The width of a rectangle is 4 units less than the length. The area of the rectangle is 12 units. What is the width, in units, of the rectangle?

Answers

Answer 1

The width of a rectangle is 4 units less than the length. The width, in units, of the rectangle is 2 units.

Represent the length and width by L and W.

Then W = L - 4.

The area of the rectangle is 12 units

= Length x width  

=  L x W

=  L(L - 4)

=L^2 - 4L = 12

L^2 -4L - 12 = 0

Now on solving this quadratic equation we get

L^2 -4L - 12 = 0

L^2 - 6L  + 2L -12 = 0

L(L - 6 ) -2(L - 6) = 0

(L-6)(L-2) = 0

This factors easily into

(L - 2)(L - 6) = 0

so L must be 2,6.  

When L = 2

The width of the rectangle is W = L - 4 = 2 - 4 = -2 units.

We ignore the negative values.

when L= 6

The width of the rectangle is W = L - 4 = 6 - 4 = 2 units.

The width of a rectangle is 4 units less than the length. The width, in units, of the rectangle is 2 units.

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Related Questions

A package of 5 pairs of insulated gloves costs ​$25.95. What is the unit price of the pairs of ​gloves

Answers

The unit price of the pair of gloves is $5.19.

Here, a package of 5 pairs of insulated gloves costs $25.95.

We have to find the unit price of the pairs of gloves.

5 pairs of insulted gloves = $25.95

So we have to find the value of 1 pair of gloves, so by dividing the value by 5 we will get the value of 1 pair of gloves.

Unitary method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit.

So by using the unitary method we have:

1 pair of insulated gloves = 25.95/ 5

                                          = 5.19

Therefore the unit price of the pair of gloves = is $5.19.

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HELP ME PLEASEEEEEEEEE

Answers

it would be B because it can be reduced to -8

Xin owns a trucking company. for every truck that goes out, xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile driven for gas and maintenance. on one particular day, the driver drove an average of 50 miles per hour and xin's total expenses for the driver, gas and truck maintenance were $1457.50. write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. define the variables that you use to write the system.

Answers

The number of miles that the truck drove is 550 miles.

How to illustrate the information?

From the information, Xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile. This can be illustrated as:

20x + 2.25y = 1457.50 ....... i

x = number of hours

y = number of miles driven

The driver drove an average of 50 miles per hour. This will be illustrated as:

y/x = 50

y = 50x

Substitute into equation i

20x + 2.25y = 1457.50

20x + 2.25(50x) = 1457.50

20x + 112.50x = 1457.50

Collect like terms

132.50x = 1457.50

Divide

x = 1457.50 / 132.50

x = 11

y = 50x = 50 × 11 = 550 miles

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One number is 13 less than another number. Let x represent the greater number

Answers

Answer:

x - 13

Step-by-step explanation:

To get this equation, we must look at the description.

13 less than x makes an equation of x - 13.

The answer is x - 13.

Hope this helps!

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The rectangle below has been drawn on a centimetre square grid.
What is the perimeter of the rectangle?
Give your answer in centimetres (cm).
4 cm

Answers

The equation for a rectangle's perimeter is P = length + breadth + length + breadth. Alternatively, P=2(length + breadth). The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter.  

What is the rectangle's perimeter? The complete distance that the rectangle's outside boundary covers is referred to as its perimeter. Its length is expressed in units. The perimeter is calculated using the formula: Perimeter, P = 2 (Length + Width).The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.Simply add the lengths of the three sides to calculate the perimeter as all the sides are measured in cm. You may occasionally need to use what you already know about a polygon to determine its perimeter.The area of a rectangle is calculated using the formula A=LW A = L W, where A is the area and L and W are the length and breadth of the rectangle, respectively. The formula for a rectangle's perimeter is P=2(L+W), where P stands for the perimeter, L for length, and W for width.

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Please help me it a test grade and it's do today

Answers

Answer:

[tex]x = 16[/tex]

Step-by-step explanation:

Because of the fact, the angle is ∠BCA = 10x - 10 and ∠ABC = 30 lies on a straight line and ∠BCA is obtuse while ∠ABC is acute, we can just set them equal to 180 to find the value of x.

So we will set up the equation:
   10x - 10 + 30 = 180

1. Combine Like Terms (eg. -10 and 30)
[tex]10x - 10 + 30 = 180[/tex]
= [tex]10 x + 20 = 180[/tex]

2. Subtract 20 on both sides
[tex]10x + 20 = 180[/tex]
       [tex]-20 -20[/tex]

= [tex]10x = 160[/tex]
3. Divide 10 into both sides
[tex]\frac{10x}{10} = \frac{160}{10}[/tex]

And we will get:
[tex]x = 16[/tex]

Check Your Work!
Now if we replace x in the equation for 16 like below we do in fact get 180:
[tex]10(16) - 10 + 30 = 180[/tex]
[tex]160 - 10 + 30 = 180[/tex]

[tex]150 + 30 = 180[/tex]

[tex]180 = 180[/tex]

So in short, x = 16

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.

f(x)=3(x+4)²+1

Answers

Step-by-step explanation:

the axis of symmetry for a regular parabola (opens up or down) is a line parallel to the y-axis (vertical) going through the vertex of the parabola.

the standard form of a parabola is

y = a(x - h)² + k

with (h, k) being the vertex.

so, we see for f(x) the vertex is (-4, 1).

the axis of symmetry uses the x coordinate of the vertex and is

x = -4

for h(x) we see in the graphic that the vertex is (1, -3).

so, the axis of symmetry is

x = 1

FYI - based on what we see : vertex is (1, -3), h(0) = -1 the function here would be

h(x) = 2(x - 1)² - 3

What is the area of the triangle determined by the lines y = − 1/2x + 8, y = 9x,
and the y-axis?

Answers

The triangle has an area of 3.37 square units

How to determine the area of the triangle?

The equations are given as

y= -1/2x + 8

y = 9x

On the y-axis, the value of x is 0

i.e. x = 0

Substitute 0 for x in the equations y= -1/2x + 8 and y = 9x

So, we have

y= -1/2(0) + 8 = 8

y = 9(0)  = 0

The base of the triangle is the difference between these values

So, we have

Base = 8 - 0

Base = 0

Substitute y = 9x in y= -1/2x + 8

So, we have

9x = -1/2x + 8

This gives

9.5x = 8

Divide both sides

x = 16/19

The area of the triangle is then calculated as

Area = 0.5 * Base * x

This gives

Area = 0.5 * 8 * 16/19

Evaluate

Area = 3.37

Hence, the area of the triangle is 3.37 square units

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(2,-5) and (-1,1) are in the line, put it in standard form. Please help me I don’t understand it

Answers

The points (2, - 5) and (- 1, 1) lie on the equation of the line - 2 · x - y = 1.

What is the equation of the line in standard form?

According to Euclidean geometry, a line can be constructed from two distinct points on a plane. Then, we can find the equation of the line based on the coordinates of two points set on Cartesian plane, whose standard form is shown below:

a · x + b · y = 1

In this question we have the coordinates of two points: (2, -5), (- 1, 1). If we substitute in the equation of the line, then we find the following system of linear equations:

2 · a - 5 · b = 1

- a + b = 1

Then, we find the solution to the system by using numerical methods:

(a, b) = (- 2, - 1)

The equation of the line - 2 · x - y = 1 contains the points (2, - 5) and (- 1, 1).

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Five mi is approximately equal to 8 km. Use mental math to estimate
the distance in kilometers to a town that is 30 mi away.

Answers

Using the conversion factor, we know that 30 miles are approximately 48 km.

What is the conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an equal value. For instance, 12 inches equals one foot when converting between inches and feet.

So, 30 miles is how many kilometers:

We know that 1 mile = 1.60934 km

Then, 5 miles:

1.60934 × 5 = 8.04672 km

Similarly 30 miles:

1.60934 × 30 = 48.2803

Rounding off: 48 km approximately

Therefore, using the conversion factor, we know that 30 miles are approximately 48 km.

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The greater of two numbers is 5 more than the smaller. If the
smaller is added to twice the greater, the result is 22. Find both
of the numbers.

Answers

Answer:

First number = 4

Second number = 9

Step-by-step explanation:

If the first number = x, the second number = x + 5.

The calculation can be expressed as follows:

x + 2(x + 5) = 22

First, expand the bracket 2(x + 5):

x + 2x + 10 = 22

Combine like terms:

3x + 10 = 22

Subtract 10 from both sides:

3x = 12

Divide both sides by 3:

x = 4

First number = 4

Second number = 4 + 5 = 9

Emily has 4 less skittles than Sarah. Janessa has half as many skittles as Sarah. Together they have a total of 46 skittles.
How many skittles does Janessa have?

Answers

Answer: Janessa would have 27 and Emily would have 19.

Can somebody help me find the last three answers of the quartile and interquartile range it’s for tommorow somebody please

Answers

The 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.

What is a quartile of a data set and how is it conceived?
A quartile is a set of values with three points that divides a data set into four equally sized portions. The values that divide a list of numerical data into three quarters are known as quartiles. The center of the three quadrants measures the point of distribution's center and displays data that are close to the center. Only half of the data set is represented by the lower part of the quarters, which is below the median, while the upper section represents the other half, which is above the median. The distribution or dispersion of the data set is shown overall by the quartiles.
When the data points are organized in ascending order, 25% of them are found in the lower quartile, often known as the first quartile (Q1). When presented in increasing order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).
Mathematically, First quartile (Q1) = [(n+1)/4] term
Third quartile (Q3) = [3(n+1)/4] term
The interquartile range is calculated as: Upper Quartile – Lower Quartile = Q3 - Q1

Arranging the given values in ascending order, we have the data set:
40, 42, 46, 47, 51, 55, 58, 67, 67, 68, 69
The total number of terms in the data set = n = 11
Using the formulae established in the literature, we have:
Now, first quartile = Q1 = [(11+1)/4] term = 3rd term = 46
Again, third quartile = Q3 = [3(11+1)/4] term = 9th term = 67
Therefore, interquartile range = Q3 - Q1 = 67 - 46 = 21
Thus, the 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.

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-2x + 6x – 9 = 15 solve for ex show your work that why i give so much

Answers

Answer:

x=6

Step-by-step explanation:

1. Combine like terms

2. Add 9 to both sides

3. Divide by 4 on both sides

4. Arrive at solution

5. Plug solution in to equation.

Answer:

-3

Step-by-step explanation:

first you start with by adding 9 to both sides to balance

-2x+6x-9=15

          +9 +9

Giving you -2x+6x=24 now you start by dividing

I started by dividing -2

-2x+6x=24

÷(-2)      ÷(-2)

Giving you x+6x=(-12) again divide

x+6x=(-12)

 ÷6   ÷6

Giving you x+x=(-6) we know that x+x is = to 2x next we divide agian

2x=(-6)

÷2  ÷2

Giving you the answr x=(-3)

4
If ƒ (x) = 4 — x, evaluate f (2k + 4).
k=1

Answers

The value of f(2k+4) for k=1 and f(x)= 4-x is -2

What is the value of a function?

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value.

We are given a function f(x)= 4-x

We have to find f(2k+4).

[tex]f(2k+4)=4-2k-4[/tex]

Now substitute k=1

We get,

[tex]f(2+4)=4-2-4\\f(6)=-2[/tex]

Hence, The value of function f(2k+4) at k=1 for the function f(x)=4-x is -2

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Solve the inequality x(2x+3) > 20

Answers

The inequality of the equation x(2x+3) > 20 is x<-4 or x>5/2.

Given, the expression is x(2x+3) > 20

open the brackets.

⇒ 2x²+3x>20

⇒ 2x²+3x-20>0

Factorize the equation.

⇒ 2x²+8x-5x-20>0

⇒ 2x(x+4)-5(x+4)>0

⇒ (x+4)(2x-5)>0

hence, (x+4)>0 or (2x-5)>0

(x+4)>0

⇒ x<-4

(2x-5)>0

⇒ 2x > 5

⇒ x >5/2

Hence we get the required inequality for the given equation.

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find the area of the surface shown below

Answers

Problem

Solution

For this case the surface area is given by:

[tex]SA=\frac{2\cdot2}{2}+2\cdot2+\frac{2\cdot5}{2}+\frac{9\cdot3.5}{2}[/tex]

And solving we got:

[tex]SA=2+4+5+63=74its^2[/tex]

write each number as a time period. Be sure each fraction is lowest terms 8:00 am to 9:20 am Explain

Answers

Answer:

800/920

400/460

40/46

20/23

Provide an example and explain the steps to convert a fraction into a percent.

Answers

The most appropriate choice for percentage and fraction will be given by-

The process of conversion of fraction to percentage has been explained.

What is fraction and percentage?

Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

If a number is taken as fraction of 100 then the fraction is known as percentage.

To convert a fraction into percentage, we have to simply multiply the fraction with 100.

For example.

Suppose we have a fraction [tex]\frac{1}{4}[/tex], we need to convert  [tex]\frac{1}{4}[/tex] to percentage.

So on multiplying [tex]\frac{1}{4}[/tex] by 100, we obtain = [tex]\frac{1}{4} \times 100[/tex] = 25%

So, [tex]\frac{1}{4}[/tex] is equivalent to 25%

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What is the point-slope form of the line with slope −3/7 that passes through the point (5, 8)?



Responses

y−8=−37(x−5)


y+8=−37(x+5)


y−5=−37(x−8)


y+5=−37(x+8)

Answers

The point slope from the line with slope -3/7 that passes through the point (5,8) is y-8 = -3/7 ( x-5).

Two crucial constants are present in a linear function: the slope, which is represented by the letter m, and the y-intercept, which is represented by the letter b. Y = m x + b is the slope-intercept equation's formula. The point-slope equation is a different manner that we can occasionally express the equation of a line. It reads as follows y-y₀ = m(x-x₀).

Given that :

Slope m = -3/7

passes through the point p ( 5, 8 )

Equation is  y-y₀ = m(x-x₀)

y-8=-3/7 ( x-5)

here the point slope is y-8=-3/7 ( x-5)

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A family used a professional decorator to help furnish their new home. The decorator selected $1,580 worth of furnishings. The family paid for the furnishings, plus 4.5% tax on the purchases. The decorator’s fee was 12% of the purchases, not including the tax. Question 1 Part A Write an equation in the form of y=kx, using x to represent the decorator’s fee. Then use the equation to calculate the amount of that fee.Part B Write an equation in the form of y=kx to represent the tax. Then use the equation to calculate the amount of tax.Part C What is the total cost that the family paid?


PLEASE HELP!!!THANK YOU!!

Answers

As per direct variation,

Part A) Decorators fee is $198.132

Part B) Tax for the purchase is $71.10

Part C) The total amount spend by the family is $1849.232.

Direct variation:

Direct variation depicts a simple relationship between two variables . We say y varies directly with x if:

y=kx

for some constant kk , called the constant of variation or constant of proportionality. Which means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

Given,

A family used a professional decorator to furnish their new home.

The decorator selected $1,580 worth of furnishings for their home.

The payment will be made by the family for the furnishings, plus 4.5% tax on the purchases.

The decorator’s fee was 12% of the furnishings , excluding the tax.

Here we need to find the following:

Part A) Decorator's fee

Part B) Tax amount

Part C) Total cost.

We know that, the decorator’s fee was 12% of the purchases.

So, the equation is then be calculated as:

y = kx

where,

y = decorators fee

k = percentage of decorators fee for the purchases

x = amount paid

y = 12% × $1651.10

= 0.12 × $1651.10

Therefore, the decorators fee is $198.132

Decorator selected furnishings cost = $1,580.

Tax = 4.5%

Decorator’s fee = 12% of the purchases.

So, it can be calculated as,

Tax = 4.5% × 1580

Tax = 0.045 × 1580

Therefore, the tax for the purchase is $71.10

Amount paid = 1580 + 71.10 = 1651.10

Now, the total amount paid by the family is,

=> purchase amount + decorator fee

=> 1651.10 + 198.132

=> 1849.232

Therefore, the total amount spend by the family is $1849.232.

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What is distance between (-2, 4) and (3, 7)? Round to the nearest tenth if necessary (example 5.6).
The distance is what?

Answers

The distance between the two points (-2, 4) and (3, 7) is found as 5.83.

What is termed as the distance formula?Any distance formula, as the name implies, provides the distance (the length of a line segment). The length of a line segment connecting two points, for example, is the distance between them. The Pythagorean theorem is used to deduce the formula for the distance between two points in a two-dimensional plane, which can also be extended to find distance between two points inside a three-dimensional plane.

For the given question;

The two coordinates are-

(x1, y1) = (-2, 4)

(x2, y2) = (3, 7)

The distance between two points are calculated as-

d = √(x1 - x2)² + (y1 - y2)²

Put the values;

d = √(-2 - 3)² + (7 - 4)²

d = √25 + 9

d = √34

d = 5.83

Thus, the distance between the two points (-2, 4) and (3, 7) is found as 5.83.

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Please help now need it soon!! :) Please and thank you!!

Zach spent 2/6 of his paycheck on a new video game the cost of the videogame was $58 what was the total amount of his paycheck?

Answers

The total amount of Zach's paycheck was $174.

The fraction of the paycheck spent by Zach on the new video game is 2/6. The cost of the video game is $58. We need to find the total amount that Zach had in the paycheck.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.

Let the total amount of the paycheck be "x". Using the information above, we can form an equation as given below :

(2/6)*x = 58

x = (6/2)*58

x = 174

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-3.7+1/4 Write your answer as a decimal to the nearest hundredth.

Answers

The answer as a decimal to the nearest hundredth is -3.45.

What is termed as the decimals?A decimal is a number with a whole as well as a fractional part. Decimal numbers are between integers but also reflect numerical value for whole plus some fraction of a whole. A decimal number has two parts: a whole number component and a fractional component. A decimal place value system is identical to the whole number value system for the entire part of a decimal number.

For the given question;

The expression is given as;

= -3.7 + 1/4

Now, the fraction 1/4 can be written in decimal as 0.25.

Put the value of 1/4.

=  -3.7 + 0.25

The subtraction of larger negative to smaller positive gives negative number.

= -3.45

Thus, the answer as a decimal to the nearest hundredth is -3.45.

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6. Mr. Jamison, an art teacher, would like to
purchase enough supplies to get his class
stocked. He picks up 8 dozen sketch pencils, 6
dozen colored pencils, and 3 dozen art gum
erdsers. If the sales tax rate is
8%,
approximately what will his bill be?
I NEED AN EXPLANATION!! pls

Answers

If Mr. Jamison bought 8 dozen sketch pencils, 6dozen colored pencils and 3 dozen art gum, with a sales tax of 8 percent, considering each dozen of sketch pencils costed $x, colored pencils costed $y and art gums costed $z, the total bill approximately would be

$[(8x + 6y + 3z) + 0.08(8x + 6y + 3z)].


As per the question statement, Mr. Jamison bought 8 dozen sketch pencils, 6dozen colored pencils and 3 dozen art gum, with a sales tax of 8 Percent, and since no information is provided about the price of the sketch pencils, colored pencils or art gums, let us consider that each dozen of sketch pencils costed $x, colored pencils costed $y and art gums costed $z.

We are required to calculate the total approximate bill, Mr. Jamison would have to pay for the items he picked up.

To solve this question, first we will have to calculate the total price of the items he picked, without any taxes, i.e.,

$[(8 * x) + (6 * y) + (3 * z)] = $(8x + 6y + 3z).

Now an 8% sales tax on the price of the items bought will be

8% of $[(8x + 6y + 3z), i.e.,

[(8/100) * (8x + 6y + 3z)]

= $[0.08(8x + 6y + 3z)]

Therefore, total bill = (Total item costs + tax)

                                = $(8x + 6y + 3z) + $[0.08(8x + 6y + 3z)]

                                = $[(8x + 6y + 3z) + 0.08(8x + 6y + 3z)]

Dozen: A grouping or set of twelve objects, shapes or numbers is known as Dozen.

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WRITE AN EQUATION TO REPRESENT YOUR ANSWER.
FORMAT: variable term + constant = total

Ginny is making cookies for a bake sale. The recipe she is using makes 24 cookies in a batch. Ginny took 198 cookies to the bake sale after 18 burned. How many batches of cookies did she make?

Answers


Explanation:
Let's say b is the batches. Since 24 is a batch of cookies we can multiply it's by the how much batches or b. Which is 24b.
We subtract by 18 since 18 of the cookies burned. So it's 24b-18.
The total is 198 since shebring them to the baking show the rest except the 18 cookies

Equation: 24b-18= 198

If need to solve:
24b-18= 198
+18. +18
24b = 216
÷24. ÷24
b = 9
Answer: 9 batches

Let f(x) = x² - 8x +7.
What is the vertex f(x)?
O Vertex: (9,-4)
O Vertex: (4, -9)
O Vertex: (-4.9)

Answers

The vertex f(x) = x² - 8x +7 is (4,-9)

What is quadratic equations?

A quadratic equation is a second-order polynomial equation with a single variable, such as x = ax2 + bx + c = 0, where a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated. Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

Given Data

Establishing the axis of symmetry is the first step that you should take (the x co-ordinate of the vertex). You must factor the equation in order to do this. You need to find two values that sum up to -8 and multiply to +7 in order to factor this easy trinomial. This pair of numbers, -1 and -7, means:

-7 x -1 = +7 \s-7 + -1 = -8

Now, you take these two components and mark each one with an x in brackets as follows:

f(x) = (x -1)(x-7)

Set each bracket to zero now, and then solve. Get x = 7 and x = 1, respectively. Add the zeros together and divide by 2 to find the axis of symmetry:

[tex]\frac{7+1}{2}[/tex]

= 4

Consequently, x=4 is the equation for the axis of symmetry.

You may now insert the axis of symmetry into the equation (either the factored version or the original; in this case, factored would be the simplest) to obtain the best value (y co-ordinate of the vertex):

f(4) = (4-1)(4-7)

f(4) = (3)(-3)

f(4) = -9

Therefore, -9 is the ideal value.

Together, it makes the vertex (4, -9)!

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Cannon wants to put as much as he can into a retirement account as soon as he starts working. He deposits $25,000 at then end of each year for 5 years in an account paying 6% interest compounded annually. How much will he have in the account at the start of the 6th year? A) $140,927.34 B) $174,382.96 C) $395,240 D) $557,593.99

Answers

The compound interest formula is given by the formula

[tex]A\text{ = }p(1+\frac{r}{100})t[/tex]

Where A = Amount after t years

r = rate = 6

t = time = 5

p = $ 25000

For the first year

[tex]\begin{gathered} A=\text{ 25000(1+0.06)} \\ =25000\times1.06=26500 \end{gathered}[/tex]

For the second year

P=26500+25000=51500

[tex]\begin{gathered} A=51500(1+0.06) \\ =515000\times1.06=54590 \end{gathered}[/tex]

For the third year

P=54590 + 25000=79590

[tex]\begin{gathered} A=79590\text{ }\times1.06 \\ =84365.4 \end{gathered}[/tex]

For the fourth year

P=84365.4 + 25000=109365.4

[tex]\begin{gathered} A=\text{ 109365.4}\times1.06 \\ =115927.324 \end{gathered}[/tex]

For the fifth year

P= 115927.324 + 25000 =140927.324

[tex]\begin{gathered} A=\text{ 140927.324}\times1.06 \\ =149382.962 \end{gathered}[/tex]

At the start of the 6th year

P= 149382.962+25000= 174382.96

Answer = $174382.96

Option B is correct

302)+5)-1+4 (202)- 3) ≤125
True or False

Answers

The inequality (302+5)-1+4 (202)- 3) ≤ 125 is false for the given question.

What is inequality?

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on either side are not equal.

It indicates that the expressions on the left and right should be greater or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is defined by the inequality symbols '≠'.

We have given the inequality  

(302+5)-1+4 (202)- 3) ≤ 125

Lets simplify

(302+5)-1+4 (202)- 3) ≤ 125

1111 ≤ 125

Thus, The inequality is false.

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A recipe calls for 1 1/4 cups of flour to make 1 dozen cupcakes. How many cups of flour are needed to
make 36 cupcakes?

Answers

Since 1 dozen = 12, 12 cupcakes = 1 1/4 cups of flour

36/12 = 3

36 = 1 1/4(3)
36 cupcakes = 3 3/4 cups of flour

Answer:

8 1/4 cups

Step-by-step explanation:

You multiple 11/4 by 3 and change the answer to a mixed fraction

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