Jack pays 15% tax on his total salary. If he earns $22,500 a year, how much salary amount does he have left after paying tax?

Answer:

(x - 2) or (x + 5)

Step-by-step explanation:

Step 1: Write quadratic

x² + 3x - 10

Step 2: Factor

(x - 2)(x + 5)

Answer:  x2 + 3x – 10= (x+5)⋅(x−2)= -6

so x=-6

Step-by-step explanation:  "x2"   was replaced by   "x^2".

Factoring  x2+3x-10  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  -10  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -10 = -10  

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   3 .

     -10    +    1    =    -9  

     -5    +    2    =    -3  

     -2    +    5    =    3

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  5  

                    x2 - 2x + 5x - 10

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-2)

             Add up the last 2 terms, pulling out common factors :

                   5 • (x-2)

Step-5 : Add up the four terms of step 4 :

                   (x+5)  •  (x-2)

            Which is the desired factorization

so (x + 5) • (x - 2)= x=-6

Answer:

The answer is 77

Step-by-step explanation:

So, first put them in number order: 65, 73, 77, 77, 81, 83, 98. Then, we cross out the first and the last number. Now the numbers we have are 73, 77, 77, 81, 83. Then, we do that again. 77, 77, 81. One more time. 77 is the number we have left. Easy, right?

The value of x in the triangle is 90 degrees.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles).

This is also known as the Exterior Angle theorem.

The triangle is an isosceles triangle. Therefore, the base angles are equal.

Hence,

180 - 135 = 45°(sum of angles on a straight line)

Therefore, using external triangle theorem,

45 + x = 135

subtract 45 from both sides of the equation

45 - 45 + x = 135 - 45

x  = 90 degrees.

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The interval that describes where the graph of this function is negative is: C. 2 < x < ∞

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

Generally speaking, a function is typically used for mapping an input variable to an output variable. In Mathematics, the value of y on the y-axis of a graph must be less than 0 (x < 0) for the graph of any function to be negative.

By critically observing the graph of this function, we can logically deduce that at point x = 2 is where the value of y becomes less than 0 (x < 0) and continues to infinity. Therefore, the graph of this function is negative is at an interval of 2 < x < ∞.

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Answer:

(4,5)

Step-by-step explanation:

\(x + 4y = 24\\subtract x from both sides\\4y=24-x\\divide both sides by 4\\y= 6 -- 1/4x\\set equations equal to eachother\\6--1/4x = -x + 9\\subtract 6 from both sides\\-1/4x = -x + 3\\add x to both sides\\\\3/4x = 3\\multiply both sides by 4/3 to get\\x = 4\\\\sub in x into one equation, I picked the first \\\\-4 + 9 = y\\-4 + 9 = 5\\\\\\y = 5, x = 4\)

Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

Answer:

yes they are congruent

Step-by-step explanation:

Answer: 222.78

Step-by-step explanation:

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Answer:

16

Step-by-step explanation:

93:6=15.5 As the box can't be half so 16 boxes. In 15 she will pack in each 6 books and in other box 3 books

Answer:

She will need 16 boxes with space for 3 more books

Step-by-step explanation:

Answer:

Step-by-step explanation:

Could you show two points need to be calculated? A and D are the same in this case

To verify the inequality without evaluating the integrals, we can use the properties of integrals.

First, we know that the integral of a positive function gives the area under the curve. Therefore, the integral of √(1-x^2) from -1 to 1 gives the area of a semicircle with radius 1. This area is equal to π/2, which is approximately 1.57.
Next, we can use the fact that the integral of a function over an interval is less than or equal to the product of the length of the interval and the maximum value of the function on that interval. Since the function √(1-x^2) is decreasing on the interval [-1,1], its maximum value is at x=-1, which is √2/2.
Using this property, we have:
∫1 -1 √(1-x^2) dx ≤ (1-(-1)) * √2/2 = √2
Finally, we can use a similar argument to show that the integral is greater than or equal to 2. Therefore, we have:
2 ≤ ∫1 -1 √(1-x^2) dx ≤ √2
To verify the inequality 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2 using properties of integrals, let's first establish that the integrand is non-negative on the interval [-1, 1]. Since 0 ≤ x^2 ≤ 1, we have 0 ≤ 1 - x^2 ≤ 1, so √(1 - x^2) is non-negative.
Now, consider the areas of two squares: one with side length 2 and the other with side length √2. The area of the first square is 2² = 4, and the area of the second square is (√2)² = 2. Since the integrand lies between 0 and 1, the area under the curve is less than the area of the first square but more than half of it (as it resembles half of the first square).
Therefore, 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2, as the area under the curve is between half of the first square's area and the second square's area.

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Answer:

The line's slope equals the difference between points' y-coordinates divided by the difference between their x-coordinates. Select any two points on the line of best fit. These points may or may not be actual scatter points on the graph. Subtract the first point's y-coordinate from the second point's y-coordinate.

The constant value in the polynomial expression is 12

The roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero. If a is the root of the polynomial p(x), then p(a) = 0.

Given here, the expression as (x+2)(x-2)-(x+4)(x-4) now using the identity  a²-b²=(a+b) (a-b) we get

(x+2)(x-2)-(x+4)(x-4) = x²-4-x²+16

                                 =12

Hence, The constant value in the polynomial expression is 12

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Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

The mean of X is y, and the variance of X is also y.

To find the mean and variance of the random variable X, which follows a Poisson distribution with parameter y, we need to use the relationship between the exponential distribution and the Poisson distribution.

Given that Y follows an exponential distribution with parameter λ, we know that the probability density function (PDF) of Y is:

f_Y(y) = λ * e^(-λy) for y ≥ 0

To find the mean of X, denoted as E(X), we can use the property of the exponential distribution that states the mean of an exponential random variable with parameter λ is equal to 1/λ. Therefore, we have:

E(Y) = 1/λ

Now, let's consider X, which follows a Poisson distribution with parameter y. The mean of a Poisson random variable is equal to its parameter. Hence:

E(X) = y

To find the variance of X, denoted as Var(X), we use the relationship between the exponential and Poisson distributions. The variance of an exponential distribution is given by 1/λ^2, and for a Poisson distribution, the variance is equal to its parameter. Therefore:

Var(Y) = (1/λ)^2

Var(X) = y

So, the mean of X is y, and the variance of X is also y.

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The base area of this rectangular prism in square feet is 40 square feet.

Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. Volume is defined as the space occupied by an item inside the confines of three-dimensional space. It is also known as the object's capacity. The volume of a thing is the amount of space it takes up. In other words, volume is a measure of an object's size in the same way that height and breadth are. Volume is the quantity of water that an item can store if it is hollow (empty).

Here,

V=B*H

B=x

H=4 ft

V=160 cubic ft

V=B*h

160=4x

x=40 square feet

The base area, in square feet, of this rectangular prism is 40 square feet.

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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Answer:

h = 12 units, r = 10 units

Step-by-step explanation:

\(v=\pi (10)^{2} (12)=\pi (100)(12)=1200\pi\)

Hope this helps

the surface with the given vector equation is a plane.

a plane can be defined by a point and a normal vector. In this case, the point is (0,3,1) and the normal vector is the cross product of the two tangent vectors of the parameterization: (1,0,4) x (0,-1,5) = (-4,-5,-1). So, the equation of the plane can be written as -4x-5y-z+28=0.

the vector equation r(u,v)=(u+v)i+(3-v)j+(1+4u+5v)k represents a plane with equation -4x-5y-z+28=0.

The given vector equation represents a plane.


The given vector equation is r(u,v) = (u+v)i + (3-v)j + (1+4u+5v)k. To identify the surface, we can find the normal vector of the surface.

1. Take partial derivatives of r with respect to u and v:
∂r/∂u = (1)i + (0)j + (4)k
∂r/∂v = (1)i + (-1)j + (5)k

2. Compute the cross product of these partial derivatives to get the normal vector:
N = ∂r/∂u × ∂r/∂v
N = ( (0)(5) - (4)(-1) )i - ( (1)(5) - (4)(1) )j + ( (1)(-1) - (1)(1) )k
N = (4)i - (1)j - (2)k

Since we have a constant normal vector, this indicates that the surface is a plane.


The surface with the given vector equation, r(u,v) = (u+v)i + (3-v)j + (1+4u+5v)k, is a plane.

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Step-by-step explanation:

5x = 125

x = 125/5

x= 25

plZ mark my answer as brainlist plzzzz hope this will be helpful to you ☺️.

The attached graph describes the relationship between the amount of money raised and the number of students who attend the dance

The parameters that will help us to determine the graph are

Decorations for the dance cost $80,

The club is charging $10 per student that attends

This forms a linear equation:

y = mx + b

y = 10x - 80

Plotting the graph:

That is the full solution of the equation

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Answer: x= 5/2, y= 11, z= 3/2

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point form:

(5/2, 11, 3/2)

The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\)

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)\)

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression \(-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\) subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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Answer:

x=3 C

Step-by-step explanation:

5x-13=-3x+11

8x-13=11

8x=24

x=3

Answer:

the answer is x=3

Step-by-step explanation:

i hope this help you

Answer:

45 minutes

Step-by-step explanation:

Answer:

probably atleest a hour so it will be 4:30 and then you'll be at home at 4:45

Step-by-step explanation:

I calculated it in 60 seconds

The surface area of a sphere with radius r is 12.56r² and the volume is 4.19r³.

Given the radius of a sphere as r. We are required to find the surface area and volume of a sphere. Surface area of the sphere: The formula for the surface area of the sphere is 4πr².π = 3.14. Putting the value of π, we get:

Surface area of the sphere

= 4πr²

= 4×3.14×r²

= 12.56r²

Volume of the sphere: The formula for the volume of the sphere is given as $\frac{4}{3}$πr³

Putting the value of π, we get,

Volume of the sphere = $\frac{4}{3}$πr³= $\frac{4}{3}$ × 3.14 × r³= 4.19r³

Thus, the surface area of a sphere with radius r is 12.56r² and the volume is 4.19r³.

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Answer:

  (x -10)²/64 +(y +8)²/100 = 1

Step-by-step explanation:

You want the equation of the ellipse with center (10,-8), a focus at (10, -14), and a vertex at (10, -18).

The length of the semi-major axis is the distance between the center and the give vertex: a = -8 -(-18) = 10 units.

The distance from the center to the focus is -8 -(-14) = 6.

The distance from the center to the covertex is the other leg of the right triangle with these distances as the hypotenuse and one leg.

  b = √(10² -6²) = √64 = 8 . . . . units

The equation for the ellipse with semi-axes 'a' and 'b' with center (h, k) is ...

  (x -h)²/b² +(y -k)²/a² = 1

  (x -10)²/64 +(y +8)²/100 = 1

__

Additional comment

The center, focus, and given vertex are all on the vertical line x=10, This means the major axis is in the vertical direction, and the denominator of the y-term will be the larger of the two denominators.

You will notice the center-focus-covertex triangle is a 3-4-5 right triangle with a scale factor of 2.

Answer:

x=18

Step-by-step explanation:

x-4=14

  +4  +4

x=18

If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,

Rs 30 = 45 book

Rs 30 = 45

Rs 1 = 45 / 30

Rs 24 = 3/2 × 24

Rs 24 = 34 books

Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

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