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y=-( (sqrt(x+2)) /(x/2-3) )^2 + 8
Find the domain and range

Answer:

y=.75x+100

Step-by-step explanation:

y=mx+b

m=slope (rate)

b=y-intercept (starting point)

y=.75x+100

The linear equation that models this situation, using 'p' for profit and 'n' for number of units sold, is p = 0.75n + 100.

The situation described is one of a linear relationship between the number of units sold (n) and the profit (p). In this case, we are given the initial profit (the y-intercept) of $100 (a = 100) and the profit per unit sold (the slope) of $0.75 (b = 0.75). Therefore, the linear equation modeling this situation in slope-intercept form would be p = 0.75n + 100.

In this equation, n represents the number of units sold and p represents the profit. For every unit sold (increase in n by 1), the profit (p) increases by $0.75. The $100 represents the initial profit, or the starting point of sales, which in this case is after covering the start-up costs.

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Answer:

135

Step-by-step explanation:

1 of every 1+2 = 3 items sold was a hamburger.

# of hamburgers = (1/3)·405 = 135

To solve the problem, we first create and solve an algebraic equation. The equation shows that the hamburger shop sold 135 hamburgers on Sunday.

The given problem is a classic example of algebraic equations. We know that the total number of hamburgers and cheeseburgers sold was 405. And we know that the number of cheeseburgers sold was two times the number of hamburgers. Let's denote the number of hamburgers sold as H, and the number of cheeseburgers as C. From the information provided, we have two equations:

Now, we can substitute the first equation into the second, replacing C with 2H:

This simplifies to:

Finally, to find H, we divide both sides of this equation by 3:

Therefore, 135 hamburgers were sold on Sunday.

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We can let x represent the width of the barn in feet. Then the length of the barn is 2x. The portion of width not used for stalls is (x-10). The height of that is (x-6).

So, the product of length, width not used for stalls, and height must be 1920 ft³. The equation for that is ...

... 2x(x -10)(x -6) = 1920 . . . . the equation

Solution

I generally find it convenient to use a graphing calculator to find the solutions to higher-order equations. Rearranging this so we're looking for a zero, it becomes ...

... 2x(x -10)(x -6) -1920 = 0

The graph shows one real root, at x = 16.

The dimensions of the lower floor should be 16 feet wide, 32 feet long, and a ceiling height of 10 feet.

_____

Alternate solution

Dividing by 2, we have

... x(x-6)(x-10) = 960

If we look at the factors of 960, we find that it is the product of 16, 10, and 6, which would let us assign x=16.

___

There are 28 divisors of 960. According to the Rational Root theorem, any of them might be a solution. There are arguments that can be made regarding reasonable dimensions that suggest x will be more than 12 (6 ft ceiling, 2 ft aisle). So, the number of trial-and-error possibilities is reduced somewhat.

The dimensions of the lower barn floor should be a width of 8 feet, a length of 16 feet, and a height of 2 feet, determined by setting up and solving a polynomial equation based on the given parameters.

The problem can be solved using polynomial equations. First, let's denote the width of the lower barn floor as x. Given that the length of the barn is twice the width, the length is 2x. The height of the lower barn floor is 6 feet less than the width of the barn, so it's x - 6 feet.

The volume of a rectangular solid is given by length times width times height. So according to the information provided, we can set up the following polynomial equation: 2x * x * (x - 6) = 1920.

By simplifying the equation, we get 2x^3 - 12x^2 - 1920 = 0.

This equation can be solved using various methods such as the rational root theorem, synthetic division, or factoring. After solving, we find that the root x = 8 is the only physically meaningful solution (length width and height must be positive). Therefore, the width of the lower floor should be 8 feet, the length should be 2 * 8 = 16 feet, and the height should be 8 - 6 = 2 feet.

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Answer:

c = 7p

Step-by-step explanation:

If 1 person buys the platter, the bill is c = 1 × $7.

If 2 people buy the platter, the bill is c = 2 × $7.

If 3 people buy the platter, the bill is c = 3 × $7.

(Do you see the pattern yet?)

If "p" people buy the platter, the bill is c = p × $7.

We ususally say "c is in dollars" and drop the "$" sign from the equation. When p is multiplied by 7, we conventionally write it as 7p.

... c = 7p

Your selection is correct: 180 hours

The pool is apparently 18000 gallons (= 60 gal/h × 300 h). The combined flow from the two hoses is ...

... (40 gal/h) + (60 gal/h) = 100 gal/h

So, the time required with the two hoses is ...

... 18000 gal/(100 gal/h) = 180 h

Answer:

C) 180 hours

Step-by-step explanation:

Edge 2020

Answer:

(x, y) = (-0.3, -1.6)

Step-by-step explanation:

The graph below shows these equations graphed. Their point of intersection is (-0.3, -1.6).

_____

Analytical solution

You can equate the expressions for y to get ...

... 12x +2 = 2x -1

... 10x = -3  . . . . subtract (2x+2)

... x = -0.3 . . . . . divide by 10

... y = 2(-.3)-1 = -1.6 . . . . use the 2nd equation to find y.

Answer:

1416.71

Step-by-step explanation:

Total Pay= 1843.45

Deductions

Fica = 7.65% of 1843.45  = 141.02

With holding = 9 % of 1843.45 = 165.9

state withholding =6.5 % of 1843.45 = 119.82

total deductions = 141.02 + 165.9 + 119.82

                           =426.74

Remaining money= 1843.45-426.74

                              = 1416.71

Answer:

510.01 is the right answer

Step-by-step explanation:

7. Law of cosines

a² = b² + c² - 2bc cos A

where a is the side opposite to ∠A and b and c are adjacent sides to ∠A.

Here, a=BC= 3.8

b=CA =4.8

c = AB = 3.2

Substituting the values in the formula,

3.8² = 4.8² + 3.2² - 2(4.8)(3.2) cos A

30.72 cos A =23.04 + 10.24 -14.44=18.84

cos A = 18.84/30.72 = 0.6133

∴ cos A =0.6133

8. It is a right angled triangle.

Pythagoras theorem

hypotenuse² = Perpendicular² + base²

Here, hypotenuse = 6.7, base = 5.4

Perpendicular² = 6.7² -5.4²=44.89 - 29.16 =15.73

Perpendicular = √15.73 = 3.966 = 3.97

∴ The length of the missing side is 3.97.

9. Given:   Side of new cube = 5 * Side of original cube

Let the side of the original cube measure 1 unit.

So, volume of original cube = side³ = 1

The side of new cube = 5 * 1 =5 units

So, volume of new cube = side³ = 5³ =125

The volume of the bigger cube is 125 times larger than the original cube.

10. Given : Height of the cone = 7 in

Radius of the base of the cone = 2 in

Volume of cone = (1/3) πr²h

                           =(1/3)π(2²)(7)

                           =29.32 cubic inches

∴ Volume of the cone is 29.32 cubic inches.

11. The given equation is:

x² -18x +10 =0

(x² -18x + 9²) +10 -9² =0

(x-9)²-71 =0

(x-9)² =71

x-9 =√71

x = 9 + √71

∴ x = 9+√71

hey mate..

the position at which the tips of the scissors will be FARTHER APART is at position B.

as the angle made by the scissors at the centre is greater in position B.

Answer:

d) V/(lh) = w

Step-by-step explanation:

The appropriate solution divides the equation by the coefficient of w, which is lh. In answer selection (d), that is done by first dividing by l, then by h.

_____

Comment on the solution

One could just divide by l·h and be done with it.

Answer:

5

Step-by-step explanation:

It is 5 because no matter how many stamps he sells, he has $5.

Answer:

The y-intercept of Ben's graph is [tex]y = 5[/tex].

Step-by-step explanation:

The function for Ben's amount of money y, depending on the number of stamps sold x, is as follows:

[tex]y = ax + b[/tex]

In which a is the price of each stamp and b is his initial money.

Building the function:

Ben has $5. This means that if he sells no stamps, he is still going to have $5. So [tex]b = 5[/tex].

For each stamp sold, he gains $3. So if sells 1 stamp, he will have $8, if he sells 2, he will have $11. So [tex]a = 3[/tex].

The function is:

[tex]y = 3x + 5[/tex]

Which will be the y-intercept of Ben's graph?

This is the value of y when x = 0.

So

[tex]y = 3*0 + 5 = 5[/tex]

The y-intercept of Ben's graph is [tex]y = 5[/tex].

Answer:

3

Step-by-step explanation:

Terms combine to simplify the expression somewhat.

... = x^6y^3·(4 -3 -1) +x^2y^2·(2 -1) +y

... = x^2y^2 +y

... = (xy)^2 +y

For your given values, this is ...

... ((-2)(-1))^2 +(-1)

... = 2^2 -1 = 3

A. $30,000

Let c represent the cost of Colin's car. Then ...

... c = (3 3/4) × $8000 = (3 × $8000) + ((3/4) × $8000)

... = $24000 + 6000

... c = $30,000

The cost of Colin's car is $30,000.

Answer:

A. $30,000

Step-by-step explanation:

To solve this you just have to do a simple rule of three, where in one side has the price of the car that his parents bought for 8,000 dollars and calculate the money that colin´s car costed in the other side:

[tex]\frac{8000}{1}= \frac{x}{3\frac{3}{4} } \\x=\frac{3,75*8000}{1}\\ x=30000[/tex]

So now we know that the car that Colin bought was 3.75 times as expensive as his parents 8,000 dollar car, that means it costed 30,000 dollars.

Answer:

B. h=2A/(b1+b2) . . . . parentheses are needed

Step-by-step explanation:

Multiply the equation by the inverse of the coefficient of h. That coefficient is (b1 +b2)/2, so its inverse is 2/(b1 +b2). Parentheses are needed.

... 2A/(b1 +b2) = h

_____

Comment on the answer choices

As written, none of them are correct. The denominator can only be written without parentheses if the division bar is horizontal, and so serves also as a grouping symbol.

Answer:

132°

Step-by-step explanation:

Sum of the interior angles of a polygon is given by the formula:

[tex](n-2)*180[/tex]

Where [tex]n[/tex] is the number of sides of the polygon.

The figure shows a 5 sided polygon (aka Pentagon). So the sum of all the angles is:

Sum = [tex](5-2)*180\\=3*180\\=540[/tex]

If we add up all the expressions/angles given and equate to 540, we can figure out [tex]x[/tex]. So:

[tex]84+13x+6+9x-16+92+12x=540\\34x+166=540\\34x=540-166\\34x=374\\x=\frac{374}{34}=11[/tex]

But angle B measures [tex]12x[/tex], so plugging in [tex]x=11[/tex], we have:

Angle B = [tex]12x=12(11)=132[/tex]°

Second answer is right.

Answer:

x = -11

Step-by-step explanation:

Complimentary so you set them equal to each other.

6x + 185 = 8x + 207

-2x = 22

x = -11

AAS Congruence Postulate proves that ∆MNQ ≅ ∆PNQ

Considering    ΔMNQ   and   ΔPNQ

                         ∠QMN   =      ∠QPN   (given)

                          ∠QNM   =       ∠ QNP  ( both are right angles)

                            Side NQ is common

∴        ΔMNQ   and   ΔPNQ are congruent by AAS congruency since two angles and a side are considered to prove the congruency.

The correct answer is option B.   AAS congruency postulates.

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The slope of AB is ...

... slope = (change in y)/(change in x) = (-6-(-3))/(8-2) = -3/6 = -1/2

The slope of AD is ...

... slope = (change in y)/(change in x) = (0 -(-3))/(8 -2) = 3/6 = 1/2

We note that the differences have the same magnitudes in both cases (y changes by 6; x changes by 3). This tells us the line segments are the same length. (Each side of the figure is equivalent to the hypotenuse of a right triangle with legs 3 and 6.)

The opposite reciprocal of a number is found by dividing -1 by that number. Thus the opposite reciprocal of the slope of AB is ...

... -1/(-1/2) = (-1/1)·(-2/1) = 2

This value is not the same as the slope of AD, so the slopes are NOT opposite reciprocals.

_____

Plotting the points, we see that we have a rhombus, not a rectangle (or square).

Answer:

d. 8

Step-by-step explanation:

Given: -3x + 2y = 1 and x = 5

Now plug x =5 in the given equation and find the value of y.

-3(5) + 2y = 1

-15 + 2y = 1

2y = 1 + 15

2y = 16

Dividing both sides by 2, we get

y = 8

Thank you.

Answer: [tex]y=8[/tex]

Step-by-step explanation:

1. You already know the value of the variable [tex]x[/tex], which is:

[tex]x=5[/tex]

2. Therefore, you need to substiute the value  [tex]x=5[/tex] into the equation [tex]-3x+2y=1[/tex] and then you must solve for [tex]y[/tex], as following:

[tex]-3x+2y=1\\-3(5)+2y=1\\-15+2y=1\\2y=1+15\\2y=16\\y=\frac{16}{2}\\y=8[/tex]

3. The result is: [tex]y=8[/tex]

Answer:

The correct option is B.

Step-by-step explanation:

The given function is

[tex]f(x)=x[/tex]

The new function is

[tex]g(x)=-\frac{1}{2}f(x)[/tex]

[tex]g(x)=-\frac{1}{2}x[/tex]        .... (1)

It is in the form of

[tex]g(x)=mx[/tex]                   .... (2)

Where, m is a constant.

If m is negative, then there is a vertical reflection over x-axis. If the constant is greater than 1, we get a vertical stretch and  if the constant is between 0 and 1, we get a vertical compression.

From (1) and (2), we get

[tex]m=-\frac{1}{2}[/tex]

Since the value of m is negative and absolute value of m is between 0 and 1, therefore the graph g(x) shows the vertical reflection over x-axis and vertical compression.

Option B is correct.

Final answer:

The graph of f(x) = x, when modified to -1/2 f(x), undergoes a vertical reflection over the x-axis and a vertical compression by a factor of 1/2, resulting in answer B.

Explanation:

When the function f(x) = x is replaced with -1/2 f(x), the effect on the graph is two-fold. Firstly, there is a vertical reflection over the x-axis because of the negative sign.

This means that the graph is flipped over the x-axis, with points that were above the x-axis now being below it, and vice versa.

Secondly, there is a vertical compression by a factor of 1/2 due to the multiplier of -1/2. This compresses the graph towards the x-axis, making it 'flatter' than the original graph of f(x) = x.

Therefore, the correct answer to the question is B) vertical reflection over the x-axis and vertical compression.

Step-by-step explanation:

sqrt of 81 is 9 so rational

Sqrt of 89 is irrational

Sqrt of 121 is 11 so rational

Sqrt of 131 is irrational.

Answer:

Her error was overestimating by 33.3%  

Step-by-step explanation:

To calculate a relative error (or percent error), we need to identify the absolute error first. In this case, the absolute error is the difference between Lauren's estimate and the actual outcome: 15 jacks - 20 estimated jacks = -5. The fact that this error is negative is only to indicate that Lauren overestimated (as opposed to underestimated). Usually, the absolute value is taken.

As next step, the absolute error is made to a relative one by dividing by the ground truth, which is the actual outcome of 15 jumping jacks. The relative error = |-5|/15 = 1/3. Expressed in percent: 33.3%. Lauren made an error of 33.3% (overestimate).

A) (3, 1)

B) (3, 1), (2, -1)

C) (1, 3)

A) The problem statement tells you the point (3, 1) is on both lines.

B) The problem statement tells you the line goes through points ...

... (3, 1) and (2, -1).

C) The problem statement tells you point (1, 3) is a solution to p(x). It also happens that g(1) = 2·1.5¹ = 3, so (1, 3) is also a solution to g(x).

(1, 3) is a solution to p(x) = g(x) because p(1) = 3 = g(1).

Answer:

7.9 ft

Step-by-step explanation:

The hypotenuse is the side opposite of the right angle, hence the hypotenuse for this triangle is 11 ft.

Side [tex]x[/tex] is adjacent to the angle given. So we need adjacent and we have hypotenuse. Which trigonometric ratio relates adjacent and hypotenuse? It is COSINE.

Thus, we can write:

[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(44)=\frac{x}{11}[/tex]

Cross multiplying, we can solve for [tex]x[/tex]:

[tex]cos(44)=\frac{x}{11}\\x=cos(44)*11\\x=7.91[/tex]

Rounding to nearest tenth, we have [tex]x=7.9[/tex] ft.

Answer:

[tex]1.13x[/tex]

Step-by-step explanation:

We have been given that Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13% monster truck tax. We are asked to find the total amount paid by Camacho for the monster truck.

The total cost of monster truck would be x plus 13% of x.

[tex]\text{The total cost of monster truck}=x+\frac{13}{100}x[/tex]

[tex]\text{The total cost of monster truck}=x+0.13x[/tex]

[tex]\text{The total cost of monster truck}=1.13x[/tex]

Therefore, Camacho paid [tex]1.13x[/tex] dollars in total for the truck.

Final answer:

To find the total cost of the monster truck, convert the 13\% tax to decimal form (0.13), multiply it by the price of the truck (xx dollars), then add the result to the original price to get the total cost, which is 1.13xx.

Explanation:

To determine the total amount Camacho will pay for the monster truck, we need to calculate the sales tax and add it to the original price of the truck. The sales tax is 13\%, which can be converted to a decimal for calculation purposes. First, convert 13\% to a decimal by dividing by 100, which gives us 0.13. Then multiply 0.13 by the price of the truck (xx dollars) to find the amount of tax Camacho will have to pay.

After calculating the tax, you can find the total cost by adding the tax to the original price of the truck.

Step 1: Convert 13\% to a decimal = 0.13
Step 2: Multiply the price of the truck (xx dollars) by 0.13 to find the tax = 0.13 * xx
Step 3: Add the tax to the original price to find the total cost: xx + (0.13 * xx).

Total cost = xx + 0.13xx = 1.13xx

Answer:

333°

Step-by-step explanation:

Minor arc ST is the difference between minor arc RT and minor arc RS:

... 153° -126° = 27°

Major arc SPT is the remainder of the circle:

... 360° -27° = 333°

Answer:

slope = .4

She ran .4 laps per min.

She ran 12 laps in 30 minutes

Step-by-step explanation:

The slope is the rate of change.  It can be found by using the formula

slope = (y2-y1)/(x2-x1)

 The given points are (11, 4.4)  (5.5 ,2.2)

slope = (2.2-4.4(/ (5.5-11)

           = -2.2/-5.5

          .4

The slope represents .4 laps per min  since y is in laps and x is in minutes.

If she  ran 30 minutes, we multiply the time by the slope to calculate the laps.

30 * .4 = 12

She ran 12 laps.

A) The slope is the change in Y over the change in X.

Using the 2 points given on the graph (11,4.4) and (5.5, 2.2)

The first number in the parenthesis are the X value and the 2nd numbers are the Y values.

Slope = (4.4 - 2.2) / (11-5.5)

= 2.2 / 5.5

= 0.4

B) From the slope, she ran 0.4 laps per minute.

C) To find the total laps, multiple laps per minute by total minutes:

30 minutes x 0.4 laps per minute = 12 laps.

Answer:

213.7°

Step-by-step explanation:

The bearing of B from D is angle ADB, which is ...

... ∠ADB = arctan(30/45) ≈ 33.7°

The bearing of D from B is that angle plus 180°, so is ...

... 180° +33.7° = 213.7°

_____

We use angle ADB because the reference direction for bearings is North.

The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).

So let's break down this sentence (Let n = unknown number):

Now, let's solve our prior equation found in A. To solve for the unknown number, n, we need to isolate the variable onto 1 side of the equation. Firstly subtract both sides by 16 to cancel out the + 16 on the left side:

[tex]\frac{2n+1}{5}=2[/tex]

Next, multiply both sides by 5 to cancel out the division on the left side:

[tex]2n+1=10[/tex]

Next, subtract both sides by 1 to cancel out the + 1:

[tex]2n=9[/tex]

Lastly, divide both sides by 2 to cancel out the multiplication:

[tex]n=\frac{9}{2}\ \textsf{OR}\ 4.5[/tex]

In short, the number is 9/2 or 4.5.