Jordan built her cat Tuna a new scratching post. She needs to cover the post with carpet.

How much carpet does Jordan need to cover the surface of the post, including the bottom?

Answer:

The Radius of circle is 7.15 cm  

Step-by-step explanation:

Given as :

A Triangle is inscribed into circle

The center of circle is O

The Diameter of circle = AK = d

The hypotenuse of triangle being the diameter of circle

The Area of triangle = 50 cm²

Let The radius of circle = r cm

The Triangle is right angle at c

So , ∠ACK = 90°

∠CAK = 42°

∠AKC = 180° - (90° + 42°)

So, ∠AKC = 48°

Now, ∵ Area of triangle ACK = 50 cm²

So, [tex]\dfrac{1}{2}[/tex] × AC × CK = 50

Or, AC × CK = 50 × 2

i.e , AC × CK = 100        ..........1

From figure

Sin 48° =  [tex]\dfrac{AC}{AK}[/tex]

Or, 0.74 =  [tex]\dfrac{AC}{d}[/tex]

∴ AC = 0.74 d             ..........2

Similarly

Sin 42° =  [tex]\dfrac{CK}{AK}[/tex]

Or, 0.66 =  [tex]\dfrac{CK}{d}[/tex]

∴ CK = 0.66 d               .............3

Putting eq 2 and 3 value into eq 1

i.e  AC × CK = 100  

Or, 0.74 d  × 0.66 d = 100  

Or, 0.4884 × d² = 100  

∴ d² = [tex]\dfrac{100}{0.4884}[/tex]

Or, d² = 204.75

Or, d = [tex]\sqrt{204.75}[/tex]

Or, d = 14.30

So, The diameter of circle = d = 14.30 cm

Now, Radius of circle = [tex]\dfrac{\textrm diameter}{2}[/tex]

Or, r =  [tex]\dfrac{\textrm 14.30 cm}{2}[/tex]

i.e r = 7.15 cm

So, The Radius of circle =  r = 7.15 cm

Hence, The Radius of circle is 7.15 cm  Answer

Answer:

Choice B and Choise C.

Step-by-step explanation:

Equivalent expressions are those expressions that have the same value but they look different.

Given the following expression provided in the exercise:

[tex]6.53 - (-4.11) + 7.92[/tex]

You need to remember the multiplication of signs in order to find the equivalent expressions:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]

Then:

- Eliminating the parentheses, you get this equivalent expression:

[tex]6.53 +4.11 + 7.92[/tex]

- Since the mulplication of two negative signs gives yous a positive sign, you can rewrite the original expression in this form:

[tex]-(-6.53)+4.11-(-7.92)[/tex]

This is an equivalent expression to [tex]6.53 - (-4.11) + 7.92[/tex]

Answer:

b & c

Step-by-step explanation:

I did it on khan academy and it was right

The required polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5  is [tex]y^2-5y-4[/tex]

Step-by-step explanation:

We need to find polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5

Let the required polynomial be x

We are given:

[tex]y^2-5y+1-(x)=5[/tex]

We need to find the value of x

[tex]-x=5-y^2+5y-1\\-x=-y^2+5y+4[/tex]

Divide both sides by - 1

[tex]x=y^2-5y-4[/tex]

So, the required polynomial that should be subtracted from the polynomial [tex]y^2-5y+1[/tex] to get the difference equal to 5  is [tex]y^2-5y-4[/tex]

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Answer:

8 vehicle.

Step-by-step explanation:

Given: Monthly salary of salesperson is $2400

          Incentive of salesperson is $250 per vehicle sold.

First, lets compute income to earned apart from salary.

∴ Deduct salary from the target amount

[tex]\$ 4400-\$ 2400= \$ 2000[/tex]

∴ $2000 need to be earned only through incentive, which is $250 per vehicle sold.

Now, solving to get number vehicles to be sold to earn $2000 as incentive.

Number of vehicle= [tex]\frac{2000}{250}= 8\ vehicles[/tex]

∴ 8 vehicles need to be sold by salesperson to get total earning as $4400.

The salesperson needs to sell 8 vehicles to earn a total of $4400 in a month.

To determine the number of vehicles a salesperson needs to sell to earn a total of $4400, we can set up an equation based on the information provided.

The salesperson earns a fixed monthly salary of $2400 and an additional $250 for each vehicle sold. Let's denote the number of vehicles sold as x

We want the total earnings  E to be $4400, so we set up the equation:

 4400 = 2400 + 250x

Now, we solve for x

250x = 4400 - 2400

x= 8

 Therefore, the salesperson needs to sell 8 vehicles to earn a total of $4400 in a month.

Answer:

[tex]y=8x-2[/tex]

Step-by-step explanation:

Here is the complete question: At a restaurant jars of tomato are stored in boxes in the pantry. each box contains 8 jars of tomato sauce. A cook uses 2 jars from 1 of the boxes. Which function shows the relationship between y, the total number of jars of tomato sauce remaining in the pantry, and x, the number of boxes in the pantry?

Given: Each boxes contain 8 jars of tomato sauce.

           Cook uses 2 jars from 1 of the boxes.

As we know total number of boxes is "x".

Number of jars in the pantry is [tex]8\ jars \times x\ boxes= 8x \ jars[/tex]

∵ cook uses 2 jars from one box.

∴ [tex]y=8x-2[/tex] ( y is used to show relationship)

The relationship between y, the total number of jars of tomato sauce remaining in the pantry, and x, the number of boxes in the pantry is [tex]y=8x-2[/tex].

Answer:

Option A) no solution

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The solution of the system of equations is the intersection point both graphs

In this problem the lines are parallel

so

The lines do not intersect

Therefore

The system has no solution ( Is an inconsistent system)

Answer:

b

Step-by-step explanation:

i just did the usa test prep

Answer:

3/-7

Step-by-step explanation:

They’re correct!

[tex]\text{Solve:}\\\\-5(1+5p)=7p-5\\\\\text{Distribute the -5 to the variables inside the parenthesis}\\\\-5 - 25p=7p-5\\\\\text{Add 5 to both sides}\\\\-25p=7p\\\\\text{Subtract 7p from both sides}\\\\-32p=0\\\\\text{Divide both sides by -32}\\\\\boxed{p=0}[/tex]

43 pounds is a reasonable range for the total weigh of 6 packages.

Step-by-step explanation:

Given,

Number of packages shipped = 6

Weight of lightest = 24 pounds

Weight of heaviest = 67 pounds

Let,

a, b, c, d be the weight of other four packages.

24, a, b, c, d, 67 (written in lighter to heavier weight order)

Range is defined as the difference between the lowest and highest values.

Range = Highest weight - Lowest weight

Range = 67 - 24 = 43 pounds

43 pounds is a reasonable range for the total weigh of 6 packages.

Keywords: range, difference

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The reasonable range for the total weight of the 6 packages is 24 pounds to 67 pounds.

The reasonable range for the total weight of the 6 packages is 24 pounds to 67 pounds.

Since the lightest package weighs 24 pounds and the heaviest package weighs 67 pounds, any total weight between these two values would be reasonable.

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The house will be 10.9 inches high on the blueprint.

Step-by-step explanation:

Given,

Scale on blue print;

6 inch = 11 feet

We will find unit rate in terms of foot.

1 foot = [tex]\frac{6}{11}\ inches[/tex]

Therefore;

20 feet = [tex]\frac{6}{11}*20 = \frac{120}{11}[/tex]

20 feet = 10.9 inches

The house will be 10.9 inches high on the blueprint.

Keywords: unit rate, division

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The house would be approximately 10.91 inches tall on the blueprint to represent a 20-foot actual height.

The student asked how many inches high a house would be on a blueprint if the actual home is to be 20 feet tall, and a blueprint states that a 6-inch line represents 11 feet on the actual home. To solve this, we set up a proportion to determine the blueprint's height. The proportion is 6 inches/11 feet = x inches/20 feet, where x represents the height on the blueprint. First, write the proportion as 6 inches/11 feet = x inches/20 feet. Then, cross-multiply to get 11 feet * x inches = 6 inches * 20 feet. To find x, divide both sides of the equation by 11 feet, getting x = (6 inches * 20 feet) / 11 feet. After calculating, we find that x ≈ 10.91 inches. Therefore, on the blueprint, the house would be approximately 10.91 inches tall to represent an actual height of 20 feet.

Answer:

35 hotdogs and 52 sodas were sold.

Step-by-step explanation:

Create equations to represent the problem.

let "d" be the number of hotdogs sold

let "a" be the number of sodas sold

1.5d + 0.5a = 78.50     Equation for money made

d + a = 87                    Equation for items sold

Rearrange d + a = 87 to isolate one of the variables.

a = 87 - d

Substitute a for 87-d into the other equation. Isolate using reverse operations.

1.5d + 0.5a = 78.50

1.5d + 0.5(87 - d) = 78.50     Distribute over brackets by multiplying

1.5d + 43.5 - 0.5d = 78.50    Collect like terms

43.5 + d = 78.50          1.5d - 0.5d is 1d. You don't need to write "1".

43.5 + d - 43.5 = 78.50 - 43.5   Isolate d, subtract 43.5 from both sides

d = 35    Number of hotdogs sold

Substitute d for 35 in the simpler equation

d + a = 87

35 + a = 87     Subtract 35 form both sides to isolate "a".

a = 87 - 35

a = 52      Number of sodas sold

Therefore 35 hotdogs and 52 sodas were sold.

Final answer:

To find the amount of cloth left over, subtract the amount used from the total amount. Jaquan had 9.5 yards of cloth left over, which can be expressed as the fraction 19/50.

Explanation:

To find the amount of cloth left over, we need to subtract the amount used from the total amount. Jaquan bought 25 yards of cloth, used 4.9 yards for a decoration, and used 10.6 yards to make costumes. To find the amount left over, we subtract the sum of 4.9 yards and 10.6 yards from 25 yards: 25 - 4.9 - 10.6 = 9.5 yards.

The amount of cloth left over can be expressed as a fraction by dividing the amount left over by the total amount. So, 9.5 yards can be written as the fraction 9.5/25, which can be simplified by dividing both the numerator and denominator by 0.5 to get 19/50. Therefore, the amount of cloth left over is 19/50.

Answer:

[tex]4^7[/tex]

Step-by-step explanation:

If we use one of the property of exponents rules:

[tex]4^4*4^3=4^4^+^3=4^7[/tex]

Answer:

[tex]10\pi\ cm[/tex] or [tex]31.4\ cm[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=15\ cm[/tex]

substitute

[tex]C=2\pi (15)[/tex]

[tex]C=30\pi\ cm[/tex]

step 2

Remember that the circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find the length of an arc by a central angle of 120 degrees

[tex]\frac{30\pi}{360^o}=\frac{x}{120^o}\\\\x=30\pi(120^o)/360^o\\\\x= 10\pi\ cm[/tex]

The exact value of the length of the arc is [tex]10\pi\ cm[/tex]

assume

[tex]\pi=3.14[/tex]

[tex]10(3.14)=31.4\ cm[/tex] ---> approximate value

Answer:

Step-by-step explanation:

About 31.4 based on the other answers I have seen.

Answer:

[tex]A=\$584.43[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=17\ years\\ P=\$150\\ r=8\%=8/100=0.08[/tex]  

substitute in the formula above

[tex]A=150(e)^{0.08*17}[/tex]  

[tex]A=150(e)^{1.36}[/tex]  

[tex]A=\$584.43[/tex]  

Answer:

x=-8 y=-2

Step-by-step explanation:

substitute x for 2y-4

7(2y-4)+5y=-66

factor

14y-28+5y=-66

add 28 on both sides

14y+5y=-38

19y=-38

divide by 19 on both sides

y=-(38/19)

y=-2

Plug -2 into the first equation for y

x=2(-2)-4

x=-4-4

x=-8

Answer:

circumference is 59.6075

area is 282.743

Step-by-step explanation:

   To find the circumference and area of the circle, we need to first find the radius. This can be achieved using the distance formula.

   The distance formula goes as follows: for any two points on an coordinate plane, the distance can be calculated using a certain method. This method is the derived from the Pythagorean Theorem. Basically, you find the distance from right to left and square it, and then find the distance from up to down and square it. You add these two values together and then square root the whole thing. I know, its complicated.

   To apply this to your problem, we do 2-(-1) to find the distance from right to left (x-distance) and then we do 5-(-4) to find the distance from up to down (y-distance). 2-(-1)=3 and squaring that we get 9. 5-(-4)=9 and squaring that we get 81. Adding these two values together, we get 90 and square rooting it we get [tex]\sqrt{90}[/tex].

   The formula for circumference of a circle is 2Pi * radius and plugging in our values we get 2Pi * [tex]\sqrt{90}[/tex] which gives us approximately 59.6075.

   The formula for area of a circle is Pi * radius^2 and plugging in our values we get Pi * [tex]\sqrt{90}[/tex] ^2 which gives us approximately 282.743.

Answer:

21 miles

Step-by-step explanation:

Hence, the actual distance between Paige's house and the mall is [tex]21[/tex] miles.

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Sonoma bikes [tex]5[/tex] miles to Paige's house. On a map, they measure that distance as [tex]\frac{5}{6}[/tex]cm. The same map shows that the mall is [tex]3\frac{1}{2}[/tex]cm from Paige's house.

Let the actual distance between Paige's house and the mall is [tex]x[/tex]

So,

[tex]\frac{5}{\frac{5}{6}}=\frac{x}{\frac{7}{2}}\\\\\\5(\frac{6}{5})=x(\frac{2}{7})\\\\\\6=\frac{2x}{7}\\\\\\x=6(\frac{7}{2})\\\\\\x=\frac{42}{2}\\\\\\x=21[/tex]

Hence, the actual distance between Paige's house and the mall is [tex]21[/tex] miles.

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Answer:

84

Step-by-step explanation:

7x12

Answer:

The measure of arc AC is [tex]136^o[/tex]

Step-by-step explanation:

Notice that angle BAC (whose measure is given as 34 degrees) is an inscribed angle, and according toe the inscribed angle theorem, the measure of an inscribed angle is half the measure of the central angle that subtends the same chord.

Then, the central angle that subtends the cord BC, is twice 34 degrees ([tex]2\,*\,34^o = 68^o[/tex])

Then, since they give us also the measure of the arc AB which is [tex]156^o[/tex], then the measure of arc AC can be estimated as the needed measure to complete [tex]360^o[/tex] as the sum of all three arcs. That is:

[tex]AC + AB+ BC = 360^o\\AC + 156^o+2\,*\,34^o = 360^o\\AC + 156^o+68^o = 360^o\\AC=360^o-156^o-68^o\\AC=136^o[/tex]

Answer:

use the distributive property to distribute the 8

-16+16n+3n=40+5n

-16+19n=40+5n

-16=40+5n-19n

-16=40-14n

-14n+40= -16

-14n= -16-40

-14n= -56

n= -56/-14

n= 4

Answer: n=4

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helps you out! If you need anymore help with math, let me know and I will be more than happy to help you! ☺

-Karleif Jonsi-

Answer:

Option E) is correct

If n is an odd number then 2(n+1) represents an even number.

Step-by-step explanation:

Let X=set of all odd numbers

that is [tex]X={\{1,3,5,7...}\}[/tex]

Let Y=set of all even numbers

that is [tex]Y={\{2,4,6,8...}\}[/tex]

Verify that 2(n+1) represents an even number where n is an odd number:

Put n=1 in 2(n+1) we get

2(1+1)=2(2)=4

Put n=3 in 2(n+1) we get

2(3+1)=2(4)=8

Put n=5 in 2(n+1) we get

2(5+1)=2(6)=12

and so on.

From above results we get 2(n+1) represents an even number and is belongs to the set Y when n is an odd number.

Therefore Option E) is correct

If n is an odd number then 2(n+1) represents an even number.

Option A: d(t) = 360-60t is the right answer

Step-by-step explanation:

We will write the given problem in terms of function to find the correct answer.

Let d(t) be the function and t be the number of hours.

Total distance is 360 miles and with each passing hour the distance will reduce 60 miles

So,

The function is:

[tex]d(t) = 360-60t[/tex]

Hence,

Option A: d(t) = 360-60t is the right answer

Keywords: Functions, word problems

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Answer:

Step-by-step explanation:

(-2,6),(1,1)

slope = (1 - 6) / (1 - (-2) = -5/3

y - y1 = m(x - x1)

slope(m) = -5/3

(-2,6)....x1 = -2 and y1 = 6

and we get :

y - 6 = -5/3(x - (-2)...which can further be simplified to :

y - 6 = -5/3(x + 2) <=== ur answer

Answer: the answer that actually makes since is multiply 8 times 41.75 that also equals out to 334 which would be accurate

Step-by-step explanation:

Answer:

multiply 8 times 41.75

Step-by-step explanation:

i got it right on my test

Answer: 2 bookcases.

Step-by-step explanation:

Let be "x" the number of bookcases that the custodian will be able to repaint completly with 5 gallons of paint.

According to the data given, the custodian needs 2 gallons of paint to repaint one bookcase. Since all the bookcases are equal, you can set up the following proportion:

[tex]\frac{2}{1}=\frac{5}{x}[/tex]

Now you must solve for "x" in order to find its value:

[tex](x)(\frac{2}{1})=5\\\\2x=5\\\\x=\frac{5}{2}\\\\x=2.5[/tex]

Notice that the custodian will be able to repaint 2 bookcases completely, then you can say that:

[tex]x\approx2[/tex]

The custodian will be able to repaint 2 bookcases with 5 gallons of paint.

To determine the number of bookcases the custodian will be able to repaint with 5 gallons of paint, we need to divide the total amount of paint by the amount of paint required for each bookcase. Each bookcase requires 2 gallons of paint, so we divide 5 gallons by 2 gallons per bookcase:

5 gallons ÷ 2 gallons/bookcase = 2.5 bookcases

Since we cannot have 0.5 of a bookcase, the custodian will be able to repaint 2 bookcases with 5 gallons of paint.

Answer:

A related subtraction fact would be either

12-5=7  or

12-7=5

Step-by-step explanation:

Answer:

a related subtraction fact for 5+7=12 would be 12-7=5

Answer:

[tex]293,148\ mm^2[/tex]

Step-by-step explanation:

The cup has cylivdrical shape. Find the volume of the cylinder using formula

[tex]V=\pi r^2h,[/tex]

where

r = base radius

h = height

In your case,

r = 36 mm

h = 72 mm

then

[tex]V=\pi \cdot 36^2\cdot 72=93,312\pi \ mm^2\approx 293,148\ mm^2[/tex]