The functions f and g are defined as follows.g(x) = 4x-2-Xf(x)=-3x-1Find f (5) and g(-3).Simplify your answers as much as possible.f(s) = 0:Х?&(-3) = 0
Answers
We need to find f(5) and g(-3)
First, we will solve f(5), for this, we have the following function:
[tex]\begin{gathered} f(x)=-3x-1 \\ f(5)=-3\cdot(5)-1 \\ f(5)=-15-1 \\ f(5)=-16 \end{gathered}[/tex]Second, we will solve g(-3), for this, we have the following function:
[tex]\begin{gathered} g(x)=4x^2-x \\ g(-3)=4(-3)^2-(-3) \\ g(-3)=4\cdot9+3 \\ g(-3)=36+3 \\ g(-3)=39 \end{gathered}[/tex]In conclusion, f(5) = -16 and g(-3) = 39
Related Questions
Use the drawing tools to form the correct answer on the graph.Graph the composite function &(/(e)¡(=)-2I• 5g(I) =1 - 1
Answers
Solution:
Given:
The functions are given below as
[tex]\begin{gathered} f(x)=-2x-5 \\ g(x)=x-1 \end{gathered}[/tex]To find:
[tex]g(f(x)[/tex]To figure out the value of the composite function, we will replace x with (-2x-5) in g(x)
[tex]\begin{gathered} g(f(x))=-2x-5-1 \\ g(f(x))=-2x-6 \end{gathered}[/tex]Hence,
Using a graphing tool, we will have the composite function be
Let f(x) = (5)2+1. Which is equal to f(-3)?
Answers
Let's solve f(x) = (5)2+1 for f(-3):
Replacing x by -3, we have:
f (-3) = - 11
But there is no value for x, in the given function, there isn't a coefficient for x.
Can you please check the problem?
Simplify a^6 and a^2A: 2a^12B: 2a^8C: a^12 D: a^8
Answers
Using the following property:
[tex]x^y\cdot x^z=x^{y+z}[/tex]so:
[tex]a^6\cdot a^2=a^{6+2}=a^8[/tex]Answer:
a⁸
REWRITE EACH PROBLEM AS A MULTIPLICATION QUESTION!!!Students were surveyed about their favorite colors. 1/4 of the students preffered red, 1/8 of the students blue, and 3/5 of the remaining students preffered green. If 15 students preffered green, how many student were surveyed?
Answers
Let there are x total student surveyed, the 1/4x students prefer red, 1/8x prefer blue.
Determine the remaining students.
[tex]\begin{gathered} S=x-\frac{x}{4}-\frac{x}{8} \\ =\frac{8x-2x-x}{8} \\ =\frac{5}{8}x \end{gathered}[/tex]Determine the students that prefer green.
[tex]\frac{3}{5}\cdot\frac{5}{8}x=\frac{3x}{8}[/tex]The students who preferred green is 15. So equation for x is,
[tex]\begin{gathered} \frac{3x}{8}=15 \\ x=\frac{15\cdot8}{3} \\ =40 \end{gathered}[/tex]So total students that were surveyed is equal to 40.
How do u figure out what x is in a normal distribution question
Answers
Data:
• Mean (μ) = 50
,• Standard deviation (σ) = 3
,• P( ,x >=47 ,)
Procedure:
1. Since μ = 50 and σ = 3:
[tex]P(x\le47)=P(X-\mu<47-50)=P(\frac{x-\mu}{\sigma}<\frac{47-50}{3})[/tex][tex]Z=\frac{x-\mu}{\sigma}[/tex][tex]\frac{47-50}{3}=-1[/tex]2. Replacing the values:
[tex]P(x\le47)=P(Z\le-1)[/tex]With this, we do not have to figure out what x is.
3. Using the standard normal table:
[tex]P(Z\le-1)=0.1587\approx0.16[/tex]Answer: A. 0.16
Please solve the problem in the attachment and provide the steps, the reason why your answer is correct and why all the other answer choices are incorrect.
Answers
Answer:
A
[tex]A\text{. Rectangles also have four right angles}[/tex]Explanation:
We want to find a counterexample to disprove the conjecture below;
- A square is a figure with four right angles.
To disprove this, we need to find a shape that also has four right angles but is not a square.
So, from the option the only shape that also has four right angles is a rectangle.
Therefore, the counterexample to disprove the conjecture is;
[tex]A\text{. Rectangles also have four right angles}[/tex]For how many books produced will the costs from the two methods be the same
Answers
Answer:
[tex]4780\text{ books}[/tex]Explanation:
Here, we want to get the number of books for which the cost of the two methods will be the same
What we have to do here is to get the cost of each method, then equate to find the number of books
Let the number of books be b
For the first method, we have it that:
[tex]\begin{gathered} 70976\text{ + }9.75(b) \\ =\text{ 70976 + 9.75b} \end{gathered}[/tex]For the second method, we have it that:
[tex]\begin{gathered} 16006\text{ + }21.25(b) \\ =\text{ 16006 + 21.25b} \end{gathered}[/tex]To get the number of books, we have to equate both
Mathematically, that would be:
[tex]\begin{gathered} 70976\text{ + 9.75b = 16006 + 21.25b} \\ 70976-16006\text{ = 21.25b-9.75b} \\ 54970\text{ = 11.5b} \\ b\text{ = }\frac{54970}{11.5} \\ b\text{ = 4,780} \end{gathered}[/tex]If Guillermo deposits $5000 into an account paying 6% annual interest compounded monthly, how long until there is $8000 in the account?
Answers
We have the following:
The formula in this case is the following:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]solving for t:
replacing
A is 8000, P is 5000, n is 12 and r is 6% (0.06)
[tex]\begin{gathered} 8000=5000(1+\frac{0.06}{12})^{12t} \\ \frac{8000}{5000}=1.005^{12t} \\ \ln (\frac{8}{5})=12\cdot t\ln (1.005)_{} \\ t=\frac{\ln (\frac{8}{5})}{12\ln (1.005)} \\ t=7.85 \end{gathered}[/tex]therefore, the answer is 7.9 years
Which expressions are equivalent to the one below? Check all that apply.ln(e5)A.1B.5C.5 • ln eD.5e
Answers
SOLUTION:
We want to find the equivalent expression to;
[tex]ln(e^5)[/tex]We can rewrite it as;
[tex]\begin{gathered} 5ln(e) \\ =5 \end{gathered}[/tex]Thus, the answers are;
[tex]5Ine\text{ }and\text{ }5[/tex]OPTION B and C
what is 6 exponent 7 * 4 exponent 4 * 2 / 6 exponent 5 * 4 exponent 4 * 2.2
Answers
given
[tex]\frac{6^7\cdot4^4\cdot2}{6^5\cdot4^4\cdot2^2}[/tex][tex]=6^{7-5}\cdot4^{4-4}\cdot2^{1-2}=6^2\cdot4^0\cdot2^{-1}=\frac{6^2\cdot1}{2}=\frac{36}{2}=18[/tex]Note 4 exponent 0 = 1
12)50 students took a quiz with five questions. The frequency table below shows the results of the quiz. Use the frequency table to answer the following questions. ValueFrequencyRelative FrequencyCumulative Frequency040.084180.1612260.1218320.04204150.3355150.350
Answers
e) Finding how many students answered at most 4 questions.
The number of students that answered at most 4 questions correctly is:
Students answered 0 questions correctly + Students answered 1 question correctly + Students answered 2 questions correctly + Students answered 3 questions correctly + Students answered 4 questions correctly
So, the number of students is:
4 + 8 + 6 + 2 + 15 = 35
35 students answered at most 4 questions correctly.
f) Finding the sum of relative frequency.
The sum of relative frequency is:
0.08 + 0.16 + 0.12 + 0.04 + 0.3 + 0.3
Sum = 1.
The sum of the relative frequency in a distribution is always 1.
g) Creating a histrogram
To create a histogram, create a bar for each result correct. The values of the frequency will be used in the y-axis.
Find a recursive formula for the following sequence:4, 11, 25, 53, 109, ...
Answers
Notice the following pattern in the given sequence:
[tex]\begin{gathered} 11=4\cdot2\text{ +3,} \\ 25=11\cdot2+3, \\ 53=25\cdot2+3, \\ 109=53\cdot2+3. \end{gathered}[/tex]Therefore, the n-term of the sequence has the following form:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]Answer:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]MATH HELP WILL MARK BRAINLEST
Answers
Hi I need help with this i’m in a hurry so can you please just tell me the answer lol sorry i’m just in a little rush
Answers
Step 1
In the example why is the area of one triangle multiplied by 2.
This is because the hexagon is divided into one rectangle and 2 congruent triangles. Therefore, the area of the two triangles will be the same since they are congruent triangles. In order to get the area of the hexagon, the area of one of the triangles is mutiplied by 2 and added to the area of the rectangle.
Step 2
Find the dimension of one of the shaded triangle from Bev's pattern.
[tex]\begin{gathered} \\ \text{For Bev's triangle;} \\ \text{base}=4 \\ \text{height}=3 \\ Slantheight^2=(\text{ }\frac{base}{2})^2+height^2 \\ Slantheight^2=(\frac{4}{2})^2+3^2 \\ Slantheight^{}=\sqrt[]{2^2+9} \\ Slantheight=\sqrt[]{13}\text{unit} \end{gathered}[/tex]The dimensions will therefore be;
[tex]\begin{gathered} \text{base= 4unit} \\ \text{slant height=}\sqrt[]{13}unit \\ \text{slant height=}\sqrt[]{13}unit \end{gathered}[/tex]What can you say about the shaded area of all the shaded triangles in Bev's pattern.
[tex]\begin{gathered} \text{Area of given triangle=6unit}^2 \\ \text{Area of Bev's triangle=}\frac{1}{2}\times4\times3=6unit^2 \end{gathered}[/tex]The area of all shaded triangles in Bev's pattern are equal. This is because all the shaded triangles have the same dimensions and can be said to be congruent. Hence, they will have the same area.
I need help with this question... the correct answer choice
Answers
Solution:
The original parallelogram is as shown below with its coordinates;
The transformation that carries the parallelogram below onto itself is a rotation of 180 degrees counterclockwise about the origin.
When rotating a point 180 degrees counterclockwise about the origin, the point (x,y) will become (-x,-y)
This means to transform 180 degrees counterclockwise, we negate the x and y-coordinates of the original form.
The transformation is as shown below;
Therefore, the correct answer is a rotation of 180 degrees counterclockwise about the origin.
Lana owns an office supply shop. At the beginning of each school year, she chooses two or three products to donate to the local middle school.
The table shows the school supplies that Lana has in her shop and how many of each kind she has in stock. Lana is considering different options of supplies to donate. For each option, determine the greatest number of identical boxes she could pack and the number of each supply item she could put in the boxes.
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
A option 1: pencils and erasers: ____boxes with ____ pencils and ____ erasers
B option 2: notebooks and folders: ____ boxes with ____notebooks and ____ folders in each box.
C option 3: erasers, markers, and folders: ____ boxes with ____ erasers ____ markers and ____ folders in each box.
Answers
Option-1: 221 boxes with 78 pencils and 143 erasers.
Option-2: 525 boxes with 195 notebooks and 330 folders in each box.
Option-3: 583 boxes with 143 erasers 110 markers and 330 folders in each box.
Given that,
Owning an office supplies store is Lana. Each school year, she selects two or three items to give to the neighborhood middle school.
We have to find the correct answer for the given options.
The table is
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
Option1:
Pencils and erases:
78+143=221
221 boxes with 78 pencils and 143 erasers.
Option 2:
Notebooks and folders:
195+330=525
525 boxes with 195 notebooks and 330 folders in each box.
Option 3:
Erasers, markers, and folders:
143+110+330= 583
583 boxes with 143 erasers 110 markers and 330 folders in each box.
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Kelly and nadir both had maths tests last week, Kelly scored 47/68 and nadir scored 35/52. Who got the higher percentage score
Answers
Answer:
Kelly got a higher percentage score.
Step-by-step explanation:
35 / 52 = 0.673
47 / 68 = 0.691
jessica needs to bake 50 muffins her baking pan holds 12 muffins how many rounds of baking will she need to do
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Let x be the number of rounds of baking. Jessica's baking pan holds 12 muffins. Total 50 muffins is to be made. Hence, we can write,
[tex]\begin{gathered} 12x=50 \\ x=\frac{50}{12}=\frac{25}{6}=4\frac{1}{6} \end{gathered}[/tex]So, we obtained that x is equal to 4 1/6. The number of rounds cannot be a fraction. Here, the number of rounds is equal to the sum of 4 and a fraction 1/6. So, we can say that 5 rounds is needed to make 50 muffins.
An electronics store purchases laptops for $425.00. They use a markup rate of 60%. How much do they sell the laptop to their customers?
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Given that An electronics store purchases laptops for $425.00.
markup rate of 60%.
Selling price is:
[tex]\begin{gathered} SP=425+(0.60)425 \\ Sp=425+255 \\ SP=680 \end{gathered}[/tex]they sell the laptop to their customers at $680.
The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
Answers
In linear equation, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
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.converge or diverge? If it converges, to what value does it converge?
Answers
Given the series;
[tex]\sum ^{\infty}_{n\mathop=0}3(\frac{1}{5})^{n-1}[/tex]To obtain the sum of the series above and decide if it converges or diverges, we will
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}0}3(\frac{1}{5})^{n-1}=\sum ^{\infty}_{n\mathop{=}0}3(5)^{-(n-1)} \\ =\sum ^{\infty}_{n\mathop{=}0}3(5)^{(1-n)} \\ =\sum ^{\infty}_{n\mathop{=}0}15\times5^{-n} \\ =15\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n \end{gathered}[/tex]Simplify the resulting geometric series and decide if it converge or diverge
[tex]\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n\Rightarrow is\text{ an infinite geometric series, with first term a= 1 and common ratio r=}\frac{1}{5}[/tex]Solve for the sum to infinity of the geometric series
[tex]S_{\infty}=\frac{a}{1-r}=\frac{1}{1-\frac{1}{5}}=\frac{1}{\frac{4}{5}}=\frac{5}{4}[/tex]The sum of the series wil be
[tex]15\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n\Rightarrow15\times\frac{5}{4}=\frac{75}{4}[/tex]Hence,
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}0}3(\frac{1}{5})^{n-1}=\frac{75}{4} \\ \text{The series converges} \end{gathered}[/tex]Determine the interest rate capitalized once in a year which can triple any amount in 6 years
Answers
ANSWER
interest rate = 20%
EXPLANATION
let P = x, A = 3x, t = 6 and R = ?
[tex]A\text{ = P}\ast(1+R)^t[/tex][tex]\begin{gathered} 3x=x(1+R)^6 \\ 3=(1+R)^6 \\ 1+R=3^{\frac{1}{6}} \\ 1+R\text{ = 1.2} \\ R\text{ = 1.2 - 1} \\ R\text{ = 0.2} \\ R\text{ = 20\%} \end{gathered}[/tex]-9 is to the _____ of -3 on a number line so -9 is _____ than -3.right left more less
Answers
Answer:
-9 is to the left of -3
-9 is less than -3
Explanation:
If we're to write -9 and -3 on a number line from right to left, we'll see that -3 is going to come before -9, which means that -9 is to the left of -3.
On a number line, any number to the left of another number is less than the other number.
Since -9 is to the left of -3, so -9 is less than -3
What is the best estimation of the equation [-å? Drag the numbers into the boxes. Numbers may beused once, twice, or not at all.1142011/21/8
Answers
Answer:
[tex]1-\frac{1}{2}=\frac{1}{2}[/tex]Explanation:
Given the below expression;
[tex]\frac{7}{8}-\frac{6}{11}[/tex]We can see that 7/8 is closer to 1 and that 6/11 is closer to 1/2, so we'll now have;
[tex]1-\frac{1}{2}=\frac{2-1}{2}=\frac{1}{2}[/tex]So the best estimation of the equation is 1 - 1/2 = 1/2
Elaine drives her car 50 miles and has an average of a certain speed. If the average speed had been 4mph more, she could have traveled 58 miles in the same length of time. What was her average speed?
Answers
Hello there. To solve this question, we'll have to remember some properties about average speed.
When we're talking about moving in a straight line, the average speed is given by the ratio between the displacement ΔS and the interval of time Δt, namely
[tex]v=\frac{ΔS}{Δt}[/tex]In this case, say we have an average speed of v and the initial displacement ΔS = 50 miles in a certain interval of time Δt, such that
[tex]v=\frac{50}{Δt}[/tex]We know that if the average speed had been 4 mph more, then Elaine could have traveled 58 miles in the same length of time.
This means that v + 4 (that is, the average speed plus 4 mph) is equal to the ratio:
[tex]v+4=\frac{58}{Δt}[/tex]To solve this for v, we can start assuming that the interval of time Δt is not equal to zero, so do the average speed in the second equation.
Divide the first equation by the second, such that
[tex]\begin{gathered} \frac{v}{v+4}=\frac{\frac{50}{Δt}}{\frac{58}{Δt}} \\ \\ \frac{v}{v+4}=\frac{50}{58} \end{gathered}[/tex]Cross multiply the numbers, that is:
[tex]\begin{gathered} 58v=50\cdot(v+4) \\ 58v=50v+200 \end{gathered}[/tex]Subtract 50v on both sides of the equation
[tex]8v=200[/tex]Divide both sides by a factor of 8
[tex]v=25\text{ mph}[/tex]So this is her average speed.
V8 Splash $2.28 64 oz Walmart 0.04 cents per ozV8 Splash $ 2.49 64 oz Kroger 3.89 cents per ozWhich is the better deal?
Answers
Given:
V8 Splash $2.28 64 oz Walmart 0.04 cents per oz
V8 Splash $ 2.49 64 oz Kroger 3.89 cents per oz.
Best deal is
V8 Splash $2.28 64 oz Walmart 0.04 cents per oz
Question
Hong hikes at least 1 hour but not more than 4 hours. She hikes at an average rate of 2.7 mph. The function f(t)=2.7t represents the distance she hikes in t hours.
What is the practical range of the function?
Responses
all real numbers from 1 to 4, inclusive
all multiples of 2.7 between 2.7 and 10.8, inclusive
all real numbers
all real numbers from 2.7 to 10.8, inclusive
Answers
The practical range of the function is D. all real numbers from 2.7 to 10.8, inclusive.
What is a range?A function's range refers to all of the possible values for y. The formula for determining a function's range is y = f. (x). A function's range is the set of all its outputs. After we have substituted the domain, the range of a function is the complete set of all possible resulting values of the dependent variable (y, usually).
In this case, since the range is the value that satisfies the given function. For function f(t) = 2.7t the practical range of the function can be solved by substituting the lowest time and the highest possible time which are 1 and 4.
At t = 1 f(t) = 2.7 and at t = 4 f(t) = 10.8. so the range is all real numbers from 2.7 to 10.8, inclusive.
Therefore, the correct option is D.
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Harmie's average s-day natural gas usage rate is 5.g therms AR are sdays What day- and 8-day natural gas usage rates? are her
Answers
We know that Harmie's average 5-day natural gas usage rate is 5.9 therms/5 days.
We have to calculate the 1 day average usage rate and 8 day average usage rate.
We can calculate this by transforming the denominator from 5 days, as it is in the information given, to 1 day and 8 days respectively:
[tex]\frac{5.9\text{ therms}}{5\text{ days}}\cdot\frac{1\text{ day}}{1\text{ day}}=\frac{5.9}{5}\cdot\frac{\text{therms}}{1\text{ day}}=\frac{1.18\text{ therms}}{1\text{ day}}[/tex][tex]\frac{5.9\text{ therms}}{5\text{ days}}\cdot\frac{8\text{ days}}{8\text{ days}}=(\frac{5.9\cdot8}{5})\cdot\frac{\text{therms}}{8\text{ days}}=\frac{9.44\text{ therms}}{8\text{ days}}[/tex]Answer: 1.18 therms / 1 day, 9.44 therms / 8 days [Option 1]
The table below shows the probability distribution of a random variable X Х P(X) -10 0.07 -9 0.09 -8 0.67 -7 0 -6 0.17 What is the expected value of X? Write your answer as a decimal.
Answers
Teshawn, this is the solution to the problem:
We use the following formula to calculate the expected value of x, as follows:
Expected value of x = -10 * 0.07 + - 9 * 0.09 + -8 * 0.67 + -7 * 0 + -6 * 0.17
Expected value of x = -0.7 + -0.81 + - 5.36 + 0 + - 1.02
Expected value of x = -0.7 - 0.81 - 5.36 - 1.02
Expected value of x = -7.89
The mean height of men is known to 5.9 ft with a standard deviation of 0.2 ft. The height of a man (in ft) corresponding to a z-score of 2 is:Group of answer choices6.16.36.25.9
Answers
The average height is μ= 5.9ft and has a standard deviation of σ=0.2ft.
You have to determine the height (X) for the Z-score z=2
To determine this value, you have to use the formula of the standard deviation:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]First, write the equation for X:
-Multiply both sides by sigma:
[tex]\begin{gathered} Z\sigma=\sigma\frac{X-\mu}{\sigma} \\ \\ Z\sigma=X-\mu \end{gathered}[/tex]-Add mu to both sides of it:
[tex]\begin{gathered} (Z\sigma)+\mu=X-\mu+\mu \\ X=(Z\sigma)+\mu \end{gathered}[/tex]Replace the expression obtained for X with the known values of z, sigma, and mu
[tex]\begin{gathered} X=2\cdot0.2+5.9 \\ X=\text{0}.4+5.9 \\ X=6.3 \end{gathered}[/tex]The height of a man that corresponds to z=2 is 6.3 ft