Determine that 4/16 and 5/20 forms as proportional relationship.

Given rectangle: 2 feet by 8 feet. Similar rectangle: Option A (4 feet by 16 feet).

Use the concept of the rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Given that,

Rectangle dimensions: 2 feet by 8 feet

And here are the options provided:

A) 4 feet by 16 feet

B) 6 feet by 12 feet

C) 12 feet by 32 feet

D) 22 feet by 28 feet

To determine if two rectangles are similar,

Compare their corresponding side lengths.

In this case,

A rectangle with dimensions 2 feet by 8 feet.

After simplifying it we can write 1:4

Let's check each option to see if it matches the similarity:

A) 4 feet by 16 feet:

The ratio of the corresponding side lengths is 2:8, which simplifies to 1:4. However, the given rectangle has side lengths of 4:16,

Which simplifies to 1:4 as well.

So, option A is similar to the given rectangle.

B) 6 feet by 12 feet:

The given rectangle has side lengths of 6:12,

Which simplifies to 1:2.

So, option B is not similar to the given rectangle.

C) 12 feet by 32 feet:

The given rectangle has side lengths of 12:32,

Which simplifies to 3:8.

So, option C is not similar to the given rectangle.

D) 22 feet by 28 feet:

The given rectangle has side lengths of 22:28,

Which simplifies to 11:14.

So, option D is not similar to the given rectangle.

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Complete the square in the denominator to get

tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1

… = (tan(t ) + 7)² - 1

Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes

[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}[/tex]

Separate the integrand into partial fractions:

[tex]\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)[/tex]

Then we get

[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt =  \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}[/tex]

Step-by-step explanation:

41a+11a-2b+3c

52a-2b+3c

Step-by-step explanation:

(41a-2b+3c) +11a

open the bracket

41a-2b+3c+11a

collect like terms

41a+11a-2b+3c

52a-5bc

so final answer is 52a-5bc

because they are not like terms they are unlike terms

Answer:

d. 60000000000

Step-by-step explanation:

Answer:

The answer is D. 60,000,000,000

Step-by-step explanation:

Answer: 2/7 of a gallon (in decimal it’s 0.286)

Step-by-step explanation: This one’s really easy.

2/7 of 1 gallon. Checking: so that if you multiply it by 7 it equals to 2

The gallon he used each hour he works is 2/7.

What is unit rate?

A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity.

The common examples used are:

Distance per second

Kilometer per hour

Meter per second

Earning per month

Given,

he used 2 gallons liquid for every 7 hours he works.

gallons used for per hour = 2/7

Hence, He used 2/7 gallons per hour.

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Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.

Let the total surface of the rectangular box be expressed as:

S = 2xy + 2yz + 2xz

where,

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz .................(1)

Given:

Volume V = xyz = 8000 .............(2)

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since, Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20*20*20.

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Answer:

x = -6,3,15,-12; y = 11,5,-3,15

Step-by-step explanation:

Domain is the x value, so plugged in the x values into the equation and got the y values or range.

Answer:

 x:  y:

-6  11

3       5

15 -3

-12    15

Answer:

a =4,b=2, c=3

Step-by-step explanation:

Answer:

7:41

Step-by-step explanation:

8:08 - 7 Minutes = 8:01

8:01 - 20 Minutes = 7:41

Answer:

-6i

Step-by-step explanation:

Complex roots have to come in conjugate pairs

So if we have 6i as a root, we must have -6i as a root

Answer:

-6i

Step-by-step explanation:

Hello, because this polynomial function has real coefficients and 6i is a zero, the conjugate of 6i is a zero as well. It means -6i is a zero.

The degree is 4 the number of zeroes is less or equal to 4 and we have already, 6, 4, 6i and -6i. So we have all the zeroes.

Thank you

A(t) = 100t^2 + 500t + 625

3,025 square pixels

Answer:

A(t) equals 100t²+ 500t + 625.

The area of the square image after 3 seconds is 3,025 square pixels.

Answer:

y=-1/2x+3

Step-by-step explanation:

y=mx+c

5=-1/2*4+c

5=-2+c

c=5-2

c=3

y=-1/2x+3

Answer:

0

Step-by-step explanation:

the derivative is zero since it has no variable

Answer:

0

Step by step explanation:

f'(x)=lim f(x+h)-f(x)/h

now since 7 is constant with no variable

f'(x)= lim(7-7)/h

f'(x)=0

Answer:

4.8

Step-by-step explanation:

The scale factor is (3.6)/3=1.2. Hence x/4=1.2, x=4.8

Answer:

Product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A

Step-by-step explanation:

Product A

Total number of people tested = 50

Total number o who experienced relief using product A

                                                  = 35

% of people who got relief using product A

                                                   = 35/50 x 100%

                                                   = 70%

Product B

Total number of people tested = 25

Total number of people who experienced releif using product B

                                                  = 19

% of peope who got relief using product B

                                                  = 19/25 x 100%

                                                  = 76%

From the above:

76% of people got relieved whilst using product B

70% who got relieved using product A.

Therefore, product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A

Answer:

2hrs 24mins

Step-by-step explanation:

Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.

Ans LCM(24, 36, 48) = 144 mins

= 2hrs 24mins

Answer:

The answer is 2 hours and 24 minutes

Step-by-step explanation:

Hope you get this right:)

Answer:

Hey there!

Tangent 70=12/y

Tangent 70y=12

y=12/Tangent 70

y=4.37 cm

Let me know if this helps :)

Answer:

The answer is "[tex]\bold{\frac{2}{5}\ \ and \ \ \frac{6}{13}}[/tex]".

Step-by-step explanation:

You have 4/10 opportunities to choose a white ball, and there'll be 7 white balls and 6 black balls out of 13, and so the second time they choose a white one is 7/13, as well as the second time they choose a black, 6/13. people will also have a 4/10 chance.  

There are 6/10 chances which users pick its black ball and 4 white balls would still be picked, but 9 black balls and out 13 balls and thus, its second and third time you select the white one is 4/13 but you are likely to pick a black for the second time is 9/13.  

Taking the diagram of the next tree. The very first draw is marked with a and the second draw is marked with b.

[tex]\to P(a) = \frac{4}{10}\ \ \ \ \ \ \ \ \ P(b) = \frac{6}{10}\\\\\to P(\frac{a2}{a1}) = \frac{7}{13} \ \ \ \ \ \ \ \ \ \ P(\frac{a}{b}) = \frac{4}{13}\\\\\to P(\frac{b2}{a1}) = \frac{6}{13} \ \ \ \ \ \ \ \ \ \ P(\frac{b2}{b1}) = \frac{9}{13}[/tex]

Calculating the second drawn ball is white:

[tex]\to P(b2)=P(a)P(\frac{a2}{b1})+P(b)P(\frac{a}{b})\\[/tex]

              [tex]=\frac{4}{10}\frac{7}{13}+\frac{6}{10}\frac{4}{13}\\\\=\frac{28}{130}+\frac{24}{130}\\\\=\frac{28+24}{130}\\\\=\frac{52}{130}\\\\=\frac{2}{5}\\\\[/tex]

In point b:

[tex]\to P(\frac{b}{a1})= \frac{P(B)P(\frac{a}{b})}{P(a)P(\frac{a2}{b1})+P(b)P(\frac{a}{b})\\}[/tex]

              [tex]=\frac{\frac{6}{10} \frac{4}{13}}{\frac{52}{130}}\\\\=\frac{\frac{24}{130}}{\frac{52}{130}}\\\\=\frac{24}{130} \times \frac{130}{52}\\\\=\frac{24}{52}\\\\=\frac{6}{13}\\[/tex]

Answer:

Option B, cotangent is the reciprocal of tangent

That option is correct

A company breaks even for a given period when sales revenue and costs incurred during that period are equal. Thus the break-even point is that level of operations at which a company realizes no net income or loss.

A company may express a break-even point in dollars of sales revenue or number of units produced or sold. No matter how a company expresses its break-even point, it is still the point of zero income or loss.

In order to grasp the concept of breakeven, it’s important to understand that all costs are not created equal: Some are fixed, and some are variable. Fixed Costs are expenses that are not dependent on the amount of goods or services produced by the business. They are things such as salaries or rents paid per month. If you own a car, then your car payment and insurance premiums are fixed costs because you pay them every month whether you drive your car or not. Variable Costs are volume related and are paid per quantity or unit produced. For your car, your variable costs are things like gas, maintenance, or tires because you only incur these costs when you drive your car. The more miles you drive, the more your gas expenses go up—such costs vary with the level of activity.

Before we turn to the calculation of the break-even point, it’s also important to understand contribution margin.

Answer:

Option B,

They're similar because two pairs of corresponding angles in the two trapezoids are congruent

Answer:

They're not similar because only one pair of corresponding angles in the two trapezoids is congruent.

Step-by-step explanation:

[tex]\text{(H, A and S), (Y, D and T) and (H, D and S)}[/tex]

Answer:

A

Step-by-step explanation:

A 1.75 * 10^6 = 1750000

B  1.25 * 10^6 = 1250000

C 2.75*10^5  = 275000

D 3.82*10^5 = 82000

option A (1.75 * 10⁶) represents the largest number among the given options.

To determine which of the given numbers represents the largest number, we can compare the exponents of 10 in each option.

A. 1.75 * 10⁶

B. 1.25 * 10⁶

C. 2.75 * 10⁵

D. 3.82 * 10⁵

Comparing the exponents:

A: 10⁶

B: 10⁶

C: 10⁵

D: 10⁵

Since both options A and B have an exponent of 10⁶, we need to compare the coefficients.

1.75 is greater than 1.25, so option A (1.75 * 10⁶) represents the largest number among the given options.

Therefore, the answer is A. 1.75 * 10⁶.

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Answer:

20,000

Step-by-step explanation:

To round a number to the nearest ten thousands place, we have to look at the thousand place and see whether it crosses the "hill" of 5 as it's digit.

The thousand digit is 8, so it will round UP, making 18,652 become 20,000.

Hope this helped!

Answer:

[tex]\boxed{20,000}[/tex]

Step-by-step explanation:

Hey there!

Well the ten thousands number is 1 and the 1rst thousands place number is 8 so since 8 is more than 5 we have to round 1 UP to 2,

so the answer is 20,000.

Hope this helps :)

Answer:

[tex]C'(x)=-\frac{148}{x^2}[/tex]

[tex]R'(x)=-0.06[/tex]

Step-by-step explanation:

Marginal average Cost function:

[tex]\frac{d}{dx}(\frac{148+6.3x}{x})=-\frac{148}{x^2}[/tex]

Marginal average Revenue function:

[tex]\frac{d}{dx}(\frac{3x-0.06x}{x})=-0.06[/tex]

Answer:

Step-by-step explanation:

yess

Answer:

x = - 11

Step-by-step explanation:

Given

5x + 2 = 4x - 9 ( subtract 4x from both sides )

x + 2 = - 9 ( subtract 2 from both sides )

x = - 11

Answer: x = -11

Step-by-step explanation:

Move all terms containing  x  to the left side of the equation.

A mathematical statement that says two expressions have the same value; any number sentence with an  = .

Answer:

106.25km

Step-by-step explanation:

8.5cm = 0.000085km

map:real life

1:1250000

0.000085km : 0.000085km * 1250000 = 106.25km

Answer:

C. $4.12

Step-by-step explanation:

From 9 a.m. to noon, it's 3 hours.

From noon to 4 p.m. it's 4 hours.

Total rental time: 3 hours + 4 hours = 7 hours

Total rental cost: $28.84

rental cost per hour = (rental cost)/(number of hours)

rental cost per hour = $28.84/(7 hours) = $4.12/hour

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To calculate the equation of the line first find the slope

Slope of the line using points

(0 , 0) and (4 , -2) is

[tex]m = \frac{ - 2 - 0}{4 - 0} = \frac{ - 2}{4} = - \frac{1}{2} [/tex]

Now use the formula

y - y1 = m(x - x1) to find the equation of the line using any of the points

Using point (0,0)

That's

[tex]y - 0 = - \frac{ 1}{2} (x - 0)[/tex]

The final answer is

[tex]y = - \frac{1}{2} x[/tex]

Hope this helps you

Answer:

F

Step-by-step explanation:

Answer:

181 1/2 hours a month.

Step-by-step explanation:

You multiply the days per month=22

By the hours they work per day=8 1/4

(Optional) You turn 1/4 into .25

Then: 22 × 8.25= 181.5/181 1/2

I hope this answer helps you out. Brainliest would be appreciated. Have a very nice day/night.