Answer:
[tex]g(x)=\frac{1}{4}x-3[/tex]
Step-by-step explanation:
we have
[tex]f(x)=4x+12[/tex]
Find the inverse
step 1
Let
y=f(x)
[tex]y=4x+12[/tex]
step 2
Exchange the variables (x for y and y for x)
[tex]x=4y+12[/tex]
step 3
Isolate the variable y
we have
[tex]x=4y+12[/tex]
Subtract 12 both sides
[tex]x-12=4y[/tex]
Divide by 4 both sides
[tex]y=\frac{x-12}{4}[/tex]
simplify
[tex]y=\frac{1}{4}x-3[/tex]
step 4
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{1}{4}x-3[/tex]
we have that
[tex]g(x)=f^{-1}(x)[/tex]
therefore
[tex]g(x)=\frac{1}{4}x-3[/tex]
In this equation 5Z=-3 (z+7) in which order would you solve the problem? Put the steps below in the correct order
A. Use distribute property to simplify the right side (multiply the Z in the seven by -3)
B. Add 3z to both sides
C. Divided by -8 on both sides
Answer:
Use distributive property, add 3z to both sides, divide by -8 on both sides
Step-by-step explanation:
You have to do parenthesis first, then equal both sides, then divide
The slope of the line modeled by 4y = x is 4.
Answer:
The statement is false
Step-by-step explanation:
we have
[tex]4y=x[/tex]
Solve for y
That means ----> Isolate the variable y
Divide by 4 both sides
[tex]y=\frac{1}{4}x[/tex]
This is the equation of a proportional relationship between the variable x and the variable y
where the constant of proportionality k or slope m is equal to 1/4
therefore
The statement is false
Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.
m∠A=m∠B, m∠C=m∠A+30°, m∠E=m∠F=x, m∠D=2x−20°.
Answer:
Yes, △ABC ∼ △FED by AA postulate.
Step-by-step explanation:
Given:
Two triangles ABC and FED.
m∠A = m∠B
m∠C = m∠A + 30°
m∠E = m∠F = [tex]x[/tex]
m∠D = [tex]2x-20[/tex]°.
Now, let m∠A = m∠B = [tex]y[/tex]
So, m∠C = m∠A + 30° = [tex]y+30[/tex]
Now, sum of all interior angles of a triangle is 180°. Therefore,
m∠A + m∠B + m∠C = 180
[tex]y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50[/tex]
Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.
Now, consider triangle FED,
m∠D+ m∠E + m∠F = 180
[tex]2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50[/tex]
Therefore, m∠F = 50°
m∠E = 50° and
m∠D = [tex]2x-20=2(50)-20=100-20=80\°[/tex]
So, both the triangles have congruent corresponding angle measures.
m∠A = m∠F = 50°
m∠B = m∠E = 50°
m∠C = m∠D = 80°
Therefore, the two triangles are similar by AA postulate.
A shopper bought a 12-pound bag of oranges for 18.75. What is the unit price per ounce?
Answer:
About $0.10 per ounce
Step-by-step explanation:
12 pound costs $18.75. Lets find the cost per pound first:
Cost Per Pound = [tex]\frac{18.75}{12}=1.5625[/tex]
We know, there are 16 ounces in 1 pound.
We know 1 pound costs 1.5625
To find cost per ounce, we have to divide this by 16.
So,
Cost Per Ounce = [tex]\frac{1.5625}{16}=0.097[/tex]
Rounded to nearest cent, that would be 10 cents per ounce
tanA / 1-tan^2 = √3 /2
Answer:
A = π/6 + kπ, or A = 2π/3 + kπ
Step-by-step explanation:
tan A / (1 − tan² A) = √3 / 2
Cross multiply and simplify:
√3 (1 − tan² A) = 2 tan A
√3 − √3 tan² A = 2 tan A
3 − 3 tan² A = 2√3 tan A
0 = 3 tan² A + 2√3 tan A − 3
Solve with quadratic formula:
tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)
tan A = [ -2√3 ± √(12 + 36) ] / 6
tan A = (-2√3 ± √48) / 6
tan A = (-2√3 ± 4√3) / 6
tan A = -√3 or √3/3
Solve for A:
A = 2π/3 + kπ, or A = π/6 + kπ
What is 4 and square root of 72
Answer:
square root of 72 is approximately 8.49
i hope that right!
Step-by-step explanation:
6. What is 4% of 640?
Answer:
25.6
Step-by-step explanation:
Convert the percentage to decimal form by dividing by 100.
4% of 640
= 0.04(640)
= 25.6
What is the equation of the line that passes through the point (7,-6)and has a slope of -2
Answer:
The equation of the required line is: 2x + y = 8
Step-by-step explanation:
When a point on the line and the slope of the line are given, we use the slope - one - point form to determine the equation of the line.
Say, [tex]$ (x_1, y_1) $[/tex] is the point passing through the line and the slope of the line is say, [tex]m[/tex]. Then the equation would be:
[tex]$ (y - y_1) = m(x - x_1) $[/tex]
Here [tex]$ (x_1, y_1) = (7, -6) $[/tex] and slope, [tex]$ m = - 2 $[/tex].
Therefore, the equation of the line becomes:
[tex]$ y - (-6) = -2(x - 7) $[/tex]
[tex]$ \implies y + 6 = -2x + 14 $[/tex]
Rearranging we get:
[tex]$ 2x + y - 8 = 0 $[/tex] which is the required equation of the line.
Solving a Real-World Problem
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has
already pick
ushels, and she picks at a rat
hel per hour. The scenario is represented as
ah+15 = 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels o
strawberries?
hours
16
hours
10
hours
unu
hours
) Intro
Done
Answer: The answer is 5 and 3/5 hours
Step-by-step explanation:
Answer:
5 and 3/5 hours
Step-by-step explanation:
7. The cost of renting the party room for 10 people is $117.50. The cost of renting the room is $151.25 for 15 people. Write an equation that represents the cost of renting the party room in terms of the number of people attending the party .
Answer:
C = 6.75n + 50
Step-by-step explanation:
The equation for the cost of renting the party room can be written in the form;
C= mn+k ......i
Where C = cost
n = number of people
Substituting the 2 cases into the equation we have,
Case 1
117.5 = 10m + k ......1
Case 2
151.25 = 15m + k .....2
Subtracting eqn 1 from 2 we have
151.25 - 117.50 = 15m - 10m
5m = 33.75
m = 33.75/5 = 6.75
Substituting m = 6.75 into eqn 1, we have
117.50 = 10(6.75) + k
k = 117.5 - 67.50
k = 50
Therefore, rewriting the eqn i, we have
C = 6.75n + 50
refer to the graphic novel frame below. write and solve an equation to find how many movies they have time to show.
Answer:
Number of movies that can be shown = 2
Step-by-step explanation:
Given:
Movie night duration = 4 hours
Duration of each movie = 1.75 hours
Time given for eating popcorn = 0.5 hours
Time alloted for movies (excluding popcorn time) = 4 - 0.5 = 3.5 hours.
Number of movies that can be shown = [tex]\frac{Total\ time\ alloted\ for\ movie}{Time\ for\ 1\ movie}=\frac{3.5}{1.75}= 2[/tex]
To determine the number of movies that can be watched, an equation M*X <= T can be formulated where M is the length of the movie, X is the number of movies, and T is the total time available. To find X, divide T by M. This works when the time for each movie is the same.
Explanation:Without the actual graphic novel frame, it's hard to provide a specific equation. However, I can give you an example on how to approach this situation. Let's assume each movie is of length 'M' minutes and you have a total of 'T' minutes available for watching movies.
,
Let 'X' be the number of movies you can watch. You would write this as a mathematical equation like this: M*X <= T. This equation states that the total time spent watching movies should be less than or equal to the total time available.
,
To solve the equation, you would divide both sides of the equation by 'M'. The result will be X <= T/M. If you know the values of 'M' and 'T', you can plug them in here to get the maximum number of movies you can watch.
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Louisiana biologists tagged 250 fish in the oxbow lake False River on October 5. On a later date, they found 7 tagged fish in a sample of 350 fish. Estimate the total number of fish in False River to the nearest hundred.
At a school, the school population is 2/5 boys. There are 450 boys in the school. How many total students are in the school?
A bag contains quarter and dimes in a ratio of 3:5. If there is $6 in quarters in the bag, how many dimes are there?
1. Set up a ratio:
7 tagged / 350 fish = 250 tagged / x fish
Solve for x:
x = (350 * 250) / 7
x = 12,500 fish
2. Divide number of boys by the population ratio:
450 / 2/5 = (450 *5) /2 = 2250 / 2 = 1125 total students.
3. 4 quarters = $1, so they have 24 quarters total.
The ratio 3:5 means for every 3 quarters there are 5 dimes.
24 quarters / 3 = 8
8 x 5 = 40 dimes.
(1) The population of fish in the False river is 12500.
(2) There are 1125 total number of students in the school .
(3) There are 40 dimes in the bag.
(1) Number of fish tagged by Louisiana biologists = 250
On the next day a sample was collected from the False river
The number of fish in the sample = 350
Number of tagged fish in the sample = 7
Let the population of fish in the False river = P
Takin the ratio we can
[tex]\rm \dfrac{7}{350}= \dfrac{250}{P} \\\\P = (250)(350)/(7)\\P = 12500[/tex]
So the population of fish in the False river = 12500
(2) The number of boys in the school = 450
Let the total number of students in the school be B
According to the given condition
[tex]\rm \dfrac{2}{5}\times B = 450\\\\B = (450\times 5) /2 \\B = 2250/2 =1125[/tex]
So the total number of students in the school = 1125
(3) Let the number of dimes in the bag be x
According to the given condition we can write
[tex]\rm \dfrac{Number\; of\; quarters }{Number\; of\; dimes } = \dfrac{3}{5} ........(1)[/tex]
Also it is given that there are $6 in quarters in the bag.
$1 = 4 quarters
So $6 has [tex]\rm 4\times 6 = 24 \; quarters[/tex]
So we can put this value in equation (1)
[tex]\dfrac{24}{x} =\dfrac{3}{5} \\\\x = 40 dimes[/tex]
So we can conclude that there are 40 dimes in the bag.
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A bag of candy was 3/4 full. Abby ate 2/8 of this amount. How much candy did she eat
What is the area of an equilateral triangle that has a perimeter of 36 centimeters? Round to the nearest square centimeter.
Find base and height of the triangle to find area.
Base=Perimeter/3
Base=36/3=12 cm
Height²=12²-6²
Height²=108
Height=(6√3) cm
area=base×height
area=1/2×12×6√3=62 cm² approx.
answer: 3rd choice
Answer:
Find base and height of the triangle to find area.
Base=Perimeter/3
Base=36/3=12 cm
Height²=12²-6²
Height²=108
Height=(6√3) cm
area=base×height
area=1/2×12×6√3=62 cm² approx.
answer: 3rd choice
Step-by-step explanation:
Complete the explanation of the error.
If x2=16, then x=4
The value of x could also be....
Answer:
8 or -4
Step-by-step explanation:
The error is they believed x2 meant x^2 OR they forgot that x could also equal to -4.
x^2 = 16 has two solutions. They are 4 and -4. So the value of x could also be -4.
HELP PLS IM IN CLASS RN!!!
Answer:
48 inches
Step-by-step explanation:
Dagne can jump 13.2 inches that is 27.5% of her height. Let x inches be Dagne's height.
Then
x inches - 100%
13.2 inches - 27.5%
Write a proportion:
[tex]\dfrac{x}{13.2}=\dfrac{100}{27.5}[/tex]
Cross multiply:
[tex]27.5x=13.2\cdot 100\\ \\27.5x=1,320\\ \\x=\dfrac{1,320}{27.5}\\ \\x=48\ inches[/tex]
help me???????????????????
Answer:
To answer X and Y, all you need is a little common sense and a little bit of algebraic thinking. -x can equal: -x = 0? -6?, etc. Y could equal: 3?, 6?, 12?, etc. But the answer will always no matter what number will be 6.
let f = {(-2,4), (-1,2), (0,0), (1,-2), (2,-5)}
let g= {(-3,3), (-1,1), (0,-3), (1,-4), (3,-6)}
what is g(f(2))?
Answer:9
Step-by-step explanation:4
-6x+3y=-7−6x+3y=−7minus, 6, x, plus, 3, y, equals, minus, 7
x
Answer: none
Step-by-step explanation: since -6x+3y can't equal to -7−6x+3y
There are 452 pictures of dogs in 4 equal groups. How many pictures are in each group? Explain how you can use place value to place the first digit in the quotient. Please show with working
By dividing 452 pictures of dogs by 4, we find that each of the 4 equal groups has 113 pictures. The division process involves using place value and the standard algorithm for long division.
Explanation:To find out how many pictures of dogs are in each group, we need to divide the total number of pictures by the number of groups. The question states there are 452 pictures of dogs and these are divided into 4 equal groups. We can use long division to solve this.
Step-by-Step Solution:
Write down the division: 452 ÷ 4.
Start by looking at the hundreds place in 452. There are 4 hundreds in 452. Since 4 divided by 4 is 1, we put 1 in the hundreds place of the quotient.
Multiply the divisor (4) by the quotient (100) to get 400.
Subtract 400 from 452 to get 52.
Now, look at the tens place in 52. There are 5 tens in 52, and since 5 divided by 4 is 1 with a remainder, we put 1 in the tens place of the quotient and have a remainder of 12 after subtracting 40 (1 x 4 tens) from 52.
Next, look at the ones place in 12. There are 12 ones, and since 12 divided by 4 is 3, we put 3 in the ones place of the quotient.
After placing 3 in the ones place, we have no remainder, which means the division is complete and the quotient is 113.
Therefore, each group has 113 pictures of dogs.
Mike and Menna were instructed to graph the function y = 12 x + 1. Their graphs are shown.
The figure shows two graphs in the xy-plane. The graph on the left is labeled as Mike's Graph. The values on the x-axis range from negative 8 to 8 in increments of 2 and the values on the y-axis range from negative 8 to 8 in increments of 2. A line is shown which intersects the x-axis at negative 0.5 and y-axis at 1. The graph on the right is labeled as Menna's Graph. The values on the x-axis range from negative 8 to 8 in increments of 2 and the values on the y-axis range from negative 8 to 8 in increments of 2. A line is shown which intersects the x-axis at 2 and y-axis at 1.
Which student graphed the function correctly?
What mistake did the other student make?
Answer:
The function is y = 2x + 1.
And mike graphed the function correctly.
Menna took the point where the function touches x-axis incorrectly.
Instead of (-1/2,0), Menna took it as (-2,0)
Step-by-step explanation:
The equation y = mx +c indicates a straight line whose slope is m
And y-intercept is c.
y-intercept is nothing but the distance between origin and point where the graph crosses the y-axis (0,c).
Now, this graph crosses x-axis when y = 0.
⇒ mx + c = 0; ⇒ x = [tex]\frac{-c}{m}[/tex].
Now, by comparing y = 2x + 1 with y = mx + c.
m=2 and c=1
⇒ the graph should crosses y-axis at (0,c) = (0,1)
And touch x-axis at ([tex]\frac{-c}{m}[/tex] , 0) = ([tex]\frac{-1}{2}[/tex],0)
⇒ mike graphed the function correctly.
Menna took the point where the function touches x-axis incorrectly.
Instead of (-1/2,0), Menna took it as (-2,0)
Answer:
Step-by-step explanation:
y = 2x + 1.
Please help me! I'm having trouble solving this! In the △PQR, PQ = 39 in, PR = 17 in, and the height PN = 15 in. Find QR. Consider all possible cases.
Answer: 44
Step-by-step explanation:
we will find RN and NQ, then add together to give us RQ.
To find RN;
RP= 17 PN = 15 and RN =?
using pythagoras theorem,
adj^2 = hyp^2 - opp^2
RN^2 = RP^2 - PN^2
?^2 = 17^2 - 15^2
?^2 = 17^2 - 15^2
?^2 = 289 - 225
?^2 = 64
? = √64
? = 8
RN=8
To find NQ,
PN = 15 PQ=39 and NQ=?
using pythagoras theorem
NQ^2 = PQ^2 - PN^2
?^2 = 39^2 - 15^2
?^2 = 1521 - 225
?^2 = 1296
? = √1296
? = 36
NQ= 36
RQ = RN + NQ
RQ= 8 + 36
RQ=44
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
[tex]AB=\dfrac{38}{3}\ units[/tex]
Step-by-step explanation:
ABCD is a rhombus, then
[tex]AB=BC=CD=DA[/tex]
Since
[tex]BC=2x+8\\ \\CD=5x+1,[/tex]
then
[tex]BC=CD\Rightarrow 2x+8=5x+1[/tex]
Solve this equation:
[tex]2x-5x=1-8\\ \\-3x=-7\\ \\3x=7\\ \\x=\dfrac{7}{3}[/tex]
Then
[tex]BC=2\cdot \dfrac{7}{3}+8=\dfrac{14}{3}+8=\dfrac{14+8\cdot 3}{3}=\dfrac{14+24}{3}=\dfrac{38}{3}\ units[/tex]
Therefore,
[tex]AB=\dfrac{38}{3}\ units[/tex]
An account earned interest of 3% per year. The beginning balance was $150. The equation t=log1.03 (E/150) represents the situation, where t is the time in years and E is the ending balance. If the account was open for 8 years, what was the ending balance?
Answer:
190.02
Step-by-step explanation:
Trust
The ending balance of the account after 8 years is approximately $184.16.
Explanation:To find the ending balance of the account after 8 years, we can use the equation t=log1.03(E/150), where t is the time in years and E is the ending balance. Since the account was open for 8 years, we can substitute t=8 into the equation.
8=log1.03(E/150)
To solve for E, we can isolate it by first multiplying both sides of the equation by 150 and then raising both sides to the power of 1.03.
E/150=1.03⁸
E=150*1.03⁸
Using a calculator, we can find that E is approximately $184.16.
What is the value of the expression shown below?
2 over 3 to the power of 2 + 5 × 2 − 4
6 and 8 over 9
6 and 4 over 9
6 and 2 over 3
6 and 1 over 3
(2/3)²+5×2-4
(4/9)+5×2-4
(4/9)+10-4
10 4/9 - 4
6 4/9
answer: second choice
The solution to the equation x? = 45 is between
Answer:
9
Step-by-step explanation:
9 times 5 =45
Answer:
9
Step-by-step explanation:
When you do the math, 9 multiplied by 5 will get you 45
How do you find the sum of cube ?
Answer:
[tex](2x+5)(4x^{2} -10x+25)=0[/tex]
Step-by-step explanation:
Given:
The given equation is.
[tex]8x^{3} +125=0[/tex]
Find the some of cube.
Solution:
[tex]8x^{3} +125=0[/tex]
[tex]2^{3}x^{3} +5^{3}=0[/tex]
[tex](2x)^{3} +5^{3}=0[/tex]----------(1)
The sum of the cube formula is given below.
[tex](a^{3} +b^{3})=(a+b)(a^{2} -ab+b^{2} )[/tex]-----------(2)
By comparing equation 1 and equation 2
[tex]a=2x, b=5[/tex]
substitute a and b value in equation 2
[tex]((2x)^{3} +5^{3})=(2x+5)((2x)^{2} -(2x)(5)+5^{2})[/tex]
[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -(10x)+25)[/tex]
[tex]((2x)^{3} +5^{3})=(2x+5)(4x^{2} -10x+25)[/tex]
Therefore the sum of the cube [tex](2x+5)(4x^{2} -10x+25)=0[/tex]
What is the x-coordinate of the point that divides the
directed line segment from Kto J into a ratio of 1:3?
K(9,2)
1 2 3 4 5 6 7 8 9 10 11 12 x
top Tuppo
OOOO
J (1.-10)
The x-coordinate of the point that divides the directed line segment from K to J into a ratio of 1:3 is 7
Step-by-step explanation:
The formula for x-cooridnate of a point that divides a line in ratio m:n is given by:
[tex]x = \frac{nx_1+mx_2}{m+n}[/tex]
Given
K(9,2) = (x1,y1)
J(1,-10) = (x2,y2)
m = 1
n = 3
Putting the values in the formula
[tex]x = \frac{(3)(9)+(1)(1)}{1+3}\\x = \frac{27+1}{4}\\x = \frac{28}{4}\\x = 7[/tex]
Hence,
The x-coordinate of the point that divides the directed line segment from K to J into a ratio of 1:3 is 7
Keywords: Ratio, fraction
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Factor completely. x^2-4
Answer:
(x - 2)(x + 2).
Step-by-step explanation:
This is the difference of 2 squares:
a^2 - b^2 = (a - b)(a + b)
So
x^2 - 4 = (x - 2)(x + 2).
Abdul rented a truck for one day. There was a base fee of $16.95 , and there was an additional charge of 73 cents for each mile driven. Abdul had to pay $146.16 when he returned the truck. For how many miles did he drive the truck?
Abdul drove the truck for 177 miles.
Explanation:To find the number of miles driven by Abdul, we need to subtract the base fee from the total amount he paid and then divide the result by the additional charge per mile. Let's represent the number of miles driven by x.
Total amount paid - Base fee = Additional charge per mile * Number of miles driven
$146.16 - $16.95 = $0.73 * x
Simplifying the equation: $129.21 = $0.73x
Dividing both sides by $0.73, we get: x = 177
Therefore, Abdul drove the truck for 177 miles.
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