Answers
Answer:
(i) 5
(ii) - 1
(iii) - 1
(iv) 0
(v) 1
(vi) 1
Step-by-step explanation:
See the graph attached to this question.
The blue graph shows y = f(x) and the red graph shows y = g(x).
(i) (f + g)(- 3) = f(-3) + g(-3) = 4 + 1 = 5
(ii) (g - f)(- 2) = g(- 2) - f(- 2) = 2 - 3 = - 1
(iii) (fg)(2) = f(2) × g(2) = (- 1) × (1) = - 1
(iv) [tex](\frac{g}{f})(3) = \frac{g(3)}{f(3)} = \frac{0}{- 3} = 0[/tex]
(v) (fog)(1) = f[g(1)] = f(1) = 1
(vi) (gog)(- 1) = g[g(-1)] = g(2) = 1 (Answer)
After using the graph with the values of f and g we find the values as follows:
(i) (f+g)(-3) = 5
(ii) (g-f)(-2) = -1
(iii) (fg) (2) = -1
(iv) (g/f) (3) = 0
(v) (f o g) (1) = 1
(vi) (g o g)(-1) = 1
i) ( f +g ) (-3)
= ( f (-3) + g(-3) )
Values we got from the graph are:
f(-3) = 4
g(-3) = 1
After substituting these values in the given equation we get
( f + g) (-3) = 5
ii) ( g - f ) (-2)
= ( g(-2) - f(-2) )
Values we got from the graph are:
g(-2) = 2
f(-2) = 3
After substituting these values in the given equation we get
( g - f ) (-2) = - 1
iii) ( fg) (2)
= ( f(2) g(2))
Values we got from the graph are:
f(2) = -1
g(2) = 1
After substituting these values in the given equation we get
( fg)(2) = -1
iv) (g/f) (3)
( g(3) / f(3) )
Values we got from the graph are:
g(3) = 0
f(3) = - 3
After substituting these values in the given equation we get
( g / f ) (3) = 0
v) ( f o g ) (1)
= ( f(1) o g(1) )
Values we got from the graph are:
g(1) = 1
f(1) = 1
After substituting these values in the given equation we get
( f o g ) (1) = 1
vi) ( g o g ) (-1)
= ( g(-1) o g(-1) )
Values we got from the graph are:
g(-1) = 2
g(2) = 1
After substituting these values in the given equation we get
( g o g ) (-1) = 1
Related Questions
Isabel will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $46 and costs an additional $0.13 per mile driven.
The second plan has an initial fee of $55 and costs an additional $0.11 per mile driven.
For what amount of driving do the two plans cost the
Answers
To compare the two plans and find the amount of driving for which they cost the same, we can set up an equation and solve for x. The two plans cost the same for 450 miles of driving.
Explanation:To compare the two plans and find the amount of driving for which they cost the same, we need to set up an equation. Let's assume the amount of driving is represented by the variable x. The total cost for Plan 1 can be calculated as:
Total cost = $46 + $0.13x
The total cost for Plan 2 can be calculated as:
Total cost = $55 + $0.11x
We can set the two equations equal to each other and solve for x:
$46 + $0.13x = $55 + $0.11x
$0.02x = $9
x = $9 / $0.02 = 450
Therefore, the two plans cost the same for 450 miles of driving.
Mr. Jones took a survey of college students and found that 60 out of 65 students are liberal arts majors. If a college has 8,943 students, what is the expected number of students who are liberal arts majors? answer fast
Answers
Should be 5812.95 Students
A cube has volume 1331 cm3.
Calculate the length of one edge of the cube.
Answers
11 x 11 x 11 = 1331
The length of one edge of a cube with a volume of 1331 cm³ is 11 cm, derived by taking the cube root of the volume.
Explanation:To calculate the length of one edge of a cube when the volume is given, we use the formula for the volume of a cube: Volume = side³, where 'side' is the length of one edge of the cube.
The cube in question has a volume of 1331 cm³. To find the length of one edge of the cube, we need to take the cube root of the volume. The cube root of 1331 cm³ is 11 cm, meaning each side of the cube measures 11 cm.
The cube root is calculated because raising a number to the third power cubes it, and taking the cube root is the inverse operation. This process allows us to determine the original value that was cubed to get the volume.
an = 12 – 5(n − 1)
What is the 30th term of the sequence?
Answers
Answer:
- 133
Step-by-step explanation:
To find the 30 th term substitute n = 30 into the formula, that is
[tex]a_{30}[/tex] = 12 - 5(30 - 1) = 12 - (5 × 29) = 12 - 145 = - 133
Final answer:
The 30th term of the sequence defined by an = 12 – 5(n – 1) is – 133.
Explanation:
To calculate the 30th term of the sequence given by an = 12 – 5(n – 1), we start by substituting the value of n with 30.
[tex]a_{30}[/tex] = 12 – 5(30 – 1)
[tex]a_{30}[/tex] = 12 – 5(29)
[tex]a_{30}[/tex] = 12 – 145
[tex]a_{30}[/tex] = – 133
The 30th term of the sequence is – 133.
Hector spent three force of this money the day after he cashed his paycheck of $50 let him represent the amount of money Hector spent
Answers
Answer:
Hector has spent $37.5.
Step-by-step explanation:
Given:
Total money he cashed = $50
Also Given:
Hector spent [tex]\frac{3}{4}[/tex] of his money the day after he cashed his paycheck of $50.
Let 'm' be the amount of money hector spent.
Now according to question;
amount of money hector spent is equal to [tex]\frac{3}{4}[/tex] times the amount of money he cashed his paycheck.
framing in equation form we get;
[tex]m =\frac{3}{4}\times 50 = \$37.5[/tex]
Hence hector has spent $37.5.
1) For the data in the table, does y vary directly with x? If it does, write an equation for the direct
variation.
Answers
Answer:
Yes, y varies directly with x.
[tex]y=\frac{11}{8} x[/tex]
Step-by-step explanation:
[tex]\frac{y}{x}=\frac{11}{8} =\frac{22}{16} =\frac{33}{24}[/tex]
Hence [tex]y[/tex] varies directly with [tex]x[/tex].
[tex]\frac{y}{x}=\frac{11}{8} \\\\ y=\frac{11}{8} x[/tex]
The coordinates of the vertices of triangle ABC are A (1,-1),B (1,4), and C (8,4). what is the length in units of the line segment that connects vertex A and vertex B
Answers
The length of the line segment that connects vertex A and vertex B is 5 units
Step-by-step explanation:
Let us revise some facts about the horizontal and vertical segments
The segment is horizontal if the y-coordinates of all points on the segment are equalThe length of the horizontal segment whose endpoints are [tex](x_{1},y)[/tex] and [tex](x_{2},y)[/tex] is [tex]x_{2}-x_{1}[/tex]The segment is vertical if the x-coordinates of all points on the segment are equalThe length of the vertical segment whose endpoints are [tex](x,y_{1})[/tex] and [tex](x,y_{2})[/tex] is [tex]y_{2}-y_{1}[/tex]In Δ ABC
∵ A = (1 , -1)
∵ B = (1 , 4)
∵ C = (8 , 4)
∵ The x-coordinate of point A = 1
∵ The x-coordinate of point B = 1
∴ The x-coordinates of points A and B are equal
- The x-coordinates of A and B are equal, then the line AB is a
vertical segment
∴ The length of AB is the difference between the y-coordinates
of points A and B
∵ The y-coordinate of point A = -1
∵ The y-coordinate ob point B = 4
∴ The length of AB = 4 - (-1)
∴ The length of AB = 4 + 1
∴ The length of AB = 5 units
The length of the line segment that connects vertex A and vertex B is 5 units
Learn more:
You can learn more about the length of the segments in brainly.com/question/6564657
#LearnwithBrainly
Answer:
5 units
Step-by-step explanation:
If there's 140 calories in 2 thirds cup, how many calories in 2 cups?
Answers
Answer:
420cal = 2 cups
Step-by-step explanation:
140cal = 2/3 cup
xcal= 2 cups
Divide 2/(2/3) = 3
Multiply both sides by 3 (answer)
140cal= 2/3 cups (3)
420cal = 2 cups
The 2 cups Contain 420 Cal.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
2/3 Cup contain = 140 Cal
So, 1 cup contain = 140 ÷ ( 2/3)
= 140 x 3/2
= 70 x 3
= 210
Then, In 2 cups = 210 x 2
= 420 Cal
Hence, 2 cups Contain 420 Cal.
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
Practice 0.4+y_>7 answer plssss
Answers
For this case we have the following inequality:
[tex]0.4 + y\geq 7[/tex]
If we subtract 0.4 from both sides of the inequality we have:
[tex]y \geq7-0.4\\y \geq6.6[/tex]
Thus, the solution is given by all the values of "y" greater than or equal to 6.6.
The graph of the solution is attached.
Answer:
[tex]y\geq6.6[/tex]
X-4y=-18
Graphing linear equations
Answers
Answer:
as illustrated
Step-by-step explanation:
X-4y= - 18
find 2 points on the line
x = 0 y = 4.5 (0, 4.5)
x = 4 y = 5.5 (4, 5.5)
Answer:
Please Check the image for the answer to your question hope this helps!
What is 6x+4x-3x the x's are variables so can someone please help me please help me
Answers
Answer:
[tex]6x + 4x - 3x = 10x - 3x = 7x[/tex]
Andrew's rotation maps point M(9, -1) to M'(-9, 1). Which describes the rotation?
180° rotation
270° clockwise rotation
90° counterclockwise rotation
90° clockwise rotation
Answers
Answer:
180° rotation
Step-by-step explanation:
sign changes when we rotate a point to 180 degrees. so 9 became -9 and -1 became 1, which gave us the clue that it's 180° rotation
The given situation described 180° rotation
Given information:Andrew's rotation maps point M(9, -1) to M'(-9, 1).
Rotation:Since signing is changed when we rotate a point to 180 degrees. So here 9 became -9 and -1 became 1, which provides us the clue that its 180° rotation.
learn more about the point here: https://brainly.com/question/24450263
Susie and jack are on a basketball team. The total amount of points scored was 86. If Susie has 5 more than as many points as jack then how many points do they each have
Answers
Answer:
The points each have scored are Susie 45.5 points and jack 40.5 points.
Step-by-step explanation:
Given:
Susie and jack are on a basketball team.
The total amount of points scored was 86.
Susie has 5 more than as many points as jack.
Now, to find the points they each have:
Let the points of jack be [tex]x[/tex].
Then the points of Susie be [tex]5+x[/tex].
There total points scored = 86.
According to question:
[tex]x+(x+5)=86.[/tex]
⇒ [tex]x+x+5=86.[/tex]
⇒ [tex]2x+5=86.[/tex]
Subtracting both sides by 5 we get:
⇒ [tex]2x=81.[/tex]
Dividing both sides by 2 we get:
⇒ [tex]x=40.5.[/tex]
Jack scored = 40.5 points.
Putting the value of [tex]x[/tex] to get the points of Susie:
[tex]x+5[/tex]
⇒ [tex]40.5+5 = 45.5[/tex]
Susie scored = 45.5 points.
Therefore, the points each have scored are Susie 45.5 points and jack 40.5 points.
Tell whether each equation has one, zero, or infinitely many solutions.
5(x - 3) +6= 5x - 9
Answers
5(x - 3) +6 = 5x - 9 has infinitely many solutions
Solution:Given equation is 5(x - 3) +6 = 5x - 9
We have to find whether the given equation has one, zero, or infinitely many solutions
Let us solve the given equation
5(x - 3) + 6 = 5x - 9
Let us use BODMAS rule to solve the given equation
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right
So let us first solve for brackets in given equation
5x - 15 + 6 = 5x - 9
5x - 9 = 5x - 9
0 = 0
Since the statement is true, there are infinitely many solutions
an object travels along a horizontal straight path at a constant rate the object travels 1/20 of the length of the path in 3/4 seconds at that rate how many seconds does it take the object to travel the entire length of the path
Answers
Answer:
15 sec.
Step-by-step explanation:
Given: Object travels 1/20 of the length of the path in 3/4 seconds.
Let the entire length of the path be "x".
Now, solving to find the total time taken to travel entire length.
First step, Object travel= [tex]\frac{1}{20}\times x = \frac{x}{20}[/tex]
Next putting the value in the ratio of Length: time.
[tex]\frac{\frac{x}{20} }{\frac{3}{4} }[/tex]
And another ratio of entire length and total time
[tex]\frac{x}{Total\ time}[/tex]
Now, using scissor method fractioning to solve the ratio or fraction
⇒[tex]\frac{\frac{x}{20} }{\frac{3}{4} }= \frac{x}{Total\ time}[/tex]
To divide fraction, take reciprocal of the divisor and multiply the dividend.
⇒ [tex]\frac{x}{20} \times \frac{4}{3} = \frac{x}{Total\ time}[/tex]
⇒[tex]\frac{4x}{20\times 3} = \frac{x}{Total\ time}[/tex]
Cross multiplying both side.
⇒ [tex]Total\ time= \frac{20x\times 3}{4x}[/tex]
⇒ [tex]Total\ time= \frac{20\times 3}{4}[/tex]
⇒[tex]Total\ time= 5\times 3= 15\ sec[/tex]
∴ Total time taken by Object to travel entire length is 15 sec.
1. 4/5 - (-3/10)=
2. 5.5 - 8.1=
3. -5 - 5/3=
4. -8 3/8 - 10 1/6=
5. -4.62 - 3.51=
Answers
Answer:
Step-by-step explanation:
4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10
5.5-8.1=-2.6
-5-5/3=-15/3-5/3=-20/3
-8 3/8-10 1/6=-67/8-61/6=-445/24
-4.62-3.51=-8.13
1.) 1.1
2.) -2.6
3.) ≈ -6.67
4.) ≈ -18.54
5.) -8.13
Write 2x^2+7x -3 in the form of a(x+m)^2 +n
Answers
Answer: Search it up
Step-by-step explanation:
It shows you all the steps and will help you
Ryan has $40 in the bank. He writes
a check for $64.75 and then uses his
check card to buy gas for $40. What is
his new balance?
Show work and explain clearly
Answers
40-64.75= -24.75
You do -24.75-40
-24.75-40= -64.75
He owes $64.75
Suppose that y varies inversely with x, and y=2 when x=10.
(A) write an inverse variation equation that relates x and y
(b) find y when x= 4
Answers
Answer:
see explanation
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
(A)
To find k use the given condition y = 2 when x = 10
k = yx = 2 × 10 = 20, thus
y = [tex]\frac{20}{x}[/tex] ← equation of variation
(B)
When x = 4, then
y = [tex]\frac{20}{4}[/tex] = 5
helppppppppppp me pleaseeee
Answers
Answer:
Step-by-step explanation:
8) a) No: of sides of a regular polygon = 360° / exterior angle
= 360°/18° = 20 sides
b) Sum of interior angles of regular polygon = (n-2) * 180° {n-no:of sides}
= (20-2)*180° = 18*180° = 32400°
9) Let the exterior angle be x.
So, interior angle = 140° + x
Interior angle + exterior angle = 180°
140° +x + x = 180°
140° +2x = 180°
2x = 180° - 140°
2x =40°
x = 40°/2 = 20°
Exterior angle = 20°
Interior angle = 160°
No: of sides of a regular polygon = 360° / exterior angle
= 360°/20° = 18 sides
Hint: Always sum of exterior angles of regular polygon is 360°
Find the value of x in each case. Give reasons to justify your solutions!
B, C ∈ AD
Answers
Step-by-step explanation:
DCF is 90°
so to find BCE
BCE+64+90=180
BCE=26°
CBE is (180-3x)
taking triangle BEC
(180-3x)+x+26=180
180-3x+x+26=180
-2x+26=0
-2x=-26
x=13
arrange the following decimals in descending order 0.3 , 0.07 , 0.91 , 1.0
Answers
1.0 0.91 0.3 0.07
descending
largest to smallest
Answer:
1.0, 0.91, 0.3, 0.07
Step-by-step explanation:
first take the decimal number(s) in front and put then first.
then take the ones closest to one
then thanks the ones closer to half
then, finally take the ones closer to zero
write an integer for $50 withdrawal
Answers
Answer: -50
Step-by-step explanation: A withdrawal means that you're decreasing the amount of money you have.
So a withdrawal of $50 can be written as -50.
5. Find the sum of the first 35 terms of the arithmetic sequence when a = 5 and d = 4
Answers
Answer:
The sum of the first 35 terms of the arithmetic sequence when a = 5 and d = 4 is 2555.
Step-by-step explanation:
Given:
a = 5
d = 4
To Find :
The sum of first 35 terms of the arithmetic sequence = ?
Solution:
Step 1 : finding the 35th term
[tex]a_n = a_1 +(n-1)d[/tex]
[tex]a_35 = 5 +(35-1)4[/tex]
[tex]a_35 = 5 +(34)4[/tex]
[tex]a_35 = 5 +136[/tex]
[tex]a_35 = 141[/tex]
Step 2: Finding the sum of first 35 terms
[tex]S_n = \frac{n(a_1 +a_n)}{2}[/tex]
Substituting the values
[tex]S_n = \frac{35(5+141)}{2}[/tex]
[tex]S_n = \frac{35(146)}{2}[/tex]
[tex]S_n = \frac{35(146)}{2}[/tex]
[tex]S_n = \frac{5110)}{2}[/tex]
[tex]S_n = 2555[/tex]
Rewrite the following linear equation in slope-intercept form. Write youk
answer with no spaces.
y+4= -2(x - 1)
Answers
Answer:
y=-2x-2
Step-by-step explanation:
y+4=-2(x-1)
y+4=-2x+2
y=-2x+2-4
y=-2x-2
Question 2 (6 points)
You invest $15,000 in a savings account with an annual interest rate of 2.5% in
which the interest is compounded quarterly. How much money should you expect to
have in the account after 5 years? Show your work to receive full credit!
Answers
Answer:
$16,991
Step-by-step explanation:
Rate = r = 2.5%
Times = b = 4
A = P [1 + (r / b)]ⁿᵇ
A = $15,000 [1 + (0.025 / 4]⁵ ˣ ⁴
A = $15,000 [1 + 0.00625]²⁰
A = $15,000 [1.00625]²⁰
A = $15,000 x 1.132708
A = $16,991
20% tip on a bill of 31.60
Answers
Answer:
6.32
Step-by-step explanation:
There's an easy trick for this. Move the decimal point once to the left, and then multiply by 2.
31.60 turns into 3.16 (which is 10% btw)
Multiply 3.16 by 2 and you get 6.32, or 20% of 31.60. Hope this helped!
4. What is the equation of the midline of the sinusoidal function?
Answers
The midline equation for the sinusoidal function is y = 4 sin(ωx + ∅) - 3, derived by calculating the amplitude and vertical shift within the general function equation.
A function is a mathematical expression, rule, or law that defines the relationship between one variable and another. In mathematics, functions play a crucial role in representing physical relationships and various mathematical concepts. One specific type of function is the sinusoidal function, characterized by its repetitive pattern within a specific time interval.
The general form of a sinusoidal function is given by the equation:
y = A sin(ωx + ∅) + c
Here, A represents the amplitude, ω is the argument, ∅ is the phase difference, and c is the vertical shift known as the midline.
To find the equation of the midline, we use the formula:
A = (Maximum value - Minimum value) / 2
Given that the maximum value is 1 and the minimum value is -7, the amplitude (A) is calculated as:
A = (1 - (-7)) / 2 = 4
The vertical shift (c) is determined to be -3. Substituting these values into the general equation, we obtain the equation of the midline for the sinusoidal function:
y = 4 sin(ωx + ∅) - 3
In summary, the equation of the midline for the sinusoidal function is y = 4 sin(ωx + ∅) - 3.
The amplitude and vertical shift inside the general function equation are used to obtain the midline equation for the sinusoidal function, which is y = 4 sin(ωx + ∅) - 3.
A mathematical phrase, rule, or law that establishes the connection between two variables is called a function.
Functions are essential to the representation of both mathematical concepts and physical relationships in mathematics.
The sinusoidal function is one particular kind of function that is distinguished by its repeating pattern inside a predetermined time frame.
The following formula provides the generic form of a sinusoidal function:
sin(ωx + ∅) + c = A
In this case, amplitude is denoted by A, argument by ω, phase difference by ∅, and vertical shift, or midline, by c.
We utilise the to determine the midline's equation.
A is equal to (Maximum - Minimum) / 2.
A = (1 - (-7)) / 2 = 4 is the formula for calculating the amplitude (A), given that the maximum value is 1 and the minimum value is -7.
It is found that the vertical shift (c) is -3. The equation of the midline for the sinusoidal function is obtained by substituting these values into the general equation: y = 4 sin(ωx + ∅) - 3
In conclusion, y = 4 sin(ωx + ∅) - 3 is the equation of the midline for the sinusoidal function.
how many times dose 10 go into 450
Answers
Answer:
10 go into 450 45 times
Step-by-step explanation:
william drives 55 mph to abilene. How many miles will we have driven after driving for 3 hours
Answers
Answer:
165
Step-by-step explanation:
55* 3 = = 165