After a 65% reduction, you purchase a new washing machine on sale for $224. What was the original price of the washing machine?
The original price was ___$

f(x) = x^2

write new equation after translation using vertex form;

(x+4)^2 - 2

simplify; convert to standard form

(x+4)(x+4) - 2

x^2 + 8x - 2

The function after translation is g(x) = x²+ 8x - 2.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

f(x) = x²

Now, g is a translation left 4 units and down 2 units of the graph of f.

So, g(x)= (x+4)² - 2

Then, in the standard form

g(x) = (x+4)(x+4) - 2

g(x) = x²+ 8x - 2

Hence, the function is g(x) = x²+ 8x - 2.

Learn more about Transformation here:

https://brainly.com/question/11709244

#SPJ2

0.8465 is the probability that the system operates if the probability that each component functions equals to 0.90, 0.99, and 0.95 respectively.

As the components are in a series system, this means that all the components have to function in order for the system to operate, and the failure of any one of the components to function will result in the system not operating.

Therefore, the probability for the system to operate is the probability that all the components c1, c2, and c3 function together

The probability of multiple events occurring together can be found by multiplying the probabilities of each event by one another.

Therefore;

Probability = 0.90 × 0.99 × 0.95

Probability = 0.84645

Rounding it off to 4 decimals as follows;

Probability = 0.84645 = 0.8465

Therefore, the probability that the system operates is calculated to be 0.8465.

To learn more about probability, click here:

https://brainly.com/question/251701

#SPJ4

Answer:

$7.95 per visit

Step-by-step explanation:

To find the unit rate, divide dollars by number of visits.

79.5 ÷ 10 = 7.95

Answer:

"What is 180 lbs to kg?" is the same as "What is 180 pounds to kilograms?" or "What is 180 pounds to kg?" or "What is 180 lbs to kilograms?" Here we will show you how to convert 180 lbs to kg.

There are 0.45359237 kilograms per pound and there are 2.204622622 pounds per kilogram. Therefore, you can get the answer to "180 lbs to kg?" two different ways. You can either divide 180 by 2.204622622 or multiply 180 by 0.45359237. Therefore, the answer is

Step-by-step explanation:

81.6466

0.6054 is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree.

What are examples and probability?

this is binomial with parameter n=21 and p=0.39

a)

probability = P(X<=5)= ∑x=0x     (nCx)px(1−p)(n-x)    =  0.1124

b)

probability = P(X=8)= (nCx)px(1−p)(n-x)    =    0.1763

c)

probability = P(8<=X<=13)= ∑x=x1x2     (nCx)px(1−p)(n-x)    =  0.6054

Learn more about probability

brainly.com/question/11234923

#SPJ9

Based on the given expression; there are three terms;

and one coefficient; 7

A term refers to any value (variable or constant) or expression separated from another term by a space or an appropriate character or symbol, in an overall expression.

Coefficient refers to be a constant by which an algebraic term is multiplied.

f + 15 + 7g

There are three terms in the expression;

From the task given above,

The coefficient of 7g is 7

Also the coefficient of f is 1.

Therefore, the terms in the expression are f, 15 and 7g.

Read more on terms and coefficients:

https://brainly.com/question/11988485

#SPJ1

Circle A and Circle B's connection

Circle A's size is more significant than Circle B's size.

As a result, circle A's radius exceeds circle B's radius.

The connection between segments

1.

Let M be the location where Segment QT and ER intersect.

Additionally, tangents from an outside point to a circle have identical lengths.

QM = ME———— (1)

MT=MR————(2)

Including (1) and (2)

MR + ME = QM + MT

Q T=ER

2.

Tangents from an exterior point to a circle have identical lengths.

We may write the following segments are equal using this property.

UP=U Q

ZC=ZR

VC=VS

NR=NS

KC=K T

What are Tangents?

A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:

As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):

Utilizing the differentiation principles, determine the gradient function's derivative.

To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate

Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).

Circle's Tangent

A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.

Geometric Tangent

Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.

Learn more about Tangent https://brainly.com/question/19064965

#SPJ1

Using Complete the Square method, we find out that [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.

It is given to us that the expression is -

[tex]x^{2} -5x+8[/tex] ----(1)

We have to express it in the form of[tex](x-a)^{2}+b[/tex] where a and b are top-heavy fractions.

In order to achieve the required expression in the form of  [tex](x-a)^{2}+b[/tex] we have to use "Completing the Square" method.

The given expression from (1) is -

[tex]x^{2} -5x+8[/tex]

This expression is in the form of [tex]ax^{2} +bx+c[/tex]

Adding and subtracting [tex](b/2)^{2}[/tex] terms into the expression, we get

[tex]x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8[/tex] -----(2)

Equation (2) can also be represented as -

[tex](x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8[/tex]

[tex]= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex]------- (3)

We see that equation (3) is in the form of [tex](x-a)^{2}+b[/tex].

So, we can derive that -

[tex]a=\frac{5}{2}[/tex]

and, [tex]b=\frac{7}{4}[/tex].

Thus, [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] through "Complete the Square" method as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.

To learn more about complete the square method visit https://brainly.com/question/4822356

#SPJ9

The volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.

For the given question;

The volume of air inhale (and exhale) once = 0.475 liters

Number of breathing in 1 minutes = 18 times.

Thus, the volume of air inhaled in 1 minutes is 0.47×18 = 8.46 litres.

This can be written as;

1 minutes ------- > 8.46 litres of air.

For calculating in 8 hours that is 8×60 = 480 minutes, multiply the both side by 480 in above equation;

1× 480 minutes ------- >  480×8.46 litres of air.

480 minutes --------> 4060.8 litres of air.

Therefore. the volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.

To know more about the unitary method, here

https://brainly.com/question/1955459

#SPJ9

Answer:

yes

Step-by-step explanation:

Goggle

When Rectangle A measures 9 inches by 3 inches and rectangle B is a scaled copy of Rectangle A, the possible dimensions will be:

From the information, Rectangle A measures 9 inches by 3 inches. Therefore, the ratio will be:

=Length / Width

= 9 / 3

= 3:1

Therefore, a scaled copy will have an equivalent ratio of 3:1.

This can be 3 inches by 1 inches and 6 inches by 2 inches. Their ratio is:

= 6/2 = 3:1.

Learn more about scale on:

brainly.com/question/13754381

#SPJ1

Answer:

you'll need a graph to answer this

The Hillsdale is 8 km from the Kinsley's house

Let Kinsley's house be A

     Summerfield be B

     Hillsdale be C

The Kinsley's house due west of Summerfield be AB which is 6 km and The distance between Summerfield and Hillsdale is BC which is 10 km

Distance between Kinsley's house and Hillsdale can be calculated using Pythagoras' theorem, which states that the square of the hypotenuse is equal to the sum of the square of the other two sides.

        BC² = AB² + AC²

 We need AC, so let us rewrite this equation

        AC² = BC² - AB²

        AC²  =  10² - 6²

        AC² = 100 - 36

        AC² = 64

        AC = √64

        AC = 8 km

Therefore, Kinsley's house is due south of Hillsdale from 8 km

Learn more about Pythagoras theorem in

https://brainly.com/question/343682

#SPJ9

Answer : 3500

Reasoning 2589+2920+3500=9009

Then 9009/3 = 3003

Round 3003 to 3000 and there's your answer

Answer:

2x + 14

Step-by-step explanation:

8 + 2(x + 3) = 2x + 14

2x + 14 = 2x + 14

0 = 0; True

All real numbers

If 4 teenagers can clean in 6 hours, 1 teenager will take 4x more time

1 teenager will take 24 hours = k

No. of teenagers (p) is proportional to time (t):

p = k/t

3 = 24/t

t = 24/3 = 8 hours

So it will take 8 hours for 3 teenagers to clean a house.

8 hours

Step-by-step explanation:

teenagers. hours

4. 6

3. ?

it is actually direct multiplication where you multiply the upper numbers,4 × 6 ,then divide by the lower value, 3. This gives 24 /3 which gives you 8 .

The number of adults, high school​ students, and children not yet in high school attended this​ year are respectively; 70, 100, 120

We are told that a total of 290 people attended the high school play.

If x represents number of adults, y represents number of high school students and z represents number of children, then we have;

x +  y +  z =  290  ----  (1)

The admission prices were $14 for​ adults, $7 for high school​ students, and $3 for children not yet in high school. The ticket sales totaled $2040 . Thus;

14x + 7y + 3z = 2040  ----  (2)

The principal suggested that next year they raise prices to $17 for​ adults, $8 for high school​ students, and $4 for children not yet in high school. Total cost of $2470. Thus;

17x + 8y + 4z = 2470  ----  (3)

Solving the three equations simultaneously gives;

x = 70, y = 100, z = 120

Read more about 3 simultaneous equations at; https://brainly.com/question/28048601

#SPJ1

The amount of time it would take this object to hit the ground is 2.56 seconds.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.

The height (h) in meters, of this falling object is related to the time by the following function:

h = -4.9t² + d

Substituting the given parameters into the formula, we have;

0 = -4.9t² + 32

4.9t² = 32

Time, t² = 32/4.9

Time, t² = 6.53

Time, t = √6.53

Time, t = 2.56 seconds.

Read more on time here: https://brainly.com/question/26746473

#SPJ1

Answer:

24

Step-by-step explanation:

the equation is 6s^2, where s=2. This equals 24

Answer:

Step-by-step explanation: area of one square 2x2 right, then you multiply to get 4 then x6 because of the six sides to a cube then you get 24

The most appropriate choice for trigonometric function will be given by -

sin 45° =  [tex]\frac{1}{\sqrt{2} }[/tex]

cos 45° =  [tex]\frac{1}{\sqrt{2} }[/tex]

tan 45° =  1

cot 45° =  1

sec 45° =  [tex]\sqrt{2}[/tex]

cosec 45° =  [tex]\sqrt{2}[/tex]

What are trigonometric functions?

Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.

There are six trigonometric functions-

[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin \theta[/tex] = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]

[tex]cos\theta[/tex] = [tex]\frac{Base}{Hypotenuse}[/tex]

[tex]tan\theta[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]

[tex]cot\theta[/tex] = [tex]\frac{Base}{Perpendicular}[/tex]

[tex]sec\theta[/tex] = [tex]\frac{Hypotenuse}{Base}[/tex]

[tex]cosec\theta[/tex] = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]

Here,

The diagram of the square has been attached with this answer

∠ABC = 90° [Side of a square is 90°}

∠BAC = [tex]\frac{90}{2}[/tex]

          = [tex]45[/tex]°

Side of square = 1 unit

Length of diagonal of a square = [tex]\sqrt{2}[/tex] [tex]\times[/tex] side

                                                    = [tex]\sqrt{2}[/tex] [tex]\times[/tex] [tex]1[/tex]

                                                    = [tex]\sqrt{2}[/tex] units

From [tex]\Delta[/tex] ABC,

sin 45° = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]

           = [tex]\frac{BC}{AC}[/tex]

           = [tex]\frac{1}{\sqrt{2} }[/tex]

cos 45° = [tex]\frac{Base}{Hypotenuse}[/tex]

           = [tex]\frac{AB}{AC}[/tex]

           = [tex]\frac{1}{\sqrt{2} }[/tex]

tan 45° = [tex]\frac{Perpendicular}{Base}[/tex]

           = [tex]\frac{BC}{AB}[/tex]

           = [tex]\frac{1}{1}[/tex]

           = 1

cot 45° = [tex]\frac{Base}{Perpendicular}[/tex]

           = [tex]\frac{AB}{BC}[/tex]

           = [tex]\frac{1}{1}[/tex]

           = 1

sec 45° = [tex]\frac{Hypotenuse}{Base}[/tex]

           = [tex]\frac{AC}{AB}[/tex]

           = [tex]\frac{\sqrt{2} }{1}[/tex]

           = [tex]\sqrt{2}[/tex]

cosec 45° = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]

           = [tex]\frac{AC}{BC}[/tex]

           = [tex]\frac{\sqrt{2} }{1}[/tex]

           = [tex]\sqrt{2}[/tex]

To learn more about Trigonometric functions, refer to the link:

https://brainly.com/question/1143565

#SPJ9

Answer: 1: 6√6 = 36

hope this helps, good luck!

The number that Joseph is thinking of that is between 15 and 30 is 16.

The first step is to determine the squares between 15 and 30. The square of a number is the product of a number with itself. For example, 16 is a square number.

Squares between 15 and 30 = 16, 25

The next step is to determine the even number. An even number is a number that is perfectly divisible by 2. An example of an even number is 4.

The even number that is a square between 15 and 30 is 16.

The last step is to determine the composite number. A composite number is a number that has more than 2 factors.

Factors of 16 = 1, 2, 4, 8, 16

To learn more about even numbers, please check: https://brainly.com/question/2289438

#SPJ1

The x value of 24 makes the equation to be true

The equation is given as

x/2 - 2 = x/4 + 4

Add 2 to all sides of the equation

So, we have

x/2 = x/4 + 6

Subtract x/4 from all sides of the equation

So, we have

x/2 - x/4 = 6

Multiply through by 4

So, we have

2x - x = 24

So, we have

x = 24

Hence, the value of x in the equation is 24

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

Answer: The answer is a scale factor of 6

Step-by-step explanation:

5 feet is 60 inches, and on the drawing the closet is 10 inches while the real closet is 5 feet, so just divide 60 by whatever gets you 10.

Answer:

$46.64

Step-by-step explanation:

convert 6% to .06

multiply that by 44

you get 2.64.

add that to 44 to get a final ansewr of 46.64 dollers

Answer:

15

Step-by-step explanation:

B*3

5*3

15

Answer:

Step-by-step explanation: if b= 5 the the equation will be (5)^3 you multiply and get 15

( 8.43 , 21.57) is ist a plausible 99% confidence interval for the new slope.

In algebra, what is an interval?

95% of confidence interval  = (10 ,20)

                                        x = 10 + 20 /2 = 15

margin of error = 20 - 10 /2 = 10/2 = 5

SE = Margin of error/2  = 5/1.96  = 2.551

99% confidence interval = x ±  z/2   * 3E

                                        =  15 ± 2.576 * 3E.

                                        = 15 ± 2.576 * 2551

                                         = 15 ± 6.571376

                                       = (15- 6.571376  ,  15 + 6.571376)

                                       = ( 8.43 , 21.57)

Learn more about interval

brainly.com/question/13708942

#SPJ9

Answer:

f(4) = 8

Step-by-step explanation:

Hello!

You can find f(4) by substituting 4 for x in 3x - 4.

The value of f(4) is 8.

Answer:

Step-by-step explanation:

h(x)=-2x-3 h(6)

A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four. There is no proportionality between the quantity of turkey subs delivered and the amount billed.

Given that,

A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four.

We have to find the relation ship between the quantity of turkey subs delivered and the amount billed.

The reciprocal of the ratio of subs to amount charges is

We get,

3/20 and 4/26

Since,  

3/20≠4/26

Therefore, There is no proportionality between the quantity of turkey subs delivered and the amount billed.

To learn more about amount visit: https://brainly.com/question/16629663

#SPJ1