Tom buys a UNC jersey with a 20% discount coupon.
Which response accurately calculates his new cost C
with respect to the original costs x?
a. C=x-0.20
B. C = 0.80x
C. C = 1.20x
d. C = x-0.80

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{4}\\ o=\stackrel{opposite}{5.4} \end{cases} \\\\\\ x=\sqrt{ 4^2 + 5.4^2}\implies x=\sqrt{ 16 + 29.16 } \implies x=\sqrt{ 45.16 }\implies x\approx 6.7[/tex]

Answer:

$120

Step-by-step explanation:

Job1:

       To find the tax, multiply the payment per week ($70) by 0.1.

         Tax = payment * tax rate

                = 70 * 10%

                [tex]\sf = 70 * \dfrac{10}{100}\\\\ = \$7[/tex]

Now, to find his earning after deduction of tax, subtract 7 from 70.

Amount after deduction of tax = 70 - 7

                                                  = $ 63

Job2:

       Tax = 60 * 5%

              = 60 * 0.05

               = $3

  Amount after deduction = 60 - 3

                                           = $ 57

Total amount Byron takes home = 63 + 57

                                                      = $120

The volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

To find the volume of the solid obtained by rotating the region enclosed by the given graphs about the y-axis, we can use the method of cylindrical shells.

First, let's sketch the region to visualize it better.

The region is enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0.

Let's find the intersection points of these curves by setting them equal to each other:

18 - x = 3x - 6

Simplifying the equation, we have:

4x = 24

x = 6

So, the intersection point is (6, 12).

Now, we can integrate to find the volume of the solid.

The radius of each cylindrical shell is the distance from the y-axis to the curve y = 18 - x.

This can be expressed as x.

The height of each cylindrical shell is the difference between the two curves, which is (18 - x) - (3x - 6).

The volume of each cylindrical shell is given by the formula:

V = 2πrhΔx, where r is the radius, h is the height, and Δx is the width of each shell.

Integrating from x = 0 to x = 6, we can find the total volume:

V = ∫[0,6] 2πx[(18 - x) - (3x - 6)] dx

V = ∫[0,6] 2πx(24 - 4x) dx

V = 2π ∫[0,6] (24x - 4x²) dx

V = 2π [12x² - (4/3)x³] | [0,6]

V = 2π [(12(6)² - (4/3)(6)³) - (12(0)^2 - (4/3)(0)^3)]

V = 2π [(12(36) - (4/3)(216)) - (0 - 0)]

V = 2π [(432 - 288) - (0 - 0)]

V = 2π (432 - 288)

V = 2π (144)

V = 288π

Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

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Answer:

15 °C

Step-by-step explanation:

°C = (°F - 32) * (5/9)

Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.

Initial temperature: 77 °F

Converting to Celsius:

°C = (77 - 32) * (5/9)

°C ≈ 25

The temperature dropped by 10 °C, so the final temperature is:

Final temperature = Initial temperature - Temperature drop

Final temperature ≈ 25 - 10 = 15 °C

Therefore, the temperature after the storm was approximately 15 °C.

The perimeter of the trapezoid is 106 meters.

The area of the trapezoid is 1360 square meters.

To calculate the perimeter and area of an isosceles trapezoid, we need to use the given measurements:

The length of the minor base (34 m), the height (20 m), and the length of the oblique side (29 m).

First, let's calculate the length of the major base (the other parallel side). In an isosceles trapezoid, the major base and minor base have the same length.

So, the length of the major base is also 34 m.

The perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter can be calculated as follows:

Perimeter = length of minor base + length of major base + 2 × length of oblique side

Perimeter = 34 m + 34 m + 2 × 29 m

Perimeter = 34 m + 34 m + 58 m

Perimeter = 106 m

To calculate the area of the trapezoid, we can use the formula:

Area = (sum of the lengths of the bases) × height / 2

Area = (34 m + 34 m) × 20 m / 2

Area = 68 m × 20 m / 2

Area = 1360 m²

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By translation, the images of the vertices Q and S are Q'(x, y) = (- 1, 4) and S'(x, y) = (- 3, 2).

In this problem we find the representation of a parallelogram, which is formed by four vertices. The images of the vertices can be found by means of translation, whose formula is introduced below:

C'(x, y) = C(x, y) + T(x, y)

Where:

If we know that Q(x, y) = (4, 1), S(x, y) = (2, - 1) and T(x, y) = (- 5, 3), then the images of the points are:

Q'(x, y) = (4, 1) + (- 5, 3)

Q'(x, y) = (- 1, 4)

S'(x, y) = (2, - 1) + (- 5, 3)

S'(x, y) = (- 3, 2)

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Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed

The nth roots of perfect nth powers evaluates to:

[tex]\sqrt[5]{-32}[/tex] = -2

[tex]-\sqrt[4]{256}[/tex] = -4

Perfect nth Power is an integer which is obtained from multiplying a single integer by itself n times.

The nth root of a Perfect nth Power is an integer which when multiplied by itself n times it will produce the original value under the radical.

To find the nth roots of perfect nth powers with signs, you can use the following steps:

1. Write the perfect nth power as a product of nth roots.

2. Find the nth root of each factor.

3. Combine the nth roots to get the final answer.

[tex]\sqrt[5]{-32}[/tex] = [tex]\sqrt[5]{-2^{5} }[/tex]

         = -2

-[tex]\sqrt[4]{256}[/tex] = -[tex]\sqrt[4]{4^{4} }[/tex]

           = -4

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x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

[tex]\theta = 60; \theta \approx 83; \theta \approx 277; \theta = 300[/tex]

Note that the approximate value you should calculate properly with the inverse cosine function of your calculator to the number of digits you want.

Step-by-step explanation:

you already have a cosine. You might as well change that sine in a cosine too:

[tex]8(1-cos^2\theta) +6cos\theta-9=0\\8cos^2\theta -6cos\theta+1 =0[/tex]

(note that in the second line I also switched every sign by multiplying by -1 just to have a positive lead coefficient - just a pet peeve of mine. Now replace [tex]x=cos\theta[/tex] and let's solve

[tex]8x^2-6x+1=0\\\frac\Delta4 = 9-8 = 1\\x=\frac {3\pm1}8[/tex]

At this point we're back to the replacement. We have two options

[tex]cos\theta = \frac48 = \frac 12 \implies \theta = 60\°; \theta = 300\°\\cos\theta =\frac 18 \implies \theta \approx 83\°; \theta \approx 277\°[/tex]

Answer:

x = 8

Step-by-step explanation:

Intersecting tangent and secant theorem:

If a tangent and a secant are drawn to the circle from a point from outside, the square of the measure of the tangent is equal to the product of the measures of the secant segment and its external secant segment.

         x² = (4+12)*4

         x² = 16 * 4

         x² = 64

        x = √64

         x = 8

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).

Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).

Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:

1. (f x g)(x):

We start by substituting g(x) into f(x) wherever we see an x in f(x):

(f x g)(x) = f(g(x)) = f(1/x)

Substitute 1/x into f(x):

(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)

2. (g x f)(x):

We start by substituting f(x) into g(x) wherever we see an x in g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2))

Substitute √(x + 2) into g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))

Therefore, we have:

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

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The volume of the container is 180 cubic meters.

Given,

Length of the container = 4 meters

Width of the container = 3 meters

Height of the container = 15 meters

Let the container is a cuboid, as the shape of the container isn't mentioned.

Now, we know that,

The volume of a cuboid = Length of the cuboid × Width of the cuboid × Height of the cuboid

Therefore, the volume of the given container of cuboid shape = 4 × 3 × 15 cubic meters.

                                                             = 180 cubic meters.

Hence, the volume of the container is 180 cubic meters.

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The quantities in the two columns cannot be compared due to the absence of specific point values. D.

The given question presents two columns, Column A and Column B, representing the slopes of lines through different sets of points.

The actual points themselves are not provided in the question.

Without the specific point values, it is not possible to determine the slope values or compare the quantities in Column A and Column B.

The slope of a line is determined by the change in the y-coordinate divided by the change in the x-coordinate between two points.

Since the coordinates of the points are missing, it is impossible to calculate the slopes accurately or make any comparison between the quantities in Column A and Column B.

Without the points, it is not possible to determine the slopes or establish any relationship between the quantities in Column A and Column B.

To draw any conclusions or comparisons, the coordinates of the points through which the lines pass are crucial.

Without that information, we lack the necessary data to assess the slopes and make any meaningful comparison.

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Answer:

x = -6 and y =5

Step-by-step explanation:

2x + 5y = 13    (call this equation '1')

-4x - 3y = 9    (call this '2')

multiply '1' by 2

4x + 10y = 26       (call this '3')

eliminate by adding '2' and '3':

(-4 + 4)x + (-3 + 10)y = 9 + 26

7y = 35

y = 5

sub that into '1':

2x + 5(5) = 13

2x + 25 = 13

2x = 13 - 25 = -12

x = -6

sub both x = -6 and y =5 into '2' to make sure everything adds up:

-4(-6) - 3(5) = 24 - 15 = 9

so x = -6 and y = 5

Given statement solution is :- 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

To find the percentage of pupils who passed the final examination, you can use the following formula:

Percentage = (Number of pupils passed / Total number of pupils) * 100

Given that 90 pupils passed the final examination out of a total of 150 pupils, we can substitute these values into the formula:

Percentage = (90 / 150) * 100

Percentage = 0.6 * 100

Percentage = 60%

Therefore, 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

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Answer:

Let's assume the number of adults attending the performance is represented by 'x', and the number of children attending is represented by 'y'.

According to the given information, the entrance fee for adults is R50 each, and for children is R20 each.

The total amount raised by the school is R31,400. We can write an equation based on the total amount raised:

50x + 20y = 31,400

This equation represents the total value of the entrance fees paid by adults and children.

To solve this equation, we need another equation to relate the variables 'x' and 'y'.

Since we don't have any other information about the number of adults or children, we cannot determine their relationship based on the given information. Therefore, we cannot find a unique solution for 'x' and 'y' unless there is additional information provided.

If there is additional information or if you have any specific values for 'x' or 'y', I can assist you in solving the equation and finding the number of adults and children attending the performance.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine whether y is a function of x in the equation x+4y=8, we can solve for y in terms of x:

x + 4y = 8

4y = 8 - x

y = (8 - x)/4

Copy

Since every value of x corresponds to exactly one value of y, y is a function of x.

Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

The number of students who passed with I, II, and III divisions are 35, 70, and 49, respectively.

We have,

Let's denote the number of students who passed with I, II, and III divisions as x, y, and z, respectively.

Given that the total number of students who appeared in the examination is 210, and 56 students failed, we can calculate the number of students who passed:

Number of students who passed = Total students - Number of students who failed

= 210 - 56

= 154

According to the given ratio, the number of students who passed with I, II, and III divisions are in the ratio of 5:10:7.

We can express this ratio in terms of x, y, and z as:

x : y : z = 5 : 10 : 7

To find the actual number of students who passed with I, II, and III divisions, we can set up the following equation based on the ratio:

5k + 10k + 7k = 154

22k = 154

k = 154 / 22

k = 7

Now, we can find the number of students who passed with I, II, and III divisions:

Number of students who passed with I division = 5k = 5 x 7 = 35

Number of students who passed with II division = 10k = 10 x 7 = 70

Number of students who passed with III division = 7k = 7 x 7 = 49

Therefore,

The number of students who passed with I, II, and III divisions are 35, 70, and 49, respectively.

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The end behavior of the graph of the function f(x) = -5(4x - 2) as x approaches infinity can be described as follows:

As x approaches infinity (or positive infinity), the value of 4x becomes infinitely large compared to the constant -2. Therefore, we can ignore the constant (-2) and simplify the function as f(x) = -5(4x) = -20x.

Since the coefficient of x is negative (-20), the graph of the function will decrease without bound as x approaches infinity. In other words, the function will approach negative infinity (or -∞) as x becomes infinitely large.

Similarly, as x approaches negative infinity, the value of 4x becomes infinitely large in the negative direction. Thus, we can simplify the function as f(x) = -5(4x) = -20x.

Since the coefficient of x is negative (-20), the graph of the function will also decrease without bound as x approaches negative infinity. Therefore, the function will approach negative infinity (or -∞) as x becomes infinitely negative.

The measure of arc XYL + measure of arc VUL + measure of arc VIX = 360°.  Therefore, the correct answer is option D.

The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference.

From the given circle, measure of arc XYL + measure of arc VUL + measure of arc VIX = 360° (Complete angle)

Therefore, the correct answer is option D.

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answer:

a) 8

_ or 50%

16

b) 8 or 50%

_

16

c) 11 or 68.75%

_

16

The expression √(x²y²)  when simplified is i. xy

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

√(x²y²)

When the expression is expanded, we have

√(x²y²) = √(x² * √(y²)

Evaluae the exponents in the expression

So, we have

√(x²y²) = x * y

Evaluae the products in the expression

So, we have

√(x²y²) = xy

Hence, the expression when simplified is i. xy

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Answer:

  15.  f(-2) = 2

  17.  f(x) = 1 for x = ±1.7

Step-by-step explanation:

You want various values of the function and its inverse relation for f(x)=x²-2.

The value of f(x) is found by locating the value x on the x-axis and following the vertical line until it intersects the graph. Find the y-coordinate of that point.

The value of x for f(x) = k is found by locating k on the y-axis and following the horizontal line to the points of intersection with the graph. The x-coordinates of the points are the values of interest. Interpolation is often required.

The graph intersects the vertical line at x=-2 where y = 2.

  f(-2) = 2

The horizontal line at y=1 intersects the graph in two places, located symmetrically about the y-axis. The leftmost point is approximately (-1.7, 1). The rightmost point is approximately (1.7, 1).

  x ≈ -1.7 or +1.7

__

Additional comment

The instructions are to use the figure to answer the question. We interpret that to mean that you are to read the answers from the graph.

You can also use the figure to determine the equation for the graph (part of our problem statement, above). Then you can find the solutions by using the equation.

  f(x) = 1

  x² -2 = 1

  x² = 3

  x = ±√3 ≈ ±1.732 . . . . the values for problem 17

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Answer:

x = 8 and y = -4

Step-by-step explanation:

3x + 4y = 8    (call this equation '1')

x - y = 12      (call this '2')

multiply '2' by 3:

3x - 3y = 36  (call this '3')

subtract '1' from '3':

(3x - 3y = 36)  -  (3x + 4y = 8)

0x + -7y = 28

-7y = 28

y = -4.

sub that back into '1':

3x + 4y = 8

3x + 4(-4) = 8

3x - 16 = 8

3x = 8 + 16 = 24

x = 8.

sub both y =-4 and x =8 into '2' to check if everything adds up:

x - y = 12

8 - -4 = 8 + 4 = 12

so x = 8 and y = -4

The values of x we found are x = 14 and x = 0.

To find the value of x in the given set of equations and expressions, we need to solve each equation individually and substitute the value of x into subsequent expressions. Let's solve each equation step by step:

Equation 21: 21 = B + 2 + 3x

To isolate 3x, we subtract 2 from both sides: 21 - 2 = B + 3x

19 = B + 3x

Equation 25: 25 = 2x - 3

To isolate 2x, we add 3 to both sides: 25 + 3 = 2x

28 = 2x

Divide both sides by 2: x = 14

Equation 24: 24 = G + LL + F

We don't have enough information to solve this equation since we don't know the values of G, LL, and F.

Equation 22: 22 = 5x + H + 10

To isolate 5x, we subtract H and 10 from both sides: 22 - H - 10 = 5x

12 - H = 5x

Equation 23: 23 = x + 8 + x + 3 + 12

Combining like terms: 23 = 2x + 23

Subtracting 23 from both sides: 0 = 2x

Divide both sides by 2: x = 0

Therefore, the values of x we found are x = 14 and x = 0.

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Step-by-step explanation:

To find the area of the square all you need to do is to find the length of the hypotenuse of the triangles

this will help us find the length of the square if we are given the values of the shorter lengths as shown up

we can calculate the length of the hypotenuse by using the Pythagorean theorem

[tex] \sqrt{a^{2} + b^{2} } = c[/tex]

we are given the sides of the shorter lengths being 5 and 3 we can then substitute them into the formula

let us label the missing length the hypotenuse as x

[tex] \sqrt{ {3}^{2} + {5}^{2} } = x[/tex]

[tex] \sqrt{34} = x[/tex]

[tex]5.83[/tex]

we get that 5.83 rounded to two decimal places is the length of the hypotenuse

we also know that it is the length of the square so

5.83 × 5.83 = Area of Square

34cm² = Area of Square