How to find the center, radius, and equation of the sphere

Answer:

C. 14

Step-by-step explanation:

Supplementary angles add up to 180°

\(8x + 4 + 64 = 180\)

\(8x + 68 = 180\)

\(8x = 112\)

\(x = 14\)

Answer:

C

Step-by-step explanation:

8x + 4 and 64 are a linear pair and sum to 180° , that is

8x + 4 + 64 = 180

8x + 68 = 180 ( subtract 68 from both sides )

8x = 112 ( divide both sides by 8 )

x = 14

First we have to draw a simple figure with the coordinates.

As we can see it seems a trapezoid. option D

Hrishik worked 13 hours and Jatan worked 26 hours in the given week.

Assume that Hrishik puts in x hours per week at his job. The issue states that because Jatan works two times as many hours as Hrishik does each week.

If they both put in 39 hours a week, we can construct the following equation:

x + 2x = 39

combining comparable phrases

3x = 39

by 3 and dividing both sides:

x = 13

As a result, Hrishik puts in 13 hours per week while Jatan puts in twice that amount, or 2 x 13 = 26 hours per week. As a result, throughout the specified week, Hrishik worked 13 hours and Jatan 26.

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Answer:

y= x+1

y= x-5

There are 0 solutions because the lines will never intersect (which is due to their slopes being the same).

Step-by-step explanation:

Because we don't have any numbers we're supposed to esitmate, but the important thing to realize is that the slopes are identical

so let's say our equations are

x+1

x-5

2.)

There are 0 solutions because the lines will never intersect (because their slopes are the same)

Answer:

see explanation

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

Therefore if the lines are parallel, they never intersect and hence there is no solution.

The lines given appear to be parallel and so there is no solution.

Answer:

37.7 feet

Step-by-step explanation:

Given that:

Measurements of Frankie's yard = 20ft x 32ft

He wants to build a path from one corner to another.

To find:

The length of path = ?

Solution:

Let us consider a rectangle \(ABCD\) as shown in the attached image in the answer area.

We are given the two adjacent sides of a rectangle and we have to find diagonal of the rectangle.

To find the diagonal, we can use the Pythagorean Theorem.

We are given the base and perpendicular of the right angled triangle and we have to find the hypotenuse.

According to Pythagorean theorem:

\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\)

\(Diagonal = 20^2 + 32^2\\\Rightarrow Diagonal = 400 + 1024\\\Rightarrow Diagonal = \bold{37.7\ ft}\)

Step-by-step explanation:

It is a cyclic quadrilateral.

The sum of interior angles of this polygon is equal to 180 degrees.

ATQ,

2x+26y=180

x+13y=90 ....(1)

3x+21y=180

x+7y=60 ....(2)

Subtract equation (1) from (2).

x+7y-(x+13y) = 60-90

x+7y-x-13y=-30

-6y=-30

y = 5

Put the value of y in equation (1

x+13(5) = 90

x+65=90

x = 90-65

x = 25

So,

∠DAB = 26y = 26(5) = 130°

∠ABC = 3x = 3(25) = 75°

∠BCD = 2x = 2(25) = 50°

∠ADC = 21y = 21(5) = 105°

    x = 25, y = 5

    m∠DAB = 26(y) = 180°

    m∠ABC = 3x = 75°

    m∠BCD = 2x = 50°

    m∠ADC = 21y = 105°

From the picture attached,

By using the property of cyclic quadrilateral,

m∠A + m∠C = 180°

26y + 2x = 180

13y + x = 90 --------(1)

m∠B + m∠D = 180°

3x + 21y = 180

x + 7y = 60 --------(2)

Subtract equation (2) from (1),

(13y + x) - (x + 7y) = 90 - 60

6y = 30

y = 5

Substitute y = 5 in equation (1),

13(5) + x = 90

x = 90 - 65

x = 25

Substitute the values of 'x' and 'y' to get the measures of the angles,

m∠DAB = 26(y) = 180°

m∠ABC = 3x = 75°

m∠BCD = 2x = 50°

m∠ADC = 21y = 105°

         Therefore, values of the variables will be,

                            x = 25, y = 5

                            m∠DAB = 26(y) = 180°

                            m∠ABC = 3x = 75°

                            m∠BCD = 2x = 50°

                            m∠ADC = 21y = 105°

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Answer:

$110.88

Step-by-step explanation:

Let L be the length of the first fence surrounding the garden and P its perimeter.

For a square, P = 4L,

So, L = P/4

Since P = 36 feet,

L = P/4

= 36/4

= 9 feet

Let L' be the length of the second fence. Given that second fence is 3 feet away from the first fence, it follows that L' = L + 3

= 9 + 3

= 12 feet.

So, the perimeter of the second fence is P' = 4L'

= 4 × 12 feet

= 48 feet.

So, the total length of the two fences is P" = P + P'

= 36 feet + 48 feet

= 84 feet

Since the cost of the material to build the two fences is $1.32 per foot, the total cost of the fences is cost per foot × total length of fences = $1.32 × 84 = $110.88

Answer:

6ehshsusushsushshsgshshdhxhdhdd

By studying the mean and standard deviation,

The value of test statistic z is 1.897

What is mean and standard deviation?

Suppose there is a data set. Mean is the average of all the values of the data set

Before knowing about standard deviation, it is important to know about variance first.

Variance is the sum of the square of deviation from mean.

On taking the square root of variance, standard deviation is obtained.

Population mean = 5.5

Population standard deviation = 2

Sample size = 10

Sample mean = 6.7

Test statistic z =

                        \(\frac{6.7 - 5.5}{\frac{2}{\sqrt{10}}}\\\\1.897\)

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15 Kilocalorie (international) (kcal) = 15000 Calorie (cal)

The kilocalorie, sometimes call kilogram calorie is a measurement unit of energy. It is defined as the amount of energy needed to raise the temperature of one kilogram of water by one degree Celsius. The symbol of kilocalorie is kcal. The kilocalorie is commonly used in measuring the calorific, heating, or metabolizing value of foods. It is equal to 1000 calories, or approximately 4.2 kilojoules.

The calorie is a pre-SI metric unit of energy. Its symbol is cal, and first defined as a unit of heat by Nicolas Clément in 1824. The calorie is commonly used in the field of chemistry, and in many countries it is commonly used as a unit of food energy. There are two defined for the calorie, gram calorie (approximately equals 4.2 joules) and kilogram calorie (approximately equals 4.2 kilojoules).

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The range of the exponential function y = bx is all real numbers except 0.

The exponential function y = bx is defined as the equation where b is the base and x is the exponent. The range of this equation is all real numbers except 0. This is because when x is negative, the value of y will be a fraction (or a decimal) which is always a real number except for 0. When x is positive, the value of y will be a multiple of b which is also always a real number except for 0.

Therefore, the range of the exponential function y = bx is all real numbers except 0.

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The senate has 4+22 = 26 members this year.

Let x be the number of Democrat members in the senate.

Last year, the number of Republican members was x+20

This year, the number of Republican members is (x+20) - 2 = x+18

This year, the number of members in the senate is 2/3*(x+18) = 2/3*x+12

So the number of members in the senate this year is x+12

To find the value of x, we can use the fact that the number of members in the senate this year is the same as last year.

x + (x + 20) = x + 12

x+x+20 = x + 12

2x = 8

x = 4

So the senate has 4 Democrat members and x+18 = 4+18 = 22 Republican members.

Therefore the senate has 4+22 = 26 members this year.

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The equation in slope-intercept form is y = 4x + 1

Given,

Points (x, y) = (-1, 5)

Parallel to y = 4x - 5

Now,

Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "4" (the coefficient that accompanies "x").

Therefore the equation of a parallel line has to be of the form:

y = 4x - b

5 = 4(-1) - b

5 = -4 - b

b = -4 - (-5)

b = -4 + 5

b = 1

So the equation now becomes:

y = 4x + 1

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True, you can use universal generalization (UG) to obtain a universal statement by generalizing only from a free variable, and not from a constant. Generalization involves making a statement that applies to all instances of the variable, while constants remain fixed and do not change in value.

True. Universal generalization (UG) allows us to derive a universal statement by generalizing from a free variable. General sampling deals with the fact that if something is true for everything, it must also be true for every specific thing called the constant c. Existential generalization deals with the fact that the special case c is true for at least one thing if it is true.

A free variable is a variable that is not bound by a quantifier, meaning it is not restricted to a specific value or range of values. In contrast, a constant is a variable that is already assigned a specific value and cannot be generalized over. Therefore, UG can only be applied to free variables and not constants.

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the eigenvalues of A are λ₁ < λ₂ < λ₃, where λ₁ is approximately -0.6594, λ₂ is approximately 0.2469, and λ₃ is approximately 0.4125.

What is Eigenvalues?

Eigenvalues are a concept in linear algebra that are associated with square matrices. An eigenvalue of a matrix represents a scalar value that, when multiplied by a corresponding eigenvector, yields the same vector after transformation by the matrix. In other words, eigenvalues are the solutions to the equation (A - λI)v = 0, where A is the matrix, λ is the eigenvalue,

To find the characteristic polynomial and eigenvalues of the matrix A, we start by setting up the equation |A - λI| = 0, where A is the given matrix, λ is the eigenvalue, and I is the identity matrix.

The given matrix A is:

A =

-0.00 1.33 0.67

1.00 1.00 -0.33

-0.33 -0.67 -0.67

Next, we subtract λI from A, where I is the 3x3 identity matrix:

A - λI =

-0.00 - λ 1.33 0.67

1.00 1.00 - λ -0.33

-0.33 -0.67 - λ -0.67

Expanding the determinant of this matrix, we get the characteristic polynomial:

P(λ) = det(A - λI) = (-0.00 - λ) [(1.00 - λ)(-0.67 - λ) - (-0.33)(-0.67)] - [1.33(1.00 - λ) - (0.67)(-0.33)]

Simplifying this expression, we get:

P(λ) = λ^3 + 0.67λ^2 - 0.13λ + 0.224

Therefore, the characteristic polynomial of A is P(λ) = λ^3 + 0.67λ^2 - 0.13λ + 0.224.

To find the eigenvalues, we solve the equation P(λ) = 0. Unfortunately, the given polynomial does not factor easily, so we need to use numerical methods or a calculator to find the roots.

Using a numerical method or calculator, we find the eigenvalues of A to be approximately:

λ₁ ≈ -0.6594

λ₂ ≈ 0.2469

λ₃ ≈ 0.4125

Arranging the eigenvalues in ascending order, we have:

λ₁ < λ₂ < λ₃

So the eigenvalues of A are λ₁ < λ₂ < λ₃, where λ₁ is approximately -0.6594, λ₂ is approximately 0.2469, and λ₃ is approximately 0.4125.

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Answer:

x = 25°

Step-by-step explanation:

3x + 2x + x + 30° = 180°

6x + 30° = 180°

6x = 150°

x =25°

=> 3x = 25 * 3 = 75°

=> 2x = 25 * 2 = 50°

=> x + 30° = 25° + 30° = 55°

Steps to solve:

(-7b + 8C) - (12a + 14) + (5a + 5b)

~Remove parenthesis and combine like terms

(-7b + 5b) + (8c) + (-12a + 5a) + 14

-2b + 8c - 7a + 14

~Put in order

-7a - 2b + 8c + 14

Best of Luck!

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

3/16

Step-by-step explanation:

In the equation y=mx+b the b is the y intercept

I hope this helps! :) If it does could you please mark me brainliest

The x-intercept of the line cannot be determined with the given information as there is no point in the table where the y-coordinate is zero.

To find the x-intercept of a line, we need to determine the value of x when y equals zero.

In other words, we are looking for the x-coordinate where the line intersects the x-axis.

Given the table of (x, y) pairs, we can observe that one of the pairs is (-2, 21).

However, this point does not lie on the x-axis, as the y-value is not zero.

Let's examine the other pairs:

(-12, 14)

(8, 28)

Since we are looking for the x-intercept, we need to find the point where y equals zero.

None of the given points satisfy this condition.

Based on the information provided, we do not have sufficient data to determine the x-intercept of the line.

Without any points where y equals zero, we cannot pinpoint the exact x-coordinate where the line intersects the x-axis.

It's important to note that the x-intercept represents the point(s) where a line crosses the x-axis.  

If we had a point where y equals zero, we could determine the x-coordinate at that point.

However, in this case, the information given does not allow us to identify the x-intercept.

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A regression model allows us to examine how the probability distribution of a dependent variable, Y, might be related to one or more independent variables (collectively called X). Therefore, the correct answer is (a) regression model.

A regression model is a statistical tool used to model the relationship between a dependent variable (often denoted as Y) and one or more independent variables (often denoted as X). It can help us understand how changes in the independent variables affect the values of the dependent variable, and can be used to make predictions or estimate values of the dependent variable based on specific values of the independent variables.

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Answer:

y = -13.5

x = -10.5

Step-by-step explanation:

Hi there!

Let the two numbers be equal to x and y.

The difference of two numbers is 3 ⇒ x - y = 3

Their sum is - 24 ⇒ x + y = -24

Solve using elimination:

x - y = 3

x + y = -24

Add the two equations:

x + x - y + y = 3 - 24

2x = -21

x = -10.5

Solve for y:

-10.5 - y = 3

- y = 3 + 10.5

y = -13.5

I hope this helps!

Answer: -1/5 would be the answer. Or in decimal form it would be -0.2

Answer:

\(-\frac{5}{25}\) is already a fraction

Equation of Change in bank balance is x - $128

A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).

Given Data

Let x be the overall bank balance

Equation

Change in bank balance = x - 4(32)

Change in bank balance = x - 128

Thus, equation of Change in bank balance is x - $128

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Answer:

hey

Step-by-step explanation:

r u in red oak too?

9514 1404 393

Answer:

  ±√58 ≈ ±7.616

Step-by-step explanation:

The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.

  |x| = √(3² +7²) = √58

The motion is bounded between positions ±√58.

_____

Here's a way to get to the relation used above.

The sine of the sum of angles is given by ...

  sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)

If this is multiplied by some amplitude A, then we have ...

  A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)

Comparing this to the given expression, we find ...

  A·cos(c) = 3   and   A·sin(c) = -7

We know that sin²+cos² = 1, so the sum of the squares of these values is ...

  (A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²

That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...

  x = A·sin(θ +c) . . . . for some angle c

  x = (√58)sin(θ +c)

This has the bounds ±√58.

Answer:

C. 11/21

Step-by-step explanation:

Find the probability that he scores in general, by dividing 33 by 63:

33/63

Simplify this by dividing the numerator and denominator by 3:

= 11/21

So, the probability that he will score his next shot is 11/21

The correct answer is C. 11/21

Answer:

y=6

Step-by-step explanation:

Answer:

The 5th one

Step-by-step explanation:

Common sense