distance he drove is equal to the total distance minus the boat trip:

275 - d = x * 60

So we can substitute this into the first equation:

d/40 + (275 - d)/60 = 5

Expanding and simplifying this equation gives us:

6d = 1800

Finally, dividing both sides by 6 gives us:

d = 300

So the boat trip was 300 miles long.

Step-by-step explanation:

Let's call the distance of the boat trip "d".

Since the whole trip took 5 hours, and Maxwell was driving for part of it, we know that:

d/40 + x/60 = 5

where x is the number of hours Maxwell spent driving.

We also know that the distance he drove is equal to the total distance minus the boat trip:

275 - d = x * 60

So we can substitute this into the first equation:

d/40 + (275 - d)/60 = 5

Expanding and simplifying this equation gives us:

6d = 1800

Finally, dividing both sides by 6 gives us:

d = 300

So the boat trip was 300 miles long.

Answer:

Step-by-step explanation:

We will have 0.44 or 44% of original money after 8 quarters. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Four fundamental mathematical operations can be used to represent any real number, and they are as follows:

1. The sum of the numbers is calculated using the addition operator ('+').

2. Subtraction with the "-" sign, which results in the difference between the numbers.

3. Multiply ('×') the result when it is the product of the numbers.

4. Division ('÷'), which yields the numbers' quotient.

We are given that we started the company with $5,000,000 and we lose 7% of that start up cash every quarter.

So,

Amount lost every quarter = $5,000,000 * 7% = $350,000

Now,

Amount lost in 8 quarters = $350,000 * 8 = $2,800,000

Therefore,

Money left = $5,000,000 - $2,800,000 = $2,200,000

Thus,

Percentage left of original money = $2,200,000/$5,000,000 * 100 = 44%

Hence, we will have 0.44 or 44% of original money after 8 quarters.

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The number of pints of ice cream used for each sundae is 0.8 pints.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

4 pints of icecream = 5 sundaes

Divide both sides by 5.

4/5 pints of icecream = 1 sundaes

0.8 pints of icecream = 1 sundaes

Thus,

0.8 pints of ice cream is used for each sundae.

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The length of line segment Dc is equal to 35 units.

In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Since side length DE is parallel to AB and side DE is 5 less than side length DC, we have the following:

DE = DC - 5

In Geometry, the corresponding side lengths of two similar geometric figures are proportionate and as such, we have the following:

DC/AC = DE/AB

DC/56 = DC - 5/48

48DC = 56(DC - 5)

48DC = 56DC - 280

56DC - 48DC = 280

8DC = 280

DC = 280/8

DC = 35 units.

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Answer:

B = 10/19 it's a fraction btw