What is the simplified form of the following expression?
2√27+√12-3√3-2√12
O√3
O 9√3
O 11 √3
O 15√3

Answer:

28 DVDs

Step-by-step explanation:

Given information from the question, we can deduce:

2 weeks = 4 DVDs

1 week =

[tex] \frac{4}{2} \\ = 2[/tex]

2 DVDs on average.

Which means,

14 weeks = 2 × 14 = 28 DVDs

Therefore, Katy will buy 28 DVDs in 14 weeks.

Using proportions, it is found that the work required to compress the spring an additional one-half inch is of 1.0625 ft-lb.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For 4 inches, 8.5 ft-lb of work is needed, hence for a single inch the amount needed is:

8.5/4  = 2.125.

Hence for half an inch, the amount if:

0.5 x 2.125 = 1.0625 ft-lb.

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Answer:

X = -10

Step-by-step explanation:

2 = -8 -X

2+X = -8

X = -10

Answer:

x = - 10

Step-by-step explanation:

Comment

The trick to any equation like this one is to get the numbers on one side and the term with an unknown on the other side. That way, your last step is to divide by the number in front of the letter into a number on the other side.

Solution

2 = - 8 - x                                 Add 8 to both sides

2 + 8 = -8 + 8 - x                      Combine

10 = - x                                     The number in front of x is - 1. Divide.

10/-1 = -x/-1                        

-10 =x

The letter usually has to be expressed as a number greater than 0. In other words x is positive for this question

The interpretation of x in the equation 75•x + 19•y = T, used by the geographer, based on the land area of Aruba, 75 m², and Bermuda, 19 m², is the population in a square mile of Aruba

The land area of Aruba = 75 m²

Land area of Bermuda = 19 m²

The total number of residents is given in the question by the equation;

75•x + 19•y = T

Therefore;

x = The number of people in a square mile in Aruba

y = The number of people in a square mile in Bermuda

Which gives;

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The exponential growth rate is obtained as 0.1099.

Now we know that an exponential function has to do with an exponential increase or decrease. An exponential function could increase or decrease and this means that the constant of the function could be a decay constant or a growth constant.

When we have an exponential function, we have to apply the general formula; P(t) = P(o)e^rt

Po = initial number

P(t) = number at time t

r = rate of growth

t = time taken

Thus;

270=90e^10r

270/90 = e^10r

3 = e^10r

ln3 = 10r

r = ln3/10

r = 0.1099

After 13 hours;

P(t) = 90e^(0.1099 * 13)

P(t) = 376

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The number of students in the class is 9200.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Given that,

The percent of students pursuing economics is 29%.

And, the number of students pursuing economics is 2688.

Suppose the total number of students are x.

Then, the following equation can be written for the given case,

29% of x = 2668

=> 29/100 × x = 2668

=> x = 2668 × 100/29

       = 9200

Hence, the total number of students in the freshman class is 9200.

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The correct option is C no, both 3.61^2 and 3,62^2 are greater than 13.

To check this, we can just square both of the bounds that he found, and see if it makes sense.

Walter says hat:

3.61 < √13 < 3.62

Then we must have:

(3.61)^2 < 13 < (3.62)^2

The lower bound is 3.61, if we square it we get:

3.61*3.61 = (3 + 0.61)*(3 + 0.61) = 9 + 6*0.61 + 0.61*0.61 = 13.0321

Now, this is larger than 13, so the above inequality is false, which means that Walter is incorrect, because both 3.61 and 3.62 are larger than √13 , then the correct option is C.

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Answer:

c

Step-by-step explanation:

c

Answer:

66.0 (nearest tenth)

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the poor drawing)

This is a pure trigonometry question.

Based on the question, we can use the TOA CAH SOH method.

[tex] \cos(x) = \frac{adj}{hypo} \\ \cos(32) = \frac{56}{x} \\ x \cos(32) = 56 \\ x = \frac{56}{ \cos(32) } \\ = 66.0 \: (nearest \: tenth)[/tex]

Answer:

(2030)4

Step-by-step explanation:

Base 6 to decimal calculation:

(352)6 = (3 × 62) + (5 × 61) + (2 × 60) = (140)10

Decimal to base 4 calculation:

Divide by the base to get the digits from the remainders:

= (2030)4

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The answer is 2030.

First, convert from base 6 to base 10.

Now, convert from base 10 to base 4.

Connecting the digits, the answer is : 2030

Answer:

12.8 km

Step-by-step explanation:

each mile has 1.6 km in it so in order to find the total distance in km we need to multiply the miles by 1.6= 8 miles x 1.6 =12.8 km

Answer:

4 is correct answer.

Step-by-step explanation:

That because it contains property of communicative. That is a×b=b×a.

Answer: Reagan's pay was increased by 62%

Step-by-step explanation:

First, lets find the difference between the two pays:

$347,247 - $214,350 = $132,897

Let 214350 = 100%

Dividing 132,897 by 214350 to find the percent increase

[tex]\bold{\frac{132,897}{214,350} }=0.62\times100=62[/tex]

Therefore, Reagan's pay was increased by 62%

Answer:

youre answer is here I hope it's right

x=24

Answer:

(0, -5/2).

Step-by-step explanation:

The coordinates of the mid point of (x1, y1) and (x2, y2) are

(x 1 + x2)/2 , (y1 + y2)/ 2

So here we have:

(-3 + 3)/ 2, (-4 + -1)/2

= 0/2, -5/2

= (0, -5/2).

The verbal expression for the mathematical expression 5(x - 4) + 2 is the number 5 times the difference between an unknown x and the number 4 and plus 2.

It is defined as the combination of constants and variables with mathematical operators.

It is given that a mathematical expression as below:

= 5(x - 4) + 2

Here x is the unknown number

The number

Number 5 times the difference between an unknown x and number 4 and plus 2

Thus, the verbal expression for the mathematical expression 5(x - 4) + 2 is number 5 times the difference between an unknown x and number 4 and plus 2.

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Answer:

$63.36

Step-by-step explanation:

The home audio system costs $264 wholesale.

The system's price had been increased by 60 percent at the electronics retailer.

Consequently, the increased cost is 60/100x264=$158.40.

The audio system's total cost is now $422.40 (264 + 158.40).

Given that Lori received a commission of = 15% on $422.40, her commission is now (15/100) x 422.40

= $63.36

Option (b) -6 and 7 is the correct option.

The zeroes of the function f and g are x=7 and x=-6 respectively.

The values of x that satisfy the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Put x-7=0

X=7

Now, put x+6=0

So, x=-6

The zeroes of the function f and g are 7 and -6 respectively.

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Answer: A: y= 3x + 3

Step-by-step explanation:

The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.

The dot product associated to sides AB and BC is 0.

In this question we must find the dot product of two vectors associated with two surrounding sides of a triangle. First, we need to find the vectors associated to sides AB and BC:

Side BA

BA = (5, 3) - (0, 0)

BA = (5, 3)

Side BC

BC = (- 3, 5) - (0, 0)

BC = (- 3, 5)

By definition of dot product, the result associated to the two sides of the triangle is:

BA • BC = (5, 3) • (- 3, 5)

BA • BC = (5) · (- 3) + (3) · (5)

BA • BC = - 15 + 15

BA • BC = 0

The dot product associated to sides AB and BC is 0.

The statement is poorly formatted, the correct form is shown below:

If A(x, y) = (5, 3), B(x, y) = (0, 0) and C(x, y) = (- 3, 5) are the vertices of a triangle then the value of the dot product between vectors AB and BC is:

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Answer:

The distance formula is 22.360679775

if you round it to the nearest tenth, then the answer is 22.4

Step-by-step explanation:

(-6, -12) and (4,8)

(x2 - x1)² + (y2 - y1)²

Place the x and y values

(4 - - 6)² + (8 - - 12)²

= 10² + 20²

= 100 + 400 = 500

√500 = 22.360679775

Round it to the nearest tenth, and you will get 22.4

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Answer: Distance = 10√2

Step-by-step explanation:

Given formula

[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given information

(x₁, y₁) = (-6, -12)

(x₂, y₂) = (4, 8)

Substitute given information into the formula

[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance~=~\sqrt{((4)-(-6))^2+((8)-(-12))^2}[/tex]

Simplify values in the parenthesis

[tex]Distance~=~\sqrt{(4+6)^2+(8+12)^2}[/tex]

[tex]Distance~=~\sqrt{(10)^2+(20)^2}[/tex]

Simplify the exponents

[tex]Distance~=~\sqrt{100+400}[/tex]

Simplify the radical number

[tex]Distance~=~\sqrt{500}[/tex]

[tex]Distance~=~\Large\boxed{10\sqrt{5}}[/tex]

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The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

Please notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

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Answer:

Step-by-step explanation:

Comment

The semicircle comes out towards we the viewer, then it goes upwards, and what one gets is 1/2 a sphere. If one keeps on rotating in the direction of the arrow eventually winding up where one started, the result is a full sphere.

Answer: Sphere

Answer:

s = 55 degrees

t  = 35 degrees

Step-by-step explanation:

I am not sure what the question is, but I am assuming that you are trying to find the value for s and t

S and 125 are supplemental.  That means that they add to 180.  180 - 125 = 55.

The two angles opposite of s together add up to 125.  I know that one angle is 90, so t is 125 -90 or 35

Answer:

  62.5 feet

Step-by-step explanation:

The markings on the angles in the figure tell you the triangles are similar. Similar triangles have proportional corresponding sides. This is used to write and solve an equation for x.

The angles in each triangle are marked with the following symbols:

The purpose of the marks is to signify that angles with the same mark are congruent. When the angles of one triangle are congruent to the angles of another triangle, the two triangles are similar.

Similar triangles have another feature: corresponding sides are proportional. That is, their ratios are identical.

This can be taken a couple of different ways:

In the given triangles, we can identify the corresponding sides as ...

  smaller triangle : larger triangle

  between right angle and double arc angle — 36 ft : 50 ft

  hypotenuse — 45 ft : x ft

Our description of similarity tells us we can write the statements of proportionality as either of ...

For proportions written in this way, the "outer" and "inner" products are the same. This is sometimes expressed by saying "the product of the means is equal to the product of the extremes."

  a : b = c : d   ⇒   ad = bc

When the ratios are written as fractions, this result is what you get from "cross multiplication":

  a/b = c/d   ⇒   ad = bc . . . . . the result of multiplying both sides by bd

Once the proportion is written in this product form, the value of any of the variables can be found by dividing both sides of the equation by the coefficient of that variable.

Using either of the proportions we wrote above, the product form is ...

  36x = 45·50

  x = (45·50)/36 . . . . . . divide by the coefficient of x

  x ≈ 62.5 . . . . feet

The distance from the playground to the swimming pool is 62.5 feet.

Answer:

Step-by-step explanation:

(a) The velocity when the particle reaches B is 8 m/s.

(b) The distance between point A and B is 5.33 m.

(c) The value of t when the particle reaches C is 1.63 seconds.

(d) The distance AC​ is 8.7 m.

The velocity when the particle reaches B is calculated as follows;

v = ∫a. dt

where;

v =  ∫(4t . dt)

v = 4t²/2

v = 2t²

v(2) = 2(2)²

v(2) = 8 m/s

Thus, the velocity when the particle reaches B is 8 m/s.

x = ∫v

where;

x = ∫2t². dx

x = ²/₃t³

x(2) = ²/₃(2)³

x(2) = 5.33 m

Thus, the distance between point A and B is 5.33 m.

when the particle reaches point C, final velocity, vf = 0

vf = v + at

where;

0 = 8 - 3t(t)

0 = 8 - 3t²

3t² = 8

t² = 8/3

t² = 2.67

t = √(2.67)

t = 1.63 seconds

x = ∫vf

x = ∫(8 - 3t²)

x = 8t  - t³

x(1.63) = 8(1.63) - (1.63)³

x(1.63) = 8.7 m

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Answer:

Book 3

Step-by-step explanation:

So we have four statements:

1: Book 1 or Book 2

2: Book 3 or Book 4

3: Book 4

4: Not Book 3

We also have the condition that only 1 of the statements are correct, and more important, the other 3 are incorrect.

So it may be a bit difficult to see at first, but the solution, has to be book 3. The reason for this is if we assume statement 1, statement 2, or statement 3 is true, that would imply that the statement 4 is false, meaning the solution is in book 3.

If we assume that statement 2 is true, then statement 4 is false, meaning that book 3 has the solution, which aligns statement 2. It also aligns with statement 1 being false, because it's not book 1 or 2, and it also aligns with statement 3 being false, because the solution is not in book 4.

Let's look at why assuming any other statement to be true, leads to contradictions.

So let's assume the first statement is true, this means the solution is book 1 or 2. But this means the statement 4 is false, meaning book 3 has the solution. This contradicts the first statement which we assume is true, thus the first statement is not true.

Let's now assume the third statement is true, this means statement four is false meaning it's book 3, but this contradicts the third statement which says it's book 4. Thus this statement cannot be true

Let's assume the last option is true, this means book 3 has no solution, and since all the other are false, book 4 has no solution, book 3 or 4 has  no solution, book 1 or 2 has no solution either. This means that none of the books have solutions, and assuming one of the books does have a solution, this statement cannot be true.

Step-by-step explanation:

So, there is something known as a removable discontinuity, and it's essentially where you can define f(x) using the most simplified fraction, where you could normally not define f(x).

So we have the following equation:

[tex]f(x) = (\frac{x+5}{x+1}\div\frac{(x+3)(x-2)}{(x-4)(x+1)})-\frac{1}{x-2}[/tex]

As you may know, we cannot divide a number by the value of zero. When the denominator is equal to zero, on the graph this will appear as a vertical asymptote, where x approaches the value that makes the denominator zero, but never actually reaches it.

If you look at each denominator, you can set them equal to zero to find the vertical asymptotes

x+1 = 0

x=-1

There should be a vertical asymptote at x=-1, since it would make two of the denominators equal to -1, but let's divide the two fractions first.

Original Equation

[tex]f(x) = (\frac{x+5}{x+1}\div\frac{(x+3)(x-2)}{(x-4)(x+1)})-\frac{1}{x-2}[/tex]

Keep, change, flip

[tex]f(x) = (\frac{x+5}{x+1}*\frac{(x-4)(x+1)}{(x+3)(x-2)})-\frac{1}{x-2}[/tex]

Multiply the two fractions

[tex]f(x) = (\frac{(x+5)(x-4)(x+1)}{(x+1)(x+3)(x-2)})-\frac{1}{x-2}[/tex]

Notice how the x+1 is in the numerator and fraction? That means we can cancel it out!

[tex]f(x) = (\frac{(x+5)(x-4)}{(x+3)(x-2)})-\frac{1}{x-2}[/tex]

In this simplified version of the fraction, we can technically define f(-1), but in the original version, since it's not defined there is a removable discontinuity at x=-1, meaning there is no vertical asymptote, but the function is still not defined at f(-1), and there will be a hole at that point.