Find the vertex of the parabola whose equation is y = -2x2 + 8x - 5.

A-(2, 27)
B-(2, 19)
C-(2, 3)

WILL MARK BRAINLIEST -JAYVEE

a. The third-order Taylor polynomial,  P3(x) = f(xo) + f'(xo)(x - xo) + (f''(xo)(x - xo)^2)/2 + (f'''(xo)(x - xo)^3)/6.

b. The polynomial P3(x) obtained in part a can be used to approximate f(0.1).

c. The polynomial P3(x) obtained in part a can be used to approximate the integral of (1+x)/(1+x^2) from 0 to 0.1.

a. To calculate the third-order Taylor polynomial P3(x) about xo for f(x), we need to find the values of f(x), f'(x), f''(x), and f'''(x) at x = xo. Once we have these values, we can use the formula: P3(x) = f(xo) + f'(xo)(x - xo) + (f''(xo)(x - xo)^2)/2 + (f'''(xo)(x - xo)^3)/6. Plugging in the values of f(xo), f'(xo), f''(xo), and f'''(xo) will give us the third-order Taylor polynomial.

b. The polynomial P3(x) obtained in part a can be used to approximate the value of f(0.1). We can substitute x = 0.1 into P3(x) to obtain the approximation.

c. Similarly, the polynomial P3(x) obtained in part a can be used to approximate the integral of (1+x)/(1+x^2) from 0 to 0.1. We can evaluate the polynomial P3(x) at x = 0.1 and substitute the result into the integral expression.

In summary, the third-order Taylor polynomial P3(x), about xo, for f(x) is calculated using the formula involving the values of f(xo), f'(xo), f''(xo), and f'''(xo). This polynomial can then be used to approximate the value of f(0.1) and the integral of a given function.

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The volume of the solid with a circular base of radius 3, where every plane cross-section perpendicular to the x-axis is an equilateral triangle, is option D) 36√3.


When each plane cross-section perpendicular to the x-axis is an equilateral triangle, we can see that the height of each equilateral triangle is equal to the diameter of the circular base, which is 6. Therefore, the height of the solid is 6.

To find the volume of the solid, we can use the formula for the volume of a cone, since the solid resembles a cone with equilateral triangular cross-sections. The volume of a cone is given by V = (1/3)πr^2h, where r is the radius of the circular base and h is the height.

Plugging in the values, we have V = (1/3)π(3^2)(6) = 18π. Simplifying, we get V = 54π.

Now, since the answer choices are in terms of √3, we can approximate π as 3.14. Therefore, V ≈ 54(3.14) = 169.56.

Rounding to the nearest whole number, the volume is approximately 170.

However, none of the answer choices provided are 170. The closest option is D) 36√3, which is approximately 187.45. Therefore, the correct answer is D) 36√3.


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Answer:

(5,-1)

Step-by-step explanation:

Answer:

-5.75736     or    [tex]\frac{1}{-10+3√2}[/tex]

Step-by-step explanation

Answer:

Graph B. is the one

Step-by-step explanation:

Can i have brainliest

Answer:

b is the right answer

Step-by-step explanation:

(x,y)

There are 380 ways to determine the first and second place in the race.

In a race, there are 20 runners. Trophies for the race are awarded to the runners finishing in first and second place. In how many ways can first and second place be determined?When the trophies for the race are awarded to the runners finishing in first and second place, then it means that there are only two trophies to be awarded. Now, the number of ways in which the two trophies can be awarded can be calculated by permutation, which is a way of counting the arrangements or selections of objects in which order is important.

To determine the number of ways first and second place can be determined in a race with 20 runners, we can use the concept of permutations.

The first-place finisher can be any one of the 20 runners. After the first-place finisher is determined, there are 19 remaining runners who can finish in second place. Therefore, the number of ways to determine the first and second place is given by:

Number of ways = 20 * 19 = 380

So, there are 380 ways to determine the first and second place in the race.

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The exact value of A in the general solution y = A + cx is 75

From the question, we have the following parameters that can be used in our computation:

y = A + cx

The differential equation is given as

y - xy' = 75

When y = A + cx is differentiated, we have

y' = c

So, we have

y - xc = 75

Recall that

y = A + cx

So, we have

A + cx - xc = 75

Evaluate the like terms

A = 75

Hence, the value of A in the general solution is 75

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The value of a in the given function is 4

To find the value of a in the equation f(g(x)) = (1 - x²)³, we need to substitute the function g(x) = a + x² into the function f(x) = (5 - x)³.

Replacing x in f(x) with g(x), we have:

f(g(x)) = (5 - g(x))³.

Substituting g(x) = a + x², we get:

f(g(x)) = (5 - (a + x²))³.

f(g(x)) = (5 - a - x²)³.

Comparing this expression with (1 - x²)³, we can equate the corresponding terms:

5 - a - x² = 1 - x².

5 - a = 1.

a = 5 - 1

a = 4

Therefore, the value of a is 4.

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Answer:

-5/4

Step-by-step explanation:

Pick two points on the line

(-4,0) and (0,-5)

We can use the slope formula

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

   = ( -5 -0)/(0 - -4)

    = (-5-0)/(0+4)

    = -5/4

Answer: -5/4

Step-by-step explanation:

Pick two points on the line

(-4,0) and (0,-5)

We can use the slope formula

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

  = ( -5 -0)/(0 - -4)

   = (-5-0)/(0+4)

   = -5/4

- Chilio

Answer:

Step-by-step explanation: 1.4 x the amount of years = 7 then 23000 divided by 7 = 3,285.7

(a) The Z-Score is 1.78,

(b) The two sample-sizes are 5070 and 1268,

(c) The researchers should choose the 2% margin-of-error.

Part (a) : To find Z, we use the confidence-level (CL) to find the corresponding Z-score.

The confidence-level (CL) is given as 92.5%, which corresponds to an area of 0.925 under the standard normal-distribution curve. Since the remaining area on both tails is (1 - 0.925) = 0.075, we divide this value by 2 to get the area for one tail: 0.075/2 = 0.0375,

The "Z-score" that corresponds to area of 0.0375 in one tail. The Z-score is approximately 1.78,

Part (b) : To determine the two sample sizes for the 1% and 2% margin of error, we use the formula,

Sample size (n) = (Z² × σ²)/(E²),

For a 1% margin-of-error (E = 0.01),

We have,

n₁ = (1.78² × 0.4²)/(0.01²),

n₁ ≈ 5070

For a 2% margin of error (E = 0.02),

We have,

n₂ = (1.78² × 0.4²)/(0.02²),

n₂ ≈ 1268

Part (c) : The researchers should choose the margin-of-error that results in the least possible number of respondents since they have a limited budget.

Comparing the two sample-sizes, we find that sample-size for 2% margin of error (n₂ ≈ 1268) is smaller than the sample-size for the 1% margin of error (n₁ ≈ 5070).

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Given: A = 43.7°, a = 8.7, and b = 10.3We can find the number of possible triangles by using the Law of Sines, which states that a / sin A = b / sin B = c / sin C, where a, b, and c are the side lengths and A, B, and C are the opposite angles. Let's first use the Law of Sines to find the value of sin B: a / sin A = b / sin B => sin B = b sin A / a.

Substituting the given values, we get: sin B = 10.3 sin 43.7° / 8.7≈ 0.641Now we know the value of sin B. We can use the inverse sine function (sin⁻¹) to find the possible values of angle B: B = sin⁻¹ (0.641)≈ 40.4° or B ≈ 139.6°Note that there are two possible angles for B because sine is a periodic function that repeats every 360°.Now that we know the possible values of angle B, we can use the fact that the sum of the angles of a triangle is 180° to find the possible values of angle C: C = 180° - A - B. For B = 40.4°, we get: C = 180° - 43.7° - 40.4° = 95.9°For B = 139.6°, we get: C = 180° - 43.7° - 139.6° = -2.3°Note that we get a negative value for angle C in the second case, which is not possible because all angles of a triangle must be positive. Therefore, the second case is not valid and we only have one possible triangle. Answer: There is only one possible triangle.

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Answer:

it's the third option

Step-by-step explanation:

I think I'm pretty sure

hope this helped ;)

Answer:

The angle that will be congruent to angle 4 is :

                             Angle 1

Step-by-step explanation:

It is given that:

angle 4 and angle 5 are complements.

Also, angle 1 and angle 5 are complements.

Congruent complementary Theorem--

It states that if two angles are complementary to the same angle, then the two angles are congruent to each other.

Here both angle 1 and angle 4 are complementary to the same angle i.e. angle 5.

Area= 1/2 (a+b)h

1/2(1in. +3in.)1in.

1/2(4in.)1in.

2in.× 1in.

2in. Therefore the area is 2in.

Answer:

121 centimeters ²

Step-by-step explanation:

Area of a square = length ²

Each side of a square = 5x

find the area of the square when x = 2.2 centimeters

Area of a square = length ²

= (5x)²

= 5x * 5x

= 5(2.2) * 5(2.2)

= 11 * 11

= 121 centimeters ²

Area of a square = 121 centimeters ²

Trick question! All are rational numbers.

..................................................................................

On average, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00.

The F-ratio is a statistic used in analysis of variance (ANOVA) tests to compare the variances between groups. In the context of hypothesis testing, the F-ratio measures the ratio of the variability between groups to the variability within groups. When the null hypothesis is false, it means that there is a significant difference between the groups being compared.

If the null hypothesis is false, it implies that there are systematic differences between the groups, resulting in larger variation between groups compared to within groups. This leads to a higher F-ratio value. The F-ratio is calculated as the ratio of the mean square between groups to the mean square within groups. As the differences between groups become more pronounced, the F-ratio increases, indicating a greater likelihood of rejecting the null hypothesis.

Therefore, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00, indicating significant variability between groups.

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Answer:

she needs 1/3 chocolate bars

Step-by-step explanation:

8 × 2/3

=5 1/3

Answer:

Rewrite the question correctly! it's totally absurd

Realizing that the mental barriers of being scared to be wrong or too slow were getting in the way and stopping his kids from even attempting to solve problems, Gallin decided to change his approach.

Answer:

y=7, x=7

Step-by-step explanation:

They both equal y, so you can set the right part of the equations equal to each other

4x-21=2x-7

solve for x

2x-21=-7

2x=14

x=7

knowing x, we can now substitute back into one of the original equations to find y

y=4(7)-21=28-21=7

or

y=2(7)-7=14-7=7

Answer:

I got about 28.01 ft you might want to round or something

hope this helped

The required stopping distance of the car is 17.24 metes.

A child appears to be running into the street ahead. It takes 2.3 seconds for the driver to react and begin to brake, but this time at a rate of -7.5 m/s2. What is the stopping distance for the car in this situation is to be determined.

Speed is ratio of distance to the time. speed = distance / time.

The intial speed of the driver is 11m/s

Now total stopping distance = thinking distance + break applying distance
                                           =  v*t  + u²/2a
                                           =  11 * 2.3 - 11²/2*7.5
                                           = 17.24 meters,

Thus, the required stopping distance of the car is 17.24 metes.

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Answer:

6t(2t - 1)

Step-by-step explanation:

12t² - 6t

Common factor: 6t

Factored:

6t(2t - 1)

The equation rearranged to isolate c is c = b / (a - b/d).

To isolate c in the equation a = b(1/c - 1/d), we can follow these steps:

Start with the equation a = b(1/c - 1/d).

Distribute b to the terms inside the parentheses: a = b/c - b/d.

Move the term b/c to the other side of the equation by subtracting it from both sides: a - b/c = -b/d.

Multiply both sides of the equation by c to eliminate the denominator in the left term: c(a - b/c) = -b/d * c.

Simplify the left side by distributing c: ac - b = -bc/d.

Move the term -bc/d to the other side of the equation by adding it to both sides: ac - b + bc/d = 0.

Factor out c on the right side of the equation: ac + c(-b/d) - b = 0.

Combine like terms: ac - (b/d)c - b = 0.

Factor out c: c(a - b/d) - b = 0.

Add b to both sides of the equation: c(a - b/d) = b.

Finally, isolate c by dividing both sides of the equation by (a - b/d): c = b / (a - b/d).

Therefore, the equation rearranged to isolate c is c = b / (a - b/d).

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Answer:

4(x+5)

Step-by-step explanation:

according to your question

The counterclockwise circulation of the vector field F around the closed curve C is 112/3 (or approximately 37.33).

To compute the counterclockwise circulation of the vector field F = (-2x + 10y)i + (6x - 8y)j around the closed curve C, we can apply Green's Theorem.

Green's Theorem states that the counterclockwise circulation of a vector field around a closed curve C is equal to the double integral of the curl of the vector field over the region R enclosed by the curve.

First, let's obtain the curl of the vector field F:

curl(F) = (∂F₂/∂x - ∂F₁/∂y)k

= (6 - (-2))k

= 8k

Now, let's obtain the region R enclosed by the curve C. The curve is described by two functions:

Upper curve: y = -3x^2 + 7

Lower curve: y = 4x^2

To get the limits of integration, we need to determine the x-values where the curves intersect. Setting the upper and lower curves equal to each other:

-3x^2 + 7 = 4x^2

7 = 7x^2

x^2 = 1

x = ±1

Since we are only considering the first quadrant, we take the positive value, x = 1.

The limits of integration for x will be from 0 to 1.

For y, the limits are determined by the upper and lower curves:

y = -3x^2 + 7

y = 4x^2

The limits of integration for y will be from 4x^2 to -3x^2 + 7.

Now, we can set up the double integral to calculate the counterclockwise circulation using Green's Theorem:

Circulation = ∬R curl(F) · dA

= ∬R 8k · dA

= 8 ∬R dA

Integrating with respect to x and y over the region R:

Circulation = 8 ∫[0,1] ∫[4x^2, -3x^2 + 7] dy dx

Evaluating the double integral will give us the counterclockwise circulation of F around the closed curve C.

Circulation = 8 ∫[0,1] ∫[4x^2, -3x^2 + 7] dy dx

First, we integrate with respect to y:

Circulation = 8 ∫[0,1] [y] |[4x^2, -3x^2 + 7] dx

= 8 ∫[0,1] ((-3x^2 + 7) - 4x^2) dx

= 8 ∫[0,1] (-7x^2 + 7) dx

= 8 [-7/3 * x^3 + 7x] |[0,1]

= 8 [(-7/3 * 1^3 + 7 * 1) - (-7/3 * 0^3 + 7 * 0)]

= 8 [-7/3 + 7]

= 8 [-7/3 + 21/3]

= 8 [14/3]

= 112/3

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The statement is incorrect since one stadium can hold only 80,000 people while the population of Dallas is approximately 1.3 million. 10 stadiums would, therefore, hold a total of 800,000 people.

The Cowboys Stadium in Dallas is a world-famous stadium, with a capacity of up to 80,000 people. The population of Dallas, Texas, USA, is approximately 1.3 million, according to data from 2020.

In other words, Gabriel's assertion that the whole of Dallas could be seated in ten Cowboys Stadiums is incorrect.

Although that's a significant figure, it's just over half of the city's entire population, and more than half of its people would have to be turned away if there were only ten Cowboys Stadiums present.

Therefore, it is essential to double-check such assertions before making them and presenting them as facts. It is better to research and verify information, rather than make claims that are incorrect and spread false information.

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Answer:

87°

Step-by-step explanation: