(x - 6)^2 - 12 = x^2- 12x + c. What is the value of c?

The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

What is the right triangle is triangle?

A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using this information, we can determine which of the given sets of side measures could form a right triangle:

A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:

(61 m)² = (60 m)² + (11 m)²

61² = 60² + 11²

61² ≠ 60² + 11²

Since the left side does not equal the right side, these sides cannot form a right triangle.

B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(34 in)² = (24 in)² + (28 in)²

34² = 24² + 28²

34² = 24² + 28²

The left side equals the right side, so these sides could form a right triangle.

C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(55 ft)² = (45 ft)² + (35 ft)²

55² = 45² + 35²

55² = 45² + 35²

The left side equals the right side, so these sides could form a right triangle.

D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:

(48 cm)² ≠ (46 cm)² + (15 cm)²

48² ≠ 46² + 15²

Since the left side does not equal the right side, these sides cannot form a right triangle.

Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

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Answer:

1°

Step-by-step explanation:

cos x= LJ/JK=2.8/9.3

⇒x ≈1°

The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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The most appropriate choice for parabola will be given by-

Equation of  parabola that passes through the point (2, 2) and has a

vertex of (3, -1) is

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

What is parabola?

Parabola is a curve where every point on the curve is equidistant from a fixed point called the focus and a fixed line  called the directrix.

Equation of parabola is \(y = a(x - h)^2+k\) where (h,k) is the vertex of the parabola

Here,

Equation of the parabola with vertex (3, -1) is

\(y = a(x - 3)^2-1\)

The parabola passes through (2, 2)

\(2 = a(2-3)^2-1\\2 = a-1\\a=2+1\\a=3\)

Equation of  parabola that passes through the point (2, 2) and has a

vertex of (3, -1) is

\(y = 3(x-3)^2 - 1\\\)

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

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Answer:

420 + 15 = 435

360 + 45 = 405

435 - 405 = 30.

30 minutes less sunlight

Step-by-step explanation:

Answer:

The east side gets 30 minutes less sunlight.

Step-by-step explanation:

To find the answer we have to subtract 6 hours 45 minutes from 7 hours 15 minutes. As we see that 15 is less than 45, we turn 7 hours 15 minutes to 6 hours 75 minutes, and now we can subtract. 6 hours 75 minutes - 6 hours 45 minutes = 30 minutes. Now, we see that the answer is 30 minutes less sunlight.

Answer:

D. Translate ΔPQR by the rule (x + 1, y − 1), and dilate ΔP′Q′R′ by a scale factor of 2 from point R.

Step-by-step explanation:

I got it correct on the quiz, so you should to. Trust Me.

Answer: D: Translate ΔPQR by the rule (x + 1, y − 1), and dilate ΔP′Q′R′ by a scale factor of 2 from point R.

Step-by-step explanation:

Answer:

The slope is 1.

Step-by-step explanation:

The solution to the functional notations would be either yes or no if the function on the left hand side and right hand side are the same. Hence we would have:

c. No:   f ( x )   ≠    f ( -x )

d. Yes:   ( - x )  = - f ( x )

Function notation is way of writing functions so that they can easily be understood in the mathematical sense. This method is applied in the question to help read the meaning in the question without much explanations.

Given data

f ( x )  =  x^3

f ( -x )  =  - x^3

c. No   f ( x )   ≠    f ( -x )

f ( x )  =  x^3   and f ( -x )  =  - x^3

f ( x ) is not equal to f ( -x )

plugging the values for the left hand side of the equation gives

x^3

and plugging the values for the right hand side of the equation gives

- x^3

since the left hand side of the equation is not equal to the right hand side of the equation it means that the both sides of the equation are not equal hence equation sated in c is not correct

f ( x )  ≠    f ( -x )  ( take note of the sign )

d. Yes   ( - x )  = - f ( x )

( - x ) is equal to - f ( x )

This represents odd functions where the negative sign persists at the left hand side and the right hand side of the equation. Odd function do appear for functions which have negative signs and have odd exponents  too.

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Answer:

x2 + (y – 3)2 = 36

x2 + (y + 8)2 = 36

Step-by-step explanation:

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,

⇒ x² + (y - 3)² = 36

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Since, The standard form for finding the equation of a circle is expressed as;

⇒ (x - a)² + (y - b)² = r²

where;

(a, b) is the center of the circle

And, r is the radius of the circle

Given that;

Diameter = 12 units

And, Radius = 12/2 = 6 units

If the center lies on the y-axis, the center will be at (0, 3)

Substituting into the formula, we will have;

⇒ (x - 0)² + (y - 3)² = 6²

⇒ x² + (y - 3)² = 36

Thus, The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,

⇒ x² + (y - 3)² = 36

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Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer: 3

Step-by-step explanation: 2 * 3 equals 6 and 6+4=10

Hopefully I did that right I am sorry if I didn't

Answer:

p=16

Step-by-step explanation:

Answer:

p=16

Step-by-step explanation:

p/4+10=14

p/4+10-10=14-10

p/4=4

(Multiply all terms by the same value to eliminate fraction denominators)

p/4=4

4xp/4=4x4

you then get p=16.

and that is your answer.

i hope this helps.           :)

Answer:

Step-by-step explanation:

17

Orthogonal projection of a vector v onto a subspace V in R^3, we need to determine the projection vector that lies in the subspace V and is closest to the vector v.

Let's assume the subspace V in R^3 is spanned by a set of vectors {v_1, v_2, v_3}. To find the orthogonal projection of v onto V, we can use the formula:

proj_v(v) = ((v · v_1) / (v_1 · v_1)) * v_1 + ((v · v_2) / (v_2 · v_2)) * v_2 + ((v · v_3) / (v_3 · v_3)) * v_3,

where "·" denotes the dot product.

However, you have not provided the vectors that span the subspace V. Without that information, we cannot compute the orthogonal projection directly. Please provide the vectors that span the subspace V, and I would be happy to help you calculate the orthogonal projection of v onto V.

Once the spanning vectors of V are provided, we can substitute them into the formula and compute the dot products and scalar multiplications to obtain the orthogonal projection proj_v(v) of v onto the subspace V. The resulting vector will be the projection vector that lies in the subspace V and is closest to v.

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Answer:

0.64615384615

Step-by-step explanation:

(2.5 + 2.75)/(8 + 1/8)

5.25/8 1/8

1/8 = 0.125

5.25/8.125 =

=0.64615384615

Hope this helps! I might be wrong

Answer: A (2.5)

Step-by-step explanation: got it right on edge 2021

Answer:

x = 56 degrees

Step-by-step explanation:

Why? they are interior opposites. Even if you would try to measure it with a protractor on your screen, it will sure to be ending up with the same angle! I hope this helps, mate. Good luck!

I don't know i'm super sorry

Each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.Option B,E,F.

Each chart has the following three components:

1. B. A center line representing the average: This line is drawn to show the average value or mean of the data being analyzed. It provides a reference point to compare the data points above and below it.

2. E. An upper line representing the maximum acceptable variation upwards: This line is drawn to indicate the upper limit of acceptable variation or deviation from the average. It helps identify if the data points exceed the acceptable range.

3. F. A lower line representing the maximum acceptable variation downwards: This line is drawn to indicate the lower limit of acceptable variation or deviation from the average. It helps identify if the data points fall below the acceptable range.

These three components together create a control chart, which is a graphical representation used in statistical process control. Control charts help monitor and analyze data over time, allowing organizations to identify trends, detect abnormalities, and make data-driven decisions to improve processes and quality.

In summary, each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.

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Complete Question:

Determine whether the given value is a statistic or a parameter. A sample of 818 adults showed that 39% voted in the past election. Choose the correct answer below.

A. The value is a parameter because it is a numerical measurement describing some characteristic of a parameter sample.

B. The value is a statistic because it is a numerical measurement describing some characteristic of a statistic population.

C. The value is a statistic because it is a numerical measurement describing some characteristic of a statistic sample.

D. The value is a parameter because it is a numerical measurement describing some characteristic of a parameter population.

Answer:

C. The value is a statistic because it is a numerical measurement describing some characteristic of a statistic sample.

Step-by-step explanation:

If a sample of 818 adults showed that 39% voted in the past election. Therefore, the value is a statistic because it is a numerical measurement describing some characteristic of a statistic sample.

In Statistics, a sample can be defined as a set of data (individuals, observations or objects) collected from a larger statistical population using specific procedures. Therefore, a sample is a subset or part of population.

The difference between a statistic and a parameter is that; statistic is a numerical measurement describing some characteristic of a statistic sample while parameter is a numerical measurement describing some characteristic of a population.

In this scenario, a sample of 818 adults from the total population showed that 39% voted in the past election. The data collected represents a sample and as such, it is a statistic value.

The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

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Answer:

Height = 13.5 cm

Perimeter = 81 cm

Step-by-step explanation:

The Area of a parallelogram is given as the product of the base and its height.

A = base * height

Area, A = 364.5 cm²

Base, b = 27cm

Height, h =?

Hence,

364.5 cm² = 27cm * h

h = 364.5 cm² / 27cm

h = 13.5 cm

Perimeter of parallelogram :

P = 2(a + b)

a = height of sides ; b = base

P = 2(13.5cm + 27cm)

P = 2(40.5)

P = 81 cm

The remainder when 101⁴⁸⁰⁰⁰⁰⁰⁰²³ is divided by 35 is 12.

Now, let's look at how we can use the Chinese Remainder Theorem to compute 101⁴⁸⁰⁰⁰⁰⁰⁰²³ mod 35. First, we need to express 35 as a product of prime powers:

=> 35 = 5 x 7.

Then, we can consider the congruences 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ a (mod 5) and 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ b (mod 7), where a and b are the remainders we want to find.

Since 101 is not divisible by 5, we have 101⁴ ≡ 1 (mod 5). Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁴)¹²⁰⁰⁰⁰⁰⁰⁰⁵ ≡ 1 (mod 5).

This means that a = 1.

Since 7 is a prime number, φ(7) = 6, so we have 101⁶ ≡ 1 (mod 7). Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁶)⁸⁰⁰⁰⁰⁰⁰⁰³ ≡ 1 (mod 7).

This means that b = 1.

Now, we need to find a number that is equivalent to 1 modulo 5 and 1 modulo 7. This number is

=> 1 x 7 x 1 + 5 x 1 x 1 = 12.

Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ 12 (mod 35).

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To verify that y = e^(-x/4) is an explicit solution of the differential equation 4y'(x) * y(x) = 0, we need to find the derivative of y(x), substitute the given function and its derivative into the equation, and check if the equation holds true.


1. Find the derivative of y(x) = e^(-x/4) with respect to x:
y'(x) = d/dx (e^(-x/4)) = (-1/4) * e^(-x/4)

2. Substitute y(x) and y'(x) into the differential equation:
4 * (-1/4) * e^(-x/4) * e^(-x/4) = 0

3. Simplify the equation:
(-1) * e^(-x/2) = 0


Since the simplified equation, (-1) * e^(-x/2) = 0, is not true for any x, the function y = e^(-x/4) is NOT an explicit solution of the given differential equation 4y'(x) * y(x) = 0 on the interval I.

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The volume of solid B is 1350 \(cm^{3}\).

What is the volume ratio?

The side length ratio raised to the third power represents the volume ratio for the two solids.

If two solids are comparable, their volumes will have a ratio that is equal to the cube of their corresponding side ratios.

Given that both solids are similar.

The volume of solid A = 400 \(cm^{3}\)

height of solid A = 10 cm

height of solid B = 15 cm

the volume of solid B = ?

Now,

volume of solid A/ volume of solid B = (height of solid A)^3/(height of solid B)^3

or, \(\frac{400}{x} = \frac{10^{3} }{15^{3} }\)

or, \(x = \frac{400*15^{3} }{10^{3}}\)

or, \(x = \frac{400*3375 }{1000}\) = 1350

Hence, the volume of solid B is 1350 \(cm^{3}\).

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Answer: 1

Step-by-step explanation:

Explanation and steps in photo

The total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.

In the question, we are given that a package weighs P pounds, P being a whole number. To ship this package by express costs $1.65 for the first five pounds and 12c for each additional pound. The total shipping cost was $3.45.

We are asked for the package weight in pounds.

First, we design a general cost function.

The cost is given to be $1.65 for the first 5 pounds, and 12c for each additional pound.

The weight of the package is given to be P pounds.

We assume the total cost function to be C(P), a function of the weight of the package, P pounds.

Thus, the total cost function can be shown as the sum of $1.65 and 12c or $0.12 multiplied with (P - 5), as it is the cost for additional pounds after 5 pounds.

Thus, the total cost function, C(P) = 1.65 + 0.12(P - 5).

Now, we are given that the total shipping cost was $3.45.

Thus, to find the weight of the package, we equate the total cost function, C(P) to 3.45, to get:

1.65 + 0.12(P - 5) = 3.45,

or, 1.65 + 0.12P - 0.6 = 3.45,

or, 0.12P + 1.05 = 3.45,

or, 0.12P = 3.45 - 1.05,

or, 0.12P = 2.40,

or, P = 2.40/0.12 = 20.

Thus, the total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.

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The system of equations can be used to find the roots of the considered  equation is y = 4+x^2 and y= x^3 + 2 + x

We do same operations on both the sides so that equality of both expressions doesn't get disturbed. Solving equations generally means finding the values of the variables used in it for which the considered equation is true.

Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are infinite number of solutions.

For the given case, we are given with the equation \(4+x^2 = x^3 + 2 + x\)

We can take two equations as:

\(y = 4+x^2 \\y= x^3 + 2 + x\)

And when we will try to solve this system of equation, we will end up substituting the value of y in terms of x, and therefore, ending up on the same equation \(4+x^2 = x^3 + 2 + x\)

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Answer:

D

y=4x^2

y=x^3+2x

Step-by-step explanation:

im trying to pass just like yall, Good luck to all

Answer: Option d.  0.26

Step-by-step explanation:

Since the addition of complementary angles = 90°

75° + x = 90°

x = 90° - 75 °

x = 15°  ( the complementary angle )

sine 15° = 0.25882

             = 0.26 correct to two decimal places