These 3 points are on a parabola defining the edge of a ski:

(-4,1)
(-2,0.94)
(0,1)
The general form for the equation of a parabola is .


1.
Use the x- and y-values of 1 to build a linear equation with 3 variables: A, B, and C.
Repeat this process with the other 2 points to build a 2nd linear equation.
Record all three equations in the box below.

2.
Build a matrix equation that represents this system of equations. Record your matrix equation here.

3.
Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix. Record your result here.

4.
Use the inverse matrix to solve the system of equations. Record the equation of the parabola here.

Answer:

The 1st one is 540π

The 2nd one is 1696.46

Step-by-step explanation:

To find the volume of a cylinder, you do the following:

[tex](r)^2\pi \times h[/tex]

Where r represents the radius of the circle and h represents the height. Because it's multiplication, we can change it to:

[tex]r^2\times h \times \pi[/tex]

So since the radius is 6, 6^2 is 36. Then we multiply by 15, to get 540. Then now since we don't need to multiply the pi, you just leave it as 540π.

For the second one, multiply 540 by pi to get the answer, then round it to the nearest hudredth to get 1696.46.

Answer:

c

Step-by-step explanation:

y=[tex]\sqrt{x+7}[/tex]

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

the sides of a 30 60 90 triangle are x, 2x, and [tex]x\sqrt{3}[/tex], with [tex]x\sqrt{3}[/tex] being opposite to the 60 degree angle, and x being adjacent to the 60 degree angle. If [tex]x\sqrt{3}[/tex] = 15 (as given from the image), you can calculate x to be [tex]5\sqrt{3}[/tex].

The answer to this question is choice C

Using the Pythagorean Theorem, the altitude to side c has a length of 11.3 inches.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

To find the altitude relative to side c, we bisect this side, which cuts it's length into half(now of 4 inches), forming a right triangle in which:

Hence:

[tex]x^2 + 4^2 = 12^2[/tex]

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

x = 11.3 inches.

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The total amount after 2 years is $2180

The given parameters are:

Principal, P =$2000

Rate, r =4.5%

The interest in 2 years is calculated as:

I = PRT

So, we have:

I = 2000 * 4.5% * 2

Evaluate

I = 180

Hence, the interest after 2 years is $180

This is calculated as:

Amount = P + I

So, we have:

Amount = $2000 + $180

Evaluate

Amount = $2180

Hence, the total amount after 2 years is $2180

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Answer:

-9

Step-by-step explanation:

1.  f(x) = 3(4-x)

2. f(x) = 3(4-7)

3. f(x) = 3(-3)

4. f(x) = -9

[tex]\Large\Box\underline{\textsf{A. What is Asked}}[/tex]

What is the value of the function f(x)=3(4-x) when x=7?

[tex]\Large\Box\underline{\textsf{This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{4cm} \textsf{Put in 7 for x,}\\\textbf{since we're given} \\ that x = 7. \\ \blacksquare^\bigstar\blacksquare \end{minipage}}[/tex]

[tex]\bf{\Box\!\!\!\!\!\bullet f(x)=3(4-7)=3(-3)=\overbrace{-9}}\xleftarrow{ANSWER}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                [tex]\bf{=-9}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Putting different values in the variable could give the total money spend.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Marcy had $10.00 to spend at the state fair. She spent all of it on the ride tickets.

The rides cost either $0.50, $1.00, or $1.25 each.

The equation form;

0.50x + 1.00y + 1.25z = 10

Putting different values in the variable could give the total money spend.

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Answer:

10

Step-by-step explanation:

i add the n subtrasct

the i east

foodooodododo]

999937

3;33

This exercise is about Linear Functions. From the values given, we can state that:

Given that the table represents a  linear function, so the function is a straight line.

Taking two points

(-12, 17)

(-10, 19)

To determine the slope between (-12, 17) and (-10, 19), we need to use the formula:

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

Recall that:

(x1, y1) = (-12, 17); and

(x2, y2) = (-10, 19)

m = 19 -17/-10 -17

m = 1

Leveraging the point-slope to create the linear equation, we have:

y-y1 = m(x-x1)

where m is the slope of the line and (x₁, y₁) is the point substituting the values m = 1 and the point (-12, 17). Hence, we have:

y-y1 = m(x-x1)

→ y-17 = 1 (x-(-12))

→ y - 17 = x +12

y = x + 12 + 17

y = x + 29 ..................................Linear Equation

Next, we substitute x = -8 into the Linear Equation

y = (-8) + 29
y = 21

Hence, the missing y = 21; and

The missing x = -8

If we substitute y = 23 into the equation, we have:

y = x + 29
23 = x + 29
x = 29 - 23

x = 6

Thus, when the value of y = 23, the missing x is = 6

Conclusively,

The value of missing x = 6

The value of missing y = 21

Full Question

Determine any data values that are missing from the table, assuming that the data represent a linear function.

X Ix ly |-12 17 -10 19 -8 23

a. Missing x:-6 Missing y:22

b. Missing x:-7 Missing y:22

c. Missing x:-7 Missing y:20

d. Missing x:-6 Missing y:21

Please select the best answer from the choices provided.

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The fraction π/4 comes from the the ratio of the area of the circle to the area of the square from a cross section.

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

Given that:

Volume of cone = (π/4) * volume of pyramid it fits inside

Ratio of area of cone to area of square = πr²/(2r)²  = πr²/4r² = π/4

The fraction π/4 comes from the the ratio of the area of the circle to the area of the square from a cross section.

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(B.) It is the ratio of the area of the circle to the area of the square from a cross section.

Based on the calculations, we can predict that 2, 3, 4, 5, etc., will make the inequality true.

In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.

Evaluating the given inequality, we have:

-1 ≤ x/2

-2 ≤ x

x ≥ 2.

Therefore, we can predict that 2, 3, 4, 5, etc., will make the inequality true.

Next, we would complete the table to check our prediction:

x        -4     -3     -2      -1     0    1      2    3    4  

x/2     -2    -1.5    -1    -0.5   0   0.5   1    1.5   2

When x = -2:

-1 ≤ -2  (false)

When x = 2:

-1 ≤ 1 (true)

When x = 3:

-1 ≤ 3  (true)

When x = 4:

-1 ≤ 4  (true)

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Complete Question:

1. a. Consider the inequality -1 ≤ x/2.

i. Predict which values of will make the inequality true.

ii. Complete the table to check your prediction.

Answer:

A

Step-by-step explanation:

We know the graph must be a dotted line.

Also, since there is a > sign, the line must be shaded above.

This leaves A as the answer.

The range for the following inequality rounded to nearest hundredth is 46.57≤x≤52.45

In mathematics, an inequality is a relation that holds between two values when they are different. The notation a ≠ b means that a is not equal to b. It does not say that one is greater than the other, or even that they can be compared in size . Inequality are the sign which assign the great and less of amount between to numbers,`<. .>

Let's solve your inequality step-by-step.

16≤1.02x−31.5≤22

Add 31.5 to all parts:

16+31.5≤1.02x−31.5+31.5≤22+31.5

Adding we get:

47.5≤1.02x≤53.5

Divide all parts by 1.02:

47.5/1.02≤1.02x/1.02≤53.5/1.02

Dividing we get:

46.568627≤x≤52.45098

Rounding it to nearest hundredth we get

46.57≤x≤52.45

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Answer:

about 13.9%

Step-by-step explanation:

[tex] \frac{17.699}{127} (100\%) = 13.9\%[/tex]

The probability that all three of the tosses come up heads is 1/8.

Probability determines the odds that an event would happen. The odds of the event happening lies between 0 and 1.

The probability that all three of the tosses come up heads = number of tosses in which the three dimes come heads up / total number of possible outcomes

= 1/8

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Step-by-step explanation:

3x + 2y = 12

2y = 12 - 3x

y = 6 - 3/2 x

so, it is a regular line, not horizontal, not vertical.

the easiest way to graph it is to find the 2 intercepts at the x- and at the y-axis (setting x = 0 gives us the y value for the y-axis intercept, setting y = 0 gives us the x value for the x-axis intercept).

then use a ruler and draw a line through both points and well beyond these 2 points.

x = 0

3×0 + 2y = 12

2y = 12

y = 6

point (0, 6)

y = 0

3x + 2×0 = 12

3x = 12

x = 4

point (4, 0)

The solution to When asked to find the sum of two mixed numbers with different denominators, you should before you add, find a common denominator.

For instance,

4 1/3 + 3 2/5

= 13/3 + 17/5

find common denominator

= (65+51) / 15

= 116/15

= 7 11/15

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The function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers

The given parameters are:

f(x) = 3x - 6; g(x) = 8x +4

The composite function is calculated as:

(f.g)(x) = f(x) * g(x)

This gives

(f.g)(x) = (3x - 6) * (8x + 4)

Expand

(f.g)(x) = 24x^2 + 12x - 48x - 24

Evaluate the difference

(f.g)(x) = 24x^2 - 36x - 24

The above function is a quadratic function;

Quadratic functions have a domain of all set of real numbers

Hence, the function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers

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Answer:

Dude their answers are the same

Step-by-step explanation:

Adding a negative is the same as subtracting

Answer:

Yes, they're both correct

Step-by-step explanation:

They are both correct because both equations are equal. You could rewrite 7x + (-3) as 7x + 1(-3) and when you "distribute" the positive 1 the equation becomes 7x-3 which is the same thing as 7x-3. When you're subtracting 1 you're also technically adding negative 1

When proving the properties of logarithms when exponents must be used, the property that is used in all of these is D. [tex]log_{b} (b^y) = y[/tex]

When proving any property of logarithms that have to do with exponents, one property that should always be used is  [tex]log_{b} (b^y) = y[/tex].

Expressing y as a product of [tex]log_{b} (b^y)[/tex] is the most basic property of using exponents on logs because it has both product, quotient, and power rules of logarithms.

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The first thing we need to do is evaluate the function at its endpoints.

[tex]f(-2)=-1\\\\f(5)=-183[/tex]

Then, we need to find the critical points to find if the stationary points give the absolute min/max values.

[tex]f'(x)=12x^2 - 36x-48=0\\\\x^2 - 3x-4=0\\\\(x-4)(x+1)=0\\ \\ x=-1, 4[/tex]

[tex]f(-1)=33\\\\f(4)=-217[/tex]

So, the absolute maximum is 33 and the absolute minimum is -217

Answer:

1,013,824 different completed answer sheets are possible

Step-by-step explanation:

So let's start with part A. There is 6 questions which have 2 options, because it's a true-false question. With the first question, you can choose 2 options, true or false, from there you can choose true or false. I've attached a diagram which further illustrates this. So as you can see as you answer each question, the amount of combinations get's multiplied by 2, or in other words, the amount of combinations can be expressed as: [tex]2^n[/tex] where n=amount of questions. Since there are 6, there are [tex]2^6[/tex] combinations which is 64 total combinations by the time you answer all 6 questions.

So now from here you can choose either part B or C, and I'm assuming you can't do both, you chose one. So we can treat them as completely separate scenarios, and then after that add the amount of combinations from doing part A/B and part A/C.

So let's start with the scenario that you do part B after part A. part B consists of 6 multiply choice questions and it has 5 options per question. If you remember, the first question, you had 2 initial options, and for each of those 2 initial options, you had 2 more (true/false), then you had 4, then for each of those 4 you had 2, then you had 8. So this relationship can generally be treated as: [tex]a^n[/tex] where a = amount of options, and n = amount of questions. This is because for each question, you're going to have a options, so the first question is going to be "a" amount of  combinations, then the second question, for each combination which is currently a, you're going to have "a" combinations, so now you have a*a combinations and so on... So here you're going to have: [tex]5^6[/tex] choices. which is 15,625. But remember, this is after doing part A. So this means you can extend these amount of combinations to the 64 amount of combinations. I attached another graph to help you understand this. This means you will have 15,625 * 64 combinations which is 1,000,000 combinations if you chose part A then part B

Now let's look at the scenario you chose part A then part C. This isn't an extension onto part B, so we can see them as two separate scenarios. So like two completely different graphs. So for part C, we can use the general equation we used in the previous question: [tex]a^n[/tex]. In this case there are 3 questions, and 6 options, so the amount of combinations is: [tex]6^3[/tex] which is 216, now for reasons explained in the previous paragraph, you need to multiply this by the 64 combinations from part A. This gives you 216 * 64 = 13,824.

So now we calculated part A/B combinations = 1,000,000

and part A/C combinations = 13,824

So adding these together you get: 1,013,824 combinations

Answer:

288π

Step-by-step explanation:

Volume of a cylinder = πr²h

r = radius = 6

h = height = 8

Volume = πr²h

Volume = π × 6² × 8

Volume = π × 36 × 8

Volume = 288π

The amount of money​ you'll have at the end of 10 years is $3900.

Given that, P=$3000, R=3% and T=10 years.

The formula to find the simple interest is [tex]Interest=\frac{P \times T \times R}{100}[/tex].

Now, simple interest [tex]=\frac{3000 \times 10 \times 3}{100}=\$900[/tex].

Amount=Simple Interest+Principal

=900+3000=$3900

Therefore, the amount of money​ you'll have at the end of 10 years is $3900.

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Answer:

Step-by-step explanation:

Formula

c^2 = a^2 + b^2

Givens

Solution

c^2 = 3^2 + 8^2                 Substitute givens

c^2 = 9 + 64                       Combine

c^2 = 73                             Take the square root of both sides

√c^2 = √73  

c = √73                        \

Exact answer

c = √73                                73 is prime. It will break down no further

Approximate answer

c = 8.54400                         Both zeros must be entered

For all rectangles, the area is the length multiplied by the height. For squares (a special type of rectangle), the length and height are the same, so you just use [tex]s^2[/tex], where [tex]s[/tex] is the side length.

[tex]A=s^2=16^2=\boxed{256}[/tex]

The formula for the area of the circle is [tex]\pi r^2[/tex], where [tex]\pi[/tex] is pi, a constant, and [tex]r[/tex] is the radius of the circle, or the length from the center point to the edge.

We're given the side length of the square, which is the same as the diameter of the circle (length from edge to edge going through the center point). Divide the diameter by [tex]2[/tex] to get the radius of [tex]8[/tex] kilometers.

[tex]A=\pi r^2=\pi8^2=\boxed{64\pi}\approx201.1[/tex]

The area of the blue section is simply the area of the square minus the area of the circle since we just want what's left over.

[tex]A=\boxed{256-64\pi}\approx54.9[/tex]

You can keep the answer exact (the boxed expression) or use the approximate value of 54.9, depending on the instructions for the assignment.