Help!!!!!!Angle DFG and angleJKL are complementary angles. If the measure if the angle DFG=x+2 and the measure of the angle JKL =x+9 then find x.

Answer:

\(\sf 11,600,000,000,000 = 1.16 \times 10^{13}\)

\(\sf 307,000,000=3.07 \times 10^{8}\)

\(\sf 3.78\times 10^{4}\)

Step-by-step explanation:

Scientific notation:  \(\sf a \times 10^b\)

(where \(\sf 1 \leq |a| < 10\) and b is the power of 10 required so that the notation is equivalent to the original number)

Move the decimal point back 13 places then multiply by \(\sf 10^{13}\):

\(\sf 11,600,000,000,000 = 1.16 \times 10^{13}\)

Move the decimal point back 8 places then multiply by \(\sf 10^{8}\):

\(\sf 307,000,000=3.07 \times 10^{8}\)

Divide the total debt by the population to calculate how much each person would owe if the debt was divided equally among everyone in the US:

\(\sf \dfrac{11,600,000,000,000}{307,000,000}=\dfrac{1.16 \times 10^{13}}{3.07 \times 10^{8}}=\dfrac{1.16}{3.07} \times \dfrac{10^{13}}{10^{8}}\)

Apply exponent rule \(\dfrac{a^b}{a^c}=a^{b-c}\)

\(\sf \dfrac{1.16}{3.07} \times \dfrac{10^{13}}{10^{8}}=0.3778501629... \times 10^{13-8}\)

                   \(\sf =0.378\times 10^{5}\)

                   \(\sf =3.78\times 10^{4}\)

(remembering that the first part "0.378" needs to be equal to or greater than 1, but smaller than 10)

The function f(x) represents the linear relationship between f(x) and x because the slope remains constant.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope remains constant throughout the data.

Then the slope of the function f(x) at different stages is given as,

⇒ (14 - 10) / (2 - 1)

⇒ 4

⇒ (22 - 18) / (4 - 3)

⇒ 4

Then the slope of the function g(x) at different stages is given as,

⇒ (12- 10) / (2 - 1)

⇒ 2

⇒ (22 - 16) / (4 - 3)

⇒ 6

The function f(x) represents the linear relationship between f(x) and x because the slope remains constant.

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Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

To find the percentage by which Sara needs to reduce the price to provide the same value for money as Zak's idea, we need to compare the original price and the new price under Zak's idea.

Let's assume the original price of a box of pet food is P and the original amount of pet food in each box is A.

According to Zak's idea, the company will put 50% more pet food into each box without changing the price. Therefore, the new amount of pet food in each box will be 1.5A.

To calculate the value for money under Zak's idea, we divide the amount of pet food by the price:

Value for money (Zak's idea) = (1.5A) / P

Now, let's consider Sara's idea. She wants to reduce the price but keep the amount of pet food unchanged. Let's assume Sara reduces the price by a percentage represented by x.

Under Sara's idea, the new price of a box of pet food will be P - (x/100)P = P(1 - x/100).

Since Sara wants her idea to provide the same value for money as Zak's idea, we can equate the two value for money expressions:

(1.5A) / P = (A) / (P(1 - x/100))

Cross-multiplying and simplifying the equation:

1.5A * P(1 - x/100) = A * P

1.5(1 - x/100) = 1

Simplifying further:

1 - x/100 = 2/3

-x/100 = -1/3

x/100 = 1/3

x = 100/3

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

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Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.

Answer: 2/90 = 1/45

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

1.47826086

rounded to the nearest tenth is 1.5

From the question

A pepperoni pizza has a radius of 10 inches

A pizza is in a circle shape then area of circle (A) is given as

r = 10 inches

Hence we have

Therefore, the area of the pepperoni pizza is 314 inches squared

Answer:

0.0

Step-by-step explanation:

To find 0.007 divided by 0.498, we can perform the following calculation:

0.007 / 0.498 ≈ 0.0141

Rounding this to the nearest tenth gives:

0.0141 ≈ 0.0

Therefore, the result, rounded to the nearest tenth, is 0.0.

The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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Answer:

-19x

Step-by-step explanation:

to make this equation easier, remove the variables (-8-11) which equals -19. You can then say the answer is -19x

The total cost of purchasing the number of shirts after the coupon and sales tax are applied is $40.32.

The discount that the coupon offers is 25% and the price of the shirts before discounts is $50.

The price after the discount is:

= 50 x (1 - 25%)

= $37.50

The price including the sales tax:

= 37.50 x (1 + 7.5%)

= $40.32

Rest of the question is:

The coupon discount on a group of shirts that cost $50 is 25%. What would be the total cost of purchasing the number of shirts needed to use your coupon after your coupon is applied and a 7.5% sales tax is charged on the purchase?

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1. The area of triangle ABC = 10 units²

2. The area of triangle DEC = 2.5 units²

3. No

4. Scale factor = 2

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The figure is given in the question, as shown

As per the question, the required solution would be as:

1. the area of triangle ABC = 1/2 x 5 x 4  = 20/2 = 10 units²

2. the area of triangle DEC = 1/2 x (5/2) x (4/2)  = 20/8 = 2.5 units²

3. No

4. scale factor = 5/(5/2) = 2

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The question seems to be incomplete the missing part has been attached below

The missing numbers are a = 25 and b = 92.

Let's start by finding the mean of the given numbers. The mean is calculated by summing all the numbers and dividing the sum by the total count. In this case, we have:

(a + 31 + 42 + 65 + b) / 5 = 51

Now, we can simplify the equation:

a + 31 + 42 + 65 + b = 51 x 5

a + 138 + b = 255

Next, we know that the greatest number is 67 more than the least number:

b = a + 67

Now we can substitute this value into the previous equation:

a + 138 + (a + 67) = 255

Combining like terms:

2a + 205 = 255

Subtracting 205 from both sides:

2a = 50

Dividing both sides by 2:

a = 25

Substituting this value back into the equation b = a + 67:

b = 25 + 67

b = 92

Therefore, the missing numbers are a = 25 and b = 92.

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Answer:D

Step-by-step explanation:

The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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Answer:

I believe it’s b

Step-by-step explanation:

Answer:

g(x)=(x+2)^2

Step-by-step explanation:

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

39/2

Step-by-step explanation:

This is out of context

Answer:

1950/100

Step-by-step explanation:

The expression factoring out the greatest common factor is  (3pf - 21p²)(f + 2).

We have the expression as

3pf² - 21p²f + 6pf - 42p²

Now, factorising the expression as

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +2)

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Answer:

Step-by-step explanation:

-4(7-1) = (-4)7 + (-4)(-1) = -24

Answer:

60.6

Step-by-step explanation:

tan(theta) = P/B

tan(24) = 27/x, x=27/tan(24)=60.6

Answer:

9x+3

Step-by-step explanation:

Using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem.

In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

A second-order equation of the form ax² + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.

So, we have the equation:

x²-3x+ 5 = 0

Now, solve it using the quadratic formula as follows:

x²-3x+ 5 = 0

a = 1

b = -3

c = 5

x = -(-3)±√(-3)² -4*1*5/2

Solve this further:

x = 3±√11/2

Therefore, using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

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Correct question:

Solve x²-3x+ 5 = 0.

A.3+√-29 +VE/2 and 3- 2-29

B. 3+√29 and 3-√29

C. 3+√-11 and 3-√-11/2

D. 3+√11/2 and 3-√11/2

Answer:

7777.5 ft^3

Step-by-step explanation:

First, separate the solid into two, the triangular prism and the rectangular prism. Then, find the area of both solids.

\(A_{triangular prism}=BA *h\)

\(A_{triangular prism} = (\frac{1}{2} * 17 * 19) *15\)

\(A_{triangular prism}=161.5*15\)

\(A_{triangular prism}=2422.5ft^3\)

\(A_{rectangular prism} = l * w * h\)

\(A_{rectangular prism}=17*15*21\)

\(A_{rectangular prism}=5355ft^3\)

Finally, add together both values

\(A_{total}=A_{triangular prism}+A_{rectangular prism}\)

\(A_{total}=2422.5+5355\)

\(A_{total}=7777.5ft^3\)