Answers
Answer:
[tex]g^-^1(x)=-8[/tex]
[tex]h^-^1(x)=\frac{x-4}{3}[/tex]
[tex](h^-^1 \ o\ h)(-3)=-3[/tex]
Step-by-step explanation:
When given the following functions,
[tex]g=[(-2,-7),(4,6),(6,-8),(7,4)][/tex]
[tex]h(x)=3x+4[/tex]
One is asked to find the following,
1. Question 1
[tex]g^-^1(4)[/tex]
When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;
[tex]g^-^1(4)[/tex]
[tex]g(4)=6\\g(6)=-8\\g^-^1(4)=-8[/tex]
2. Question 2
[tex]h^-^1(x)[/tex]
Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,
[tex]h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)[/tex]
[tex]h^-^1(x)=\frac{x-4}{3}[/tex]
3. Question 3
[tex](h^-^1 \ o\ h)(-3)[/tex]
This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function ([tex]h^-^1[/tex]) and simplify. Then substitute (-3) into the result.
[tex]h^-^1\ o\ h[/tex]
[tex]\frac{(3x+4)-4}{3}\\\\=\frac{3x+4-4}{3}\\\\=\frac{3x}{3}\\\\=x[/tex]
Now substitute (-3) in place of (x),
[tex]=-3[/tex]
Related Questions
f(x+k) what is the value of k
Answers
Answer:
k = -3
Hope this helps!
Answer:
Step-by-step explanation:
f(x+k) is a horizontal shift of -k units.
Since the vertex went from 1 to -2, k = 3.
Rubber balls are packaged in a box with dimensions 8.5 cm, 5 cm, 5 cm.
Each ball has a diameter of 3 cm. If there are a dozen balls in the box, how
much space in the box is not occupied by the rubber balls? Round your
answer to the nearest tenth.
Answers
Answer:
42.9 cm^3
Step-by-step explanation:
Volume of the box= (base x width x height) = 8.5 x 5 x 5 = 212.5 cm^3
Radius of a ball = 1.5 cm
Volume of a ball = 4/3 * radius^3 * pi = 4/3 x 1.5^3 x pi = 14,137167 cm^3
Volume of the balls = 14,137167 x 12 = 169,646003 cm^3
Final answer = 212.5 - 169,646003 = 42.9 cm^3
a walking path across a park is repersented by the equation y=-2x-7. A new path will be built perpendicular to this path the paths will intercept at the point (-2,-3) identify the equation that represents the new path
Answers
Answer:
y + 3 = (1/2)(x + 2)
Step-by-step explanation:
The slope of the original path is -2. Any new path perpendicular to this one will have a slope which is the negative reciprocal of -2, which here is 1/2.
Use the point-slope formula y - k = m(x - h):
y - (-3) = (1/2)(x - (-2)), or
y + 3 = (1/2)(x + 2) represents the new path.
4x^2-400=0
square roots and solving quadratics
Answers
Answer:
x = ±10
Step-by-step explanation:
4x² - 400 = 0
Add 400 to both sides
4x² = 400
Divide both sides by 4
x² = 100
Take the square root of both sides
x = ±10
A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $20.00 to prepare, and it costs $125.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs
Answers
Answer:
25
Step-by-step explanation:
From the given information;
Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.
= 1000x
Thus, the required number of hours it will take can be computed as:
[tex]\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}[/tex]
cost per hour = 125
If each plate costs $20 to make, then the total number of plate will equal to 40x
∴
The total cost can be computed as:
[tex]C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)[/tex]
[tex]C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)[/tex]
At C'(x) = 0
[tex]\dfrac{12500}{x^2} = 20[/tex]
[tex]\dfrac{12500}{20} = x^2[/tex]
[tex]x^2= 625[/tex]
[tex]x = \sqrt{625}[/tex]
x = 25
[tex]C'' (x) = -12500 \times \dfrac{-2}{x^3} +0[/tex]
[tex]C'' (x) = \dfrac{25000}{x^3}[/tex]
where; x = 25
[tex]C'' (x) = \dfrac{25000}{25^3}[/tex]
C''(x) = 1.6
Thus, at x = 25, C'' > 0
As such, to minimize the cost, the printer needs to make 25 metal plates.
Question 7
Find the volume.
Answers
Answer:
A: 686π≈2,156
Step-by-step explanation:
First, you need to find the area of the circle then times that by 14.
π[tex]r^{2}[/tex] Formula for the area of a circle
π[tex]7^{2}[/tex] r stands for radius, so you divide the diameter by 2 and get 7.
π49 This is the area of the circle
π49×14 Now multiply by 14
=686π This is your answer.
=2155.13256 When you times it by pi this is what you get
=2156 This is your answer if you want it rounded up
A number that has both a whole number and a fraction is called a(n)
O A) improper fraction
OB) mixed number
OC) whole fraction
OD) combined number
Answers
Answer:
mixed number <3
Step-by-step explanation:
vause it is
A 6-digit PIN number is selected. What it the probability that there are no repeated digits?
The probability that no numbers are repeated is
Write your answer in decimal form, rounded to the nearest thousandth.
Submit Question
Answers
Answer: 0.1512
So I know that there are 10 possible digits that can be selected, each time the pool of selected digits gets smaller.
The first digit cannot be zero therefore there are 9 possibilities for this digit. Then, seeing as the order doesn't matter, but repeats do, so I thought a permutation would be the correct method to apply.
9 * ((9!)/(9-5!)) = 136,080 (<-- total number of 6 digit numbers)
Without repeats and no 0 as first digit
Total number of 6 digit numbers = 10^6
Therefore the probability of this scenario happening is:
(139,080/10000000) = 0.13608
Answer:
we got 10 digits to choose from for the first digit, 9 for the second and so on
[tex]10 \times 9 \times 8 \times 7 \times 6 \times 5[/tex]
scenarios that got no repeated digits.
the total number of possible PINs with 6 digits is
[tex]10 \times 10 \times 10 \times 10 \times 10 \times 10[/tex]
or just 10⁶
so the fraction we are looking for is the number of valid states decided by all possible states.
[tex] \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5}{ {10}^{6} } [/tex]
=0.1512
rounded to the nearest thousandth it's
0.151
(actually, I didn't expect the probability to be around 15 percent)
hope it helps. asked question whenever you like
kind regards
Alex
Kareem's rectangular flower bed measures 3ft long and 2ft wide. He wants to cover the flower bed in mulch. He knows the area each bag of mulch covers, but only in square centimeters
Answers
Hey buddy I am here to help!
Area of flower bed = 3 x 2 = 6ft
1 ft = 30.48cm
6 x 30.48 = 182.88cm2
which statement is true?
Answers
Answer:
The slope of function A is greater than the slope of function B
hope it is helpful to you
HPC Education
Year 5* 6 Problem Solving Questions
10. Megan and Olivia had some money. They made a donation of $100 together. Megan donated of
her money. After donating $24, Olivia found that she had $32 more than Megan. What was the
sum of money both of them had at first
Answers
solve the following equation algebraically please
Answers
Answer:
b. x = ±2
Step-by-step explanation:
3x² = 12
Divide both sides by 3
x² = 4
Taske the square root of both sides
x = ±2
Will mark brainlest!
formula of (x+1)cube
Answers
Answer:
(x+1)^3=x^3+3x^2+3x+1
Answer:
[tex](x+1)^{3} = x^{3} + 3x^{2} +3x+1[/tex]
Step-by-step explanation:
[tex](x+1)^{3} = x^{3} + 3x^{2} +3x+1[/tex]
[tex](A+B)^{3} = A^{3} + 3A^{2}B+3AB^{2} + B^{3}[/tex]
x + 2∕5 = 1∕3 for x.
Answers
Answer:
?
Step-by-step explanation:
?
.....................................:.
Answers
Answer:
..........................................................................................................................................................................
Answer:
um..BG should also be equal to 12 I guess
A roundabout is a one-way circular intersection.
About how many feet would a car travel if it drove
once around the roundabout? Round to the
nearest foot.
Answers
Answer:
[tex]471\:\mathrm{ft}[/tex]
Step-by-step explanation:
In one full rotation around the roundabout, the car is travelling a distance equal to the circumference, or the perimeter, of the circle. The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2r\pi[/tex]. In the diagram, the diameter is labelled 150 feet. By definition, the radius of a circle is exactly half of the diameter of the circle. Therefore, the radius must be [tex]\frac{150}{2}=75[/tex] feet. Thus, the car would travel [tex]2\cdot 75\cdot \pi=471.238898038=\boxed{471\:\mathrm{ft}}[/tex]
if someone can explain this it would really help.
Answers
Answer:
6
Step-by-step explanation:
KL = 26-(11+9) = 26-20 =6
Answer:
KL is 6
Step-by-step explanation:
IL is 26, IJ = 9 JK= 11
IL= IJ + JK + KL
26= 9 + 11 + KL
Rearrange
KL= 9 + 11 - 26
= 6
Find the surface area of the
prism.
Answers
Answer:
D. 464 ft²
Step-by-step explanation:
Area of trapezoidal prism = h(b + d) + l(a + b + c + d)
Where,
h = 4 ft
a = 5 ft
b = 6 ft
c = 5 ft
d = 12 ft
l = 14 ft
Plug in the values into the formula
Area of trapezoidal prism = 4(6 + 12) + 14(5 + 6 + 5 + 12)
= 4(18) + 14(28)
= 72 + 392
= 464 ft²
A) Abdul invests 400$ at 6.05% per year simple interest, calculate how much interest Abdul receives
B) Samia receives 400$ for 2 years at 6% per year compound interest, give your answer in 2 decimal places
Answers
Answer:
$24.20
amount invested = $356
Interest = $44
Step-by-step explanation:
Samia receives a total amount of 400$ for 2 years at 6% per year compound interest, give your answer in 2 decimal places
Simples interest = amount invested x time x interest rate
400 x 0.065 x 1 = $24.20
b. interest = amount received - amount invested
Amount invested = amount received / (1 + r)^n
r = interest rate
n = number of years
400 / (1.06)^2 = 356
Interest = 400 - 356 = $44
Answer this question for points
Answers
Answer:
kjhgfdcxcfvghj
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
Consider function h.
Answers
Answer:
33
Step-by-step explanation:
A man leaves the town of Elmsville at 8:00 am and drives to Oak City at a constant rate of 50 miles per hour. Two hours later, a woman leaves Elmsville following the same route to Oak City. The man and woman arrive in Oak City at 3:00 p.m. What was the rate of the woman
Answers
Answer: 70 mph
Step-by-step explanation:
Given
A man leaves the town of Elmsville at 8:00 am and reach oak city at 3 Pm
Rate of driving is 50 miles per hour
time taken by man [tex]t=7\ hr[/tex]
Woman leaves 2 hour later and reach by 3 Pm, so time taken is [tex]5\ hr[/tex]
Distance traveled by both the person is same
[tex]\therefore 50\times 7=v\times 5\quad[v=\text{rate of woman}]\\\\\Rightarrow v=\dfrac{50\times 7}{5}\\\\\Rightarrow v=70\ mph[/tex]
Thus , the rate of woman is 70 miles per hour.
What is the length of sides of the square shown below? 45 2 90 A. 2sqrt(2) B. 4sqrt(2) C. 1 OD. sqrt(2) E. 4 F. 2
Answers
Answer:
Uh oh! It looks like your question is missing some crucial information.Step-by-step explanation:
There is no " square shown below"
Can someone help me?
Answers
Answer:
The slope is 2
Step-by-step explanation:
Slope formula:
m=(y2-y1)/(x2-x1)
Given:
y2 = -10
y1 = -6
x2 = 2
x1 = 4
Work:
m=(y2-y1)/(x2-x1)
m=(-10 + 6)/(2 - 4)
m= (-4)/(-2)
m = 2
Calculator
What is M
Put your answer in the box
°
Answers
Answer:
2
Step-by-step explanation:
9m + 25m + 22 = 90
34m = 90 - 22
34m = 68
m = 68 / 34
m = 2
Answer:
m = 2
Step-by-step explanation:
GLI forms a 90 degree angle
Set your formula up as
90 = 9m + 25m + 22
90 - 22 = 34m
68 = 34m
68/34 = m
2 = m
PLEASE HELP !! Whoever gets it right gets brainliest
Answers
Answer:
21
Step-by-step explanation:
4x-2=3x+19
4x-3x=19+2
x=21
Answer:
x = 21
Step-by-step explanation:
These are opposite angles and are therefore equal.
Equate the two angles to solve for x.
4x-2 = 3x+19
subtract 3x-2 from either side (i.e. numbers on the left, and variables on the right)
4x-2 -(3x-2) = 3x+19 - (3x-2)
x = 21
check: 4x-2= 82, 3x+19=82, so solution is good.
Value-Mart had 2,371 customers last week. Each customer donated $2 to the food bank. How much money did Value-Mart raise for the food bank? *
Answers
9514 1404 393
Answer:
$4,742
Step-by-step explanation:
The total of donations is the product of the number of donations and the amount of each.
(2371 customers) × ($2/customer) = $(2371×2) = $4742
Value-mart raised $4,742 for the food bank last week.
_____
You could find the total donated by adding the 2371 donations. Multiplication was invented to make repeated addition easier. When the sum consists of 2371 instances of $2, we can find the total by multiplying $2 × 2371.
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
You find that the going rate for a home mortgage with a term of 30 years is 7% APR. The lending agency says that based on your income, your monthly payment can be at most $770. How much can you borrow? (Round your answer to the nearest cent.)
Answers
Answer:
115736.83
Step-by-step explanation:
Effective rate:
.07/12= .005833333333
[tex]770(\frac{1-(1+.005833333)^{-30*12}}{.005833333333})=115736.83[/tex]
Step-by-step explanation:
Answer:
115736.83
Step-by-step explanation:
Effective rate:
.07/12= .005833333333
770(\frac{1-(1+.005833333)^{-30*12}}{.005833333333})=115736.83770(
.005833333333
1−(1+.005833333)
−30∗12
)=115736.83
factorize,
m
[tex] {m }^{2} - 40 + 6m[/tex]
Answers
Answer:
Step-by-step explanation:
m^2-40+6m
=m^2+6m-40
=m^2-(10-4)m-40
=m^2-10m+4m-40
=m(m-10)+4(m-10)
=(m+4)(m-10)
What is the area of the parallelogram shown
Answers
9514 1404 393
Answer:
60 square units
Step-by-step explanation:
The area is given by the formula ...
A = bh
The base of this parallelogram is 15 units, and its height is 4 units. The area is ...
A = (15 u)(4 u) = 60 u²
The area is 60 square units.