Answer: f⁻¹(x)=x/5
Step-by-step explanation:
To find the inverse function, you replace the y with x, and x with y.
x=5y
y=x/5
f⁻¹(x)=x/5
PLS HELP ASAP Event A and event B are independent events. Given that P(B)=13 and P(A∩B)=16, what is P(A)?
Answer:
Step-by-step explanation:
hello,
As A and B are two independent events we can say that P(A∩B)=P(A)P(B)
P(A)=P(A∩B)/P(B)=16/13
thanks
PLEASE HELP ME!!! Write 5 Euclid's postulates
Answer:
The postulates are as follows:
A straight line segment may be drawn from any given point to any other.A straight line may be extended to any finite length.A circle may be described with any given point as its center and any distance as its radius.All right angles are congruent.If a straight line intersects two other straight lines, and so makes the two interior angles on one side of it together less than two right angles, then the other straight lines will meet at a point if extended far enough on the side on which the angles are less than two right angles.Which of the following is a term in the algebraic expression:
p2 + 12p-14?
A. 12
B. p3
C. 3
D.P
Answer:
Hello!
____________________
Your answer would be (C).
Hope this helped you!
In the right triangle LMN L and M are complementary angles and sin L is 19/20 what is cos M
Hey there! I'm happy to help!
There is a rule in trigonometry that says that the sine of one angle is equal to the cosine of that angle's complement.
Complementary angles are ones that equal 90 degrees when added.
We see that L and M are complementary angles, so we can apply this rule.
The sine of L is 19/20. We know that the sine of angle L is equal to the cosine of L's complement from our rule, which is M. This means that the cosine of M is equal to 19/20.
Have a wonderful day!
Gym A charges a $25 membership fee and a $25 monthly fee. Gym B charges a $55 membership fee and a $10 monthly fee. After how many months will the total amount of money paid to both yoga clubs be the same? What will the amount be?
Answer: 75
solve:
For gym A
total cost= membership fee+monthly fee
membership fee=25
monthly fee=25
cost of x month=25x
total cost=25+25x
for gym B
membership fee=10
total cost=55+10x
now total cost are same
25+25x=55+10x
15x=30
x=30/15
x=2.
2 months
and amount =25+25*2=75
Answer:
2 months, they will have paid 75 dollars
Step-by-step explanation:
Gym A
25+ 25m where m is the number of months
Gym B
55 + 10m
Set them equal
25+25m = 55+10m
Subtract 10m from each side
25+25m-10m = 55+10m-10m
25+15m = 55
Subtract 25 from each side
25+15m-25 = 55-25
15m = 30
Divide by 15
15m/15 = 30/15
m=2
After 2 months
25+25(2) = 25+50 = 75
The cost is 75 dollars
Select the correct answer. What is the average rate of change of f(x), represented by the graph, over the interval [-1, 1]? A. 2 B. 3 C. 5 D. 6
Answer:
C
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [- 1, 1 ] , thus
f(b) = f(1) = 5 ← from graph
f(a) = f(- 1) = - 5 ← from graph , thus
average rate of change = [tex]\frac{5-(-5)}{1-(-1)}[/tex] = [tex]\frac{10}{2}[/tex] = 5 → C
It takes Carrie 58 minutes to get home. If Carrie leaves for home at 1:32, what time will she arrive?
Answer:
2:30
Step-by-step explanation:
58+32=90
90-60=30
2:30 is the answer
Answer: she will get home at 2:30
Step-by-step explanation:
If you start at 1:32 then take 28 min from 58 then you get 2:00
Finally add 30 yo that and get 2:30.
If you add 36, 35, 34, 33, and 32, the sum is . If you sum the numbers from 1 to 36, the sum is . The fraction (the first sum / the total sum) to the nearest tenth = %. The lender will multiply this fraction by the total interest. The cumulative interest = (the percentage calculated above) x ($808.13) = $. The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is: $
Complete Question
Consider a three-year loan (so we'll assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using standard amortization, the monthly payment is $161.33. In this example, we will not worry about exact or ordinary interest because the total interest to be paid is $808.13. After the fifth month the borrower decides to prepay the whole loan. Under a standard amortization plan the borrower would have paid $198.28 in cumulative interest. However, using the Rule of 78 a lender would calculate the fraction of the total interest based on two series:
[tex]\dfrac{(n+35)+(n+34)+(n+33)+(n+32)+(n+31)} {(n)+(n+1)+...+(n+35)}[/tex]
Answer:
See below
Step-by-step explanation:
36+35+34+33+32=170
If you add 36, 35, 34, 33, and 32, the sum is 170.Now, 1,2,3,...36 forms an arithmetic series whose first and last term are 1 and 36 respectively. Its sum is determined using the formula: [tex]S_{n}=\frac{n}{2}(a+l) \\[/tex]
[tex]S_{36}=\frac{36}{2}(1+36) =18*37=666[/tex]
If you sum the numbers from 1 to 36, the sum is 666.[tex]=\dfrac{170}{666}= 0.255=25.5\% $(to the nearest tenth)[/tex]
The fraction (the first sum / the total sum) to the nearest tenth = 25.5%.The lender will multiply this fraction by the total interest.
The cumulative interest [tex]= 25.5\% \times \$808.13 = \$206.07[/tex]The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is:
$206.07-198.28=$7.79
Answer:
If you add 36, 35, 34, 33, and 32, the sum is . If you sum the numbers from 1 to 36, the sum is . The fraction (the first sum / the total sum) to the nearest tenth = %. The lender will multiply this fraction by the total interest. The cumulative interest = (the percentage calculated above) x ($808.13) = $. The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is: $
1
SEE ANSWER
ADD ANSWER
Step-by-step explanation:
It is asking what is the measure of the inscribled angle JHI
Answer:
45 degrees
Step-by-step explanation:
central angle = the arc
inscribed angle = 1/2 the arc
A loan of $8,000 is paid back in two years in monthly payments of $400. The percentage interest on the loan was
(a) 5%
(b) 8 ⅓%
(c) 16 ⅓%
(d) 20%
Answer:
D
Step-by-step explanation:
The number of months in two years is 24 months.
Now, with a repayment plan of $400 per month, the total amount returned will be 400 * 24 = $9,600
Now, $8,000 was borrowed but $9,600 was returned
The amount of interest is 9600-8000 = 1600
So what percentage of 8,000 is 1600?
1600/8000 * 100 = 16/80 * 100 = 1/5 * 100 = 20%
Allen is running a marathon. He would like to finish the race in under 5.5 hours. He has already run 3 hours. The inequality 3 + t less-than 5.5 represents the situation. Which number line shows how much longer Allen can run and still meet his goal?
Answer:
Kindly check attached picture for number line.
Step-by-step explanation:
Total time Allen would love to complete race is less than 5.5 hours
Time elapsed = 3 hours
Inequality representing the problem above :
3 + t < 5.5
Where t will mean the time left.
Solving for t
t < 5.5 - 3
t < 2.5
Time left is < 2.5 hours.
Answer:
Open Circle to the left from 2.5
Step-by-step explanation:
Please help, thx if you do :) Twice the complement of an angle is 26° less than the supplement of the angle. Find the angle. A. 64° B. 166° C. 154° D. 26°
Answer:
x=26 degrees (D)
Step-by-step explanation:
Let's say x is the angle.
90-x would be the complement of the angle
180-x is the supplement
We can make the equation
supplement-26=2complement as the question states that twice the complement is 26 less than the supplement.
We can now substitute the 90-x and 180-x in their respective positions to get (180-x)-26=2(90-x) if we simplify this we get 180-x-26=180-2x which if we take away 180-x from both sides we get that -26=-x or 26=x
Consider the graph shown.
What is the slope-intercept form of the equation of the line?
Plz help
Answer:
y = [tex]\frac{2}{3}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 4)
m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]
The line crosses the y- axis at (0, 2) ⇒ c = 2
y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line
in our solar system, 6 of the 8 planets have moons, what percentage of the plants have moons?
Answer:
75%
Step-by-step explanation:
Percentage of planets having moons = 6 /8 *100 = 75%
a) Complete the table of values for y = 3x – 1
X
-2
-1
0
1
2
3
y
I
-4
5
Answer:
x | y
− 2 − 6
− 1 − 3
0 0
1 3
2 6
hope this helps!
The table of values for the equation y = 3x - 1, is attached.
x y
-2 -7
-1 -4
0 -1
1 2
2 5
3 8
What are equations?Equations are relations between two or more variables, used to find the value of an unknown variable from the known value of other variables.
How do we solve the given question?We are given the equation y = 3x - 1. We are asked to complete the table, for the given values of x: -2, -1, 0, 1, 2, 3.
To find the y variable, for the given x's, we substitute each value of x, one at a time in the equation.
Value of y when x = -2 is, y = 3(-2) -1 = - 6 - 1 = -7.Value of y when x = -1 is, y = 3(-1) -1 = - 3 - 1 = -4.Value of y when x = 0 is, y = 3(0) -1 = 0 - 1 = -1.Value of y when x = 1 is, y = 3(1) -1 = 3 - 1 = 2.Value of y when x = 2 is, y = 3(2) -1 = 6 - 1 = 5.Value of y when x = 3 is, y = 3(3) -1 = 9 - 1 = 8.We put all these values of y, for the corresponding value of x in the table. The completed table is attached.
Learn more about equations at
https://brainly.com/question/4344214
#SPJ2
A
B
C
D
WHICH ONE??
PLEASE HELP ME !!!
Answer:
Is it B?
Step-by-step explanation:
ab^2 + 2a^2b + 4a + 2b
ab(b+2a) +2(2a+b)
ab(b+2a) +2(b+2a)
(ab+2)(b+2a)
that's why ab+2 is the answer.
This is just probability, please help me !
Answer:
4/5
Step-by-step explanation:
Two are white.
10 total marbles.
10 - 2
8 are not white.
8/10
Simplify or reduce.
⇒ 4/5
find the value of t perimeter
Answer:
t = 15.2 is the answerStep-by-step explanation:
1. Make an equationnumbers to find perimeter = perimeter
Side + Side + 2 unknown sides = perimeter
12 + 7.8 + 2t = 50.2
2. Simplify like terms19.8 + 2t = 50.2
3. Solve19.8 + 2t = 50.2
-19.8 - 19.8
2t = 30.4
t = 15.24. Check:12 + 7.8 + t + t = 50.2
12 + 7.8 + (15.2) + (15.2) = 50.2
50.2 = 50.2 Correct!Hope this helped,
Kavitha
Answer:
t = 15.2 miles
Step-by-step explanation:
First, let's add the top and bottom numbers together.
7.8 + 12 = 19.8 mi
Next, we subtract that from 50.2 to get the combined value of both t's.
50.2 - 19.8 = 30.4 mi
Finally, we can divide 30.4 by 2 to get the value of t.
30.4 ÷ 2 = 15.2 mi
To check our answer, we can add all the sides up to see if they equal to 50.2. 15.2 + 15.2 = 30.4
30.4 + 12 + 7.8 = 50.2
The surface area of a cube is 78 cm^2. What is the volume of the cube, rounded to
the nearest tenth of a cm^3?
Answer:
46.87
Step-by-step explanation:
V=*(A^3/2
)/36
V=*(46.87^3/2
)/36
5. Solve 2(1 - x) > 2x.
a. x > 2
b. x < 2
c. x < 0.5
d. x > 0.5
Answer:
I do not know for sure but i think it might be B.
Step-by-step explanation:
Im not the smartest so yeah hopefully that is the answer you are looking for tho :D
How many liters of water must Sharon add to 2 liters of a sugar and water solution that is 36% sugar to create a solution that is 12% sugar? Answer: liters
Answer:
4 liters.
Step-by-step explanation:
From the question above, we are required to find the amount of water that should be added to a sugar and water solution.
Let x represent the amount of water that would be added by Sharon.
2×36/100= 12/100(2+x)
2×0.36= 0.12(2+x)
Cross multiply both sides
0.72= 0.24+0.12x
Collect the like terms
0.72-0.24= 0.12x
0.48= 0.12x
Divide both sides by the coefficient of x which is 0.12
0.48/0.12= 0.12x/0.12
x= 4
Hence Sharon should add 4 liters of water to 2liters of sugar and water solution that is 36% sugar to form a solution of 12% sugar.
Answer:
4 liters is the correct answer
Step-by-step explanation:
Multiply the polynomial.
(4x+2)(x-2)
PLEASE HELP!!! ASAP!!!
Answer:4x2−6x−4
Step-by-step explanation:
(4x+2)(x−2)
=(4x+2)(x+−2)
=(4x)(x)+(4x)(−2)+(2)(x)+(2)(−2)
=4x2−8x+2x−4
=4x2−6x−4
Answer:
(4x+2)(x-2)
= 4x(x-2) +2(x-2)
=4x^2-8x + 2x-4
=4x^2 - 6x -4
I will mark brainiest if correct Let f(x)=5x−7 and g(x)=x+3. Find f(g(x)) and g(f(x)).
Step-by-step explanation:
f(g(x))= 5(g(x))- 7 = 5(x+3) - 7 = 5x +8
g(f(x)) = f(x) +3 = 5x -7 +3= 5x -4
helppp
Determine the x-intercept of the line whose equation is given:
y = StartFraction x Over 2 EndFraction minus 3
a.
(6, 0)
b.
(negative 6, 0)
c.
(0, three-halves)
d.
(Negative three-halves, 0)
Answer:
A
Step-by-step explanation:
If you put your function in a graphing calculator you will get (6,0)
What value of x is in the solution set of 2x-3> 11 - 5x?
-3
2
Answer:
x >2
Step-by-step explanation:
2x-3> 11 - 5x
Add 5x to each side
2x+5x-3> 11 - 5x+5x
7x -3 > 11
Add 3 to each side
7x-3+3 > 11+3
7x >14
Divide by 7
7x/7 > 14/7
x >2
Can someone help me solve (a) and (c) pls.
Thanks
Answer:
Area of ABCD = 959.93 units²
Step-by-step explanation:
a). By applying Sine rule in the ΔABD,
[tex]\frac{\text{SinA}}{46}=\frac{\text{Sin}\angle{DBA}}{35}[/tex]
[tex]\frac{\text{Sin110}}{46}=\frac{\text{Sin}\angle{DBA}}{35}[/tex]
Sin∠DBA = [tex]\frac{35\times \text{Sin}(110)}{46}[/tex]
m∠DBA = [tex]\text{Sin}^{-1}(0.714983)[/tex]
m∠DBA = 45.64°
Therefore, m∠ADB = 180° - (110° + 45.64°) = 24.36°
m∠ADB = 24.36°
c). Area of ABCD = Area of ΔABD + Area of ΔBCD
Area of ΔABD = AD×BD×Sin([tex]\frac{24.36}{2}[/tex])
= 35×46Sin(12.18)
= 339.68 units²
Area of ΔBCD = BD×BC×Sin([tex]\frac{59.92}{2}[/tex])°
= 46×27×(0.4994)
= 620.25 units²
Area of ABCD = 339.68 + 620.25
= 959.93 units²
The diagram shows a parallelogram.
4 cm
7 cm
100°
Work out the area of the parallelogram.
Give your answer to 2 significant figures.
Answer:
27.44 square cm
Step-by-step explanation:
If the length of parallelogram is a and b and angle between side a and b is [tex]\alpha[/tex].
Then area of parallelogram = [tex]a*b*sin(\alpha ) = ab sin(\alpha )[/tex]
Given side length 4 cm and 7 cm
angle between them = 100°
value of sin(100°) = 0.98
Thus, area of given parallelogram = 4*7*sin(100°) = 28*0.98 = 27.44
Thus, area of given parallelogram is 27.44 square cm.
A triangle is drawn on a coordinate plane. Point A is at (2,6), Point B is at (4,10), and Point C is at (8,5). What is the midpoint of side AB
Question 1: Explain how the letter x (or any letter) is used when writing expressions, and give an example. How are expressions different than equations?
Question 2: Identify the parts (include: terms, coefficients, variables and constants) of the following expression and translate it into a verbal expression:
2(3x – 2y) + 7
Question 3: Identify the like terms, explain how you know they are like terms, and simplify the expressions:
10y + 3x + 10 +x -2y
3x – y + 4x + 6 – 2y
Question 4: Explain how to evaluate the expression 8x2 + 25y, when x = 3 and y = 2
Question 5: Explain how to write an equivalent expression for the expression
3(4x + 2y) + 5x.
Be sure to explain which properties you used. What method can you use to prove the 2 expressions are equivalent?
Answer:
Question 1:
The letter x or any letter used when writing an expression is representative of unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea
Question 2:
The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7
Question 3:
In the first expression, the like terms are;
10y and (-2y),
3x and x
In the second expression, the like terms are;
-y and -2y
3x and 4x
The first expression simplifies to 8y + 4x + 10
The second expression simplifies to 7x - 3y + 6
Question 4:
The expression is evaluated as 122
Question 5:
The equivalent expression of the expression 3(4x + 2y) + 5x, is 17x + 6y
To prove when x = 1 and y = 2 we have;
3(4×1 + 2×2) + 5×1 is 29
17×1 + 6×2 is 29 which are equivalent in value
Step-by-step explanation:
Question 1:
The letter x or any letter used when writing an expression is representative of unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea
Example;
If x is the symbol representing the average number of oranges sold in 1 hour, then the expression for the number of oranges sold per day of 24 hours = 24·x
An expression is a written mathematical symbolic statement that shows the the finite merging together of representative symbols by the mathematical operations that govern the present constraints
An equation is a statement that two expressions are equal
Question 2:
The given expression is 2(3x - 2y) + 7
The parts are;
The coefficient of (3x - 2y) = 2
The constant term = 7
The variables are x and y
Which gives
The coefficient of the variable x = 6
The coefficient of the variable y = -4
The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7
or
The expression can be translated as two times the bracket open three times (variable) x minus two times (variable) y bracket close plus the constant 7
or
The expression can be expanded as 2(3x - 2y) + 7 → 6·x - 4·y + 7 which is expressed verbally as follows;
Six times (variable) x minus four times (variable) y plus the constant 7
Question 3:
The expressions are;
10y + 3x + 10 + x - 2y..........................(1)
3x - y + 4x + 6 - 2y,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2)
In the first expression, the like terms are;
10y and (-2y),
3x and x
In the second expression, the like terms are;
-y and -2y
3x and 4x
They are like terms because they can be simply added together to simplify the expressions as follows
10y + 3x + 10 + x - 2y gives 10y - 2y + 3x + x 10 to give 8y + 4x + 10
Also
3x - y + 4x + 6 - 2y gives 3x+ 4x - y - 2y + 6 to give 7x - 3y + 6
Question 4:
The expression 8x² + 25·y when x = 3 and y = 2 is evaluated by replacing (putting) the value x and y (into the expression)
The expression is then evaluated as 8×3² + 25×2 which is the same as 72 + 50 or 122
Question 5:
To write the equivalent expression of the expression 3(4x + 2y) + 5x, we expand the expression as follows;
3×4x + 3×2y + 4x which is 12x + 6y + 4x
We combine like terms;
12x + 5x + 6y which is 17x + 6y
To prove we can check by substituting a value for each of the variables x and y such as x = 1 and y = 2
3(4×1 + 2×2) + 5×1 is 29
17×1 + 6×2 is 29
what is a other name for the set of all x-values
Answer:
its domain
Step-by-step explanation:
Answer:
i believe it is A- range.
Step-by-step explanation:
i took the quiz