Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.
Answers
Answer:
[tex]k=4[/tex]
Step-by-step explanation:
So we have the graphs of f(x) and g(x).
And we know that g(x) is defined as f(kx), where k is some constant.
First, from the graph we can note two points:
For g(x), we have the point (1,10) and for f(x), we have the point (4,10).
In other words:
[tex]g(1)=10[/tex]
And since we know the g(x) is f(kx), this means that:
[tex]g(1)=10\\g(1)=10=f(1(k))=10[/tex]
And we know the for f(x) to be 10, the initial value is 4. Therefore:
[tex]f(1(k))=10=f(4)\\1k=4\\k=4[/tex]
Therefore, the value of k is 4.
Answer:
[tex]\huge \boxed{k=4}[/tex]
Step-by-step explanation:
The graph of g(x) crosses the point (1, 10).
The graph of f(x) crosses the point (4, 10).
So, g(1) = 10. The x (input) is 1. The output is 10.
f(4) = 10. The x (input) is 4. The ouput is 10.
g(1) = f(4)
g(x) = f(k ⋅ x)
g(1) = f(k ⋅ 1)
f(k ⋅ 1) = f(4)
k ⋅ 1 = 4
k = 4
Related Questions
Claire is going to an amusement park. The price of admission into the park is $30, and once she is inside the park, she will have to pay $4 for every ride she rides on. How much money would Claire have to pay in total if she goes on 9 rides? How much would she have to pay if she goes on r rides?
Answers
Answer:
1. $66
2. 30 + 4r
Step-by-step explanation:
Let
Price of admission into the park=$30
Price of every ride in the park=$4
Number of rides =x
Total cost of going to the park= 30+4x
1. How much money would Claire have to pay in total if she goes on 9 rides
Total cost of going to the park= 30+4x
When x=9
=30+4x
= 30 + 4(9)
=30 + 36
=$66
2. How much would she have to pay if she goes on r rides?
When x=r
Total cost of going to the park= 30+4x
= 30 + 4(r)
=30 + 4r
Answer:
Cost for 9 rides=$66, Cost for r rides=30+4r
Step-by-step explanation:
Cost for 9 rides: 30+4(9)=66
Cost for r rides: 30+4r
FOR BRAINLIEST!!! ASAP SUPER EASY!!
One coin is randomly selected from a jar containing 20 pennies, 15 nickles, 3
dimes, and 12 quarters. Find the odds of a value greater than $0.10. *
6:19
3:47
12:50
08:12
Answers
Step-by-step explanation:
Total coins in the jar = 50. Number of coins with a value less than $0.05 = 20 (the pennies). ... Probability of picking a penny = 20/50 = 40%. ... 'Odds' = 3 to 2 against it.
simplify -4xy+8yx-8yx
Answers
Answer:
=-4xy+8yx-8yx
=-4xy
Step-by-step explanation:
+×-=-
Triangle A B C is shown. Angle C A B is a right angle. Angle A B C is 30 degrees and angle B C A is 60 degrees. The length of A C is 9 and the length of hypotenuse C B is 18. Which trigonometric ratios are correct for triangle ABC? Select three options.
Answers
Answer:
SinB = 1/2, SinC = √3/2 and
TanC = √3
Step-by-step explanation:
The question lacks options. Find the complete question in the comment section.
Given triangle ABC, we will use the SOH, CAH, TOA trig identity to get the correct ratio.
Given the hypotenuse BC = 18 and one of the other two sides AC = 9, we can get the third side AB using Pythagoras theorem.
BC² = AC²+AB²
18² = 9²+AB²
2² = 1²+AB²
AB² = 4-1
AB² = 3.
AB = √3
Making <ABC as reference angle, AC will be opposite and AB will be the adjacent.
Sin<ABC = opp/hyp = AC/BC
Sin<ABC = 1/2
Cos<ABC = adj/hyp = AB/BC
Cos<ABC = √3/2
Tan<ABC = opp/adj = AC/AB
Tan<ABC = 1/√3
Making <BCA as reference angle, AB will be opposite and AC will be the adjacent.
Sin<BCA = opp/hyp = AB/BC
Sin<BCA = √3/2
Cos<BCA = adj/hyp = AC/BC
Cos<BCA = 1/2
Tan<BCA = opp/adj = AC/AB
Tan<BCA = √3
Frim the above calculation, the correct options are sin<ABC = 1/2, Sin<BCA = √3/2 and Tan<BCA = √3
(b) For a function h(theta)=sin3 theta (Theta is in Radian).
Find h(pi/3)
Find h(pi/2)
Answers
Part (i)
Plug in theta = pi/3 to get
h(theta) = sin(3theta)
h(pi/3) = sin(3*pi/3)
h(pi/3) = sin(pi)
h(pi/3) = 0 ... use a calculator or the unit circle
Answer: 0=================================================
Part (ii)
Plug in h = pi/2
h(theta) = sin(3theta)
h(pi/2) = sin(3pi/2)
h(pi/2) = -1
Answer: -1please help me on this
Answers
Answer:
its the third one. just multiply every number by 1.5 not that hard
Step-by-step explanation:
I'm not sure how to do this question
Answers
Answer:
£20.44
Step-by-step explanation:
Step 1: find the area of the total area of the garden.
Total area = l*w
Where,
l = 10 m
w = 6 m
Total area of garden = 10*6 = 60m²
Step 2: find the area of the vegetable patch.
Area of vegetable patch = l*w = 2*1.5 = 3m²
Step 3: find the area covered by pond.
Area covered by pond = πr²
Take π as 3.14
r = 2m
Area of pond = 3.14*2² = 12.56 m²
Step 4: find the area of the remainder of the garden to be reseeded.
Area of the remainder of the garden = total area of the garden - (area of the vegetable patch + area of pond)
= 60 - (3 + 12.56)
= 60 - 15.56
Area of the remainder of the garden = 44.44 m²
Step 5: calculate the total cost to reseed the garden.
Given that a bag of seed to cover 10m² is £4.60, total cost to reseed the remainder of the garden measuring 44.44 m² can be calculated bas follows:
10 m² = £4.60
44.44 m² = [tex] \frac{44.44*4.60}{10} = 20.44 [/tex]
The answer is £20.44
Find the measure of angle A. This is for my math class, and I’ve been stuck on this for a while. Please help!
Answers
Answer:
20°
Step-by-step explanation:
The sum of angles in a ∆ = 180°
Therefore, [tex] (17x - 1) + (3x - 4) + 25 = 180 [/tex]
Use this expression to find the value of x, then find the measure of angle A.
[tex] 17x - 1 + 3x - 4 + 25 = 180 [/tex]
[tex] 17x + 3x - 1 - 4 + 25 = 180 [/tex]
[tex] 20x + 20 = 180 [/tex]
Subtract 20 from both sides
[tex] 20x + 20 - 20 = 180 - 20 [/tex]
[tex] 20x = 160 [/tex]
Divide both sides by 20
[tex] \frac{20x} = \frac{160}{20} [/tex]
[tex] x = 8 [/tex]
Find measure of angle A.
Angle A is given as [tex] 3x - 4 [/tex]
Plug in the value of x and solve
[tex] A = 3(8) - 4 = 24 - 4 = 20 [/tex]
How many real solutions exist for this system of equations?
A. Zero
B. One
C. Two
D. Infinite
Answers
A) zero as the value of determinant is imaginary
The number of real solutions of the equations y = x - 3 and y = x² - 6x + 10 will be zero. Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
y = x - 3
y = x² - 6x + 10
Compare both equations, then we have
x² - 6x + 10 = x - 3
Simplify the equation, then we have
x² - 7x + 13 = 0
The solution to the equation, then we have
x = [7 ± √(49 - 52)] / 2
x = 7/2 ± (√3/2)i
The number of real solutions of the equations y = x - 3 and y = x² - 6x + 10 will be zero. Then the correct option is A.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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The ratio of the profit, material cost and production labour of an article is 5:7:13.
If the material cost is 840 more than that of labour , find the total cost of producing the article. Plsss help me.
Answers
Answer:
The cost of producing the article is -3500 (Negative cost)
Step-by-step explanation:
The given parameters are
The ratio of the profit to material cost to production labor = 5:7:13
The amount of the material cost = 840 + Labor cost
Let the total cost = X
Therefore, we have;
The fraction of the total cost that is material cost = 7/(5 + 7 + 13) = 7/25
Therefore, the material cost = 7/25 × X
The fraction of the total cost that is labor cost = 13/(5 + 7 + 13) = 13/25
Therefore, the labor cost = 13/25 × X
However, the amount of the material cost = 840 + Labor cost, which gives;
7/25 × X = 13/25 × X + 840
7/25 × X - 13/25 × X = 840
-6/25 × X= 840
X = 840/(-6/25) = 840×(-25/6) = -3500
The cost of producing the article = -3500.
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points) No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Answers
Step-by-step explanation: 4c+6a<120 and 4c+4a<100
The perimeter of the square is equal to the perimeter of the triangle. What are the side lengths of each figure? square: ? units Question 2 triangle shorter side: ? units Question 3 triangle longer sides: ? units, ? units
Answers
Answer:
Square= 12 units
Triangle long sides= 19 units
Triamgle short side= 10 units
Step-by-step explanation:
It is a square, so all sides are the same. That means 3x+3 equals 4x. What number can be subsituted into x to equal 4? If x is 3, then 3x+3 would be 3(3)+3. It equals 12. 4 times 3 is also 12. It works! That also means the square's side is 12 units.
Square= 12 units
So, x=3
The triangle's longer sides are 7x-2. Subsitute x in, which is 3, and you get 7(3)-2. It equals 19. The two longer sides of the triangle are the same length, so both are 19 units.
Triangle long sides= 19 units
The triangles shorter side is 2x+4. Subsitute 3 in for x and you get 2(3)+4. It equals 10, so the shorter side is 10 units.
Triangle short side= 10 units
Answer:
Square: 12 unites
triangle shorter side: 10 units
triangle longer sides: 19 units, 19 units
Step-by-step explanation:
Hello!
First, we make the equations to find the perimeters of each shape by adding all the sides
Square: 4x + 4x + (3x+ 3) + (3x + 3)
Triangle: (7x - 2) + (7x - 2) + (2x + 4)
Since the perimeters are equal we can show that
4x + 4x + (3x+ 3) + (3x + 3) = (7x - 2) + (7x - 2) + (2x + 4)
Now we can solve for x.
Combine like terms
14x + 6 = 16x
Subtract 14x from both sides
6 = 2x
Divide both sides by 2
3 = x
Now we know what x is we can put that into the sides of the shapes
Square
4(x)
Put in x
4(3) = 12
The Square is 12 units
Triangle Short Side
2x + 4
Put in x
2(3) + 4
6 + 4
10
The shorter side of the triangle is 10 units
Triangle Longer Side
7x - 2
Put in x
7(3) - 2
21 - 2
19
The longer sides are 19 units
Hope This Helps!
PLEASE HELP On the number line, graph the solution to the inequality -5(x+1) > 7x + 31? Can you tell me how to go about doing this problem I have tried a few methods but can't figure it out.
Answers
Answer:
I don't know how to insert a number line, but you have to put on it x<-3. You have to plot it, then put a open circle at -3, and draw an arrow, pointing it farther into the negitive side of the number line.
Step-by-step explanation:
The equation shows the relationship between the amount of money (y) remaining in Leigh's money box and the number of months (X)
Function 2
y = -9x + 60
Which statement explains which function shows a greater rate of change?
O Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.
O Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $60 each month.
O Function 2 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $60 each month.
O Function 2 shows a greater rate of change, because Morgan spends $50 each month and Leigh spends -$9 each month.
Answers
Answer:
A. The first choice.
Step-by-step explanation:
Look at function 1.
Month 1 -----> $50
Month 2 ----> $40
The difference between month 2 and moin th 1 is 1 month.
The difference between $40 and $50 is -$10. In other words, in function 1, the amount, y, went down $10 in a month. The rate of change of function 1 is -$10/month.
Function 2
y = -9x + 60
The rate of change is the slope. The slope of function 2 is -9. In function 2, the amount of money changes -$9/per month.
Answer: A. The first choice.
Please Geniuses, look at the picture and answer me, RESCUE ME.
Q1. if A:B= 6:5 and B:C= 18:6, then find A:C in its simplest term
A. 18:15
B. 15:18
C. 6:5
D. 5:6
Answers
Answer:
1. [tex] \{ \bold{ \sf{Expenditure \: on \: food = \:1200 dollars\: }}[/tex]
2. [tex] \sf{a \: : \: c \: = 18 \: : \: 5}[/tex]
Step-by-step explanation:
1. [tex] \sf{here \: total \: expenditure = 3000 \: dollars}[/tex]
[tex] \sf{expenditure \: on \: food \: = \: \frac{3000}{360} \times 144}[/tex]
[tex] \sf{expenditure \: on \: food{ = 1200 \: dollars}}[/tex]
Note : Whole circle represents the total expenditure.
i.e 360° represents $ 3000
1° represents $ [tex] \sf{ \frac{3000}{360} }[/tex]
144 ° represents $ [tex] \sf{ \frac{3000}{360} \times 144}[/tex]
-------------------------------------------------------------
2. [tex] \sf{here \: a:b \: = 6:5 \: = \: \frac{6}{5} }[/tex]
[tex] \sf{b : \: c \ \: = 18 \: : \: 6} \: = \: \frac{18}{6} [/tex]
[tex] \sf{now \: a:b \times b:c = \frac{a}{b} \times \frac{b}{c} = \frac{a}{c} }[/tex]
⇒[tex] \sf{a:c = \frac{6}{5} \times \frac{18}{6} }[/tex]
⇒[tex] \sf{a:c = \frac{18}{5} }[/tex]
⇒[tex] \sf{a:c = 18:5}[/tex]
Hope I helped!
Best regards!!
Mean of 11,10,12,12,9,10,14,12,9 is
Answers
Answer: Hi!
To find the mean of a data set, you have to add the numbers in the set and then divide the sum by the number of values that are in the set.
11 + 10 + 12 + 12 + 9 + 10 + 14 + 12 + 9 = 99
There are 9 values in the data set, so we divide 99 by 9:
99 ÷ 9 = 11
The mean of this data set is 11.
Hope this helps!
Answer: 11
Order the Numbers
Before: 11,10,12,12,9,10,14,12,9
After: 9,9,10,10,11,12,12,12,14
Add
9+9+10+10+11+12+12+12+14=99
Divide
99÷9=11
Simplify the expression by combining like terms:
k3+ m + m - k3 +Ka+ K2
Answers
Explanation:
k3 + m + m - k3 + Ka + K2
= 2m + Ka + K2
what is the value of 20+30(7+4)+5+2(7+99?
Answers
Answer:
the answer is 567
Step-by-step explanation:
20+30(11)+5+2(106)
20+330+5+212
= 567
please help me with this question!!
Answers
Answer:
C.
Step-by-step explanation:
Will end up being 0 since it is the final number in the equation and goes along with PEMDAS sequence.
The indoor pool has a temperature of 24 The outdoor pool has a temperature of 23 Which pool has a higher temperature And which pool temperature has a greater absolute value
Answers
Answer:
The indoor pool has a higher temperature and also has the greatest absolute value.
Step-by-step explanation:
The indoor pool has a higher temperature becasue 24 is greater than 23. It also has a bigger absolute value because the absolute value how much a number is from 0.
So the absolute value of 24 is 24.
The absolute value of 23 is 23.
24 is greater so the indoor pool also has a bigger absolute value.
How many pennies could you have if:
When you break the pennies into groups of 2, you have 1 penny left over AND when you break the pennies into groups of 3, you have 1 penny left over?
Answers
Answer:
The number of pennies owned is 7 pennies
Step-by-step explanation:
The given parameters are;
The number of pennies left over when we break the pennies into groups of 2s = 1 penny
The number of pennies left over when we break the pennies into groups of 3s = 1 penny
Let the number of pennies owned = c
What we are given are as follows;
2 × a = c - 1
3 × b = c - 1
2 × a = 3 × b
a/b = 3/2
Therefore, if we multiply 2 by 3, and 3 by 2 we get 6
2 × 3 = 6, similarly 3 × 2 = 6
If we put 6 = c - 1, we get;
c = 6 + 1 = 7
c = 7
The number of pennies owned = 7 pennies.
You and three friends are eating a pizza with 12 pieces. Each person eats the same number of pieces. Let x represent the number of pieces each person eats. Which of the following equations is an algebraic model for the situation?
a. 3x= 12
b. 1/3x=12x
c. 4x =12
d. 1/4x=12
Answers
Answer:
C. 4x = 12
Step-by-step explanation:
You and three friends= you + 3 friends=4 people
Pizza= 12 pieces
Each person eats equal pieces of pizza
x= number of pieces each person ate
Equation
4x=12
Divide both sides by 4
x=12/4
=3
x=3
Therefore, each person ate 3 pieces of pizza each
Check:
4x=12
4(3)=12
12=12
Evaluate x5 + y(-4)
When x = -4, y = 7
Answers
Answer:
-48
Step-by-step explanation:
Plug x and y in to the expression,
-4(5) + (7)(-4) = -20 - 28 = -48
solve the equation for t
Answers
Answer:
t= -3.7
Step-by-step explanation:
1. 5( t+3)= -3.5
2. 5t+15= -3.5
3. 5t= -18.5
4. t= -3.7
Base 5
3213
3444
+ 3323
Answers
Answer:
21040
Step-by-step explanation:
As with base-10 addition, when the sum is equal to the base or more, a "carry" is generated into the next place value column. Useful equivalents here are ...
5₁₀ = 10₅
6₁₀ = 11₅
7₁₀ = 12₅
9₁₀ = 14₅
10₁₀ = 20₅
The addition is shown in the attachment. The sum is 21040₅.
_____
The equivalent decimal addition problem is 433+499+463=1395.
Twelve relatives always give gifts to one another. They have been doing it for eight years. How many exchanges have happened so far?
Answers
Answer:
660 exchanges
Step-by-step explanation:
Number of relatives = 12
Number of years = 5
Since each relative gives gift to one another each year:
Then each relative hands out 11 gifts (person giving out the gift will not be counted) to the others, and others also do the same.
Therefore, yearly exchange :
(Number of relatives * number of gifts given out per person)
(12 × 11) = 132
Number of exchanges after 5 years :
(Number of yearly exchanges × number of years)
(132 × 5) = 660
Type the correct answer in each box. If necessary, use / for the fraction bar(s). John recorded the number of cars passing a traffic signal at intervals of 2 minutes. He plotted his data on this graph.
Answers
Answer:
Slope of the line is = [tex] \frac{5}{2} [/tex]
y-intercept = 5
Step-by-step explanation:
Slope (m) is can be calculated using the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinates of any two points located on the line. Let's use, (14, 40) and (10, 30).
Let,
[tex] (14, 40) = (x_1, y_1) [/tex]
[tex] (10, 30) = (x_2, y_2) [/tex]
Plug the above values into the formula to find the slope (m).
[tex] m = \frac{30 - 40}{10 - 14} [/tex]
[tex] m = \frac{-10}{-4} = \frac{5}{2} [/tex]
Slope of the line is = [tex] \frac{5}{2} [/tex]
Find y-intercept using y = mx + b
Where m = slope, and b = y-intercept
Use (10, 30) as (x, y).
30 = 5/2*10 + b
30 = 25 + b
30 - 25 = b
5 = b
b = 5
10. Three oil tankers together contain 37 litres of oil. If two tankers have 11 litres and
12 litres of oil. Find the oil in the third tanker.
Answers
Answer:
Step-by-step explanation:
total quantity of oil = 37 litres
quantity of oil in first tank = 11 litres
quantity of oil in second tank = 12 litres
Total quantity of oil in first and second tanks = 11 + 12 = 23 litres
∴ quantity of oil in the third tank = 37 - 23
= 14 litres
Hope this helps
plz mark as brainliest!!!!!!!!!!!
A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth. 3.54 cm 3.91 cm 4.24 cm 4.95 cm
Answers
Answer:
[tex]\Huge \boxed{\mathrm{3.91 \ cm}}[/tex]
Step-by-step explanation:
The triangle BDE is a right triangle.
Line segment DE = 2.5 cm
Line segment BE = 3 cm
We can apply Pythagorean theorem to solve for the diameter of the pipe or the hypotenuse of the right triangle BDE.
[tex]c=\sqrt{2.5^2 +3^2 }[/tex]
[tex]c=\sqrt{15.25} = 3.90512483795...[/tex]
We can round up the length to nearest hundredth.
[tex]3.90512483795 \approx 3.91[/tex]
The diameter of the pipe is 3.91 cm.
The smallest diameter of pipe that will fit the fiber optic line is 3.91 cm if the company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm option (B) is correct.
What is a rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
We have:
A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm.
As we know, the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides is known as the Pythagoras theorem.
Applying Pythagoras theorem in the triangle DEB:
DE² + BE² = DB²
2.5² + 3² = DB²
DB² = 6.25 + 9
DB² = 15.25
DB = 3.905 ≈ 3.91 cm
Thus, the smallest diameter of pipe that will fit the fiber optic line is 3.91 cm if the company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm option (B) is correct.
Learn more about the rectangle here:
https://brainly.com/question/15019502
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Help me on this please.
Answers
Answer: Choice A)
Approximately 0.4 units or about 24 miles approximately
=========================================================
Explanation:
B = Santa Barbara's location
C = Santa Cruz Island's location
Point B is located at (34.4, 119.714)
Point C is located at (34, 119.726)
Use the distance formula to find the distance from B to C
[tex]d = \sqrt{ (x_1-x_2)^2 + (y_1-y_2)^2}\\\\d = \sqrt{ (34.4-34)^2 + (119.714-119.726)^2}\\\\d = \sqrt{0.160144 }\\\\d \approx 0.40017995951821\\\\d \approx 0.4\\\\[/tex]
Unfortunately, there isn't enough info to be able to go from 0.4 units to roughly 24 miles, so I don't know how your teacher is doing that step. But luckily, only choice A mentions 0.4, so this has to be the answer.