3. Triangle ABC has the following coordinates. A=(-6,5), B=(-4,2), C=(-6,2) What are the coordinates of triangle A'B'C' if it is created by dilating triangle ABC with the origin (0,0) as the center of dilation and with a scale factor of 4?

The polynomial [tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex] simplifies to [tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18.[/tex]

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is defined as a sum of terms, where each term consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.

The general form of a polynomial is:

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a₀

To simplify the expression[tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex], we need to perform the multiplication and combine like terms.

First, we multiply each term in the first polynomial by each term in the second polynomial:

[tex](x^2 + 3x + 3) * (-2x^2 - x + 6) = x^2 * (-2x^2 - x + 6) + 3x * (-2x^2 - x + 6) + 3 * (-2x^2 - x + 6)[/tex]

Expanding each term, we get:

=[tex](-2x^4 - x^3 + 6x^2) + (-6x^3 - 3x^2 + 18x) + (-6x^2 - 3x + 18)[/tex]

Now, we combine like terms:

=[tex]-2x^4 + (-x^3 - 6x^3) + (6x^2 - 3x^2 - 6x^2) + (18x + 18x - 3x) + 18[/tex]

Simplifying further:

=[tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18[/tex]

The simplified expression in polynomial standard form is:

-2x^4 - 7x^3 - 3x^2 + 33x + 18

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Jerry's error is that he incorrectly assumes that the measure of angle ABC is equal to the sum of the measures of angles A and C. Hence Statement B is answer.

This is not true because angle ABC is an inscribed angle, which means its measure is half the measure of the intercepted arc.

In this case, the intercepted arc is AC. Since angle A measures 135 degrees and angle C measures 119 degrees, the sum of their measures is 254 degrees. However, angle ABC is not equal to 254 degrees.

To find the measure of angle ABC, we need to find the measure of arc AC. Since arcs A and C are equal in measure, we can find the measure of arc AC by subtracting angle A's measure (135 degrees) from the full circle measure (360 degrees).

Therefore, the measure of arc AC is 360 - 135 = 225 degrees. Since angle ABC is an inscribed angle, its measure is half the measure of arc AC, which is 225/2 = 112.5 degrees.

Hence Statement B is answer.

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Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

So, the system of equations to be solved is

a + c= 131

9.60a + 5.20c= 1020

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable c from the first equation:

c= 131 -a

Substituting the expression in the second equation:

9.60a + 5.20×(131 -a)= 1020

Solving:

9.60a + 5.20×131 -5.20a= 1020

9.60a + 681.2 -5.20a= 1020

9.60a -5.20a= 1020 - 681.2

4.4a= 338.8

a= 338.8÷ 4.4

a= 77

In summary, 77 adult tickets were sold that day.

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For the data point (2, 5), the residual is 5 - 6 = -1. For the data point (3, 6), the residual is 6 - 8 = -2. For the data point (4, 11), the residual is 11 - 10 = 1. For the data point (5, 14), the residual is 14 - 12 = 2. For the data point (6, 15), the residual is 15 - 14 = 1.

To plot the residuals for the given linear function, we need to calculate the difference between the actual y-values of the data points and the corresponding predicted y-values based on the linear function.

Let's start by calculating the predicted y-values using the linear function y = 2x + 2 for each x-value in the dataset:

For x = 2, the predicted y-value is 2(2) + 2 = 6.

For x = 3, the predicted y-value is 2(3) + 2 = 8.

For x = 4, the predicted y-value is 2(4) + 2 = 10.

For x = 5, the predicted y-value is 2(5) + 2 = 12.

For x = 6, the predicted y-value is 2(6) + 2 = 14.

Now we can calculate the residuals by subtracting the predicted y-values from the actual y-values.

To visualize these residuals, we can create a scatter plot with the x-values on the horizontal axis and the residuals on the vertical axis. Each data point will represent the x-value from the dataset and its corresponding residual. The residuals can be either positive or negative, so we should include both sides of the vertical axis.

By plotting the residuals, we can observe the deviations between the actual y-values and the predicted y-values based on the linear function. This plot helps us assess how well the linear function fits the data and identify any patterns or trends in the residuals.

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Having the information that segment AC ≅ segment EF, angle B ≅ angle E, and segment BC ≅ segment FE is sufficient to prove that triangles ΔABC and ΔDEF are congruent by the Side-Angle-Side (SAS) criterion.

To prove that triangles ΔABC and ΔDEF are congruent using the Side-Angle-Side (SAS) criterion, we need the following additional information:

The length of segment AC is equal to the length of segment EF: This establishes that one pair of corresponding sides is congruent.

The measure of angle B is equal to the measure of angle E: This provides the congruent angle between the corresponding sides.

The length of segment BC is equal to the length of segment FE: This establishes that the other pair of corresponding sides are congruent.

By having this information, we can apply the SAS congruence criterion. The SAS criterion states that if two triangles have a pair of corresponding sides that are congruent, and the included angles are congruent, then the triangles are congruent.

In this case, having segments AC ≅ EF, angle B ≅ angle E, and segment BC ≅ FE would be sufficient to prove that ΔABC ≅ ΔDEF by SAS.

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Answer:h equals 12

Step-by-step explanation:

Step-by-step explanation:

in the formula

y = Ae^rt

y is 675,000

A is 250,000

r is 0.08

to get the value of t

y = Ae^rt

y/A = e^rt

ln(y/A) = rt

[ln(y/A)]/r = t

Answer:

Step-by-step explanation:

The given expression is: 14x^(2n+1) + 7x^(n+3) - 21^(n+2)

Unfortunately, it seems there is a missing exponent for the term "21" in the expression. Please provide the correct exponent for 21, and I'll be happy to help you further simplify the expression.

The mean of the scores to the nearest tenth is 83.7.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given the question above, we need to find the mean of the scores to the nearest tenth.

We can find the mean by using the formula below:

[tex]\text{Mean} = \dfrac{\text{Sum of all the observations}}{\text{Total number of observations}}[/tex]

Now,

[tex]\text{Mean} = \dfrac{70(6)+75(3)+80(9)+85(5)+90(7)+95(8)}{6+3+9+5+7+8}[/tex]

[tex]\text{Mean} = \dfrac{420+225+720+425+630+760}{38}[/tex]

[tex]\text{Mean} = \dfrac{3180}{38}[/tex]

[tex]\text{Mean} = 83.7[/tex]

Therefore, the mean of the scores to the nearest tenth is 83.7.

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Answer:

cos Z = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

cos Z = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{YZ}{XZ}[/tex] = [tex]\frac{10}{26}[/tex] = [tex]\frac{5}{13}[/tex]

If 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially.

To determine how many plants to start with initially, we need to perform a series of calculations based on the information provided.

On Monday 23 plants were planted, on Tuesday 28 plants were planted and on Wednesday 29 plants were planted. If on Thursday there were a total of 90 plants, we can add all the plants planted until Thursday and then subtract them from the total to obtain the initial amount.

Adding the plants planted:

23 + 28 + 29 = 80

Then, we subtract this amount from Thursday's total:

90 - 80 = 10

Therefore, we started with 10 plants initially.

In summary, if 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially. This is obtained by adding the plants planted until Thursday and then subtracting that amount from the total for Thursday.

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The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;

1. ΔAJK ~ ΔSWY according to the SAS similarity postulate

2. ΔLMN ~ ΔLPQ according to the AA similarity postulate

3. ΔPQN ~ ΔLMN

LM = 12, QP = 8

4. ΔLMK~ΔLNJ

NL = 21, ML = 14

Similar triangles are triangles that have the same shape but may have different sizes.

1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;

24/16 = 3/2

18/12 = 3/2

The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.

2. The ratio of the corresponding sides in each of the triangles are;

MN/LN = 8/10 = 4/5

PQ/LQ = 12/(10 + 5) = 12/15 = 4/5

The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule

3. The alternate interior angles theorem indicates;

Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;

ΔPQN ~ ΔLMN by the AA similarity postulate

LM/QP = (x + 3)/(x - 1) = 18/12

12·x + 36 = 18·x - 18

18·x - 12·x = 36 + 18 = 54

6·x = 54

x = 54/6 = 9

LM = 9 + 3 = 12

QP = x - 1

QP = 9 - 1 = 8

4. The similar triangles are; ΔLMK and ΔLNJ

ΔLMK ~ ΔLNJ by AA similarity postulate

ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)

ML/NL = LK/LJ = (24 - 8)/24

(24 - 8)/24 = (6·x + 2)/((7·x + 7)

16/24 = (6·x + 2)/(7·x + 7)

16 × (7·x + 7) = 24 × (6·x + 2)

112·x + 112 = 144·x + 48

144·x - 112·x = 32·x = 112 - 48 = 64

x = 64/32 = 2

ML = 6 × 2 + 2 = 14

NL = 7 × 2 + 7 = 21

MN = 2 + 5 = 7

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Answer:

Step-by-step explanation:

To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:

a) g(0)

To find g(0), substitute x = 0 into the function:

g(0) = 2(0)^2 - 2(0) + 9

g(0) = 0 - 0 + 9

g(0) = 9

b) g(-1)

To find g(-1), substitute x = -1 into the function:

g(-1) = 2(-1)^2 - 2(-1) + 9

g(-1) = 2(1) + 2 + 9

g(-1) = 2 + 2 + 9

g(-1) = 13

c) g(2)

To find g(2), substitute x = 2 into the function:

g(2) = 2(2)^2 - 2(2) + 9

g(2) = 2(4) - 4 + 9

g(2) = 8 - 4 + 9

g(2) = 13

d) g(-x)

To find g(-x), substitute x = -x into the function:

g(-x) = 2(-x)^2 - 2(-x) + 9

g(-x) = 2x^2 + 2x + 9

e) g(1 - t)

To find g(1 - t), substitute x = 1 - t into the function:

g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9

g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9

g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9

g(1 - t) = 2t^2 - 2t + 9

Therefore:

a) g(0) = 9

b) g(-1) = 13

c) g(2) = 13

d) g(-x) = 2x^2 + 2x + 9

e) g(1 - t) = 2t^2 - 2t + 9

The solution to the system of equations is (a) (1, 0)

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

The graph

The point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (1, 0)

This means that

x = 1 and y = 0

Hence, the solution to the system of equations is (a) (1, 0)

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Answer:

Step-by-step explanation:

[tex]P(\text{not vanilla})=1-\frac{3}{22}=\frac{19}{22}[/tex]

Odds are 19 to 3.

Answer:

acute triangle

Step-by-step explanation:

for the given sides to form a triangle

the sum of any 2 sides must be greater than the third side

given 56 , 90 , 100

56 + 90 = 146 > 100

56 + 100 = 156 > 90

90 + 100 = 190 > 56

the condition is met so the 3 lengths will form a triangle.

let a = 56 , b = 90 and c = 100 , where c represents the longest of the 3 sides , then

• if a² + b² = c² , then triangle is right

• if a² + b² > c² , then triangle is acute

• if a² + b² < c² , then triangle is obtuse

a² + b² = 56² + 90² = 3136 + 8100 = 11,236

c² = 100² = 10, 000

since a² + b² > c² , then triangle is acute

Answer:

The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.

Step-by-step explanation:

The given directrix of the parabola is y = 2, which is a horizontal line.

This means that the parabola is vertical, with a vertical axis of symmetry.

The focus of a parabola is a fixed point located inside the curve. The y-coordinate of the given focus is y = -10. As this is below the directrix, it means that the parabola opens downwards.

The standard form of a vertical parabola is:

[tex]\boxed{(x-h)^2=4p(y-k)}[/tex]

where:

As the focus is (3, -10), then:

[tex](h, k+p)=(3,-10)[/tex]

     [tex]\implies h = 3[/tex]

[tex]\implies k+p=-10[/tex]

As the directrix is y = 2, then:

[tex]k - p=2[/tex]

To find the value of k, sum the equations involved k and p to eliminate p:

[tex]\begin{array}{crcccr}&k &+& p& =& -10\\+&k& -& p& = &2\\\cline{2-6}&2k&&& =& -8\\\cline{2-6}\\\implies &k&&&=&-4\end{array}[/tex]

To find the value of p, substitute the found value of k into one of the equations:

[tex]-4-p=2[/tex]

        [tex]p=-4-2[/tex]

        [tex]p=-6[/tex]

Therefore, the values of h, k and p are:

The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.

The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.

In Mathematics, the standard form of the equation of the directrix lines for any parabola is given by this mathematical equation:

(x - h)² = 4p(y - k).

Where:

Since the directrix is horizontal, the axis of symmetry would be vertical. This ultimately implies that, we would have the following parameters;

directrix is y = 2

Focus, (h, k + p) = (3, -10)

Next, we would determine the value of k as follows;

k + p = -10     .......equation 1

k - p = 2     .......equation 2

By solving the equations simultaneously, we have:

2k = -8

k = -4

For the value of p, we have the following from equation 2:

k - p = 2

-4 - p = 2

p = -4 - 2

p = -6

In conclusion, we can logically deduce that the parabola opens downward because the p-value is negative.

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The equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Given:Hunger of Harry as a function of time,H(t)H(t) can be modeled by a sinusoidal expression of the form,a⋅cos(b⋅t)+da⋅cos(b⋅t)+d, where Harry wakes up at t=0t=0t=0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs.

Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs.

Therefore, the equation of the form for H(t)H(t) will be,H(t) = A.cos(B.t) + C where, A is the amplitude B is the frequency (number of cycles per unit time)C is the vertical shift (or phase shift)

Thus, the maximum and minimum hunger of Harry can be represented as,When t=0t=0t=0, Harry's hunger is at maximum, i.e., H(0)=30kgH(0)=30kg30, start text, space, k, g, end text.

When t=2t=2t=2, Harry's hunger is at the minimum, i.e., H(2)=15kgH(2)=15kg15, start text, space, k, g, end text.

According to the given formula,

H(t) = a.cos(b.t) + d ------(1)Where a is the amplitude, b is the angular frequency, d is the vertical shift.To find the value of a, subtract the minimum value from the maximum value.a = (Hmax - Hmin)/2= (30 - 15)/2= 15/2 = 7.5To find the value of b, we will use the formula,b = 2π/period = 2π/(time for one cycle)The time for one cycle is (2 - 0) = 2 hours.

As Harry's hunger cycle is a sinusoidal wave, it is periodic over a cycle of 2 hours.

Therefore, the angular frequency,b = 2π/2= π

Therefore, the equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5

Answer: H(t) = 7.5.cos(π.t) + 22.5.

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Answer:

arc VL = 91°

Step-by-step explanation:

the chord- chord angle WBF is half the sum of the arcs intersected by the angle and its vertical angle , that is

[tex]\frac{1}{2}[/tex] (WF + VL) = ∠ WBF

[tex]\frac{1}{2}[/tex] (143 + VL ) = 117° ( multiply both sides by 2 to clear the fraction

143° + VL = 234° ( subtract 143° from both sides )

VL = 91°

Answer:

  (a)  10, $2088.81

  (b)  see attached

  (c)  B. increases at a slower rate

Step-by-step explanation:

Given the cost function g(x) = -1736.7 +1661.4·ln(x) for the average dollar cost of health insurance in year x after 2000, you want the cost in 2010, a graph for the years 2006 to 2015, and a description of the shape of the curve.

The value of x is years after 2000, so for the year 2010, the value of x is ...

  x = 2010 -2000 = 10

Substituting 10 for x in the function will give the cost in 2010. That is ...

  g(10) = -1736.7 +1661.4·ln(10) ≈ 2088.81

The cost in 2010 is about $2088.81.

The second attachment shows a graphing calculator's rendition of the graph. We note it has positive slope everywhere, but does not intersect the lines y=1000 or y=3000. This eliminates choices A, C, and D, leaving choice B for the graph.

The logarithm function has positive and decreasing slope. The function here is a scaled and shifted version of the logarithm function, but it still has positive and decreasing slope. That is, ...

 the average cost increases at a slower rate as time goes on

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Answer:

5⁴

Step-by-step explanation:

625= 5×5×5×5

The correct combination is option a) 1 twenty, 3 tens, and 5 singles, which allows us to make change for $55 without making change for a twenty dollar bill.

The correct answer is a) 1 twenty, 3 tens, 5 singles.

To make change for $55 using exactly nine bills without making change for a twenty dollar bill, we need to avoid using any combination that includes a twenty dollar bill.

Option a) includes 1 twenty, 3 tens, and 5 singles. The total value of these bills is 20 + 3(10) + 5(1) = $55. This combination allows us to make the exact change for $55 without including a twenty dollar bill.

Option b) includes 4 tens, 2 fives, and 5 singles. The total value of these bills is 4(10) + 2(5) + 5(1) = $55. Although this combination also makes the exact change for $55, it includes four tens, which can be exchanged for a twenty dollar bill.

Option c) includes 2 twenties, 1 ten, and 6 singles. The total value of these bills is 2(20) + 10 + 6(1) = $57. This combination exceeds $55 and also includes two twenty dollar bills, making change for a twenty dollar bill.

Option d) includes 2 twenties, 2 fives, and 5 singles. The total value of these bills is 2(20) + 2(5) + 5(1) = $55. However, this combination includes two twenty dollar bills, making change for a twenty dollar bill.

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The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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Answer: 2,2

Step-by-step explanation:

trust me

Answer:

[tex](y+1)^2=8(x+3)[/tex]

Step-by-step explanation:

The focus of a parabola is a fixed point located inside the curve. It is equidistant from the vertex and the directrix.

The directrix is a line that is located outside the curve. As the directrix on the given graph is a vertical line, the parabola is horizontal (sideways). The directrix is located to the left of the focus, which means the parabola opens to the right.

The axis of symmetry is perpendicular to the directrix and passes through the focus. So the axis of symmetry in this case is y = -1.

The vertex is the turning point of the parabola. It is located on the axis of symmetry, and is halfway between the focus and the directrix. Therefore, the y-coordinate of the vertex is y = -1. Given the focus is (-1, -1) and the directrix is x = -5, the vertex is (-3, -1).

The standard equation of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

As the vertex is (-3, -1), then h = -3 and k = -1.

Use the formula for the focus to find the value of p:

[tex]\begin{aligned}(h+p, k)&=(-1,-1)\\(-3+p, -1)&=(-1, -1)\\\implies -3+p&=-1\\p&=2\end{aligned}[/tex]

To write an equation for the parabola based on the given focus and directrix, substitute the values of h, k and p into the standard equation :

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

[tex](y+1)^2=8(x+3)[/tex]

Therefore, the equation of the parabola is:

[tex]\boxed{(y+1)^2=8(x+3)}[/tex]

The equation of the parabola with focus (-1, -1) and directrix x = -5 is (x + 1)² = 16(y + 1).

The equation of a parabola with a focus at (-1, -1) and a directrix of x = -5 can be written in standard form as:

(x - h)² = 4p(y - k)

Where (h, k) represents the vertex of the parabola and p is the distance between the vertex and the focus (or directrix).

In this case, the x-coordinate of the focus (-1, -1) is h = -1, and the y-coordinate is k = -1. The directrix is a vertical line x = -5, which means the parabola opens to the right.

Step 1: Determine the value of p

The distance between the vertex and the directrix is given by the absolute difference of their x-coordinates. In this case, p = |-5 - (-1)| = |-5 + 1| = 4.

Step 2: Write the equation

Substituting the values into the standard form equation, we have:

(x - h)² = 4p(y - k)

(x - (-1))² = 4(4)(y - (-1))

(x + 1)² = 16(y + 1)

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The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

Answer:

A. 16% of scores are at his/her score or below

Step-by-step explanation:

When a student's score is at the 16th percentile, it means that their score is equal to or better than 16% of the scores in the population. In other words, 16% of the scores are at their score or below.

Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.