please help me. i don’t understand how to interpret the (f o g)(x) And (g o f)(x)

Answer:

r=8

Step-by-step explanation:

59 =7r+3

Subtract 3 from each side

59 -3 = 7r+3-3

56 = 7r

Divide each side by 7

56/7 = 7r/7

8 =r

Answer:

[tex]\boxed{\bold{r=8}}[/tex]

Step-by-step explanation:

Switch sides

[tex]\bold{7r+3=59}[/tex]

Subtract 3 from both sides

[tex]\bold{7r+3-3=59-3}[/tex]

Simplify

[tex]\bold{7r=56}[/tex]

Divide both sides by 7

[tex]\bold{\frac{7r}{7}=\frac{56}{7}}[/tex]

Simplify

[tex]\bold{r=8}[/tex]

Answer:

405

Step-by-step explanation:

This is a geometric sequence, so we need the common ratio and the first term

To find the common ratio, we take the second term and divide by the first term

15/5 =3

The common ratio is 3

We are multiplying by 3 each time

The first term is 5

The formula is

an = a1 * (r) ^ (n-1)  where n is the term number

We want the 5th term

a5 = 5 * (3) ^ (5-1)

a5 = 5 *3^4

    = 5 *81

    = 405

The fifth term is 405.

[tex]a_{n}[/tex] = [tex]a_{1}[/tex]* [tex]r^{n-1}[/tex]

In this formula,[tex]a_{1}[/tex] is the first term,

r is the common ratio, and

n is the term number.

From the given sequence 5, 15, 45,..., we can identify the following:

[tex]a_{1}[/tex] = 5

r = 15 / 5 = 3 (common ratio)

Now, we need to find the fifth term (n = 5):

[tex]a_{5}[/tex] = 5 * [tex]3^{5-1}[/tex]

  = 5 * [tex]3^{4}[/tex]

  = 5 * 81

  = 405

So, the fifth term of the geometric sequence is 405.

Answer:

a=-b? That might be wrong, sorry. But that's what it sounds like.

Step-by-step explanation:

The equation that represents the direct variation between the numbers a and b is b = -a.

The equation that represents the direct variation between the numbers a and b is given by b = -a. In direct variation, when one variable increases, the other variable also increases, but in this case, they increase in opposite directions. For example, when a = -2, b = 2, and when a = 2, b = -2. Therefore, b varies directly with a, but in the opposite direction.

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Answer:

B

Step-by-step explanation:

Since a function would mean that a customer is able to purchase 1.1 of an item or 1.5 of an item, which is false. It also means that the customers pay the same price for a different amount of items.

Answer: The answer is A

It is a function because the input can be either 1 or 2 items, but the output will always be the same price.

According to the stated relation, (# sale items purchased, price), the input is the number of sale items purchased and the output is the price. The input values of a function can be different and have the same output value. However, a function cannot have different outputs for the same input.

The Y axis, would be when y = 0.

Point B is located on the Y -axis, so the coordinates would be the same.

For A and C the Y coordinate would remain the same and the X coordinate would be  the opposite ( from negative to positive).

A (-4,4) would become (4,4)

B (0,0) would stay the same so would be (0,0)

C (-5,-2) would become (5,-2)

The coordinates after reflection across the y-axis are:

- Point [tex]\( A' \): \((4, 4)\)[/tex]

- Point [tex]\( B' \): \((0, 0)\)[/tex]

- Point [tex]\( C' \): \((5, -2)\)[/tex]

Step 1: Identify the original coordinates of the points.

- Point [tex]\( A \)[/tex] is at [tex]\((-4, 4)\).[/tex]

- Point [tex]\( B \)[/tex] is at [tex]\((0, 0)\).[/tex]

- Point [tex]\( C \)[/tex] is at [tex]\((-5, -2)\).[/tex]

Step 2: Apply the reflection across the y-axis.

- Reflecting a point across the y-axis changes the sign of the x-coordinate, while the y-coordinate remains unchanged.

Step 3: Calculate the new coordinates.

For Point [tex]\( A \):[/tex]

- Original coordinates: [tex]\((-4, 4)\)[/tex]

- Reflected coordinates: [tex]\((4, 4)\)[/tex]

 - Negate the x-coordinate: [tex]\(-(-4) = 4\)[/tex]

 - Keep the y-coordinate the same: [tex]\(4\)[/tex]

For Point [tex]\( B \):[/tex]

- Original coordinates: [tex]\((0, 0)\)[/tex]

- Reflected coordinates: [tex]\((0, 0)\)[/tex]

 - Negate the x-coordinate: [tex]\(-0 = 0\)[/tex]

 - Keep the y-coordinate the same: [tex]\(0\)[/tex]

For Point [tex]\( C \):[/tex]

- Original coordinates: [tex]\((-5, -2)\)[/tex]

- Reflected coordinates: [tex]\((5, -2)\)[/tex]

 - Negate the x-coordinate: [tex]\(-(-5) = 5\)[/tex]

 - Keep the y-coordinate the same: [tex]\(-2\)[/tex]

Step 4: Write the coordinates of the reflected points.

- Point [tex]\( A' \): \((4, 4)\)[/tex]

- Point [tex]\( B' \): \((0, 0)\)[/tex]

- Point [tex]\( C' \): \((5, -2)\)[/tex]

So, the coordinates after reflection across the y-axis are:

- Point [tex]\( A' \): \((4, 4)\)[/tex]

- Point [tex]\( B' \): \((0, 0)\)[/tex]

- Point [tex]\( C' \): \((5, -2)\)[/tex]

take square root of 121, which is 11

so -12, 3, 10,

The values that satisfy the inequality x² > 121 are -12 and 13, as their squares are greater than 121.

The question asks which values satisfy the inequality x² > 121. To find the solutions, we need to consider when x² is greater than the square of 11, since 121 is 11². There are two cases:

Case 1: x is greater than 11.

Case 2: x is less than -11.

Now, evaluating the provided options:

A) -12: (-12)² = 144 which is greater than 121. Hence, -12 is a solution.

B) 3: (3)² = 9 which is not greater than 121. Therefore, 3 is not a solution.

C) 13: (13)² = 169 which is greater than 121. Thus, 13 is a solution.

D) 10: (10)² = 100 which is not greater than 121. So, 10 is not a solution.

Therefore, the correct answers that satisfy the given inequality are -12 and 13.

Final answer:

Min's hose will fill up 14 gallons of water if it runs for 2/3 of an hour, based on its rate of 21 gallons per hour.

Explanation:

The question asks us to calculate how many gallons of water Min's hose can pump if it runs for 2/3 of an hour, given that it pumps water at a rate of 21 gallons per hour.

First, we need to find out how much water the hose would pump in one hour and then calculate 2/3 of that amount:

Full capacity in one hour: 21 gallons

Capacity in 2/3 of an hour: (21 gallons) * (2/3) = 14 gallons

So, Min's hose will fill up 14 gallons of water if it runs for 2/3 of an hour.

The expression 9-(-5) simplifies to 9 + 5, which equals 14 when the numbers are added together.

To solve the expression 9-(-5), you should remember that subtracting a negative number is the same as adding its positive counterpart. Therefore, we change the subtraction of a negative number to the addition of a positive number. Following these steps, we have:

9 - (-5) = 9 + 5

Now, we simply add the numbers together:

9 + 5 = 14

So, the expression 9-(-5) equals 14.

Answer:

FDFDD

Step-by-step explanation:

There are many ways to write a transformation.

This shows the translation as a function.

f(x) = y = | x |

f(x-11)

This shows the translation as a column vector.

[tex]\left[\begin{array}{ccc}-11\\0\end{array}\right][/tex]

Answer:

2

Step-by-step explanation:

4 = 2 * 2

10 = 2 * 5

12 = 2 * 2 * 3

16 = 2 * 2 * 2 *2

Answer:

GCF is 2.

Step-by-step explanation:

GCF is just the greatest factor of the whole number series.

Everything is divisible by 2 and not anything greater in this number series.

Therefore the GCF is 2.

Answer:

A. c=1, d=3

Step-by-step explanation:

If x>0 and y>0, then

[tex]\sqrt{\dfrac{50x^6y^3}{9x^8}}=\sqrt{\dfrac{25\cdot 2y^2\cdot y}{9x^2}}=\dfrac{5y\sqrt{2y}}{3x}.[/tex]

If

[tex]\dfrac{5y\sqrt{2y}}{3x}[/tex]

is equal to

[tex]\dfrac{5y^c\sqrt{2y}}{dx},[/tex]

then

[tex]y=y^c\Rightarrow c=1,\\ \\3x=dx\Rightarrow d=3.[/tex]

Answer:

The answer is B.

Step-by-step explanation:

The architect wants to place a window in the center of the wall containing these two points: (3, 15) and (18, 2).

The coordinates of the center of the window are those of the mid-point betwween the two points: ( (3+18)/2, (15+2)/2 ) = (10.5, 8.5)

The answer is B.

Answer:

Step-by-step explanation:

ignore the text n focus on the coordinates (3, 15) and (18, 2) and that "the architect wants to place a window in the center of the wall containing these two points."

so the window will be right in the middle of (3, 15) and (18, 2).

take the average of the coordinates: (3+18)/2=10.5 n (15+2)/2=8.5

ans is B. (10.5,8.5)

Answer:

The third one is the one I would choose

Hope this helped :)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

([tex]\frac{f}{g}[/tex])(x)

= [tex]\frac{3x+5}{3x^2-x-10}[/tex] ← factor denominator

= [tex]\frac{3x+5}{(x-2)(3x+5)}[/tex] ← cancel (3x + 5), leaving

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

The denominator cannot be zero as this would make the fraction undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve x - 2 = 0 ⇒ x = 2 ← excluded value

domain is the set of all real numbers except 2

Answer:

A

Step-by-step explanation:

30/.5 = 60

60 + 10 = 70

Answer:

hi there your answer is:  A) 70

Step-by-step explanation:

STEP 1 : 30 ÷ 1/2 = 60

Step 2:   60 + 10 = 70

i hope this you out

Have a great evening

FaithRawlins14

Answer:

ann would have $1700 left for bills or rent food etc

Step-by-step explanation:

Ann's proposed monthly budget takes into account her $2,700 net income and fixes expenses for her dog and new car. After allocating for these expenses, the budget proposes estimated allocations for rent, utilities, groceries, entertainment, and savings, with an emphasis on setting aside roughly 10% for savings as a good financial habit.

To create a reasonable monthly budget for Ann who has a net monthly income of $2,700, we need to allocate funds to her known expenses and then distribute the remaining amount to cover other typical living costs such as rent, utilities, groceries, and savings. Ann has two fixed expenses mentioned: dog-related expenses that cost about $150 every month, and her transportation expenses which are $800 for her new car. Once we subtract these amounts from her monthly income, we can allocate the rest to other necessary expenses.

Here is a proposed monthly budget for Ann:

Net Monthly Income: $2,700

Dog-Related Expenses: -$150

Transportation (Car Expenses): -$800

Rent: -$900 (estimate based on average rent costs)

Utilities: -$150 (estimate including electricity, water, and gas)

Groceries: -$300 (estimate for a single person)

Entertainment: -$100 (for dining out, movies, etc.)

Savings: -$200 (aiming for roughly 10% savings as good financial practice)

Answer:

y - 5 = 3 (x + 1)

Step-by-step explanation:

Start with the pertinent equation of a straight line:  the point-slope form:

y-k = m(x-h), where (h,k) is the given point and m is the given slope.

Then y - 5 = 3(x-(-1) ), or y - 5 = 3 (x + 1).

Answer:  [tex]y-5=3(x+1)[/tex]

Step-by-step explanation:

By definition the equation of the line written in point-slope form is the following:

[tex]y-y_1=m(x-x_1)[/tex]

Where ([tex]x_1,y_1[/tex]) is a point of the line and m is the slope.

You know that the slope is 3 and the ine that passes through (-1, 5).

Then, when you substitute these values into the equation, you obtain:

  [tex]y-5=3(x-(-1))[/tex]

 [tex]y-5=3(x+1)[/tex]

Answer:

4.47 units

Step-by-step explanation:

Answer:

[tex]\textsf{A)}\;\;\; -2, \; \left|-\dfrac{4}{5}\right|, \; |-1|, \;|3.5|, \;|-4.2|[/tex]

[tex]\newline[/tex]

Step-by-step explanation:

[tex]\newline[/tex]

Given numbers:

[tex]\newline[/tex]

[tex]|-4.2|, \;\left|-\dfrac{4}{5}\right|, \; |-1|, \;-2, \; |3.5|[/tex]

[tex]\newline[/tex]

The absolute value of a number represents the distance of a number from zero on the number line, regardless of direction. This means that the absolute value of a number is always non-negative. For example, |-4.2| = 4.2, because the distance from -4.2 to 0 is 4.2 units.

[tex]\newline[/tex]

Evaluate each term:

[tex]\newline[/tex]

[tex]|-4.2|=4.2[/tex]

[tex]\left|-\dfrac{4}{5}\right|=\dfrac{4}{5}=0.8[/tex]

[tex]|-1|=1[/tex]

[tex]-2=-2[/tex]

[tex]|3.5|=3.5[/tex]

[tex]\newline[/tex]

Now, arrange them from least to greatest:

[tex]\newline[/tex]

[tex]-2, \;0.8, \;1, \;3.5, \;4.2[/tex]

[tex]\newline[/tex]

Therefore, the list of numbers in the correct order from least to greatest is:

[tex]\newline[/tex]

[tex]\large\boxed{-2, \; \left|-\dfrac{4}{5}\right|, \; |-1|, \;|3.5|, \;|-4.2|}[/tex]

The equation was solved step by step to find that Roman initially had $20.

Roman has a certain amount of money. If he spends $15, then he has 1/4 of the original amount left. To find out how much money Roman had originally, we can set up an equation. Let's call the original amount of money x. After spending $15, Roman has x - 15 dollars left, which we are told is 1/4 of the original amount, x.

So, the equation we can write is:
x - 15 = 1/4 x

To solve for x, we multiply each side of the equation by 4 to get rid of the fraction on the right side:
4(x - 15) = x

Which simplifies to:
4x - 60 = x

Then we subtract x from both sides to get x on one side:
3x - 60 = 0

Now, we add 60 to both sides to solve for x:
3x = 60

Finally, we divide both sides by 3 to find x:
x = 20

Therefore, Roman originally had $20.

Answer:

Step-by-step explanation:

1 + 6 = 7

2 + 5 = 7

3 + 4 = 7

4 + 3 = 7

2 + 5 = 7

1 + 6 = 7

6 + 5 = 11

5 + 6 = 11

8 / 36 = 4 / 18 = 2 / 9

Answer: 0.032

Step-by-step explanation: poof

Answer:

15.75 + 15.75= 31.50

31.50- 23.75= 7.75

so 7.75

Answer:

A(7,5)

Step-by-step explanation:

This is correct because the area of a triangle is b × h = a.

Answer:

The measure of ∠ABC  is 45°.

Step-by-step explanation:

Given : The vertices of a triangle are A(7,5) B(4,2) and C(9,2).

To find : What is ∠ABC ?

Solution :

First we side the length of the sides,

Using Distance formula,

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

Length of side AB, A(7,5) and B(4,2)

[tex]c= \sqrt{(7-4)^2 + (5-2)^2} \\c= \sqrt{(3)^2 + (3)^2} \\c= \sqrt{9+9} \\c= \sqrt{18}[/tex]

Length of side BC, B(4,2) and C(9,2)

[tex]a= \sqrt{(4-9)^2 +(2-2)^2} \\a= \sqrt{(-5)^2 + 0} \\a= \sqrt{25} \\a= 5[/tex]

Length of the side AC, A(7,5) and C(9,2)

[tex]b = \sqrt{(7-9)^2 +(5-2)^2}\\ b= \sqrt{(-2)^2 + (3)^2} \\b= \sqrt{4+ 9}\\b=\sqrt{13}[/tex]

By the Law of Cosines,

[tex]\cos B=\frac{a^2 + c^2 -b^2}{2ac}[/tex]

Substitute the values,

[tex]\cos B=\frac{(5)^2 + (\sqrt{18})^2 - (\sqrt{13})^2}{2\times 5\times \sqrt{18}}[/tex]  

[tex]\cos B =\frac{25+18-13}{10\sqrt{18}}[/tex]  

[tex]\cos B=\frac{30}{10\sqrt{18}}[/tex]  

[tex]\cos B =\frac{3}{\sqrt{18}}[/tex]  

[tex]\cos B= \frac{3}{3\sqrt{2}}[/tex]  

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

Taking Inverse Cosine function,

[tex]B= \cos^{-1}( \frac{1}{\sqrt{2}})[/tex]  

[tex]B=45^\circ[/tex]  

Therefore, The measure of ∠ABC  is 45°.

Answer:

52

Step-by-step explanation:

3.25 pints = 52 fluid ounces since there are 16 fl oz in one pint.

The question deals with the distribution of students' residences relative to their school. Calculations suggest 22% live between 1 and 2 miles away, 10% live between 2 to 3 miles away, and the remaining students live more than 3 miles away from the school.

The question relates to the distribution of students' residences in relation to the school. Given that, at one school, half of the students live within 1 mile, 78% live within 2 miles, and 0.1 of the students live between 2 and 3 miles from the school. This implies that 22% of students live between 1 and 2 miles of the school (the difference between 78% and the half who live within 1 mile), and 0.1 of the students live further than 2 miles but less than 3 miles from the school. So, the remaining students, which is 100% minus (half + 22% + 0.1*100%), live more than 3 miles away from the school.

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To find the probability that a randomly chosen student at the local community college lives within five miles of the campus or receives some kind of financial aid, the formula for the union of two events can be used. Substituting the given probabilities, the probability is found to be 0.35.

To find the probability that a randomly chosen student at the local community college lives within five miles of the campus or receives some kind of financial aid, we need to understand the given information.

We know that 20% of the students live within five miles of the campus and 30% receive financial aid. Of those who live within five miles, 75% receive financial aid.

To find the probability, we can use the formula for the union of two events:

P(A or B) = P(A) + P(B) - P(A and B)

In this case, A represents living within five miles of the campus and B represents receiving financial aid. Substituting the given probabilities, we have:

P(lives within five miles or receives financial aid) = 0.20 + 0.30 - (0.20 * 0.75)

P(lives within five miles or receives financial aid) = 0.20 + 0.30 - 0.15

P(lives within five miles or receives financial aid) = 0.35

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Answer:C.

Its C because 2/5+3/10=7/10.

Answer:

C

Step-by-step explanation:

CCCC!!

Answer:

666.4 dollars per day

Step-by-step explanation:

Total milk farmer has is 490 gallons

He keeps 1/35 of 490 gallons

so he keeps = 1/35*490= 14 gallons

He sells remaining milk.

Remaining milk = 490-14 = 476 gallons

1 gallon = 4 quart  (conversion formula)

so 476 gallon = 4 * 476 = 1904 quart

selling price of 1 quart = 35 cents = 0.35 dollars

so selling price of 1904 quart  = 0.35*1904 = 666.4 dollars

So he makes 666.4 dollars per day.