What is the area of ΔABC given m∠B = 83°, a = 25 feet, and c = 40 feet? (2 points)
561.46 feet2
496.27 feet2
186.23 feet2
128.51 feet2

Answer:

The factored form is,

\((4a^2+2a+1)(4a^2-2a-1)\)

Step-by-step explanation:

We have,

\(16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\\)

Using the difference of square formula,

\(x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)\)

Which is the factored form,

Answer:

112

Step-by-step explanation:

f(7) = 7^2 + 9*7 = 49 + 63 = 112

Q9.1: To justify the proposal, we need to compare the benefits of the road expansion (in terms of reduced travel time) with its costs. The value of time represents the monetary value individuals place on their time spent traveling. In this case, the value of time is $1.5 per minute.

First, let's calculate the reduction in travel time resulting from the road expansion. We compare the two road performance functions: t1​ = 30 + 6×10−6q and t2​ = 20 + 3×10−6q. By subtracting t2​ from t1​, we can determine the time savings: Δt = t1​ - t2​ = (30 + 6×10−6q) - (20 + 3×10−6q)    = 10 + 3×10−6q Next, we multiply the time savings by the number of trips (q) to obtain the total time savings: Total Time Savings = Δt × q = (10 + 3×10−6q) × q Now, we can determine the monetary value of the time savings by multiplying the total time savings by the value of time ($1.5 per minute): Monetary Value of Time Savings = Total Time Savings × Value of Time                             

= (10 + 3×10−6q) × q × $1.5  If the monetary value of the time savings exceeds the construction cost of $9.6×107, then the proposal is justified. Q9.2: To determine the construction cost at which the proposal becomes justified, we set the monetary value of the time savings equal to the construction cost and solve for q: (10 + 3×10−6q) × q × $1.5 = $9.6×107 By solving this equation for q, we can find the corresponding construction cost at which the proposal becomes justified.

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Answer:

\(5 \frac{1}{9}\)

\(6 \frac{2}{5}\)

Step-by-step explanation:

We can convert these improper fractions into mixed numbers by seeing how many times the denominator goes into the numerator.

In \(\frac{46}{9}\), 9 goes into 46 5 times, with a remainder of 1. So:

\(5 \frac{1}{9}\).

In \(\frac{32}{5}\), 5 goes into 32 6 times with a remainder of 2, so:

\(6 \frac{2}{5}\).

Hope this helped!

Answer:

5 1/9 and 6 2/5

Step-by-step explanation:

The simplest way to convert improper fractions into mixed fractions is by long division (see attached).

Answer:

-20, I believe is the answer.

The value of X from the given diagram of a hexagon would be = 13. That is option B.

A hexagon can be defined as the type of a polygon that has 6 sides with the sum of its exterior angle as 360°.

That is from the given diagram;

62+(4x+7)+(6x-5)+41+(3x+6)+(7x+11) = 360

Bring the like terms together;

62+41+7+6 -11-5+4x+6x+3x+7x = 360

100 + 20x = 360

20x = 260

X = 260/20

X = 13

Therefore the Value of X from the hexagon given above = 13. This value can be used to determine the various unknown values of the exterior angle of the hexagon.

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Nader can spend on the purchase of a car if the interest rate is 9.8%/a, compounded annually, is $8715.82

Compound interest is the interest that is earned on the principal amount of a loan or investment, as well as the interest that is earned on the accumulated interest.

In this case, Nader wants to purchase a used car and can afford to pay $280 per month for three years. He has found the best interest rate he can get, 9.8%/a, compounded monthly. However, if the interest rate is compounded annually, the most he could spend on the vehicle will be different.

To calculate this, we need to use the formula for compound interest, which is

A = P(1 + r)ˣ,

where A is the total amount, P is the principal amount, r is the interest rate, and x is the time period.

When we apply the values on it, then we get,

=> A = $8702.85(1 + 9.8)³

=> A = $8715.82

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Step-by-step explanation:

When you divide by a number, you basically are multiplying by the reciprocal

The reciprocal of 2 is 1/2

4/10 ÷ 2 = 4/10 × 1/2 = 2/10

4/10 × 1/2 = 2/10

Using a number line,

Start at 4/10 and move down by 2 until you reach 0

Start at 4/10 and move up by 1/2 from 0 until you reach 4/10

(Count the number of humps)

Both will be the same

Answer: The answer is triangle ABC ~ triangle EDC because m<3=m<4 and m<1=m<5.

Step-by-step explanation: The reason this would be is that both triangles are equilateral, so all the sides are the same.

Now that we know that the triangles are similar to each other, then we can eleminate the last two answers. The best possible answer would be triangle ABC ~ triangle EDC because m<3=m<4 and m<1=m<5.

This can be seen by using the chain rule, where the derivative of cscx can be written as d/dx(cscx) = d/dx(1/sinx) = (−1/sinx)(cosx) = (−1/sinx)(−cotx) =−cscxcotx.

The attempt to derive the derivative of cscx is as follows:

(cscx)(−cotx) = −cscxcotx

(cscx)' = (−cscxcotx)'

= (−cscx)'(cotx) + (−cotx)'(cscx)

= (−cscx)(−cscx) + (−cscxcotx)

The error first appears in the third step, where the derivative of cscx is incorrectly taken as (−cscx). The correct derivative of cscx is −cscxcotx. This can be seen by using the chain rule, where the derivative of cscx can be written as d/dx(cscx) = d/dx(1/sinx) = (−1/sinx)(cosx) = (−1/sinx)(−cotx) =−cscxcotx.

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Answer:

X=-10 Y=-3

Step-by-step explanation:

Answer:

5:4, 5 to 4

Explanation:

Given the ratio 5/4, we can also write it in the forms below:

The Law of Sines is used to solve a triangle that is not a right triangle and that has two angles and a side opposite one of those angles given. For this given problem, the measure of angle C is given and we can use the law of sines to solve the problem.

What is the Law of Sines?The law of sines is a trigonometric formula that is used to solve triangles for an unknown side or angle of the triangle. It can be used to solve a triangle when we have two sides and the angle opposite one of them (AAS), or when we have two angles and a side opposite one of them (ASA).

Step 1: Find angle AUsing the law of sines, we can find the measure of angle A:sin A/a = sin C/csin A/16.1 = sin 35°/crossoversin A = 16.1 sin 35° / crossmultiplysin A = 9.24° (approx)This gives us one possible value of angle A. However, we are given two possible triangles, so let's check the other one. If this value of A is too big to be a possible angle, then we will have to use the other triangle.

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After deducting the amounts for Federal tax, Social Security, and other deductions, the net pay for working 40 hours at an hourly wage of $8.95 is $276.61. Option A.

To calculate the net pay, we need to subtract the deductions from the gross pay.

Given:

Hours worked = 40

Hourly wage = $8.95

Federal tax deduction = $35.24

Social Security deduction = $24.82

Other deductions = $21.33

First, let's calculate the gross pay:

Gross pay = Hours worked * Hourly wage

Gross pay = 40 * $8.95

Gross pay = $358

Next, let's calculate the total deductions:

Total deductions = Federal tax + Social Security + Other deductions

Total deductions = $35.24 + $24.82 + $21.33

Total deductions = $81.39

Finally, let's calculate the net pay:

Net pay = Gross pay - Total deductions

Net pay = $358 - $81.39

Net pay = $276.61

Therefore, the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33 is $276.61. SO Option A is correct.

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Note the correct and the complete question is

What is the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33?

A.) $276.61

B.) $326.25

C.) $358.00

D.) $368.91

The reasonable fraction for the part of the pan of brownies Kayla gave away is 1/2.

Kayla gave 1/3 of a pan of brownies to Ella and 1/6 of the pan to Eli.

Therefore, the part given away will be the addition of the fractions. This will be:

= 1/3 + 1/6

= 2/6 + 1/6

= 3/6

= 1/2

Therefore, 1/2 of the brownies were given away.

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Using the Law of Sines and Cosines, we get all possible values of ∠H are approximately 60.6° and 69.0°.

We can use the Law of Cosines to find the length of side GH

GH² = g² + h² - 2gh cos(G)

GH² = (9.3)² + (9.6)² - 2(9.3)(9.6)cos(109°)

GH ≈ 3.585 cm

Next, we can use the Law of Sines to find the measure of angle H

sin(H)/GH = sin(G)/HI

sin(H)/3.585 = sin(109°)/HI

sin(H) ≈ 3.585(sin 109°)/HI

H ≈ arcsin[3.585(sin 109°)/HI]

Since we do not know the length of side HI, we cannot determine the exact value of angle H. However, we can find the possible range of angle H by assuming that HI is the longest side of the triangle (making angle H the smallest) and the shortest side of the triangle (making angle H the largest).

If HI is the longest side, then H ≈ arcsin[3.585(sin 109°)/9.3] ≈ 60.6°

If HI is the shortest side, then H ≈ arcsin[3.585(sin 109°)/9.6] ≈ 69.0°

Therefore, the possible values of angle H are between approximately 60.6° and 69.0°.

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Answer:

21 is: \(\frac{4}{9}\) x + \(\frac{31}{72}\)

22 is: 4 \(\frac{39}{44}\)

23 is:\(\frac{1}{4}\) x + \(\frac{31}{72}\)

24 is:  \(\frac{-2}{11}\) x + \(\frac{7}{11}\)

Step-by-step explanation: Hope this helps and good luck mark brainliest if u want :)

The second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve.

To find the leftmost point on the curve defined by the parametric equations x = t² + 2t and y = t² - 2t + 3, we need to find the value of t that corresponds to this point. We can do this by analyzing the derivative of the curve with respect to t.

The leftmost point on the curve corresponds to the point where the slope of the curve is zero or undefined. This occurs when the derivative of y with respect to x is zero or undefined.

We can express y as a function of x by eliminating t from the given parametric equations. Solving for t in terms of x, we get:

t = -1 ± √(x + 1)

Substituting this value of t in the equation for y, we get:

y = (x + 1) ± 4√(x + 1) + 3

y = ±4√(x + 1) + x + 4

To find the leftmost point on the curve, we need to find the value of x that corresponds to this point. We can do this by finding the minimum value of x for which y is defined.

Differentiating y with respect to x, we get:

dy/dx = 1 + 2/√(x + 1)

Setting dy/dx = 0, we get:

1 + 2/√(x + 1) = 0

2/√(x + 1) = -1

Solving for x, we get:

x = 3

Note that this value of x is within the given range of -2 ≤ t ≤ 3. Therefore, the leftmost point on the curve is the point corresponding to t = 1.

To justify that we have found the requested point, we can analyze the second derivative of y with respect to x. The second derivative will tell us whether the point corresponds to a local minimum, local maximum, or inflection point.

Differentiating dy/dx with respect to x, we get:

d²y/dx² = -2/\((x + 1)^{(3/2)}\)

Substituting x = 3, we get:

d²y/dx² = -2/64

Since the second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve. Therefore, we have found the leftmost point on the curve as requested.

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The question is -

Identify the requested point and justify that you have found the requested point by analyzing an appropriate derivative. x = t² + 2t, y = t² - 2t + 3, - 2 ≤ t ≤ 3 Leftmost point

A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.

In light of the conditions stated, come up with: \($\frac{8 \frac{3}{4}}{2 \frac{1}{7}}$\) To improper fractions, change the mixed numbers to: \($\frac{\frac{35}{4}}{\frac{15}{7}}$\) Multiply the reciprocal of a fraction to get its division: \($\frac{35}{4} \times \frac{7}{15}$\)

Mark this common element as a no-go: Multiplying \($\frac{7}{4} \times \frac{7}{3}$\) Mark the common element as absent: Multiplying \($\frac{7 \times 7}{4 \times 3}$\) . Put the following in one fraction : \($\frac{49}{12}$\) . The product or quotient should be

calculated.Find the biggest number that is greater than \($\frac{49}{12}$\) and less than or equal to it . A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.Otherwise, you or a device will need to count 127 turns (the irreducible repeat, independent of thread pitch), after which the half nut must be closed.

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Let's denote the amount invested in CDs as x. Since EDCC invested $60,000 more in bonds than in CDs, the amount invested in bonds would be x + $60,000.

The remaining amount, $140,000 - (x + (x + $60,000)) = $140,000 - (2x + $60,000) = $80,000 - 2x, is invested in stocks.

Now, let's calculate the annual income from each investment:

Income from CDs = x * 0.0325 = 0.0325x

Income from bonds = (x + $60,000) * 0.027 = 0.027x + $1,620

Income from stocks = ($80,000 - 2x) * 0.078 = $6,240 - 0.156x

The total annual income is given as $5,930, so we can set up the following equation:

0.0325x + 0.027x + $1,620 + $6,240 - 0.156x = $5,930

Combining like terms and solving for x:

0.0325x + 0.027x - 0.156x = $5,930 - $1,620 - $6,240

-0.0965x = -$1,930

x = -$1,930 / -0.0965

x ≈ $19,987.11

Therefore, approximately $19,987.11 was invested in CDs.

The amount invested in bonds would be x + $60,000 ≈ $19,987.11 + $60,000 ≈ $79,987.11.

The amount invested in stocks would be $80,000 - 2x ≈ $80,000 - 2 * $19,987.11 ≈ $40,025.78.

So, approximately $19,987.11 was invested in CDs, $79,987.11 was invested in bonds, and $40,025.78 was invested in stocks.

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If the median of a set of scores is greater than the mean, then the distribution will be option (c) It is positively skewed.

The relationship between the median and mean of a distribution can give an indication of the shape of the distribution. If the median is lower than the mean, it suggests that the distribution is positively skewed.

Option a) It is leptokurtic refers to the degree of peakedness of the distribution, which is not directly related to the relationship between the median and mean.

Option b) It is platykurtic refers to a distribution that has less peakedness than a normal distribution, which is also not directly related to the relationship between the median and mean.

Option d) It is negatively skewed is the opposite of the correct answer and suggests that the median is higher than the mean, indicating a negatively skewed distribution.

Therefore, the correct option is (c) It is positively skewed.

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The given question is incomplete, the complete question is:

If the median of a set of scores is lower than the mean, what does that suggest about the shape of the distribution?

Group of answer choices

a) It is leptokurtic

b) It is platykurtic

c) It is positively skewed

d) It is negatively skewed

Hence, a cylinder with height h and base area \(\pi r^{2}\) may be proven to have the same volume as a triangular prism.

Two parallel circular bases joined by a curving surface form the three-dimensional geometric object known as a cylinder. Due of its parallel and congruent bases, it is a sort of prism.

When someone uses the word "cylinder,” they often mean a right circular cylinder with circles for bases and an axis that is perpendicular to the bases' planes.

A cylinder's volume may be calculated using the formula V = \(r^{2}\)h, where r denotes the perimeter of the base and h the height of the cylinder. L = 2rh, where r is the radius of a base and h is the height of the cylinder, is the formula for a cylinder's lateral surface area.

Cavalieri's principle states that if two solid objects have the same height and every cross-section taken perpendicular to a common axis has the same area, then the two objects have the same volume.

Let's consider the given triangular prism with base area  \(\pi\)\(r^2\) and height h. If we take a cross-section perpendicular to the base at a height y, we get a circle with radius r multiplied by a triangle with base 2r and height y. The area of this cross-section is:

\(A(y) = \pi r^2 + (2r)(y) / 2\)

Simplifying, we get:

\(A(y) = \pi r^2 + ry\)

Now, let's consider a cylinder with base area pi r² and height h. If we take a cross-section perpendicular to the height at a height y, we get a circle with radius r multiplied by a rectangle with base 2r and height h. The area of this cross-section is:

\(A'(y) = \pi r^ + (2r)(h) = \pi r^2 + 2rh\)

By Cavalieri's principle, the triangular prism and the cylinder have the same volume if A(y) = A'(y) for all y from 0 to h. Let's check:

\(\pi r^² + ry = \pi r^² + 2rh\)

\(ry = 2rh\)

\(y = 2r\)

So, we see that the areas are equal for all y between 0 and h, except at \(y = 2r.\) However, this is just a single point and has no effect on the volume,

Therefore,  the cylinder with base area \(\pi\)\(r²\) and height h has the same volume as the triangular prism, with base area \(\pi\)r² and height h.

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Answer:

1. zero triangles

2. one triangle

3. two triangles

4. zero triangles

5. one triangle

Step-by-step explanation:

Answer:

1. zero triangles

2. one triangle

3. two triangles

4. zero triangles

5. two triangle

Step-by-step explanation:

Answer:

Let's simplify step-by-step.

−x+5−7x−8

=−x+5+−7x+−8

Combine Like Terms:

=−x+5+−7x+−8

=(−x+−7x)+(5+−8)

=−8x+−3

not sure if I'm correct but this is just to simplify

The domain of a function is usually all real numbers. The range of f(x)=2^x would be the y values. This would include all values that would be the output for the y value. An example of this would be if you used 2 as x then the function would read f(x)=2^2.

Using it's concept, it is found that the range of the function f(x) for the domain {0, 1, 2} is given by: {3,5,7}.

In this problem, the range will be given by the output values of the function, hence:

Hence, the range is {3,5,7}.

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Answer:

6π

Step-by-step explanation:

(135/360)×π×4²

(135/360)×π×16

=6π

The equation for the price of house after x years is,

Simplify the equation to obtain the equation for value of house after x years.

So option B is correct.

The accumulated value in 5 years of the  investment compounded quarterly is approximately: $18578.946

Compound interest differs from simple interest in that the interest received in one period will itself accrue in the next period. As a result, the amount in the account increases exponentially.

The future value of a compounding account depends on the number of compounding periods per year. Another factor is the annual interest rate. The higher the APR, the greater the cumulative value over time.

The formula for compound interest is:

FV = P(1 + (r/m))^(mt)

where:

FV is the future value of the investment.

P is the principal or initial amount invested.

r is the annual interest rate.

m is the number of compounding per year.

t is the time in years,

P = $16000

t = 5

m = 4

r = 3% = 0.03

Thus:

FV = 16000(1 + (0.03/4))^(4 * 5)

FV = $18578.946

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Complete Question is:

​$16000 is invested for 5 years with an APR of3 ​% and quarterly compounding.

Write a numerical expression that would compute the value of the investment after 5 years.

Answer:

2x+4y=48

5x+2y=64

x= 10

y=7

(10, 7)

Step-by-step explanation:

5(2x+4y=48)

-2(5x+2y=64)

10x+20y=240

-10x-4y= -128

___________

16y=112

__. ___

16. 16

y=7

2x+4(7)=48

2x+28=48

-28 -28

_________

2x=20

__. __

2. 2

x=10

The ticket price for one adult  is $10 and  for one child it is $7.

Two or more expressions with an Equal sign is called as Equation.

Given,

Let x be the cost of an adult ticket

Let y be the cost of a child ticket.

The price of 2 adult tickets and 4 child tickets is $48

2x+4y=48...(1)

The price of 5 adult tickets and 2 child tickets is $64.

5x+2y=64...(2)

Multiply equation 2 with 2.

10x+4y=128..(3)

Now subtract equation 3 from equation 1.

2x+4y-10x-4y=48-128

-8x=-80

Divide both sides by 8

x=10

Now plug in x value in equation 1.

2x+4y=48.

2(10)+4y=48

20+4y=48

4y=48-20

4y=28

Divide both sides by 4

y=7

Hence, the ticket price for one adult  is $10 and  for one child it is $7.

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