Answer: 1/12
step by step equation:
find f(g(2)) if f(x)= 4x^2-1 and g(x) = 3x+2
The value of the function f(g(2)) is 255.
The two function given is f(x) = 4x^2 - 1 and g(x) = 3x + 2
We have to find the value of the function f(g(2)).
First we will find the function f(g(x))
f(g(x)) = f(3x+ 2)
=4[tex](3x +2)^{2}[/tex] - 1
= 4( 9[tex]x^{2}[/tex] + 12x + 4) - 1
= 36x² + 48x + 16 - 1
= 36x² + 48x + 15
Now we have to find f(g(2)) for which we have to put the value of x as 2.
f(g(2)) = 36(2)² + 48 (2) + 15
= 36× 4 + 48 ×2 + 15
= 144 + 96 + 15
= 255
Therefore the value of the function f(g(2)) is 255.
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Evalúe the limit. Show steps
Answer: sqrt{3} over 2, this also equivalent to 0.866025
Line ℓ has equation y=
–x–3. Find the distance between ℓ and the point I(2,5).
The distance between line y= -x-3 and the point (2,5) is 5√2units.
The distance(d) between the line ax+by+c=0 and point (x₁,y₁) is calculated using the formula
d= |ax₁+by₁+c|/√a²+b² , where a and b are the coefficients of x and y .
In the question ,
the equation of the line ℓ is given by y = -x-3
rewriting the equation in standard form x+y+3=0
So the distance between the line x+y+3 and the point (2,5) can be calculated by substituting the values in the formula, we get
d=|1(2)+1(5)+3|/√1²+1²
= |2+5+3|/√2
= 10/√2
Simplifying further , we get
= 5√2
Therefore , the distance between line y= -x-3 and the point (2,5) is 5√2 units.
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can someone help me with this
If each of the 4 sloping side ahs length 10 cm
This implies they have length 40 cm altogether
To find the base length, simply subract the 40 cm from the total length of 68cm
68 - 40 = 28
each base length = 28/4 = 7cm
Area of the square base is = l x l = 7 x 7 = 49 cm²
6. A certificate of deposit (CD) is a savings instrument that many banks offer. It usually gives a
higher interest rate, but you cannot access your investment for a specified length of time.
Suppose you deposit $3000 in a CD paying 6% interest, compounded monthly. How much will
you have in the account after 20 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases} \\\\\\ A=3000\left(1+\frac{0.06}{12}\right)^{12\cdot 20} \implies A=3000(1.005)^{240}\implies A \approx 9930.61[/tex]
Share:
Share £20 pounds in the ratio 2:3
Share 15cm in the ratio 1:2
Divide £24 in the ratio 1:3
Share 35 sweets in the ratio 4:3
The share base on the ratio are as follows:
The share is £8 to £12The share is 5 cm to 10 cmThe share is £6 to £18The share is 20 sweet to 15 sweet.How to find the share base on the ratio?A ratio compares values. A ratio says how much of one thing there is compared to another thing.
Therefore, lets use the ratios to share the items.
Share £20 pounds in the ratio 2:3
2 / 5 × 20 = 40 / 5 = 8
Therefore, the share is £8 to £12
Share 15cm in the ratio 1:2
1 / 3 × 15 = 15 / 3 = 5 cm
Therefore, the share is 5 cm to 10 cm
Divide £24 in the ratio 1:3
1 / 4 × 24 = 24 / 4 = 6
Therefore, the share is £6 to £18
Share 35 sweets in the ratio 4:3
4 / 7 × 35 = 20 sweets
Therefore, the share is 20 sweet to 15 sweet.
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HELP! ALgebra 2
A soccer ball is kicked into the air so that its height, h, in feet, after t seconds is given by the function:
h(t)= -16t^2+96
What is the maximum height the ball reaches?
How long is the ball in the air?
The maximum height reached by the ball in discuss as described is; 96 while the time spent by the ball in the air is; 0 seconds.
What is the maximum height the ball reaches and how long was the ball in the air?It follows from the task content that the maximum height of the ball in the air is to be determined and so.is the time spent by the ball in the air.
Therefore, since the correct form of the function given is;
h(t) = -16t² + 96
By expressing the function above in vertex form; it follows that we have;
h(t) = -16 (t - 0)² + 96.
This vertex form function above therefore translates to the fact that the point, (0, 96) represents the vertex of the balls motion curve.
Ultimately, the maximum height reached by the ball is; 96 and the time it takes to reach this height is; 0 seconds.
PS; The scenario above in real life situation would translate to dropping a ball from the top.
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Maddox has $100 and plans to spend $20 each time he goes to the movies. At this rate,how many times can Maddox go to the movies?O $5O 5 timesО 4 timesO $120
ANSWER
EXPLANATION
addox has $100.
He plans to spend $20 each time he goes to the movies.
To find out how many times he can go to the movies,
a balloon is released from the top of a platform that is 50 m tall the balloon Rises at the rate of 4 meters per second identify the input variable output variable initial value and rate of change
Let's begin by identifying key information given to us:
Height = 50 m
velocity = 4m/s
The input variable is the number of seconds
The output variable is the theight of the ballon
The equation:
[tex]\begin{gathered} y=4x+50 \\ \text{Comparing this equation with the standard equation,}y=mx+b \\ \Rightarrow m=4,b=50 \\ m=4 \end{gathered}[/tex]Therefore, the rate of change equals 4
Find the product.
(b-na)(4b+9na)
Enter the correct answer.
The product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
How do you find the product of an expression?Algebraic expressions can be multiplied using the following procedures. You can start by calculating the algebraic sum of the like and unlike terms, multiplying the term coefficients, and adding the variable powers with the same base.
Given:
To find the product of (b-na)(4b+9na).
To determine the product, multiply each term of the first expression by each term of the second expression.
(b-na)(4b+9na)
= 4b² + 9abn - 4abn - 9a²n²
= 4b² + 5abn - 9a²n²
Therefore the product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
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(-8.8)(-9) = ? im confused?
Answer: 79.2
Step-by-step explanation: if you take -8.8 x -9 take out the negative completely because we are multiplying 2 negatives you never have to worry about the them. 8.8 x 9 = 79.2
side note: + x + = + - x - = + - x + = - + x - = -
Mathataur weighs 230,998,888,201 grams, and Mathamoth weighs 44,002,156 grams. About how many times greater is the weight of the Mathataur than the weight of the Mathamoth?
Answer:234534 pounds greater
Step-by-step explanation: 230,99987389x7=76
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 44% probability of winning the first contract. If they win the first contract, the probability of winning the second is 66%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 54%.
A. What is the probability that they win both contracts?
B. What is the probability that they lose both contracts?
C. What is the probability that they win only one contract?
A) The probability that the Aerospace Company wins both contracts is 29.04%.
B) The probability that the Aerospace Company loses both contracts is 70.96%.
C) The probability that the Aerospace Company wins only one contract is 23.76%.
What is the probability?Probability describes the chance or likelihood of an expected event occurring out of many outcomes.
Probability is a ratio of an outcome versus many possible events.
Probability is represented as a percentage, fraction, or decimal, like a ratio.
How the probabilities are calculated:The probability of winning the first contract = 44%
The probability of losing the first contract = 56% (1 - 44%)
The probability of winning the first and the second contract = 66%
The probability of losing the first and the second contract = 34% (1 - 66%)
The probability of losing the first contract and winning the second = 54%
A) The probability that they win both contracts = the probability of winning the first contract multiplied by the probability of winning the second contract.
= 29.04% (44% x 66%)
B) The probability that they lose both contracts = 1 minus the probability of winning both contracts.
= 70.96% (1 - 29.04%)
C) The probability that they win only one contract = the probability of winning the first contract multiplied by the probability of winning only the second contract.
= 23.76% (44% x 54%)
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Your friend says that the solutions to the inequality 9x-12x≤9 are xs-3. Solve the inequality correctly. What error did your friend
make?
holow and fill in the answer box to complete your choice
Answer:
[tex]9x - 12x \leqslant 9[/tex]
[tex] - 3x \leqslant 9[/tex]
[tex]x \geqslant - 3[/tex]
The inequality sign must be reversed when multiplying or dividing each side of an inequality by a negative number.
(02.01, 02.02 HC)Vanessa and William are stuck simplifying radical expressions. Vanessa has to simplifyx3William has to simplify 15xx.x4. Usingx6full sentences, describe how to fully simplify Vanessa and William's expressions. Describe if Vanessa and William started with equivalentexpressions or if they started with expressions that are not
ANSWER:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=x^{\frac{1}{2}} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the given expression is the following:
[tex]\frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}[/tex]The other expression is the following:
[tex]\sqrt[16]{x\cdot \:x^3\cdot \:x^4}[/tex]We simplify in each case:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{4}{3}-\frac{5}{6}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=\sqrt[16]{x^{1+3+4}}=\sqrt[16]{x^8}=x^{\frac{8}{16}}=x^{\frac{1}{2}} \end{gathered}[/tex]This means that the expressions are equal
If Alejandra estimates that one outfit welghs two pounds and one pair of shoes welghs three pounds, which graph represents the number of
outfits and shoes that Alejandra can pack while staying under the weight limit?
A graph which represents the number of outfits and shoes that Alejandra can pack while staying under the weight limit is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In this scenario, the x-axis represents the number of outfits while the y-axis represents the number of shoes. Additionally, since one pair of shoes weighs three (3) pounds and one outfit weighs two (2) pounds, the x and y coordinates would be given by this inequality:
2x + 3y < 30
Making y the subject of formula, we have:
3y < -2x + 30
Dividing all through by 3, we have:
3y/3 < -2x/3 + 30/3
y < -2x/3 + 10
Note: For 30 pounds, there would be 10 shoes (0, 10) while for 30 pounds, there would be 15 outfits (15, 0).
In conclusion, the boundary line is dashed or dotted to indicate that the boundary is not part of the solution because the inequality symbol is less than (<).
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A rectangle is 4 meters longer than it is wide. Find the dimensions of the rectangle if its area is 165 sq-meters.
Answer:
width = 11 and length = 15
Step-by-step explanation:
→ Find algebraic length and width
width = x ∴ length = x + 4
→ Find area
x ( x + 4 ) = x² + 4x
→ Equate to area
x² + 4x = 165
→ Solve
x = 11
→ Find length and width
width = 11 and length = 15
Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces
the brakes. He works no more than 54 hours a week. He routinely completes at least 2 shocks replacements and 6
brake replacements a week. If he charges $400 for labor replacing shocks and $250 in labor for replacing brakes, how
many jobs of each type should he complete a week to maximize his income?
Answer:
18 Shocks replacments and 0 Brakes
Step-by-step explanation:
if he did That he will make 7200$ a week
I need help with this please because I got answer C but I’m not sure I’m right
Since supplementary angles are two angles with a sum of 180°, then the supplement of ∠WTV is the angle ∠WTZ. Therefore, the answer is the option C.
Meghan has her own business. When she makes money, it is called income. When she spends money, it is called expenses. Choose the phrases below to explain how to use positive or negative integers to represent income and expenses.
You would use
Choose...
integers to represent income because it is a
Choose...
amount.
You would use
Choose...
integers to represent expenses because they are
Choose...
income.
The positive integer represents an addition to the income while.a negative integer represents a subtraction.
How to illustrate the information?Positive integers are used to represent income since they indicate an increase rather than a decrease in the financial value of the company. In other words, cash is coming in rather than leaving. A positive number 10 is used as an example to illustrate an increase in operating revenue when there is profit on items sold, say $10.
When you express an expense with a negative number, you're actually subtracting money value rather than adding it. In other words, money is leaving the company rather than being brought in. For instance, when a transportation expense is incurred to deliver items to the customer, it is recorded as an expense deducted from, let's say, the business' revenue sales. Since they are already identified and recognized as expenses and deducted nonetheless, they are typically shown in brackets in accounting to signify negative worth.
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To make orange paint he must mix yellow and red paint in the ratio 6:4 if he uses 9 litres of yellow paint how much red paint should he use
Answer:6 liters of red paint
Step-by-step explanation:
Calculate the first two terms: 34÷6
Calculate the first two terms: 6
Answer:6
At the neighborhood grocery, 0.5 pounds of chicken thighs cost $3.14 Taub spent $29.83 on chicken thighs. How many pounds of chicken thighs did she buy, to the nearest hundredth of a pound?
Taub bought 4.75 pounds of chicken thighs at the neighborhood grocery.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion, we have:
0.5 pounds of chicken thighs = 3.14 dollars
X pounds of chicken thighs = 29.83 dollars
Cross-multiplying, we have:
3.14X = 0.5 × 29.83
3.14X = 14.915
X = 14.915/3.14
X = 4.75 pounds of chicken thighs.
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Leila is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories.Leila wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this.(BOLD ANSWER WHEN FINISHED
Answer:
[tex]25f+100c<600[/tex]Step-by-step explanation:
Let f be the number of french fries in the lunch
Let c be the number of chicken wings.
Then, if Leila wants her child to eat less than 600 calories and each french fry has 25 calories and each chicken wing has 100 calories. The linear inequality that represents this situation:
[tex]25f+100c<600[/tex]Please help me I’m miserable because I was sick.It’s 2:00AM and this is due at 8 somebody please help me
Answer:
see explanation
Step-by-step explanation:
(a)
the angles shown are alternate interior angles and are congruent
(c)
since they are congruent , then
- 1 + 8x = 7x + 11 ( subtract 7x from both sides )
- 1 + x = 11 ( add 1 to both sides )
x = 12
(d)
then
7x + 11 = 7(12) + 11 = 84 + 11 = 95
- 1 + 8x = - 1 + 8(12) = - 1 + 96 = 95
Can i get some help
Answer:
Explanation:
iven the function:
Which expression is equivalent to 3w-4-w-93w−4−w−9?
The most appropriate choice for simplification of algebraic expression will be given by -
-92w -17 is the correct answer
What is simplification of algebraic expression?
At first it is important to know about algebraic expression. Algebraic expression consist of numbers and variable connected by addition, subtraction, multiplication, division.
Simplification of algebraic expression is the process of calculating the algebraic expression into lower form by combining all the like terms together. Here, BODMAS rule is used. B stands for bracket, O stands for of, D stands for division, M stands for multiplication, A stands for addition, S stands for subtraction.
3w - 4 - w - 93w - 4 -w - 9
3w - w - 93w -w -4 - 4 - 9
-92w -17
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Write a quadratic function given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
y=(x+3)(x=2)
y=(x-3)(x+2)
y=3(x-3)(x-2)
y=3(x-3)(x+2)
Quadratic function is 3(x+3)(x-2) given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
What is quadratic function?In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
Standard form, vertex form, and intercept form are three alternative ways a quadratic function can be expressed. The basic forms of each of them are as follows:
f(x) = ax² + bx + c in standard form, where a 0.
Vertex form: (h, k) is the vertex of the parabola representing the quadratic function, and f(x) = a(x - h)² + k is the equation.
The quadratic function's x-intercepts are (p, 0) and (q, 0), and its intercept form is f(x) = a(x - p)(x - q), where a 0.
Given Data
Roots (-3,0) and (2,0)
Point (1,-12)
y = a(x-(-3) (x-2)
y = a(x+3)(x-2)
Equating points
-12 = a(1+3)(1-2)
-12 = a(4)(-1)
-12 = -4a
a = 3
f(x) = 3(x+3)(x-2)
Function is 3(x+3)(x-2).
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{3}{8}-\frac{1}{6}
8
3
−
6
1
Step-by-step explanation:
A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. To simplify a fraction: divide the top and bottom by the greatest number that will divide both numbers exactly.
I hope this helps.
Step-by-step explanation:
8/3
8-3=6
6/3
6-3=
3The graph of y=f(x) is the solid black graph below. Whoch function represents the dotted line
The function that represents the dotted line of the graph using transformation rules is; f(x - 1) - 4.
How to Interpret Translation of Graphs?For the function f(x) of the given graph, when we look at the solid line, we see that it has a root at x = -1 which means it has a zero at x = -1.
However, when observing the dashed line, we see that it has a root at x = 0 which means it has a zero at x = 0.
Thus, we can deduce from transformation rules that the function was moved by 1 unit to the right to get the new function.
Secondly, we observe that the dashed line is also below the function f(x), and we observe further that 4 was subtracted. Therefore, when we use the transformation rules again for subtracting from a function, we get the final function as; f(x - 1) - 4.
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I need the answer for this question...
Expand and simplify the following 2(7s+ 4) + 6
Answer: 14s + 14
Step-by-step explanation:
- multiply in the 2 to the 7 and 4
14s + 8 +6
- add 8 + 6
14s + 14
Answer:
14s+14
Step-by-step explanation:
2(7s+4)+6
Simplify each term.
Apply the distributive property.
2(7s)+2x4 + 6
Multiply 7 by 2
14s +2 x 4 + 6
Multiply 2 by 4
14s + 8 + 6
Add 8 and 6
14+44