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2 months ago

Guest #7232

2 months ago

The volume is V=a^3

a=120 cm and a=1.2m

V=120^3=1,728,000 cm^3

V=1,728 m^3

a=120 cm and a=1.2m

V=120^3=1,728,000 cm^3

V=1,728 m^3

Question

1/5 and 10/50 equivalent

Solution 1

â‡’Â

1/5 x 2 =Â 2/10

1/5 x 3 =Â 3/15Â

1/5 x 4 =Â 4/20

1/5 x 5 =Â 5/25

and so on...

â‡’Â

10/50 x 2 = 20/100

10/50 x 3 = 30/150

10/50 x 4 = 40/200

10/50 x 5 = 50/250

and so on....Â

Solution 2

1/5 equivalent

3/15

2/10

10/50 equivalent

100/500

1000/5000

3/15

2/10

10/50 equivalent

100/500

1000/5000

Question

Which expression is equivalent to 4 sqrt 24x^6y/128x^4y^5

Solution 1

The first step for finding out if the expression provided is equivalent toÂ is to reduce the fraction with.

Now reduce the fraction with y.

Finally,, reduce the fraction with 8 to get your final answer.

Let me know if you have any further questions.

:)

Now reduce the fraction with y.

Finally,, reduce the fraction with 8 to get your final answer.

Let me know if you have any further questions.

:)

Question

The yard behind the Cindyâ€™s house is rectangular in shape and has a perimeter of 72 feet. If the length l of the yard is 18 feet longer than the width w of the yard, what is the area of the yard, in square feet?

Solution 1

Think of it like this. Â The perimeter is 72 feet. Â The length, l, is 18 feet longer than the width, w. Â So, l=w+18.

Perimeter is calculated by adding the lengths of all four sides together, AKA adding the length twice and the width twice: l+w+l+w.

Since l=w+18, we can substitute this in for l in the expression above: l+w+l+w=w+18+w+w+18+w

Simplified, we combine like terms, the w's and the 18's: 4w+36. Â This is the perimeter.

The perimeter is 72 feet, so 72=4w+36. Â To find the width, we need to isolate w. Â First, subtract 36 from both sides: 72-36=4w+36-36. Â Simplified: 36=4w. Â Then, divide 4 on both sides to get w alone. Â 36/4=4w/4. Â w=9. Â Therefore, the width of the rectangle is 9 feet.

Since the length of the rectangle is w+18, and w=9, we know that l=9+18=27. Â So w=9, and l=27. Â The length is 27 feet.

In a rectangle, we find area by multiplying length by width: A=lw. Â To find the area of the yard, multiply 27 by 9: A=27*9=243. Â Since 27 and 9 are both measurements in feet, the answer is 243 square feet.

Answer: The area of the yard is 243 square feet.

Perimeter is calculated by adding the lengths of all four sides together, AKA adding the length twice and the width twice: l+w+l+w.

Since l=w+18, we can substitute this in for l in the expression above: l+w+l+w=w+18+w+w+18+w

Simplified, we combine like terms, the w's and the 18's: 4w+36. Â This is the perimeter.

The perimeter is 72 feet, so 72=4w+36. Â To find the width, we need to isolate w. Â First, subtract 36 from both sides: 72-36=4w+36-36. Â Simplified: 36=4w. Â Then, divide 4 on both sides to get w alone. Â 36/4=4w/4. Â w=9. Â Therefore, the width of the rectangle is 9 feet.

Since the length of the rectangle is w+18, and w=9, we know that l=9+18=27. Â So w=9, and l=27. Â The length is 27 feet.

In a rectangle, we find area by multiplying length by width: A=lw. Â To find the area of the yard, multiply 27 by 9: A=27*9=243. Â Since 27 and 9 are both measurements in feet, the answer is 243 square feet.

Answer: The area of the yard is 243 square feet.

Question

The center of a circle is at (-5, 7) and its radius is 6 units. Which of the following is the equation for this circle? A) (x - 5)2 + (y + 7)2 = 36
B) (x + 5)2 + (y - 7)2 = 36
C) (x - 5)2 + (y + 7)2 = 12
D) (x + 5)2 + (y - 7)2 = 12

Solution 1

(x + 5)Â² + (y - 7)Â² = 36 is the equation.

Option B is your answer if I read that right.Â

Option B is your answer if I read that right.Â

Solution 2

The correct answer is (x + 5)Â² + (y - 7)Â² = 36

Question

A family of four (two kids and two parents) spend the day at an amusement park. At the end of the day, the family adds up all of the receipts from their meals: $16.25, $17.96, $3.58, $4.61, $5.23. What is the mean and median cost spent? What does the mean cost represent? Why is the mean cost significantly different from the median cost? Which measurement of central tendency is a better representation of the amount of money that the family spent at the amusement park?

Solution 1

A family of four spent the following for their meals $16.25, $17.96, $3.58, $4.61, $5.23.

Mean cost spent is calculated by:

Total Cost/Number of Meals

(16.25+17.96+3.58+4.61+5.23)/5

47.63/5

$9.53

Mean Cost represents the average amount per meal the family has spent.

Median cost is the cost that in the middle of the five costs which is $5.23.

The mean cost is significantly different from the median cost because it is higher.

Median cost is a better representation of the amount of money that the family spent because, with regard to meal costs, this means that exactly half of the meals in the amusement park are above this price ($5.23) and exactly half are below.Â

Â

Question

Which function is equivalent to y= -cot(x)? A. y= -tan(x)
B. y= -tan (x+ pi/2)
C. y= tan(x)
D. y= tan (x+pi/2)

Solution 1

We know that

tan (A+B)=sin (A+B)/cos (A+B)

sin (A+B)=sin A*cos B+sin B*cos A

cos (A+B)=cos A*cos B-sin A*sin B

so

for (x+pi/2)

A=x

B=pi/2

sin A=sin x

sin B=1

cos A=cos x

cos B=0

sin (A+B)=sin x*0+1*cos x------> cos x

cos (A+B)=cos x*0-sin x*1------> -sin x

tan (x+pi/2)=cos x/(-sin x)------> -cot x

**the answer is the option**

**D. y= tan (x+pi/2)**

tan (A+B)=sin (A+B)/cos (A+B)

sin (A+B)=sin A*cos B+sin B*cos A

cos (A+B)=cos A*cos B-sin A*sin B

so

for (x+pi/2)

A=x

B=pi/2

sin A=sin x

sin B=1

cos A=cos x

cos B=0

sin (A+B)=sin x*0+1*cos x------> cos x

cos (A+B)=cos x*0-sin x*1------> -sin x

tan (x+pi/2)=cos x/(-sin x)------> -cot x

Solution 2

**Answer:**

D. y = tan(x + pi/2)

**Step-by-step explanation:**

this is the correct answer on ed-genuity, hope this helps! :)

Question

Calculate:
âˆš5/2-âˆš5+2/2+âˆš5

Solution 1

-âˆš5/2+âˆš5+1

-âˆš5/2+2âˆš5/2+1

âˆš5/2+1

(âˆš5+2)/2

-âˆš5/2+2âˆš5/2+1

âˆš5/2+1

(âˆš5+2)/2

Solution 2

So,

First, we have to simplify the expression.

We can see that there is a negative square root of 5 and a positive square root of 5. Â They cancel out. Â In addition, we know that two-halves are equal to 1.

Since the square root of 5 can be thought of as 5 to the one-half power, we should evaluate that first.

Substitute 2.236 for the square root of 5.

Multiply.

1.118 + 1

Add.

2.118

So the expression is approximately equal to 2.118 (exactly 2.1180339887498948482045868343656).

First, we have to simplify the expression.

We can see that there is a negative square root of 5 and a positive square root of 5. Â They cancel out. Â In addition, we know that two-halves are equal to 1.

Since the square root of 5 can be thought of as 5 to the one-half power, we should evaluate that first.

Substitute 2.236 for the square root of 5.

Multiply.

1.118 + 1

Add.

2.118

So the expression is approximately equal to 2.118 (exactly 2.1180339887498948482045868343656).

Question

What are the domain, range, and asymptote h(x) = (0.5)x -9

Solution 1

1. You have the following function given in the problem:

Â h(x) = (0.5)x -9

Â 2. As you can see, the function has the form f(x)=mx+b, therefore, the functionÂ h(x) = (0.5)x -9 is known as "linear function".

Â 3. When you graph it, you obtain a line.

Â -**The domain of the function is:**

**Â R( All the real numbers)**

Â -**The range of the function is:**

**Â R (All the real numbers)Â **

Â -Â h(x) = (0.5)x -9 is asymptotic toÂ**h(x) = (0.5)x -9**

Â h(x) = (0.5)x -9

Â 2. As you can see, the function has the form f(x)=mx+b, therefore, the functionÂ h(x) = (0.5)x -9 is known as "linear function".

Â 3. When you graph it, you obtain a line.

Â -

Â -

Â -Â h(x) = (0.5)x -9 is asymptotic toÂ

Question

A map is drawn using a scale of 80 mi to 1 cm. On the map , the two cities are 7.5 cm apart. What is the actual distance between the two cities ??

Solution 1

We know that

scale =measure in the map/measure in the actual

measure in the actual=measure in the map/scale

scale=1 cm/ 80 mi

for

measure in the map=7.5 cm

measure in the actual=?

measure in the actual=7.5 /(1/80)-----> 7.5*80-----> 600 mi

**the answer is**

**the actual distance between the two cities is 600 miles**

scale =measure in the map/measure in the actual

measure in the actual=measure in the map/scale

scale=1 cm/ 80 mi

for

measure in the map=7.5 cm

measure in the actual=?

measure in the actual=7.5 /(1/80)-----> 7.5*80-----> 600 mi

Question

Find the sum of the summation of 2 i minus 12, from i equals 7 to 16. 22
110
220
440

Solution 1

Sum: S

S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]

S=2(7+8+9+10+11+12+13+14+15+16)-10(12)

S=2(115)-120

S=230-120

S=110

Answer: Second option 110

S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]

S=2(7+8+9+10+11+12+13+14+15+16)-10(12)

S=2(115)-120

S=230-120

S=110

Answer: Second option 110

Solution 2

**Answer: Second option is correct.**

**Step-by-step explanation:**

Since we have given that

Hence, the value of summation is 110.

**Therefore, Second option is correct.**

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