Answer:
[tex](fof^{-1})(x)=x[/tex]
Step-by-step explanation:
Composition of two functions f(x) and g(x) is represented by,
(fog)(x) = f[g(x)]
If a function is,
f(x) = (-6x - 8)² [where x ≤ [tex]-\frac{8}{6}[/tex]]
Another function is the inverse of f(x),
[tex]f^{-1}(x)=-\frac{\sqrt{x}+8}{6}[/tex]
Now composite function of these functions will be,
[tex](fof^{-1})(x)=f[f^{-1}(x)][/tex]
= [tex][-6(\frac{\sqrt{x}+8}{6})-8]^{2}[/tex]
= [tex][-\sqrt{x}+8-8]^2[/tex]
= [tex](-\sqrt{x})^2[/tex]
= x
Therefore, [tex](fof^{-1})(x)=x[/tex]
Please please help!!! Study the diagram of circle Z. Points P, O, Q, and R lie on circle Z in such a way that OP¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯. If m∠QZR=(2x+9)∘ and m∠PZO=(4x−11)∘, what is the value of x?
x=3.3
x=15.3
x=10
x=12
Answer:
The correct option is
x = 10
Step-by-step explanation:
in a circle Given that chord [tex]\overline {OP}[/tex] is congruent to [tex]\overline {QR}[/tex], we have;
Measured angle m∠RZQ is congruent to measured angle m∠PZO
Congruent chords are subtended by congruent angles at the center of the circle
Therefore we have;
4·x - 11 is equal to 2·x + 9
4·x - 2·x = 9 + 11
2·x = 20
x = 10
The value of the measured angles are;
4·x - 11 = 4×10 - 11 = 40 - 11 = 29°
The value of x is 10°.
Answer:
x=10
Step-by-step explanation:
4·x - 11 is equal to 2·x + 9
4·x - 2·x = 9 + 11
2·x = 20
x = 10
The value of the measured angles are;
4·x - 11 = 4×10 - 11 = 40 - 11 = 29°
The value of x is 10°
Definition:A sailboat set a course of N 25° E from a small port along a shoreline that runs north and south. Sometime later the boat overturned and the crew sent out a distress call. They estimated that they were 12 miles away from the nearest harbor, which is 28 miles north of the port they had set sail from. If a rescue team leaves from the harbor, find all possible courses the team must follow in order to reach the overturned sailboat.
Answer:
S 75°E
S 55°E
Step-by-step explanation:
Take the law if sines of a triangle:
[tex] \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC} [/tex]
Where,
a = 28 miles
B = 25°
b = 12 miles
First solve for A, using the law of sines:
[tex] \frac{a}{sinA} = \frac{b}{sinB} [/tex]
[tex] \frac{28}{sinA} = \frac{12}{sin25} [/tex]
Cross multiply:
[tex] 28 sin25 = 12 sinA [/tex]
[tex] 11.83 = 12 sinA [/tex]
[tex] Sin A = \frac{11.83}{12} [/tex]
[tex] Sin A = 0.986 [/tex]
[tex]A = sin^-^1(0.986)[/tex]
[tex] A = 80.44 degrees [/tex]
Since A = 80.44° find A supplement, A`:
A` = 180 - 80.44
A` = 99.56°
If A` + B < 180°, find C.
Thus,
A` + B = 99.56 + 25 = 124.56
We can see that A` + B < 180
Find C:
C = 180 - (80.44+25) = 74.56° ≈ 75°
C` = 180 - (99.56+25) = 55.44° ≈ 55°
Rewrite in bearing form:
S 75°E
S 55°E
BRAINLIEST PLS HELP ASAP LINEAR EQUATIONS
Answer:
first one
Step-by-step explanation:
Tracey bought 10 movies
some cost 13 and the others 16
Let x be the movies that cost 13 and y ones that cost 16
we can state that
x+y = 10since Tracey both ten
13x+ 16y = 139since the total price is 139
so the system is :
[tex]\left \{ {{13x+16y=139} \atop {x+y=10}} \right.[/tex]
Please help me!
30g of cornflakes contain 2.5g of fat
How many grams of fat are there in 566g of cornflakes?
Give your answer to 1 dp
Answer:
47 .2 Grams 0f FatStep-by-step explanation:
[tex]30g ----> 2.5g -fat\\566g ----> xg -fat\\30x = 1415\\\frac{30x}{30} =\frac{1415}{30} \\\\x = 47.1666\\\\x = 47.2g of Fat[/tex]
Amanda teaches violin lessons for $21.30 per hour. How many hours of lessons must Amanda give to make no less than $894.60?
No less than 42 lessons
No less than 35 lessons
No less than 45 lessons
No less than 33 lessons
Answer:
No less than 42 lessons
Step-by-step explanation:
To find the total numbers of hours needed to teach, divide the total amount of money needed by the amount of money made an hour.
$894.60/$21.30 = 42
Is 2+4x-5x^2 in standard form?!
Answer:
y=-5x^2+4x+2
Step-by-step explanation:
Answer:
-5x² + 4x + 2
Step-by-step explanation:
Standard Form: ax² + bx + c
All you need to do is rearrange to have the highest degree first.
PLEASE HELP ASAP
Right triangle ABC is located at A (−1, −2), B (−1, 1), and C (3, 1) on a coordinate plane. What is the equation of a circle A with radius segment AC?
A (x + 1)2 + (y + 2)2 = 9
B (x + 1)2 + (y + 2)2 = 25
C (x − 3)2 + (y − 1)2 = 16
D (x − 3)2 + (y − 1)2 = 25
Answer:
b
Step-by-step explanation:
Answer:
B) (x + 1)2 + (y + 2)2 = 25
Step-by-step explanation:
What is the y-intercept of the graph of the function f(x) = x^2 + 3x + 5?
Answer:
(0,5)
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y.
y=x^2 + 3x + 5
y=(0)^2 + 3(0) +5
y=0+0+5
y=5
Since there is no x coordinate for a y-intercept, the answer is (0,5)
Answer:
A. (0, -5) is the right answer on edge 2021
HELPPPP Enter the ratio as a fraction in lowest terms (2 ft to 24 in.)Enter the ratio as a fraction in lowest terms
(27 minutes to 24 minutes) Enter the ratio as a fraction in lowest terms (no decimals).
(8.0 calories to 5.6 calories)
Answer:
I think the answers are 1 to 1 ,9 to 8 , 10 to7
find the exact length of the third side
Answer:
8
Step-by-step explanation:
We will the pythagorian theorem :
let x be the third side x²+6²= 10²x²= 100-36 x=[tex]\sqrt{64}[/tex] x=8Answer:
b=8
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle:
a^2+ b^2 = c^2 where a and b are the legs and c is the hypotenuse
a=6 and b = 10
6^2 + b ^2 = 10^2
36+ b^2 = 100
b^2 = 100-36
b^2 = 64
Taking the square root of each side
sqrt(b^2) = sqrt(64)
b = 8
Which number is greater: 35% or 3.5?
Answer: 3.5
Step-by-step explanation:
Tournament scores for 92 golfers are distributed normally. Two
statistics from this tournament are given below.
mean score 74
standard deviation 2.5
What is the approximate percentage of golfers that scored
between 69 and 79?
A. 27%
B. 68%
C. 74%
D. 95%
Answer: D. 95%
Step-by-step explanation: If the difference of the scores given is 5 above and below the mean, that represents 2 standard deviations.
In normal distribution, 2 standard deviations above and below the mean represent 95% of all the inputs.
The test statistic of z equals = 2.94 2.94 is obtained when testing the claim that p not equals ≠ 0.877 0.877. A. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. B. Find the P-value. C. Using a significance level of alpha α equals = 0.01 0.01, should we reject Upper H 0 H0 or should we fail to reject Upper H 0 H0?
Answer:
Step-by-step explanation:
The claim being tested is that p not equals ≠ 0.877
A) This is the alternative hypothesis and it is a two tailed test. It means that it can be in either direction.
B)Given that z = 2.94, the p value would be determined from the normal distribution table. Since the curve is symmetrical and it is a two tailed test, the p for the left tail and the right tail would be considered. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the test z score in the right tail is 1 - 0.998 = 0.002
We would double this area to include the area in the left tail of z = - 2.94 Thus
p = 0.002 × 2 = 0.004
C) Since alpha, 0.01 > than the p value, 0.004, then we would reject the null hypothesis, H0
1/4 of a pipe is white , 1/2part of the remaining is blue. If the remaining part is black and the length of this blackpart is 5 1/4cm, find the length of the pipe.
Answer: 14 cm
Step-by-step explanation:
let's total length = h
white = 1/4h
remain = h - 1/4h
=3/4h
blue = 1/2 of remaining
=1/2 of 3/4h
=3/8h
remain part black = 3/4h - 3/8h
=3/8h
according to the question
3/8h = 5 1/4 cm
h = 14 cm
length of the pipe is 14 cm
Answer:
14The length of the pipe is 14.
Solution,
Let the total length be X cm
[tex]x - \frac{x}{4} -{ (x - \frac{x}{4} ) \times \frac{1}{2}} = 5 \frac{1}{4} \\ x - \frac{x}{4} - \frac{x}{2} + \frac{x}{8} = \frac{21}{4} \\ \frac{8x - 2x - 4x + x}{8} = \frac{21}{4} \\ \frac{3x}{8} = \frac{21}{4} \\ 3x \times 4 = 21 \times 8 \\ 12x = 168 \\ x = \frac{168}{12} \\ x = 14[/tex]
Hope this helps..
Good luck on your assignment..
Jackie loves to cook fried foods. She recorded the total amount of oil that she used each month in the table below.
In January, she used 3/5 of the amount of oil that she used in February.
Fill in the amount of oil that Jackie used in January in the table below.
Month Liters of oil used
january ?
February 2/3
March 1 1/2
Answer:
In January
she used 3/5 of what she used in February.
In February she used 2/3 litres of oil.
So it is 3/5 of 2/3 to find what amount she used in January.
3/5 × 2/3 = 6/15
If we simplify 6/15 we find 2/5 as our answer.
So our answer is 2/5 litres.
Find the volume of the composite figure below
Answer:
1386 in³
Step-by-step explanation:
Volume of the composite cone = volume of a hemisphere + volume of a cone
=>Find the volume of cone
Volume of cone = ⅓πr²h
π = 3.142
r = 7 in
h = =√(15² - 7²) [using Pythagorean theorem to solve for height given the slant height and radius]
h = √(225 - 49)
h = √176 ≈ 13 in
Volume of cone = ⅓*3.142*7²*13
= ⅓*2001.454 ≈ 667 in³
=>Find volume of hemisphere.
Volume of hemisphere = ½*volume of sphere = ½*4/3πr³ = ⅔πr³
π = 3.142
r = 7 in
Volume = ⅔*3.142*7³ ≈ 719 in³
Volume of composite figure = 667+719 = 1386 in³
In the diagram below, AB is parallel to CD. What is the value of x?
Answer:
A. 120 degrees.
Step-by-step explanation:
The two angles are alternate angles, which means they are congruent. So, x is also 120 degrees.
Hope this helps!
Can someone plz help me Solve this Equation Solve for X
Answer:
x = 4
Step-by-step explanation:
If two secants are drawn to a circle from one exterior point, then the product of the exterior segment and whole segment is same. i.e 6×(6+x) = 5×(5+x+3)
=> 6x+36 = 5x + 15 +25
=> x = 40-36
=> x = 4
I hope it's the right answer.
Answer:
x = 4
Step-by-step explanation:
Given 2 secants drawn to a circle from an external point, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
6(6 + x) = 5(5 + x + 3), that is
36 + 6x = 5(8 + x) = 40 + 5x ( subtract 5x from both sides )
36 + x = 40 ( subtract 36 from both sides )
x = 4
The question i want to know is linked below. Please help :)
Answer:
Hey there!
To solve this problem, we want to find the LCM (least common multiple) of the two numbers.
The numbers are 25 and 30.
25=5x5
30=2x3x5
LCM is 5x5x2x3, or 150.
Thus, in 150 minutes is when the next bus will leave.
150 mins is equal to 2 hours and 30 mins, or 2.5 hours.
8 AM + 2.5 hrs = 10:30 AM.
Thus, the next time the busses leave together would be at 10:30 AM.
Let me know if this helps :)
Two similar triangles are shown.
to create
AXYZ was dilated, then
AQAG
translated
reflected
dilated
rotated
Answer: reflected
Step-by-step explanation:
The triangle ΔXYZ was dilated and then it was reflected to create ΔQAG.
What are the types of translations?There are three types of translations -
reflectionrotationdilationGiven is a triangle ΔXYZ.
It is asked to find the type of translation that would result in ΔQAG.It can be seen in the figure that the triangle XYZ is reflected across the given line to form triangle QAG.So, we can we can replace the blank with Option - 2 : reflected.Therefore, the triangle ΔXYZ was dilated and then it was reflected to create ΔQAG.
To solve more questions on graph rotation, visit the link below-
https://brainly.com/question/19527326
#SPJ7
A line contains the point (8,-5). If the slope of the line is write the equation of the line using point-slope form
Answer:
[tex]\bold{y+5=\frac57(x-8)}[/tex]
Step-by-step explanation:
[tex]y-y_1=m(x-x_1)[/tex] - point-slope form of Equation of the Line
[tex](8,-5)\ \ \implies x_1=8\,,\ y_1=-5\\\\m=\frac57\\\\equation:\\{}\qquad\qquad y-(-5)=\frac57(x-8)\\\\{}\qquad\qquad y+5=\frac57(x-8)[/tex]
The revenue for a company producing widgets is given by y=-25x^2-50x+200, where x is the price in dollars for each widget. The cost for the production is given by y=25x-10. Determine the price that will allow the production of the widgets to break even.
Answer:
When they create 3.44 products and make a revenue of $76.027, they will break even.
Step-by-step explanation:
To do this, simply graph the 2 equation in a graphing calculator and analyze the graph for where the 2 graphs intersect. Discard the negative intersection because we cannot have a negative production. You should see that your intersection point is (3.441, 76.027).
A system of equations is shown on the graph below. How many solutions does this system have?
Answer:
[tex]\boxed{1 \: \: \mathrm{solution}}[/tex]
Step-by-step explanation:
The point where two lines intersect is the solution to the system of equations.
The two lines intersect at (-1, 2).
x = -1
y = 2
y = 2x + 4
y = -x + 1
Plug y as -x+1 in the first equation.
-x + 1 = 2x + 4
-x - 2x = 4 - 1
-3x = 3
x = -1
Plug x as -1 in the second equation.
y = -(-1) + 1
y = 1 + 1
y = 2
Answer:
Hey there!
Only one solution, because they intersect at only one point.
Hope this helps :)
Sam is two times Sydey's
their combined
age is 36. What is Sydney's age.
Answer:
12 years old
Step-by-step explanation:
Let's call Sydney's age x and Sam's age 2x. We can write:
x + 2x = 36
3x = 36
x = 12 so the answer is 12 years old.
Which number is the opposite of -3? Starting at -3, how many steps does it take to get to the opposite of -3? What does this number of steps represent?
Answer:
3
Step-by-step explanation:
The Absolute value of -3 is 3 because it's the distance away from 0. Both have the same distance away from 0.
The opposite number of the integer number negative 3 will be 3.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The number that produces zero when multiplied by an is known as the additive inverse of a number, or a, in arithmetic. The opposite, a shift in the sign, and negation are other names for this number.
The number is given below.
⇒ - 3
The opposite of the number negative 3 will be given as,
⇒ - (-3)
⇒ 3
The opposite number of the integer number negative 3 will be 3.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
If (x + 2) is a factor of x3 − 6x2 + kx + 10, k
Answer:
k = -11
Step-by-step explanation:
Let [tex]p(x) = x^3-6x^2+kx+10[/tex]
And x+2 is a factor of p(x)
Let x+2 = 0 => x = -2
Putting in p(x)
=> p(-2) = [tex](-2)^3-6(-2)^2+k(-2)+10[/tex]
By remainder theorem, Remainder will be zero
=> 0 = -8-6(4)-2k+10
=> 0 = -8-24+10-2k
=> 0 = -22-2k
=> -2k = 22
Dividing both sides by -2
=> k = -11
Which system below has no solution? y = 4x and y = 2x - 3 y = -4x and y = 2x - 3 y = -4x and y = 2x + 3 y = -4-x and y = 2x - 3
Answer:
y=4x
Step-by-step explanation:
this is because all other systems are defined and can be solved simultaneously...
pls lime and follow me ...i follow back...thanks
Dave ran 3.52 miles in the same time
that Eric ran 2.44 miles. How much
further did Dave run than Eric?
Helppp!!!! please!!!
Answer:
F. cylinder
Step-by-step explanation:
A cylinder has a circle for its base, which has no vertices and is not a polygon. This, therefore, disqualifies a cylinder as a polyhedron.
What is the value of the angle marked with 2?
Answer:
Step-by-step explanation:
Consecutive angles cut by a common transversal are supplementary. That means that
x + 87 =180 Subtract 87 from both sides.
x+87-87=180-87
x = 93