Answer:
4x³
Step-by-step explanation:
substitute x = f(x) into g(x)
(g ￮ f)(x)
= g(f(x))
= g(x³ - 1)
= 4(x³ - 1) + 4
= 4x³ - 4 + 4
= 4x³
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 1 < x < 5.
2
f(x)
1
77
2
68
3
59
4
50
5
5
41
-
Given:
Function interval
[tex]1\leq x\leq5[/tex][tex]\begin{gathered} x\rightarrow f(x) \\ \\ 1\rightarrow77 \\ \\ 2\rightarrow68 \\ \\ 3\rightarrow59 \\ \\ 4\rightarrow50 \\ \\ 5\rightarrow41 \end{gathered}[/tex]Find-: Average rate of change.
Sol:
The average rate of change is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two-point.
[tex]\begin{gathered} (x_1,y_1)=(1,77) \\ \\ (x_2,y_2)=(2,68) \end{gathered}[/tex]So average rate of change is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{68-77}{2-1} \\ \\ m=\frac{-9}{1} \\ \\ m=-9 \end{gathered}[/tex]The average rate of change is -9.
ind the point at which the line f ( x ) = − 4 x − 1 intersects the line g ( x ) = − 2 x + 1
Answer:
(-1,3)
Step-by-step explanation:
Where the two lines intersect, they have equal values
-4x-1 = -2x + 1
-2 = 2x
x = -1
Now, you have 'x' ....use this value in either of the equations to find 'y'
-2 (-1) + 1 = y = 3
(-1,3)
please help me please
It's a line that slopes down
The second choice is the answer because the slope is negative.
Question 10(Multiple Choice Worth 1 points)
(08.01 LC)
Susan wants to conduct a survey to find how much time the students of her school spent eating in a local cafeteria. Which of the following is an appropriate statistical question for this survey?
Who eats at the cafeteria on weekends?
How many students eat in the cafeteria on Mondays?
How many students eat in the cafeteria once a week?
How many hours during the week do you eat in the cafeteria?
The bank that the Payans would like to borrow from uses the back-end ratio to determine loan qualification, approving applications if the back-end ratio is less than 36%. So, the Payans have collected some information on what the bank will consider to calculate the ratio, including what they estimate their monthly mortgage payment will be.According to the Payans' back-end ratio calculation, the bank will ______(most likely, not) lend the Payans $250,000 to purchase the home because their back-end ratio is_____(equal to, higher than, lower than) 36%
Approved if back-end ratio is less than 36%
Total income: $10,000
Total expenses:
$1,100 + $150 + $500 + $1,000 + $400 = $3,150
Back-end ratio: (Total expenses) / (Total Income) x 100
= (3150/10000)x100 = 31.5%
According to the Payans' back-end ratio calculation, the bank will most likely lend the Payans $250,000 to purchase the home because their back-end ratio is lower than 36%
Let d represent the number of $2 decreases i price. Let r be the company’s revenue. Write a quadratic function that reflects the company’s revenue.
Answer:
Let d be the number of $2 decreases, and r be the company´s revenue, then the company can sell:
[tex]800+40d[/tex]cellphones per week at a price of:
[tex]80-2d[/tex]dollars.
Therefore, the quadratic equation that represents the revenue is:
[tex](800+40d)(80-2d)\text{.}[/tex]Now, graphing the above equation we get:
From the above graph, we can determine the vertex and the vertex gives us for which value of d the company gets the maximum revenue.
The company should charge $80-10($2)=$80-$20=$60.
According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD. Construct diagonal A C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the same theorem. __________. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.
The parallelogram can be redrawn as,
To Prove: The opposite side of the parallelogram are equal.
Given: In the given parallelogram AB is parallel to CD and BC is parallel to AD.
Construction: Diagonal AC is drawn.
Proof:
[tex]\begin{gathered} AC=AC\text{ (Common)} \\ \angle BAC=\angle DCA\text{ (Alternate angles)} \\ \angle BCA=\angle DAC\text{ (Alternate angles)} \\ \Delta ABC\cong\Delta CDA\text{ (ASA)} \\ AB=CD\text{ (CPCT)} \\ BC=DA\text{ (CPCT)} \end{gathered}[/tex]Thus, traingle ABC is congruent to triangle CDA by ASA congruency theorem is the missing information from the paragraph.
The scatterplot shows the average miles per gallon
versus the age, in years, of cars at a used car dealership.
Fuel Efficiency
Miles per Gallon
35
30
25
20
15
10
5
●
0 1 2 3 4 5 6 7 8 9 10
Age (Years)
Select the most likely value of r for this data set.
O-0.78
O-0.35
O 0.15
O 0.88
Answer:
-0.78
Step-by-step explanation:
The close to 1 or -1 it is the straight the line will be. 0 will be no correlation.
What is the solution to the equation?
Hello!
Let's solve:
[tex]\dfrac{2}{5}(15x+40)} =6x+10\\\\\\\text{Multiply the '2/5' into the function inside the parentheses}\\\dfrac{2}{5} *15x + \dfrac{2}{5} *40=6x+10\\\\6x + 16 =6x+10\\\\\\\text{Subtract '6x' from both sides}\\6x + 16-6x=6x+10-6x\\16 = 10[/tex]
Since 16 doesn't equal 10 ==> There are no solution
Hope that helps!
How many times larger is (1.008 x 101) than (6 x 10-f)?
0.168
5.95
11.682
16.8
Answer:
11.682 many times larger
Answer:
16.8
Step-by-step explanation:
To find how many times larger (1.008 × 10¹) is than (6 × 10⁻¹), divide the first expression by the second expression:
[tex]\implies \dfrac{1.008 \times 10^1}{6 \times 10^{-1}}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{ab}{cd}=\dfrac{a}{c} \times \dfrac{b}{d}:[/tex]
[tex]\implies \dfrac{1.008}{6} \times \dfrac{10^1}{10^{-1}}[/tex]
Divide the numbers 1.008 and 6:
[tex]\implies 0.168 \times \dfrac{10^1}{10^{-1}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 0.168 \times 10^{(1-(-1)}[/tex]
Simplify:
[tex]\implies 0.168 \times 10^{2}[/tex]
[tex]\implies 0.168 \times 10 \times 10[/tex]
[tex]\implies 1.68 \times 10[/tex]
[tex]\implies 16.8[/tex]
Find θ where θ = sin-1(-.5) where 0 < θ < 2π. Select all the correct choices. Select one or more: a. 11pi/6 b. pi/6 c. 5pi/6 d. 210 degrees e. 30 degrees
The value of inverse trigonometric function θ = sin-1(-.5) is 30°
What is an inverse trigonometric function?
The inverse trigonometric functions perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are especially applicable to the right angle triangle.
Here, the given inverse trigonometric function is θ = sin⁻¹(0.5)
Now solving the given inverse trigonometric function by consider 0.5 value in terms of sine that is :
0.5 = sine (30°)
Now, substituting back this value in place of 0.5 and solve for θ :
θ = sin⁻¹(0.5)
θ = sin⁻¹(sin(30°))
Now the inverse of sinθ is θ itself
θ = 30°
Therefore, The value of inverse trigonometric function θ = sin-1(-.5) is 30°.
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Create your own quadratic equation whilst explaining how to use the quadratic formula to solve it. Be specific, using a, b, and c of your equation and give solutions to theequation you chose.
Let the quadratic equation is
[tex]x^2-8x+16=0[/tex]Here, a is the coefficient of x^2, b is the coefficient of x and c is the constant.
For the equation we have a = 1, b = -8 and c = 16.
We know that the quadratic formula is given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]So, the solution of the quadratic equation is:
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(16)}}{2(1)} \\ x=\frac{8\pm\sqrt[]{64-64}}{2} \\ x=\frac{8\pm\sqrt[]{0}}{2} \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]Thus, there are two real and equal solutions for the given quadratic equation that is x = 4 and x = 4.
One positive integer is 2 less than twice another. The sum of their squares is 745.
The numbers are 13 and 24
What is Integers?
The negative numbers are the additive inverses of the corresponding positive numbers.[2] In the language of mathematics, the set of integers is frequently denoted by the boldface Z or blackboard bold displaystyle mathbb Z mathbb Z.[3][4][5] An integer is the number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer with a minus sign
y=first number
x=2y-2 (second number)
y^2+(2y-2)^2=745
y^2+4y^2-8y+4=745
5y^2-8y+4-745=0
5y^2-8y-741=0
Now, from the equation we can solve
5y^2 -65y +57y - 741 = 0
5y(y - 13) + 57(y - 13) = 0
(5y + 57)(y - 13)= 0
now, since the Integers are positive so the value obtained from (5y + 57) = 0 can't hold true.
So, y-13 = 0
y = 13
The first number is : 13
The second number is :
x = 2(13) - 2
x = 26 - 2
x = 24
The second number is : 24
Hence, the numbers are 13 and 24
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exercise after work, Albert (A) went running and Tanisha (T) walked for exercise. Their times and distances are showing in the graph below. How much as Albert running than Tanisha walking in miles per hour? Explain how you found your answer.
In the picture, there are two lines that graph distance versus time, so the slope of the line is teh rate or the speed of Albert or Tanisha.
We need to calculate the slope of each line. We can note that the two lines start in the origin point (0, 0), so:
[tex]\begin{gathered} \text{For Albert, we can s}ee\text{ that the point (10, 1) is in the line, so:} \\ slopeofAlbert=m_A=\frac{1}{10}=0.1\frac{miles}{\min ute} \\ \text{For Tanisha, we can se}e\text{ thet the point (}20,\text{ 1) is in the line. so:} \\ slopeofTanisha=m_T=\frac{1}{20}=0.05\frac{miles}{\min ute} \end{gathered}[/tex]The different between the slopes (speed) is:
[tex]\begin{gathered} m_A-m_T=0.1\frac{miles}{\min ute}-0.05\frac{miles}{\min ute}=0.05\frac{miles}{\min ute} \\ In\text{ miles/hours is:} \\ m_A-m_T=0.05\frac{miles}{\min ute}\cdot\frac{60\text{minutes}}{1\text{hour}}=3\frac{miles}{hour} \end{gathered}[/tex]Albert goes 3 miles/hour faster than Tanisha
6 hours into minute i want answer of this
Answer: 6 hours into minutes is 360
Step-by-step explanation:
Convert 120 inches to feet. There are 12 inches in a foot. O A. 1200 feet B. 1440 feet C. 20 feet O D. 10 feet
There are 12 inches in a foot.
To convert 120 inches to feet we can use the next proportion:
[tex]\frac{12\text{ inches}}{120\text{ inches}}=\frac{1\text{ foot}}{x\text{ feet}}[/tex]Solving for x:
x = 1*120/12
x = 10 feet
Consider the following graph. Does a graph represent a function? Yes or no?
Concept
A technical definition of a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Next
The graph is a function because every input has unique output.
Final answer
It is a function
The length of a rectangular piece of steel in a bridge is 2 meters less than triple the width. The perimeter of the piece of steel is 60 meters. Find the length of the pieceof steel. Find the width of the piece of steel.
Let "x" represent the width of the rectangular steel, then the length, which is 2meters less than triple the width, can be expressed as "3x-2".
The perimeter of the rectangular piece is 60meters.
The formula for the perimeter is the following:
[tex]P=2w+2l[/tex]Replace the formula with the expressions for the width and length and the given perimeter of the piece of steel:
w=x
l=3x-2
P=60
[tex]60=2x+2(3x-2)[/tex]From this expression, you can determine the value of x.
-First, distribute the multiplication on the parentheses term
[tex]\begin{gathered} 60=2x+2\cdot3x-2\cdot2 \\ 60=2x+6x-4 \end{gathered}[/tex]-Second, simplify the like terms and pass "-4" to the left side of the expression by applying the opposite operation "+4" to both sides of it
[tex]\begin{gathered} 60=8x-4 \\ 60+4=8x-4+4 \\ 64=8x \end{gathered}[/tex]-Third, divide both sides by 8 to determine the value of x
[tex]\begin{gathered} \frac{64}{8}=\frac{8x}{8} \\ 8=x \end{gathered}[/tex]The value of x is 8m, which means that the width of the piece of steel is 8m
To determine the length you just have to replace the expression by x=8
[tex]\begin{gathered} l=3x-2 \\ l=3\cdot8-2 \\ l=24-2 \\ l=22 \end{gathered}[/tex]The length is 22m
I need help finding
The proeprty of rhombus is that
The diagnol of a rhombus VX bisect the angle WVY in two equal parts .
Therefore, the angle YVX = angle XVW.
[tex]\angle YVX=(9n+4)^{\circ}[/tex]The another property of rhombus is that the diagnol are perpendicular .
[tex]3n^2-0.75=90[/tex]f(x) = (x-1.5)^2 find the vertex
The given function is
[tex]f(x)=(x-1.5)^2[/tex]It is important to know that the function is in vertex form
[tex]f(x)=a(x-h)^2+k[/tex]Where h and k are the coordinates of the vertex.
Having said that, we can deduct that the vertex of the given function is (1.5, 0) because those are the values for h and k.
Hence, the answer is V(1.5, 0).plss help me with this i need help
Question is down below Answer choices are the same for each drop down menu.
Given:
The triangles EFG and PQR are given.
To find: The correct answer
Explanation:
a) An angle bisector:
As we know,
An angle bisector is a line or ray that divides an angle into two congruent angles.
Here, The line FJ is the angle bisector for angle F.
Thus, the angle bisector is line FJ.
b) Perpendicular bisector:
As we know,
A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point.
Here, the line SL bisects another line segment PQ at a right angle, through the intersection point S.
Thus, the perpendicular bisector is SL.
c) A point is equidistant from the line segment FE and EG:
The point that is equidistant to all sides of a triangle is called the incenter.
Here, H is the point that is equidistant from the line segment FE and EG.
Thus, the point is H only.
d) A point is equidistant from the points P and Q:
The point that is equidistant to all vertices of a triangle is called the circumcenter.
Here, L is the point that is equidistant from the points P and Q.
Thus, the point is L only.
2xy + 4 = -2y - x, solve for x
Answer:
x = -2/y -1
Step-by-step explanation:
2xy + 4 = -2y -----> x = -2y -y
Step 1: Divide 2y to all sides. 2xy÷2y + 4÷2y= -2y÷2y. Since we are divinding y with y it cancels out, so it will be -2÷ 2 = -1
Step 2: x + 2y = -1
Step 3: Then subtract 2y and move it to the other side.
x = -2/y -1
Another way of explaining it:
2xy + 4 = -2y
Step 1: Divide 2 to all sides. 2xy÷2 +4÷2 = -2y÷2
Step 2: xy + 2 = -y
Step 3: Subtract the 2 and move it to the other side.
xy + 2 = -y
-2. -2
Step 4: xy = -2 -y
Step 5: Then we divide the y to all sides. xy÷y = -2÷y - y÷y
Step 6: xy÷y = -2 ÷ y -2 ÷y. We're trying to get x by itself.
Step 7: x = -2/y -1. Since we are divinding y with y it cancels out, so it will be
Answer: x = -2/y -1
(Any Further Questions or Confusion Please Let Me Know)
Write the statement in if-then form.
Prime numbers only have two factors, 1 and itself.
Answer:
If the wide variety has only two factors, 1 and itself, then it if truth be told is top in a very huge way. If the variety has usually greater than two factors, then it is for all intents and functions composite in a refined way.
Answer:
See below
Step-by-step explanation:
If a number only has factors of one and itself, then the number is a prime number.
Geometric properties of the section are
Answer:
The geometric properties of sections, which are indicators of the structural performance and load resistance capacity of sections, are characterized by the section shape and dimensions, regardless of material properties.
Determine the slope of any line perpendicular to the line illustrated in the graph below.
Points (2, -1) and (1,-4)
Finding slope
[tex]m=\frac{-4+1}{1-2}=\frac{-3}{-1}=3[/tex]For slope for the perpendicular line
[tex]m=\frac{-1}{3}[/tex]Jay had 60 tickets he could turn in at the end of the year for extra-credit points he had earned during the year. Some tickets were worth two points and others were worth five points. If he was entitled to a total of 231 extra-credit points, how many two-point tickets did he have?
Answer:
23 2-points + 37 5-points = 231
Step-by-step explanation:
Answer:
53 two-point tickets.
Step-by-step explanation:
This is a system of equations:
x + y = 60
2x + 5y = 231
Then..
-2x - 2y = -120
2x + 5y = 231
Then...
3y = 111
y=7
All you need to do now is plug it in:
x + 7 = 60
60-7 = x
x = 53
A space shuttle 275 miles above the earth is orbiting the earth once every 4 hours. How far does the shuttle travel in 1 hour? (Assume the radius of the earth is 4,000 miles.) Answer exactly or round to the nearest mile
The space shuttle travels about 6713 miles per hour. Rounded to the nearest mile, this is approximately 6713 miles per hour.
What is a radius ?
In mathematics, the radius is a term used to describe the distance from the center of a circle or a sphere to any point on its surface. It is denoted by the letter "r".
The orbit of the space shuttle is circular, so the distance it travels in one orbit is equal to the circumference of the circle with a radius of 275 + 4000 = 4275 miles (275 miles above the Earth's 4000 mile radius).
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is the mathematical constant pi (approximately 3.14). Therefore, the distance traveled by the shuttle in one orbit is:
C = 2π(4275) ≈ 26851 miles
Since the shuttle orbits once every 4 hours, its average speed is:
distance/time = 26851/4 ≈ 6713 miles per hour
Therefore, the space shuttle travels about 6713 miles per hour. Rounded to the nearest mile, this is approximately 6713 miles per hour.
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Hello, I could use some help understanding this question please.
To determine the total number of employees, we need to determine first how many are men in the company.
To determine the number of men in the company, we can use the given ratio 7 men is to 5 women and apply direct proportion.
[tex]\frac{7men}{5women}=\frac{?}{135women}[/tex]To solve for the number of men (?), let's apply cross multiplication in the equation above.
[tex]\begin{gathered} \frac{7men\times135women\text{ }}{5women\text{ }}=? \\ \frac{945}{5}=\text{?} \\ 189men=? \end{gathered}[/tex]Hence, there are 189 men in the company.
In total, there are 189 men + 135 women = 324 employees in the company.
sixyt students are competing in a video game challenge. if 2 students comete against each other in every round how many different combinations can be made for the first round of the challenge
Answer:
i believe its 30
Step-by-step explanation:
well i think you would divide sixty by 2 which is thirty.
IM SO SORRY IF IM WRONG- THIS IS JUST WHAT I THINK!