The width of a rectangle is 3 units less than the length. The area of the rectangle is 18
units. What is the length, in units, of the rectangle?

Answers

Answer 1

Answer:

First let the length be a variable (eg: x) so that we can form an expression and solve.

Let the length of the rectangle be x units.

Form an expression for the width of the rectangle using the information given.

Width = (x - 3) units

Area of rectangle = length x width

Using the formula, form an equation.

x(x - 3) = 18

Simplify and solve for x.

x² - 3x = 18

x² - 3x - 18 = 0

(x - 6)(x + 3) = 0

x - 6 = 0 or x + 3 = 0

x = 6 or x = - 3 (reject)

The length cannot have a negative value so reject - 3.

Hence, the length of the rectangle is 6 units.


Related Questions

can someone help me out with this?

Answers

Answer:

area of triangle is length *breathe

4.5 * 5.5 = 24.75


What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?

Answers

Around 10 of not a clue. Good luck on that!

Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for sor">=" for >.5(-3,0)5(0, -3)

Answers

we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is

[tex]\begin{gathered} m=\frac{-3-0}{0-(-3)} \\ m=\frac{-3}{3} \\ m=-1 \end{gathered}[/tex]

where we used the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Then, our searched line has the form:

[tex]y=-x+b[/tex]

where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:

[tex]\begin{gathered} -3=-(0)+b \\ b=-3 \end{gathered}[/tex]

then, the searched line in slope-intercept form is

[tex]y=-x-3[/tex]

Therfore, the given area can be modeled as

[tex]y>-x-3[/tex]

because when a line is dashed it doesn't belong to the given area.

Need help solving this problemNote for part A I got 4/22 and it was incorrect

Answers

First, we need to find the total frequency. This is given by adding all the given frequencies. That is,

[tex]\begin{gathered} f_{\text{total}}=4+6+7+5 \\ f_{\text{total}}=22 \end{gathered}[/tex]

and the relative frequency is the division of the frequency of the corresponding interval by the total frequency,

[tex]f_{\text{rel}}=\frac{f_{\text{ interval}}}{f_{total}}[/tex]

Therefore, the answers are:

a) 4/22 but written in simple form:

[tex]\frac{2}{11}[/tex]

b)

[tex]\frac{5}{22}[/tex]

For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar-water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?

Answers

The container whose sugar water mixture is a darker shade of red is: A. the small bowl's mixture is a darker shade of red.

What is a ratio?

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this scenario, the ratio of the sugar water mixture in the small bowl (S) to the sugar water mixture in the large bucket (L) can be represented by this mathematical expression:

S:L = 1:3

Also, when red coloring is added to both containers, we have:

S:L = 1r:3r

In this context, we can reasonably and logically deduce that the mixture in the small bowl would have a darker shade of red because it is less diluted in comparison with the sugar water mixture in the large bucket.

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Complete Question:

For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?

answer choices

The small bowl's mixture is a darker shade of red.

The large bucket's mixture is a darker shade of red.

Neither. The mixtures are the same shade of red.

If f(x) = 12x and g(x) = -4x-12, find (f ·g)(x).

A.) -48x^2 - 12x
B.) -48x^2 - 144x
C.) -4x^2 - 144x
D.) -192x^2

Answers

Answer:

[tex]-48x^2 - 144x[/tex]

Step-by-step explanation:

[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =12x(-4x-12) \\ \\ =-48x^2-144x[/tex]

Please answer attached question with diagram :)

Answers

The translation observed by shape A after reflection is

x direction -5y direction -2

What is translation?

Translation refers to a linear movement used in describe repositioning of image during transformation

Transformation is the generally the repositioning of an image. Transformations are usually described in a cartesian plane for ease of comprehension.

The shape A after reflection had a new position. The new position was moved downwards, in the y direction by 2 units representing -2

The shape was further moved to the left 5 units in the x direction  representing -5

Hence we say that c = -5 and d =  -2

This describes the position of the image now labeled shape B

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5/3x+1/3x=11 1/3+8/3x

Answers

Answer:

-111/2

Step-by-step explanation:

Please look at the attachment below! :D

100 brainly!! Which of the following values are in the range of the function graphed below? Check all that apply.

Answers

Answer:

B

Step-by-step explanation:

fine the value of x. please help

Answers

Answer:

141 degrees

Step-by-step explanation:

The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38

Here is a sketch of the unique triangles that can be
made with angle measures 80° and 20° and side
length 5.
PLEASE HELPPPP



ASAAAAPPPPP DUE AT END OF TODAY

Answers

Option (B) describes the correct unique possibilities of the given triangle.

What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. △ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Triangles can be divided into three types based on the lengths of their sides, and these are Scalene, Isosceles, and Equilateral.

So, according to the given image:

We can easily observe that the triangle is an isosceles triangle with base angles being equal and the third angle being the smallest.Then, the correct option about the triangle will be an option (B).

Therefore, option (B) describes the correct unique possibilities of the given triangle.

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PLS HELP ASAP
!!!!!!

Answers

They’re equal too, the first option because you first have to solve the equation using order of operations and 2 to the third power is 8 and divided by 32 is 4 and 4+3 =7 and the square root of 49 is also 7 because 7•7 so they’re equivalent

Using the drawing tools to form the correct answer on the provided graph

Answers

Horizontal line with the given function: y = 4

Explanation:

Since the midline of a sine function is the horizontal centerline about which the functions oscilliart above and below, the corresponding line here is y = 4 with x = 0.

NB:

The midline is parrallel to y = 0 ~ the x-axis.

Find the derivatives of the following using increment method.1.y = 6x² +10x - 3

Answers

Given

[tex]y=6x²+10x-3[/tex]

Find

derivatives using increment method.

Explanation

Given

[tex]y=6x²+10x-3[/tex]

replace x and y by

[tex]\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}[/tex]

so ,

[tex]\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}[/tex]

now divide by

[tex]\Delta x[/tex]

so ,

[tex]\begin{gathered} y^{\prime}=\frac{12\Delta x^2+10\Delta x+6\Delta^2x^2}{\Delta x} \\ \\ y^{\prime}=12x+10+6\Delta x \end{gathered}[/tex]

now taking limit

[tex]\begin{gathered} \lim_{\Delta x\to0}y^{\prime}=\lim_{\Delta x\to0}(12x+10+6\Delta x) \\ \\ y^{\prime}=12x+10 \end{gathered}[/tex]

Final Answer

Therefore , the derivative of the function using increment method is 12x + 10

2x + y = 2
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, -3) so that it will satisfy the given equation.

Answers

Answer:

2.5

Step-by-step explanation:

Plug is -3 for y and solve for x

2x -3 = 2  Add 3 to both sides

2x = 5  Divide both sides by 2

x = [tex]\frac{5}{2}[/tex] o r 2[tex]\frac{1}2}[/tex] or 2.5

WILL MARK BRAINLIEST FOR THE BEST AND MOST ANSWERED OUT REPLY

1. A recent election poll claims that Candidate A is projected to win the election with 53% of the vote. If a sample of 2436 voters is polled, determine if Candidate A can be guaranteed a win with 95% confidence.

Select an answer
a. yes
b. no
c. Not enough information

Explain why or why not using two sentences.​

Answers

Using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.

So, candidate A has a projection of winning 53% votes.

A sample of 2436 voters is pulled, then:

2436/100 × 53 = 1,291 votes

Can candidate A be guaranteed 95% votes which are:

2436/100 × 95 = 2,314 votes

Difference: 2,314 - 1,291 = 1,023

Therefore, using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

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You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point S ?

Answers

If the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The speed of the swamp vehicle = 3.2 miles per hour

From the figure we can see the two triangles ΔXVM and ΔXYZ

Here we have to use the ratio of the two similar triangles

The ratio will be

VW/WX = YZ/ZX

Substitute the values in the equations

10/6 = YZ/3

We have to find the distance from point Z to point Y

YZ = (10/6)×3

= 5 Miles

We know

Speed = Distance / Time

Time = Distance / speed

= 5/3.2

= 1.56 hours

Hence, if the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The complete question is

You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y ?

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Divide. Enter the correct answer.
17+2=

Answers

17 divided by 2= 8.5

In the community of Greendale, a local restaurant donates 15% of the total sales to student-based clubs on certain funding nights.

A- Write an equation to represent the relationship between the dinner sales (d) and the amount (a) the organization will receive.

B- What is the constant of proportionality? Interpret the constant proportionally for the problem situation.

C- How much will the organization receive if dinner sales are $3600?

NEED BY 2:35 CENTRAL TIME!!! OFFERING 35 POINTS! MIDDLE SCHOOL MATH!

Answers

The equation that represents the relationship between dinner sales and the amount the organisation would receive is a = 0.15d

The constant of proportionality is 0.15.

Th amount the organisation will receive if dinner sales is $3600 is $540

What is the relationship between dinner sales and the amount the organisation would receive?

The equation that would be used to represent the relationship between dinner sales and the amount the organisation would receive is a linear equation.

A linear equation is an equation that has one variable that is raised to the power of one. A linear equation can either be either be a positive function or a negative equation. When a linear equation is drawn on a graph, the graph is a straight line.

The form of the linear equation would be:

total amount received by the organisation = percentage x amount the restaurant receives.

a = 0.15d

0.15 is the constant of proportionality. It is the value that relates the amount the organisation would receive and the amount the restaurant would receive.

a = 0.15 x 3600

a = $540

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Britany is bringing birthday cake and cookies to her office. She has already spent $10.00 on the cake. Cookies cost $0.70 each, and she does not wish to spend more than $34.50 for all desserts. If x represents the number of cookies she can buy, which of the following inequalities symbolizes this situation?
A.
$10.00x + $0.70 < $34.50
B.
$0.70x + $10.00 < $34.50
C.
$0.70x + $10.00 < $34.50
D.
$10.00x + $0.70 < $34.50

Answers

Considering the definition of an inequality, the correct answer is option C. the inequiality $0.70x + $10.00 < $34.50 symbolize this situation

Definition of inequality

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.

The solution of an inequality is the set of numbers that make the inequality true.

Inequality in this case

In this case, you know that:

Britany has already spent $10.00 on the cake. Cookies cost $0.70 each. She does not wish to spend more than $34.50 for all desserts.

Being "x" the number of cookies Britany can buy, the inequality that expresses the previous relationship is

10 + 0.70x <34.50

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find the value of x in each case

Answers

Answer:

x=23

Step-by-step explanation:

The amount of degrees in a triangle is 180 degrees.

line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180

5x=115

x=23

PLEASE HELP!!!!!
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2?
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18

Answers

The equation of a line that passes through the point (4, 3) and has a slope of 1 / 2 is y = 1 / 2 x + 1.

How to find the equation of a line?

The equation of a line that passes through a point can be describe as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, the line passes through (4, 3) and the slope is 1 / 2.

Hence, let's find the y-intercept using (4, 3)

y = 1 / 2 x + b

3 = 1 / 2 (4) + b

3 = 2 + b

b = 3 - 2

b = 1

Therefore, the equation of the line is y = 1 / 2 x + 1.

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what are the coordinates of a’?

Answers

the answer is A, (1,3)

Graph, on a separate piece of paper, the equation of a line with a slope of −3 and a y-intercept of 2.

Select the points that appear on the graph.

Multiple select question.
cross out

A)
(0, 0)

cross out

B)
(0, 2)

cross out

C)
(1, 1)

cross out

D)
(1, −1)

cross out

E)
(2, 0)

Answers

Based on the slope of the line and the y-intercept, when graphed, the points that will appear on the graph will be:

B. (0, 2) D. (1, -1)

How to graph the line?

The equation of a line takes the form:

y = mx + b

m = slope

b = y - intercept

This line would therefore take the equation form:

y = - 3x + 2

When graphed, the graph would be as attached.

As shown by the graph, the points that will appear include:

(0 , 2) (1 , - 1)

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Simplify 6 + 2(5 – 8)2 + 7

Answers

The answer is very simple. .

6 + 2 (5 - 8 ) ² + 7

Firstly we solve what is inside the parenthesis

[tex]6\text{ + 2}\cdot(-3)^2\text{ + 7}[/tex][tex]6\text{ + 2 (9) +7}[/tex]

Then we solve the multiplications

[tex]6\text{ + 18 + 7 }[/tex]

Finally we solve the sums.

[tex]\text{ 6 +18 + 7 = }31[/tex]

That is the solution.

the d score is a standardized measure of the degree to which the independent variable caused a change in the dependent variable. this is also known as the

Answers

The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.

What is a dependent variable?

A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.

In conclusion, the standard change illustrates the change.

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What is the length of AC?

Answers

Answer:

126 units!

Step-by-step explanation:

I hope this helped!! c:

Orlando is getting balloons for his grandmother's birthday party. he wants each balloon string to be 6 feet long. at the party store, string is sold by the yard. if orlando wants to get 72 balloons, how many yards of string will he need?

Answers

144 yards of string will need to use balloons for the party.

Given,

The length of balloon string Orlando wanted = 6 feet

Number of balloons = 72

We have to find the total length of strings wanted for 72 balloons in yards.

1 yard = 3 feet

Now,

Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet

Now convert 432 feet into yard

That is,

432 / 3 = 144 yards

So,

144 yards of string will need to use balloons for the party.

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suppose that you need to build as many chairs as possible. each chair requires one seat, one back, and four legs. if you have 12 seats, 15 backs, and 44 legs, which of the chair components limits the number of chairs you can make? legs seats backs how many chairs can you make with the 12 seats, 15 backs, and 44 legs? what chair components will be leftover after making as many chairs as possible? seats and backs legs and backs seats and legs

Answers

The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

What is meant by probability?

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.

seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible

backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible

legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible

The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

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Determine the rate at which the sloth travels.
Justify your answer.
Distance (ft)
987654MN-
6.
3-
2
1
0
Speed of a Sloth
1 2
3 4
Time (min)

Answers

The rate at which the sloth travels as required in the task content is; -22ft/min.

Speed as a rate of distance with respect to time.

It follows from the task content that the rate at which the sloth travels is to be determined.

Since the correct representation of the data is such that the distance and corresponding time pairs are as follows;

(98, 1) , (76, 2) , (54, 3), (32, 4).

Hence, the rate of distance change per time is the speed of the sloth and hence, the rate of distance change is;

Rate = ∆Distance/∆time.

Rate, R = (98 - 76)/(1 - 2)

Rate, R = 22/-1

R = -22 ft/min.

Ultimately, the rate at which the sloth travels is therefore; -22 ft/min.

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