Answer:
1st q answer is f(x) is one- to -one function and 2nd q answer is 2
Answer:
1) f(x) is one - to - one function2) 2Step-by-step explanation:
inverse of f(x)Let f(x) = y
y = 2x - 3
x = y + 3 / 2
inverse of f(x) = x + 3 / 2
g(x) = inverse of f(x)f [g(2)]
f [2+3/2]
f [5/2]
(2×5/2)-3
5-3
= 2
Therefore f [g(2)] = 2PLS HELP IF POSSIBLE ASAP
The value of y if x is equal to 5 is 75 and the value of y when x = 7 is 8/7
Direct and inverse variationVariations shows the relationship between variables.
4) If y varies directly as x², hence;
y = kx²
27 = 9k
k = 3
In order to determine y if x = 5
y = 3(5*5)
Y = 75
Hence the value of y if x is equal to 5 is 75
5) If y varies inversely as x, hence;
y = k/x
k = xy
k = 16(1/2)
k = 8
If x = 7, the value of y will be;
y = 8/7
Hence the value of y when x = 7 is 8/7
Learn more on variation here: https://brainly.com/question/13998680
#SPJ1
Kylie borrowed a book from a library. The library charged a fixed rental for the book and a late fee for every day the book was overdue. The expression below shows the charges Kylie paid for the book when she returned it x days after the
due date:
2 +0.25x
What does the constant term of the expression represent?
The late fee for the book
The fixed rental for the book
The number of books borrowed
The number of days the book was overdue
Answer:
B - fixed rental for the book.
Since for everyday the book is late the fee is 0.25 multiplied by X, X is the days the book is not returned.
Thus, the constant would be 2, 2 is the constant whereby the rental for the book regardless of other variables.
Who wants to solve a question.
Answer:
Step-by-step explanation:
5(p-3)
the 3 lbs she uses are being subtracted and then is being multiplied per lb
Alexa needs 20.5 pints of blueberries to
jam. She picked 7.75 pints on Friday and
pints on Saturday. How many more pints
she need to pick?
Answer:
Your question does not make much sense but that was only because you were missing one variable which was 4.25 which was what you picked up on Saturday. but anyways you just add 7.75 and 4.25 and you'd end up with 12 so she has 12 pints of the blueberries she needs and to find out the remanding you just subtract from the 20.5 but its better to look at it like 20.50 because that's what it is and then you subtract 12 from 20.50 and you are left with 8.50.
Your answer is 8.5
Where would 1.84 be on a number line?
Answer:
It is located to the right of the 0 on the line,
Step-by-step explanation:
the numbers are increasing going from left to right. 1.84 is located 1.84 from 0.
PLEASE HELP ME, I BEG OF YOU TO HAVE MERCY ON MY POOR SOUL
1. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)
2. Using the slope and y-intercept, write the equation of the trend line (y = mx + b).
3. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.
4. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.
The regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph.
It's a kind of linear regression that uses scatter data to figure out the best way to define the dot's relationship.
From the data given, we can write the slope and y-intercept form:
y = mx + b
here, m = 10 and b = 300
y = 10x + 300
The number of fat grams in an item has that number of fat calories.
As we have the regression line:
y = 10x + 300
Put x = 1 in the regression line:
y = 10(1) + 300
y = 310 calories
For x = 14
y = 10(14) + 300 = 440
But the actual value from the graph is 330.
Thus, the regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ1
Add2√3+√5 and√3 -3√5
Answer:
[tex] \sqrt[2]{3} + \sqrt{5} = \sqrt[2]{8} [/tex]
[tex] \sqrt{3 } - \sqrt[3]{5} = \sqrt[3]{2} [/tex]
Factorize:
a⁴-a³+2a²
[tex] {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} [/tex]
Factor the expression with the common factor that is "a²".[tex] \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}[/tex]
MissSpanishAnswer:
a²(a²-a+2)
Step-by-step explanation:
Solution Given:
a⁴-a³+2a²
first taking common a²
we get
a²(a²-a+2) which is a required answer.
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
The options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'The complete question is given below:-
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
△XYZ ~ △X'Y'Z'AngleXZY ≅ AngleY'Z'X'YX ≅ Y'X'XZ = 2X'Z'mAngleYXZ = 2mAngleY'X'Z'What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.
This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.
Therefore the options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'Learn more about translation on:
https://brainly.com/question/12861087
#SPJ1
the equation for the circle shown below is x2 + y2 = 64 What is the length of the circles radius
Answer:
radius = 8
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 64 ← is in this form
with r = [tex]\sqrt{64}[/tex] = 8
The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches. What is the slant height? Use 3.14 for Pi. Round your answer to the nearest whole number.
The slant height of the given cone will be 12.06 inches.
What is slant height?The measurement from the base to the peak along the "center" of a lateral face of an object, such as a cone, is its slant height.
Given that:-
The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches.The slant height will be calculated as:-
Surface area = π r l
151.58 = π x 4 x l
l = 151.58 / ( π x 4 )
l = 12.06 inches.
Therefore slant height of the given cone will be 12.06 inches.
To know more about slant height follow
https://brainly.com/question/6613758
#SPJ1
3. The elevation of a hilltop is 250 feet above sea level. The
hill slopes gradually to a valley that is 100 feet below sea
level. The hilltop and the valley are 28,000 feet apart. What
is the average rate of change in elevation from the hilltop tot
the valley?
Answer:
0.00893 feet elevation per 1 foot distance.
Step-by-step explanation:
The hill reaches an elevation of 250 ft (above sea level) over the course of 28,000 feet. The average rate of change would be (250 ft)/(28,000 ft), or 0.00893 feet elevation/1 foot distance.
((0.00893 (feet up/foot distance))*(28,000 feet distance) = 250 feet up (elevation).
solve: √2x-8= √x+4 the equation.
Answer:
(a) x = 12
Step-by-step explanation:
The radicals in this equation can be eliminated simply by squaring both sides. Then the resulting linear equation is solved in two steps.
__
square[tex]\left(\sqrt{2x-8}\right)^2=\left(\sqrt{x+4}\right)^2\\\\2x-8=x+4\qquad\text{simplify}\\\\x-8=4\qquad\text{subtract $x$}\\\\\boxed{x=12}\qquad\text{add 8}[/tex]
_____
Additional comment
You know the contents of each radical must not be negative. That means 2x-8 ≥ 0, or x≥4. We know x=4 doesn't work in the equation (0≠√8), so we only need to check the answers x=12 and x=7. Of those, only x=12 satisfies the equation.
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
1. 6 km ≈ 3.73 mi
2. 2.5 L ≈ .66 gal
3. 90 lb ≈ 40.82 kg
tôi là người Việt Nam ai giúp giải bài này nha bài 2 ạ
Help ASAP, with a explanation :)
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE I NEED HELP
Answer:
B.
Step-by-step explanation:
It is the only one that is not a fraction or a decimal that terminates or repeats.
find y in terms with z. help me please :)
Answer:
y = 5z
Step-by-step explanation:
added in the picture
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow y = 5z [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[ let the point at which line segments SV and RT intersects be O ]
[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]
[ linear pair ]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]
[ Exterior angle = sum of opposite interior angles ]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]
( let it be equation 1 )
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]
[ Sum of angles of Triangle ]
[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]
( let it be equation 2 )
____________________________________
By comparing both equations :
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]
[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]
( Add 180° on both sides )
[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]
[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]
[tex]\qquad \tt \rightarrow \: y = 5z[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?
Answer:
D) 20
Step-by-step explanation:
Hope It Helps!!!
Suppose that the weight (in pound) of an airplane is a linear function of the amount of fuel (In gallons) in it's tank. When carrying 20 gallons of fuel, the airplane weighs 2210 pounds. When carrying 54 gallons of fuel, it weighs 2397 pounds. How much does the airplane weigh if it's carrying 60 gallons of fuel?
Answer:
For 60 gallons of fuel, the airplane would weigh 2430 gallons.
Step-by-step explanation:
Concept: Use the values and conditions to make a linear equation of a straight line. Let the y-axis be fuel and x-axis be airplane weight. The given points are (2210, 20) and (2397, 54). Use these points to make an equation of line.
[tex]\frac{y-20}{x-2210} =\frac{54-20}{2397-2210} \\\frac{y-20}{x-2210} = \frac{34}{187}[/tex]
Let this be the equation of straight line.
We have to find the airplane weight at 60 gallons of fuel. This means y = 60 and we have to find the x.
[tex]\frac{60-20}{x-2210} =\frac{34}{187} \\x-2210=\frac{(187)(40)}{34} \\x-2210=220\\x=2430[/tex]
So, the airplane weight is 2430 gallons.
For more details, refer the following link
https://brainly.com/question/13243410
#SPJ10
Photo attached
A. -2
B. -1
C. 1/-2
D. 1/2
Step-by-step explanation:
(X1,Y1) = (-2,2)
(X2,Y2) = (0,1)
• Find slope.
m = (Y2 - Y1)/(X2 - X1)
m = (1 - 2)/(0 - (-2))
m = -1/2
The answer is C.
A ship is carrying gold bars and silver bars in the ratio 13:17. The ship's load
weighs 600 kg in total. If each bar weighs 5 kg, how many gold bars is the
ship carrying
Using proportions, considering the weight of each bar and the ratio, it is found that the ship is carrying 52 gold bars.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each bar weighs 5 kg, and the total weight is of 600 kg, hence the number of bars is given by:
n = 600/5 = 120.
The proportion of gold bars is given by:
p = 13/(13 + 17) = 13/30
Hence, out of 120 bars, the number of gold bars is given by:
nG = 120 x 13/30 = 4 x 13 = 52.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
A circle with the equation (x + 6)2 + (y + 3)2 = 16 is reflected over the line x = 2.
What is the equation of the image?
( x + 10) 2 + ( y + 3) 2 = 16
( x - 10) 2 + ( y + 3) 2 = 16
( x + 6) 2 + ( y + 7) 2 = 16
( x + 6) 2 + ( y - 7) 2 = 16
Answer: [tex](x-10)^{2}+(y+3)^{2}=16[/tex]
Step-by-step explanation:
We know the center of the original circle is (-6, -3). After reflecting this over the line x=2, the new center is now (10, -3).
Thus, the equation of the circle is [tex](x-10)^{2}+(y+3)^{2}=16[/tex].
+
Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week. She wants to go on a trip with her friend and needs to
make $95 dollars this week to cover the cost of the trip. Write a system of inequalities to represent this
situation.
The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Carla babysits and tutors to make extra money.
She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week.
Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.
Then the system of inequalities to represent this situation will be
Let x be the number of babysits hours and y be the number of tutor's hours.
x + y ≤ 15
5x + 10y ≤ 95
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ1
A car travels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles pr
hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of
car for the whole trip?
O20.0 mph
37.5 mph
40.0 mph
O45.0 mph
O80.0 mph
Click Save and Submit to save and submit. Click Save All Answers to save all answers.
Answer:
Definition: The average speed over the course of mobion can be calculated using the formula Total Distance Traveled Average Speed = Time of Travel A car fravels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles per hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of the car for the whole trip? 20.0 mph 37.5 mph 40.0 mph 45.0 mph 80.0 mph QUESTION 13 Wriat is the height h, of the equilateral triangle shown below? Aak Sareend Sabmit ro save and submit. Click Save AlAnseers to save all ansuers Save
Average speed of the whole trip is equals to 37.5 mph.
What is average speed?
" Average speed is defined as the ratio of the total distance travelled to the total time taken."
Formula used
Average speed = [tex]\frac{Total distance travelled }{Total time taken}[/tex]
According to the question,
Total distance travelled = 300miles
Speed for first 150 miles = 30 miles per hour
For, 30 miles = 1hour
⇒150 miles = 5 hours
Speed for remaining 150 miles = 50 miles per hour
For, 50 miles = 1hour
⇒150 miles = 3 hours
Substitute the value in the formula to get average speed,
Average speed = [tex]\frac{300miles}{(5 + 3)hours}[/tex]
[tex]=\frac{300}{8}\\ \\= 37.5 miles per hour[/tex]
Hence, average speed of the whole trip is equals to 37.5 mph.
Learn more about average speed here
https://brainly.com/question/12322912
#SPJ2
Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.
Answer:
Step-by-step explanation:
Equation of the line in slope- intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here, m is the slope and b is the y-intercept
Find the slope with the given two points.
[tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]
Slope = -2/3 and choose any one the given points.
Substitute m = -2/3 and (5,6) in the above equation and find 'b'
[tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]
Equation of the line:
[tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]
What is one of the solutions to the following system of equations?
x² + y² = 25
y - 3x = -5
Answer:
x = 0 y = -5
x = 3 y = 4
Step-by-step explanation:
x² + y² = 25
y - 3x = -5
-----------------------
y = 3x-5
x² + y² = 25
x² + (3x-5)² = 25
(3x-5)(3x-5) = 9x² -15x -15x + 25
x² + 9x² -15x -15x + 25 = 25
x² + 9x² -15x -15x = 0
x² + 9x² - 30x = 0
10x² - 30x = 0
x(10x-30)=0
x = 0
10x-30=0
x = 3
y - 3x = -5
y - 3(0) = -5
y = -5
y - 3(3) = -5
y - 9 = -5
y = 4
Answer:
(4,3) and (0,-5) are both solutions where we have (x,y).
Step-by-step explanation:
Here are simplified steps:
https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input
Symbolab is an excellent tool for just most math.
Mr.krabs sold a total of 29 krabby patties and krabby shakes. krabby patties cost $3 each while krabby shakes cost $2 each and he made a total of $70 . how many krabby patties and krabby shakes did mr.krabs sell?
Answer:
s = 12 and p = 17
Step-by-step explanation:
→ Set up 2 simultaneous equations
p + s = 29
3s + 2p = 70
→ Rearrange the first equation for p as the subject
p = 29 - s
→ Substitute into 2nd equation
3s + 58 - 2s = 70
→ Solve
s = 12
→ Substitute into first equation
p + 12 = 29
→ Solve
p = 17
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks. If at year’s end an auditor
checks your accounting records and randomly selects one week to check the company’s payroll, what is the probability that the auditor will select a week in which you paid overtime wages and hired
temporary help?
The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.
What is probablitity?
Probability, can be define as the ratio of favorable outcomes to the n number of total events.
Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
p(b) = temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
= 0.81 + 0.46 -1
= 0.28
The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
Learn more about probability here:
brainly.com/question/14290572
#SPJ1
y = x2 − 2x − 19
y + 4x = 5
Answer:
(x=4, y=-11) (x=-6, y=29)
Step-by-step explanation:
The solution is in the picture above...
