The functional value of f(-3a + 7) is 24a - 56
What is a function?
A rule that assigns a specific element of B to each element of A is known as a function from A to B. Both A and B are referred to as the function's domain and codomain, respectively. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
There are different operations on functions like addition, subtraction, multiplication, division, and composition of functions.
Here we have,
the given function is
f(b) = -8b
f(-3a + 7) = -8(-3a + 7)
= 24a - 56
Hence, the functional value of f(-3a + 7) is 24a - 56
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Given the information in the image below, find the measure of angle N. Explain how you arrived at this answer. Be sure to use key terms such at “isosceles triangle,” vertical angles,” and “congruent,” etc. You should at least have four sentences.
In the triangle LMN angle N is 76 degree.
Given,
In the question:
There is two isosceles triangle in the figure:
Triangle JKL and Triangle LMN
Angle J = 64 degree
To find the angle Angle N
Now, According to the question:
The triangle is isosceles.
<J = 64 degrees
All triangles have 180
<JLK = 180 - 64 - 64
Angle JLK = 52degree.
Angle JLK = MLN = 52 degree (Vertical opposite angle )
M is the left over from the 2 equal angles.
N = 180 - <M - < MLN
N = 180 - 52 - 52
N = 76 degree
Hence, In the triangle LMN angle N is 76 degree.
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your home feels cold to you at 60 f. you turn up the heat in order to raise the temperature by 15 degrees. what will the resulting temperature be
Answer:
45f.
Step-by-step explanation:
home is 60f.cold
we turn heat in order to raise the temprature by15
and 60minus 15 is 50
Answer:
75f
Step-by-step explanation:
since you raise the temperature you need to add those 2numbers together so 60+15=75f degrees
What is the average rate of change of the exponential function g(x)=2^x-1 between x=3 and x=7?
The average rate of change over the interval x = 3 and x = 7 is 30
How to determine the average rate of changeThe average rate of change of a function, graph, table or ordered pair is simply the slope of the relation
The equation is given as
g(x) = 2ˣ - 1
The interval is given as:
x = 3 and x = 7
Start by calculating g(3) and g(7)
So, we have
g(3) = 2³ - 1 = 7
g(7) = 2⁷ - 1 = 127
So, the average rate over these intervals is calculated as:
Average rate = [g(b) - g(a)]/[b - a]
This gives
Average rate = [g(7) - g(3)]/[7 - 3]
Substitute known values
Average rate = [127 - 7]/[7 - 3]
Simplify
Average rate = 120/4
Average rate = 30
Hence, the average rate of change is 30
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In a survey of 164 pet owners, 61 said they own a dog, and 66 said they own a cat. 11 said they own both a dog and a cat. How many owned neither a cat nor a dog?
The given information is:
- They surveied 164 pet owners
- 61 own a dog
- 66 own a cat
- 11 own both a dog and a cat
We have to find how many owned neither a cat nor a dog.
We can represent this survey in the following diagram:
To find the solution we need to subtract the number of people who said they own a dog, own a cat, and own both, from the total number of people in the survey, so:
[tex]\begin{gathered} People\text{ who own neither a dog nor a cat}=164-61-66-11 \\ P=26 \end{gathered}[/tex]The people who own neither a dog nor a cat are 26.
Find the slope of the line that passes through (-92, 21) and (-93, 35).
Answer:
slope = - 14
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 92, 21 ) and (x₂, y₂ ) = (- 93, 35 )
m = [tex]\frac{35-21}{-93-(-92)}[/tex] = [tex]\frac{14}{-93+92}[/tex] = [tex]\frac{14}{-1}[/tex] = - 14
Find the nth term of this quadratic sequence
4. 7, 12, 19, 28. . . .
Answer:
[tex]a_n=n^2 + 3[/tex]
Step-by-step explanation:
To find the nth term of a quadratic sequence, we need to determine the quadratic function that generates the sequence.
Given quadratic sequence:
4, 7, 12, 19, 28, ...
Begin by calculating the first differences between consecutive terms:
[tex]4 \underset{+3}{\longrightarrow}7 \underset{+5}{\longrightarrow} 12\underset{+7}{\longrightarrow} 19\underset{+9}{\longrightarrow} 28[/tex]
As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):
[tex]3\underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7\underset{+2}{\longrightarrow}9[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of the n² term is half of the second difference.
As the second difference is 2, the coefficient of the n² term is 1.
Now we need to compare n² with the given sequence (where n is the position of the term in the sequence).
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}n&1&2&3&4&5\\\cline{1-6}n^2&1&4&9&16&25\\\cline{1-6}\sf operation&+3&+3&+3&+3&+3\\\cline{1-6}\sf sequence&4&7&12&19&28\\\cline{1-6}\end{array}[/tex]
We can clearly see that the algebraic operation that takes n² to the terms of the sequence is add 3.
Therefore, the expression to find the the nth term of the given quadratic sequence is:
[tex]\boxed{a_n=n^2 +3}[/tex]
1 What is the first operation you should use to
solve the equation 5x + 4 = 1?
Answer:
exponents / the little x next to the 5
Answer: You move "x"s to one side, numbers to another and so the first operation is moving +4 to another side and making it -4
let f(x)=-5-10x and g(x)=1/5x+1. Fine f(g(x))
Answer:
I hope I did it right
A six sided die is rolled and a coin is tossed. Find Plodd and T).11/121/41/2
You have to calculate the probability of obtaining an odd number after rolling the die and obtaining tail after tossing a coin, symbolically:
[tex]P(O\cap T)[/tex]Where
"O" represents the event " rolling an odd number"
"T" represents the event "tossing a coin and obtaining tail"
The events are independent, which means that the intersection between both events is equal to the product of the individual probability of each event:
[tex]P(O\cap T)=P(O)\cdot P(T)[/tex]So, first, we have to calculate the probabilities of "rolling an odd number" P(O) and "tossing a coin and obtaining tail" P(T)
-The die is six-sided and numbered from 1 to 6, assuming that each possible outcome has the same probability, we can calculate the probability of rolling one number (N) as follows:
[tex]\begin{gathered} P(N\text{)}=\frac{\text{favorable outcomes}}{total} \\ P(N)=\frac{1}{6} \end{gathered}[/tex]The possible outcomes when you roll a die are {1, 2, 3, 4, 5, 6}
Out of these six numbers, three are odd numbers {1, 3, 5}, this is the number of favorable outcomes of the event "O", and the probability can be calculated as follows:
[tex]\begin{gathered} P(O)=\frac{\text{favorable outcomes}}{total} \\ P(O)=\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]So, the probability of rolling an odd number is P(O)=1/2
-When you toss a coin, there are two possible outcomes: "Head" and "Tail", assuming that both outcomes are equally possible.
For the event "toss a coin and obtain tail" there is only one favorable outcome out of the two possible ones, so the probability can be calculated as:
[tex]\begin{gathered} P(T)=\frac{\text{favorable outcomes}}{total} \\ P(T)=\frac{1}{2} \end{gathered}[/tex]The probability of tossing a coin and obtaining a tail is P(T)=1/2
Once calculated the individual probabilities you can determine the asked probability:
[tex]P(O\cap T)=P(O)\cdot P(T)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]A paint sample needs 3 drops of blue paint to 4 drops of green paint to make 5 gallons of paint. How many gallons of paint will be made if 28 drops of color is used?
The number of gallons of paints that will be made if 28 drops is used is 20 gallons
What is rate?A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.
The total number of drops used to make 5 gallons is 7drops, i.e 4+3=7
this means to make 1 gallon 5/7 drops of color will be used
Therefore for 28 drops , 5/7×20 gallons will be made
= 20gallons
Therefore the gallons made with 28drops is 20gallons.
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What is the answer to this
The amount invested at 8% is $26,333.33.
The amount invested at 2% is $8,666.66.
What is simple interest?
Simple compound interest is a method of calculating the amount of interest charged for a fixed rate and total over a fixed period of time. With simple interest, the principal is always the same, unlike compound interest, which adds interest to the previous year's principal to calculate the next year's interest.
interest = principal * rate * time
Given data:
Principal = $35000
Interest = $2280
time = one year.
Let 'x' represent the amount invested at 8%, then '35000-x' represents the amount invested at 2%.
interest = principal * rate * time
2280 = 0.08x + 0.02(35000 - x)
2280 = 0.08x + 700 - 0.02x
2280 - 700 = 0.06x
x = 1580/0.06
x = 26333.33
and
35000 - x = 35000 - 26333.33
x = 8666.66
Hence, The amount invested at 8% is $26,333.33.
The amount invested at 2% is $8,666.66.
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how do i find each system of equations for these answers x-y=4 2 x+y=5
The value of x and y of system of equations are 3 and -1. A group of equations involving one or more variables is known as a system of equations.
How to solve system of equations ?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.
Solution for x-y=4, 2x+y=5
x - y = 4
2x + y = 5
Substitute 4 = x+ y
2(4+y) + y =5
Simplify
8 + 3y = 5
Isolate y for 8 + 3y = 5 ; y = -1
For x = 4 + y
Substitute y= -1
x= 4-1
x=3
The solutions to the system of equation are :
x =3 , y = -1
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Camila invested $4,400 in an account that is earning an interest rate 90% every year. Camilla wants to create an exponential equation that allows her to track the interest earned over time, M(t).
Given:
Principal Amount, P = $4,400
Interest rate, r = 90%
Here, Camilla needs to create an exponential equation that allows her tract the interest earned over time.
This is a Compound interest problem.
To find create an exponential equation, apply the formula below:
[tex]I=P(1+r)^t-P[/tex]WHere:
P is the principal amount = $4,400
r is the rate = 90% = 0.90
t is the time (number of years)
Input values into the equation above:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Therefore, the exponential equation that allows her to track the interest earned over time is:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Plugging the value for the number of years for t, you will get the interest earned over time, t.
ANSWRER:
[tex]M(t)=4400(1+0.9)^t-4400[/tex]Which phrase represents this expression?
(62−42)×3
We can represent the expression (62−42)×3 in phrase as "three times the difference of 62 and 42".
In the given question we have to write a phrase that represent a given expression.
The given expression is (62−42)×3.
We can phrase a given expression by writing expression in to words. We write epression in to word according to the given expression.
As we can see that we subrating 62 by 42
So we can write it as difference of 62 and 42.
Then we multiplying with 3. So the expression in phrase is;
"three times the difference of 62 and 42"
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As I am completely new to thisPlease, explain thoroughly on how to solve A step by step explanation on how to solve *in the simplest way possible would be amazing, thanks in advance
ANSWER:
D. 44
STEP-BY-STEP EXPLANATION:
The percentage of a number is calculated by multiplying the percentage number in its decimal form by the number whose percentage is to be calculated.
A percentage number is converted to a decimal by dividing that number by 100, so it would finally look like this:
[tex]\begin{gathered} p=1100\cdot\frac{4}{100} \\ \\ p=44 \end{gathered}[/tex]So the correct answer is D. 44
A 4500 square foot roll of plastic wrap costs $23.95. If 120 square feet is need for a party game, what is the monetary value of that 120 square foot piece of plastic wrap? Interpret the answer.
120 square feet of plastic wrap costs $0.64.
64 square feet of plastic wrap costs 1.20.
Plastic wrap costs $0.64 per square foot.
$0.64 is the cost of plastic wrap.
Monetary value of 120 square foot piece of plastic wrap is $0.64
Direct variation means when ratio of two variable say cost and item always remains same.
example if cost of 2 pen is $1
then it will cost $2 for 4 pens
Given :
A 4500 square foot roll of plastic wrap costs $23.95
we have to find cost of 120 square foot roll of plastic for party game
Cost of 4500 square foot roll = $23.95
Cost of 1 square foot roll = [tex]\frac{23.95}{4500}[/tex]
= $0.00532
Cost of 120 square foot long roll = cost of 1 square foot roll × 120
= 0.00532 × 120
=0.63833
rounding off
$0.64 is cost of 120 square foot long plastic roll
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What is the value of this expression when x = 8 and y = 2?
9+y^2⋅x−y^3
Enter your answer in the box.
Answer:
The answer will
be 0
Step-by-step explanation:
=9+4×8-8
=13×0
=0
3x - 5 = Px – 6
Which values l,when substituted for p in the given equation,result in a linear equation with only one solution
Answer:
Any value other than 3 will work.
If triangle XYZ is equilateral and WXY is isosceles, what is the measure of WZY?
Answer: ∠WZY=150°
Step-by-step explanation:
Analysis :
ΔWXY is an isosceles triangle
perpendicular to WX intersecting:
XY at A
∠XWA = 21°
∠WXA = 90°-21° = 69°
Now, ΔXYZ is equilateral,
∠XYZ = ∠YXZ = 60°
Then,
∠WXZ = ∠WXA - ∠YXZ
= 69°-60°
= 9°
Since the angles of a triangle = 180°
∠WZY = ∠WZX = 180° - ∠XWA - ∠WXZ
= 180° - 21° - 9°
= 150°
How many pennies do you save on the twenty-third day?
Solution:
Given:
[tex]\begin{gathered} Day1=1penny \\ Day2=2pennies \\ Day3=4pennies \\ Day4=8pennies \end{gathered}[/tex]An exponential function is of the form:
[tex]y=ab^x[/tex]To get the exponential function for the relation;
[tex]\begin{gathered} For\text{ day 1:} \\ 1=ab^1.........................(1) \\ For\text{ day 2:} \\ 2=ab^2.........................(2) \\ For\text{ day 3:} \\ 4=ab^3 \\ \\ \\ \\ Hence,\text{ equation \lparen2\rparen divided by equation \lparen1\rparen;} \\ \frac{2}{1}=\frac{ab^2}{ab} \\ 2=b \\ b=2 \\ \\ Substituting\text{ b into equation \lparen1\rparen;} \\ ab=1 \\ a(2)=1 \\ 2a=1 \\ a=\frac{1}{2} \\ \\ \\ \\ Hence,\text{ the function is;} \\ y=\frac{1}{2}(2^x) \end{gathered}[/tex]Part A:
Relating this to the parameters given:
The exponential function that models the problem is;
[tex]f(t)=\frac{1}{2}(2^t)[/tex]Part B:
On the twenty-third day,
[tex]\begin{gathered} when\text{ }t=23,\text{ the pennies saved will be;} \\ \\ f(t)=\frac{1}{2}(2^{23}) \\ f(t)=\frac{2^{23}}{2} \\ f(t)=4,194,304\text{ pennies} \end{gathered}[/tex]Therefore, he would have saved 4,194,304 pennies on the twenty-third day.
I didn’t understand when my teacher taught this. Could you help show me how to solve this
The function given is,
[tex]f\left(x\right)=\frac{x+6}{\left(x+12\right)^2}[/tex]The graph of the function will be shown below
a) The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).
Hence, from the graph above the zeros of the function is at
[tex]x=-6[/tex]b) The function's domain is
[tex]\:\left(-\infty \:,\:-12\right)\cup \left(-12,\:\infty \:\right)[/tex]c) The function's long-run behaviour is that:
[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:0[/tex]Hence, the answer is
[tex]0[/tex]What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
The value of equation is x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".
Given,
In the question:
The equation is :
2[tex]x^{2}[/tex] – 7 = 9
To solve the above equation and explain which method to solve the equation?
Now, According to the question:
2[tex]x^{2}[/tex] – 7 = 9
2[tex]x^{2}[/tex] = 9 + 7
2[tex]x^{2}[/tex] = 16
[tex]x^{2}[/tex] = 8
x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex]
{There is no one- time item}
The method is used for solving equation is the "Direct keeping Method"
Hence, The value of equation is x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".
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Answer:
Use the square root property of equality.
There is no x term.
Add and divide to isolate x^2.
Step-by-step explanation:
The population of a town in Texas is modeled by the function f(x)=16,007(1.031)x. If the initial population (that is, the population when x=0) was measured January 1, 2014, what will the population be on January 1, 2030? Round your answer to the nearest whole number, if necessary.
From the information available, the initial population was 16,007. That figure was taken as at the year zero which is January 1, 2014.
This means
[tex]\begin{gathered} Yr1=2015-2014 \\ Yr2=2016-2014 \\ Yr3=2017-2014 \end{gathered}[/tex]This trend would be used until we get to January 1, 2030, when we would calculate as follows;
[tex]Yr16=2030-2014[/tex]Note that the years count from Jan 1 to Jan 1.
The function that models the yearly growth is;
[tex]f(x)=16007(1.031)^x[/tex]Using the first year, 2014 which is year zero, the result would remain 16,007. That is;
[tex]\begin{gathered} f(0)=16007(1.031)^0 \\ f(0)=16007\times1 \end{gathered}[/tex]For the 16th year, which is year 2030, we woud now have the following;
[tex]\begin{gathered} f(16)=16007(1.031)^{16} \\ f(16)=16007(1.629816253511204) \\ f(16)=26,088.4687699\ldots \end{gathered}[/tex]Rounded to the nearest whole number, this figure becomes;
ANSWER:
[tex]\text{Population}\approx26,088[/tex]The price of a go kart that Rafael wants to buy is $2,589 when the go kart goes on sale next month, the price will be $2,119. Which is the best estimate of the amount of money that Rafael will save if he waits to buy the go kart next month?
Current price of go-kart = $2,589
Price of go-kart next month = $2,119
If Rafael decides to buy the go-kart next month,
He will save $2,589 - $2,119 = $470
By definition of estimation
Estimation is an approximate calculation or judgment of the value, number, quantity, or extent of something
Approximating to the nearest hundred
$470 = $500
Therefore, Rafael will save an estimate of $500 if he wants to buy the go-kart next month
How much must be doposited today into the following account in order to have $45,000 in 6 years for a down payment on a house? Assume no additional deposits are made.An account with annual compounding and an APR of 7%
Solution
[tex]F=p(1+\frac{r}{n})^{nt}[/tex]where:
F=future value = 45000
P=present value
r=rate (as a decimal) = 7%=0.07
n=number of compounding periods per year = 1
t=number of years = 6
[tex]\begin{gathered} F=p(1+\frac{r}{n})^{nt} \\ 45000=p(1+\frac{0.07}{1})^{1(6)} \\ 45000=P(1+0.07)^6 \end{gathered}[/tex][tex]\begin{gathered} 45000=P(1.07)^6 \\ 45000=P(1.50073) \\ P=\frac{45000}{1.50073} \\ P=29985.4 \end{gathered}[/tex]Therefore the present value deposited today = $29,985.40
Write an equation of the line that passes through the given point and has the given slope (3, −2); slope 13
Answer:
y=1/3x-3
Step-by-step explanation:
1. What is the general formula for calculating the volume of a uniform shape?
Suppose the linear regression line y=-0.3x+11.2 predicts the time, in minutes, it takes you to finish an obstacles course after training for x days. About how much time would it take you to finish the course after training for 5 days.
SOLUTION
From the equation, to find the time in minutes which is y, we plugging 5 (from 5 days) for x into the equation, we have
[tex]\begin{gathered} y=-0.3x+11.2 \\ y=-0.3(5)+11.2 \\ y=-1.5+11.2 \\ y=9.7\text{ minutes } \end{gathered}[/tex]Hence the answer is option B
ch/#/test-player II 100% There is 1 teacher for every 18 students on a school trip. How many teachers are there if 72 students go on the school trip? Move values to create a proportion that can be used to solve the problem. 6 18 36 72
Let x be the number of teachers that go on the school trip
1 : 18 = x : 72
1/18 = x/72
cross-multiply
18x = 72
Divide both-side of the equation by 18
x = 4
Therefore, 4 teachers went on the school trip
what is 360x 10 to the 3rd power?
Answer: 360,000
Reason:
Think of 360 as 360.0
We move the decimal point 3 spots to the right to get to 360,000.0 or simply 360,000; this movement of 3 to the right is directly because of the exponent over the 10.
The 10^3 represents "thousand", so "360 x 10^3" is "360 thousand" = 360,000.