In ΔFCE, the ratio of ∠F to ∠C is 2:5. The measure of ∠E is one hundred ten degrees more than the sum of the measures of ∠F and ∠C. What is the measure of each angle in ΔFCE?

x int = 15

y int = -10

y intercept can be found bt setting X to 0

x intercept can be found by setting Y to 0

2(0) - 3y = 30 --> -3y = 30 --> y = -10

2x - 3(0) = 30 --> 2x = 30 --> x = 15

alternatively, y int is "b" in eq. y = mx + b

-3y = 30 -2×

y = -10 + (2/3)x

y = (2/3)x - 10

b = -10

Hi! The answer would be 445.272727273

Glad I can help :)

Answer:

[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]

Step-by-step explanation:

Given polynomial function:

[tex]f(x) = 6x^3-x^2-9x+4[/tex]

If (2x - 1) is a factor of the given function, then 2x - 1 = 0.

Therefore:

[tex]\implies 2x-1=0[/tex]

[tex]\implies x=\dfrac{1}{2}[/tex]

To divide the given function by the factor (2x - 1), we can perform synthetic division.

As the leading coefficient of the divisor is not 1, divide the dividend and divisor by the leading coefficient of the divisor (2):

[tex]\textsf{Dividend}: \quad 3x^3-\dfrac{1}{2}x^2-\dfrac{9}{2}x+2[/tex]

[tex]\textsf{Divisor}: \quad \left(x-\dfrac{1}{2}\right)[/tex]

Perform Synthetic Division

Place ¹/₂ in the division box.

Write the coefficients of the dividend in descending order.

(Note: As no terms are missing, we do not need to use any zeros to fill in missing terms).

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\end{array}[/tex]

Bring the leading coefficient straight down:

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}&\downarrow&&&\\\cline{2-5}&3\end{array}[/tex]

Multiply the number you brought down with the number in the division box and put the result in the next column (under the -¹/₂ ):

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&\frac{3}{2}&&\\\cline{2-5}&3\end{array}[/tex]

Add the two numbers together and put the result in the bottom row:

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&&\\\cline{2-5}&3&1\end{array}[/tex]

Repeat:

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&\\\cline{2-5}&3&1&-4\end{array}[/tex]

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&-2\\\cline{2-5}&3&1&-4&0\end{array}[/tex]

The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend.

The last number in the bottom row is the remainder.

Therefore, the factored function after synthetic division is:

[tex]f(x)=(2x-1)(3x^2+x-4)[/tex]

The quadratic factor can be factored further:

[tex]\implies 3x^2+4x-3x-4[/tex]

[tex]\implies x(3x+4)-1(3x+4)[/tex]

[tex]\implies (x-1)(3x+4)[/tex]

Therefore, the fully factored function is:

[tex]f(x)=(2x-1)(x-1)(3x+4)[/tex]

To find the roots of the function, set each factor to zero and solve for x:

[tex]2x-1=0 \implies x=\dfrac{1}{2}[/tex]

[tex]x-1=0 \implies x=1[/tex]

[tex]3x+4=0 \implies x=-\dfrac{4}{3}[/tex]

Therefore, the roots of the given function are:

[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]

Answer:

[tex]x=-3,x=-3,x=7[/tex]

Step-by-step explanation:

[tex]We\ know\ that\ the\ roots\ of\ an\ equation\ are\ its\ intercepts\ cut\ on\ the\ x-axis.\\We\ can\ observe\ that\ the\ graph\ of\ y=f(x)\ cuts\ the\ x\ axis\ at\ the\ point (7,0)\\ and\ touches\ the\ x-axis\ at\ (-3,0).\\[/tex]

[tex]Hence,\\The\ curve\ represents\ a\ cubic\ polynomial\ with\ double\ roots\ (-3,0),(-3,0)\\ as\ well\ as\ a\ distinct\ root:\ (7,0)[/tex]

For answering 5 questions wrong Hunter's score is 75 and for for answering x question wrong his score will be  f(x)=100-5*x.

A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.

Hunter is taking a multiple choice test with a total of 100 points available.

Each question is worth exactly 5 points,

From that the number of questions in the test is ,[tex]\frac{100}{5}=20[/tex]questions

Hunter's test score (out of 100) if he got 5 questions wrong,

20-5=15 questions correct.

Each question carries 5 marks, then 15*5= 75 marks.

Hunter score will be 75 marks.

And again each question carries 5 marks, If hunter answers x questions wrong his score will be f(x)=100-5*x.

It is a linear equation.

Hence, for answering 5 questions wrong Hunter's score is 75 and for for answering x question wrong his score will be f(x)=100-5*x.

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The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

Given that line passes through (0,0) and (2,1)

(Note that any two points are sufficient to determine the equation of the line)

The slope = change in y/change in x

                 = (1-0)/(2-0)

                 = 1/2

Hence answers are:

Variable y varies directly with x. (if x increases y also increases and vice versa)

The constant of variation = slope of line = 1/2

The constant of variation is 2 is wrong since slope = 1/2

The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.

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The surface area of the ramp is 3672 in².

Option A is the correct answer.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The ramp consists of three rectangular surfaces and two triangles.

Now,

Triangle.

Base = 48 in

Height = 14 in

Area of a triangle.

= 1/2 x base x height

= 1/2 x 48 x 14

= 48 x 7

= 336 in²

Rectangle.

Since the back and the bottom rectangle are not included.

Front rectangle.

Length = 50 in

Width = 60 in

Area = 50 x 60

Area = 3000 in²

Now,

The surface area of the ramp.

= 300 + 2 (336)

= 3000 + 672

= 3672 in²

Thus,

The surface area of the ramp is 3672 in².

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The expected value of each grab bag is $1.67 for two pairs of lined gloves, $9.87 for one pair of lined gloves and one pair of knit gloves, and $16.80 for two pairs of knit gloves.  the total profit made from selling all 60 grab bags is $149.40.

For the 2 bags that have two pairs of lined gloves, the total cost is:

2 pairs * $25/pair = $50

Total gloves = 4

For the 16 bags that have one pair of lined gloves and one pair of knit gloves, the total cost is:

1 pair lined gloves * $25/pair + 1 pair knit gloves * $12/pair = $37

Total gloves = 4

For the 42 bags that have two pairs of knit gloves, the total cost is:

2 pairs * $12/pair = $24

Total gloves = 4

The probability of selecting a bag with two pairs of lined gloves is:

2/60 = 1/30

The probability of selecting a bag with one pair of lined gloves and one pair of knit gloves is:

16/60 = 4/15

The probability of selecting a bag with two pairs of knit gloves is:

42/60 = 7/10

The expected value of a bag with two pairs of lined gloves is:

(1/30) * $50 + (0) * $37 + (0) * $24 = $1.67

The expected value of a bag with one pair of lined gloves and one pair of knit gloves is:

(4/15) * $37 + (0) * $50 + (0) * $24 = $9.87

The expected value of a bag with two pairs of knit gloves is:

(7/10) * $24 + (0) * $50 + (0) * $37 = $16.80

The total cost of the gloves used to make the grab bags is:

2 bags * $50/bag + 16 bags * $37/bag + 42 bags * $24/bag = $1,650

The total revenue from selling all 60 grab bags is:

60 bags * $29.99/bag = $1,799.40

Therefore, the total profit is:

$1,799.40 - $1,650 = $149.40

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The value of x is given as follows:

x = 34.

The angle measures are given as follows:

In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.

Angles A and B are consecutive, hence the value of x is obtained as follows:

2x + 10 + 3x = 180

5x = 170

x = 34.

Then the angle measures are given as follows:

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The total weight in the bag is given as follows:

8.2 pounds.

The total weight is obtained applying the proportions in the context of the problem.

From the table, the weight of each equipment is given as follows:

Hence the total weight of a bag with 4 balls, 2 gloves, and 2 bats is given as follows:

4 x 0.35 + 2 x 0.77 + 2 x 2.63 = 8.2 pounds.

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Answer: The ratio $42/81$ can be simplified by dividing both the numerator and denominator by the greatest common factor of 42 and 81, which is 9.

$42/81 = (42 \div 9) / (81 \div 9) = 4/9$

So, the ratio $42/81$ can be expressed as the simplified fraction $\frac{4}{9}$.

Step-by-step explanation:

Answer: c[tex]\leq[/tex]-17/4

Step-by-step explanation:

-8c+13[tex]\geq[/tex]47

-8c[tex]\geq[/tex]47-13

-8c[tex]\geq[/tex]34

c[tex]\leq[/tex] -17/4 or -4 1/4

Since there are 20 professors and each professor is on exactly 3 committees, there must be a total of 60 committee positions.

Let's assume that it is not possible to select a distinct representative from each committee. This means that there must be some committee that does not have a distinct representative.

Let's consider the professors on this committee. Since each professor is on exactly 3 committees, each of the professors on this committee must also be on 2 other committees.

Let's consider the 2 other committees for each of the professors on this committee. Since there are 6 professors on the committee, there are a total of 12 other committees to consider.

Each of these 12 committees must have a representative chosen from the remaining 14 professors, since we have assumed that it is not possible to select a distinct representative from the original 10 committees.

However, since there are only 14 professors remaining, and each professor can only be on 3 committees, it is not possible to choose a representative from all 12 of these committees without choosing at least one professor to be on 4 committees. This is a contradiction, since we have assumed that each professor is on exactly 3 committees.

Therefore, our assumption that it is not possible to select a distinct representative from each committee must be false, and it is indeed possible to do so.

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The average rate of change over the interval (-2,0) is -2.

The average rate of change describes how quickly one quantity changes in comparison to another. It indicates how much the function changed per unit during the specified interval.

Given that the interval is (-2,0). The coordinate of the point from the interval -2,0 is ( -2 , 4 ).

The average rate of change will be calculated as:-

Rate of change = ΔY / ΔX

Rate of change = ( 4 - 0 ) ( -2 - 0 )

Rate of change = -2

Therefore, the average rate of change will be -2.

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(a) The diver hit the water after 2.5 seconds

(b) The diver hit the water with a velocity of 80 ft/s

Since the cliff diver plunges from a height of 100 ft above the water surface and the distance the diver falls in seconds is given by the function d(t) = 16t². We can say d(t) = 100ft. So we have:

d(t) = 16t² = 100

t² = 100/16

t² = √(100/16)

t = 10/4

t = 2.5 seconds

The derivative of the distance will give us the velocity. That is:

v(t) = d'(t) = 32t

Substitute t =2.5  into v(t):

v(2.5) = 32(2.5)

v(2.5) = 80 ft/s

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The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.

The probability of all three of the selected homes having a security system is 0.3277, which can be calculated using the formula P(A and B and C) = P(A) x P(B) x P(C). In this case, P(A) is the probability of the first home having a security system, which is 8/11 (since 8 out of 11 homes have a security system). P(B) is the probability of the second home having a security system, which is 7/10 (since 7 out of 10 remaining homes have a security system). P(C) is the probability of the third home having a security system, which is 6/9 (since 6 out of 9 remaining homes have a security system). Therefore, P(A and B and C) = (8/11) x (7/10) x (6/9) = 0.3277.

The probability of none of the three selected homes having a security system is 0.0414, which can be calculated using the formula P(A and B and C) = P(A') x P(B') x P(C'). In this case, P(A') is the probability of the first home not having a security system, which is 3/11 (since 3 out of 11 homes do not have a security system). P(B') is the probability of the second home not having a security system, which is 3/10 (since 3 out of 10 remaining homes do not have a security system). P(C') is the probability of the third home not having a security system, which is 3/9 (since 3 out of 9 remaining homes do not have a security system). Therefore, P(A and B and C) = [tex](3/11) x (3/10) x (3/9) = 0.0414[/tex].

The probability of at least one of the selected homes having a security system is 0.9709, which can be calculated using the formula P(A or B or C) = 1 - P(A' and B' and C'). In this case, P(A' and B' and C') is the probability of none of the three selected homes having a security system, which is 0.0414 (as calculated above). Therefore, P(A or B or C) = 1 - 0.0414 = 0.9709.

The events are dependent because each selection is affected by the previous selections. For example, the probability of the second home having a security system is affected by whether or not the first home had a security system. If the first home had a security system, then there are 7 out of 10 remaining homes with a security system; if the first home did not have a security system, then there are 8 out of 10 remaining homes with a security system.

The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.

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The Average Minute to Clean up a Car is 0.7794.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The equation of the graph is y=0.7794x-1435.5.

When we compare the equation with the standard form of equation y=mx+b.

The m will be 0.7794 which means slope is 0.7794.

Hence,  0.7794 is the Average Minute to Clean up a Car.

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The system of equations has one solution, which is (2, 3).

To find the solution to a graphed system of equations, you need to find the points where the graphs of the two equations intersect. These points represent the coordinates of the solution, which are the values of x and y that make both equations true simultaneously.

The system of equations as shown in the graph has one solution, which is: (2, 3). This is because the liens intersect at the point (2, 3).

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The interest rate that can explain how $4081 grew to $8404.54 in 21 years with annual compounding is option (a) 3.5%, rounded to the nearest tenth.

The interest rate and the compounding frequency determine the growth of the initial amount over time. In this problem, we need to find the interest rate that can explain how an initial amount grew to a specific amount over a certain number of years.

The problem asks us to find the interest rate that can explain how an initial amount of $4081 grew to $8404.54 in 21 years with annual compounding. We can use the formula for compound interest to solve this problem:

[tex]A = P(1 + r/n)^{nt}[/tex]

where A is the future value of the investment, P is the initial amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we know that P = $4081, A = $8404.54, n = 1 (annual compounding), and t = 21. We need to find the value of r that makes the equation true.

We can rearrange the formula to solve for r:

[tex]r = n[(A/P)^{1/nt} - 1][/tex]

Substituting the known values, we get:

[tex]r = 1[(8404.54/4081)^{1/(1*21)} - 1][/tex]

r = 0.0353 or 3.53%

This means that if the initial amount was invested with an annual interest rate of 3.5%, it would have grown to the given future value after 21 years.

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The value of the range is 33

From the question, we have the following parameters that can be used in our computation:

61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94

To find the range of a set of numbers, we need to subtract the smallest number from the largest number.

In this set of numbers:

The smallest number is 61 and the largest number is 94.

Therefore, the range of this set of numbers is:

94 - 61 = 33

Hence, the range of the given set of numbers is 33.

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Answer:

35 + 83) − (72 − 63) = 109

Step-by-step explanation:

To subtract the polynomials (35 + 83) − (72 − 63), we'll simplify each term in the polynomials first and then subtract the corresponding terms:

(35 + 83) = 118

(72 - 63) = 9

Now we can subtract the corresponding terms:

118 - 9 = 109

So the result of (35 + 83) − (72 − 63) is 109.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer:

Okay first do what is in the parenthesis:

35 + 83 = 118

72 - 63 = 9

Now subtract:

118 - 9 = 109

The answer is: 109

Step-by-step explanation:

Hope it helps!

Answer:

it could be D but D gives us 661.63 C gives us 613.07 B gives us 892.165 and A gives us 883.98 so your closes answer is D

Step-by-step explanation:

8.42x109=917.78-253.8=663.98

Answer:

first 2 pairs

Step-by-step explanation:

[tex]\frac{6}{100}[/tex] = 6 ÷ 100 = 0.06 ← equivalent

[tex]\frac{7}{10}[/tex] = 7 ÷ 10 = 0.7 ← equivalent

[tex]\frac{5}{10}[/tex] = 5 ÷ 10 = 0.5 ≠ 0.05

[tex]\frac{32}{100}[/tex] = 32 ÷ 100 = 0.32 ≠ 3.2

Option A. No, this is not possible. Since A and B are not mutually exclusive events, we have P(A ∩ B) = P(A) + P(B) - P(A ∪ B), where P(A ∪ B) is the probability that the selected student has either a Visa or a MasterCard.

Since 0.5 > 1 - P(A ∪ B) = P(A') ∩ P(B'), we must have P(A') ∩ P(B') < 0, which is impossible.

B. The probability that the selected student has at least one of these two types of cards is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.7 + 0.4 - 0.3 = 0.8.

C. The probability that the selected student has neither type of card is given by P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.8 = 0.2.

D. The probability of the event A ∩ B' is given by P(A ∩ B') = P(A) - P(A ∩ B) = 0.7 - 0.3 = 0.4.

E. The probability that the selected student has exactly one of the two types of cards is given by P((A ∩ B') ∪ (A' ∩ B)) = P(A ∩ B') + P(A' ∩ B) = 0.4 + 0.1 = 0.5.

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The inequality changes if both sides of the expressions are switched or multiplied by a negative sign

Inequalities are expressions not separated by an equal sign.

From the given inequalities

For -10.5 < 3e

3e > -10.5

e > -10.5/3

This shows that the sign changes

For b/6≤ 7

b ≤ 6(7)

b≤ 42

The inequality sign does not change.

For the inequality -4.5c > 9

4.5c < -9
c < -9/4.5

c < -2

The inequality sign changes.

For the inequality -21/5 ≤  -5/2 d

21/5 ≥ 5/2d

5/2d≤ 21/5

d ≤42/25

The inequality sign does not change

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The total amount spend is 391.88

The noun discount refers to an amount or percentage deducted from the normal selling price of something.

If 14 bag of mix cement are bought and and every third bag is discounted

no of bag on discount = 14/3 = 4 remainder 2

therefore 4 bags will be on discount

discount on a bag = 3.88× 75/100

= 291/100 = 2.91

therefore each bag on discount will cost = 3.88 - 2.91

= 0.97

for 4 bags = 0.97 ×4 = 3.88

for remaining 10 bags = 3.88 × 10

= 388

therefore the total amount = 388+3.88

= $391.88

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Answer:-17

Step-by-step explanation:

b=7,then

b^2=49

square root of 49-4*3*2=-17

The measure of the angle B is found to be 184 degrees.

The angles given in question:

line AB || DC

∠B = 9x + 2

∠C = 5x - 4

So,

∠B + ∠C = 180 ( co interior angles )

9x + 2 + 5x - 4 = 180

9x  - 2 = 180

9x = 180 + 2

x = 182/9

Then,

∠B = 9x + 2

∠B = 9*182/9 + 2

∠B = 182 + 2

∠B = 184

Thus, the measure of the angle B is found to be 184 degrees.

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The diagram of the correct question is attached.