One side of a rectangle is 6 yd longer than three times another side. The area of the rectangle is 72 yd2. Find the length of the longer side.

Answers

Answer 1

Answer:

18 yds

Step-by-step explanation:

Let the length and width be L and W respectively.

Then L· W = area = 72 yd², so that L = (72 yd²) / W.

But also L = 3W + 6 yd.  Subbing this into  L· W = area = 72 yd², we get:

(3W + 6) · W = 72, or

3W² + 6W - 72 = 0.  Since all  four terms are evenly divisible by 3, we get:

W² + 2W - 24 = 0, which factors as follows:

(W + 6)(W - 4) = 0.  Then W + 6 = 0, or W = -6 (makes no sense for a length), and W - 4 = 0 yields W = 4 yds.

If the shorter side is of length 4 yds, then the longer side is of length

L = 3(4 yds) + 6 yds = 18 yds

Answer 2

Answer:

18 yd

Step-by-step explanation:

(3x + 6) * x = 72

Use the distributive property

3x^2 + 6x = 72

3x^2 + 6x - 72 = 0

3(x^2 + 2x - 24) = 0

X^2 + 2x - 24 = 0

X can equal -6 and 4.

4 only works for this problem

4 * 3 = 12

12 + 6 = 18

So, the answer is 18 yd.

Let’s check our work.

3 * 4 = 12

12 + 6 = 18

18 * 4 = 72

So, we know for a fact that the longer side is 18 yd long.

I hope I helped!

Let me know if you need anything else!

~ Zoe


Related Questions

Which pattern folds into the triangular prism?

The letter choice is in the 2nd picture

Answers

Answer:

the answer will be the letter W

Step-by-step explanation:

Answer:

W

Step-by-step explanation:

Think about folding the two triangles up in W. You can then fold the outermost rectangles up to form a triangular prism.

Also, notice that the folded figure has two blue triangles and no other picture has two blue triangles besides W.

51000 decreased by 6.4%

Answers

Answer:

47736

Step-by-step explanation:

First, subtract 0.064 from 1.000.  You should get 0.936.

Second, multiply 51000 by this 0.936:

0.936(51000) = 47736

51000 decreased by 6.4% is 47736.

To find 6.4% of 51000 and then subtract that value from 51000, follow these steps:

First, calculate 6.4% of 51000.

This can be done by converting the percentage to a decimal and then multiplying:

6.4% = 0.064

0.064 × 51000

= 3264

Next, subtract this value from the original number:

51000 - 3264

= 47736

So, 51000 decreased by 6.4% is 47736.

Complete question:

What is the value of 51000 decreased by 6.4%?

jerone has 2 ps4 and 3 xbox . a ps4 has 200 gigabytes and an xbox has 300. How many gigabytes of ram do each console have together

Answers

Answer:

500?

Step-by-step explaination

Wait don't you just add 200 and 300? Or is there some special equation for finding out gigabytes??

500 gigs.

Just add 200 + 300.

(I hope this question isn’t serious..)

Does each set of side lengths form a right triangle?

Answers

Answer: Read the explanation

Step-by-step explanation: (27+32)^2 does NOT equal 45^2, which means its not a right triangle.

(9+40)^2 DOES equals 41^2. Therefor making it a right triangle

Answer:

27ft, 32ft, 45ft : Not a Right triangle

9ft, 40ft,41ft:      Right triangle

Step-by-step explanation:

45^2  (?)  27^2 + 32^2

2025 (?) 729 + 1024

2025 ≠ 1753; Not a Right triangle

41^2 (?) 9^2 + 40^2

1681 (?) = 81 + 1600

1681 = 1681 ; Right triangle

g(x)=4+1 what is g(3)

Answers

Answer:

13

Step-by-step explanation:

Assuming g(x)=4x+1, then g(3) is 4(3)+1=12+1=13. So g(3)=13.

how much more is 1.8 • 10^11 greater than 7.2 • 10^10

Answers

Answer:

1.8.10=1.80000000000

7.2.10=7.2000000000

Step-by-step explanation:

[tex]To find out how much 1.8 * 10^11 is greater than 7.2 * 10^10, you can subtract the two values:(1.8 * 10^11) - (7.2 * 10^10)To simplify this expression, you need to have the exponents match. You can do this by rewriting 7.2 * 10^10 as 0.72 * 10^11:(1.8 * 10^11) - (0.72 * 10^11)Now, subtract the coefficients:(1.8 - 0.72) * 10^11Calculate the subtraction:1.08 * 10^11So, 1.8 * 10^11 is 1.08 * 10^11 greater than 7.2 * 10^10[/tex]

solve using the substitution method x = 10 y = 2x- 6

Answers

Answer:

y=14

Step-by-step explanation:

y=2(10)-6

y=14

You want to make a rectangular box, open at the top, by cutting the same size square corners out of a rectangular sheet of cardboard and then folding up the sides. The cardboard measures 11 in. by 14 in. What are the dimensions of the box that will have greatest volume if the possible corner cuts measure 1 in., 2 in., 3 in., or 4 in.?

Answers

Answer:

2 in.

Step-by-step explanation:

If we cut squares from all 4 corners and make it into a open rectangular box, the length of the square cut will become the height of the rectangular prism.

If we cut 1 inch side square:

The 11 inch side will become 11 - 2(1) = 9 and 14 inch side will become 14 - 2(1) = 12. Height is 1. So Volume would be 9 * 12 * 1 = 108

If we cut 2 inch side square:

The 11 inch side will become 11 - 2(2) = 7 and 14 inch side will become 14 - 2(2) = 10. Height is 2. So Volume would be 7 * 10 * 2 = 140

If we cut 3 inch side square:

The 11 inch side will become 11 - 2(3) = 5 and 14 inch side will become 14 - 2(3) = 8. Height is 3. So Volume would be 5 * 8 * 3 = 120

If we cut 4 inch side square:

The 11 inch side will become 11 - 2(4) = 3 and 14 inch side will become 14 - 2(4) = 6. Height is 4. So Volume would be 3 * 6 * 4 = 72

Hence, the greatest volume is when we cut 2 inch side square.

The answer is 2in hope this helps

WILL GIVE BRAINLYEST Use the given information to write an equation of the circle.
center at ​(-7​,-3​), radius 2

Answers

Answer:

(x + 7)² + (y + 3)² = 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 7, - 3) and r = 2, so

(x - (- 7))² + (y - (- 3))² = 2², that is

(x + 7)² + (y + 3)² = 4

Surface area of prisms and cylinders

Answers

Answer:

12. 785.375 in^2

13. 20.666 in.

14. 9cm

Step-by-step explanation:

12. The surface area of a cylinder is given by the surface area of each end plus the surface area of the side:

Surface area = 2 π r^2 + 2 π r h

we know that r = diameter / 2 = 10in/2 = 5in

height = 20 in

Then:

Surface area = 2 π r^2 + 2 π r h =  2 π (5in)^2 + 2 π (5in) (20in) = 785.375 in^2

13. A rectangular prism has 2 ends and 4 sides. Opposite sides have the same area. The surface area is the sum of the areas of all six sides. Then we have:

Area=2b+ph  

where:  

b= area of a base  = 6 in^2

p= perimeter of a base  = 18 in

h= height of the prism

Area = 384 sqrt units

Solving for "h" we have:

Area=2b+ph -> h = (area - 2b)/p = 20.666 in

Then: Area= 20.666 in.

14. We know that the surface area of a cylinder is:

Surface area = 2 π r^2 + 2 π r h

Solving for "h" we have:

h = (Surface area - 2 π r^2)/ 2 π r

Where r = 4cm

Surface area = 326.73 cm^2

h = (Surface area-2πr^2)/2πr=(326.73 cm^2-2π(4cm)^2)/2π(4cm) = 9cm

h =9cm

The total cost of a suit and a coat is
$291. The coat cost twice as much as
the suit. How much did the coat cost?​

Answers

The coat costs $194 while the suit costs $97

To find out how much the coat costs when a suit and a coat together cost $291 and the coat costs twice as much as the suit, we use algebra to deduce that the suit costs $97 and the coat costs $194.

To solve the problem of determining how much the coat costs when the total cost of a coat and a suit is $291, and the coat costs twice as much as the suit, we can set up a system of equations. Let's define s as the cost of the suit and c as the cost of the coat. Following the given information, we have two equations:

s + c = $291 (the total cost of the suit and the coat)c = 2s (the coat costs twice as much as the suit)

Substituting the second equation into the first one gives us:

s + 2s = $291

Combining like terms, we get:

3s = $291

Dividing both sides by 3 to solve for s, we find:

s = $97

Now that we have the cost of the suit, we can use the second equation to find the cost of the coat:

c = 2s = 2 times $97 = $194

Therefore, the coat costs $194.

steps to sloving -2(x+3)=-10​

Answers

Answer:

x = 2

Step-by-step explanation:

[tex]-2(x+3)=-10[/tex]          divide both sides by (-2)

[tex]\dfrac{-2(x+3)}{-2}=\dfrac{-10}{-2}[/tex]

[tex]x+3=5[/tex]            subtract 3 from both sides

[tex]x+3-3=5-3[/tex]

[tex]x=2[/tex]

Answer:

x = 2

Step-by-step explanation:

It is given an expression with variable x

-2(x + 3) = -10​

To find the steps to solving expression

Le expression be,

-2(x + 3) = -10​

-2x + (-2 * 3) = -10

-2x - 6 = -10

-2x = -10 + 6

-2x = -4

2x = 4

x = 4/2 = 2

Therefore x = 2

how do you find the mean, median and range​

Answers

for mean you add every number and divide it by the amount of numbers in the data set

for median you put the numbers in order and find the middle number, if there is no middle get the mean for the two middle numbers

range is basically the lowest and highest number

Answer:

Mean= Average

Median= Middle number after numbers are lined up in order

Mode= Repeated Number

Step-by-step explanation:

Why might Jules use a Credit Card rather than a check to make a purchase

Answers

He does not have enough money in his checking account

Answer:

B

Step-by-step explanation:

Given the following graph, would the point (1,2) Be a solution of the inequality? Explain.

Answers

ANSWER

The point (1,2) is not a solution

EXPLANATION

We could see that, the point (1,2) lies exactly on the boundary line.

Since the boundary line is dashed, the points on the boundary line are not solution.

Alternatively:

We deduce the inequality from the graph to be;

[tex]y < 3x - 1[/tex]

If the point (1,2) is a solution,then it must satisfy the inequality.

[tex]2 \: < \: 3(1) - 1[/tex]

[tex]2 \: < \: 2[/tex]

This statement is false.

Hence, the point (1,2) is not a solution.

3m-n=km-8 solve for m

Answers

Answer:

m= -8-n/3-k

Step-by-step explanation:

Help pleaseeeeeeeeeeeeeeeeeee

Answers

The first equation

6x^2 -18x-24=0

-the graph opens up

6(x^2 -3x -4)=0

6(x^2 -3x +9/4-4-9/4)=0

6(x-3/2)-25x6/4=

6(x-3/2)-75/2

-Vertex is at (3/2, -75/2)

-Axis of symmetry is x=3/2

Second equation

3r^2 -16r -12=0

-the graph opens up

...

Answer Please!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

8/15 square inches

Step-by-step explanation:

Just multiply the 2 fractions to get the area.

A=L*W

A=area

L=length

W=width

PLEASE HELPPPP!!!!
given f (x)= -5x+1. what is f (-3)

Answers

Answer:

16

Step-by-step explanation:

f (x)= -5x+1.

Let x = -3

f(-3) = -5(-3) +1

      =15 +1

     = 16

Answer:

f(- 3) = 16

Step-by-step explanation:

To evaluate f(- 3) substitute x = - 3 into f(x)

f(- 3) = ( - 5 × - 3) + 1 = 15 + 1 = 16

Emilio's savings account had a balance of $621.96 at the end of July. During August, he made three savings account deposits of $83.11, $52.89, and $307.84 and one withdrawal of $129.00. At the end of August his account earned $11.50 in interest. Will Emilio meet his savings account goal of $1,000 by September 1st?

A
Yes, and he will have $51.70 more than expected.

B
No, and he would still need $51.70.

C
Yes, and he will have $77.30 more than expected.

D
No, and he would still need $77.30.

Answers

Answer:

B. He would still need 51.50

Step-by-step explanation:

First I added up all the deposits Emilio made

so: 621.96+83.11+52.89+307.84=1065.8

then i subtract 129 from the total (1065.8)

which equals 936.8 and I add the 11.5 interest.

which equals 948.3 which is 51.70 less than 1000. Therefore, Emilio still need 51.70 in order to meet his saving accounts goal.

Amanda wants to examine the eating habits of 100 random students at lunch to determine how many students eat in the cafeteria

Answers

Answer:

well she can count up the average amount of tables, and the average amount of students in the school, later determine how many kids sit at the tables, for example, if there's five tables, and in each table there are five students, round those up and you have 25 students, only Amanda's answer would be much higher depending on the school and cafeteria

Five times the sum of a number and 3 equals 4?

Answers

Answer:

5 * (n+3) = 4

n = -11/5

Step-by-step explanation:

5 * (n+3) = 4

Distribute

5n +15 =4

Subtract 15 from each side

5n +15-15 = 4-15

5n = -11

Divide by5

5n/5 = -11/5

n = -11/5

Which set of side length form a right triangle?
A) 3ft, 5ft, 6ft
B) 15ft, 39ft, 36ft
C) 7ft, 10ft, 26ft
D) 12ft, 13ft, 14ft

Please explain when you answer

Answers

B. 15ft, 36ft, 39ft

use pythagorean theorem

a²+b²=c²

225+1296=1521

write a recursive rule for the arithmetic sequence 22,15,8,1

Answers

Answer:

a=1

an= an-1 -7

Step-by-step explanation:

A= 1 the answer is A=1

find the value of x that makes triangle LMN congruent to triangle NOL by SSS. A. 1 B. 2.3 C.6 D.7

Answers

Answer:

The correct answer is option C.  6

Step-by-step explanation:

It is given that,  LMN congruent to triangle NOL by SSS

From the figure we can write, MN = LO

To find the value of x

we have, MN = LO

13x + 1 = 5x + 49

13x - 5x = 49 - 1

8x = 48

x = 48/8 = 6

Therefore x = 6

The correct answer is option C.  6

Three fourths through the soccer season,Gustafo has 24 goals.He averages 4 goals per game.How many more games will it take Gustafo to have at least 40 goals before the season is over?

Answers

Answer:=40

He needs 4 more games because 4*10

Step-by-step explanation:

Final answer:

Gustafo needs to score 16 more goals to reach 40 goals. Since he scores 4 goals per game on average, he will need 4 more games to reach his goal.

Explanation:

To determine the number of games Gustafo needs to reach at least 40 goals, we first have to find out how many goals he still needs to score. Right now, Gustafo has 24 goals. So, 40 (the total number of goals he needs) - 24 (the goals he already has) = 16 goals he still needs to score.

Since Gustafo scores an average of 4 goals per game, we then divide the number of goals he still needs to score by his average goals per game to find out how many games it will take. So, 16 (goals needed) ÷ 4 (average goals per game) = 4 games. Thus, Gustafo needs to play 4 more games to reach at least 40 goals before the season is over.

Learn more about Score Calculation here:

https://brainly.com/question/30759870

#SPJ3

if the apothem is 13 square root 3 ft what is the area of the hexagon

Answers

Answer:

The area of the hexagon is [tex]1,014\sqrt{3}\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular hexagon is equal to

[tex]A=\frac{1}{2}Pa[/tex]

where

P is the perimeter

a is the apothem

Find the length side of the hexagon

Let

b-----> the length side of the hexagon

Remember that

The formula to calculate the length side given the apothem is equal to

[tex]b=\frac{2a}{\sqrt{3}}[/tex]

we have

[tex]a=13\sqrt{3}\ ft[/tex]

substitute

[tex]b=\frac{2(13\sqrt{3})}{\sqrt{3}}[/tex]

[tex]b=26\ ft[/tex]

Find the perimeter P

[tex]P=6b=6(26)=156\ ft[/tex]

Find the area of the hexagon

[tex]A=\frac{1}{2}(156)(13\sqrt{3})=1,014\sqrt{3}\ ft^{2}[/tex]

Find the slope that is parallel to the equation 2x +3y 15
b) Find the slope that is perpendicular to the equation 2x + 3y 15​

Answers

Answer:

a) -2

b) 1/2

Step-by-step explanation:

2x + y = 15           Subtract 2x from both sides

y = -2x + 15           The slope is -2

Parallel lines have the same slope.

Perpendicular lines have negative inverse slopes.

-2    flips to 1/2

Which number line represents the solution set for the inequality –(1/2)x ≥ 4?

Answers

When the sign is ≤ or ≥ (less/greater than or equal to), the dot is filled in.

When the sign is < or >, the dot is not filled in and looks like this o

To find out which number line represents the solution set, simplify the inequality and isolate x

[tex]-\frac{1}{2}x\geq4[/tex]    Multiply -2 on both sides to get rid of -1/2

[tex](-2)(-\frac{1}{2}x)\geq4(-2)[/tex]

x ≤ -8       (The sign flips when you multiply/divide a negative number on both sides of the inequality)

so you get x is greater than or equal to -8, so you have a filled in circle on -8, and the arrow should be going to the right since x is greater than -8

answer : second choice / b

we have

-1/2x >_ 4

Solve the inequality

Multiply by both sides-----> remember change inequality sign

x<_ -4(2)

x<_ -8

the solution is the interval-----------> (-∞,-8]

using a graph tool

see the attached figure

the solution is the shaded area:

If point (a, b) is in the second quadrant, in what quadrant is (a,-b). (-a, b), (-a,-b), (b, a)

Answers

Final answer:

Point (a, -b) will be in the third quadrant, (-a, b) will be in the first quadrant, (-a, -b) will be in the fourth quadrant, and (b, a) will be in the fourth quadrant.

 

Explanation:

The original point (a, b) is in the second quadrant, which means the value of 'a' is negative and 'b' is positive. For the point (a, -b), the x-coordinate remains the same (negative) and the y-coordinate becomes negative, so this point will be in the

third quadrant

. For (-a, b), both the x and y coordinates change sign. The 'x' becomes positive and 'y' remains positive, landing this point in the

first quadrant

. For (-a, -b), both coordinates are positive, which puts this point in the

fourth quadrant

. Lastly, for (b, a), the 'x' coordinate is positive and 'y' coordinate is negative (since 'a' is negative), which means this point will be in the

fourth quadrant

as well.

Learn more about Quadrants in Cartesian Coordinate System here:

https://brainly.com/question/8278191

#SPJ3

Points resulting from the transformation of (a, b) in the second quadrant lie in various quadrants based on their signs. (a, -b) is in the fourth quadrant, (-a, b) is in the third quadrant, and both (-a, -b) and (b, a) are in the first quadrant.

Given that point (a, b) is in the second quadrant, we need to determine the quadrants of the points (a, -b), (-a, b), (-a, -b), and (b, a).

(a, -b): Since a is positive and -b is negative, this point lies in the fourth quadrant.(-a, b): Here, -a is negative and b remains positive, placing this point in the third quadrant.(-a, -b): Both -a and -b are negative, so this point lies in the first quadrant.(b, a): With b positive and a positive, this point would fall in the first quadrant.

To summarize, if the original point is in the second quadrant of the Cartesian coordinate system, the points (a, -b) is in the fourth quadrant, (-a, b) is in the third quadrant, (-a, -b) is in the first quadrant, and (b, a) is in the first quadrant as well.

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