Given data:
The given expression is f(x)+34.
The given graph can be obtained by shifting f(x) in the positive direction of y by 34 units.
F(x)=f(x)+34
Thus, the last option is correct.
Val measures the diameter of a ball as 14 inches. How many cubic inches of air does this ball hold, to thenearest tenth? Use 3.14 forn.The ball holds aboutcubic inches of air.
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]In this problem we have
r=14/2=7 in ----> the radius is half the diameter
pi=3.14
substitute the given values
[tex]\begin{gathered} V=\frac{4}{3}_{}\cdot(3.14)\cdot(7^3) \\ V=1,436.0\text{ in\textasciicircum{}3} \end{gathered}[/tex]answer is 1,436.0 cubic incheshow to find the length of side x. really having a hard time on this
Since the figure is a square the diagonal divide it in two congruent right triangles. One of them is shown below:
Since we have right trisang
Select all the answers that are congruent to angle 6.
∠2 and ∠6 are corresponding angles
∠3 and ∠6 are alternate angles
∠6 and ∠7 are vertical angles
independent vs dependent equation5х – Зу = 10 бу = kx - 42
We will assume that we want to know if the system of equations is independent or dependent:
[tex]\begin{cases}5x-3y=10\text{ (1)} \\ 6y=kx-42\text{ (2)}\end{cases}[/tex]where k is a real number. We will try to find the solutions to the system, and we will try to give values to k for which the system becomes independent or dependent.
We will use substitution, we solve for the variable x on the first equation to obtain:
[tex]\begin{gathered} 5x-3y=10 \\ 5x=10+3y \\ x=\frac{10+3y}{5} \end{gathered}[/tex]And now we replace it onto the second equation:
[tex]\begin{gathered} 6y=k(\frac{10+3y}{5})-42 \\ 6y=\frac{10k+3ky}{5}-42 \\ 6y=\frac{10k+3ky-210}{5} \\ 30y=10k+3ky-210 \\ 30y-3ky=10k-210 \\ y(30-3k)=10k-210 \\ y=\frac{10k-210}{30-3k} \end{gathered}[/tex]And the value of x will be:
[tex]\begin{gathered} x=\frac{10+3(\frac{10k-210}{30-3k})}{5}=\frac{10+\frac{10k-210}{10-k}}{5} \\ =\frac{10(10-k)+10k-210}{5(10-k)} \\ =\frac{100-10k+10k-210}{50-5k} \\ =-\frac{110}{50-5k} \\ =-\frac{22}{10-k} \end{gathered}[/tex]This means that a solution of the system will be:
[tex]\begin{cases}x=-\frac{55}{10-k} \\ y=\frac{10k-210}{30-3k}\end{cases}[/tex]Now, for finding the values which make the system dependent. This happens when the lines have the same slope, this is, when:
[tex]\begin{gathered} \frac{-5}{-3}=\frac{k}{6} \\ \frac{5}{3}=\frac{k}{6} \\ 30=3k \\ 10=k \end{gathered}[/tex]We did the division of the opposite of the coefficient of x, over the coefficient of y. This means that the system will be independent for each value of k different than 10, and will be dependent for k=10.
Consider the scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5800. By 2012 the population had dropped to 4,600. Assume the trend continues predict the population in 2016.
Given:
In 2010 the population was 5800.
2012 the population had dropped to 4,600.
Let 't=0' be the year 2010.
P(t) represents the year population of the town t years after 2010.
Slope of a function P(t) is
[tex]\begin{gathered} m=\frac{4600-5800}{2012-2010} \\ m=-600 \end{gathered}[/tex]Population of town t years after 2010.
[tex]P(t)=-600(t)+5800[/tex]Population in the year 2016 that is t=6
[tex]\begin{gathered} P(6)=-600(6)+5800 \\ =2200 \end{gathered}[/tex]Population in the year 2016 is 2200
The Knitting Club members are preparing identical welcome kits for new members. The Knitting Club has 45 spools of yarn and 75 knitting needles. What is the greatest number of identical kits they can prepare using all of the yarn and knitting needles?
Common factors of 45 : 1,3,5,9,15,45
Common factors of 75 : 1,3,5,15,25,75
Common factors: 1,3,5,15
GReatest common factor = 15
15 identical kits
Tim bought a new car for 25,000 one year later the value of the car decrease to 20,000 what is the percentage of the decrease of the car
Answer:
The percentage decrease in the value of the car is;
[tex]20\text{\%}[/tex]Explanation:
Given that the initial price of the car is;
[tex]25,000[/tex]And after one year the price decreased to;
[tex]20,000[/tex]The percentage change in the price will be;
[tex]\begin{gathered} \text{ \%P }=\frac{25000-20000}{25000}\times100\text{\%} \\ \text{ \%P }=\frac{5000}{25000}\times100\text{\%} \\ \text{ \%P }=0.2\times100\text{\%} \\ \text{ \%P }=20\text{\%} \end{gathered}[/tex]Therefore, the percentage decrease in the value of the car is;
[tex]20\text{\%}[/tex]Assume the given function is one-to-one. Find the indicated value:If f(3)=2 then f^{-1}(2)=AnswerIf f^{-1}(-2)=-1 then f(-1)=?Answer
The question asks us to perform the inverse of two functions.
To solve this question, we need to understand how the inverse of a function works.
The inverse of a function is defined thus:
[tex]\begin{gathered} \text{if }f(x)=y \\ x=f^{-1}(y) \end{gathered}[/tex]With this definition, we can solve the questions.
Question 1:
[tex]\begin{gathered} f(3)=2 \\ \therefore f^{-1}(2)=3_{} \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} f^{-1}(-2)=-1_{} \\ \\ \therefore f(-1)=-2 \end{gathered}[/tex]Thus, the answers are
[tex]\begin{gathered} \text{Question 1:} \\ f^{-1}(2)=3 \\ \\ \text{Question 2:} \\ f(-1)=-2 \end{gathered}[/tex]
Set up and solve a proportion for the following application problem. If 6 pounds of grass seed cover 366 square feet, how many pounds are neededfor 4392 square feet?am 24/7onlinepounds
We know that 6 pounds cover 366 square feet, then we have the ratio:
[tex]\frac{6}{366}[/tex]Let x be the amount we need to cover 4392 square feet, then we have the ratio:
[tex]\frac{x}{4392}[/tex]Since the ratios have to be equal we have the proportion:
[tex]\frac{x}{4392}=\frac{6}{366}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{x}{4392}=\frac{6}{366} \\ x=4392\cdot\frac{6}{366} \\ x=72 \end{gathered}[/tex]Therefore, 72 pounds are nedded for 4392 sq ft.
A new bank customer with $2,500 wants to open a money market account. The bank is offering a simple interest rate of 1.8%.
a. How much interest will the customer earn in 30 years?
b. What will the account balance be after 30 years?
a. The customer will earn $_ in interest.
Using the simple interest formula, the interest will the customer earn in 30 years is $1350, the account balance be after 30 years is $3850 and the customer earn $1350 interest.
In the given given that;
A new bank customer with $2,500 wants to open a money market account.
The bank is offering a simple interest rate of 1.8%.
So the Principal Amout(P)=$2500
Interest Rate(R)=1.8%
(a) So we have to find the interest will the customer earn in 30 years.
So the time (T)=30 years
So the formula of Simple Interest;
I=PRT/100
I=2500*1.8*30/100
I=1350
So the interest will the customer earn in 30 years is $1350.
(b) Now we have to find the account balance be after 30 years.
The account balance = Principal Amount+Interest Amount
The account balance = 2500+1350
The account balance = $3850
(c) Now we have to find the customer will earn $_ in interest.
The customer earn $1350 interest.
To learn more about Simple Interest link is here
brainly.com/question/17304471
#SPJ1
what's the answer please help
Domain are the "x"'s in this example Domain = [-2, 2]
Range are the "y" in this example Range = [-3, 3]
The second choice is correct.
Find 3 ratios that are equivalent to the given ratio. 3 6 Find 3 ratios that are equivalent to the given ratio. g B. 18 9 DA. 24 6 D. 18 C. 6 24 1 F. 2 12 O E. 18 OH. 6 12 g G. 12
Fill in the missing number to complete the pattern.18, 12, _ , 0
The given pattern starts with an 18, then we have a 12, we can go from 18 to 12 by subtracting 6 from the initial number. By subtracting 6 from 12, we get the number that goes on the right side of 12, that is:
12 - 6 = 6
Then, fill the missing number with a 6.
18, 12, 6, 0
I need help. I have no idea on this question
ANSWER:
The total surface area is 450 mm^2
STEP-BY-STEP EXPLANATION:
We have a pyramid with a triangular base, which the formula to calculate the total surface area is the following
[tex]\begin{gathered} A_T=A_B+A_L \\ A_B=\frac{b\cdot h}{2} \\ A_L=3\cdot\frac{b\cdot l}{2} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} A_T=\frac{20\cdot15}{2}+3\cdot\frac{20\cdot10}{2} \\ A_T=150+300 \\ A_T=450 \end{gathered}[/tex]Find the area of the figure. (Sides meet at right angles.)4 m5 m15 m5 m5 m4 m4 m
The area of the figure will be the area of the rectangle of the top, plus the area of the rectangle of the bottom:
The area of the rectangle of the top is:
[tex]A1=w1\cdot h1=5\cdot4=20m^2[/tex]The area of the rectangle of the bottom is:
[tex]A2=w2\cdot h2=14\cdot4=56m^2[/tex]so, the total area is:
[tex]A=A1+A2=20m^2+56m^2=76m^2[/tex]The graph below shows the cost for going roller skating at 2 roller rinks . Bianca is going roller skating with a group of friends . Roller Rink A charges $3.00 per person and a $60 group fee . Roller Rink B charges $7.00 per person and an $8.00 group fee . When comparing costs ,which statement is true ? • Roller Rink B always cost less • Roller Rink A always cost less • Roller Rink B costs less if Bianca's group has fewer then 13 people• Roller Rink A costs less if Bianca's group has fewer then 13 people
In this case we can see that the cost of each company is increasing but the slopes are diferent. also we can see that the cost of company B is is cheaper at the begining but after some peaple is more expensive so the correct statement will be:
Roller Rink B costs less if Bianca's group has fewer than 13 people
when plqying a math game in class you drew 5 cards and had to find the sum of the numbers. your numbers were -9 3 2 - 5 4. what was the sum of your hand
We are required to sum up the numbers obtained. Our approach is to add the negative numbers separately and the positive numbers separately and then add up both.
[tex]\begin{gathered} (-9)+3+2+(-5)+4=3+2+4+(-9)+(-5) \\ 3+2+4=9 \\ -(9+5)=-14 \\ \text{Adding both} \\ 9+(-14)=9-14=-5 \end{gathered}[/tex]-5 is our answer.
To determine the number of trout in a lake, a conversationist catches 141 trout, tags them and trows them back into the lake. Later, 45 trout are caught and 15 are tagged. How many trout would the conversationist expect to be in the lake???
which of the following represents a line that is parallel to the line with equation y = – 3x + 4 ?A. 6x +2y = 15B. 3x - y = 7 C. 2x - 3y = 6D. x + 3y = 1
In order to have parallel lines, the slopes of the lines need to be the same.
In order to check the slope for each option, let's put the equations in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
So we have that:
A.
[tex]\begin{gathered} 6x+2y=15 \\ 2y=-6x+15 \\ y=-3x+7.5 \end{gathered}[/tex]B.
[tex]\begin{gathered} 3x-y=7 \\ y=3x-7 \end{gathered}[/tex]C.
[tex]\begin{gathered} 2x-3y=6 \\ 3y=2x-6 \\ y=\frac{2}{3}x-2 \end{gathered}[/tex]D.
[tex]\begin{gathered} x+3y=1 \\ 3y=-x+1 \\ y=-\frac{1}{3}x+\frac{1}{3} \end{gathered}[/tex]So the only option with a line with a slope of -3 is Option A.
The function f(x)= 4x is one to one Find A and B
Given:
[tex]f(x)=4x[/tex]a)
[tex]\begin{gathered} x=4f^{-1}(x) \\ f^{-1}(x)=\frac{x}{4}\text{ , for all x} \end{gathered}[/tex]Option C is the final answer.
b)
[tex]\begin{gathered} f(f^{-1}(x))=f(\frac{x}{4}) \\ =4(\frac{x}{4}) \\ =x \end{gathered}[/tex][tex]\begin{gathered} f^{-1}(f(x))=f^{-1}(4x) \\ =\frac{4x}{4} \\ =x \end{gathered}[/tex][tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]Which normal distribution has a wider spread: distribution A with a mean of one and a standard deviation of two, or distribution B with a mean of two and a standard deviation of one?
The normal distribution with mean of one and standard deviation of two has the wider spread.
Normal distribution:
Normal distribution defines a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Given,
Here we have the distributions,
Distribution A with a mean of one and a standard deviation of two, or Distribution B with a mean of two and a standard deviation of one
Now, we have to identify the normal distribution has a wider spread.
Here the normal distribution with a mean of 1 and standard deviation of 2 will be wider than a distribution with a mean of 2 and standard deviation of 2.
Because, the distributions with greater standard deviations indicate greater variability/spread of its variables around the mean.
To know more about Normal distribution here.
https://brainly.com/question/15103234
#SPJ1
The side walls of a regular quadrilateral pyramid are equilateral triangles with sides equal to 8 cm. Calculate the pyramid:1) the sum of the lengths of all the sides;2) the area of the base;3) the length of the height of the side wall;4) the area of the side wall.
a) 64cm
b) 64 square cm
c) 4√3 cm
d) 16√3 square cm
Explanations:A regular quadrilateral pyramid with equilateral triangles is as shown below;
1) The pyramid has 8 side lengths, hence the sum of the length of all the sides is given as:
[tex]\begin{gathered} Sum\text{ of side lengths}=8\times8cm \\ Sum\text{ of side lengths}=64cm \end{gathered}[/tex]2) Since the triangular sides are equilateral, the base of the pyramid will be a square with side length of 8cm. The area of the base is expressed as:
[tex]\begin{gathered} A=length\times length \\ A=8cm\times8cm \\ A=64cm^2 \end{gathered}[/tex]3) Since one side wall is an equilateral triangle, the height will be perpendicular to the base as shown:
In order to determine the height, we will use the Pythagorean theorem as shown:
[tex]\begin{gathered} 8^2=h^2+4^2 \\ h^2=8^2-4^2 \\ h^2=64-16 \\ h^2=48 \\ h=\sqrt{48}=4\sqrt{3}cm \\ \end{gathered}[/tex]4) The area of the side wall is equivalent to the area of the triangle expressed as:
[tex]\begin{gathered} Area\text{ of side wall}=\frac{1}{2}\times base\times height \\ Area\text{ of side wall}=\frac{1}{2}\times8cm\times4\sqrt{3} \\ Area\text{ of side wall}=16\sqrt{3}cm^2 \end{gathered}[/tex]Which of the following would be the best equation for the function of the values for Janet’s reading?A) p = 6hB) p = 20hC) h = 20pD) 20 + p = h
In order to obtain the best equation for the function of the values for Janet’s reading, we will apply the equation of a straight line between two points.
The formula to calculate the equation of a line between two points is,
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let us now pick any two points from the table given
[tex]\begin{gathered} (x_1,y_1)=(1,20) \\ (x_2,y_2)=(6,120) \end{gathered}[/tex][tex]\begin{gathered} \text{where,} \\ p=y \\ h=x \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{y-20}{x-1}=\frac{120-20}{6-1} \\ \end{gathered}[/tex]Simplify
[tex]\begin{gathered} \frac{y-20}{x-1}=\frac{100}{5} \\ \frac{y-20}{x-1}=20 \\ y-20=20(x-1) \\ y=20(x-1)+20=20x-20+20=20x \\ y=20x \\ \therefore p=20h \end{gathered}[/tex]Hence, the answer is
[tex]p=20h\text{ (OPTION B)}[/tex]Listed are the fractions of the total number of books Allisa put in a bookcase 2/5 history books 1/3 math books 1/10 art books Allisa will fill the remainder of the bookcase with science books Drag and drop the fractions into the boxes that show the fraction of the total number of books that are history, math, or art books in the bookcase and the fraction of the total number of books that will be science
Answer:
Books in Bookcase = 5/6
Science Books = 1/6
Explanation:
Given:
Total number of books Alissa put in a bookcase;
2/5 history books
1/3 math books
1/10 art books
We can go ahead and determine the fraction of the total number of books that are history, math, or art books in the bookcase by adding the given fractions together as seen below;
[tex]\frac{2}{5}+\frac{1}{3}+\frac{1}{10}=\frac{12+10+3}{30}=\frac{25}{30}=\frac{5}{6}[/tex]So the fraction of the total number of books that are history, math, or art books in the bookcase is 5/6
Let x represent the fraction of the total number of books that will be science.
We can go ahead and determine the value of x by subtracting the fraction of the total number of books that are history, math, or art books in the bookcase from 1;
[tex]x=1-\frac{5}{6}=\frac{6-5}{6}=\frac{1}{6}[/tex]So the fraction of the total number of books that will be science is 1/6
Brenda had $23 to spend on two notebooks. After buying them she had $19. How much did each notebook cost
4x – 2y = 20-8x + 4y = -40
We have the system of equations:
[tex]\begin{gathered} 4x-2y=20 \\ -8x+4y=-40 \end{gathered}[/tex]We can tell that the equations are linear combination of each other: if we multiply the first equation by -2 we get the second equation.
[tex]\begin{gathered} -2(4x-2y)=-2(20) \\ -8x+4y=-40 \end{gathered}[/tex]So in fact we have only one equation and two unknowns, so there are infinite solutions to this system.
We can write the solution as:
[tex]\begin{gathered} 4x-2y=20 \\ 2y=20-4x \\ y=10-2x \\ y=-2x+10 \end{gathered}[/tex]Answer: the system has infinte solutions, expressed in the line y=-2x+10.
Differentiate a trig function that is greater than a power of 1, and involve either quotient, chain, or product rule.Differentiate a sine and cosine function that involves product and chain rule. Find the equation of the tangent line at x = a special triangle point (i.e. /4, /6, /3).Differentiate a function that involves both trig and exponential functions.[hint: add your own twist to this question for level 3/4]Differentiate an exponential function. [hint: add your own twist to this question for level 3/4]Differentiate a function where you have “y” and “x” on both sides of the equation and they cannot be simplified by collecting like terms or isolating y (i.e. y on one side and y^2 on the other). [hint: add your own twist to this question for level 3/4]
Solution:
Given a trigonometric function that is greater than power of 1 as shown below:
[tex]y=sin^2x\text{ ---- equation 1}[/tex]To differentiate the function, we use the chain rule.
According to the chain rule,
[tex]\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}[/tex]From equation 1, let
[tex]u=sin\text{ x --- equation 2}[/tex]This implies that
[tex]\begin{gathered} y=u^2 \\ \Rightarrow\frac{dy}{du}=2u \end{gathered}[/tex]From equation 2,
[tex]\begin{gathered} \begin{equation*} u=sin\text{ x} \end{equation*} \\ \Rightarrow\frac{du}{dx}=cos\text{ x} \end{gathered}[/tex][tex]\begin{gathered} Recall\text{ from the chain rule:} \\ \frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx} \\ \Rightarrow2u\times\text{cos x} \\ \frac{dy}{dx}=2ucos\text{ x} \\ but\text{ } \\ u=sin\text{ x} \\ \therefore\frac{dy}{dx}=2(sin\text{ }x)(cos\text{ }x) \end{gathered}[/tex]Hi, what is the LCM of the numbers 3 and 15
Answer:
15
Step-by-step Explanation:
LCM is the least common multiple, that is, is the least number that is a multiple of both numbers.
To find it, first, let's write the multiples of 3:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
Now, let's write the multiples of 15:
Multiples of 15: 15, 30, 45, ...
If you compare the multiples of 3 and 5, we can see that they have some common multiples, as 15 and 30.
From this common multiples, 15 is the smallest number. So, 15 is the LCM of 3 and 15.
Answer: 15.
Given `lim_(x -> 2) 2x - 3 = 1`, use the formal definition of a limit to find the value of δ that corresponds to ε = 0.3.
A. 0.05
B. 0.15
C. 0.30
D. 0.50
Answer: B. 0.15
Your Welcome :)
6(k-8)=96k=?help please!
answer: k = 24
