Follow the process of completing the square to solve x2 - 10x + 8 = 0. What is the value of the constant that will be isolated on the right side of the equation in step 3? -8 -12 -32

edg2021

Answer:

The arc length of a circle is 31.5.

Step-by-step explanation:

The arc length can be found as follows:

[tex] arc = r\theta [/tex]

Where:

arc: is the length of the arc of the circle

r: is the radius = 7

θ: is the angle = 4.5 rad        

[tex] arc = r\theta = 7*4.5 = 31.5 [/tex]

Therefore, the arc length of a circle is 31.5.

I hope it helps you!

Answer:

11+3x=68

x=19

Step-by-step explanation:

11+3x=68 is your equation.

subtract 11 from both side to get 3x alone

3x=68-11

3x=57

divide 3 from both sides to get x alone

x=57/3

x=19

19 is your number.

Answer:

25%

Step-by-step explanation:

Question:

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.

Type of Crust Number Sold

Thin crust          312

Thick crust          245

Stuffed crust          179

Pan style                  304

Based on this information, of the next  4500 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answer:

1060 thick crusts

Step-by-step explanation:

Given

The above table

Required

Expected number of thick crust for the next 4500

For last week data, calculate the proportion of thick crust sold

[tex]\hat p = \frac{Thick\ crust}{Total}[/tex]

[tex]\hat p = \frac{245}{312+245+179+304}[/tex]

[tex]\hat p = \frac{245}{1040}[/tex]

[tex]\hat p = 0.235577[/tex]

For the next 4500;

[tex]n = 4500[/tex]

The expected number of thick crust is (E(x)):

[tex]E(x) = \hat p * n[/tex]

[tex]E(x) = 0.235577 * 4500[/tex]

[tex]E(x) = 1060.0965[/tex]

[tex]E(x) \approx 1060[/tex]

Answer: The domain of the function y = (x - 4)(x - 6) is all real numbers, since there are no restrictions on the values that x can take. The range of the function is also all real numbers.

To see why this is the case, we can rewrite the function in standard form by expanding the product: y = (x - 4)(x - 6) = x^2 - 10x + 24. This is a quadratic function with a positive leading coefficient, so its graph is a parabola that opens upwards. The vertex of the parabola is at x = -b/2a = 10/2 = 5, and y = (5 - 4)(5 - 6) = -1. Since the parabola opens upwards, it extends infinitely upwards from its minimum value at the vertex. Therefore, the range of the function is all real numbers greater than or equal to -1.

So, the domain of y = (x - 4)(x - 6) is all real numbers and its range is all real numbers greater than or equal to -1.

Step-by-step explanation:

Answer:

[tex]y = {x}^{2} - 10x + 24[/tex]

Domain: all real numbers

Range: all real numbers > -1

Let V be the volume of the conical vessel and r and h be the radius and height of the vessel respectively. Given that: V = (1/3)πr²hLet V' be the volume of the water that is added to the vessel. The volume of the water in the vessel with a depth of 12 cm is given by: V₁ = (1/3)πr₁²h₁where h₁ = 12 cm. We know that 23 cubic meters of water are poured into the vessel, which is equivalent to 23,000 liters or 23,000,000 cubic centimeters.

Thus:23,000,000 = (1/3)πr₁²(12)Simplifying and solving for r₁, we get: r₁ = 210.05 cm Using similar triangles, we know that :r/h = r₁/h₁ where r is the radius of the water surface when the depth is 18 cm. Thus: r/h = 210.05/12Therefore:r = (210.05/12)·18 = 3,152.5/6 ≈ 525.4 cm The new volume of the water with a depth of 18 cm is given by: V₂ = (1/3)πr²h₂where h₂ = 18 cm.

Therefore: V₂ = (1/3)π(525.4)²(18) ≈ 21,154,116.9 cubic centimeters The additional volume of water needed is therefore: V' = V₂ - V₁ = 21,154,116.9 - 23,000,000 ≈ -1,845,883.1 cubic centimeters.

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Answer:

67-32=a

if his mom is 67 and he is 32 years younger 67 minus 32 would equal a which is his age

A wardrobe with 3 pants, 5 shirts, and 7 ties, has a possible outcome of 105 outfits and not 15. So the answer is False

False. The number of total possible outfits is not 15. To calculate the number of possible outfits, we need to multiply the number of choices for each item together. In this case, we have 3 choices for pants, 5 choices for shirts, and 7 choices for ties. Therefore, the total number of possible outfits would be 3 x 5 x 7 = 105.

The statement incorrectly states that there are only 15 possible outfits. It's important to consider that when selecting multiple items, the total number of combinations is found by multiplying the number of choices for each item together. In this scenario, with 3 pants, 5 shirts, and 7 ties, there are 105 possible outfits, not 15.

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The average fixed cost of each case will be $25

Average fixed cost = fixed cost / number of cases.

$4500/ 180= $25

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Our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.

To prove the statement using a proof by contradiction, we assume the opposite, namely, that the average of four real numbers is less than all of the numbers. Let's denote the four numbers as a, b, c, and d. We assume that the average of these numbers, which we'll denote as avg, is less than a, b, c, and d.

Now, let's consider the sum of these four numbers: a + b + c + d. The average of these numbers, avg, is calculated by dividing the sum by 4. Therefore, we have avg = (a + b + c + d)/4.

If avg is less than a, b, c, and d, then (a + b + c + d)/4 < a, (a + b + c + d)/4 < b, (a + b + c + d)/4 < c, and (a + b + c + d)/4 < d.

Now, let's consider the sum of these inequalities: (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 < a + b + c + d.

Simplifying the left-hand side, we have (a + b + c + d) + (a + b + c + d) + (a + b + c + d) + (a + b + c + d) < 4(a + b + c + d).

This simplifies to 4(a + b + c + d) < 4(a + b + c + d), which is a contradiction. The left-hand side is greater than the right-hand side, which contradicts our initial assumption.

Therefore, our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.

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Value of x corresponding to P81 is 59.06.

A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3.

The task is to find P81, which separates the bottom 81% from the top 19%.

For any normally distributed variable z with mean u and standard deviation o, the cumulative distribution function is defined as the probability of a standard normal variable being less than or equal to z.

A standard normal distribution has a mean of 0 and a standard deviation of 1.

That is, the variable z can be calculated as: z = (x - u) / o

The value P(z < z0) can be read off a standard normal table for any value z0.

As the normal distribution is symmetric, we can use the fact that P(z < -z0) = 1 - P(z < z0).

We now calculate z as follows: z0 = (P81 + 1) / 2 = 0.9051

From a standard normal table, we can see that P(z < 0.9051) = 0.8186.

Therefore, P(z < -0.9051) = 1 - P(z < 0.9051) = 0.1814.

Now we calculate the corresponding value of x:

z = (x - u) / o-0.9051 = (x - 67.3) / 9.3x = 59.06

Therefore, P81 corresponds to the value x = 59.06.

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Answer:

83°

Step-by-step explanation:

WZ is a straight line. Angles at a straight line add up to 180°.

180 - 97 =83°

Answer:

C

Step-by-step explanation:

y=5x reads "y equals (5 times x)", which we can rephrase to "the value of y is 5 times the value of x"

y=x+5 reads "y equals (x plus 5)", which we can rephrase to "the value of y is 5 more than the value of x".

Ergo, answer C is what we're looking for.

Answer: C

Step-by-step explanation:

in y=5x, we can see a 5 placed in front of x. If there is no addition, subtraction, or division sign between a number and a variable, it always means it's multiplication.

We know now that this is 5 times x.

In y=x+5, we see that 5 is being added to x. Therefore, y is 5 more than x.

So there you have it.

Answer:

Equation below

Step-by-step explanation:

An equation that represents the relationship between m and n is 2(n - 150) - (m + 150) = 50 .

The expression that represents Malik's score after he gets 150 points = m + 150

The expression that represents Nora's score after she loses 50 points = n - 150

Nora's score after her score is doubled = 2(n - 150)

The difference between Nora and Malik's score is 50. This can be represented as:  2(n - 150) - (m + 150) = 50

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Answer:

slope=2/3

y intercept=4

Step-by-step explanation:

Answer:

[tex] \sin(m < q) = \frac{7}{9} \\ \sin(m < q) =(0.77777777778) \\ m < q = { \sin 0.77777777778}^{ - 1} \\ m < q = (51.05755873102)[/tex]

The number of edges in the complete bipartite graph is 36

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

K = (4, 9)

The above means that

The vertices in the sets of the bipartite graph are

Set 1 = 4

Set 2 = 9

The number of edges in the complete bipartite graph is then calculated as

Vertices = Set 1 * Set 2

So, we have

Vertices = 4 * 9

Evaluate

Vertices = 36

Hence, there are 36 edges in the bipartite graph

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Answer:

Upper right corner.

Step-by-step explanation:

I took the test and that one was right. Hope this helps!

Answer:

36 kilograms

Step-by-step explanation:

Since she made 8 kilograms of dough over the span of 2 hours, you divide 8 by 2 and get 4 then you have to multiply 9 hours by 4 kilograms of dough to get 36 kilograms of dough.

Answer:

110.92

Step-by-step explanation:

Assuming that the parameters (P), (h), and (B) all represent dimensions of the given prism, then based on the given information, the following can be concluded:

P = 6.6

h = 4.5

B = 2.2

The surface area is the two-dimensional area around a three-dimensional surface. In other words, if one was going to wrap the figure, the surface area is the amount of paper one would need. One can find the surface area by finding the area of each individual side and then adding all the results together. To find the area of a 2-dimensional figure by multiplying the length by the width.

(4.5) * (6.8) = 30.6

(4.5) * (6.8) = 30.6

(2.2) * (6.8) = 14.96

(2.2) * (6.8) = 14.96

(4.5) * (2.2) = 9.9

(4.5) * (2.2) = 9.9

Now add up all of the values,

30.6 + 30.6 + 14.96 + 14.96 + 9.9 + 9.9

= 110.92

Answer:

QT=8 VQ=17 this is what i came up with because i myself have ur question and i don't know what it is?

Yes, if ƒ is differentiable on (0, 1), then ƒ is uniformly continuous on (0, 1).

In mathematics, the concept of differentiability plays a crucial role in understanding the behavior of functions. If a function ƒ is differentiable on the interval (0, 1), it means that the derivative ƒ'(x) exists for every point x in that interval.

The answer states that if a function is differentiable on (0, 1), then it is uniformly continuous on the same interval.

To understand this result, we need to consider the properties of differentiability and uniform continuity.

Differentiability implies that the function has a well-defined tangent line at every point within the interval. This implies that the function cannot exhibit abrupt changes or discontinuities, as it must be smooth and continuous.

Uniform continuity, on the other hand, deals with the behavior of a function as the input values get arbitrarily close to each other. It ensures that the function does not exhibit extreme fluctuations or rapid oscillations.

If a function is differentiable on (0, 1), then it satisfies the conditions required for uniform continuity. This is because the derivative of the function acts as a measure of its rate of change.

If the derivative is bounded (i.e., it does not become infinitely large or small), then the function can be guaranteed to be uniformly continuous.

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The length of the curve y = tan x, -7/3 ≤ x < 0 is approximately 4.481 units.

To calculate the length of the curve, we can use the arc length formula. For a function y = f(x) on the interval [a, b], the arc length is given by the integral:

L = ∫[a,b] √(1 + (f'(x))²) dx,

where f'(x) represents the derivative of f(x) with respect to x.

In this case, the function is y = tan x and the interval is -7/3 ≤ x < 0. To find the derivative, we differentiate y = tan x with respect to x, which gives:

y' = sec² x.

Now we can substitute these values into the arc length formula:

L = ∫[-7/3,0] √(1 + (sec² x)²) dx.

Simplifying the expression under the square root gives:

L = ∫[-7/3,0] √(1 + tan⁴ x) dx.

To evaluate this integral, we can make a substitution. Let u = tan x. Then du = sec² x dx. Using this substitution, the integral becomes:

L = ∫[tan(-7/3),tan(0)] √(1 + u⁴) du.

Now we need to find the limits of integration. Since -7/3 ≤ x < 0, we can evaluate the tangent function at these values to get:

L = ∫[tan(-7/3),0] √(1 + u⁴) du.

Finally, we can use numerical methods or a calculator to evaluate this integral. The result is approximately 4.481 units.

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Answer:

2x+25/12

Step-by-step explanation:

Hope this helps and have a great day!!!!!

Answer:

(6, 4 )

Step-by-step explanation:

Given the 2 equations

9x - 2y = 46 → (1)

x + 2y = 14 → (2)

Adding the 2 equations term by term will eliminate the y- term

10x + 0 = 60

10x = 60 ( divide both sides by 10 )

x = 6

Substitute x = 6 into either of the 2 equations and solve for y

Substituting into (2)

6 + 2y = 14 ( subtract 6 from both sides )

2y = 8 ( divide both sides by 2 )

y = 4

solution is (6, 4 )

Answer:

3 2/5

Step-by-step explanation:

Add the distance she already ran, and subtract the sum from the total she needs to run.

Add two distances she ran:

3 1/2 + 2 1/2 = 3 + 2 + 1/2 + 1/2 = 5 + 1 = 6

Subtract sum from total:

9 4/10 - 6 = 3 4/10 = 3 2/5

Answer:

She needs to run 3 4/10 more miles

Step-by-step explanation:

If you add the amount she ran on Monday and the amount she ran on Tuesday you get 6 miles then subtract the 6 miles minus 9 4/10 you will get 3 4/10.

Answer:

27 1/6

Step-by-step explanation:

14 + 12=26

4+3=7

26 7/6= 27 1/6