The expression below represents the perimeter, in feet, of Manual’s garden. 15 + 2x + 7 + 15 + 2x + 7 Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Manual’s garden. The area, measured in square feet, of Manual’s garden is found by calculating 15(2x + 7). Manual incorrectly says the area can also be found using the expression 30x + 7. Describe the error in Manual’s expression. Also, find the difference, in square feet, between the actual area of Manual’s garden and the area found using his expression as a part of your explanation. Manual’s friend Sasha designs a square garden. Each side measures 3x + 5 in length. The perimeter of Sasha’s garden is how much larger than the perimeter of Manual’s garden?​

Answers

Answer 1

The perimeter of Sasha’s garden is 8x - 24 larger than the perimeter of Manual’s garden

The equivalent expression using exactly two terms

The perimeter is given as:

P =  15 + 2x + 7 + 15 + 2x + 7

Collect like terms

P =  2x + 2x + 7 + 15 +  15  + 7

Evaluate the like terms

P = 4x + 44

The area of the garden

The area of the garden is given as:

A = 15(2x + 7).

Expand

A = 30x + 105

Manual's expression of the area is 30x + 7

Hence, Manuel's error is that he did not multiply 15 by 7 when expanding the bracket and the actual area is 30x + 105

The difference between the areas of Manual’s garden and Sasha's design

The side length of Sasha's design is:

L = 3x + 5 in

So, the area is:

A = (3x + 5)^2

Expand

A = 9x^2 + 16x + 25

The difference between both areas is:

Difference = 9x^2 + 16x - 30x + 25 - 105

Evaluate

Difference = 9x^2 - 14x - 80

Hence, the difference between the areas of Manual’s garden and Sasha's design is 9x^2 - 14x - 80

The perimeter of Sasha's garden

This is calculated using:

P = 4L

So, we have:

P = 12x + 20

The difference between both perimeter is:

Difference = 12x - 4x + 20 - 44

Evaluate

Difference = 8x - 24

Hence, the perimeter of Sasha’s garden is 8x - 24 larger than the perimeter of Manual’s garden

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Related Questions

The difference of two numbers is 18. The sum of the two numbers is 62. Let x be the greater number, and let y be the lesser number.
Please help ASAP

Answers

Answer:

x=40,y=22

Step-by-step explanation:

62/2=31

31+9=40

31-9=22

40+22=62

A rectangular pyramid has a base that measures 8 inches by 10 inches, a height of 12 inches, and a slant height of 15 inches. elena calculated the volume of the pyramid as shown. v = 1 3 bh v = 1 3 (80)(15) v = 400 in.3 what was her mistake? elena used the wrong units. elena incorrectly used the slant height instead of the height. elena multiplied incorrectly. elena should not have multiplied by one third.

Answers

Answer:

Elena incorrectly used the slant height instead of the height.

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

i got it right

A numerical measure computed from a sample, such as sample mean, is known as a.

Answers

Answer:

Sample statistic

is 10 times as much as 20 1/10 of 2,000?

Answers

Answer:

IT IS 43./45455/.34 LIKE WHEN U ADD 10 TIMES 10 AND DIVIDED 2,000 FROM 20 U THAT ANSWER

Which Stem-and-Leaf Plot matches the data set shown below?{11, 23, 13, 17, 13, 24, 22, 32, 12, 35} PLEASE HELP ME

Answers

Answer:

I am going to use a dot to represent a line:

1 . 1, 2, 3, 3, 7

2. 2, 3, 4

3. 2, 5

What is ur fav.
1) Chocolate 2) Vanilla 3) Strawberry 4) Mint Chocolate Chip 5) Cotton Candy 6) Coffee

Pick a number and put your name in the comments below with the number u picked

Answers

Answer:

cotton candy 6 I'm sure that's is answer thank you

pls help find the lateral surface area of this prism in square centimeters, i give brainliest!! :)

Answers

Answer:

1232 square meters

Step-by-step explanation:

The lateral surface area are all the rectangles.

1st rectangle:

A = lw

A = 25(22)

A = 550

2nd rectangle:

A= lw

A = 7(22)

A = 154

3rd rectangle:

A = lw

A = 24(22)

A = 528

Add the areas together.

550 + 154 + 528 = 1232

Help me please! so jarring

Answers

Answer:

y = -5x + 4.

Step-by-step explanation:

y = mx + c  is the general form

- where m = the slope of the line and c is the y-value where the graph cuts the y-axis.

The graph passes through the points (0, 4) and (1, -1) so the slope

= (Y2 - y1) / (x2 - x1)

= (-1-4) / (1-0)

= -5 = m.

and c = 4.

please help me solve this

Answers

[tex]~~~~~\sin 30^{\circ} = \dfrac{x}{6}\\\\\implies \dfrac 12 = \dfrac x6\\\\\implies x = \dfrac 62 \\\\\implies x= 3.0~ \text{cm}[/tex]

[tex]\huge\underline\mathcal{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

The question can be easily solved applying trigonometry ~

We know that ,

[tex]\bold{ \sin(\theta) = \frac{perpendicular}{hypotenuse}} \\ [/tex]

Given - θ = 30° and hypotenuse = 6cm

To find - the perpendicular , i.e. , value of x

Substituting the values in the formula of sin θ

[tex] \sin(30\degree) = \frac{x}{6} \\ [/tex]

now , we know that sin 30° = 1/2

[tex]\therefore \: \implies \frac{1}{2} = \frac{x}{6} \\ [/tex]

on cross multiplying ,

[tex]\implies \: 2x = 6 \\ [/tex]

dividing both sides of the equation by 2 ,

[tex] \implies \: \cancel \frac{2x}{2} = \cancel\frac{6}{2} \\ \\ \implies \: \boxed{x = 3 \: cm}[/tex]

hope helpful ~

please helpp
2. A line goes through the points {8, 9} and {-2. 4}.
(a) What is the slope of the line? Show all steps of work for full credit. (2 pts)





(b) Write the equation of the line in point-slope form. Show your work (state the point and slope you are using). (2 pts)
POINT (Ordered Pair): ¬¬¬_______________
SLOPE:_______________
EQUATION:____________________________

(c) Write the equation of the line in slope-intercept form. Show all steps of work for full credit. (2 pts)

Answers

Answer:

a)

[tex] \frac{2}{5} [/tex]

b)

Step-by-step explanation:

slope formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

[tex] \frac{4 - 9}{ - 2 - 8} [/tex]

=

[tex] \frac{2}{5} [/tex]

b) using point (-2,4)

[tex]y - y1 = m(x - x1)[/tex]

[tex]y - 4 = \frac{2}{5} (x - ( - 2)[/tex]

Now distribute

[tex]y - 4 = \frac{2}{5} x + \frac{4}{5} [/tex]

add 4 to each side

[tex]y = \frac{2}{5} x + \frac{24}{5} [/tex]

can use the other point given if you want

A basketball team made $3,094 selling team hats. Each hat sold for $34. How many hats did the team sell?

Answers

Answer:

The team sold 91 hats.

Step-by-step explanation:

$3,094 ÷ %34 = 91

Answer: 91 hats
Why?
3,094 divided by 34.

#46 will give brainliest

Answers

Answer:

50

Step-by-step explanation:

This is the equation:
x = 5 + 3y
We know that:
x - y = 35

Meaning we only need to solve for y now:

(5 + 3y) - y = 35
5 + 2y = 35
2y = 30
y = 15

Meaning the final formula is

x = 5 + 3(15)
x = 50

Let's set some variables before we solve:

First number ⇒ xSecond number ⇒ y

Okay's lets read the question

'x' is 5 more than three times 'y'

           ⇒ [tex]x = 3y +5[/tex]

               ⇒ [tex]x-3y=5[/tex]

Their difference is 35

           ⇒ [tex]x - y = 35[/tex]

Let's put the two equations together and solve

  [tex]x-3y=5 --equation1\\[/tex]

  [tex]x-y=35 -- equation2[/tex]

 (equation2) - (equation1)

  [tex]2y = 30\\y = 15 -- equation 3[/tex]

  (equation 3)'s value of y into (equation2)

  [tex]x - 15= 35\\x = 50[/tex]

Thus: [tex]x = 50[/tex] and [tex]y = 15[/tex]

The larger number is 50

Answer: 50 or Choice 3

Hope that helps!

 

What is the slope of the line through (-5, 13) and (2,-1)

Answers

          [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

       What is the slope of the line through (-5, 13) and (2, -1) ?

  [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

We can use the slope formula :-

[tex]\Large\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]

Now , We replace letters with numbers ,

[tex]\Large\text{$\displaystyle\frac{-1-13}{2-(-5)}$}[/tex]

On simplification,

[tex]\Large\text{$\displaystyle\frac{-14}{2+5}$}[/tex]

On further simplification ,

[tex]\Large\text{$\displaystyle\frac{-14}{7}$}[/tex]

[tex]\diamond[/tex] Finally, We get

[tex]\longmapsto\sf\underline{\boxed{\tt{slope=-2}}}[/tex]

Good luck with your studies.

#TogetherWeGoFar

[tex]\rule{300}{1}[/tex]

The slope of the line joining the points (a,b) and (c,d) is given by

[tex]{\boxed{\bf{Slope(m)=\dfrac{d-b}{c-a}}}}[/tex]

Putting the values, we have:

[tex]{:\implies \quad \sf m=\dfrac{-1-13}{2-(-5)}}[/tex]

[tex]{:\implies \quad \sf m=\dfrac{-14}{2+5}}[/tex]

[tex]{:\implies \quad \sf m=\dfrac{-14}{7}=\boxed{\bf{-2}}}[/tex]

PLEASE HELP ASAP!! DUE IN 10 MINUTES!! I'LL MARk BRAINLIEST ADN HIGH POINTS!! PLEASE HELP!!

Answers

Answer:

*speedrunning intensifies*

A:

Min is 15

LQ is 23

Median is 36

UQ is 38

B:

IQR is 38 minus 23, or 15, I guess that the data is not very consistent and it is spread out?

C:

Min is calculated by looking at the end of the far left line

LQ is the far left of the box

Median is the line inside the box

UQ is the the far right of the box

IQR is UQ subtract LQ

I answered because I wanted you to get brainliest!

A circular plate has circumference 20.7 inches. What is the area of this plate? Use 3.14 for a.
The area of this plate is about square inches.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest
thousandth as needed.)

Answers

Answer:

34 in²

Step-by-step explanation:

20.7 / 3.14 = 6.592 = diameter

6.592 / 2 = 3.296 = radius

3.296²(3.14) = 34.1

≈ 34 in²

5 / 949 If they decide to drive 949 mi to Denver instead, how many miles will they drive each day?

Answers

Data is unclear.
If the question is asking how many miles will be driven each day over the course of 5 days in order to reach 949 miles, the answer is 949/5=189.8

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 15 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. . Store Shelf Space Weekly Sales 1 5 1.3 2 5 1.6 3 5 1.4 4 10 1.7 5 10 1.9 6 10 2.3 7 15 2.2 8 15 2 9 15 1.8 10 20 2.2 11 20 2.4 12 20 2.9 13 25 2.9 14 25 2.7 15 25 2.5 Using the regression line for this problem, the approximate Weekly Sales for shelf space that is :_________,i. 30. ii. 3.12 iii. 3.1 iv. 3.04 v. 2.99

Answers

The Weekly Sales for 30 shelf spaces is 3.04

How to determine the Weekly Sales for 30 shelf spaces?

The proper table is added as an attachment.

Next, we determine the regression equation using a graphing calculator.

From the graphing calculator, we have the following calculation summary:

Sum of X = 225Sum of Y = 31.8Mean X = 15Mean Y = 2.12Sum of squares (SSX) = 750Sum of products (SP) = 46

The regression equation is represented as:

y = bx + a

Where

b = SP/SSX = 46/750 = 0.06133

a = MY - bMX = 2.12 - (0.06*15) = 1.2

So, we have:

ŷ = 0.06133x + 1.2

When x =30, we have:

ŷ = 0.06133 * 30 + 1.2

Evaluate

ŷ = 3.04

Hence, the Weekly Sales for 30 shelf spaces is 3.04

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Find the errors and solve the problem correctly!
Thanks

Answers

The sequence converges to 5 as n goes to ∞. We can prove this rigorously:

The claim is that, for [tex]n\in\Bbb N[/tex],

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = 5[/tex]

By definition of the limit, this means for any ε > 0, there exists some N such that for any n larger than N, we have

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| < \varepsilon[/tex]

In order to ensure this inequality, we work backwards to find N in terms of ε :

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| = \left| \dfrac{5n-1 - 5(n+1)}{n+1} \right| = \dfrac4{|n+1|} < \varepsilon[/tex]

n is a natural number, so n + 1 > 0 and |n + 1| = n + 1. Then

[tex]\dfrac4{n+1} < \varepsilon \implies \dfrac{n+1}4 > \dfrac1\varepsilon \implies n+1 > \dfrac4\varepsilon \implies n > \dfrac4\varepsilon - 1[/tex]

Let N be the smallest natural number greater than or equal to 4/ε - 1, i.e.

[tex]N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then the proof follows: suppose

[tex]n \ge N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then

[tex]n \ge \left\lceil\dfrac4\varepsilon - 1\right\rceil \implies n > \dfrac4\varepsilon - 1 \\\\ \implies n+1 > \dfrac4\varepsilon \\\\ \implies \dfrac4{n+1} < \varepsilon \\\\\implies \left|\dfrac{5n-1}{n+1}-5\right| < \varepsilon[/tex]

as required.

Or we can avoid the rigor and use some facts we know about limits:

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = \lim_{n\to\infty} \frac{5-\frac1n}{1+\frac1n} = 5[/tex]

since 1/n converges to 0 as n goes to ∞.

what is blank % of 18 = 9

Answers

Answer:

50 percent, trust me.

Answer: 50%

Step-by-step explanation: 50/100 x 18 = 9

50/100 can also be written as 0.5

0.5 x 18 = 9

of = multiply

Which equation describes the line with a slope of -3 that contains the point (2,4)?

Answers

Answer: y = 2x - 11

Step-by-step explanation:

A linear equation has the following form.

y = a . x + b

where,

y: independent variable

a: slope

x: independent variable

b: y-intercept

The slope is 2, so a is 2. The ordered pair (4, -3) means that when x takes the value 4, y takes the value -3. We can replace these values in the general equation to find the y-intercept.

y = a . x + b

-3 = 2 . 4 + b

b = -11

The linear equation is

y = 2x - 11

Answer:

C. is the correct option

Step-by-step explanation:

When we find the equation using the point and slope formula, we get y=-3x+10

As you can see, that doesn't match any of the answers, since it is in the point-slope formula.

We can start solving all the equations to rule out the correct one, but to save yourself from reading all of this, I'll just do there C.

For this equation, we will distribute the 3, and then add 4 to both sides.

y-4=-3(x-2) --->  y-4=-3x+6 ---> y-4(+4)=-3x+6(+4) ---> y=-3x+10

This leads back to the original equation so we know it is correct.

2,994 divided by 128 i need help

Answers

23.390625
That is your answer

Answer:

Divide 320 by 128 to get 2

23.39062

128| 2994.00000

256

____

434

384

_____

500

384

_____

1160

1152

____

80

0

___

800

768

_____

320

256

_____

64

Stopping at 5 decimal places

The solution for Long Division of 2994/128 is 23.39062

23.39062

Which equation represents the transformed function below? on a coordinate plane, a parent function starts at (0, negative 1) and then curves up into quadrant 1 and approaches y = 1. a transformed function starts at (0, 4) and then curves up into quadrant 1 and approaches y = 6. _____ = parent function; y = log x - - - - - = transformed function y = log x 5 y = log x minus 5 y = log (x 5) y = log (x minus 5)

Answers

The parent function which starts at (0, -1) and then curves up into quadrant 1 is logx and the transformed function which starts at (0, 4) and then curves up into quadrant 1 is logx+5.

What is transformation of a function?

Transformation of a function is shifting the function from its original place in the graph.

Types of transformation-

Horizontal shift- Let the parent function is f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)-c shifts the graph c units down and by replacing parent function with f(x)+c shifts the graph c units up.

On a coordinate plane, a parent function starts at (0, -1) and then curves up into quadrant 1 and approaches y = 1. Thus, the function of this curve is,

y=logx

A transformed function starts at (0, 4) and then curves up into quadrant 1 and approaches y = 6.

y=logx +5

Thus, the parent function which starts at (0, -1) and then curves up into quadrant 1 is logx and the transformed function which starts at (0, 4) and then curves up into quadrant 1 is logx+5.

Learn more about the transformed function here:

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Answer:

yeah its a

Step-by-step explanation:

yw

Triangle ABC represents a triangular garden with side lengths AB= 10cm ,BC= 8cm and AC=15cm .

What is the smallest and largest angle of the garden?

Answers

Answer:

Largest angle is "B" and smallest angle is "A".

Step-by-step explanation:

Given ∆ABC

AB = 10 cm , BC = 8 cm , AC = 15 cm

Angle opposite to side AB is "C"

Angle opposite to side BC is "A"

Angle opposite to side AC is "B"

we know that the angle opposite to largest side is largest angle and smallest side is smallest angle.

Here,∆ABC largest side is AC and smallest side is BC.

Hence,largest angle is "B" and smallest angle is "A".

A company is designing a new cylindrical water bottle. The volume of the bottle will be 226 cm cubed. The height of the water bottle is 8.2 cm. What is the radius of the water bottle? Use 3.14 for pi


Need answer asap plsss!!

Answers

Answer:

2.96 cm to the nearest hundredth.

Step-by-step explanation:

V = 3.14 r^2 h

226 = 3.14 * r^2 * 8.2

r^2 = 226 / (3.14*8.2)

r^2 = 8.7774

r =  2.96 cm to the nearest hundredth.


Match the correct corresponding parts. Make sure your letters are in the correct order!!
SAT~GRE

Answers

Answer:

Step-by-step explanation:

calculate the length of ed and be

Answers

Answer:

ED = 6.5 cm

BE = 14.4 cm

Step-by-step explanation

AB/BC = AE/ED is less than or eqauls ED = BC×AE/AB

so

ED = 5×26/20 = 130/20 = 6.5 cm

and

AB/AC = BE/CD => BE = AB×CD/AC

so

BE = 20×18/25 = 360/25 = 14.4 cm

Which quadrilateral always has diagonals that are congruent but not necessarily perpendicular.

Answers

Step-by-step explanation:

a trapezoid.

the 2 sides on the left and the right are equal (congruent), and so are the diagonals.

but these diagonals are usually not perpendicular (perpendicular = intersecting each other at 90°).

Evan places a rectangular birdbath in his garden. The dimensions are 24, 8, and 11
2
in. Explain how to find the maximum amount of water the birdbath can hold. Then find the amount.

Answers

The maximum amount of water the birdbath can hold is 288 cubic in which is the volume of the cuboid.

What is a cuboid?

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

We have a rectangular birdbath in his garden. The dimensions are 24, 8, and [tex]1\dfrac{1}{2}[/tex] inches

The maximum amount of water in the birdbath = volume of the birdbath

[tex]\rm = 24 \times 8 \times 1\dfrac{1}{2}[/tex]

[tex]\rm = 24 \times 8 \times \dfrac{3}{2}[/tex]

= 288 cubic in

Thus, the maximum amount of water the birdbath can hold is 288 cubic in which is the volume of the cuboid.

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Can somebody help me on this

Answers

Answer:

7 + 7 = 14

you have 7 apples and add 7 more thats 14

Step-by-step explanation:

Choose all of the following statements that suggest a positive association.
A. The less education a person has, the less money they will likely earn.
B. The less fruits and vegetables a person eats, the lower their risk for cancer.
C. The smaller a person's shoe size, the larger their pant size.
D. The more you study, the more likely you are to earn a better grade.

Answers

Answer:

D

Step-by-step explanation:

It is only d because that is the only positive statement.

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