Find a quadratic function that includes the set of values below.
(0,5), (2.15), (4,9)
The equation of the parabola is y=

Answer:

b

Step-by-step explanation:

The volume in units of cubic inches is 101.63 cubic inches.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

1 quart is equal to 57.75 cubic inches. So, to convert a volume of 1.75 quarts to cubic inches, we multiply by 57.75:

1.75 quarts × 57.75 cubic inches/quart = 101.63 cubic inches

Therefore, the volume of the box of ice cream in cubic inches is 101.63 cubic inches.

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Eight faces!!!

In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices.

Hope this helps! :D

Answer: y = \(\frac{-19}{2} x + \frac{219}{2}\)

Step-by-step explanation:

1. Find the slope

2. Substitute the slope, along with x and y coordinates into linear equation to solve for y-intercept

3. Write equation

I'm kind of late but if you need more help, feel free to ask :)

Therefore, the perimeter of the square is increasing at a rate of 3 * sqrt(2) inches per minute.

Let's denote the side length of the square as "s" (in inches) and the diagonal as "d" (in inches).

We know that the diagonal of a square is related to the side length by the Pythagorean theorem:

d^2 = s^2 + s^2

d^2 = 2s^2

s^2 = (1/2) * d^2

Differentiating both sides with respect to time (t), we get:

2s * ds/dt = (1/2) * 2d * dd/dt

Since we are given that dd/dt (the rate of change of the diagonal) is 3 inches per minute, we can substitute these values:

2s * ds/dt = (1/2) * 2d * 3

2s * ds/dt = 3d

Now, we need to find the relationship between the side length (s) and the area (A) of the square. Since the area of a square is given by A = s^2, we can express the side length in terms of the area:

s^2 = A

s = sqrt(A)

We are given that the area of the square is 18 square inches, so the side length is:

s = sqrt(18) = 3 * sqrt(2) inches

Substituting this value into the previous equation, we can solve for ds/dt:

2 * (3 * sqrt(2)) * ds/dt = 3 * d

Simplifying the equation:

6 * sqrt(2) * ds/dt = 3d

ds/dt = (3d) / (6 * sqrt(2))

ds/dt = d / (2 * sqrt(2))

To find the rate at which the perimeter (P) of the square is increasing, we multiply ds/dt by 4 (since the perimeter is equal to 4 times the side length):

dP/dt = 4 * ds/dt

dP/dt = 4 * (d / (2 * sqrt(2)))

dP/dt = (2d) / sqrt(2)

dP/dt = d * sqrt(2)

Since we know that the diagonal is increasing at a rate of 3 inches per minute (dd/dt = 3), we can substitute this value into the equation to find dP/dt:

dP/dt = 3 * sqrt(2)

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The area of a shape is the amount of space the shape can take. The following are the results of the computations:

A. Number of cans that can fit along the lengths of the boxes

Given that:

\(d = 76mm\) ---- the diameter of the can

\(L_1 = 36cm\) -- the length of the first box

\(L_2 = 50cm\) -- the length of the second box

The number of cans (n) is calculated by:

\(n = \frac{Length}{diameter}\)

For the first box:

\(n_1 = \frac{L_1}{d}\)

\(n_1 = \frac{36cm}{76mm}\)

Convert mm to cm

\(n_1 = \frac{36cm}{76cm\times 0.1}\)

\(n_1 = \frac{36cm}{7.6cm}\)

\(n_1 = 4.736...\)

Remove the decimal part (do not approximate)

\(n =4\)

For the second box

\(n_2 = \frac{L_2}{d}\)

\(n_2 = \frac{50cm}{76mm}\)

Convert mm to cm

\(n_2 = \frac{50cm}{7.6cm}\)

\(n_2 = 6.578..\)

Remove the decimal part (do not approximate)

\(n_2 = 6\)

Hence, 4 cans can fit the along the lengths of the first box, while the second box can take 6 cans, along its length.

B. Number of cans that can fit along the widths of the boxes

Given that:

\(W_1 = 25cm\) -- the width of the first box

\(W_2 = 20cm\) -- the width of the second box

The number of cans (n) is calculated by:

\(n = \frac{Width}{diameter}\)

For the first box:

\(n_1 = \frac{W_1}{d}\)

\(n_1 = \frac{25cm}{76mm}\)

Convert mm to cm

\(n_1 = \frac{25cm}{7.6cm}\)

\(n_1 = 3.2894...\)

Remove the decimal part (do not approximate)

\(n_1 =3\)

For the second box

\(n_2 = \frac{W_2}{d}\)

\(n_2 = \frac{20cm}{76mm}\)

Convert mm to cm

\(n_2 = \frac{20cm}{7.6cm}\)

\(n_2 = 2.631...\)

Remove the decimal part (do not approximate)

\(n_2 = 2\)

Hence, 3 cans can fit the along the width of the first box, while the second box can take 2 cans, along its width.

C. Number of cans that can fit on the bases of the boxes

First, we calculate the area of the base of the can.

The base of the can is circular; so the area is:

\(Area = \pi r^2\)

Where:

\(r = \frac d2 = \frac{76mm}{2} =38mm = 3.8cm\)

So, we have:

\(Area = 3.14 \times 3.8^2\)

\(Area = 45.3416cm^2\)

Next, calculate the areas of the base of the box

The boxes are rectangular ; so, the area is:

\(Area=Length \times Width\)

For the first box;

\(A_1 =36cm \times 25cm\)

\(A_1 =900 cm^2\)

For the second box;

\(A_2 = 50cm \times 20cm\)

\(A_2 = 1000cm^2\)

So, the number of cans on the bases is:

\(n = \frac{Area\ of\ base}{Area\ of\ can}\)

For the first box:

\(n_1 = \frac{900cm^2}{45.3416cm^2}\)

\(n_1 = 19.85\)

Remove the decimal part (do not approximate)

\(n_1 = 19\)

For the second box;

\(n_2= \frac{1000cm^2}{45.3416cm^2}\)

\(n_2 = 22.05\)

Remove the decimal part (do not approximate)

\(n_2 = 22\)

Hence, 19 cans can fit the base of the first box, while the base of the second box can take 22 cans.

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comparing with:

Then a = 1 and b=3

To find the y-intercept, substitute x=0

The y-intercept is 1

Comparing with

The value of a =-1 and the value of b is 3

To find the y-intercept, substitute x=0 into the equation

y=-1

The y-intercept is -1

Answer:

12 minutes

Step-by-step explanation:

Since Zack can eat 5 hot dogs every minute divide the 60 hot dogs he wants to eat by 5 and you would get 12 (the amount of minutes)

I hope this is easy to understand:)

Answer:

9 minutes

Step-by-step explanation:

You want to write this as an equation in order to find out how many minutes it will take. So it will look something like this:

15+5x=60

-15       -15

Then you want to get like terms together

5x=45

And divide to get x alone

x=9.

So 9 minutes

Check the picture below.

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill\)

\(\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}\)

Answer:

Charlene claim is true.

Step-by-step explanation:

Max claims that a point on any line that is perpendicular to a segment is equidistant from a segment's endpoints.

It is not necessary as  shown in the diagram (a).

Charlene claims that the line must be a perpendicular bisector for a point on the line to be equidistant from a segment's endpoints.

It is true as shown in the diagram (b).

So, Charlene claim is true.

Answer:

245 + 35x = 560

Step-by-step explanation:

35 x 7 = 245 (for monday)
Then the equation should be

245 + 35x = 560

It looks like you solved it too, your answer is correct btw! Lmk if you need help with the steps, or anything

Also, how you make this equation is this, you put how much he earned for monday, and then add it to 35x (x being the amount of cars he did) make sure to do = 560 at the end so you can solve it :)

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Step-by-step explanation:

Since he gets  35$ for every car he washes and washed seven cars on Monday, he got 35*7=245. Now, you can minus the amount from it to 315. 315/35 is 9, so nine is your answer.

To phrase it into an equation, you can do when x=amount of cars washed, 35x=560-7*35.

Hope this helped!

Answer:

C)   y = -3x + 15

Step-by-step explanation:

Let's start with the hours required, 15.  For each day worked we can subtract 3 hours.  X days would mean 3x hours.  Subtract that from the goal of 15 hours:

15 - 3x

The time remaining, y, is given by the equation 15 - 3x.

Rearrange the equation to match the format in the options,

y = 15 - 3x

y = -3x + 15

Option C

Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The angles and length of the right triangle are as follows:

WX = 10√141 units

m∠X  = 30°

m∠V = 60°

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right angle triangle is 180 degrees.

Trigonometric ratios can be used to find the side and angles of the right triangle as follows;

Therefore,

Using Pythagoras's theorem,

WX² = (20√47)² - (10√47)²

WX² = 400(47) - 100(47)

WX² = 18800 - 4700

WX = √14100

WX = 10√141

Let's find the angles

sin m∠X  = opposite / hypotenuse

sin m∠X  = 10√47 / 20√47

sin m∠X  = 1 / 2

m∠X  = sin⁻¹ 0.5

m∠X  = 30 degrees

Therefore,

m∠V = 180 - 90 - 30

m∠V = 60 degrees

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Answer:

23,26,29,32,35,38,41,44

Step-by-step explanation:

In mathematics, WHOLE NUMBERS  are the basic counting numbers 0, 1, 2, 3, 4, 5, 6, … and so on.  Whole numbers are the real numbers which includes zero and all the positive integers. Whole numbers don't include negative numbers, fractions, or decimals.  

Answer:

"certain"

Step-by-step explanation:

by definition, any event with a probably of 1 is defined as certain (i.e certain to happen)

by contract any even with a probably of 0 is defined as impossible (i.e impossible to happen)

Answer:

b

Step-by-step explanation:

6

Answer: k = √27-i

Step-by-step explanation:

Answer:

6 4/9

Step-by-step explanation:

Answer:

6 4/9

Step-by-step explanation:

i hope this help have a nice day

Answer:

B

Step-by-step explanation:

six is 6 and since 7 is last in 6.017 then 0.007 and 0.1

i hope this helps

Answer: $28.98

Step-by-step explanation:

To find how much he spent, all you have to do is subract 45.00 and 16.02. 45.00-16.02 is 28.98. So, he spent $28.98 on the camping trip!

The rational roots of the given polynomial f(x)= 20x4 + x3 + 8x2 + x - 12 are x = -4/5 and x = 3/4.

All possible rational roots of f(x) are in the form p/q where p is a factor of constant term and q is the coefficient of leading term. Here, p= -12 and q= 20

Factors of -12= -/+(1,2,3,4,6,12)

Factors of 20= -/+(1,2,4,5,10,20)

So the rational roots = -/+ (1, 2, 3, 4, 6, 12)/ (1, 2, 4, 5, 10, 20)

Solving for x when f(x) = 0,

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

Equating all factors to zero, we get

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x = i, x = -i

Hence, the rational roots are x = 3/4, x = -4/5.

The given question is incomplete, the complete question is

What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12?

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Software engineer seeks promotion, complex problem. Expert guidance or economic literature recommended for comprehensive solution.

The given problem involves analyzing different scenarios related to a software engineer seeking a promotion in a tech firm. It covers the outcomes and implications of various options available to the employee, including taking a sabbatical for an Executive MBA degree and disclosing GPA to the manager.

To provide a complete solution and analysis for all the parts, it would require a detailed explanation and mathematical modeling. Given the complexity and length of the problem, it is not feasible to provide a complete solution within the constraints of this text-based interface.

It would be best to consult relevant economic literature or seek expert guidance to fully address and solve the problem.

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Answer:

17 feet

Step-by-step explanation:

We have to use the pythagorean theorem, this is actually a bit more complicated than it seems at a first glance.

If Tony is 8 feet to Lexi's right, then we can form a triangle as such

I can't paste it (sorry)

but we can use the formula a^2+b^2=c^2, so 15^2=225, and 8^2=64, and 225+64=289, and \(\sqrt289=17\)

so they're 17 feet apart!

(a) The value of β that makes fX(x) a valid pdf is β = 0.2.

(b) The cdf for the random variable X is FX(x) = (3\(x^3\)/10), for 0 < x ≤ 1.

(c) The probability that the random variable P(X > 2) = 0, since the range of possible values for X is from 0 to 1.

To find the value of β that makes fX(x) a valid pdf, we need to ensure that the area under the pdf from 0 to 1 is equal to 1.

∫0¹ fX(x) dx = ∫0¹ 0.6(x²/β) dx = 0.6/β ∫0¹ x² dx = 0.6/β [\(x^3\)/3]0¹ = 0.6/β * (1/3) = 1

Solving for β, we get:

0.6/β * (1/3) = 1

β = 0.6/3 = 0.2

Therefore, β = 0.2 makes fX(x) a valid pdf.

To find the cdf for the random variable X, we integrate the pdf from 0 to x:

FX(x) = ∫\(0^x\) fX(t) dt = ∫\(0^x\) 0.6(t²/0.2) dt = 3\(t^3\)/10|\(0^x\) = (3\(x^3\)/10) - 0

Therefore, the cdf for X is:

FX(x) = (3\(x^3\)/10), for 0 < x ≤ 1

To find the probability that X is greater than 2, we need to use the fact that the probability of an event outside the sample space is 0. Since the range of possible values for X is from 0 to 1, the probability that X is greater than 2 is 0.

P(X > 2) = 0

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Step-by-step explanation:

I hope this will help you