Answer:
h(x)= 3x - 6
Step-by-step explanation:
Edge 2020
The inverse of function f(x) = [tex]\frac{1}{3}x + 2[/tex] is -
y = 3(x - 2)
We have a function - f(x) = [tex]\frac{1}{3}x + 2[/tex]
We have to find the inverse of a function.
What is the necessary condition for a function to be invertible?We say that a function f : A → B is invertible if for every b ∈ B there is exactly one a ∈ A such that f(a) = b.
According to question, we have -
y = f(x) = [tex]\frac{1}{3}x + 2[/tex]
Replace x with y, to find inverse function f, and compute the resulting equation for x. Exchanging the variables, we get -
x = [tex]\frac{1}{3}y + 2[/tex]
x - 2 = [tex]\frac{1}{3} y[/tex]
y = 3(x - 2)
Hence, the inverse of function f(x) = [tex]\frac{1}{3}x + 2[/tex] is -
y = 3(x - 2)
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The combined age of three relatives is 120 years. James is three times the age of Dan, and Paul is two times the sum of the ages of James and Dan. How old is each person?
The ages of James, Paul and Dan is required.
James is 30 years old, Paul is 80 years old and Dan is 10 years old.
Let the ages of James be [tex]j[/tex], Paul be [tex]p[/tex] and Dan be [tex]j[/tex].
James is three times the age of Dan
[tex]j=3d[/tex]
Paul is two times the sum of the ages of James and Dan
[tex]p=2(j+d)\\\Rightarrow p=2(3d+d)\\\Rightarrow p=2(4d)=8d[/tex]
The combined ages of the people is 120
[tex]j+p+d=3d+8d+d\\\Rightarrow 120=12d\\\Rightarrow d=\dfrac{120}{12}\\\Rightarrow d=10[/tex]
[tex]j=3d=3\times 10\\\Rightarrow j=30[/tex]
[tex]p=8d=8\times 10\\\Rightarrow p=80[/tex]
So, James is 30 years old, Paul is 80 years old and Dan is 10 years old.
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Two linear equations are shown in the graph.
#Brainliest award
What are the coordinates of the point where the two lines intersect?
A. (–2, 3)
B. (3, 3)
C. (3, 0)
D. (–3, 3)
count the lines horizontally and vertically to see where the lines connect
x = left to right
y = up and down.
the black lines are the origins ( 0,0)
so 3 to the right of a black line and 3 up from the black line equals (3,3)
Answer is B
A bug is traveling at a rate of 18 inches per minute. Write the rate in feet per minute. (12 in. = 1 ft.)
A cylindrical rain barrel has a radius of 2 feet and holds a total of 30 cubic feet of water. How tall is the rain barrel? Use 3.14 for pi. Round your answer to the nearest hundredth.
The height of the rain barrel is required.
The height of the barrel is 2.39 feet.
r = Radius of barrel = 2 feet
V = Volume of barrel = 30 cubic feet
h = Height of barrel
Since, the barrel is cylindrical the volume of the barrel is
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{30}{3.14\times 2^2}\\\Rightarrow h=2.3885\approx 2.39\ \text{feet}[/tex]
The height of the barrel is 2.39 feet.
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A camel can drink 15 gallons of water in 10 minutes. at this rate, how much water can the camel drink in 77 minutes?
To solve this problem, we simply have to use ratio and proportion.
We know that 15 gallons is consumed in 10 minutes therefore the conversion factor is:
15 gallons / 10 minutes
Therefore in 77 minutes:
water consumed = (15 gallons / 10 minutes) * 77 minutes
water consumed = 115.5 gallons
Is 5xy + y = 9 linear?
Can you help me solve this proof please?
match each point with one of the following fractions 5/6, 7/12, 1/8, 5/16
A=5/6 B= 5/16 C= 7/12 D= 1/8
A= 1/8 B= 5/16 C= 7/12 D= 5/6
A= 7/12 B= 5/6 C = 5/16 D = 1/8
A= 5/16 B= 1/8 C = 7/12 D= 5/6
Answer:
The correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6
Step-by-step explanation:
Consider the provided fractions.
First convert each fraction into decimal form as shown:
5/6 = 0.833..
7/12 = 0.5833..
1/8 = 0.125
5/16 = 0.3125
The largest number among them is 0.833.. i.e 5/6 and the smallest number among them is 0.125 i.e 1/8
Arrange them in increasing order as shown:
0.125, 0.3125, 0.5833.., 0.833.. or 1/8, 5/16, 7/12, 5/6
Now consider the provided figure. The alphabets are showing the number are in increasing order
Thus, the correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6
Find the average value of f(x) = 1/x over the interval [e, 2e].
ln(2)/e
-1/2e^
Ln2
Ln3
the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
f(x) = 1/x over the interval [e, 2e].
i.e. we get,
[tex]\frac{1}{2e-e}[/tex] × [tex]\int\limits^{2e}_e {1/x} \, dx[/tex] =1/e. ln (x)[2e, e]
=ln(2e)/e - ln(e)/e
=[ln2+lne/e] - 1/e
=ln2/e +1/e -1/e
=ln(2)/e
hence, the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.
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Mrs. Gerhard wants to plant grass in her backyard. She wants the grass to cover all of her backyard except the play area.
How many square feet of grass will Mrs. Gerhard need to plant?
A.
12 ft2
B.
34 ft2
C.
60 ft2
D.
84 ft2
A.
12 ft2
B.
34 ft2
C.
60 ft2
D.
84 ft2
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: 15x + 10y ≥ 1100
Explain how to graph the solution set.
To graph the solution set of the inequality 15x + 10y ≥ 1100, find the intercepts of the graph and draw a line passing through them. Then, test a point not on the line to determine which side represents the solution set. The solution set of the inequality is the region below the line on the graph.
Explanation:To graph the solution set of the inequality 15x + 10y ≥ 1100, we can start by identifying the intercepts of the graph. An intercept is a point where the graph intersects either the x-axis or the y-axis. To find the x-intercept, we set y = 0 in the inequality: 15x + 10(0) ≥ 1100. Simplifying this equation, we have 15x ≥ 1100. Dividing both sides by 15, we get x ≥ 73.33. Therefore, the x-intercept is (73.33, 0).
To find the y-intercept, we set x = 0 in the inequality: 15(0) + 10y ≥ 1100. Simplifying this equation, we have 10y ≥ 1100. Dividing both sides by 10, we get y ≥ 110. Therefore, the y-intercept is (0, 110).
After finding the intercepts, we can draw a line passing through these two points. Since the inequality is ≥, the line will be solid (including the points on the line). Finally, we determine which side of the line represents the solution set. We can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality. If the inequality is true, the shaded region representing the solution set should be below the line.
If the inequality is false, the shaded region should be above the line. In this case, substituting (0, 0) into the inequality gives 15(0) + 10(0) = 0, which is less than 1100. Therefore, the shaded region should be below the line. The solution set of the inequality 15x + 10y ≥ 1100 is the region below the line on the graph.
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Jim got 30 questions correct out of a total of 35. what was the percentage he got correct?
Jim answered 30 out of 35 questions correctly, which is 85.7% correct when calculated using the percentage formula.
Explanation:Jim got 30 questions correct out of a total of 35. To find the percentage of questions he got correct, you can use the formula for calculating percentages: Percentage = (Number of correct answers ÷ Total number of questions) × 100%. Applying this formula to Jim's case: Percentage = (30 ÷ 35) × 100% = 0.857 × 100% = 85.7%. Therefore, Jim got 85.7% of the questions correct.
2. The logo shown below was created by splitting a circle into 6 equal sections. Raphael is creating a stage-sized version of this logo where the shaded portions will be covered in fabric.
If the radius of the circle is 12 feet, how much fabric will he need in order to cover the shaded portions?
In the space that is given, tell what formulas you used and show how solved to get your answer.
Let π =3.14
Answer:
226.08
Step-by-step explanation:
He first term of a sequence is 2, and each subsequent term is the reciprocal of the square of the preceding term. what is the positive square root of the fifth term?
PLEASE HELP!!
What is the slope of the line represented by the equation 2x+3y= –12 ?
A)–3/2
B)–2/3
C)2/3
D)3/2
Answer:
the correct answer is B.-2/3
Each afternoon she goes to the track and divides her time between running and jogging. she spends a total of 2 hours exercising and does a total of 10 miles. if she runs at 5 miles per hour and jogs at 2.5 miles per hour, how long did she spend on each type exercise?
Find the measures of the angles of a triangle if the measure of one angle is three times the measure of a second angle and the third angle measures 55 times the second angle decreased by 90
Find the distance between R (-1,1) and S (-4,-5) to the nearest tenth.
The distance between the points R (-1,1) and S (-4,-5) is [tex]3\sqrt{5}[/tex] units.
To find the distance between points R(-1, 1) and S(-4, -5), we can use the distance formula in a coordinate plane.
The distance formula is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Using the given coordinates:
[tex]x_1 = -1, y_1 = 1[/tex](coordinates of point R)
[tex]x_2 = -4, y_2 = -5[/tex] (coordinates of point S)
[tex]d = \sqrt{(-4 +1 )^2 + (-5 - 1)^2}[/tex]
[tex]d = \sqrt{9 +36}[/tex]
[tex]d = \sqrt{45}[/tex]
[tex]d = \sqrt{9 \times 5}[/tex]
[tex]d = 3\sqrt{5}[/tex]
Hence, the distance between the points R (-1,1) and S (-4,-5) is [tex]d = 3\sqrt{5}[/tex] units.
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Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−3).
A. 32
B. 16
C. 40
D. 26
Answer:
The answer is C, 40
If the expression below models the number of applicants for a credit card, what is the correct interpretation of the second factor?
There were 6.75 times as many people who applied in the 4th month as in the first month.
There were 1.2 times as many people who applied in the 4th month as in the first month.
There were 2.07 times as many people who applied in the 4th month as in the first month.
There were 4.8 times as many people who applied in the 4th month as in the first month.
The latest online craze is a new game, Khan on Seven. You get 100100100 points for playing the game. In addition, you get 505050 points for each seven-letter word you are able to make with the ten letters you are given. The game leader currently has 17{,}95017,95017, comma, 950 points. Sal wants to break the record, and needs 18{,}00018,00018, comma, 000 points or more to do so.
The steepness or grade of a road is expressed as a percent. if a road rises 3 feet for every 24 horizontal feet. What is the slope of the road? what percent grade is this ?
Triangle WXY is isosceles. ∠YWX and ∠YXW are the base angles. YZ bisects ∠WYX. m∠XYZ = (15x)°. m∠YXZ = (2x + 5)°. What is the measure of ∠WYX?
PLEASE EXPLAIN THE STEPS
A. 5°B.15°C.75°D. 150°
Answer:
Option D is correct.
The measure of [tex]\angleWYX = 150^{\circ}[/tex]
Step-by-step explanation:
[tex]\triangle WXY[/tex] is isosceles and [tex]\angle YWX[/tex] and [tex]\angle YXW[/tex] are base angles.
Isosceles Triangle:
A triangle with two equal sides, and two congruent base angles that means the angles are equal
By the definition, the base angles are equal i.e, [tex]m\angle YWX=m\angle YXW[/tex]
Since, YZ bisects [tex]m\angle WYX[/tex]
Angle Bisector theorem: An angle bisector is a line or ray that divides an angle into two equal angles
then, [tex]\angle WYX =2\angle XYZ[/tex] or
Substitute the value of [tex]\angle XYZ=(15x)^{\circ}[/tex] ;
[tex]\angle WYX =2(15x)^{\circ} = (30x)^{\circ}[/tex]
The sum of measures of these three angles of triangle WXY is equal to the 180 degree.
In triangle WXY we have;
[tex]\angle YXW+\angle WYX+\angle YWX=180^{\circ}[/tex]
Substitute the value of [tex]m\angle YWX=m\angle YXW=(2x+5)^{\circ}[/tex] and [tex]\angle WYX=(30x)^{\circ}[/tex] in above formula:
[tex]2\angle YXW+30x=180^{\circ}[/tex] or
[tex]2\cdot(2x+5)+30x=180^{\circ}[/tex]
Simplify:
[tex]4x+10+30x=180^{\circ}[/tex]
Combine like terms ;
[tex]34x+10^{\circ}=180^{\circ}[/tex] or
[tex]34x=170^{\circ}[/tex]
Simplify;
[tex]x= \frac{170}{34} =5^{\circ}[/tex]
Substitute the value of x in [tex]\angle WYX [/tex];
[tex]\angleWYX = (30x)^{\circ} = 30 \cdot 5 = 150^{\circ}[/tex]
Therefore, the measure of [tex]\angleWYX = 150^{\circ}[/tex]
Answer:
150 D
Step-by-step explanation:
Please help me I'm having problems with this question and I don't know what it is if you do answer this question I really appreciate it thanks
What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
A) 1
B) –1
C) i
D) –i
the answer would be B :) hope this helps
Which congruence theorems can be used to prove △EFG ≅ △JHG? Check all that apply.
HL
SAS
SSS
ASA
AAS
Answer:
ASA and AAS
Step-by-step explanation:
We do not know if these are right triangles; therefore we cannot use HL to prove congruence.
We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.
We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.
Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.
Answer: ASA and AAS
Step-by-step explanation:
Tim earned $16 babysitting and $17.50 mowing a lawn. He paid $8.50 for a movie and bought a small popcorn for $1.95. Write an expression to show how much money he has left.
The expression to show how much money he has left is $(33.5 - 10.45).
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given that, Tim earned $16 babysitting and $17.50 mowing a lawn.
What Tim has earned we'll add which is $(16 + 17.50) = $33.5.
He paid $8.50 for a movie and bought a small popcorn for $1.95.
His spendings we'll also add which is $(8.5 + 1.95) = $10.45.
Now, to write an expression for how much money he has left we'll subtract
his total spending from his total earnings which is,
= $(33.5 - 10.45).
= $23.05.
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Marjorie bought 24 bottles of juice. She drinks 2 bottles each day. Which of the following best represents the number of bottles she has left at the end of d days?
A.2d - 24
B.24d - 2
C.24 + 2d
D.24 - 2d
Answer: D.24 - 2d
Step-by-step explanation: I took the test Hope you have a good day. PEACE
A fair coin is flipped six times. what is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times?
A fair coin is flipped six times. Then 1/22 is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times
What is Probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The probability that heads occurs exactly 6 times if it is known that heads occurs at least four times is
P{H=6|H≥4}
= P{(H=6)∩(H≥4)}/P{H≥4}
= P{H=6}/P{H≥4}
We need to calculate P{H=6}
P{H=6} = C(6,6)(½)6
= (½)6
P{H≥4} = P{H=4} + P{H=5} + P{H=6}
= C(6,4)(½)4(½)2 + C(6,5)(½)5(½) + C(6,6)(½)6
= (½)6[C(6,4) + C(6,5) + C(6,6)]
= (½)6[15 + 6 + 1]
= (½)6(22)
Therefore,
P{H=6|H≥4} = 1/22
1/22 is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times
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I WILL GIVE BRAINLIEST. What is the justification for each step in solving the inequality?
75x+35≥7(11x+9)+4
75x+35≥7(11x+9)+4 Given
75x+35≥77x+63+4 Distributive Property
75x+35≥77x+67
−2x+35≥67 Subtraction Property of Order
−2x≥32
x≤−16
I just need the ones that don't have the justification next to it
Answer:
Combine like terms
Subtraction property of inequality
Division property of inequality
Step-by-step explanation:
We are given tnat
[tex]75x+35\geq 7(11x+9)+4[/tex]
We have to find the missing justification in given solution
[tex]75x+35\geq 7(11x+9)+4[/tex]
Reason:Given
[tex]75x+35\geq 77x+73+4[/tex]
Reason:Distributive property
[tex]75x+35\geq 77x+67[/tex]
Reason:combine ike terms
[tex]-2x+35\geq 67[/tex]
Reason:Subtraction property of order
[tex]-2x\geq 32[/tex]
Reason:Subtraction property of inequality
[tex]x\leq -16[/tex]
Reason:Division property of inequality