Which of the following is true with respect to the following functions:

The equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).

Given that x = -6, it means the directrix is horizontal.

Equation of parabola that opens left or write is expressed as;

( y - k )² = 4p( x - h )

Given that;

First, we find the vertex.

The vertex( h, k ) is halfway between the directrix and the focus.

Hence, x coordinate of the vertex is;

x = ( x coordinate of focus + directrix ) / 2

x = ( -4 + (-6) ) / 2

x = -10/2

x = -5

y coordinate of the vertex will be the same as that of the focus.
y = 8

Hence vertex will be;

( -5, 8 )

Next, we find the distance p from the focus to the vertex and from the vertex to the directrix.

Subtract x coordinate of vertex from x coordinate of focus.

p = -4 - ( -5 )

p = -4 + 5

p = 1

Now, we substitute these values into the equation.

( y - k )² = 4p( x - h )

( y - (8) )² = 4(1)( x - (-5) )

( y - 8)² = 4( x +5 )

Therefore, the equation for the parabola with a focus at (-4,8) and a directrix at x=-6 is ( y - 8)² = 4( x +5 ).

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Answer:

S(1,2)

Step-by-step explanation:

The value that is being altered is the y value if you go from Q to T and then T to S. The x value = 1 and remains the same for point S.

To go from Q to T, you go from 8 to 5 on the y value. Remember x remains the same. That's three units (8 - 5 = 3)

To go from T to S must be 3 units as well, since the small diagonal is bisected. 5 - 3 = 2 is the answer.

So point S is noted as S(1,2)

Answer:

-9

Step-by-step explanation:

The missing number will be labeled as x.

-15*x*8*(-4)=-4320

480x=-4320

x=-9

Using proportions, it is found that the radian measure of the central angle is given as follows:

[tex]\frac{4\pi}{3}[/tex] radians.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The entire circumference is equivalent to a central angle of [tex]2\pi[/tex] radians. Hence the radian measure of the central angle considering two-thirds of the circumference is given as follows:

[tex]\frac{2}{3} \times 2\pi = \frac{4\pi}{3}[/tex]

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Answer:

Step-by-step explanation:

c edge

5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6

6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8

7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3

8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .

9.  ∠1 and ∠7.

If two lines that are cut across by a transversal are parallel, the following special angles are formed:

Given the image given, we can identify the following special angles:

5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6

6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8

7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3

8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .

9.  ∠1 ≅ ∠3 and ∠3 ≅ ∠7. So the two angles would be ∠1 ≅ ∠7.

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Answer:

9.72 lb

Step-by-step explanation:

Yield = the amount or quantity produced or returned.

Given:

To determine how many pounds of eggplant you will be able to use, calculate 81% of the amount of eggplant purchased.

[tex]\begin{aligned}\sf 81\% \: of \: 12 \: lb & = \sf \dfrac{81}{100} \cdot 12\\\\& = \sf \dfrac{81 \cdot 12}{100}\\\\& = \sf \dfrac{972}{100}\\\\& = \sf 9.72\:lb\end{aligned}[/tex]

Therefore, you will be able to use 9.72 lb (nearest hundredth).

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Purchase=12lb

Amount to be used

You will be able to use 9.72pounds

Answer:

  D.  x ≈ 2.60

Step-by-step explanation:

The equation we have graphed is the one shown in the attachment. It is slightly different from the one in this problem statement.

It is often convenient to find a graphical solution to an equation by writing it in the form ...

  f(x) = 0

Then the solutions are the x-intercepts of the graph, points that most graphing calculators can readily identify.

We have done this here by defining ...

  [tex]y_1=3x^2-6x-4\\\\y_2=-\dfrac{2}{x+3}+1[/tex]

The graph is of y₁ -y₂. X-values where y₁-y₂ = 0 are solutions to the original equation, y₁ = y₂.

This equation is seen to have three solutions, approximately ...

  x = {-3.05, -0.55, 2.60}

Of these, only x ≈ 2.60 is listed among the answer choices.

__

Additional comment

The value of y₁ -y₂ expressed in standard form is ...

  [tex]3x^2-6x-4+\dfrac{2}{x+3}-1=0\\\\\dfrac{(x+3)(3x^2-6x-5)+2}{x+3}=0\\\\\dfrac{3x^3+3x^2-23x-13}{x+3}=0\\\\3x^3+3x^2-23x-13=0\quad(x\ne -3)[/tex]

The irrational solutions to this cubic can be found "exactly" by any of several applicable formulas. Numerical solutions are almost trivial to find with appropriate technology.

  x ≈ {−3.04857564747, −0.547524627423, 2.5961002749}.

Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Use hit and trial method

Answer is (-1,4)

Verification

Put x and. y

Option A

The relationship between d and t.

d = 49t

The correct equation is C.

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

speed = 49 miles/hour

Distance

Time

as we know :

Speed = Distance  /  Time .

Then:

49 = Distance/Time

Distance = 49*Time .

the relationship between d and t ( d = 49t).

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I understand that the question you are looking for is :

A cheetah runs at a speed of 49 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?

A. d = 49 + t

B. t = 49 + d

C. d = 49t

D. t = 49d

Using the given information, the average of r and s is 35.5

From the question, we are to determine the average of r and s

From the give information,

The average of p, q and 27 is 28.

That is,  

(p + q + 27)/3 = 28

p + q + 27 = 3×28

p + q + 27 = 84

p + q = 84 - 27

p + q = 57

Also,

The average of p, q, r, s and 27 is 31

That is,

(p + q + r + s + 27)/5 = 31
p + q + r + s + 27 = 5 × 31

p + q + r + s + 27 = 155

Thus,

57 + r + s + 27 = 155

r + s = 155 - 57 - 27

r + s = 71

The average of r and s is (r + s)/2

(r + s)/2 = 71/2

(r + s)/2 = 35.5

Hence, the average of r and s is 35.5

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Answer: 5 games

Step-by-step explanation: They need to win half their games for a .500 record and half or 30 is 15. They already won 10 so they need to win 15- 10 = 5 more games to have a .500 record.

Answer: Choice B

Work Shown:

[tex]\sqrt[3]{\text{x}^5\text{y}}\\\\(\text{x}^5\text{y})^{\frac{1}{3}}\\\\(\text{x}^5)^{\frac{1}{3}}*(\text{y})^{\frac{1}{3}}\\\\\text{x}^{\frac{5}{3}}\text{y}^{\frac{1}{3}}\\\\[/tex]

The probability that they each have a different tens digit is 0.047.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The probability of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.

Solution:- The collection contains 50 integers, hence there are [tex]^{50}C_5[/tex] different ways to select 5 different integers.

Sample space = [tex]^{50}C_5[/tex]

Each of the five numbers must correspond to one of the five available tens-digits, which are 2 through 6. There are a total of 105 ways to choose the five numbers that satisfy these properties because there are 10 ways to choose a number with a particular set of ten digits (such as 30, 31, or 39).

Therefore,

probability that each have a different tens digit = [tex]\frac{10^5}{^{50}C_5}[/tex]

                                                                                = [tex]\frac{10\times 10\times 10\times 10\times 10}{^{50}C_5}[/tex]

                                                                                = [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{(50-5)!5!} }[/tex]

                                                                                = [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{45!5!} }[/tex]

                                                                                 = 0.047

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Answer:

Zero

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

Multiply 35 by 2.5

Answer:

75 windows

Step-by-step explanation:

35 ---- 7

x ----- 15

[tex]x=\frac{(35)(15)}{7} =75[/tex]

Hope this helps

Answer:

Point Z

Step-by-step explanation:

Since the scale is one, first you go 0.5 to the left (-0.5 X) then you go 0.75 up (0.75 Y) then you have your answer.

The equations exist [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex] then the value of

x = -6, x = -2 and y = -15, y = 1.

[tex]y =4x+9[/tex] ?

The given equations are [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex]

[tex]$-\left(x\:+\:2\right)^2\:+\:1\:=\:4x\:+\:9[/tex]

[tex]$-x^{2}-4 x-3=4 x+9[/tex]

Subtract 9 from both sides, we get

[tex]$-x^{2}-4 x-3-9=4 x+9-9[/tex]

Simplifying the equation, we get

[tex]$-x^{2}-4 x-12=4 x[/tex]

Subtract 4x from both sides

[tex]$-x^{2}-4 x-12-4 x=4 x-4 x[/tex]

[tex]$-x^{2}-8 x-12=0[/tex]

Solve with the quadratic formula

[tex]$x_{1,2}=\frac{-(-8) \pm \sqrt{(-8)^{2}-4(-1)(-12)}}{2(-1)}[/tex]

[tex]$\sqrt{(-8)^{2}-4(-1)(-12)}=4[/tex]

[tex]$x_{1,2}=\frac{-(-8) \pm 4}{2(-1)}[/tex]

Separate the solutions

[tex]$x_{1}=\frac{-(-8)+4}{2(-1)}, x_{2}=\frac{-(-8)-4}{2(-1)}[/tex]

[tex]$x=\frac{-(-8)+4}{2(-1)}=-6[/tex]

[tex]$x=\frac{-(-8)-4}{2(-1)}= \quad-2[/tex]

The solutions to the quadratic equation are x = -6, x = -2

From the above equation [tex]y =4x+9[/tex],

substitute the value of x, then we get

Put, x = -6 then y = 4(-6) + 9 = -15

Put, x = -2 then y = 4(-2) + 9 = 1

The system of equations exists (–2, 1) and (–6, –15).

Therefore, the correct answer is (–2, 1) and (–6, –15).

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Answer:

(–2, 1) and (–6, –15)

Step-by-step explanation:

flvs testing (i am not completely sure btw)

just substitute that into a last equations (seperatly if you understand=== -2 and 1 as x and y; -6 and -15 as x and y)

Answer:

Step-by-step explanation:

easy

y=3x-2

-3x+y=-2

-3x=-2-y

x=2/3+1/3y

Answer:

51°

Step-by-step explanation:

posted answer to the question

Answer:

mint ----> 6

strawberry ----> 105

chocolate -----> 16

Step-by-step explanation:

90° ------> 12

so , 15° -----> 2

mint ---> 45° --> 15°× 3 ---> 2×3 --> 6

strawberry ---> 14 ---> 2×7 ---> 15° × 7 -->105°

chocolate ---> 120° ---> 8×15° --> 8×2 ---> 16

Yes, the pie chart and table show some information about the children's favorite ice cream flavors.

The pie chart shows that the most popular flavor is chocolate, with 30% of the children choosing it. Vanilla is the second most popular flavor, with 25% of the children choosing it. Strawberry is the third most popular flavor, with 20% of the children choosing it. The other flavors are less popular, with each receiving less than 10% of the votes.

The table shows the number of children who chose each flavor. There were 15 children who chose chocolate, 12 children who chose vanilla, 10 children who chose strawberry, 4 children who chose mint, 3 children who chose cookies and cream, and 2 children who chose coffee.

The pie chart and table together provide a good overview of the children's favorite ice cream flavors. Chocolate is the clear favorite, followed by vanilla and strawberry. The other flavors are less popular, but they still have some fans.

Here is a table that summarizes the information from the pie chart and table:

Flavor Number of Children Percentage

Chocolate 15 30%

Vanilla 12 25%

Strawberry 10 20%

Mint 4 10%

Cookies and cream 3 7.5%

Coffee 2 5%

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Using the normal distribution, it is found that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 83, \sigma = 6[/tex]

The proportion of students, with a grade of at least 70 is one subtracted by the p-value of Z when X = 70, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 83}{6}[/tex]

Z = -2.17

Z = -2.17 has a p-value of 0.015.

1 - 0.015 = 0.985 = 98.5% of students have at least a 70.

The proportion of students, with a grade of at least 80 is one subtracted by the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 83}{6}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% of students have an 80 or above.

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It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.

Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.

In ΔPNM, ∠N = 90°

∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)

∠P + ∠M = 90°

Clearly, ∠M is an acute angle.

Thus; ∠M < ∠N

PN < PM (The side opposite to the smaller angle is smaller)

Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

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Answer:

-5/3

Step-by-step explanation:

Do PEMDAS

8 - 11 = -3

-3 ^ 3 = -27

-(-27) = 27

I-14I = 14

3 x 14 = 42

27 - 42 = -15

2^4 = 16

16 - 7 = 9

-15/9 = -5/3

Answer:

no

Step-by-step explanation:

In a function, each "x" value [input] must have only one corresponding "y" value.

We know that points are written as (x, y)

Our points: {(3,-2), (1, 2), (-1,-4), (-1, 2)}

We can see that the x-input of -1 has two y-outputs, so this is therefore not a function

hope this helps! have a lovely day :)

The explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

The given parameters are:

The explicit form is for an arithmetic function.

An arithmetic function has an explicit form represented as:

f(n) = a + (n -1) * d

Substitute the values of n and a in the above equation

f(n) = 3 + (n -1) * -4

Evaluate the product i.e. multiply -4 by (n - 1)

f(n) = 3 -4(n - 1)

Rewrite the equation as

f(n) = -4(n - 1) + 3

The seventh term is then calculated as:

f(n) = -4(n - 1) + 3

Substitute 7 for n in the above equation

f(7) = -4(7 - 1) + 3

Evaluate

f(7) = -21

Hence, the explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

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Step-by-step explanation:

1.on foot -270

by bus-180

byMTR- 126

BY SCHOOL BUS -144

2.68%

4.94%

5.70%

7.16

9.72

10.960

The value of the x from the given equation is a +i and -i and +5i and -5i.

According to the statement

we have given that the equation [tex]x^4 + 6x^2 +5 =0[/tex]

and we have to find the value of x by the u substitution.

So,

The given equation is

[tex]x^4 + 6x^2 +5 =0[/tex]

Put [tex]x^2 = u[/tex] 

By substitution method

Then the equation become

[tex]u^2 +6u +5 = 0[/tex]

And solve the equation then

[tex]u^2+ u +5u +5 = 0[/tex]

Then

u(u +1) + 5(u +1) = 0

(u+5) (u +1) = 0

Then

the value of u is -1 and -5 then

The value of x is

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

x = √-5 And √-1

Then the value of x is +i and -i and +5i and -5i.

So, The value of the x from the given equation is a +i and -i and +5i and -5i.

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Answer:

x + y = 7

Explanation:

slope formula:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Find slope: given points: E(4, 3), F(6, 1)

[tex]\sf slope \ (m) : \dfrac{1-3}{6-4} = -1[/tex]

Find Equation: [tex]y - y_1 = m(x -x_1)[/tex]

[tex]\sf y - 3 = -1(x - 4)[/tex]

[tex]\sf y = -x + 4 + 3[/tex]

[tex]\sf y = -x + 7[/tex]

[tex]\sf x + y = 7 \quad (in \ standard \ form \ \rightarrow Ax + By = C)[/tex]

Slope of the line

Equation in point slope form

The range of the function y = -x² - 3x when the domain is {-5,0,2} is:

{-10, 0}.

The range of a function is the set that contains the output values for the given domain of the function.

In this problem, the domain is:

{-5,0,2}.

Hence the output values are:

Hence the range is:

{-10, 0}.

-10 repeats, but goes only once on the range.

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[tex]\Large\texttt{Answer}[/tex]

[tex]\bold{n-13}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Again letting n be the number

[tex]\bold{n}[/tex]

⇨ Subtract 13 from n

[tex]\bold{n-13}[/tex]

*unlike addition, the order DOES matter, because

[tex]\bold{n-13\ne 13-n}[/tex]

Hope that helped