For this right triangle shown, what is the sine of angle C?
A)
15
7
B)
15
8
C)
17
7
D)
17
8
E)
7
8

The simplified expression is x^2 - 14xy + 49y^2.

To multiply the expression (x - 7y)^2 using the Special Product Formula, we can use the formula (a - b)^2 = a^2 - 2ab + b^2.

In this case, a = x and b = 7y. Plugging these values into the formula, we get:

(x - 7y)^2 = x^2 - 2(x)(7y) + (7y)^2

Simplifying further:

= x^2 - 14xy + 49y^2

So, the simplified expression is x^2 - 14xy + 49y^2.

The expression for the new function (fog(x)) = x⁸ + 8x⁴

What is a composite function?

A composite function some called function of a function is a process whereby two functions produce a third function.

Let assume there is a function f(x) and g(x), a composite function fog(x) read  as f of g of x, produces a third function h(x).

In the given question, we are to find (fog) (x), we will replace the value of the function g(x) for x in f(x).

i.e.

f(g(x) = x² + 8x  

[tex]f(g(x) = (x^4)^2+8(x^4)[/tex]

[tex]f(g(x)) = x^8+8x^4[/tex]

The measure of m∠KPN is 68°.

Step-by-step explanation:

From the given diagram, we are given with lines passing through a point P creating different angles.

Data given,

m∠KPN = 4x°.

m∠NPO = (x+5)°.

And m∠KPO= 90°.

The m∠KPO is spitted into m∠KPN and m∠NPO.

Thus the sum of m∠KPN and m∠NPO will be m∠KPO.

⇒m∠KPN + m∠NPO =m∠KPO.

Substitute the values to find x value.

4x°+(x+5)°= 90°.

(°5x+5)=90°.

5x°=90°-5°.

5x°=85°.

x=[tex](\frac{85}{5} )[/tex].

x= 17.

⇒m∠KPN = 4x°.

=4(17)°.

m∠KPN =68°.

Thus the measure of m∠KPN is 68°.

Answer:

22.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

6.3g + 14

Answer:

6.3g + 14

Step-by-step explanation:

Answer:

$366.66

Step-by-step explanation:

You start with a credit card balance of $1950. If you reduce this balance by 13% each month for 12 months, using the formula for geometric series (a(r^n)), your final balance at the end of 12 months will be approximately $452.98.

The student's question is asking about reducing a credit card debt balance by a fixed percent each month. In this case, the student is reducing their debt by 13% every month for 12 months. To get a clear picture, let's go through this step by step.

Initially, the credit card balance is $1950. In the first month, the student reduces the debt by 13% which is $253.5. So, the remaining balance at the end of first month would be $1950 - $253.5 = $1696.5

This process is repeated each month. For example, in the second month, the student reduces the new amount of $1696.5 by 13%. The debt will continue to decrease in this manner each month.

To calculate the balance at the end of 12 months, we would use the formula for geometric series: a(r^n), where 'a' is the initial amount of debt($1950), 'r' is the percentage (1 - 13% or 0.87) and 'n' is the number of months (12).

Your final balance at the end of 12 months would be $1950*(0.87^12) which approximately equals $452.98. Hence, by reducing your debt by 13% each month for 12 months, your balance will be approximately $452.98. But remember, maintaining steady payments and not adding to the balance by new purchases is also important in managing credit card debt.

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3(4x + 2)

= 3 . 2(2x + 1)

= 6(2x + 1)

proof

• 3(4x + 2)

= 3(4(2) + 2)

= 30

• 6(2x + 1)

= 6(2(2) + 1)

= 30

15° and 165°

Step-by-step explanation:

Step 1 :

Let x and y denote the angles with x as the smaller angle and y as the larger angle

When 2 angles are supplementary, the sum of both the angles is 180 degrees.

Hence x + y = 180

Step 2:

Given that the larger angle is 15 more than 10 times the smaller angle

Hence y = 15 + 10 x

Step 3 :

Solving for the 2 equations we have

11x = 165 => x = 15

=> y = 180-15 = 165

Hence the 2 angles are 15 and 165 degrees.

Answer:

1.Distribute values

(3x+12)-(2x+8)

2.Add common terms

x+4

The population in this situation is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag.

Explanation:

The population in this situation of Mr Wilson is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag. The sample is every set of 5 note cards that is selected by the students.

The data is representative of the population because they are selected randomly without bias. Every of term has the same probability of being selected. Also it given that the cards are replaced every time, so all the students will face the same population when they are going to select a sample.

Answer:

900 g

Step-by-step explanation:

Increase by 20% means 120% of the value

120/100 × 750

900g

Answer:

Here is a similar question:

A bakery uses 10 1/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake.

The unit rate in ounces of icing per cake = 40 4/5 ounces

Step-by-step explanation:

Given:

Ounces of ice used for every 1/4 cake = 10 1/5

We have to find the unit rate.

Let the unit rate be 'x' .

Unit rate is the rate when we use unit 'one' as our reference to find any value.

Lets convert the mixed fraction of ounces.

⇒ [tex]10\frac{1}{5} = \frac{(10\times 5)+1}{5} =\frac{51}{5}[/tex]

Portion of the cake used = [tex]\frac{1}{4}[/tex]

To find the unit rate here we must divide :

⇒ [tex]x=\frac{number\ of\ ounces\ used}{portion\ of\ the\ cake}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51}{5}[/tex]  ÷  [tex]\frac{1}{4}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51}{5}\times \frac{4}{1}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{51\times 4}{5}[/tex]

⇒ [tex]x=[/tex] [tex]\frac{204}{5}[/tex]

⇒ [tex]x=[/tex] [tex]40\frac{4}{5}[/tex]  Or [tex]40.8[/tex]  

Hence, the unit rate in ounces of icing per cake = 40 4/5 ounces.

Answer:

Another similar question:

A bakery uses 10 3/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake?

Step-by-step explanation:

Answer is 42 2/5

10 3/5 ÷ 1/4 = 53/5 ÷ 1/4

= 53/5 x 1/4

= 212/5

= 42 2/5

Answer:

The answer is 24

Step-by-step explanation:

If each person eats 1/3 of the pizza then that means it takes 3 people to eat a whole pizza so you multiply three times 8 and you get twenty four.

Answer:

yes

Step-by-step explanation:

when addi g the ones place it would result in 14 so u would need to regroup the 1 into the tens place

Answer:

2/5 with an exponent of 3 is 8/125 or 0.064

Step-by-step explanation:

Given:

A fraction = 2/5

Exponent = 3

To find the value of the fraction using the exponent.

We know that :

⇒ [tex](a)^3=a\times a\times a[/tex]  

The exponents is the number of times a number is multiplied.

So,

⇒ [tex](\frac{2}{5})^3[/tex]

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

⇒ [tex]\frac{8}{125}[/tex]

On further division the number can be written as 0.064

Answer:

The number of square tiles required to cover the bathroom floor is approximately 31.

Step-by-step explanation:

The dimensions of the rectangular floor of the bathroom are:

Length = 10.5 ft.

Breadth = 6.5 ft.

The dimensions of the square tiles are:

Side = 1.5 ft.

The area of the rectangular floor of the bathroom is:

[tex]Area\ of Bathroom\ floor=Length\times Breadth\\=10.5\times6.5\\=68.25[/tex]

The area of 1 square tile:

[tex]Area\ of\ 1\ square\ tile=(SIde)^{2}\\=(1.5)^{2}\\=2.25[/tex]

The number of tiles required to cover the bathroom floor is:

[tex]Number\ of\ tiles=\frac{Area\ of\ bathroom\ floor}{Area\ of\ 1\ square\ tile} \\=\frac{68.25}{2.25}\\ =30.3333\\\approx31[/tex]

Thus, the number of square tiles required to cover the bathroom floor is approximately 31.

Answer:

D

Step-by-step explanation:

Answer:

y=-1/3x-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-9)=-1/3(x-3)

y+9=-1/3x+3/3

y+9=-1/3x+1

y=-1/3x+1-9

y=-1/3x-8

The final price of a $1049 television on a 12% sale, with a 4.5% sales tax, is $964.66.

The final price on a $1049 television that is on sale for 12% off can be found by deducting the discount from the original price, and then adding the sales tax on the discounted price.

First, let's find the discount: 12% of $1049 is (12/100)*1049 = $125.88. So, the price after discount would be 1049 - 125.88 = $923.12.

Next, we need to add the 4.5% sales tax. Sales tax is calculated on the discounted price, so 4.5% of $923.12 is (4.5/100)*923.12 = $41.54.

Finally, we add the tax to the discounted price to get the final price: $923.12 + $41.54 = $964.66. So, the final price of the television is $964.66.

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The dimensions of the rectangle shown on the coordinate plane is The base is 9 units and the height is 4 units.

Option: B.

Step-by-step explanation:

We are given with the coordinate points of a rectangle.

The points are  (1, -1), (10, -1), (10, -5), (1, -5).

From the given graph, the bigger side is the base and the height is the smaller side.

The points  (1, -1), (10, -1) and (1, -5), (10, -5) can be used to find the base of the rectangle.

The points (10, -1), (10, -5) and  (1, -1), (1, -5) can be used to find the height of the rectangle.

Let us find the base using coordinate point (1, -5), (10, -5) .

Since the base runs horizontally on the x-axis, we have to find the run.

run = [tex]x_2-x_1[/tex].

run = 10-1.

run (base)= 9 units.

Let us find the base using coordinate point (10, -1), (10, -5) .

Since the height runs vertically on the y-axis, we have to find the rise.

rise = [tex]y_2-y_1[/tex].

rise = -5-(-1).

rise=-5+1.

rise (height)= 4 units.      ( Units are always measured in positive.)

∴ The base is 9 units and the height is 4 units.

The midpoint of AB is point G

The complete question has been attached below. As you can see, we have a line segment which is defined as a part of a line that is bounded by two different points that are at the end of the segment. So here we know that:

Therefore, the midpoint can be calculated as:

[tex]M:midpoint \\ \\ \\ M=\frac{A+B}{2} \\ \\ M=\frac{-6+8}{2} \\ \\ M=1[/tex]

So the midpoint is [tex]M=1[/tex] that matches point G. Finally:

Conclusion: The midpoint of AB is point G

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Answer:

Step-by-step explanation:

If QPS is a right angle we know a right angle equals 90 degrees. so you can find your answer by doing 90-35.

Therefore getting 56.

Hope this helps :)

To solve this, you need to isolate/get the variable "c" by itself in the equation:

4c + 8c = -55 + 3c    You can first combine like terms (4c and 8c)

12c = -55 + 3c         Subtract 3c on both sides

9c = -55       Divide 9 on both sides

[tex]c=-\frac{55}{9}[/tex]

Answer:

False

Step-by-step explanation:

Whichever has more heat (in this case the stove) has more thermal energy

Step-by-step explanation:

We have,

[tex]\dfrac{6}{7} \times 42.21[/tex]

To find, the value of [tex]\dfrac{6}{7} \times 42.21[/tex] = ?

∴ [tex]\dfrac{6}{7} \times 42.21[/tex]

= [tex]\dfrac{6}{7} \times \dfrac{4221}{100}[/tex]

We know that,

The properties of rational numbers,

[tex]\dfrac{a}{b} \times \dfrac{c}{d} =\dfrac{a\times c}{b\times d}[/tex]

= [tex]\dfrac{6\times 4221}{7\times 100}[/tex]

= [tex]\dfrac{25326}{700}[/tex]

= 36.18

Thus, the value of [tex]\dfrac{6}{7} \times 42.21[/tex]= 36.18

First write 18% as a decimal by moving the decimal point two places to the left to get .18.

The word "of" means multiply, so we have (.18)(75) which is 13.5.

Answer:

13.5

Step-by-step explanation:

18% of 75

18% /100% x 75

0.18 x 75

13.5

Answer:

<ABC = 98.

Step-by-step explanation:

We know that the triangle is lying on a flat line, which is 180 degrees. We know that angle ABC and angle CBD are supplementary as they both use line ABD as their transversal.

Set up the equation (3 + 5x) + 82 = 180.

Solve for x, and you get 19.

Plug it back in to (3 + 5x), we get <ABC = 98.

Answer:

52 / 27

Step-by-step explanation:

To multiply mixed numbers, convert them into improper fractions. Multiply the two improper fractions together and simplify the result.

To multiply mixed numbers, we first convert them into improper fractions. To convert 1 1/3 into an improper fraction, we multiply the whole number (1) by the denominator (3) and add the numerator (1). This gives us 4/3. Similarly, to convert 1 4/9 into an improper fraction, we multiply the whole number (1) by the denominator (9) and add the numerator (4). This gives us 13/9.

Now, we can multiply the two improper fractions together. 1 1/3 times 1 4/9 equals (4/3) * (13/9). To multiply fractions, we multiply the numerators together and multiply the denominators together. So, (4/3) * (13/9) equals (4 * 13) / (3 * 9), which simplifies to 52/27.

Therefore, 1 1/3 times 1 4/9 in fraction form is equal to 52/27.

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