Solve the system of equations using elimination.
5x + 3y = 8
4x + y = 12
O (1, 1)
O (2.4)
O (3,0)
O (4,-4)

The measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

The measure of the numbered angles is calculated by applying the following formula as follows;

Rhombus has equal sides and equal angles.

angle 2 = angle 57⁰ (alternate angles are equal)

angle 1 = 90⁰ (diagonals of rhombus intersects each other at 90⁰)

angle 3 = angle 4 (base angles of Isosceles triangle )

angle 3 = angle 4 = ¹/₂ x 90⁰

angle 3 = angle 4 = 45⁰

Thus, the measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

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Answer:

The domain of this function is all real numbers.

The number line inequality that represents x > -7 is: Option D

In number line inequalities we know that:

A closed circle indicates "greater than or equal to" or "less than or equal to" .

Meanwhile an open circle indicates "greater than" or "less than".

A closed circle pointing to the right indicates  "greater than or equal to" while a closed circle pointing to the left indicates "less than or equal to,"

Similarly:

An open circle pointing to the right indicates "greater than" while An open circle pointing to the left indicates  "less than".

Thus , the correct number line that shows x > -7 is: Option D

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(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Answer:

40, 50, 30 Yes

13, 5, 12 Yes

10, 10, 15 Yes

41, 9, 40 Yes

Step-by-step explanation:

16, 10, 6

10 + 6 = 16

No

40, 50, 30

30 + 40 > 50

Yes

13, 5, 12

5 + 12 > 13

Yes

70, 20, 25

20 + 25 < 70

No

10, 10, 15

10 + 10 >15

Yes

41, 9, 40

9 + 40 > 41

Yes

Answer:

the effective tax rate for a taxable income of $175,000 is approximately 21.02%.

Step-by-step explanation:

Let's break down the income into the corresponding tax brackets:

The first $10,275 is taxed at a rate of 10%.

Tax on this portion: $10,275 * 0.10 = $1,027.50

The income between $10,276 and $41,175 is taxed at a rate of 12%.

Tax on this portion: ($41,175 - $10,276) * 0.12 = $3,710.88

The income between $41,176 and $89,075 is taxed at a rate of 22%.

Tax on this portion: ($89,075 - $41,176) * 0.22 = $10,656.98

The income between $89,076 and $170,050 is taxed at a rate of 24%.

Tax on this portion: ($170,050 - $89,076) * 0.24 = $19,862.88

The income between $170,051 and $175,000 is taxed at a rate of 32%.

Tax on this portion: ($175,000 - $170,051) * 0.32 = $1,577.44

Now, sum up all the taxes paid:

$1,027.50 + $3,710.88 + $10,656.98 + $19,862.88 + $1,577.44 = $36,836.68

The effective tax rate is calculated by dividing the total tax paid by the taxable income:

Effective tax rate = Total tax paid / Taxable income

Effective tax rate = $36,836.68 / $175,000 = 0.21024 (rounded to the nearest hundredth)

Answer:

all real numbers

Step-by-step explanation:

Try a negative number, a positive number and zero for x.

All of them work.

Answer: all real numbers

A function can't have more than one value for an argument. Therefore, it's either (1,1) or (1,3), but since there's not (1,3) among the possible answers, it must be (1,1).

x < 4.1, as it represents the solution set for the given inequality. A.

The solution set of the inequality x < 4.1 can be determined by examining the given answer choices:

OA. x < 4.1:

This choice represents all values of x that are strictly less than 4.1.

It is a valid solution set for the given inequality.

OB. x < -4.1:

This choice represents all values of x that are strictly less than -4.1.

It is not a valid solution set for the given inequality.

OC. x > 4.1:

This choice represents all values of x that are strictly greater than 4.1.

It is not a valid solution set for the given inequality.

OD. x ≤ 4.1:

This choice represents all values of x that are less than or equal to 4.1.

It is not a valid solution set for the given inequality because the inequality is strict (x < 4.1), not inclusive.

OE. -4.1 < x < 4.1:

This choice represents all values of x that are strictly between -4.1 and 4.1.

It is not a valid solution set for the given inequality because it does not include the possibility of x being less than -4.1 or greater than 4.1.

OF. x < -4.1 or x > 4.1:

This choice represents two separate solution sets: one for x < -4.1 and another for x > 4.1.

It is not a valid solution set for the given inequality because it combines two separate possibilities.

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Answer:

I wish you good luck in finding your answer

Answer: 115

Step-by-step explanation:

Answer: 74

Step-by-step explanation:

The volume of the pyramid can be found using the formula:

Volume = (1/3) x Base Area x Height

To find the base area, we need to find the area of the triangular base. The area of a triangle can be found using the formula:

Area = (1/2) x Base x Height

Substituting the given values, we have:

Area = (1/2) x 8 x 6 = 24 square inches

To find the height of the pyramid, we can use the Pythagorean theorem. The slant height and one-half of the base form a right triangle, so we have:

Height^2 = (Slant Height)^2 - (1/2 x Base)^2

Height^2 = 10^2 - 4^2

Height^2 = 84

Height = √84 ≈ 9.165 inches

Now we can substitute the values into the formula for the volume:

Volume = (1/3) x Base Area x Height

Volume = (1/3) x 24 x 9.165

Volume ≈ 73.96 cubic inches

Therefore, the volume of the pyramid is approximately 73.96 cubic inches.Step-by-step explanation:

Answer:

A

Step-by-step explanation:

3x16

+

4x18
+

5x17

Answer:

incorrect

Step-by-step explanation:

as 7 * 6 = 42 and r is 10

so 6r3 is incorrect

and 7 * 7 = 49 and r is 3

so 7r3 is correct

The regression line is y = -0.1471x + 2.2386.

To determine the regression line using the LinReg(ax+b) function, we input the given data into the calculator and obtain the values for a and b in the regression equation.

Using the LinReg(ax+b) function with the given data, we have:

X: {14.56, 13.58, 12.69, 14.87, 15.68, 14.28}

Y: {0.25, 0.84, 0.71, 0.65, 0.35, 0.61}

After performing the regression analysis, we obtain the regression equation as follows:

y = -0.2012x + 3.4986

Therefore, the regression line is y = -0.2012x + 3.4986.

Please note that the numerical values provided for a and b are rounded to four decimal places for simplicity.

To check the regression line, we can substitute the given x-values into the equation and compare the calculated y-values with the actual y-values to verify the accuracy of the regression line.

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Part 1- The lower class boundary for the first class is 100.

Part 2- Approximately 75% of students take exactly two courses.

Part 1:

To find the lower class boundary for the first class, we need to consider the given class intervals. The lower class boundary is the smallest value within each class interval.

Given the class intervals:

100 - 104

105 - 109

110 - 114

115 - 119

120 - 124

125 - 129

130 - 134

The lower class boundary for the first class interval (100 - 104) would be 100.

So, the lower class boundary for the first class is 100.

Part 2:

To determine the percentage of students who take exactly two courses, we need to calculate the relative frequency for that particular category.

Given the data:

of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2 - 39

3 13 0.25 -

We can see that the cumulative frequency for the second class (2 courses) is 39. To find the relative frequency for this class, we need to divide the frequency by the total number of students surveyed, which is 52.

Relative Frequency = Frequency / Total Number of Students

Relative Frequency for 2 courses = 39 / 52 ≈ 0.75 (rounded to 4 decimal places)

To convert this to a percentage, we multiply the relative frequency by 100.

Percentage of students taking exactly two courses = 0.75 * 100 ≈ 75%

Therefore, approximately 75% of students take exactly two courses.

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Question

Part 1.

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.

Lengths (mm) Frequency

100 - 104 1

105 - 109 16

110 - 114 71

115 - 119 108

120 - 124 83

125 - 129 18

130 - 134 3

What is the lower class boundary for the first class?

class boundary =

Part 2

In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please round your answer to 4 decimal places for the Relative Frequency if possible.

# of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2   39

3 13 0.25

What percent of students take exactly two courses? %

Answer:

(Sumita plans to deposit Rs. 21000 in any bank for 3 years. (a) Define compound interest. (b) How much amount will she get at 10% simple interest when she deposits it in a bank N ? Calculate it. (c) How much amount will she get at 9% interest being compounded annually when she deposits it in another bank M?Calculate it. (d) Which bank is better to deposit the sum and how much more amount will she get (e) from the bet

(a) Compound interest is the interest earned on both the initial principal amount and any accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal amount, compound interest takes into account the interest that has been added to the principal over time.

(b) To calculate the amount Sumita will get at 10% simple interest when she deposits Rs. 21,000 in bank N for 3 years, we can use the formula for simple interest:

Simple Interest = (Principal * Rate * Time) / 100

In this case:

Principal (P) = Rs. 21,000

Rate of interest (R) = 10%

Time (T) = 3 years

Simple Interest = (21,000 * 10 * 3) / 100

Simple Interest = 6,300

Amount = Principal + Simple Interest

Amount = 21,000 + 6,300

Amount = Rs. 27,300

Therefore, Sumita will get Rs. 27,300 at 10% simple interest when she deposits it in bank N.

(c) To calculate the amount Sumita will get at 9% interest compounded annually when she deposits Rs. 21,000 in bank M for 3 years, we can use the formula for compound interest:

Compound Interest = Principal * [(1 + Rate/100) ^ Time] - Principal

In this case:

Principal (P) = Rs. 21,000

Rate of interest (R) = 9%

Time (T) = 3 years

Compound Interest = 21,000 * [(1 + 9/100) ^ 3] - 21,000

Calculating the compound interest:

Compound Interest = 21,000 * (1.09^3) - 21,000

Compound Interest ≈ 21,000 * 1.29503 - 21,000

Compound Interest ≈ 27,139.63 - 21,000

Compound Interest ≈ Rs. 6,139.63

Amount = Principal + Compound Interest

Amount = 21,000 + 6,139.63

Amount ≈ Rs. 27,139.63

Therefore, Sumita will get approximately Rs. 27,139.63 at 9% interest compounded annually when she deposits it in bank M.

(d) To determine which bank is better to deposit the sum, we compare the amounts received in bank N (simple interest) and bank M (compound interest).

In bank N, Sumita will receive Rs. 27,300, while in bank M, she will receive approximately Rs. 27,139.63.

Comparing the amounts, we can see that Sumita will get a slightly higher amount in bank N.

(e) The amount she will get from the better bank (bank N) is Rs. 27,300 - Rs. 27,139.63 = Rs. 160.37 more than bank M.

Step-by-step explanation:

hope it help

The measure of the arc angle KV is 54 degrees.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore, let's find the arc angle KV in the circle as follows:

Hence,

let

arc angle KV = x

128 = 1 / 2 (202 + x)

128 = 101 + 0.5x

128 - 101 = 0.5x

27 = 0.5x

divide both sides by 0.5

x = 27 / 0.5

x = 54 degrees.

Therefore,

arc angle KV = 54 degrees.

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This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).

To find the equation of a line in point-slope form, we need a point on the line and the slope of the line.

Given the points (0, 12) and (-6, 0), we can calculate the slope using the formula:

slope = (y2 - y1) / (x2 - x1)

Using the coordinates (0, 12) as (x1, y1) and (-6, 0) as (x2, y2):

slope = (0 - 12) / (-6 - 0)

slope = -12 / -6

slope = 2

Now that we have the slope, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (0, 12) as (x1, y1) and the slope (m) as 2:

y - 12 = 2(x - 0)

Simplifying the equation:

y - 12 = 2x

This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).

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Answer:

m = -3

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

The equation is  y = -3x + 2

m = -3

So, the slope of the line is -3

Answer:

The slope is -3

Step-by-step explanation:

You were given the easiest form of linear equation, the slope-intercept form, because these are the ones that directly tell you the slope and       the y-intercept.

y=mx+b, Where m is the slope and b is the y-intercept.

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

the first 2

Step-by-step explanation:

let me know if it is wrong

Answer:

[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]

Step-by-step explanation:

To write the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8), we first need to determine the orientation of the hyperbola.

As the y-values of the foci are the same, the foci are located horizontally from the center of the hyperbola, and therefore the hyperbola is horizontal (opening left and right).

The standard equation for a horizontal hyperbola is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]

where:

The center of a hyperbola is the midpoint of the vertices.

Given that the vertices are (-1, -8) and (-11, -8), we can use the midpoint formula to find the coordinates of the center:

[tex](h,k)=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)[/tex]

[tex](h, k)=\left(\dfrac{-1-11}{2},\dfrac{-8-8}{2}\right)[/tex]

[tex](h, k)=\left(-6,-8\right)[/tex]

The value of "a" is the distance between the center of the hyperbola and each vertex.  To find the value of a, calculate the distance between the x-coordinates:

[tex]a=-1-(-6)=5[/tex]

[tex]a=-6-(-11)=5[/tex]

The value of "c" is the distance between the center of the hyperbola and each focus.  Given that the foci are (7, -8) and (-19, -8), and the center is (-6, -8), to find the value of c, calculate the distance between the x-coordinates:

[tex]c = 7-(-6)=13[/tex]

[tex]c = -6-(-19)=13[/tex]

Now we have determined the values of a and c, we can use c² = a² + b² to find the value of b:

[tex]c^2 = a^2 + b^2[/tex]

[tex]13^2 = 5^2 + b^2[/tex]

[tex]169 = 25 + b^2[/tex]

[tex]b^2=144[/tex]

[tex]b=12[/tex]

Finally, substitute the found values of a, b, h and k into the standard equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]

[tex]\dfrac{(x-(-6))^2}{5^2}-\dfrac{(y-(-8))^2}{12^2}=1[/tex]

[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]

Therefore, the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8) is:

[tex]\boxed{\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1}[/tex]

Answer:

2921

Step-by-step explanation:

[tex]2540 + 2540 * \frac{15}{100} \\\\= 2540 + 381\\\\= 2921[/tex]

Answer: 8/9

Step-by-step explanation:

64/72            Divide both the top and bottom by 8

8/9

Answer:

Step-by-step explanation:

To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.

First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.

Next, we use the z-score formula to find the corresponding value in the original distribution:

z = (x - μ) / σ

Solving for x (the maximum width of the aircraft seat):

x = z * σ + μ

Substituting the values given:

x = 2.05 * 4.36 + 37.6

x ≈ 45.98

Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).

Answer:

Step-by-step explanation:

[tex]\angle x=\angle y=\angle z=90\deg\ \text{(angle in a semi-circle is a right angle)}[/tex]

All 3 angles are examples of the theorem which states that any angle coming off the diameter of a circle going to the edge of the circle will form a right angle.

The pairs of angles that are vertical angles in the figure are R and T.

In the figure provided, vertical angles are formed by the intersection of two lines. Vertical angles are always congruent (equal in measure) to each other.

Looking at the given options:

R and T are vertical angles because they are formed by the intersection of lines.

P and D are not vertical angles. They are adjacent angles formed by the intersection of lines, but they are not directly opposite each other.

Therefore, the pairs of angles that are vertical angles in the figure are:

R and T

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Answer:

  (c)  y = 2b/(2a -c)x -2bc/(2a -c)

Step-by-step explanation:

Given the equation of line BD in point-slope form you want the simplified equation.

  y -0 = (2b/(2a -c))(x -c)

The equation is simplified by using the distributive property to eliminate parentheses.

  [tex]y-0=\dfrac{2b}{2a-c}(x -c)\\\\\\y=\dfrac{2b}{2a-c}x-\dfrac{2b}{2a-c}c\\\\\\\boxed{y=\dfrac{2b}{2a-c}x-\dfrac{2bc}{2a-c}}\qquad\text{matches choice C}[/tex]

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