SIMPLIFY THE EXPRESSION:

SIMPLIFY THE EXPRESSION:

Answers

Answer 1

Answer:

12x - 8y

Step-by-step explanation:

Combine like terms.

10x - 5y + 2x -3y =

= 10x + 2x - 5y - 3y

= 12x - 8y

Answer 2
10x+2x-5y-3y
=12x-8y
Hope it helps

Related Questions

Mustafa, Heloise, and Gia have written more than a combined total of
22
2222 articles for the school newspaper. Heloise has written
1
4
4
1

start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written
3
2
2
3

start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.
Write an inequality to determine the number of articles,

mm, Mustafa could have written for the school newspaper.

Answers

m > 8 is an inequality used to calculate the number of articles Mustafa could have written.

Let's assume that Mustafa has written m articles for the school newspaper.

Then, according to the given information:

Heloise has written 1/4 as many articles as Mustafa has, which means she has written 1/4 × m = m/4 articles.

Gia has written 3/2 as many articles as Mustafa has, which means she has written 3/2 × m = 3m/2 articles.

The combined total of articles written by all three is more than 22, so we can write:

m/4 + 3m/2 + m > 22

Simplifying and solving for m:

11m/4 > 22

m > 22 × 4/11

m > 8

Therefore, m > 8 is an inequality used to calculate the number of articles Mustafa could have written.

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A home repair crew charges $75 dollars per day plus a $250 service fee. the total amount the home repair crew charges this client is $925.how many days did the crew work?

Answers

The home repair crew worked for 9 days.

What is the duration of the home repair crew's work to charge $925?

To determine the number of days the home repair crew worked for, we can use algebra. Let's assume that the number of days they worked for is represented by "d". We know that they charge $75 per day plus a $250 service fee, so we can set up the following equation:

75d + 250 = 925

Simplifying the equation, we get:

75d = 675

Dividing both sides by 75, we get:

d = 9

However, we need to keep in mind that the $250 service fee is a one-time charge, not a daily charge. So we need to subtract that from the total amount to get the actual amount charged for the days worked:

925 - 250 = 675

Dividing 675 by the daily rate of $75, we get:

675 / 75 = 9

Therefore, the home repair crew worked for 9 days.

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Which sequence of transformations could triangle XYZ have
gone through to produce figure XYZ as shown to the right?
A Rotation 90° clockwise, translation 4 units up and 3 units right.
B. Rotation 90° counterclockwise, translation 3 units up and 4
units right.
C. Rotation 90° clockwise, reflection across the y-axis
D. Rotation 90° counterclockwise, reflection across the y-axis.
Z
YA
X'
A

Answers

The sequence of transformations the triangle XYZ have gone through to produce figure X'Y'Z' is: D. Rotation 90° counterclockwise, reflection across the y-axis.

What is transformation?

Transformation is a method required to change the orientation, or resize a given object to produce its image. Some of the types of transformation are: rotation, reflection, dilation, and translation.

Rotation requires turning a given object about a point at a certain angle.

Reflection implies flipping an object over a line as a reference point.

Dilation deals with either increasing or decreasing the dimensions of a given object.

Translation involves moving an object in a specific direction and given number of units.

Considering triangle XYZ and the figure produced, we can conclude that:

The sequence of transformations the triangle XYZ have gone through to produce figure X'Y'Z' is: D. Rotation 90° counterclockwise, reflection across the y-axis.

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Frank is packing cube-shaped containers into large boxes. he can fit
15 containers in each layer. if he stacks 8 layers into one box, what is the
volume of the box?

Answers

The volume of the large box is 120[tex]s^3[/tex].

How to find the volume?

If Frank can fit 15 cube-shaped containers in each layer and stack 8 layers into one box, then the total number of containers he can fit in one box is:

15 containers/layer x 8 layers = 120 containers

Since each container is cube-shaped, we can assume that it has the same length, width, and height. Let's represent the length of one side of the container as "s". Then, the volume of one container is:

Volume of one container = [tex]s^3[/tex]

The volume of 120 containers that can fit in one box is:

Volume of 120 containers = 120 x Volume of one container

Substituting the expression for the volume of one container, we get:

Volume of 120 containers = 120[tex]s^3[/tex]

Therefore, the volume of the large box that can hold 120 cube-shaped containers with side length "s" is 120[tex]s^3[/tex].

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Using a compass a ruler and a protractor draw a circle having

Answers

By using the compass a ruler and a protractor a circle having a Radius MO of 3 cm, Diameter OP of 6cm, Chord QR of 4cm, and Central angle <OMS of 60° has been Drawn.

Given data:

Radius MO = 3 cm

Diameter OP = 6cm

Chord QR = 4cm

Central angle <OMS = 60°

Steps to follow to draw the circle,

Step 1: Mark the M point as the center.

Step 2: Now take the compass and take a 3 cm reading on it by using the ruler.

Step 3: Draw the circle by using M as the center

Step 4: Mark a point O on the circle

Step 5: Draw a straight line segment OP passing through M

Step 6: Mark a point Q on the circle

Step 7: Using compass width and take a 3 cm reading on it and by taking Q as center cut the circle at R.

Step 8: Now join Q and R points.

Step 9: Using compass width and take a 3 cm reading on it and by taking O as the center cut the circle at S.

Step 10: Now join S and M points

Therefore, The circle, central angle on the circle, and chord on the circle are drawn.

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The complete question is,

1. Directions: Using a compass, ruler, and protractor, draw a circle having:

1.) M as the center

2.) radius MO of 3 cm

3.) diameter OP of 6cm

4.) chord QR of 4cm

5.) central angle:<OMS of 60°

If 4:15=a:2 1/2(two and a half), what is the value of a

Answers

The value of 'a' is 2/3.

What is the value of 'a' if the ratio of 4 to 15 is equivalent to the ratio of 'a' to 2 1/2?

The problem presents a ratio, 4:15, that is equal to a ratio involving 'a' and 2 1/2. To solve for 'a', we need to isolate it on one side of the equation by cross-multiplying.

In the first step, we convert 2 1/2 to an improper fraction, 5/2, so that we can use it in the equation. We then cross-multiply by multiplying both sides of the equation by 5/2.

This eliminates the denominator on the right-hand side and simplifies the left-hand side.

Solve for 'a'

To solve for 'a', we can use cross-multiplication.

First, we need to convert 2 1/2 to an improper fraction:

2 1/2 = 5/2

Now we can write the equation as:

4/15 = a/(5/2)

To solve for 'a', we cross-multiply:

4/15 * 5/2 = a

a = 2/3

Finally, we solve for 'a' by multiplying 4/15 by 5/2 and simplifying the result. The answer is 2/3, which represents the value of 'a'.

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14
Find the limit of the rational function a. as x and b. as X-→ - 00 X + 6 f(x) = +3 + 20 X+6 a. lim x x² + 20 (Simplify your answer.) X + 6 b. lim x--00x2 + 20 = (Simplify your answer.) (

Answers

Both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0

Know more about rational function,

First, let's rewrite the rational function f(x) more clearly and identify the two limits we need to find: f(x) =[tex](x + 6) / (x^2 + 20)[/tex]

a. lim (x→∞) f(x) b. lim (x→-∞) f(x)

To find these limits, we can use the following steps:

Step 1: Divide both the numerator and the denominator by the highest power of x in the denominator.

In this case, it is x^2. f(x) = [tex][(x + 6) / x^2] / [(x^2 + 20) / x^2][/tex]

Step 2: Simplify the function. f(x) =[tex][(1/x) + (6/x^2)] / [1 + (20/x^2)][/tex]

Step 3: Evaluate the limits.

a. lim (x→∞) f(x)

= [(0) + (0)] / [1 + (0)]

= 0 / 1 = 0

b. lim (x→-∞) f(x)

= [(0) + (0)] / [1 + (0)]

= 0 / 1 = 0

So, both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0

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To solve 2x + 3 = 5, Sylvia first subtracted 5 from both sides. What did she do wrong?

Answers

Answer:the two sides still equal.

Step-by-step explanation:To solve 2x + 3 = 5, Sylvia first subtracted 5 from both sides. What did she do wrong? Because Sylvia did the same operation to both sides, the equation is still correct: the two sides still equal.

Answer:

1

Step-by-step explanation:

or, 2x=5-3

or, 2x=2

or, x=2/2

x=1

Your doing practice 5

Answers

5.) The dimensions of the banner whose perimeter is given is listed below:

length = 134in

width = -59in

How to determine the dimensions of the rectangular banners?

To calculate the dimensions of the rectangular banner, the formula for the perimeter of rectangle should be used and it's given below;

Perimeter of rectangle = 2(length+width)

length = 16-2a

width = a

perimeter = 160in

That is;

160 = 2(16-2a+a)

160 = 32-4a+2a

160 = 42-2a

2a = 42-160

2a = -118

a = 118/2

= -59

Length = 16-2(-59)

= 16+118

= 134in

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.
3. a piece of paper is folded into thirds multiple times. the area, a, of the piece in square inches, after n folds, is a = 90•(1/3)n

a. what is the value of a when n=0? what does this mean in the situation?


b. how many folds are needed before the area is less than 1 square inch?

Answers

The paper initial area of the paper is 90 square inches and needs to be folded at least 5 times before its area becomes less than 1 square inch.

a. When n=0, the expression for the area of the paper after folding becomes:

a = 90•(1/3)⁰ = 90•1 = 90 square inches

This means that the initial area of the paper before any folding is 90 square inches.

b. To find out how many folds are needed before the area is less than 1 square inch, we can set the expression for the area of the paper after folding to be less than 1 and solve for n:

a = 90•(1/3)ⁿ < 1

(1/3)ⁿ < 1/90

Taking the logarithm of both sides with base 1/3, we get:

n > log(1/90)/log(1/3)

n > 4.8

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help
pls thank you
,,,,,,,,,,,,,,,,,,,,,,,,,,,

Answers

The image of P under a 270° counterclockwise rotation about the origin is (2, -8) .

How to find the image of P under the rotation?

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.

Translation, rotation, reflection, and dilation are the four common types of transformations.

Rotation simply means turning. If a point P, whose position vector is (x,y), is rotated  270° counterclockwise rotation about the origin, the position of the image P' is (y, -x).

We have: P(8, 2)

Thus, the image of P will be:

P'(2, -8)

Therefore, the image of P under a 270° counterclockwise rotation about the origin is (2, -8).

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Find the rate of change for the linear function represented in the table.

Time (minutes) Temperature (°C)
x y
0 66
5 69
10 72
15 75

Answers

The rate of change for the linear function represented in the table is 3/5.

How to calculate or determine the rate of change or slope of a line?

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (69 - 66)/(5 - 0)

Rate of change (slope) = 3/5

Based on the table, the rate of change is the change in y-axis with respect to the x-axis and it is equal to 3/5.

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anyone who is willing to answer the question in the image sent, i will give you brainiest!

Answers

Answer:

Triangles: 4(1/2)(12)(10) = 240 ft^2

Square: 10^2 = 100 ft^2

Total Surface Area: 340 ft^2

Which proportion is correct?4/10=3/61/2=7/81/2=3/64/10=7/8

Answers

Determine which proportion is correct, we will compare the cross products of each proportion. The correct proportion will have equal cross products. The correct proportion is 1/2 = 3/6.

1. 4/10 = 3/6
To check this proportion, we'll calculate the cross products:
(4 * 6) = (10 * 3)
24 = 30
Since 24 ≠ 30, this proportion is incorrect.
2. 1/2 = 7/8
To check this proportion, we'll calculate the cross products:
(1 * 8) = (2 * 7)
8 = 14
Since 8 ≠ 14, this proportion is incorrect.
3. 1/2 = 3/6
To check this proportion, we'll calculate the cross products:
(1 * 6) = (2 * 3)
6 = 6
Since 6 = 6, this proportion is correct.
4. 4/10 = 7/8
To check this proportion, we'll calculate the cross products:
(4 * 8) = (10 * 7)
32 = 70
Since 32 ≠ 70, this proportion is incorrect
So, the correct proportion is 1/2 = 3/6.

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Triangle ΔABC has side lengths of a = 15, b equals 15 times radical 3 comma and c = 30 inches.

Part A: Determine the measure of angle B period (5 points)

Part B: Show how to use the unit circle to find tan B. (2 points)

Part C: Calculate the area of ΔABC. (3 points)

Answers

a) Where the information about triangle ABC is given above, the measure of angle B is 60°

How is this so ?

Using the Cos Rules,

(15√3)² = 30² + 15² - 2(15 x 30) cos B

⇒ 657 = 1125 - 900 cosB

⇒ 2 Cos B = 1 Cos B = 1/2

So

B = Cos ⁻¹(1/2)

Hence,

B = 60°

B) Given the above,

Now, we can use the tangent function to find tan B:

tan B = sin B / cos B

  = sin (π/3) / cos (π /3)

  = (√3 / 2) / 0.5

tan B = √3

C ) the area of the rriangle is given as

s = (a + b + c) /2

Substituting

s = (15 + 15√ 3 + 30)/2

s = 30 + 15√3

Area = √ [ (30 + 15√3)(15√3) (15)(30  - 15 - 15√3))

Simplifying  we can say

Area = √(30 + 15√3  )( 15√3)(15)(15 - 5√3 )]

= √[3(10 + 5√3)(15)(3√3 - 1)]

  = √[2250 - 1125√3]

Hence,

Area ≈ 17.36in

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Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −7x2 + 26x + 3 and y = −6x2 + 23x + 5, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point?

Answers

The height at x = 2 seconds is greater (25 meters), the balloons collided at the highest point at 2 seconds. We can use quadratic functions to solve this.

To find the time in seconds that the balloons collided at the highest point, we will first find the points where the balloons have the same height (y) by setting the two quadratic functions equal to each other:
-7x² + 26x + 3 = -6x² + 23x + 5
Next, we will solve for x:
x² - 3x - 2 = 0
Now, factor the quadratic equation:
(x - 2)(x - 1) = 0


The solutions for x are 1 and 2 seconds. To find the highest point of collision, we need to determine which of these times results in a greater height. Plug each value of x into one of the original equations and compare the y values:
For x = 1:
y = -7(1)² + 26(1) + 3 = 22
For x = 2:
y = -7(2)² + 26(2) + 3 = 25
The balloons collided at the highest point at 2 seconds.

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Lochlon transfers his investment into a money market account. The account now earns compound interest of 1. 95% annually with a maturity date of 5 years

Answers

The final amount Lochlon will earn on his investment after 5 years of compound interest is $1,104.36

How we calculate the compound interest?

Compound interest is a type of interest calculation where the interest earned is added to the principal amount, and the resulting sum becomes the new principal for the next interest calculation. The formula for compound interest is:

A = [tex]P(1 + r/n)^(^n^t^)[/tex]

Where:

A is the final amount including the interest

P is the principal amount

r is the annual interest rate as a decimal

n is the number of times the interest is compounded per year

t is the time in years

In this case, Lochlon transferred his investment into a money market account that earns compound interest of 1.95% annually, with a maturity date of 5 years.

To find the final amount Lochlon will earn, we need to know the principal amount, the interest rate, the number of times the interest is compounded per year, and the time period.

Assuming Lochlon invests a principal amount of P dollars, with an annual interest rate of r = 1.95%, and the interest is compounded annually (n = 1) for a time period of 5 years (t = 5), the formula for calculating the final amount (A) is:

A = [tex]P(1 + r/n)^(^n^t^)[/tex]

= [tex]P(1 + 0.0195/1)^(^1^*^5^)[/tex]

= [tex]P(1.0195)^5[/tex]

if Lochlon invests $1,000, for example, then his final amount (A) after 5 years would be:

A = [tex]1000(1.0195)^5[/tex]

= 1000(1.10436)

= $1,104.36

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If a big sheet of white paper has a red dot in the center, the red dot is the ______, and the white space is the ______.

Answers

If a big sheet of white paper has a red dot in the center, the red dot is the  figure or object, and the white space is the ground or background.

In visual perception, the figure-ground relationship is the process by which our brains distinguish an object( the figure) from its surroundings( the ground).

This relationship is essential in our capability to fete and make sense of the visual world around us. The figure is the object of interest or focus, while the ground is the background against which it stands out.

The red dot becomes the focal point or center of attention, while the white space around it provides environment and contrast, making the dot more visible and commanding.

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An athlete runs around a rectangular housing estate 10 times. The estate is 1.08 km by 420 m. How far has the athlete run?

Answers

30 km far has the athlete run.

A rectangle may be a geometric shape that is characterized by its four sides, where opposite sides are parallel and break even within the length. It has four sides the longer side is named length and the shorter side is named as breadth.

An Athlete runs around a rectangular field = 10 times

The Length of the rectangle = [tex]1.08 km[/tex]

The Breadth of the rectangle = [tex]0.42 km[/tex]

 [tex]1km = 1000 m\\= 420 /1000 m\\= 0.42 km[/tex]

Therefore, perimeter of the rectangle = 2 (length + breadth)

                                                              =  [tex]2 ( 1.08 + 0.42)[/tex]

                                                              = [tex]2 (1. 50)[/tex]

                                                              = [tex]3 km[/tex]

So, the athlete runs around a rectangular housing 10 times = [tex]3[/tex]×[tex]10[/tex]

                                                                                                   = [tex]30 km[/tex]

Therefore, the athlete runs 30 km far.

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Which of the following is an odd function? f(x) = x3 5x2 x f (x) = startroot x endroot f(x) = x2 x f(x) = –x

Answers

The limit of [tex]L_n[/tex] as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.

To express the limit of [tex]L_n[/tex] as n approaches infinity as a definite integral, we can use the fact that the limit of a Riemann sum is equal to the corresponding definite integral. Thus, we can rewrite [tex]L_n[/tex] as:

[tex]L_n[/tex] = 1/n * (0 + 1 + 2 + ... + (n-1))

This is a Riemann sum for the integral:

[tex]\int\limits^1_0 {x} \, dx[/tex]

with n subintervals of width 1/n. Therefore, we can write:

[tex]\lim_{n \to \infty} L_n = \lim_{n \to \infty} 1/n * (0 + 1 + 2 + ... + (n-1)) = \int\limits^1_0 {x} \, dx = [x^2/2] \ from \ 0 \ to \ 1 = 1/2[/tex]

So, the limit of Ln as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.

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Justice has a box of trading cards. There are three types of trading cards in the box, a basketball, a football, and a soccer ball. The probability of picking out a basketball card is 2/5, and the probability of picking out a football card is 1/3. What is the probability Justice will randomly pick out a soccer card?

Answers

If the probability of picking out a basketball card is 2/5, and the probability of picking out a football card is 1/3, the probability of Justice randomly picking out a soccer card is 4/15.

To find the probability of Justice picking out a soccer card, we need to know the total probability of all three types of cards adding up to 1. Since there are only three types of cards, we can subtract the probability of picking a basketball card and the probability of picking a football card from 1 to find the probability of picking a soccer card.

Let P(S) be the probability of picking a soccer card.

We know that P(B) = 2/5 and P(F) = 1/3.

Therefore, the total probability of picking one of the three cards is:

P(B) + P(F) + P(S) = 1

Substituting the values we know, we get:

2/5 + 1/3 + P(S) = 1

Simplifying the equation, we get:

6/15 + 5/15 + P(S) = 1

11/15 + P(S) = 1

P(S) = 1 - 11/15

P(S) = 4/15

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1. Identify two accounts that are in good standing. Explain what evidence you found on the credit report


to indicate why these are in good standing. (4 points)

Answers

The evidence on a credit report that indicates good standing may vary depending on the individual's credit history and financial situation.

What are the accounts that are in good standing? Explain what evidence you found on the credit report.

As an AI language model, I do not have access to specific credit reports or personal information of individuals. However, I can provide you with general information on what constitutes good standing on a credit report and some examples of evidence that may indicate good standing.

A good standing on a credit report typically means that a person has been responsible with their credit and has not defaulted on their payments. This may be indicated by a high credit score, a long credit history, and a low debt-to-credit ratio.

Some examples of evidence that may indicate good standing on a credit report include:

A high credit score: A credit score is a numerical representation of a person's creditworthiness. A high credit score, typically above 700, indicates that a person is in good standing and is likely to be approved for credit or loans. A high credit score may be achieved through a consistent history of making on-time payments, a low debt-to-credit ratio, and a diverse mix of credit accounts.

A low debt-to-credit ratio: A debt-to-credit ratio is the amount of debt a person has compared to their available credit limit. A low debt-to-credit ratio, typically below 30%, indicates that a person is not overextended and is able to manage their credit responsibly. This may be achieved through regular payments and not maxing out credit cards.

Overall, the evidence on a credit report that indicates good standing may vary depending on the individual's credit history and financial situation.

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Mrs. Tucker writes the fraction 1. She asks her students to translate the fraction into a percentage. The table shows the


responses of four students.


$


Student


Elvin


Ferdinand


Gertrude


Henrietta


Response


2. 75%


275%


11. 4%


114%


Which student correctly translates Mrs. Tucker's fraction into a percentage?

Answers

The student that correctly translates Mrs. Tucker's fraction into a percentage is Elvin and the percentage is  2.75%, under the condition that Mrs. Tucker writes the fraction 1 and tells her students to convert  the fraction into a percentage

Elvin's response is correct. Ferdinand's response is incorrect due to the application of multiplication of fraction by 100 and then added a percent sign.
Gertrude's response is incorrect due to the reason of  converting the fraction to a decimal and then multiplied by 100. nt sign to

Henrietta's response is incorrect due to the fact that she added a percepercentnt sign to the decimal equivalent of the fraction instead of multiplying it by 100.
Now To convert 1/36 to a percentage, we have to  first divide the numerator by the denominator:
1 / 36
= 0.0277777777778

Secondly , we have to  multiply the result by 100 to get the percentage
0.0277777777778 × 100
= 2.7778%

Then, the correct response is 2.75% which is the percentage equivalent of 1/36 given by Elvin.

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Enzo says that he can draw an enlarge rectangle that is 16 cenimeters by 13 cenimeters which explain enzo is correct

Answers

Enzo's statement that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters is correct. To explain this, we need to understand what it means to enlarge a shape.

Enlargement is the process of making a shape bigger or smaller while maintaining its shape and proportions. In other words, if we enlarge a rectangle, we need to make sure that the length and width are increased by the same factor.

In this case, Enzo has specified the new dimensions of the rectangle as 16 centimeters by 13 centimeters. To create an enlarged rectangle with these dimensions, we need to know the scale factor of the enlargement. The scale factor is the ratio of the length of the enlarged shape to the length of the original shape. In this case, we can find the scale factor by dividing the length of the new rectangle (16 centimeters) by the length of the original rectangle.

Let's assume that the original rectangle has a length of 8 centimeters and a width of 6 centimeters. Dividing 16 by 8 gives us a scale factor of 2. This means that we need to multiply the length and width of the original rectangle by 2 to get the dimensions of the enlarged rectangle.

So, the length of the enlarged rectangle will be 8 x 2 = 16 centimeters, and the width will be 6 x 2 = 12 centimeters. However, Enzo has specified that the width of the enlarged rectangle should be 13 centimeters. This means that we need to adjust the scale factor to make the width of the enlarged rectangle 13 centimeters. Dividing 13 by 6 gives us a scale factor of approximately 2.17.

Multiplying the length and width of the original rectangle by this scale factor gives us the new dimensions of the enlarged rectangle. The length will be 8 x 2.17 = 17.36 centimeters (rounded to two decimal places), and the width will be 6 x 2.17 = 13.02 centimeters (rounded to two decimal places). Therefore, Enzo is correct in saying that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters.

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Consider the following
g(x) = 8x^2 – 4; h(x) = 1.6^x Find the derivative of f(x) = g(x) · h(x). f'(x) =

Answers

The derivative of the equation g(x) = 8x^2 – 4; h(x) = 1.6^x is f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x

To find the derivative of f(x) = g(x) · h(x), we use the product rule of derivatives, which states that if f(x) = u(x) · v(x), then f'(x) = u'(x) · v(x) + u(x) · v'(x).

Using this rule, we can find the derivative of f(x) = g(x) · h(x) as follows:

f(x) = g(x) · h(x) = (8x^2 – 4) · (1.6^x)

f'(x) = g'(x) · h(x) + g(x) · h'(x) [applying the product rule]

To find g'(x), we take the derivative of g(x) = 8x^2 – 4, which is:

g'(x) = 16x

To find h'(x), we take the derivative of h(x) = 1.6^x, which is:

h'(x) = ln(1.6) · 1.6^x [using the chain rule and the fact that the derivative of a^x is ln(a) · a^x]

h'(x) ≈ 0.470004 · 1.6^x

Now we substitute these values into the product rule formula:

f'(x) = (16x) · (1.6^x) + (8x^2 – 4) ·0.470004 · 1.6^x

Simplifying this expression, we get:

f'(x) = 25.6^x + (12.8x^2 – 6.4) ·0.470004 · 1.6^x

f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x
Therefore, the derivative of f(x) = g(x) · h(x) is:
f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x

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h(t) = -16t^2 +90t
how many seconds will it take for the ball to reach its maximum height

Answers

The amount of time it would take for the ball to reach its maximum height is 2.1825 seconds.

How to determine the time when the ball would reach its maximum height?

Based on the information provided, we can logically deduce that the height (h) in feet, of this ball above the​ ground is related to time by the following quadratic function:

Next, we would determine the maximum height of this ball by taking the first derivate in order to determine the time (t) it takes as follows;

h(t) = -16t² + 90t

h'(t) = -32t + 90

90 = 32t

t = 90/32 = 2.1825 seconds.

h(2.1825) = -16(2.1825)² + 90(2.1825)

h(2.1825) = 120.21 feet.

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Mr Louis wants to top-up his central heating oil tank.


The oil tank can take up to 1400 litres of oil.


There are already 150 litres of oil in the tank.


The price of oil is 80. 5p per litre.


As a loyal customer, Mr Louis gets a 6. 5% discount on the price of the oil.


How much discount does Mr Louis get on this purchase?


Give your answer in £.

Answers

If Mr Louis gets a 6. 5% discount on the price of the oil, Mr. Louis gets a discount of £65.41 on this purchase.

First, let's find out how many litres of oil Mr. Louis needs to fill his tank:

Maximum capacity of the tank: 1,400 litres
Current oil in the tank: 150 litres
Litres needed to top up: 1,400 - 150 = 1,250 litres

Next, we'll calculate the original price of the oil without the discount:

Price per litre: £0.805
Cost of oil needed: 1,250 litres * £0.805 = £1,006.25

Now, let's calculate the discount amount:

Discount percentage: 6.5%
Discount amount: £1,006.25 * 0.065 = £65.41

So, Mr. Louis gets a discount of £65.41 on this purchase.

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Some parallelograms are squares true or false

Answers

All squares can be parallelograms but all parallelograms are not squares.
Hope that helps :)

Answer:

True

Step-by-step explanation:

Parallelogram: A parallelogram is 4-sided shape that has parallel opposite sides

Square: A square is 4-sided shape where all sides are congruent and has 4 right angles.  A square also has 2 pairs of opposite parallel sides.


Based on these definitions, we can see that not ALL parallelograms can be squares because a parallelogram can have no right angles, or can have all 4 angles be right angles.

All squares have to be parallelograms though because a square and a parallelogram both have 2 pairs of opposite parallel sides.

Hope this helps :)


stretch your thinking write a word problem for the following
equation. 4/5 x 1/4+ 3/5=

Answers

"A recipe for chocolate chip cookies calls for 4/5 cup of sugar per batch. If a baker wants to make 3 batches of cookies, and only has 1/4 cup of sugar left in the pantry, how much additional sugar will the baker need to buy?" is an example of a word problem for the given equation.

To solve this word problem, we can use the equation 4/5 x 1/4 + 3/5 = to find out how much sugar is needed for one batch of cookies, and then multiply that amount by 3 to get the total amount of sugar needed for 3 batches.

The first part of the equation, 4/5 x 1/4, represents the amount of sugar needed for one batch of cookies, which is 1/5 cup. Adding the remaining 3/5 cup of sugar needed for the recipe gives a total of 4/5 cup of sugar per batch.

To find out how much additional sugar the baker needs to buy, we can multiply 4/5 by 3 (the number of batches), and then subtract the amount of sugar already in the pantry (1/4 cup). This gives us:

4/5 x 3 - 1/4 = 12/5 - 1/4 = 43/20

Therefore, the baker will need to buy 43/20 cups of additional sugar to make 3 batches of chocolate chip cookies.

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The volume of this rectangular prism is 216 cubic inches. What is the value of L?

Answers

After leveling the sand box, the height of the sand box is 1.57 in

What is volume?

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cuboid is expressed as;

V = l × w × h

V = 30 × 20 × 5

V = 3000 in³

After leveling, the volume decreases by 1680 in³, therefore the new volume of the sand box is

3000-1680 = 1320

Therefore the new height of the sand is calculated as;

1320 = 30 × 28 × h

1320 = 840h

divide both sides by 840

h = 1320/840

h = 1.57 in

therefore the height of the remaining sand is 1.57

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