An office building casts a shadow that is 55 m long. At the exact same time, a 5 m tree casts a shadow that is 1.1 m long. Use similar triangle ratios, to calculate the height of the office building.

Answers:

right 1, down 3 (these two answers only)

Step-by-step explanation:

There are two transformations going on. The first of which is the horizontal or x translation (aka shifting) where the 'x' turns into 'x-1'. This moves the xy axis 1 spot to the left, giving the illusion that the graph moves 1 unit to the right.

The "-3" at the end shifts the graph down 3 units. If g(x) = f(x) - 3, then g(x) is the output of f(x) but 3 less than that, which is why it shifts down 3 units.

The function g(x) represents two transformations from its parent function f(x) = 1/x: a horizontal shift to the right by 1 unit and a vertical shift down by 3 units.

When comparing the graph of the function g(x) = (1)/(x-1) - 3 with its parent function f(x) = 1/x, the transformations undergone by g(x) include:

These transformations can be understood with the help of given examples. For instance, adding or subtracting a number to/from the independent variable x, like f(x+1), results in a horizontal shift of the graph. Multiplying the independent variable by a number, say 2 as in f(2x), would cause a horizontal compression of the graph. In our case, since the function g(x) includes x-1, it is indicating a horizontal shift to the right, and since the -3 is subtracted from the entire function, it denotes a vertical shift downward.

ANSWER: Tim Carter's weekly pay was $282.25.

I will work on Tim Carter's weekly pay. Because he worked 50 hours, and there are 40 regular hours, he worked 10 overtime hours.

To find out his regular pay, we need to multiply his regular pay by his regular hours.

[tex]40 * 5.15 = 206[/tex]

Tim Carter makes $206 for his regular hours. To find out his overtime pay, we need to multiply his regular pay by his overtime hours, then multiply that product by 1.5.

[tex]10 * 5.15 = 51.5\\\\51.5 * 1.5 = 77.25[/tex]

Tim Carter makes $77.25 for his overtime hours. Lastly, add the regular pay and his overtime pay to get his weekly pay.

[tex]206 + 77.25 = 283.25[/tex]

Tim Carter's weekly pay was $283.25.

Answer:

Step-by-step explanation:

                               OT                                 Weekly Pay

Tim Carter:             10                 40x5.15= 206    5.15 x 1.5=7.725

                                                    7.725 x 10 =  77.25    206 + 77.25 = $283.25

Jesse Jones:         7.5               40x5.15= 206   5.15 x 1.5 = 7.725

                                                   7.725 x 7.5 = 57.9375 = 57.94

                                                   206 + 57.94 = $263.94

Barbara Burns:      4                  40x5.15= 206  5.15x1.5 = 7.725

                                                   7.725 x 4 = 30.90   206 + 30.90 = $236.90

Answer:

Option B is correct.

Reason:It is an argument

Step-by-step explanation:

Given: [tex]AB \cong BC[/tex]  and [tex]BC \cong EF[/tex]

By transitive property:  a = b  and b = c then, a =c

⇒[tex]AB \cong EF[/tex]

AB = EF                                [def of [tex]\cong[/tex] segment]

By Segment Addition Postulate states that given  two points A and C, and a third point B lies on the line segment AC if and only if the distances between the  points satisfy the equation

AB + BC = AC.

Since, the line segment EG , F lies on the line segment;

then, by segment addition postulates we have;

EG = EF + FG

By substitution AB=EF

⇒ EG = AB + FG                     hence proved!

Since, in the fourth statement reason is:  It is an argument

Answer:

B, it is an argument

Step-by-step explanation:

Answer:

C. 2 x (6 + 8)

Step-by-step explanation:

If you are trying to add before you multiply, you have to put a parantheses. This way, you would add 6 + 8 first, then multiply it by 2.

They are parallel to each other.

Answer:

Step-by-step explanation:

8x^2-76x+40x-380

8x^2-36x-380

Based on proportional standards, if $32 represents 1/4 of Brianna's total earnings from babysitting, then she earned a total of $128.

From the amount Brianna saved, we know that $32 represents 1/4 or 25% of the total amount she earned from babysitting. If $32 is a quarter of the total amount, then we can find the total amount by multiplying $32 by 4. This is because 1 divided by 1/4 is equal to 4. So, Brianna earned a total of $32 x 4 = $128 from babysitting. This is the solution to the problem referred to as proportional reasoning. It involves understanding the concept of fractions and simple multiplication.

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Answer:

She has 11/20 yds left

Step-by-step explanation:

We take what she had and subtract what she gave away

9/10 - 7/20

We need to get a common denominator of 20

9/10 *2/2 - 7/20

18/20 - 7/20

11/20

She has 11/20 yds left

Answer:

Step-by-step explanation:

1. When you replace f(x) by x and x by y, you have

... x = 2^y + 6

The first thing you do is subtract 6; then you take the base-2 logarithm:

... (x -6) = 2^y

... log2(x -6) = y = f^-1(x)

You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.

2. When you swap x and y and solve for y, you have ...

... x = -1/2√(y+3)

... -2x = √(y +3) . . . . . . multiply by -2

... (-2x)^2 = y +3 . . . . . square

... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3

The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.

3. The product of the two functions is ...

... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)

Every term will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.

Answer:

Question One: log_2(x - 6) = y

Question Two: First blank: 4 Second blank 0

Question Three: B

Step-by-step explanation:

f(x) = 2^x + 6

y = 2^x + 6                 Interchange the x and y

x = 2^y + 6                Subtract 6 from both sides

x - 6 = 2^y                 Take the log of both sides

log(x - 6) = log 2^y    The power can be multiplied by the log of 2

log(x - 6) = y log(2)    Divide by the log of 2

log(x - 6)/log(2) = y    This to me is the preferred answer. It allows you to calculate what the actual number is or graph it on Desmos

The answer I have given is equivalent to using base 2 as your log, but calculating that is not always easy.

log_2(x - 6) = y

Answer: D

Problem Two

You want the inverse of y = - 1/2 sqrt(x + 3)   x ≥ - 3

Note: you cannot have any number less than -3 because if you do, you will be taking the square root of -x which involves complex numbers. In addition x ≥ -3 is a domain. You have to keep that in mind when doing this question.

The domain and range of this is a little harder to figure out. The range of f(x) becomes the domain of f-1(x)

The range of f(x) is 0 <=y < - infinity

So the domain of f-1(x) <= 0

Answer: The first blank is 4 and the second one is 0

Graph: the graph is given you below the question. What it shows is the f(x) and f^-1(x) are symmetrical about y = x. Most inverses are. If you want to check your work, it is best to include a graph when doing inverses.

Problem Three

The best way to begin this problem is to apply the associative property of multiplication and start by rewriting the givens as x^(1/2)[(x - 6)(x + 3)]. Do what is in the square brackets first.

Now deal with the x^(1/2) which must be multiplied by all three terms in the square brackets.

Result: x^(5/2) - 3x^(3/2) - 18x^(1/2)

Answer: √(x^5) - 3√x^3 - 18√x

Answer: B

He filled 2 bags with trail mix.

Simply divide 3/4 into 3/8.

3/4 / 3/8 = 2

2 is the answer.

The answer to your question is 2

We start from the third equation:

4z = 16     divide both sides by 4

Put the value of z to the second equation:

y + 4 = 5      subtract 4 from both sides

Put the values of y and z to the first equation:

3x + 2(1) - 4 = 4

3x + 2 - 4 = 4

3x - 2 = 4      add 2 to both sides

3x = 6      divide both sides by 3

Answer:

C) 4 : 2 Odds of rolling a number less than 5

Step-by-step explanation:

If there are 6 sides on the dice, 4 of the sides are going to be less than 5 and two of them are not.

Answer:

4:2 Odds of rolling a number less than 5.

Step-by-step explanation:

ODDS is defined as probability that event will occur divided by probability that event will not occur.

A six sided die has 6 numbers in total.

The odds of rolling a number LESS THAN 5 is therefore:

Odds = 4:2

Last answer choice is right.

Answer: 15 cups of white rice

Step-by-step explanation:

1. 5 cups of white to 2 cups of wild

2. 10 cups of white to 4 cups of wild

3. 15 cups of white to 6 cups of wild

4. 15 + 6 = 21

To determine the amount of white rice in a 21-cup rice mixture with a ratio of five parts white rice to two parts wild rice, we find out that one part is equivalent to 3 cups (since 21 divided by 7 is 3). Multiplying 3 cups by 5 parts of white rice gives us 15 cups of white rice.

Ms. Salazar's rice mixture consists of five parts of white rice to two parts of wild rice. To find out how many cups of white rice she will use for a 21-cup mixture, first, we need to determine the total number of parts in the mixture. Five parts white rice plus two parts wild rice equals seven parts total. Since Ms. Salazar is making 21 cups of the mixture, we will divide 21 cups by the total number of parts, which is 7, to find out the measurement of one part. After this, we multiply the measurement of one part by the number of parts of white rice, which is five.

21 cups / 7 parts = 3 cups per part
3 cups per part * 5 parts white rice = 15 cups of white rice.

So, Ms. Salazar will use 15 cups of white rice in her 21-cup mixture.

Answer:

78= -2m-6+m

78= -m-6

78+6= -m

84= -m

m= -84 Answer( C)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

distribute the parenthesis and simplify

78 = - 2m - 6 + m

78 = - m - 6 ( add 6 to both sides )

84 = - m ( multiply both sides by - 1 )

- 84 = m ⇒ m = - 84 → c

The surveyor is using a trigonometric method to calculate the distance between the two houses. They form a right triangle with points A, B and C, measure the length AC and the angle at point A or C, and then calculate the distance AB using trigonometric ratios.

In this scenario, the surveyor is using a method resembling triangle-based methods in Mathematics, which specifically relates to trigonometry. To determine the distance between points A (house on shore) and B (house on island), the surveyor measures line AC, forms a right triangle ABC, and uses an instrument (like a theodolite) to measure one of the corners (usually angle at point A or C). With the measured length and angle, the distance AB can be calculated using trigonometric ratios (like sine, cosine, or tangent), depending upon the given scenario. For instance, if the angle at point A and length AC are known, then the distance AB can be calculated as AB = AC / cos(A), where A is the angle at point A.

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Answer:

The answer is 18 GB

Step-by-step explanation:

Okay to the breakdown:

This is a word problem that requires basic knowledge of equality.

So lets say that the total amount of data at the beginning of the cycle is equal to X.

We are told that the data has been used for 8 days at a daily rate of 1.5GB per day, so the total data already used will be "Days × Rate" => 8 × 1.5 = 12GB.

We are also made to know that after the 8 days we still have 6 GB left out of the initial amount X.

Let put all the above in an equation:

X - 12 = 6;

Using the approach of putting liked them together we will add 12 to both sides:

X -12 + 12 = 6 + 12 => X = 18;

So the amount at the beginning of the cycle is 18 GB.

Easy, just do 60 seconds which equals a minute. Since we know that now simply use 60 minutes to get you to an hour. If your doing minutes to hours make sure there is a 0 at the end.

Answer:

The answer is B because the numbers in the geometric sequence are being multiplied by 2.

A you earn 3 percent more money

Step-by-step explanation:

4-1

Answer:

If you are given a 4% raise and inflation is 1%, you are making 3% more.

Step-by-step explanation:

If you are given a 4% raise and inflation is 1%, you are making 3% more.

[tex]4-1=3[/tex]

Or we can say you are making more money.

This is because you are given high percent of raise as compared to the low rate or percent of inflation, that shows you are on the positive side.

Answer:

x(x -2)

Step-by-step explanation:

The given expression is [tex]x^{2} - 2x[/tex]

Here "x" is the common factor, we can take it out and write the remaining terms in parenthesis.

x(x - 2)

So the factors are x and (x-2)

Thank you.

Answer:

The passengers paid approximately 162500

Step-by-step explanation:

We are find how much the passengers paid

657 passengers * 247 per passenger

Round 657 to 650

Round 247 to 250

650 * 250 = 162500

The passengers paid approximately 162500

Answer:

The price of the popsicles are $3.15 with the coupon

Step-by-step explanation:

To find the price of the item, we need to find the discount

discount = price * percentage off

discount = 4.5 *.3

discount =1.35

New price = original price- discount

new price = 4.5 - 1.35

new price = 4.5 -1.35

new price = 3.15

The price of the popsicles are $3.15 with the coupon

Final answer:

The question as posed does not provide a complete equation to solve for x. One would need to either expand the expression using distributive property or solve for x if it were part of an equation set to zero. Additional information is required to provide a definitive value for x.

Explanation:

The question appears to ask for the value of x when multiplied by the expression (5x)(3x + 28), however, it is incomplete as there is no equation to solve (i.e., no equals sign followed by a number). If you are meant to expand the expression, you would apply the distributive property to multiply 5x by both terms inside the parentheses, giving 15x^2 + 140x.

If the intention was to solve for x given an equation like (5x)(3x + 28) = 0, then you would set each factor to zero: 5x = 0 and 3x + 28 = 0. Solving these would give you x = 0 and x = -28/3 as the solutions.

Without a complete equation, we cannot definitively solve for the value of x. If additional information is provided or if you have a specific equation involving (5x)(3x + 28), please provide that for further assistance.

Answer:

480 pennies dated after 2000.

Step-by-step explanation:

1. Pennies dated before 1980 (x) - 25%,

All pennies (1,200) - 100%.

Then

[tex]\dfrac{x}{1,200}=\dfrac{25}{100},\\ \\100x=25\cdot 1,200,\\ \\x=25\cdot 12=300.[/tex]

2. Pennies dated from 1980 to 2000 (y) - 35%,

All pennies (1,200) - 100%.

Then

[tex]\dfrac{y}{1,200}=\dfrac{35}{100},\\ \\100y=35\cdot 1,200,\\ \\y=35\cdot 12=420.[/tex]

3. Rest pennies are dated after 2000, then

[tex]1,200-300-420=480.[/tex]

Answer:

480

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Let x = tootsie rolls

y = lollipops

Toosie rolls are 3 dollars and lollipops are $5 and you only have 30 dollars.

3x+5y =30

To find the x intercept, set y=0 and solve for x

3x +0 = 30

3x = 30

Divide by 3

3x/3 = 30/3

x = 10

The x intercept is 10.  This means if you get no lollipops, you can have ten tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 30

5y = 30

Divide by 5

5y/5 = 30/5

x = 6

The y intercept is 6.  This means if you get no tootsie rolls you can have 6 lollipops.

To find the slope, solve the equation for y

3x+5y =30

Subtract 3x from each side

3x-3x+5y = -3x+30

5y = -3x+30

Divide by 5

y = -3/5 x +30/5

y = -3/5 x +6

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

If you have $45 dollars instead of 30,  this will change the x and y intercepts, but not the slope.  

3x+5y =45

To find the x intercept, set y=0 and solve for x

3x +0 = 45

3x = 45

Divide by 3

3x/3 = 45/3

x = 15

The x intercept is 15.  This means if you get no lollipops, you can have 15 tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 45

5y = 45

Divide by 5

5y/5 = 45/5

x = 9

The y intercept is 9.  This means if you get no tootsie rolls you can have 9 lollipops.

To find the slope, solve the equation for y

3x+5y =45

Subtract 3x from each side

3x-3x+5y = -3x+45

5y = -3x+45

Divide by 5

y = -3/5 x +45/5

y = -3/5 x +9

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

Answer:

If two events are mutually exclusive then they cannot occur at the same time.

Step-by-step explanation:

If two events are mutually exclusive then they cannot occur at the same time.

For example: If you take a coin, the two possible outcomes on flipping a coin will be mutually exclusive as when you flip a coin, it cannot give both heads and tails at the same time.

Hence, the two mutually exclusive events cannot occur at the same time.

Answer:

1,500 rotations

Step-by-step explanation:

To answer this, divide 2.2 m into 3300 m.  This results in 1500.

The wheels made 1,500 rotations each.