The swimsuit is on sale for 25% off its original price. If the original price was $58. What is the sale price?

Answer: 2x^3 - 7x^2 + 6x - 9 which is choice D

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Work Shown:

One way is to use the distribution rule two times

(x-3)(2x^2-x+3) = y(2x^2-x+3) ........... replace (x-3) with y

(x-3)(2x^2-x+3) = y(2x^2)+y(-x)+y(3) .... distribution rule

(x-3)(2x^2-x+3) = 2x^2*(y) - x(y) + 3(y)

(x-3)(2x^2-x+3) = 2x^2*(x-3) - x(x-3) + 3(x-3) .... replace y with x-3

(x-3)(2x^2-x+3) = 2x^3-6x^2 - x^2 + 3x + 3x - 9 ... distribution rule

(x-3)(2x^2-x+3) = 2x^3 - 7x^2 + 6x - 9

----------------------------

Or we can use the box method (see the attached image below). This is a visual way to organize the terms. You'll probably notice that the box method is basically the distribution rule. Each row is one distribution being applied. In row 1, we have x distributed to (2x^2-x+3). In row 2, we have -3 distributed to (2x^2-x+3). I color coded the table cells to highlight the like terms. Those like terms combine to -6x^2-x^2 = -7x^2 and 3x+3x = 6x as shown in the steps for the distribution above.

Each interior cell in the box is found by multiplying the corresponding outer terms. For example, in the first row, first column we have x^3 which is the result of multiplying the outer x and x^2 terms.

The correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

To find the product[tex]\((x - 3)(2x^2 - x + 3)\)[/tex], we can use the distributive property:

[tex]\((x - 3)(2x^2 - x + 3) = x(2x^2 - x + 3) - 3(2x^2 - x + 3)\)[/tex]

Now, distribute the terms:

[tex]\[= x \cdot 2x^2 - x^2 + 3x - 3 \cdot 2x^2 + 3x - 9\][/tex]

Combine like terms:

[tex]\[= 2x^3 - x^2 + 6x - 6x^2 + 6x - 9\][/tex]

Combine the x terms:

[tex]\[= 2x^3 - 7x^2 + 6x - 9\][/tex]

Therefore, the expression [tex]\((x - 3)(2x^2 - x + 3)\)[/tex]  is equal to \[tex](2x^3 - 7x^2 + 6x - 9\)[/tex].

So, the correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

Answer:

Same side: 4, 1.5, 5/3, 0.2

Opposite side: -5, -1/4

Step-by-step explanation:

We know that dilation caused by a positive factor leads to the object being on the same side and dilation caused by a negative factor leads to the object being on the opposite side. Therefore, the dilation caused by positive numbers 4, 1.5, 5/3, 0.2 will lead to object being on the same side. And dilation caused by a negative numbers -5 and -1/4 will lead to object being reflected to the opposite side

Answer:

9.00

Step-by-step explanation:

Use proportion:-

20% is equivalent to 1.80

1%  is equivalent to 1.80 / 20

100% is equivalent to (1.80 / 20 ) * 100

= 180 / 20

= 9

=  9.00

18/12=  [tex]1\frac{1}{2}[/tex] and  [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option,  [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of  [tex]1\frac{7}{8}[/tex].

A fraction represents a part of a whole.

If a fraction has a numerator that is less than the denominator then the fraction is proper.

An improper fraction has a numerator that is greater than the denominator.

A mixed number is an integer written with a fraction.

18/12 is a improper fraction, let us simplify it by dividing numerator and denominator by 6

18/12 is 3/2.

The mixed fraction of 3/2 is [tex]1\frac{1}{2}[/tex]

Now the given mixed fraction is [tex]1\frac{7}{8}[/tex]

When we convert to improper we get (8×1)+7/8 , which is 15/8

Hence, 18/12=  [tex]1\frac{1}{2}[/tex] and  [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option,  [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of  [tex]1\frac{7}{8}[/tex].

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Answer:

(-4,1)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

it would be SSS...

Step-by-step explanation:

Its meaning is "side side side''... so you see how the triangle, ABD has the dashed (same number of lines) through the lines of the triangle, it means the sides are all congruent meaning that the sides are the same

Answer:

The triangles are not congruent.

Step-by-step explanation:

The triangle ABD is an equilateral triangle, then all their sides are equal and all the angles are equal to 60º. Then x=60º and y=30º (because the sum of the internal angles of a triangle have to be 180º)

Then we can conclude that the triangles are not congruent because they share two sides, but does no have any angle in common, as we can see in the next list of the angles.

angle ADB= angle ABD= angle DAB=60º

angle BDC=30º

angle DCB=30º

angle CBD=120º

Final answer:

To find the scaled length of a line representing 5 feet on a scale drawing with a scale of 0.5 inches = 2 feet, set up a proportion and solve for x. The answer is 1.25 inches.

Explanation:

To calculate the length of a line on a scale drawing, you must use the scale provided and set up a proportion based on that scale. In this case, the scale is 0.5 inches = 2 feet. To find out what 5 feet would be on the drawing, we can set up a proportion where 0.5 inches/2 feet equals x inches/5 feet. Solving for x gives us:

0.5 inches / 2 feet = x inches / 5 feet

To keep the units consistent, we use cross-multiplication:

(0.5 inches) * 5 feet = 2 feet * x inches

2.5 inches = 2 feet * x inches

Now, divide both sides by 2 feet to solve for x:

x = 2.5 inches / 2 feet

x = 1.25 inches

Therefore, a line that represents an actual length of 5 feet would be 1.25 inches long on the scale drawing.

Emery initially borrowed $608. Each week, she paid off $76. After 2 weeks she had $456 left to pay and after 5 weeks she owed $228.

To find out the original amount borrowed, we need to determine how much Emery is paying off each week. If we look at the information given, after 2 weeks Emery still owes $456, and after 5 weeks, she owes $228. That's a difference of $228 over the span of 3 weeks, which means she is paying off $76 each week ($228 / 3 weeks = $76 per week).

Knowing this, we can figure out that she owed $608 before she started making payments (that is, $456 + $76*2 weeks = $608). Therefore, the original amount Emery borrowed from her brother was $608.

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the complete Question is given below

Emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks, she will owe $228. a. What was the original amount Emery borrowediginal amount borrowed?

Answer:

154 square inches

Step-by-step explanation:

Watch the attached figure of the square pizza box and the largest pizza that can fit into it.

Let the each side of the square pizza box be a inches.

Radius of the largest pizza that can fit into it = Half of the side of the pizza box = [tex]\frac{a}{2}[/tex]

So, area of the square box = Side * Side

                                             = a * a

                                             = a² square inches

It has also been given that the large box has an area of 196 square inches.

So,

Area of the box = a²

=> 196 = a²

Flipping the sides of the equation, we get

=> a² = 196

Taking square root on both the sides,

√a² = √196

a = 14 inches

So,

Side of square box = 14 inches

Radius of the largest pizza that can fit into it = [tex]\frac{a}{2}[/tex]

                                                                          = [tex]\frac{14}{2}[/tex]

                                                                          = 7 inches

Area of the largest possible pizza that could be placed into the box

= π *radius²                                       [since pizza is circular in shape]

= [tex]\frac{22}{7}[/tex] * 7²

= [tex]\frac{22}{7}[/tex] * 7 * 7

Cancelling out a pair of 7's from the top and bottom, we have

= 22 * 7

= 154 square inches

Answer:

6

Step-by-step explanation:

f(x) = 3x - 1

f(2) means evaluate  f(x) when x=2

f(2) = 3(2) -1

f(2) = 6-1=5

g(5) means evaluate g(x) when x=5

g(5) = -5+6

g(5) =1

f(-2) + g(5)

5+1

6

Answer:

6

Step-by-step explanation:

Answer:

the tank can hold 12.5 gallons when it is full

Step-by-step explanation:

Let's assume

tank can hold 'x' gallons when it is full

we are given

The gas gauge in a car shows it has 40% of a tank of gas

So, gas in car is

[tex]=\frac{40}{100}\times x[/tex]

and we have

the car has about 5 gallons

so, we can set it equal

and then we can solve for x

[tex]5=\frac{40}{100}\times x[/tex]

[tex]5=\frac{4}{10}\times x[/tex]

[tex]5=\frac{2}{5}\times x[/tex]

Multiply both sides 5

[tex]5\times 5=5\times \frac{2}{5}\times x[/tex]

[tex]5\times 5=2x[/tex]

[tex]25=2x[/tex]

we get

[tex]x=12.5[/tex]

So, the tank can hold 12.5 gallons when it is full

Answer:

B

Step-by-step explanation:

Answer: Negative infinity

note: if your teacher won't allow negative infinity, then try DNE for "does not exist"

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Explanation:

As x gets closer to x = 4 from the left side of this value, then x starts at something like x = 3 and moves to x = 3.5, then to x = 3.9, then to x = 3.99, then to x = 3.999, etc

We get closer to x = 4 but never actually get there. If you look at the table attached, then f(x) = 1/(x-4) will keep getting more negative with larger and larger negative values. This growth goes on forever without any bound. So the limit is equal to negative infinity.

As you can see on the graph below, the curve heads downward as you approach x = 4 from the left hand side. Imagine you are a point on the curve, or this point is on a rollercoaster (the curve being the track itself). As you get closer to 4 from the left side, you go downhill. There is on limit to how far downhill you can go.

note: the graph and table in the attachment below were made by the free graphing calculator program GeoGebra

Answer with explanation:

The given rational function is

      [tex]y= \lim_{x \to 4^{-}} \frac{1}{x-4}[/tex]

To find the vertical Asymptotes , put

→  Denominator =0

→ x-4=0

→x=4, is the Vertical Asymptote.

[tex]\mathsf{We\;know\;that : Density = \frac{Mass\;of\;the\;Object}{Volume\;of\;the\;Object}}[/tex]

[tex]\mathsf{Given : Mass\;of\;the\;Object = 20\;Grams}[/tex]

[tex]\mathsf{Given : Volume\;of\;the\;Object = 3.5\;cm^3}[/tex]

[tex]\mathsf{\implies Density = \frac{20}{3.5}(\frac{g}{cm^3})}[/tex]

[tex]\mathsf{\implies Density = 5.71\;(\frac{g}{cm^3})}[/tex]

To find the density of an object, we will use the formula for density which is \( d = \frac{m}{v} \), where:
- \(d\) represents the density of the object,
- \(m\) is the mass of the object, and
- \(v\) is the volume of the object.

Substituting the given values into the formula:
\(m = 20 \, \text{g}\) (mass of the object),
\(v = 3.5 \, \text{cm}^3\) (volume of the object),

we get:
\(d = \frac{20 \, \text{g}}{3.5 \, \text{cm}^3}\).

Dividing 20 grams by 3.5 cubic centimeters, we obtain:
\(d ≈ 5.71 \, \text{g/cm}^3\).

Therefore, the correct answer is:

C.5.71 G/CM3

Answer:

answer is 8

8+14x+6x+12=180

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

The slope of a line passing through two points (a,b) and (c,d) is given by :-

[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]

In the given graph , the line is passing through (0,0) and (1,3) .\

Then the slope of line  passing through (0,0) and (1,3) will be :-

[tex]\text{Slope}=\dfrac{3-0}{1-0}\\\\\Rightarrow\ \text{Slope}=3[/tex]

Hence, the slope of the given line= 3

∠8=180°-92°=88°

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Answer:

Step-by-step explanation:

The answer is 88 degrees i got that question right.

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is that x = 19 is the solution because 3 * 19 - 15 = 57 - 15 = 42.

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is the option: x = 19 is not the solution because 3 * 19 - 15 = 3 * 4 = 12, not 42.

To check if a value is the solution to an equation, we substitute the value into the equation and perform the necessary calculations. In this case, substituting x = 19 into the equation 42 = 3x - 15 gives us 42 = 3 * 19 - 15 = 57 - 15 = 42. Since both sides of the equation are equal, x = 19 is indeed the solution.

The question is asking to determine if x = 19 is the solution for the equation 42 = 3x – 15. To verify this, we need to substitute x = 19 into the equation. So, we have 42 = 3(19) - 15 which simplifies to 42 = 57 - 15. After subtraction on the right side, we get 42 = 42, which is a true statement. Hence, x = 19 is indeed the solution to the equation 42 = 3x – 15.

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Answer:

see explanation

Step-by-step explanation:

the result 0 = 0

means the equation has an infinite number of solutions

Answer:

All values of x make the equation true... THIS  IS THE CORRECT ANSWER!

Step-by-step explanation:

Answer:

(3, 7)

Step-by-step explanation:

The midpoint of a line joining the points  (x1, y1) and (x2, y2) has midpoint

[(x1 + x2)/ 2]. (y1 + y2)/2 ]

Substituting the given points:-

Midpoint of MN =  (-2 + 8)/2 ,  (4 + 10)/2

= 6/2 , 14/2

= (3, 7)   (answer)

To qualify for the special summer camp for accelerated students, a student must score at least approximately 978 on the standardized test, considering a score within the top 16% of all scores, given a mean score of 800 and a standard deviation of 120.

In a bell-shaped or normal distribution, the mean [tex]\(\mu\)[/tex] represents the central tendency of the data, and the standard deviation [tex]\(\sigma\)[/tex] measures the dispersion or spread of the scores. To find the score required to qualify for the top 16%, we use the z-score formula: [tex]\(z = \frac{X - \mu}{\sigma}\)[/tex], where X is the score, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.

Given the mean score [tex]\(\mu = 800\)[/tex] and standard deviation [tex]\(\sigma = 120\)[/tex], the z-score corresponding to the top 16% is found using a standard normal distribution table or statistical software. The z-score associated with the top 16% is approximately z = 1.04.

Next, use the z-score formula to solve for the score X required to be in the top 16%: [tex]\(z = \frac{X - \mu}{\sigma}\)\\[/tex]. Rearranging the formula to solve for X gives us [tex]\(X = z \cdot \sigma + \mu\)[/tex]. Substituting the z-score value and the given mean and standard deviation into the equation yields [tex]\(X = 1.04 \cdot 120 + 800 = 978\)[/tex]. Hence, a student needs to score at least approximately 978 to qualify for the special summer camp for accelerated students, given the distribution of scores on the standardized test.

Answer:

sec theta = r/v

Step-by-step explanation:

sec theta  = 1 /  sin theta

We know that sin theta = opp/ hypotenuse

1 / sin theta = hypotenuse /  opp

sec theta = hypotenuse /  opp

sec theta = r/v

Answer:

Prefix Symbol Multiplier

deci d 0.1

centi c 0.01

milli m 0.001

micro µ 0.000001

Step-by-step explanation:

A recursive rule for a geometric sequence

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

---------------------------------------------------------------

[tex]a_1=-64;\ a_2=-16;\ a_3=-4;\ a_4=-1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\\\\r=\dfrac{-16}{-64}=\dfrac{1}{4}\\\\\boxed{a_1=-64;\qquad a_n=\dfrac{1}{4}\cdot a_{n-1}}[/tex]

Answer:

D)

Step-by-step explanation:

sec(x) = 1/cos(x)

You know cos(x) = 1 for x=0, so sec(0) = 1.

You also know that sec(x) has vertical asymptotes where cos(x) = 0, at odd multiples of π/2. Only selection D matchest these characteristics.

Answer:

R=6%

Step-by-step explanation:

Given:

Total money deposited = $ 520

Total years = 5

Total earned = $156

Simple interest

To Find:

interest rate=R=?

Solution:

We know the formula for calculating total amount earned by a simple interest rate and formula for it is

I = P(rT)                     ..................(i)

where I is total amount earned

P is total money invested

r is rate

and t is time

putting the values gives us

156 = 520 (r)(5)

156 = 2600 r

dividing both sides by 2600

r = [tex]\frac{156}{2600}[/tex]

r= 0.06

We have to find R

Now from simple rules of

we know that

R = r* 100 %

so putting the value of r

R = 0.06 * 100 %

R = 6%

which is the rate at which money was invested

Answer:

65,1,5.5

Step-by-step explanation:

Replace with 1 and simplify.

Answer:

The answer is 63/10, 63/100, 63/1000

Final answer:

78,045 rounded to the nearest thousand is 78,000. You round down because the hundreds digit (0) is less than 5. This approach to rounding applies in various arithmetic contexts.

Explanation:

To round 78,045 to the nearest thousand, we need to consider the hundreds digit, which is 0. In rounding, if the hundreds digit is 5 or greater, we would round up. However, because it is 0, we keep the thousands digit the same and replace all subsequent digits with zeros. Thus, 78,045 rounded to the nearest thousand is 78,000.

When dealing with whole numbers and rounding to a certain place value, it is crucial to look at the number to the immediate right of the place value you are rounding to. If this number is 5 or higher, you round up. Otherwise, you round down. This principle is true regardless of whether you are serving a subtraction operation, like 78,500 m - 362 m which rounds to 78,100 m, or if you're dealing with large numbers in scientific notation, such as 79,345 which can be represented as 7.9345 × 104.

Answer:

600kW

Step-by-step explanation:

Referring to the fact that 10m/s of wind is 500kW so divide 500 by 10.

500/10=50

So there is 50 kW is 1m/s of wind. Now multiply 12 by 50

12x50=600

So for 12m/s of wind there is 600kW

At 12 m/s, the turbine generates 864 kW.

We can express the given relationship as P = k * v^3, where k is a constant of proportionality.

Given that a turbine generates 500 kW at a wind speed of 10 m/s, we can find k using the equation:

500 = k * 10^3

k = 500 / 1000

k = 0.5.

Now, to find out how much power the turbine would generate at 12 m/s. The calculation is :

P = 0.5 * 12^3

P = 0.5 * 1728

P = 864 kW.

The wind turbine generates 864 kW in a 12 m/s wind.