Answer:
(fog)(-3) = 125
Step-by-step explanation:
So, we need to first evaluate g(-3) and then plug the value of g(-3) into f(x) to find (fog)(-3). So, let's do that:
[tex]g(-3) = -3-2 = -5[/tex]
[tex]f(g(-3)) = f(-5) = 5(-5)^2 = 5(25) = 125[/tex]
Thus, (fog)(-3) = 125.
Paul plans to put concrete on a rectangular portion of a driveway. The portion is 12 feet long and 6 inches high. The price of the concrete is $98.00 per cubic yard. The total cost of the concrete Paul needs is $108.89. What is the width of the driveway in feet which Paul plans to put concrete?
Answer: 5 ft
Step-by-step explanation:
Step 1: Find the volume of the driveway (in cubic yds)
[tex]\$ 108.89\div\dfrac{\$98}{yds^3}=\$ 108.89\times\dfrac{yds^3}{\$98}=\boxed{\dfrac{10}{9}yds^3}[/tex]
Step 2: Use the Volume formula (V = length × width × heighth) to find w
(convert each measurement into yds)
[tex]V=l\times w\times h\\\\\dfrac{10}{9}yds^3=12ft\bigg(\dfrac{1yd}{3ft}\bigg)\times w\times 6in\bigg(\dfrac{1ft}{12in}\bigg)\bigg(\dfrac{1yd}{3ft}\bigg)\\\\\\\dfrac{10}{9}yds^3=4yds\times w\times \dfrac{1}{6}yds\\\\\\\dfrac{10}{9}yds^3=\dfrac{2}{3}yds^2\times w\\\\\\\dfrac{3}{2yds^2}\times \dfrac{10}{9}yds^3=w\\\\\\\dfrac{5}{3}yds=w\\\\\\\dfrac{5}{3}yds\times\dfrac{3ft}{1yd}=w\\\\\\\large\boxed{5 ft=w}[/tex]
You have $20. Suppose you make x dollars in tips tomorrow at work. Which inequality must be true for you to have enough money to buy a pair of jeans after work?
Answer:
B) x +20 is greater than or less to 45
Step-by-step explanation:
Answer:
x + 20 ≥ 45
Step-by-step explanation:
You currently have : $20
You will earn : $x
Tomorrow you will end up with (20 + x) dollars
the pair of jeans cost $45, in order to afford the jeans, the amount of money that you will need must be equal or more than $45
Hence,
Money you will have tomorrow ≥ 45
or
x + 20 ≥ 45 (Answer)
A cable company claims that the average household pays $78 a month for a basic cable plan, but it could differ by as much as $20. Write an absolute value inequality to determine the range of basic cable plan costs with this cable company.
A. |x − 78| ≥ 20
B. |x − 20| ≥ 78
C. |x − 20| ≤ 78
D. |x − 78| ≤ 20
Answer:
D. |x − 78| ≤ 20
Step-by-step explanation:
Given,
The monthly charges for a basic cable plan = $ 78,
Also, it could differ by as much as $20,
So, the maximum charges = $(78 + 20) ,
And, the minimum charges = $(78 - 20),
Let x represents the monthly charges ( in dollars ),
78 - 20 ≤ x ≤ 78 + 20
⇒ 78 - 20 ≤ x and x ≤ 78 + 20
⇒ -20 ≤ x -78 and x-78 ≤ 20
⇒ 20 ≥ -(x-78) and x-78 ≤ 20 ( ∵ a > b ⇒ -a < -b )
⇒ |x-78| ≤ 20
Which is the required absolute value inequality to determine the range of basic cable plan costs,
Option 'D' is correct.
Please help me with this problem ASAP!!!!
For this case we have a function of the form [tex]y = f (x)[/tex]
They ask us to find the value of the function when[tex]x = 2[/tex], that is, [tex]f (2).[/tex]
If we look at the figure, and we mark x = 2 in the graph, we obtain a value of[tex]y = 4[/tex]
So, we have that the function has a value of 4 when[tex]x = 2[/tex]
Answer:
Option C
if f(x)=3x-1 and g(x)=x+2,find (f-g)(x)
Answer:
[tex]\large\boxed{(f-g)(x)=2x-3}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x-1,\ g(x)=x+2\\\\\text{substitute:}\\\\(f-g)(x)=(3x-1)-(x+2)\\\\=3x-1-x-2\qquad\text{combine like terms}\\\\=(3x-x)+(-1-2)\\\\=2x-3[/tex]
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?
(1, 0) and (0, –1)
(–2, –3) and (1, 0)
(0, –3) and (1, 0)
(–3, –2) and (0, 1)
Answer:
Second option: (-2,-3) and (1,0)
Step-by-step explanation:
Given the system of equations [tex]\left \{ {{y = x^2 + 2x-3} \atop {y = x - 1}} \right.[/tex], you can rewrite them in this form:
[tex]x^2 + 2x-3= x - 1[/tex]
Simplify:
[tex]x^2 + 2x-3-x+1=0\\\\x^2+x-2=0[/tex]
Factor the quadratic equation. Choose two number whose sum be 1 and whose product be -2. These are: 2 and -1, then:
[tex](x+2)(x-1)=0\\\\x_1=-2\\\\x_2=1[/tex]
Substitute each value of "x" into any of the original equation to find the values of "y":
[tex]y_1= (-2) - 1=-3\\\\y_2=(1)-1=0[/tex]
Then, the solutions are:
(-2,-3) and (1,0)
ANSWER
The solutions are (-2,-3) and (1,0).
EXPLANATION
The given system has equations:
[tex]y = {x}^{2} + 2x - 3[/tex]
and
[tex]y = x - 1[/tex]
We equate both equations:
[tex] {x}^{2} + 2x - 3 = x - 1[/tex]
[tex] {x}^{2} + 2x - x - 3 + 1 = 0[/tex]
[tex] {x}^{2} + x - 2 = 0[/tex]
[tex](x - 1)(x + 2) = 0[/tex]
This implies that,
[tex]x = - 2 \: or \: x = 1[/tex]
When x=-2 , y=-2-1=-3
When x=1, y=1-1=0
The solutions are (-2,-3) and (1,0)
Solve each problem by writing and solving an equation.
For his son’s birthday party, Mr. Mori bought four equally-priced pizzas and a $3 bag of potato chips. If he spent $39, find the cost of each pizza.
Question 2 options:
Answer:
Each pizza costs for $9.
Step-by-step explanation:
We are given that Mr. Mori bought four equally-priced pizzas and a $3 bag of potato chips.
Given that he spent a total $39, we are to find the cost of each pizza.
This can be represented by an equation:
[tex]4x+3=39[/tex]
Solving it to find x.
[tex]4x=39-3[/tex]
[tex]4x=36[/tex]
[tex]x=\frac{36}{4}[/tex]
x = 9
Therefore, the cost of each pizza is $9.
Answer:
C.X=9
Step-by-step explanation:
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get? A. 4^2 − 3^3 B. 3^3 + 4^2 C. 4 − 3^3 D. 3^3 − 4^2 E. 3^2 − 4^3
Answer:
Option D. Alia gets 3³ - 4² = 11 jelly beans.
Step-by-step explanation:
Kathy gives Kelly 3³ jelly beans.
Kathy gives Alia 4² fewer jelly beans than Kelly. This means that Alia gets the number of jelly beans obtained by Kelly decreased by 4².
To summarize:
#Kelly = 3³ = 27
#Alia = #Kelly - 4² = 3³ - 4² = 27 - 16 = 11
Then, option D is correct.
If f(x)=4x+3 and g(x)= the square root of x-9, which is true? 2 is in the domain of f of g or 2 is not in the domain of f of g?
Answer:
2 is not in the domain of f of g
Step-by-step explanation:
* Lets revise at first the meaning of f of g (composite function)
- A composite function is a function that depends on another function
- A composite function is created when one function is substituted into
another function
- Example:
# f(g(x)) is the composite function that is formed when g(x) is
substituted for x in f(x).
- In the composition (f ο g)(x), the domain of f becomes g(x)
* Now lets solve the problem
∵ f(x) = 4x + 3
∵ g(x) = √(x - 9)
- Lets find f(g(x)), by replacing x in f by g(x)
∴ f(g(x)) = f(√(x - 9)) = 4[√(x - 9)] + 3
∴ f(g(x)) = 4√(x - 9) + 3
∵ The domain of f is g(x)
- The domain of the function is the values of x which make the
function defined
∵ There is no square root for negative values
∴ x - 9 must be greater than or equal zero
∵ x - 9 ≥ 0 ⇒ add 9 for both sides
∴ x ≥ 9
∴ The domain of f of g is all the real numbers greater than or equal 9
∴ The domain = {x I x ≥ 9}
∵ 2 is smaller than 9
∴ 2 is not in the domain of f of g
the lines shown below are parallel. if the green line has a slope of -1, what is the slope of the red line
Answer: -1 is the slope of the red line,
Step-by-step explanation: The slope of parallel lines are always the same. Hope this helps!
Answer:
the slope would be -1
Step-by-step explanation:
eighteen million, one hundred two thousand, seven hundred eighty-three as a whole number?
Answer:
18,102,783
Step-by-step explanation:
At the beginning of year 1, Jonah invests $300 at an annual
compound interest rate of 4%. He makes no deposits to or
withdrawals from the account.
Which explicit formula can be used to find the account's
balance at the beginning of year 6?
The explicit formula that can be used to find the account's balance at the beginning of year 6 is B = P(1 + r/n)^(nt), which gives the value as [tex]300(1.04)^6[/tex]
Explanation:The explicit formula that can be used to find the account's balance at the beginning of year 6 is:
[tex]B = P(1 + r/n)^(nt)[/tex]
Where:
B is the balance after a certain number of yearsP is the principal amount (initial investment)r is the annual interest rate (as a decimal)n is the number of times that interest is compounded per yeart is the number of yearsIn this case, Jonah's initial investment is $300, the annual interest rate is 4%, interest is compounded annually (n = 1), and the number of years is 6 (t = 6). Plugging these values into the formula:
[tex]B = 300(1 + 0.04/1)^(1*6)[/tex]
[tex]B = 300(1 + 0.04)^6[/tex]
[tex]B = 300(1.04)^6[/tex]
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A survey asked people if they prefer to read books or e-books. The results are shown in the table below. What is the
marginal relative frequency of the number of people who prefer to read books?
Male Female Total
Read books
Read e-books
D
0.57
0.49
0.43
0.42
The marginal relative frequency of the number of people who prefer to read books is 0.42
Answer:
.42
Step-by-step explanation:
In the summer a large pool evaporates water at 15% per day. If the pool starts out with 25,700 gallons of water, which function models the pool’s loss of water?
Answer:
[tex]y=25,700(0.85)^{x}[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
y ----> represent the pool’s loss of water
x ----> the number of days
a is the initial value
a=25,700 gal
b ----> is the base
r=15%=15/100=0.15
b=(1-r)=1-0.15=0.85
The function is equal to
[tex]y=25,700(0.85)^{x}[/tex]
A student factors 10x^2+3x-27 to the following
A. The expression is equivalent, and it is completely factored
The rectangular wall below is painted in 15 minutes. How many square feet per minute were painted?
The rectangular wall that is painted in 15 minute. 6.4 square feet area is painted per minute.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
The length of the rectangular wall = 12 ft.
The width of the rectangular wall = 8 ft.
The area of rectangle = 12 x 8 = 96 square feet.
Since, in 15 minutes, the rectangular wall is painted.
To find the area that painted in one minute,
Use ratio property,
15 minutes = 96 square feet painted,
1 minute = 96 / 15 square feet painted.
1 minute = 6.4 square feet.
6.4 square feet painted in 1 minute.
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Find the area of the circle d=8in
Answer: 64π
Step-by-step explanation: A = (d)^2 π
64 x π
64π
Help answer this please
Answer:
B
Step-by-step explanation:
translation means to transcribe or change from on language/definition/understanding to another.
Write as an algebraic expression and then simplify if possible The distance traveled by a train in three hours with a constant speed of r miles per hour.
Answer:
Distance = 3r
Step-by-step explanation:
We are to write an algebraic expression and then simplify it for the given situation:
The distance traveled by a train in three hours with a constant speed of r miles per hour.
We know the formula of distance linking the speed and the time.
Distance = speed × time
Substituting the given values to get:
Distance = r × 3
Distance = 3r
What is the slope-intercept form of the equation of the line that passes through the points (-3, 2) and (1, 5)?
A) y=3/4 x− 7/4
B) y=3/4 x- 9/2
C) y=3/4 x+ 7/2
D) y=3/4 x + 17/4
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-2}{1-(-3)}\implies \cfrac{3}{1+3}\implies \cfrac{3}{4}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=\cfrac{3}{4}[x-(-3)] \implies y-2=\cfrac{3}{4}(x+3) \\\\\\ y-2=\cfrac{3}{4}x+\cfrac{9}{4}\implies y=\cfrac{3}{4}x+\cfrac{9}{4}+2\implies y=\cfrac{3}{4}x+\cfrac{17}{4}[/tex]
Fracisco's game involves 3 green, 2 yellow, 4 red, and 3 black marbles. If he randomly draws three marbles from the
bag, without replacement, what is the probability that he will draw yellow, and then red, and then black?
A)1/192
B)1/72
C)3/220
D)1/55
Answer:1/55
Step-by-step explanation:
Answer: The answer is 1/55
Step-by-step explanation: because i got it right on edge. Can you mark brainliest?
need help asap please
Answer:
y = -7
Step-by-step explanation:
The easisest way to find the slope of this line is to use slope-intercept form.
Slope-intercept form:
y = mx + b
Where m = slope and b = y -intercept
In this graph, the y-intercept is -7. However, the line doesn't have a slope since its a straight horizontal line.
So, the mx part of the equation isn't a part of this new equation.
So, your equation would just y = -7
Find the product of (4x + 3y)(4x − 3y).
16x2 − 24xy + 9y2
16x2 − 9y2
16x2 + 24xy + 9y2
16x2 + 9y2
Answer:
It's B
Step-by-step explanation:
B, 16x2-9y2
Answer: The correct option is (B) [tex]16x^2-9y^2.[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=(4x+3y)(4x-3y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the given product, we will be using the following formula :
[tex](a+b)(a-b)=a^2-b^2.[/tex]
The product (i) can be calculated as follows :
[tex]P\\\\=(4x+3y)(4x-3y)\\\\=(4x)^2-(3y)^2\\\\=16x^2-9y^2.[/tex]
Thus, the required product is [tex]16x^2-9y^2.[/tex]
Option (B) is CORRECT.
What is the sum of the fractions below? 3/5x+9/5x
[tex]\dfrac{3}{5x}+\dfrac{9}{5x}=\dfrac{12}{5x}[/tex]
The sum of the given expression will be equal to 12 / 5x.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression is:-
[tex]=\dfrac{3}{5x}+\dfrac{9}{5x}[/tex]
[tex]= \dfrac{3+9}{5x}[/tex]
[tex]=\dfrac{12}{5x}[/tex]
Therefore the sum of the given expression will be equal to 12 / 5x.
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A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live
for one week without producing any additional offspring. Each replicated organism also replicates at the same rate. At hour one,
there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven?
2,801
19,531
19,607
97.655
Answer:
B. 19,531
Step-by-step explanation:
Answer:
The correct answer is option (2) 19,531
Step-by-step explanation:
Given Data;
a = 1 (first term)
r = 5 (five offspring)
n = 7 ( number of hours)
Using the formula of a geometric progression, we have
S₇ = [tex]\frac{a(r^{n} - 1) }{r -1}[/tex]
Substituting, we have
S₇ = [tex]\frac{1(5^{7} -1) }{5-1}[/tex]
S₇ = 78124/4
= 19531
Therefore, there are 19531 number of organisms at hour seven.
PLEASE HELP!
Drag the tiles to the correct boxes to complete the pairs.
Match the rational expressions to their rewritten forms.
Just Answer Please!
Answer:
1. [tex]\frac{x^2+4x-7}{x-1}[/tex]
2. [tex]\frac{x^2-2x+7}{x-1}[/tex]
3. [tex]\frac{2x^2-x-7}{x-1}[/tex]
4. [tex]\frac{2x^2-3x+7}{x-1}[/tex]
Step-by-step explanation:
1. [tex](x+5) + \frac{-2}{x-1}[/tex]
Taking LCM
[tex]=\frac{(x-1)(x+5)+(-2)}{x-1}\\ Solving:\\=frac{x(x+5)-1(x+5)-2}{x-1} \\=frac{x^2+5x-1x-5-2}{x-1} \\Adding\,\,like\,\,terms:\\=\frac{x^2+4x-7}{x-1}[/tex]
2. [tex]x-1 +\frac{6}{x-1}[/tex]
Taking LCM and solving
[tex]=\frac{(x-1)(x-1)+6}{x-1}\\=\frac{(x(x-1)-1(x-1)+6}{x-1}\\=\frac{x^2-1x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{x^2-2x+7}{x-1}[/tex]
3. [tex](2x+1)+\frac{-6}{x-1}[/tex]
Taking LCM and solving:
[tex]=\frac{(2x+1)(x-1)-6}{x-1} \\=\frac{2x(x-1)+1(x-1)-6}{x-1} \\=\frac{2x^2-2x+1x-1-6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-x-7}{x-1}[/tex]
4. [tex](2x-1)+\frac{6}{x-1}[/tex]
Taking LCM and solving:
[tex]=\frac{(2x-1)(x-1)+6}{x-1} \\=\frac{2x(x-1)-1(x-1)-6}{x-1} \\=\frac{2x^2-2x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-3x+7}{x-1}[/tex]
Answer:
I'm pretty sure that is correct.
Step-by-step explanation:
The amount of blueberries picked, in pounds, varies directly as the number of hours worked. After
10
hours,
30
pounds were picked.
What is the constant of proportionality
k
? Do not include units in your answer.
Answer:
3
Step-by-step explanation:
3 pounds were picked per hour
Answer: Hello there!
We know that the number of blueberries picked varies directly as the number of hours worked.
Direct variation means that: b = kh
where b is the number of blueberries, k is a constant of proportionality and h is the number of hours worked.
we know that in 10 hours there are 30 pounds of blueberries collected, then we can replace these numbers in the equation and solve it for k. And you want that I don't include units in the answer, so I will not include them.
30 = k*10
k = 30/10 = 3
Then the constant of proportionality is 3, whit is the amount of punds of blueberrys collected in one hour.
write the product using exponents
(-2) x (-2) x (-2)
Answer:
(-2)3 = -8
-2 × -2 = 4
4 × -2 = -8
Step-by-step explanation:
-2 multiply 3 times
negative times a negative equals a positive
negative times positive equals a negative
see results below
-2 × -2 = 4
4 × -2 = -8
which of the following best describes an altitude of a three-dimensional object?
Answer:
Option C
Step-by-step explanation:
we know that
The altitude of a three-dimensional object is equal to the height of the object, is the perpendicular distance of the base to the other base or the perpendicular distance of the base to the apex of the object
therefore
A segment that is perpendicular to the planes containing the two bases
The statement which best describes an altitude of a three-dimensional object is: C. a segment that is perpendicular to the planes containing the two bases.
What is altitude?Altitude is also referred to as an elevation and it can be defined as the vertical distance (height) above the surface of a plane.
In Geometry, the altitude of a three-dimensional object is characterized by the following:
It's equal to the height of the object.It's the perpendicular distance between two bases.It's the perpendicular distance of a base to the ap-ex of an object.Read more on altitude here: https://brainly.com/question/3946367
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find five solutions of the equation y=20x. select integers for values for x starting with -2 and ending with 2
Five solutions of y = 20x with integer values for x ranging from -2 to 2 are (-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).
To find five solutions of the equation y = 20x , we can choose integer values for x starting with -2 and ending with 2, and then calculate the corresponding values of y using the given equation.
Starting with x = -2 :
y = 20(-2) = -40
So, the first solution is (-2, -40).
Moving to x = -1:
y = 20(-1) = -20
So, the second solution is (-1, -20).
At x = 0 :
y = 20(0) = 0
So, the third solution is (0, 0).
Proceeding to x = 1 :
y = 20(1) = 20
So, the fourth solution is (1, 20).
Finally, for x = 2 :
y = 20(2) = 40
So, the fifth solution is (2, 40).
Therefore, the five solutions of the equation y = 20x with integer values for x ranging from -2 to 2 are:
(-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).