100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

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Answer:

b

Step-by-step explanation:

I think it is B because x+x is two x's so it would be 2x. I hope this helped have a good day

Answer:

98 + 99 + 100 = 297

Step-by-step explanation:

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Answer:  -2.7h−1.3j+2

Step-by-step explanation:

you just do 6-4 since those are like terms

Answer: 2.556

Step-by-step explanation:

23/9 = 2.5555555555 (endless 5)

round to nearest thousandths... three places from the decimal point.

2.5555... round up since 5 is the number next to the thousandth place.

To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.

Distance = 1/4 mile

Time = 1/12 hour

Unit rate = Distance ÷ Time

Unit rate = (1/4 mile) ÷ (1/12 hour)

We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.

Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)

Unit rate = (3/4 mile) ÷ 1 hour

Unit rate = 3/4 mile per hour

Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.

Answer:

3mph

Step-by-step explanation:

1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.

60/12 = 5

12 x 1/4 = 12/4 = 3

x = 11.9

the trigonometry ratio to use is cos

The triangle is a right angled triangle. So we would apply the trigonometry ratio SOHCAHTOA

The given angle is 32 degrees

opposite = the side opposite the angle 32 degrees

adjacent = base = x

hypotenuse = 14

Since we have been given the value of hypotenuse and we want to find the adjacent, we would apply cosine ratio (CAH)

Cos 32° = adjacent/hypotenuse

cos 32° = x/14

14(cos 32°) = x

x = 14(0.8480)

x = 11.872

To the nearest tenth, x = 11.9

Hence, the trigonometry ratio to use is cos

For circumference use C = 2πr because π is the ratio of Circumference to diameter and diameter is 2 x radius.

C = 2 x 3.142 x 9.5 cm ≈ 59.7 cm

Area of a circle is π x r² = 3.142 x (9.5 cm)² ≈ 283.6 cm²

The circumference of a circle with a radius of 9.5 centimeters is about 59.7 centimeters and the area of a circle with radius of 9,5 centimeters is about 283.6 centimeters.

Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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Correct option is False as the margin of error, E, is not related to how accurate x is as an estimate for u.

Margin of error (MOE) is a statistical term that represents the range of values that is likely to contain the true population parameter with a certain level of confidence. It is commonly used in opinion polls, surveys, and other forms of research where a sample is used to estimate a population parameter.

The margin of error, E, is not related to how accurate x is as an estimate for u. The margin of error represents the range of values that is likely to contain the true population parameter with a certain level of confidence. It is calculated based on the sample size, standard deviation, and level of confidence, and is used to construct a confidence interval for the population parameter.

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The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

790

Step-by-step explanation:

7098uuilu4645

The important difference between experimental probability and theoretical probability is that experimental probability is related to actual results of an experiment whereas theoretical probability is related to possible outcomes based on assumptions. Also In an experimental probability an experiment is performed to gather information whereas in theoretical probability does not happen.

Answer:

5,340x.095=507.3

507.3÷5=101.46

101.46÷12=$8.45 interest

5,340÷5=1068

1068÷12= $89

89+8.45=$97.45

answer $97.45 a month

The equation of pressure is given by:

\(p = \frac{f}{s} \)

where p is the pressure.

f is the applied force.

s is the surface area to which the force is applied.

I will start off by calculating the surface area of the table top given by:

\(s = l \times w = 1.8 \times 1.2 = 2.16\)

s=2.16 m²

We know that f=400 N, that is given.

\(p = \frac{400 \: n}{2.16 \: m {}^{2} } \)

Plug this on your calculator (excluding the units lol)

\(p = 185.185 \frac{n}{m {}^{2} } \)

\(p = 185 \frac{n}{m {}^{2} } \)

Answer:

C)  1 / 462

Step-by-step explanation:

22 x 21 = 462

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

41.93 degrees

Step-by-step explanation:

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

\(x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}\)

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

\(x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72\)

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Given statement solution is :- The y-intercept is (0, -3).

The term "intercept" refers to the location where a line or curve crosses a graph's axis.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

To find the x-intercept, we set y = 0 and solve for x.

0 = (1/4)x - 3

Add 3 to both sides:

3 = (1/4)x

Multiply both sides by 4 to isolate x:

12 = x

So the x-intercept is (12, 0).

We set x = 0 and then solve for y to determine the y-intercept.

y = (1/4)(0) - 3

y = -3

So the y-intercept is (0, -3).

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Answer:

answr 5

Step-by-step explanation:

answer 5

114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120

The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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Answer:

I'm pretty sure the answer is 21/20 or 1.05