Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = 2x − 2 at (1, 0).

Answer:

tbh I don't no but I need the point in sorry but can u please like this to give me points

Step-by-step explanation:

7! = 5040 ways

The value of x is x = -3.

What is solving an equation?

Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics. Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

Consider the given equation,

27 = (1/3)^x

This equation can be written as,

\(27 = \frac{1^x}{3^x}\)

Here 1^x

1\(27 = \frac{1}{3^x}\)

Take 3^x on numerator.

\(27 = 3^-^x\)

Now 27 can be written as,  \(27 = (3)(3)(3) = 3^3\)

⇒ \(3^3 = 3^-^x\)

Applying the exponent rule: \(a^b=a^c\) ⇒ b = c

So we get,

3 = -x

Multiply both sides by -1.

-3 = x

x = -3

Hence the value of x is x = 3.

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If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.

As per the question statement, 31 horses are competing in a show.

We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.

To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.

That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.

To solve this question, we just need to know the formula of permutation which goes as \([(nPr)=\frac{n!}{(n-r)!} ]\),  i.e., we are to select an ordered set or "r" from a set of "n".

As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get

\((31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.\)

That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.

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Answer:

original fraction =12/5

Step-by-step explanation:

let x = numerator

therefore

   x+3/x-7+3 =15/8

    x+3/x-4 =15/8

      8(x+3)=15(x-4)

      8x+24=15x-60

       84=7x

        84/7=x

        12=x

therefore original fraction = 12/5

Answer:

Step-by-step explanation:

The surface area of a sphere is given by the formula:

S = 4πr^2

where S is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 60 square feet. Using the formula above, we can solve for the radius:

60 = 4πr^2

Dividing both sides by 4π, we get:

15/π = r^2

Taking the square root of both sides, we get:

r = sqrt(15/π)

Using 3.14 as an approximation for π, we can evaluate this expression:

r ≈ sqrt(15/3.14)

r ≈ 2.20

Therefore, the best approximation for the radius of the sphere is 2.20 feet.

Answer:

Radius is 2.18

Step-by-step explanation:

;)

Answer:

A Toowoomba and Perth

Step-by-step explanation:

its A on e2020

The smallest portion that Ann can cut out of her plans to stay under budget is option A, Toowoomba and Perth, which has a total cost of $291.

To find the smallest portion that Ann can cut out of her plans, we need to calculate the total cost of all cities and see which one is the highest.

Total cost = $161 + $264 + $198 + $130 + $224 + $301 + $277 = $1,555

Since Ann only has $1,265 budgeted for this portion of her trip, she needs to cut out some cities to stay under budget.

Toowoomba and Perth = $161 + $130 = $291

Hobart = $301

Sydney and Newcastle = $224 + $198 = $422

Bendigo = $277

Thus, the correct option is A.

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Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

a. The present value of these receivables is $42,123.64

b. The total value at the end of 10 years is $69,257.02

c. The present value of these payments is $10,059.37

Step-by-step explanation:

Answer:

should be complementary angles

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer:

Sine of the Angle = opposite / hypotenuse

Sine Angle = 22.8 / 24

Sine Angle = .95

Angle = arc sine (.95)

Angle =  71.805 degrees

Angle = 71.8 (rounded)

Step-by-step explanation:

Answer:

71.8

Step-by-step explanation:

Answer:

Product = \(\dfrac{64}{135}\)

Step-by-step explanation:

The expression is as follows :

\(\dfrac{4}{7}\times \dfrac{8}{9}\times \dfrac{14}{15}\)

We need to find the product of the above expression

As 7 × 2 = 14

So, it will become :

\(4\times \dfrac{8}{9}\times \dfrac{2}{15}\\\\=\dfrac{4\times 8\times 2}{9\times 15}\\\\=\dfrac{64}{135}\)

So, the product of the given fractions is \(\dfrac{64}{135}\).

Answer:

64/135

Step-by-step explanation:

Answer:

2 stickers

Step-by-step explanation:

We multiply his 7 friends by 8 (stickers given to each friend) to get 56 stickers given total.

We subtract 56 from 58 to get 2 stickers remaining for Justin.

Step-by-step explanation:

Justin is giving out 8 stickers to 7 of his friends

To find out how many stickers he passed out, you would need to do 7×8

7×8 = 56

Now you want to subtract 56 from 58 to figure out how many stickers he had left

58 - 56 = 2

Justin is left with 2 stickers

I am sorry if this didn't make sense

I hope this helps!!!!

The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.

Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).

The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.

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Answer:

C. 24 ft.

Step-by-step explanation:

There is a right triangle which can be drawn in side the pyramid with height h, hypotenuse  25 ft and bas = 1/2 * 14 = 7.

So using Pythagoras:

25^2 = h^2 + 7^2

h^2 = 25^2 - 7^2

h^2 = 576

h = √576 = 24 ft.

Answer:

A is indicating a non-linear model.

Step-by-step explanation:

I suppose these are residuals of a linear model, like OLS regression.

A linear model should result with residuals centered around 0 and normally distributed within any range.

In figure A, we see that the residuals have a trend with respect to d2, signing a possible non-linearity.

The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.

The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.

The electric field because of a point charge q is written as \(E=\frac{kq}{r^2}\)

Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,

\(\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}\)

The required answer is -4824 N/C.

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Answer:

The smaller number in 0.01

Step-by-step explanation:

To find this answer, just take the fraction and find the quotient of both numbers.

1.789/178 = 0.01005056179

Now take the quotient and compare it to 0.05.

Is 0.01 larger or 0.05 - the answer is 0.01.

Questions relating Word Problems can sometimes be resolved by taking note of the definition of given clues

The amount of soda lost is approximately 28.27 in.³

The reason the above value is correct is as follows:

The known parameters about the the soda pop served by the restaurant are;

Diameter of the cylindrical pitcher in which the soda pop is sold, D = 6 inches

The height of the cylindrical pitchers, h = 8 inches

Thickness of the head of foam in the pitchers, t = 1 inches

Required:

The amount of soda lost as a result of the head of foam

Method:

Define a pitcher

Calculate the volume occupied by the head of foam

Solution:

A pitcher holds drink and usually has a lip and handle, therefore, the drink is filled level with the pitcher

The volume occupied by the head of foam = The amount of soda lost

The volume occupied by the head of foam, \(\mathbf{V_{(head \ of \ foam)}}\) = The volume of 1 inch height of the foam in the cylindrical pitcher

Volume in a cylinder = Base area × Height

\(\mathbf{Base \ area\ in \ a \ cylinder} =\dfrac{\pi \cdot D^2}{4}\)

The height of the foam = The thickness of the foam = t

∴ \(V_{(head \ of \ foam)} =\mathbf{\dfrac{\pi \cdot D^2}{4} \times t}\) =

Plugging in the values of D, and t, gives;

\(\mathbf{V_{(head \ of \ foam)}} =\dfrac{\pi \times (6 \ in.)^2}{4} \times 1 \ in. = \pi \mathbf{\times 9 \, in.^3}\)

The volume of the head of foam, given to two decimal places is presented as follows;

\(V_{(head \ of \ foam)}\) = π × 9 in.³ ≈ 28.27 in.³

The volume of the head of foam = The amount of soda lost ≈ 28.27 in.³

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A possible equation that relates distance from home (d) and the amount of time (t) is d = tx, which can be expressed as 90= 3x.

An equation relates variables using the equality symbol (=) as well as other symbols such as addition or subtraction. Due to this follow these steps:

Based on this a possible equation is:  d = tx

The missing value can be found by solving the equation 90= 3x.

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The perimeter of the shape is 10 inches.

It's important to note that the perimeter of a shape or calculated by adding all the sides together.

In this case, this is a rectangle and the perimeter will be:

Perimeter = 2(length + width)

Length = 4 inches

Width = 1 inch

Perimeter = 2(length + width)

Perimeter = 2(4 + 1)

Perimeter = 10 inches.

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The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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Answer:

D)     \(\frac{1}{6}\)

g¹(1) =  \(\frac{1}{6}\)

The inverse of the  function   \(g(x) = \frac{x^{\frac{1}{3} }-1 }{2}\)

Step-by-step explanation:

Step(i):-

Given that f(x) = (2x+1)³

 Let  y =  (2x+1)³

       \(y^{\frac{1}{3} } =2x+1\)

      \(2x = y^{\frac{1}{3} } -1\)

       \(x = \frac{y^{\frac{1}{3} }-1 }{2}\)

Step(ii):-

y = f(x) ⇒  x = f⁻¹ (y)

  ⇒ \(f^{-1} (y) = \frac{y^{\frac{1}{3} }-1 }{2}\)

     \(f^{-1} (x) = \frac{x^{\frac{1}{3} }-1 }{2}\)

The inverse of the given function  

        \(g(x) = \frac{x^{\frac{1}{3} }-1 }{2}\)

Differentiating equation (i) with respective to 'x', we get

      \(g^{l} (x) = \frac{1}{2} X \frac{1}{3} x^{\frac{1}{3} -1}\)

     \(g^{l} (x) = \frac{1}{6} x^{\frac{-2}{3} }\)

Final answer:-

Put x=1

  \(g^{l} (1) = \frac{1}{6} 1^{\frac{-2}{3} } = \frac{1}{6}\)

Answer:

b because you sub the 2 numbers i think

I think it is -4 and positive 2

Answer:

2by5=,78

Step-by-step explanation:

if you 9thru7. into8 you get 2by 7