The standard form of an absolute value function is f(x) = a|x -h| + k.Which of the following represents the vertex?
A. (-k,h)
B. (-h,k)
C. (k,h)
D.(h,k)
Please help ASAP

Answer: To complete the square, we need to add and subtract the square of half the coefficient of x:

x^2 - 4x = 2

x^2 - 4x + 4 = 2 + 4 (adding and subtracting 4)

(x - 2)^2 = 6

Now we take the square root of both sides:

x - 2 = ±√6

Adding 2 to both sides gives:

x = 2 ± √6

So the solutions are:

x = 2 + √6, 2 - √6

Step-by-step explanation:

Using area formula,

a. Area of the trapezium = 47.5m².

b. Area of parallelogram = 54inches².

The area of a thing is the amount of space it occupies in two dimensions. It is a way to count how many unit squares completely round the surface of a closed figure. The standard unit of area is the square unit, which is usually expressed as square inches, square feet, etc.

a. Sides of the trapezium are, a = 5m and b = 14m.

Height, h = 5m.

Area of the trapezium = (a+b)/2 × h

= (5 + 14)/2 × 5

= (19× 5)/2

= 95/2

= 47.5m².

b. Height of parallelogram = 6inches.

Base of parallelogram = 9inches.

Area = b × h

= 6 × 9

= 54inches².

To know more about area, visit:

https://brainly.com/question/27683633

#SPJ1

Answer:

m =  [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

First, we must rewrite 5x + 6y = - 18 to the form y = mx + b.

5x + 6y = -18

6y = -5x - 18

y = [tex]\frac{-5}{ 6}[/tex]x - 3

The equation of a perpendicular line to y = [tex]\frac{-5}{ 6}[/tex]x - 3 must have a slope that is the negative reciprocal of the original slope.

So, the slope of the perpendicular line is

m = [tex]\frac{6}{5}[/tex]

Answer: 6/5

Step-by-step explanation:

trust me

The probability of there being no defects in the entire shipment is 0.2075.

What is probability?

Probability can be used to calculate an event's probability. It can only be used to assess the possibility that an event will occur. A scale from 0 to 1, where 0 is impossible and 1 is a particular occurrence.

We are given that out of the 400 components, 68 are defective and 332 are non-defective computer components.

A random sample of 25 is taken.

So,

⇒ Probability (Defects in the shipment) =  [tex]\frac{68}{400}[/tex]

⇒ Probability (Defects in the shipment) = 0.17

Thus,

⇒ Probability (No Defects in the shipment) =25 * (1 - 0.17)

⇒ Probability ( No Defects in the shipment) = 25 * (0.83)

⇒ Probability ( No Defects in the shipment) = 0.2075

Hence, the probability of there being no defects in the entire shipment is 0.2075.

Learn more about probability from the given link

brainly.com/question/24756209

#SPJ1

Number of math textbooks is 110 and number of history textbooks is 330 were sold when a textbook store sold a combined total of 440 math and history textbooks in a week.

There are two categories of textbooks. Let "x" stand for the quantity of math textbooks and "y" for the quantity of history textbooks.

A textbook store sold a combined total of 440 math and history textbooks in a week.

Equation,

x + y = 440

The number of math textbooks sold was three times the number of history textbooks sold.

x = 3y

Substituting the values in equation x + y = 440,

3y + y = 440

4y = 440

y = [tex]\frac{440}{4}[/tex]

y = 110

Number of math textbooks = 110

Number of history textbooks:

3y

3 × 110

330

Number of math textbooks is 110 and number of history textbooks is 330 were sold when a textbook store sold a combined total of 440 math and history textbooks in a week.

To learn more about equation, visit:

https://brainly.com/question/29657992

https://brainly.com/question/29538993

#SPJ3

Answer:

308 yards^2

Step-by-step explanation:

Area = length * width

Length = 20

Width = 15.4

20 * 15.4 = 308

Answer: 308 yards

Step-by-step explanation:

The diameter of the hemisphere to the nearest tenth of a centimeter is 62.1 cm.

What is hemisphere?

A hemisphere is a three-dimensional geometric shape that consists of a half-sphere, which is a curved surface that is shaped like the surface of a ball, and a flat circular base that lies on a plane perpendicular to the sphere's axis of symmetry. A hemisphere can be thought of as the three-dimensional analogue of a circle.

The volume of a hemisphere is given by the formula:

V = (2/3)π[tex]r^3[/tex]

where V is the volume and r is the radius of the hemisphere.

We are given the volume of the hemisphere as 62617 [tex]cm^3.[/tex]

So, we have:

62617 = (2/3)π[tex]r^3[/tex]

Multiplying both sides by 3/2π, we get:

[tex]r^3[/tex] = 62617 * (3/2π)

Simplifying, we get:

[tex]r^3[/tex] = 29897.4152

Taking the cube root of both sides, we get:

r ≈ 31.04

The diameter of the hemisphere is twice the radius, so:

d = 2r ≈ 62.08

Rounding to the nearest tenth, we get:

d ≈ 62.1

Therefore, the diameter of the hemisphere to the nearest tenth of a centimeter is 62.1 cm.

To learn more about algebraic expression visit:

https://brainly.com/question/4344214

#SPJ1

Answer:

367

Step-by-step explanation:

Places in the alphabet:
T=20, H=8, E=5, R=18, E=5. 20+8+5+18+5=56. THERE=56
A=1, R=18, E=5. 1+18+5=24. ARE=24
S=19, O=15, M=13, E=5. 19+15+13+5=52. SOME=52
S=19, A=1, N=14, D=4, W=23, I=9, C=3, H=8, E=5, S=19. 19+1+14+4+23+9+3+8+5+19=105. SANDWICHES=105
O=15, N=14. 15+14=29. ON=29
T=20, H=8, E=5. 20+8+5=33. THE=33
S=19, H=8, E=5, L=12, F=6. 19+8+5+12+6=49. SHELF=49
56+24+52+19+105+29+33+49=367

After looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics.

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

A number on the left of a number line is always smaller than a number on the right.

A number to the right is always greater than a number to the left, too.

So, the inequality we have is:

1/4 + 1 < 5

Now, after observing the given lines, we can easily tell that the number line (B) represents 1/4 + 1 < 5 perfectly.

Therefore, after looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.

Know more about the number line here:

https://brainly.com/question/24644930

#SPJ1

Complete question:

Which number line shows the solution to 1/4 + 1 < 5

Answer: $939 and $689

Step-by-step explanation:

     We can create a system of equations to help us solve. Let x be one and y be the other paycheck.

           y = x - $250

           y + x = $1,628

     Next, we can solve the system of equations by graphing. The point of intersection is our solution. See attached. This gives us (939, 689), so one check was written for $939 and one was written for $689.

Answer:

The angles are congruent, the two that are touching, m<s

Step-by-step explanation:

The value of y for the inverse variation when x = -12 is derived to be equal to 1.

Inverse variation is a mathematical relationship between two variables, in which an increase in one variable leads to a proportional decrease in the other variable. Mathematically, inverse variation can be expressed as y = k/x, where y and x are the two variables, k is a constant of proportionality, and the product of y and x is always equal to k.

when x = 6 and y = -2, then k is derived as:

-2 = k/6

k = -12 {cross multiplication}

when x = -12, y is derived as:

y = -12/-12

y = 1

Therefore, the value of y for the inverse variation when x = -12 is derived to be equal to 1.

Read more about inverse variation here:https://brainly.com/question/10252139

#SPJ1

Rule 1: The output is the square of the input. For example, if the input is 3, then the output would be 9 (3 squared).

Rule 2: The output is 90 greater than the input. For example, if the input is 3, then the output would be 93 (3 + 90).

These are the two rules you've provided, and they describe how to calculate the output (y) based on the input (x).
Rule 1: The output is the square of the input.
In this rule, when you have an input value (let's call it x), you square it (multiply it by itself) to get the output value (y). Mathematically, this can be written as:
[tex]y = x^2[/tex]
Rule 2: The output is 90 greater than the input.
In this rule, when you have an input value (x), you add 90 to it to get the output value (y).

Mathematically, this can be written as:
y = x + 90.

For similar question on rules.

https://brainly.com/question/1535959

#SPJ11

The value of the expression is 9y⁵z³/x⁶

Note that index forms are described as mathematical forms of writing numbers that are large or too small in more convenient forms.

The rules of index forms are;

From the information given, we have that;

(y³z⁻¹) (3x⁻³y/z⁻²)²

expand the bracket, we get;

(y³z⁻¹) 9x⁻⁶y²/z⁻⁴

Take the inverse exponent of the denominator

(y³z⁻¹) 9x⁻⁶y²z⁴

Now, add the exponents

9x⁻⁶y³⁺²z⁻¹⁺⁴

9x⁻⁶y⁵z³

Then, we have;

9y⁵z³/x⁶

Learn about index forms at: https://brainly.com/question/15361818

#SPJ1

Answer:

215.95

Step-by-step explanation:

68.4+49.6+97.95

The argument to symbols of the logic expression is shown below

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

The argument in symbols can be expressed as:

p -> q

~p

Therefore, ~q

Where:

p = "It rains."

q = "I will watch the Real World marathon."

"->" denotes "implies".

"~" denotes "not".

So the argument can be read as "If it rains, then I will watch the Real World marathon. It did not rain.

Therefore, I did not watch the Real World marathon."

Read more about logic expression at

https://brainly.com/question/14458200

#SPJ1

Answer:

y = 150x + 3000

Step-by-step explanation:

We can express the cost (y) as a linear function of heater quantity (x) by writing the equation in the slope-intercept form (y = mx + b), where m is the slope (in this case change in cost / change in heater quantity) and b is the y-intercept (when x = 0).

To find the slope (m), we can use the slope formula, which is

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point and x2 and y2 are the other point.

If we allow (30, 7500) to represent x1 and y1 and (40, 9000) to represent x2 and y2, our slope is:

[tex]m=\frac{9000-7500}{40-30}\\ \\m=\frac{1500}{10}\\ \\m=150[/tex]

Now, we can find the y-intercept by plugging in the slope and one of the points and solving for b:

[tex]7500=150(30)+b\\7500=4500+b\\3000=b[/tex]

Thus, our equation where y (cost) is a function of x (heater quantity) is y = 150x + 3000

The interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.

Payment is the transfer of funds from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment can take various forms, including cash, check, credit card, money order, or electronic transfer. Payment can be made in person, over the phone, or online. The most important aspect of payment is that it is a legally binding contract between two parties. Payment is an important part of the economic system that facilitates the exchange of goods and services and helps to ensure that all parties involved receive what they expect from the transaction.

The interest on $58,254.26:
To calculate the interest on $58,254.26, we first need to determine the interest rate. Assuming that the interest rate is 3%, we can calculate the interest owed as follows:

Interest = Principal x Interest Rate x Time

Interest = $58,254.26 x 0.03 x 1/12

Interest = $146.38

b) The payment to principal:
To calculate the payment to principal, we need to subtract the interest from the total payment amount.

Payment to Principal = Total Payment – Interest

Payment to Principal = $329 - $146.38

Payment to Principal = $182.62

c) The new principal:
To calculate the new principal, we need to subtract the payment to principal from the original principal.

New Principal = Original Principal – Payment to Principal

New Principal = $58,254.26 - $182.62

New Principal = $58,071.64

In conclusion, the interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.

To know more about payment click-
https://brainly.com/question/29616806
#SPJ1

The company's total expenses and revenues will both be $196 when 4 attendees register.

What is Algebraic expression ?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

Let's assume that the company's goal is to break even, which means that their total revenue should be equal to their total expenses.

Let's represent the number of attendees by "x." For the company to break even, the total revenue earned from x attendees must be equal to the total expenses incurred.

Total Expenses = Fixed Cost + Variable Cost

Fixed cost = Facility rent fee = $164

Variable cost = Books and supplies per attendee = $8

Total Expenses = $164 + $8x

Total Revenue = Price per attendee x Number of attendees = $49x

To find the break-even point, we set the total revenue equal to the total expenses and solve for x:

$49x = $164 + $8x

$41x = $164

x = 4

Therefore, the company needs to have 4 attendees to break even.

To calculate the total expenses and revenues, we can substitute x = 4 into the equations we derived above:

Total Expenses = $164 + $8(4) = $196

Total Revenue = $49(4) = $196

Therefore, the company's total expenses and revenues will both be $196 when 4 attendees register.

To learn more about Algebraic expression from given link.

brainly.com/question/31238826

#SPJ1

Answer: 22

Step-by-step explanation:

The first one is 10.

The other 2 has 6, because 10-4=6

So

10+(6x2)=22

The next three terms are:

Answer:

x = 47

Step-by-step explanation:

All angles in a triangle ALWAYS add up to 180 degrees, so to find a missing angle, subtract what is already given. It will be 180 - (102+31), which is the same as 180-133 which equals 47. The basic rule is to subtract given angels from 180 to find the missing side.

Answer:

Step-by-step explanation:

,mnlnnl;

Answer:

150 men and 252 women

Step-by-step explanation:

            Men : Women = 5 : 9

Number of men = 5x

Number of women = 9x

42 women left the museum.

Number of remaining women = 9x - 42

              New ratio = 2 : 3

                      [tex]\dfrac{5x}{9x -42}=\dfrac{2}{3}\\\\\\\bf Cross \ multiply,[/tex]

                          3*5x  = 2*(9x - 42)

                          15x     = 2*9x - 2*42

                              15x = 18x - 84

                  18x - 84 = 15x

Add 84 to both the sides,

                         18x = 15x + 84

Subtract 15x from both sides,

                18x - 15x = 84

                         3x = 84

Divide both sides by 3,

                            x = 84 ÷ 3

                            x =  28

Number of men = 5 * 28 = 140

Number of women = 9*28 = 252

The approximate diameter of the garden is 12.82 feet.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Here, we have

Given: A circular garden has a circumference of 40.25 feet.

We have to find the diameter of the garden.

The formula for the circumference of a circle is given as 2πr.

We have to find the radius of the circular garden

Hence: 2πr = 40.25m

π = 3.14

To find the radius, the formula would be given as

r = C/2π

Where C = Circumference of the circle

r = (40.25/2)x 3.14

r = 63.195

d =  C/π

d = 40.25/3.14

d = 12.82

Hence, the approximate diameter of the garden is 12.82 feet.

To learn more about the circumference from the given link

https://brainly.com/question/27447563

#SPJ1

The future value of Ted's investment after 30 years would be approximately $13,711.86.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

Ted can use the formula for the future value of an annuity to calculate the future value of his investment:

FV = Pmt x (([tex](1 + r)^{n}[/tex]) - 1) / r

Where:

FV = Future Value

Pmt = Payment per period (monthly in this case)

r = Interest rate per period (monthly in this case)

n = Number of periods (in this case, 30 x 12 = 360 months)

Substituting the given values, we get:

FV = $250 x (([tex](1 + 0.062/12)^{360}[/tex] - 1) / (0.062/12)

FV = $250 x (283.8576) / 0.0051667

FV = $13,711.86

Therefore, the future value of Ted's investment after 30 years would be approximately $13,711.86.

To learn more about statistics from the given link:

https://brainly.com/question/28053564

#SPJ1

Answer:

D. 4 units

Step-by-step explanation:

Similar figures have corresponding lengths in proportion.

[tex]\frac{4x}{2x}=\frac{x+1}{x} \\ \\ 2=1+\frac{1}{x} \\ \\ 1=\frac{1}{x} \\ \\ x=1[/tex]

Therefore, the height of Figure 1 is 4.

Using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

The square's four sides are equal to one another or congruent.

The square's opposing sides run parallel to one another.

The square's diagonals form a 90° angle with one another.

The square's two diagonals are equal to one another.

Area: s²

s² + (s+3)² = 1017

s² + s² + 9 = 1017

2s² = 1017 - 9

2s² = 1,008

s² = 1008/2

s² = 504

s = ²504

s = 22.44

Round off: 22 cm

Then, (s+3) = 22 + 3 = 25 cm

Therefore using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.

Know more about squares here:

https://brainly.com/question/27307830

#SPJ1

Answer:

1. 15

2. 26

3. ≈ 7.62

4. 8

5. ≈ 23.24

6. √2

7. ≈ 19.42

8. 18

9. x≈10.29 y≈5.83

Step-by-step explanation:

Use a²+b²=c² throughout the problems and plug in the given sides and hypothenuse.

1. 9²+12²=c²

81+144=225

√225 = 15

2. 10²+24²=c²

100+576=676

√676=26

3. 7²+3²=c²

49+9=58

√58 ≈ 7.62

4. a²+6²=10²

a²+36=100

a²=64

x=8

5. a²+6²=24²

a²+36=576

a²=540

x≈ 23.24

6. 1²+1²=c²

1+1=2

x=√2

7. a²+8²=21²

a²+64=441

a²=377

x≈ 19.42

8. a²+24²=30²

a²+576=900

a²=324

x=18

9. for x:

9²+5²=x²

81+25=106

√106 ≈10.29

x ≈10.29

for y:

5²+3²=y²

25+9=34

√34 ≈5.83

y ≈5.83