Use the function below to find F(2).

The equation of the parabola is y = 2/25x^2 + 2

The complete question is in the image

The given parameters are:

Vertex, (h, k) = (0,2)

Point (x,y) = (-5, 4)

The parabola is represented as;

y = a(x - h)^2 + k

Substitute (h, k) = (0,2)

y = a(x - 0)^2 + 2

This gives

y = ax^2 + 2

Substitute (x, y) = (-5,4)

4 = a(-5)^2 + 2

This gives

4 = 25a + 2

Subtract 2 from both sides

25a = 2

Divide by 25

a = 2/25

Substitute a = 2/25 in y = ax^2 + 2

y = 2/25x^2 + 2

Hence, the equation of the parabola is y = 2/25x^2 + 2

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Answer:

15

Step-by-step explanation:

Supplementary angles add to 180 degrees

Let the supplement be x

x+165 = 180

x +165-165= 180-165

x = 15

The supplement is 15

Answer:

Hello! The answer is 15°.

Step-by-step explanation:

Supplementary angles add up to 180°.

To find the measure of each angle, we can now set up an equation because we have the total that supplementary angles add up to:

x + 165 = 180

Now, we can subtract 165 from both sides to get x by itself:

x + 165 = 180

    -165  -165

This leaves us with:

x = 15

The diameter of a sphere is a chord that passes through the centre of the sphere.

We need to complete the given statement.

The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere. If is the radius of a circle or sphere, then. The ratio of the circumference of a circle or great circle of a sphere to the diameter.

A chord of a sphere is a segment whose endpoints are on the sphere. A diameter is a chord that contains the centre.

Therefore, the diameter of a sphere is a chord that passes through the centre of the sphere.

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Answer:

refer to the above attachment

The best description of the car's motion as shown in the graph is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

In a distance-time graph, an horizontal line implies no distance was covered within that time frame, meaning there was a stop.

Thus, in the graph given, the stop occurred 1 and 2, which is equivalent to an hour. From 2 to 5 on the x-axis means there was movement for up to 3 hours.

Therefore, the best description is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

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The  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

A transformation is a rule that is used to manipulate the position of a point of geometric figure.

And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.

Hence,  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

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Answer:

x+10

Step-by-step explanation:

So they did a bet, and placed 5 cents each. George lost the bet that gives Joyce 5 points plus 5 more that make 10.

After the bet George has: x cents

Before the bet George had: x + 5 cents

Before the bet Joyce had also x + 5 cents

Since Joyce won 5 cents, after the bet she has x + 5 + 5 = x + 10 cents.

Hi! ⋇

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

  All proportions have this form:

  [tex]\sf{\dfrac{a}{b}=\dfrac{c}{d}}[/tex], Where [tex]\sf{\dfrac{a}{b}}[/tex] is equal to [tex]\sf{\dfrac{c}{d}}[/tex].

 If [tex]\sf{\dfrac{a}{b}\neq\dfrac{c}{d}}[/tex], it's not a proportion.

_________________________

  Here we have two pairs of numbers:

40,10 and 32,8.

Written As a proportion, they look like :

[tex]\sf{\dfrac{40}{10}=\dfrac{32}{8}}[/tex]

Hope this made sense to you :)

[tex]\it{Calligrxphy}[/tex]

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

-22

Step-by-step explanation:

-14+(-12）+4

=-14-12+4

=-26+4

=-22

The probability that a randomly selected male college student gains 15 lb or more during their freshman year is 11.6%

Probability is defined as the likeliness of an event to happen.

Let X be a random variable that shows the term "freshman 15" that claims that students typically gain 15lb during their freshman year at college.

It is given that

X follows is a normal distribution with a mean of 2.1 lb (μ) and a standard deviation (σ)  of 10.8 lb.

Population Mean (μ) = 2.1

Population Standard Deviation (σ) = 10.8

We need to compute Pr(X≥15). The corresponding z-value needed to be computed is:

[tex]\rm Z_{lower} = \dfrac{ X_1 -\mu }{\sigma}\\\\Z_{lower} = \dfrac{ 15-2.1 }{10.8}\\\\\\Z_{lower} = 1.19[/tex]

Then the probability is given as

[tex]\rm Pr(X \geq 16 ) = Pr (\dfrac{X -21}{10.8} \geq \dfrac{15-21}{10.8})\\\\= Pr (Z \geq \dfrac{15-2.1}{10.8}\\\\= Pr (Z\geq 1.19)\\\\ = 0.1162[/tex]

Pr(X≥15)=0.1162. (11.6%)

The probability that a randomly selected male college student gains 15 lb or more during their freshman year is 11.6%

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The bisector of angle APQ passes through O and this is illustrated below.

From the information given, the center is O. and the circle passes through O and cuts at K.

In this case, it should be noted that the circles are equal according to the SAS test.

Here, AOB + APQ = 180° (Linear pair)

2AOB = 180

AOB = 90.

Therefore, the bisector of angle APQ passes through O.

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The graph of the system of inequalities can be seen below.

Here we have the inequalities:

y < -(1/3)*x + 1

y ≤2x-3

To graph the first inequality, we need to graph the line -(1/3)*x + 1 with a dashed line (because the symbol < was used) and shade the region below that line.

For the second inequality we need to graph the line 2x-3 with a solid line this time, and again, shade the region below the line.

The graph of the system is shown in the image below.

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Rewriting the equation of the given line in slope-intercept form,

[tex]-x-4y=1\\\\-4y=x+1\\\\4y=-x-1\\\\y=-\frac{1}{4}x-\frac{1}{4}[/tex]

From this, we know the slope of the given line is -1/4.

Since parallel lines have the same slope, we know the line whose equation we want to find has a slope of -1/4.

Substituting into point-slope form,

[tex]y=-\frac{1}{4}(x+4)\\\\\boxed{y=-\frac{1}{4}x-1}[/tex]

Answer:

It is.

Step-by-step explanation:

(x, y, z) => (4, -5, -4)

substitute 4 in x, -5 in y & -4 in z for all the equations in the system.

4x + 2y + z = 2

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

2 = 2

5x - 4y - z = 44

5(4) - 4(-5) - (-4) = 44

44 = 44

3x + y + 4z = -9

3(4) + (-5) + 4(-4) = -9

-9 = -9

All equations therefore agree with the ordered triple.

the largest length of the squares will be 120m.

The largest possible length will be equal to the greatest common factor between the dimensions of the rectangular plot, so we need to find the GCF between 600 and 720.

If we decompose both numbers, we get:

600 = 2*2*2*3*5*5

720 = 2*2*2*2*3*3*5

Then the greatest common factor is: (2*2*2*3*5) = 120

So the largest length of the squares will be 120m.

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Answer: [tex]\frac{k(k+1)}{2}[/tex]

Step-by-step explanation:

This is a standard formula.

Answer:

x^2-x-2=0

Step-by-step explanation:

x^2+3=x+5

x^2-x-2=0

Answer:

abcdefghijklmnopqrstuvwxyz

Step-by-step explanation:

these are the alphabets

Answer:

[tex]y=-\frac{1}{3}x -8[/tex]

Step-by-step explanation:

1) Write down the standard form of an equation of a line and the formula to find m.

[tex]y=mx+b[/tex]

[tex]m=\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

2) Find m using the formula then substitute it into [tex]y=mx+b[/tex].

[tex]m=\frac{-5 - (-6) }{-9 - (-6)}\\m=\frac{-5 +6 }{-9 +6}\\m=\frac{1}{-3} \\m=-\frac{1}{3}[/tex]

So, [tex]y=-\frac{1}{3}x +b[/tex].

3) Find b by substituting a pair of coordinates the line goes through.

[tex]-6=-\frac{1}{3}(-6) +b\\-6=2+b\\-6 - 2=b\\-8=b[/tex]

4) Substitute b into [tex]y=-\frac{1}{3}x +b[/tex] to get your final answer.

[tex]y=-\frac{1}{3}x -8[/tex]

Angles on straight line = 180

110 + 5x = 180 degrees

-110

5x. = 70

÷ 5

x. = 14

5 x 14 = 70

Angles in triangle = 180

70 + 40 = 110

So, the missing angle inside the triangle is 70

Now to find y, use angles on straight line = 180

2y + 70 = 180

- 70

2y = 110

÷2

y = 55 degrees

Hope this helps!

The distance between (-2, 3) and (-5, 1) is √13.

or, the distance between (-2, 3) and (1, 1) is √13.

We know that the length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two points. Therefore, by measuring the length of the line segment that connects the two points, the distance between them can be determined. If (a, b) and (c, d) be two points, then the distance between them is [tex]\sqrt[]{(b - a)^{2} +(d- c)^{2} }[/tex].

Here, one point is (-2, 3).

Let the other point be (x, 1).

Given that the distance is √13.

Now, [tex]\sqrt[]{(x - (-2))^{2} +(1 - 3)^{2} } = \sqrt{13}[/tex]  

i.e. [tex]\sqrt[]{(x + 2)^{2} +( - 2)^{2} } =\sqrt{13}[/tex]

i.e. [tex]\sqrt[]{x^{2}+4x +4 +4 }=\sqrt{13}[/tex]

i.e. [tex]x^{2}+4x +8 =13[/tex]

i.e. [tex]x^{2}+4x + 8- 13=0[/tex]

i.e.[tex]x^{2}+4x -5=0[/tex]

i.e. [tex]x^{2} +5x - x -5=0[/tex]

i.e. [tex]x(x+5)-1(x+5)=0[/tex]

i.e. [tex](x+5)(x-1)=0[/tex]

i.e. [tex]x=-5,1[/tex]

So, the point is either (-5, 1) or (1, 1).

Therefore, the required point is either (-5, 1) or (1, 1).

i.e. the distance between (-2, 3) and (-5, 1) is √13.

or, the distance between (-2, 3) and (1, 1) is √13.

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Answer: $201.81

Step-by-step explanation:

The total amount of faux fur required is [tex]6(3.1)=18.6[/tex] square yards.

Multiplying this by $10.85 per square yard, we get the total cost is [tex](18.6)(10.85)=\$201.81[/tex]

The numbers of runners that are 50 and above are 3000.

Using the pie chart,

If there are 1500 runners that are under 20, therefore,

1500 = 10 / 100 × x

where

x = total number of runners

10x = 150000

x = 15000

Therefore,

the number of runners that are 50 and above = 20 / 100 × 15000 = 3000

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None solutions to the system exist.

Given statement: A system of three linear equations in three variables is inconsistent.

Concept: If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.

We know that if a system has no solution, then it is known as inconsistent.

[If there are one, two, or an infinite number of solutions to the system, then it is called consistent.]

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The integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

A demand function describes the mathematical relationship between the quantity demanded and one or more determinants of the demand, as the price of the good or service, the price of complementary and substitute goods, disposable income, etc.

Here, given differential equation;

R'(x) = 599 - 0.21[tex]\sqrt{x}[/tex]

we can also write this as;

[tex]\frac{d}{dx}R(x) = 599 - 0.21\sqrt{x}[/tex]

[tex]d R(x) = (599 - 0.21\sqrt{x} ) dx[/tex]

On integrating both sides, we get

[tex]\int\ d R(x) = \int\ (599 - 0.21\sqrt{x} ) dx[/tex]

R(x) = [tex]599x - 0.21 X \frac{2}{3}x^{3/2}[/tex] + C

R(x) = 599x - 0.14[tex]x^{3/2}[/tex] + C       ...........(i)

Also given, at x = 0, R(x) = 0, Put these values in equation (i), we get

0 = 0 - 0 + C

C = 0

Put the value of C in equation (i), we get

R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

Thus, the integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

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Tony will have 486 cookies if he bakes 10 batches more.

Take two points from table: (8, 234), (9, 252)

Find slope:

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

[tex]\rightarrow slope \ (m) : \dfrac{252-234}{9-8} = 18[/tex]

This determines that one batch of cookies has 18 cookies.

So, if he bakes 10 more batches:

(10 × 18) = 180 cookies

Total cookies he then will have:

306 cookies + 180 cookies = 486 cookies.

Answer: the correct is x=1,

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

x=1

Answer:

1

Step-by-step explanation:

you can plug it in and it gives you 3-1 which results in 2 as the question asks for

Answer:

x=4, y=-2, p=14

Step-by-step explanation:

First simplify the LHS:

[tex]LHS = (16p^8)^\frac{3}{2} \times (216p^{-3})^{-\frac{2}{3}}[/tex]

[tex]= 64 p^{12} \times \frac{1}{36} p^{2}[/tex]

[tex]=\frac{16}{9}p^{14}[/tex]

[tex]=\frac{2^4}{3^2}p^14\\=2^43^{-2}p^{14}[/tex]

Hence x=4, y=2, p=14

Answer:

16

Step-by-step explanation:

he missed 25%

if 4 = 25% then 16 questions total

4*4=16 and 25% * 4 = 100%

Answer: 16 problems

Step-by-step explanation:

First find out how many John got wrong. 100%-75%=25%. Then do cross multiplication: 4*100=25x; 400=25x. Divide 25 on both sides and... BOOM! you get 16 problems.