Write in standard form an equation of the line with the given slope through the given point.

Slope=2/5; (6,7)

The nonreal solutions to the polynomial equation are: (2 + i√11, 2 - i√11).

By critically observing the graph given, we can logically deduce that the real solutions of the polynomial are -1 and 4. This ultimately implies that, the given polynomial expression can be evaluated as follows:

(x + 1)(x - 4) = x² - 3x - 4.

x⁴ - 7x³ + 23x² - 29x - 60 = x² - 3x - 4.

Also, the nonreal solutions can be determined by dividing the polynomial expression by the real solutions as follows:

Nonreal solutions = (x⁴ - 7x³ + 23x² - 29x - 60)/(x² - 3x - 4)

Nonreal solutions = (2 + i√11, 2 - i√11).

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The area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

From the question, we are to determine the area of the shaded part

In the given diagram, the shaded part is a rectangle

Area of a rectangle = Length × Width

Length of the shaded part = 18 inches - 4 inches - 1 inch = 13 inches

Width of the shaded part = 6 inches - 2inches = 4 inches

Then,

Area of the shaded part = 13 inches × 4 inches

Area of the shaded part = 52 sq. inches

Hence, the area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

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8. The length of the support is 7. 9 m

9. The length of the conveyer is 12m

3. a = 59m

A = 44°

B = 52°

4. c = 88. 6 mm

b = 49. 1 m

B = 34°

8. We have the angle to be 20 degrees

Opposite side = x

hypotenuse = 23m

Using the sine ratio

sin θ = opposite/ hypotenuse

[tex]sin 20 = \frac{x}{23}[/tex]

Cross multiply

[tex]sin 20[/tex] × [tex]23 = x[/tex]

[tex]x = 0. 3420[/tex] × [tex]23[/tex]

x = 7. 9 m

The length of the support is 7. 9 m

9. The angle of elevation is 37. 3 degrees

Hypotenuse = 19 . 0m

Opposite = x

Using the sine ratio

sin θ = opposite/ hypotenuse

[tex]sin 37. 3 = \frac{x}{19}[/tex]

cross multiply

[tex]x = 0. 6059[/tex] × [tex]19[/tex]

x = 11.5

x = 12 m in 2 significant figures

The length of the conveyer is 12m

3. To determine the sides and angles, we use the sine rule;

[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]

For side a, we use the Pythagorean theorem

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

[tex]85^2 = a^2 + 67^2[/tex]

[tex]a = \sqrt{89^2-67^2}[/tex]

[tex]a = \sqrt{3432}[/tex]

a = 58. 58, a = 59m

To find angle A and B, use the sine rule

[tex]\frac{59}{sin A } = \frac{85}{sin 90}[/tex]

cross multiply

[tex]sin A[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]59[/tex]

make sin A subject of formula

[tex]sin A = \frac{59}{85}[/tex]

[tex]sin A = 0. 6941[/tex]

A = [tex]sin^-^1(0. 6941)[/tex]

A = 44°

[tex]\frac{67}{sin B} = \frac{85}{sin 90}[/tex]

cross multiply

[tex]sin B[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]67[/tex]

make sin b subject of formula

[tex]sin B = \frac{67}{85}[/tex]

[tex]sin B = 0. 7882[/tex]

B = [tex]sin^-^1( 0. 7882)[/tex]

B = 52°

4. To find the sides, we use the sine rule;

[tex]\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}[/tex]

Cross multiply

[tex]sin 56. 6[/tex] × [tex]c = sin 90[/tex] × [tex]74[/tex]

make 'c' subject of formula

[tex]c = \frac{74}{0. 8348}[/tex]

c = 88. 6 mm

To find length b, we use the Pythagorean theorem

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

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

[tex]b^2 = 88. 8^2 - 74^2[/tex]

[tex]b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}[/tex]

b = 49. 1 m

[tex]\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}[/tex]

cross multiply

[tex]sin B = \frac{40. 99}{74. 0}[/tex]

B = [tex]sin^-^1(0. 5539)[/tex]

B = 34°

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Answer:

No Solution

Step-by-step explanation:

1) Simplify -6 - 3 to -3.

-3 = -21

2) Since -3 = -21 is false, there is no solution.

No solution

The percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%

The given parameters are:

Mean = 169200

Standard deviation = 19400

x = 188600

Calculate the z value using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So, we have:

[tex]z = \frac{188600 - 169200}{19400}[/tex]

Evaluate

z = 1

Using the Empirical Rule, we have:

P(x > 188600) = P(z > 1.5)

From z table of probability, we have:

P(x > 188600) = 0.93319

Express as percentage

P(x > 188600) = 93.319%

Approximate

P(x > 188600) = 93%

Hence, the percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%

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The first step is to find out how question in total she is able to miss, while still passing.

We know that there are [tex]40\\[/tex] questions on the test and she must get [tex]70[/tex]% of the questions correct.

Let's calculate how many questions that is:

40 x 0.70

= 28.

Subtract

40 - 28

= 12.

She is able to get 12 answers incorrect.

Now we must find out how many questions she got wrong when she got 40% of the first 15 correct.

If she got 40% correct; She got 60% incorrect.

Let's do the math:

Multiply:

15 x 0.40

= 6

Subtract:

15 - 6

= 9

This means that she got 6 questions correct, and 9 questions incorrect.

With the total allotment of 12 incorrect answers allowed, she can only get 3 more questions wrong.

Now we must find the percentage of the remaining 25 questions she can get wrong.

She can only get 3 wrong and she must get 22 correct.

Multiply:

22 x 4

= 88.

This means that she has to get 88% of the remaining 25 questions correct.

Using a system of equations, it is found that:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:

a + 4b = 50 -> a = 50 - 4b.

Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:

3a + 12b = 150.

a + 4b = 50 -> a = 50 - 4b.

The equations are equal, hence we suppose that the costs are equal, that is:

a + 4b = 50 -> 5a = 50 -> a = 10.

Hence:

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The expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.

Quadratic equations are equations that has a leading degree of 2. The standard quadratic equation is given as;

f(x) = ax^2+bx+c

Given the product of the expression below;

f(x) = (x-3)(x-7)

Expand

f(x) = x(x) - 7x - 3x -3(-7)

f(x) = x^2 - 7x - 3x + 21

f(x) = x^2 - 10x + 21

Hence the expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.

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The future value of the investment if the interest is compounded monthly is $89,354.89.

Given that;

Using the compound interest formula;

A = P( 1 + r/n )^(nt)

We plug in our values.

A = 20000( 1 + 0.05/12 )^(12 × 30)

A = 20000( 1 + 0.0041666666666667)^(360)

A = 20000( 1.0041666666666667)^(360)

A = 20000( 4.46774965 )

A = 89354.89

Therefore, the future value of the investment if the interest is compounded monthly is $89,354.89.

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Answer:

A)

x + y = 80

y = x + 20

B) x = 30 minutes

C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.

Step-by-step explanation:

A)

x + y = 80

y = x + 20

B) x = 30 minutes

Replacing y with x + 20 in the first equation ->

x + x + 20 = 80

2x + 20 = 80

2x = 60

x = 30

C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.

The equation between the number of days remaining and number of hours is given as y= -5x+50.

Let y be the number of days remaining and x be the no.of hours.

From the graph the slope of the line is given by m.

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

m=(30 - 40)/(4 - 2)

m= -10/2 = -5.

The above slope is in between points 2 and 4. As the line has a constant rate of growth the slope is the same between any points of the line.

Therefore the equation between the no.of days remaining and no.of hours is given by

y=mx +c.

y=-5x+c

Now to find the value of c. This can be determined by substituting the x and y values at a particular instant. For x=0,y=50. Therefore by these values, we get,

50= -5(0)+c

c=50.

Therefore the relation between the number of days remaining and number of hours is given as y= -5x+50.

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The equation whose solution is the given quantity is 90,000,000 = 2,000,000w + 15,000w where w = $44.67

B = xz + yw

Where,

B = xz + yw

90,000,000 = (20 × 100,000w) + (15,000 × w)

90,000,000 = 2,000,000w + 15,000w

90,000,000 = 2,015,000w

w = 90,000,000 / 2,015,000

= 44.6650124069478

Approximately,

w = $44.67

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Answer:

11

Step-by-step explanation:

(3x-28) + (3x-30) + x = 33

7x - 58 = 33

7x = 91

x = 13

DE = 3x - 28 = 3*13 - 28 = 11

Step-by-step explanation:

solution:

given,

or, 2:5 = 8:x

or, 2/5 = 8/x [ changing into fraction form ]

or, 2x = 40 [ doing cross-multiplication ]

or, x = 20 [ dividing both sides with 2]

Answer: The graph of g(x) is narrower than f(x) and is shifted to the left 2 units and down 1 unit.

Step-by-step explanation:

See attached image.

The function f(x) = x² is transformed and became g(x) = 3(x+2)² -1 has the graph of g(x) is wider than f(x) and is shifted to the left 2 units and down 1 unit.

By applying suitable graph transformation we can shift, stretch, shrink, a given graph along x and y axis.

According to the given question given a graph f(x) = x² and g(x) is                        3(x+2)² - 1.

Let us break transformations of g(x) one by one.

g(x) = 3f(x) which implies it's amplitude or vertical stretch is increased by a factor of 3.

Now, g(x) = 3(x+2)² implies the graph is shifted towards left by 2 units as x + 2 = 0 is x = -2.

Now, g(x) = 3(x+2)² - 1 implies that the whole graph has been shifted 1 units down along the y axis.

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The mean distance increased by a factor of 2^(²/₃)

The given equation for the relationship between a planet's orbital period, T and the planet's mean distance from the sun, A is;

T² = A³.

Let the orbital period of planet X = T(X).

Let the orbital period of planet Y = T(Y).

Let the mean distance of planet X from the sun = A(X).

Let the mean distance of planet Y = A(Y).

Thus;

A(Y) = 2A(X)

Therefore;

[T(Y)]² = [A(Y)]³ = [2A(X)]^3

However, [T(X)]² = [A(X)]³

Thus;

[T(Y)]² = 2³[T(X)]² * [T(Y)]²/[T(X)]² = 2³T(Y)/T(X) = 2^(³/₂)

That's for orbital period but the mean distance will increase by 2^(²/₃)

Thus we conclude that, the mean distance increased by a factor of 2^(²/₃)

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Answer:

2 Superscript three-halves

Step-by-step explanation:

Edge

Answer:

$42,600

Step-by-step explanation:

284000 x .15

The answer choice which describes the function is; Choice B; neither symmetry about the y-axis nor has order 2 rotational symmetry about the origin.

Rotational symmetry, otherwise termed radial symmetry, is the characteristic of a shape when it looks the same after some rotation by a partial turn. On this note, since the function represents a quartic graph, it follows that the function has neither symmetry about the y-axis nor has order 2 rotational symmetry about the origin.

Therefore, the function f(x) = −4x⁴ + 3x³ − 2x² − x + 5 is neither symmetry about the y-axis nor has order 2 rotational symmetry about the origin.

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The volume of the glasses is as follows;

The volume of cylinder glass 1 = πr²h

The volume of cylinder glass 1 = 3.14 × 3² × 6

The volume of cylinder glass 1 = 3.14 × 9 × 6

The volume of cylinder glass 1 = 169.56 cm³ = 170 cm³

The volume of the glass 2 = 2 / 3 π r³ + πr²h

The volume of the glass 2 = 2 / 3 × 3.14 × 3³ + 3.14 × 3² × 3

The volume of the glass 2 = 56.52 + 84.78

The volume of the glass 2 = 141.3 cm³ = 141 cm³

The volume of conical glass 3 = 1 / 3 πr²h

The volume of conical glass 3 = 1 / 3 × 3.14 × 3² × (√7² - 3² = √40)

The volume of conical glass 3 = 9.42 × √40

The volume of conical glass 3 = 59.5773111176

The volume of conical glass 3 = 60 cm³

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The possible length of the third side will be values that are less than 41 and greater than 5

For three sides to be the sides of a triangle, the sum of any two sides of the triangle must be greater than the third.

Given the two sides of a triangle have lengths 18m and 23m, the sum of the sides is given as:

sum = 18 + 23

Sum = 41

Let the third side be x, such that;

x + 18 >23

23 + x > 18

x >  23 - 18

x > 5

Similarly

x > -5

Hence the possible length of the third side will be values that are less than 41 and greater than 5

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The value of x using the alternate exterior angle theorem is 82°

An equation is an expression that shows the relationship between two or more numbers and variables.

An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and scalene.

From the diagram:

x = 82° (alternate exterior angles)

The value of x using the alternate exterior angle theorem is 82°

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The area of the enclosed figure is 4 square units.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

The triangle's area can be described as,

Area = 1/2 x base x height.

To find the area of the enclosed figure, we need to first plot the given points and then determine the shape of the figure.

Plotting the points A, B, and C on a coordinate grid, we get:

The image is given below.

Connecting points A, B, and C, we can see that the figure formed is a right triangle with legs of lengths 4 and 2.

Therefore, the area of the enclosed figure is:

Area = (1/2) x base x height

= (1/2) x 4 x 2

= 4 square units

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The complete question:

Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure?

Point A (1, 3)

Point B  (5, 7)

Point C(5, 3)

Point A (1, 3)

The point which would lie on the graph of f(x) = log2x is; (1, 0.301).

Since it follows from the task content that the given point (–1, 0.5) lies on the graph of f –1(x) = 2x.

The subsequent graph of f(x) = log2x would result from taking logarithms in which case, we have the graph passing through points determined as follows;

f(x) = log2^x

f(x) = x log2

Hence, when x = 1;

f(1) = 1log 2

Hence, we have point; (1, 0.301).

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Answer:

$13.50

Step-by-step explanation:

If I am taking off 40%, that means that the dress now cost 60% of the original cost.  .6 x 20 is 12.

You could also calculate the 20% off and subtract that from the original cost.  .4 x 20 =8.  Now 20 - 8 is also 12.

Now, we have to calculate the tax.  10% of 12 is .1 x 12 or $1.20.  We add the tax to the 12 to get 13.50.

Answer:

A

Step-by-step explanation:

Draw a diagonal line connecting the centre to a vertex at the bottom. This makes a triangle. It is a regular pentagon so the base of that triangle is 7.6 / 2, which is 3.8. You also know that the angle from the apothem to the base is 90 degrees. You also know that you could split the centre angle into 5 triangles. 360 / 5 = 72 and we have half of it so it is 36 degrees.

Let's see what we have so far:

The base of the triangle is 3.8

The angle at the bottom is 90

The angle at the top is 36

We now have the tan and the opposite and we need the adjacent so rearrange for adjacent.

This gives you adjacent = opposite / tan(angle)

adjacent = 3.8 / tan(36)

adjacent = 5.2m

Answer: 5

Step-by-step explanation:

[tex]\sqrt{(-4-0)^2 + (1-(-2))^2}=5[/tex]

The height of the tide after eight hours is 16 feet.

From the information given, the function is given as 5cos (π/4)t + 11.

In this case, the time is given as eight hours. This will be:

f(8) = 5 × cos (π/4) × 8 + 11

f(8) = 5 × cos(2π) + 11

= (5 × 0.999) + 11

= 16 feet

The height is 16 feet.

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