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 simple interest is 2112.5 and the maturity value is 21,612.5

In the given question,

We have to find the simple interest and maturity value.

The given principal amount (P)= 19,500

The interest rate (r)= 6 1/2%

We write the interest in improper fraction. We can write it as 6 multiple with 2 then adding the result of multiplication with 1.

So the simplest form (r)=13/2%

Time = 20 months.

Now converting the months into years.

As we know that in one year have 12 months.

So the Time = 20/12

Time (T)= 5/3

The formula of simple interest is

I = P*R*T/100

Now putting the value

I = 19,500*(13/2)*(5/3)/100

Simplifying

I = 19,500*13*5/100*2*3

I = 1,267,500/600

I = 2112.5

Hence, the simple interest is 2112.5.

Now finding the maturity value(MV).

MV=P+I

MV=19,500+2112.5

MV=21,612.5

Hence, the maturity value is 21,612.5

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Answer: no slope

Step-by-step explanation:
m= y2-y1/x2-x1

m= 6-(-6)/4-4

m=12/0

m= no slope

Answer:

y = 0.8x - 0.8

Step-by-step explanation:

Δy ÷ Δx = gradient (x)

4 - -4 = 8

6 - -4 = 10

8 ÷ 10 = 0.8

equation of line; y = mx + c

substitute one of the coordinates into the equation

(6, 4) y  = 4, x = 6

4 = 0.8(6) + c

4 = 4.8 + c

- 4.8 to get the y intercept on it's own

-0.8 = y intercept (c)

confirmation

substitute the new values to get the other y

(-4, -4) y = -4 <-- should be the answer, x = -4

y = mx + c

y = 0.8(-4) - 0.8

y = -3.2 - 0.8

y = -4 the gradient and the y intercept have been proven right

5 is the difference between the two numbers 12 and 7.

Given,

In the question;

The difference between 3 times a number and 7 is 5.

Write and solve an equation to determine the number.

Now, According to the question:

Let's assume the unknown number to be x,

so three time the number would be 3x.

The difference between 3 times a number (3x) with 7 is 5, so we can write it as:

3x - 7 = 5

Now we can solve this equation to the find x (the unknown number).

3x = 5 + 7

3x = 12

x = 12/3

x = 4

Therefore 3x= 12

So, 5 is the difference between the two numbers 12 and 7.

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The values from the parent function are a = 1, b = -6, h = 3, and k = -4.

What is the vertex form of quadratic equations?

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

The given parent function is f(x) = (x - 3)² - 4.

comparing with the standard vertex form of the parabola, we get

                  a = 1, h = 3 and k = -4.

Now to find 'b', we have to simplify the given function in the form of f(x) = ax² + bx + c

                  f(x) = (x - 3)² - 4

                  f(x) = (x² - 6x + 9) - 4

                  f(x) = x² - 6x + 5

Comparing with f(x) = ax² + bx + c we get, c = -6.

Hence, The values from the parent function are a = 1, b = -6, h = 3, and k = -4.

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Answer:

Step-by-step explanation:

[tex]\sf (10-x)+(12-x)[/tex]

Simplify:-

[tex]\sf 10-x+12-x[/tex]

Combine like terms:-

[tex]\sf -x-x+10+12[/tex]

[tex]\sf (-x-x)=\bf -2x[/tex]

[tex]\sf (10+12)=\bf 22[/tex]

[tex]\sf -2x+22[/tex]

Hope this helps!

Have a great day!

After simplifying the expression, the value of y is 4.53.

In the given question,

We have to solve for y.

The given expression is 116° +15y - 4=180.

To solve for y we simplify the expression.

The expression is 116° +15y - 4=180

Now simplifying the expression.

Add 4 on both side

116° +15y - 4+4=180+4

116° +15y=184

Subtract 116 on both side

116° +15y-116°=184-116°

Simplifying

15y=184-116°

15y = 68

Divide by 15 on both side

15/15 y=68/15

y=4.53

Hence, the value of y is 4.53.

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Answer:

huhh

Step-by-step explanation:

Hi im new can u guys tell me how this work pease??

Answer:

Step-by-step explanation:

idek idek

Answer:

a) He obviously used 7 liters of cooking oil.

b) He has 24 liters of cooking oil left.

He needs to buy 7 bags of fertilizer to fertilize the garden

The radius of the garden = 10 feet

The area of the garden A = π × [tex]r^2[/tex]

Where A is the area of the garden

r is the radius of the garden

Substitute the values in the equation

A = π × [tex]10^2[/tex]

= π × 100

= 314.16 feet square

Each bag of fertilizer covers 50 square feet

Then the number of bags required to fertilize the garden = The area of the garden / 50

Substitute the values in the equation

= 314.16 / 50

= 6.28

≈ 7 bags

Hence, he need to buy 7 bags of fertilizer to fertilize the garden

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The domain of the given function f(x) = (-x - 9)^(1/2) is; C) (-∞, -9)

The domain of a function is defined as the set of all possible input values that make the function possible.

Now, we are given the function;

f(x) = (-x - 9)^(1/2)

This can also be written as;

f(x) = √(-x - 9)

Now, since the item in bracket seems to be negative, we can say that we want to find the lowest term for which the function in bracket is zero because when the function in the bracket is negative, then the function is a complex number. Thus;

At (-x - 9) = 0

-x = 9

x = -9

This will be the maximum value of x while the minimum value will be negative infinity.

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Answer:

a) -2/3

b) x^2-1/2

Step-by-step explanation:

In the equation 2[(4m * 3.5) / 400] = 171.5, the value of m is 2450

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

To solve for m, we have to expand the bracket and make m the subject of formula.

2[(4m * 3.5) / 400] = 171.5

2[14m/400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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Answer: 16

Step-by-step explanation:

Answer:

  8

Step-by-step explanation:

You want the period of a sinusoidal function that has a graph with peaks at x=1 and x=9.

The period is the difference between x-values where the function repeats itself. Typically, we can determine the period from corresponding recognizable features of the graph.

Here, the graph has peaks at x=1 and x=9. The period is the difference between these x-values:

  period = 9 - 1 = 8

The period of the function is 8 units.

__

Additional comment

In more formal terms, the period p of a function is the smallest value of p such that f(x -p) = f(p).

Answer: The correct answer is x=−1/5  and y=−1/5

Step-by-step explanation:

Solve the System by substitution:

y=6x+1 and 7x−2y=−1

Solve y=6x+1 for y:

y=6x+1

Substitute 6x+1 for y in 7x−2y=−1:

7x−2y=−1

7x−2(6x+1)=−1

−5x−2=−1 (Simplify both sides)

−5x−2+2=−1+2 (Add 2 to both sides)

−5x=1

−5x/−5 = 1/−5  (Divide both sides by -5)

x=−1/5

Substitute −1/5 for x in y=6x+1:

y=6x+1

y=6(−1/5)+1

y=−1/5   (Simplify both sides)

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Answer:

0.45833333333 or 11/23

Step-by-step explanation:

1 2/9*6/16 is simply 11/23, cross multiply and simplify

The mapping of the function f of g(x) will result to 41

A function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.

By mapping of the functions f and g defined as;

f : x » x + 5 and g : x » 8x

then;

f of g(x) = f of 8(4.5)

f of g(x) = f of 36

f of g(x) = 36 + 5

f of g(x) = 41

Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.

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The missing values for gallons of gasoline remaining is 11,6,1.

Given that equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d).

We want to find the missing values for gallons of gasoline remaining.

The given equation is g=16-(1/20)d

When the distance is 100 then we will find the gallons of gasoline remaining by substituting d=100 in given equation, we get

g=16-(1/20)100

g=16-5

g=11

When the distance is 200 then we will find the gallons of gasoline remaining by substituting d=200 in given equation, we get

g=16-(1/20)200

g=16-10

g=6

When the distance is 300 then we will find the gallons of gasoline remaining by substituting d=300 in given equation, we get

g=16-(1/20)300

g=16-15

g=1

Hence, the missing values for gallons of gasoline remaining when distance 100 is 11, when distance 200 is 6 and when distance 300 is 1.

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The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6

From the question, we have the following parameters that can be used in our computation:

Tree A

Tree B

The height after t years is

Tree = Initial height + rate * t

So, we have

Tree A = 38 + 6t

Tree B = 20 + 9t

Recall that

Tree A = 38 + 6t

Tree B = 20 + 9t

When Tree A is taller than Tree B, we have

38 + 6t > 20 + 9t

Evaluate the like terms

-3t > -18

Divide

t < 6

Hence, the interval is t < 6

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Answer:

We can see that as x increases, y decreases. This indicates a negative slope meaning that the two variables are negatively related.

Hope this helps! :)

The volume of the cylinder in cubie centimeter is 628 [tex]cm^{3}[/tex]

How to find the volume of cylinder?

1. Find the radius of the circular base: Since both circles are the same size, either one will work. Move on if you are aware of the radius. If you don't know the radius, you can divide the diameter of the circle by 2.

2. Find the height of the cylinder : Continue if you already know the height. Otherwise, measure it with a ruler. The height is determined by the separation of the two bases' edges.

diameter (d) = 20

radius = [tex]\frac{20}{2}[/tex]

        r = 10

height (h) = 2cm

volume v = [tex]\pi r^{2} h[/tex]

            v = 3.14(10*10)2

               = 628 [tex]cm^{3}[/tex]

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The size of angle QPR is 45° and the length of sides PQ and QR are both 27.20cm

An isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal angle,

since ∆PQR is a right angle isosceles triangle then, if angle Q is 90^°, QPR = PRQ=x( angles of an isosceles triangle).

Therefore 90+x+x= 180°

2x= 90

x= 45°

To find line PQ and QR, we use trigonometry ratio

cos 45°= adj/hyp

I/√2= QR/38.47

QR= 38.47/√2

= 27.20cm

QR= PQ= 27.20

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Answer:

48 fl oz = 6 c

4 gal = 16 qt

Step-by-step explanation:

4 times 4 is 16

48 divided by 8 is 6

The number is 0.75.

From the question, we have

The store was offering a 25% discount.

number = 1-0.25

=0.75

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The minus sign stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above figure) are then moved to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, or equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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Answer:

8421/10000

Step-by-step explanation:

8421/10000

The equation that models the cost of the van rental is V = $183 + (m - 120)0.39. (first option)

The number of miles that Tim and Jessica can travel roundtrip on vacation is Ashville MC (second option)

The equation that represents the total cost of renting the camper van is a linear equation. A linear equation is an equation that has single variable that is raised to the power of one.

The general form of a linear equation is: y = mx + b

Where:

The form of the linear equation is:

total cost = cost of renting the van + [(total miles driven - 120) x cost per mile)

V = $183 + (m - 120) x 0.39

V = $183 + (m - 120)0.39

Total miles that can be driven if they have to spend $598.74

$598.74 = $183 + (m - 120)0.39

$598.74 = $183 + 0.39m - 46.80

$598.74 = $136.20 + 0.39m

$598.74 - $136.20 = 0.39m

$462.54 = 0.39m

m = $462.54 /0.39

m = 1186

Distance Tim and Jessica can travel from the rental company to the destination = 1186 / 2 = 593 miles

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The completion of the inventory table is as follows:

A = $48

B = $264

C = $420

D = $304.

The above inventory table is completed using some of the inventory methods including:

FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.

Specification Identification does not base allocating the costs of goods sold and ending inventory on any assumptions. Instead, it uses specific costs.

                                     Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory   8        $6.00            $48 ($6 x 8)

Apri. 11    Purchases        24       $11.00          $264 ($11 x 24)

May 17    Purchases        30      $14.00          $420 ($14 x 30)

Dec. 5    Purchases         19      $16.00          $304 ($16 x 19)

Total                                 81                         $1,036

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