[tex]f(x) = 7x[/tex] [tex]g(x) = \sqrt{x}[/tex] [tex]h(x) = x^2 + 7[/tex]
11)
[tex]g(f(4)) = \sqrt{7 \cdot 4} = \sqrt{28} = 2\sqrt{7}[/tex]
12)
[tex]h(g(49)) = 49 + 7 = 56[/tex]
13)
[tex]g(f(x)) = \sqrt{7x}[/tex]
14)
[tex]h(g(x)) = (\sqrt{x})^2 + 7 = x + 7[/tex]
15)
[tex](g \circ h)(x) = g(h(x)) = \sqrt{x^2 +7}[/tex]
16)
Let [tex]y = f^{-1}(x)[/tex] and [tex]f(y) = x[/tex]
[tex]4y - 3 = x\\4y = x + 3\\y = \frac{x + 3}{4}\\\\f^{-1}(x) = \frac{x + 3}{4}[/tex]
17)
Let [tex]y = g^{-1}(x)[/tex] and [tex]g(y) = x[/tex]
[tex]\frac{2y + 7}{3} = x\\ 2y + 7 = 3x\\2y = 3x - 7\\y = \frac{3x - 7}{2} \\\\g^{-1}(x) = \frac{3x - 7}{2}[/tex]
True or False: The distance between -7 and -13 dn a number line
a.
b.
c.
d.
please help me
Answer:
b
Step-by-step explanation:
the answer is - 11/12
Which equations are equivalent to the given equation?
2 – 5 = 11.2
..
5=11.2-x
X=11.2+5
X=11.2-5
x-11.2=5
What is the difference? PLEASE HELP
Shanice wanted to make note cards by
cutting pieces of paper in half. Before
starting she got two more pieces to use.
When she was done she had 20 half-pieces
of paper. With how many pieces did she
start?
Answer:
8 pieces of paper
Step-by-step explanation:
Since the paper was cut into two, divide the half-pieces by 2 go get the amount of full-sized paper. And since Shanie got 2 more pieces of paper before she started, you subtract 2 from 10, which leaves you with 8 pieces of full-sized paper.
A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 60.0 min at 95.0 km/h, 10.0 min at 55.0 km/h, and 35.0 min at 45.0 km/h and spends 50.0 min eating lunch and buying gas.
(a) Determine the average speed for the trip. km/h
(b) Determine the distance between the initial and final cities along the route. km
Step-by-step explanation:
(a) The average speed of a person for the trip is given by total distance traveled divided by total time taken.
[tex]V=\dfrac{d_1+d_2+d_3+d_4}{t_1+t_2+t_3+t_4}[/tex]
Since, distance = velocity × time
Also, 1 hour = 60 min
[tex]V=\dfrac{v_1t_1+v_2t_2+v_3t_3+v_4t_4}{t_1+t_2+t_3+t_4}\\\\V=\dfrac{95\times \dfrac{60}{60}+55\times \dfrac{10}{60}+45\times \dfrac{35}{60}+0\times 50}{\dfrac{60}{60}+\dfrac{10}{60}+\dfrac{35}{60}+\dfrac{50}{60}}\\\\V=50.48\ \text{km/h}[/tex]
The average speed for the trip is 50.48 km/h
(b) Total distance,
[tex]D=v_1t_1+v_2t_2+v_3t_3+v_4t_4\\\\D=95\times \dfrac{60}{60}+55\times \dfrac{10}{60}+45\times \dfrac{35}{60}+0\times 50\\\\D=130.41\ \text{km}[/tex]
The distance between the initial and final cities along the route is 130.41 km.
how do you write 1.6 x 10^4 in standard form
Answer:
16000
Step-by-step explanation: You would count 4 places after the one to the right and how how many places that is you’d add 0s to it
Hey there!☺
[tex]Answer:\boxed{1.6\times10^4}[/tex]
[tex]Explanation:[/tex]
To write an expression in standard form, you will have to rearrange the terms. 1.6 * 10^4 is already in its standard form.
So 1.6 * 10^4 in standard form would be written like this:
[tex]1.6\times10^4[/tex]
Hope this helps!☺
What is the solution for the inequality 5−3x>26?
Enter your answer as the correct inequality. For example, if your answer is x>42, enter your answer like this: x>42
Answer:
x < -7
Step-by-step explanation:
5−3x>26
Subtract 5 from each side
5-5−3x>26-5
-3x > 21
Divide each side by -3, remembering to flip the inequality
-3x/-3 < 21/-3
x < -7
Answer:
x < -7
Step-by-step explanation:
5 - 3x > 26
5 - 3x -5 > 26 - 5
-3x > 21
-3x ÷ -3 < 21 ÷ -3
x < -7
If m∠2=40°, what is the measure of ∠1 + ∠6?
Answer:
180°
Step-by-step explanation:
The diagram for this question has been attached to this response.
From the diagram;
(i) ∠2 and ∠6 are equal since they are corresponding angles. This implies that the measure of angle 2 (m∠2) is equal to the measure of angle 6 (m∠6). i.e
m∠2 = m∠6 ---------(a)
But m∠2 = 40°
Substitute this into equation (a) as follows;
40° = m∠6
∴ m∠6 = 40°
(ii) ∠1 and ∠2 are supplementary. This implies that the sum of the measures of angle 1 (m∠1) and angle 2(m∠2) is equal to 180°. i.e
m∠1 + m∠2 = 180° ------------------(b)
But m∠2 = 40°
Substitute this into equation (b) as follows;
m∠1 + 40° = 180°
m∠1 = 180° - 40°
m∠1 = 140°
(iii) The measure of ∠1 + ∠6 is given by;
m∠1 + m∠6
Substitute the values of m∠1 = 140° and m∠6 = 40° into the expression to get
m∠1 + m∠6 = 140° + 40°
m∠1 + m∠6 = 180°
Therefore the measure of ∠1 + ∠6 is 180°
Action figures are $8 a piece at a toy store. The toy store sold 26 action figures today. How much money did the toy store receive from selling action figures today?
The toy store received $208 from selling action figures.
Knowing that each action figure is $8 in the toy store, we can multiply that by the quantity of action figures sold to get the total amount of money received.
26 times $8 is $208.
Answer:
$208
Step-by-step explanation:
If the toys are $8 a peice and they sold 24 toys then they would recive $208. Think of it this way: if you multiply 8 times 2 you get 16, then you multiply 16 by 10 to represent 20 of the action figures. That would get you $160. Then multiply 8 times 6, and that gets you 48. Now add those two together. 160+48=$208
please give an explanation
-5 ·2³+7 =-33
Answer:
2³ = 8
-5*8 = -40
-40 + 7 == -33
Step-by-step explanation:
2³ = 8
-5*8 = -40
-40 + 7 == -33
Solve the equation x = square root of 27
Answer: 5.19615242271 to be exact
Step-by-step explanation: its honestly pretty ez
what is the distributive property of (6+9v)6 ?
Answer:
36 + 54 v
Step-by-step explanation:
Answer:
36+54v
Step-by-step explanation:
times 6x6 and 6x9 then put in the v
A milestone occurring in which of these increments of time will be the farthest to the right on a timeline? A. 10 months B. 90 days C. 8 years D. 16 weeks
Answer:
Step-by-step explanation:
16
The table below shows the number of tickets sold per
day for a Sadie Hawkins dance. The gym can hold 600
people. The final day of ticket sales is Thursday. Find
the most number of tickets they can sell on Thursday.
#
Day Tickets
Sold
MON 198
TUES 96
WED 204
Answer:
102 tickets
Step-by-step explanation:
start by adding
Mon 198
Tues 96
We'd 204
then you would get 498 and max people that can fit in the gym is 600 so then you would subtract 600-498 and get 102 so the maximum amount of tickets they can sell on Thursday is 102 tickets
-7/8*(- 3/8)= whts the answer ?
[tex]\text {Hi! Let's Solve this Problem!}[/tex]
[tex]\text {We know that Multiplying a Negative to a Negative will Equal a Positive.}[/tex]
[tex]\text {\underline {Multiply}}[/tex]
[tex]\text {-7/8*(-3/8)=}[/tex]
[tex]\text {Your Answer Would Be:}[/tex]
[tex]\fbox {21/64}[/tex]
[tex]\text {Best of Luck!}[/tex]
15,000 is increased by 5%. What is the new value?
Step-by-step explanation:
105% of 15000
=105/100 × 15000/1
=15,750
1.7m^2+6.5n-4n+2.5m^2-n in simplest form
Answer:
9.5m^2+1.5n
Step-by-step explanation:
Find the values of x and y
Answer:
x = 29.44
y = 34
Step-by-step explanation:
For this problem, we will simply use trigonometry to find the values of y and x for the given triangle.
The two trigonometric functions we will use are tangent and sine.
The general form for tangent is:
tan (Θ) = opposite / adjacent
The general form for sine is:
sin (Θ) = opposite / hypotenuse
For our given triangle, let's solve for x.
tan (30) = 17 / x
x * tan(30) = (17 / x) * x
x tan(30) = 17
x tan(30) * ( 1 / tan(30) ) = 17 * ( 1 / tan(30) )
x = 17 / tan(30)
x = 29.44
Now, let's solve for y.
sin (30) = 17 / y
y * sin(30) = (17 / y ) * y
y sin (30) = 17
y sin (30) * ( 1 / sin(30) ) = 17 * ( 1 / sin(30) )
y = 17 / sin(30)
y = 34
Hence, the values of x and y in our triangle are as follows:
x = 29.44
y = 34
Cheers.
6. A high school graduate works fulltime. She needs to borrow $1,500 to
attend the local junior college, but she won't be able to pay it back for
2
years. Calculate how much she will have to pay back with these two
loan plans. Which plan should she choose? Justify your answer,
Bank A: Simple interest, 18 percent per year
Bank B: Compound interest, 12 percent per year
Answer:
I think you would have to multiply 1,500 by 12 and also by 18 to figure it out.
Step-by-step explanation:
" "
What is 1/9 as a decimal rounde to 2decimal places.
Answer:
3/11 = 0.27 is the answer of this question
What is the answer to (7-3)^2x(5-2)^3+4^2 ?
Step-by-step explanation:
(7-3)^2*(5-2)^3+4^2
=(4)^2*(3)^3+16
=16*27+16
=432+16
=448
you can sort 8 pieces of mail in 10 seconds how many pieces of mail should you be able to sort in 45 minutes?
Answer:
oh this was easy!
Step-by-step explanation:
1 minute = 60 seconds
45 min = 2700 sec
8 pieces of mail ?
------------------ = -------------------
10 seconds 2700 sec
Solve the ratio/proportion by cross multiplication
or equal ratio method by factor of 270:
? = 2160 pieces of mail
i hope this helped
Four cookies cost $7.00. At this rate, how much will 9 cookies cost?
Answer:
9 cookies will cost $15.75.
Step-by-step explanation:
$7/4c × 9c
= $63/4
= $15.75
Hope this helped!
$2.56 divided by $55.23
Answer:
21.57
Step-by-step explanation:
please answer asap. thank you :).
Answer:
A
Step-by-step explanation:
simplify the ratio
2km: 3400m
Answer:
[tex]\displaystyle \frac{10}{17}[/tex]
Step-by-step explanation:
Fraction Simplifying
We are given the ratio 2 Km:3400 m. This can be written in fraction form as:
[tex]\displaystyle \frac{2\ km}{3400\ m}[/tex]
Since 2 Km = 2000 m:
[tex]\displaystyle \frac{2\ km}{3400\ m}=\frac{2000\ \not{m}}{3400\ \not{m}}[/tex]
We need to simplify the fraction:
[tex]\displaystyle \frac{2000}{3400}[/tex]
We cancel out two zeroes, which is like dividing both numbers by 100:
[tex]\displaystyle \frac{20\not{0}\not{0}}{34\not{0}\not{0}}[/tex]
The remaining fraction is:
[tex]\displaystyle \frac{20}{34}[/tex]
Dividing both by 2:
[tex]\displaystyle \frac{10}{17}[/tex]
Since the denominator is a prime number, no more simplifying is possible, thus the given ratio is equivalent to:
[tex]\boxed{\displaystyle \frac{10}{17}}[/tex]
Identify the initial value, a, and base, b, of the function f(x)=ab^x if its graph passes through the points (0, 4) and (1, 20)
Answer:
a = 4, b = 5
Step-by-step explanation:
Given the exponential function
f(x) = a[tex]b^{x}[/tex]
Use the given points to find a and b
Using (0, 4 ) , then
4 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ) , thus
a = 4 , so
f(x) = 4[tex]b^{x}[/tex]
Using (1, 20 ) , then
20 = 4b ( divide both sides by 4 )
b = 5
Very easy! I'm still going to give 100 points because I need this answered! Brainleist will be given!
Answer:
The centroid divides the medians in a 2:1 ratio.
Step-by-step explanation:
The median of a triangle is a segment joining any vertex to the midpoint of the opposite side. The point where the three medians meet is the centroid.
The centroid divides the medians in a 2:1 ratio.
Answer:
Step-by-step explanation:
Tony's father is thinking of buying his son a six-month movie pass for $40. With the
pass, movies cost $3.00 each.
Answer:
whats the question??
Step-by-step explanation: