The composite of functions f(x) and g(x) is given by:
[tex](f \circ g)(x) = -60x + 383[/tex]
What is a composite function?The composite function of f(x) and g(x) is given by:[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = 30x - 7[/tex]
[tex]g(x) = 13 - 2x[/tex]
Hence, the composite function is:
[tex](f \circ g)(x) = f(g(x)) = f(13 - 2x) = 30(13 - 2x) - 7 = -60x + 383[/tex]
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|-3+(-1)|= simply the expression
Answer:
4
Step-by-step explanation:
First, solve in the brackets,
-3+(-1)
-3-1
-4
Since it is absolute value, take the minus sign away,
therefore the answer is 4
PLEASE HELP SUPER URGENT WILLING TO GIVE EXTRA POINTS !!!!! 4-8
A new firehouse is being built equidistant from three other fire stations. Positioned on a grid, the current fire stations would be located at (3, 7), (−1, −1), and (−4, 8). What are the coordinates of the location where the new firehouse should be built? (PLEASE INCLUDE AN EXPLANATION)
Answer:
[tex](-\frac{3}{22},\frac{185}{22} )[/tex]
Step-by-step explanation:
Step 1: Find out what the question is asking
Because we want the point to be equidistant to all the vertices of the triangle formed we want the circumcenter of the triangle as it is equidistant from all of the vertices, a circumcenter is made from the perpendicular bisectors of the triangle
Step 2: Give the vertices variables
A = (-4,8)
B = (-1,-1)
C = (3,7)
Step 2: Find the Circumcenter
Find the mid point of side AB
MAB
[tex]=(\frac{-4+(-1)}{2} ,\frac{8+(-1)}{2} )\\=(\frac{3}{2},\frac{7}{2} )[/tex]
Find the slope of side AB
mAB
[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-(-1)}{-4-(-1)} \\=\frac{9}{-3}\\ =-3[/tex]
Solve for 'b'
[tex](\frac{7}{2})=(-3)(\frac{3}{2} ) +b\\\frac{7}{2}=-\frac{9}{2}+b\\\frac{7}{2}+ \frac{9}{2}=b\\b = 8[/tex]
Therefore the equation for line AB is:
y = -3x + 8
Find the midpoint of side AC
MAC
[tex]=(\frac{-4+(3)}{2} ,\frac{8+(7)}{2} )\\=(-\frac{1}{2},\frac{15}{2} )[/tex]
Find slope of AC
mAC
[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-7}{-4-3} \\=\frac{1}{-7}\\ =-\frac{1}{7}[/tex]
Solve for 'b'
[tex]y=mx+b\\\frac{15}{2} =-\frac{1}{7} (-\frac{1}{2} )+b\\\frac{15}{2} =-\frac{1}{14} +b\\\frac{1}{14}+\frac{15}{2} = b\\b=\frac{53}{7}[/tex]
Therefore the equation for line AC is:
y = [tex]-\frac{1}{7}[/tex]x+[tex]\frac{53}{7}[/tex]
Step 3: Find the P.O.I of the 2 lines
Set both of the equation equal to each other
[tex]3x + 8=-\frac{1}{7} x+\frac{53}{7} \\3x +\frac{1}{7} x=\frac{53}{7}-8\\\frac{22}{7} x=-\frac{3}{7} \\x=-\frac{3}{22}[/tex]
We now know 'x' and we substitute x into any equation to find 'y'
[tex]y = -3(-\frac{3}{22} ) + 8\\y = \frac{9}{22} + 8\\y = \frac{185}{22}[/tex]
Therefore the new firehouse should be built at [tex](-\frac{3}{22},\frac{185}{22} )[/tex]
Subm
What is the point-slope form of the equation for the line with a slope of -2 that passes through the point (4, -6)?
Answer:
y + 6 = - 2(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y + b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 2 and (a, b) = (4, - 6) , thus
y - (- 6) = - 2(x - 4) , that is
y + 6 = - 2(x - 4)
Francesca graphs the function f(x) = 2x - 3, George graphs the function g(x) = 4x2 – 2 – 1, and Harold graphs the function h(x) = 9(f(x)). Which function does Harold graph?
A. Oh(x) = 1622 - 50x + 38
B. Oh(x) = 8x3 - 142++3
c. Oh(x) = 8r2 - 2x - 6
D. Oh(x) = 4x2 - 12x +9
Answer: A. [tex]h(x)=16x^2-50x+38[/tex]
Step-by-step explanation:
Given: Francesca graphs the function [tex]f(x) =2x - 3[/tex], George graphs the function [tex]g(x) = 4x^2 -x - 1[/tex].
Harold graphs the function [tex]h(x) = g(f(x))[/tex].
i.e. [tex]h(x)=g(2x - 3)[/tex] [put value of f(x)]
[tex]=4(2x-3)^2-(2x-3)-1\\\\= 4((2x)^2-2(2x)(3)+3^2)-2x+3-1\ \ [(a-b)^2=a^2-2ab+b^2]\\\\= 4(4x^2-12x+9)-2x+2\\\\=16x^2-48x+36-2x+2\\\\=16x^2-50x+38[/tex]
So, Harold graph [tex]h(x)=16x^2-50x+38[/tex]
Hence, the correct option is A. [tex]h(x)=16x^2-50x+38[/tex]
If f(x)=2x+1/x-4, what is the value of f^-1(3)?
Answer:
D. 13.
Step-by-step explanation:
f(x)=2x+1/x-4
let y = 2x + 1 / x - 4
xy - 4y = 2x + 1
xy - 2x = 4y + 1
x(y - 2) = 4y + 1
x = (4y + 1)/(y - 2)
So f^-1(x) = (4x + 1)/(x - 2)
and f^-1(3) = (4(3) + 1) / (3 - 2)
= 13/1
= 13.
NEED HELP ASAP algebra 2
Answer:
b = sqrt(39)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2
5^2 + b^2 = 8^2
25+b^2 =64
b^2 =64-25
b^2 =39
Take the square root of each side
b = sqrt(39)
Answer:
[tex]\sqrt{39}[/tex]
Step-by-step explanation:
Step 1: Find the unknown wide using Pythagorean Theorem
[tex]a^{2}+ b^{2} = c^{2}[/tex]
[tex]a^{2}+ 5^{2} = 8^{2}[/tex]
[tex]a^{2}+ 25 = 64[/tex]
[tex]a^{2}= 64-25[/tex]
[tex]a^{2=39[/tex]
[tex]\sqrt{a^{2}} = \sqrt{39}[/tex]
[tex]a=\sqrt{39}[/tex]
[tex]\sqrt{39}[/tex] cannot be simplified and more
Therefore the unknown side is [tex]\sqrt{39}[/tex]
What is the abscissa of origin?
Answer:
abscissa of origin is 0.
Step-by-step explanation:
The abscissa of a point is the signed measure of its projection on the primary axis, whose absolute value is the distance between the projection and the origin of the axis, and whose sign is given by the location on the projection relative to the origin (before negative; after: positive).
Which of the following is a correct interpretation of the expression 3 - (-5)?
Chanc 1 answer.
Answer:
8
Step-by-step explanation:
3 - (-5)
This can be rewitten to
3 + 5
Why?
2 negatives cancel each other out to make a positive, therefore:
3 + 5 = 8 or 3 - (-5) = 8
Answer:
8
Step-by-step explanation:3-(-5)=8 because two negatives make a positive so it is like adding 3 and 5 together to get the answer of 8.
The volume of a cube is 27 cubic meters. What is the length of one edge of the
cube?
Answer:
3 meters
Step-by-step explanation:
Step 1: State what is known
Volume of cube is 27 cubic meters
Important formula: Volume of cube = [tex]l^{3}[/tex]
Step 2: Input value into formula and solve for "l"
[tex]27=t^{3} \\\sqrt[3]27}=\sqrt[3]{t^{3} } \\3 = t[/tex]
Therefore the length of 1 edge of the cube is meters
Length of each edge of cube is 3 metres.
What is the volume of cube?
The volume of a cube defines the number of cubic units, occupied by the cube completely. The volume of cube is found by multiplying the value of the edge with itself three times that is a³.
It is given that volume of cube is 27 cubic metres.
a³ = 27
a = ∛27
a = 3
Hence, length of each side of cube is 3 metres.
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Calculate 12% simple interest to be paid on a loan of $2000 repaid in 1 1/2 year?
Answer:
1320
Step-by-step explanation:
as
SI=(P×T×R)/100
SI=(2000×12×11/2)/100
SI=132000/100
:.SI=1320
Answer:1320
Step-by-step explanation:2000×12×11/2/100
Two divide by twelve=6
2000÷100=20
20×6×11=1320
what is reflex?
what is reflex?
Answer:
An action performed without any concious thoughts
The simple definition of reflex is the sudden movement that occurs when it responds to a stimulus in the body. This movement is without any conscious thought beforehand.
For example, you are facing one way and a ball gets thrown toward you from behind. If you have fast enough reflexes, you will sense the ball coming from behind and turn around to catch it.
Best of Luck!
What is the smallest angle of rotational symmetry for the regular octagon? °
Explanation:
There are n = 8 sides in a regular octagon. The smallest angle of rotational symmetry is 360/n = 360/8 = 45 degrees. Rotating this amount will not change the regular octagon. The before and after will look identical.
ANSWER:
Your answer is 45 Degrees
Joe's boat rental rents paddle boats for $8.00 and hour and the paddles rent for $5.00 for the day. If David has $45, what is the least amount of hours he could rent the paddle boat?
Answer:
Least: 1 hour
Maximum: 5 hours
Step-by-step explanation:
Given
Boat hourly rate = $8.00
Paddle daily rate = $5.00
Required
Determine the least hour, David could use the boat
First, we need to represent this as an inequality.
Since David has $45, then
[tex]\$8.00 * x + \$5.00 \leq \$45.00[/tex]
Where x represents the number of hours
Collect Like Terms
[tex]\$8.00 * x \leq \$45.00 - \$5.00[/tex]
[tex]\$8.00 * x \leq \$40.00[/tex]
Divide both sides by $8.00
[tex]x \leq \frac{\$40.00}{\$8.00}[/tex]
[tex]x \leq 5[/tex]
Hence, the least number of hour is 1 hour while the maximum is 5 hours
Plz help ASAP WILL MARK BRAINLIEST!!
Answer:
B
Step-by-step explanation:
It is B because every number, x, you plug in 5x-3, it is y.
Answer:
B
Step-by-step explanation:
If we plug in x = 5 because every chart has x = 5 as a different answer into the equation you will find it equals 22 and only B has 22 as the answer
WILL GIVE BRAINLIEST
What did they do incorrectly
40 + 70 + ? = 360
110 + ? = 360
-110 -110
? = 250
In the equation 40+70+?=360, they are trying to find the last angle.
First they would add 40 and 70, which is 110.
So 110+?=360
360-110=?
360-110=250
Well this is wrong, because every angle in a triangle adds up to 180 degrees.
If you are adding up the angles in a quadrilateral, only then it adds up to 360 degrees.
So they did everything right, but they didn't use the right "total degrees"
This is what it was supposed to look like.
40+70+?=180
110+?=180
180-110=?
180-110=70
?=70
♡ Hope this helped! ♡
♡ Also thank you so much for 31 points. ♡
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❀ 0ranges ❀
Josue is running intervals. If he runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds, how many of each type of interval did he run?
Answer: He run 7 high-speed intervals and 8 low-speed intervals.
Step-by-step explanation:
Let x = Number of high-speed intervals.
y= Number of low-speed intervals .
He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.
4 min 56 sec = (4(60)+56) sec = 296 sec [ 1 minute = 60 seconds]
According to the question , we have the following linear equations :
[tex]x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)[/tex]
Multiply (i)by 16 , we get
[tex]16x+16y=240\ ...(iii)[/tex]
Subtract (iii) from (ii)
[tex]7y=56\\\\\Rightarrow\ y=8[/tex]
Put value of y in (i) , we get
[tex]x+8=15\Rightarrow\ x=7[/tex]
Hence, he run 7 high-speed intervals and 8 low-speed intervals.
8.8 + 7.8x = -7.9 - 5.5x
Answer:
[tex]-\frac{16.7}{13.3}[/tex]
Step-by-step explanation:
Step 1: Collect the like terms
8.8 + 7.9 = -5.5x - 7.8x
Step 2: Simplify
16.7 = -13.3x
Step 3: Divide both sides by -13.3
[tex]\frac{16.7}{-13.3} =\frac{-13.3}{-13.3}x[/tex]
[tex]x =- \frac{16.7}{13.3}[/tex]
Therefore the answer is [tex]-\frac{16.7}{13.3}[/tex]
Answer:
x = -1 34/133
Step-by-step explanation:
Given
8.8 +7.8x = -7.9 -5.5x
13.3x = -16.7 . . . . . . . . . . . add 5.5x -8.8
x = -16.7/13.3 = -167/133 . . . . divide by 13.3 and simplify
x = -1 34/133 ≈ -1.25564
how to solve sets in mathematics
Answer:
Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {},
For example, A = {1,2,3,4} is a set.
Dalila is mixing paste. For every 1 1/3 cups of water, she uses 2 1/2 cups of flour. How much flour does Dalila need for each cup of water? Show your work.
Answer:
Flour need for 1 cup of water = [tex]1\frac{7}{8}[/tex] cups
Step-by-step explanation:
Given:
Cups of water = [tex]1\frac{1}{3}[/tex] = 4/3
Cups of flour = [tex]2\frac{1}{2}[/tex] = 5/2
Find:
Flour need for 1 cup of water
Computation:
Flour need for 1 cup of water = Cups of flour / Cups of water
Flour need for 1 cup of water = (5/2) / (4/3)
Flour need for 1 cup of water = 15/8
Flour need for 1 cup of water = [tex]1\frac{7}{8}[/tex]
Given the function f(x) = -5x^2 + 2x + 9 find f(1) and f(2)
Answer:
i hope it will work
Step-by-step explanation:
f(x) = -5 x^2 + 2 x + 9
f(1)=-5(1)^2 +2(1) +9 = 6
similarly
f(2)=-5(2)^2 +2(2) +9 = -7
if its help-full then hit the stars and brain-list it
thanks
PLEASE HELP!!
When was production the lowest???
Answer:
B. 1995
Step-by-step explanation:
As per the graph the lowest production was in 1995, the production figure was around 203 billion dollars
So the answer choice is B. 1995
Need help on 22 on what to do
Answer:
4Step-by-step explanation:
[tex]f(x)=-x-11\\\\\frac{f(9)}{f(-6)}\\\\ f(9)= -9-11\\- 20\\\\f(-6) = -(-6)-11\\= 6-11 = -5\\\\\\\frac{f(9)}{f(-6)}\\ \\= \frac{-20}{-5}\\ \\= 4[/tex]
Answer:
4
Step-by-step explanation:
This means that where ever you see x in the function; f(x)= -x-11, you replace it with 9 for the numerator and -6 for the Denominator
=-(9)-11/-(-6)-11
=-9-11÷6-11
=-20÷-5
=4
2 (01.05)
Write the equation of the line that passes through (3,-2) and has a slope of 4 in point-slope form. (2 poin
Answer:
y +2 = 4(x -3)
Step-by-step explanation:
Point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
For m = 4 and (h, k) = (3, -2), the equation is ...
y +2 = 4(x -3) . . . . . matches the first choice
Elena has 2 fewer hats than fran. together the have 14 hats.
which equation represents this situation
Answer:
Elena has 6 and fran has 8
Step-by-step explanation:
A triangle has a base of (3x+7) and a height of (5x-1)a second triangle is drawn with a base that is tripled and its height is doubled. Find the difference between the area of the original triangle and the area of the new triangle
Answer:
The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2
Step-by-step explanation:
We know that the area of a triangle A = 1/2bh where b = base and h = height.
Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).
So its area A = (3x + 7)(5x - 1)/2.
Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)
So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)
So the difference between the area of the original triangle and the new triangle is
A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2
= (3x + 7)(5x - 1)(3 - 1/2)
= 5(3x + 7)(5x - 1)/2
So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2
Evaluate 0 · |-6|. -6 0 6
Answer:
0
Step-by-step explanation:
0 · |-6|
Absolute value means take the non negative number
0* 6
0
The value of the given absolute value equation 0 · |-6| is 0.
Given that an absolute value equation 0 · |-6|, we need to evaluate this.
To evaluate the expression 0 · |-6|, let's break it down step by step:
First, calculate the absolute value of -6:
|-6| = 6
Now, multiply the result from step 1 by 0:
0 · 6 = 0
When you multiply any number by 0, the result is always 0.
In this case, even though |-6| equals 6, multiplying it by 0 will make the overall result 0.
This is a fundamental property of multiplication with zero.
So, the final answer is 0.
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Find the midpoint between the pair of points.
(7,-2) and (-4, 2)
(1.5, 0)
(12,0)
(0, 1.5)
137
Answer:
(1.5,0)
Step-by-step explanation:
midpoint coordinate (x+x1/2 , y+y1/2)
x+x1=7-4/2=3/2=1.5
y+y1/2 = 2-2/2=0
Daniel buys 17 raffel ticket a total of 280 tickets were soldFind the probability that daniel does not win
Answer:
280-17=273
Step-by-step explanation:
because 80-17 equals 73 sooooooo add 200
Help ASAP....anyone please
Answer:
a(n)= 4*n+1
a(n+1)=5+4*n
Step-by-step explanation:
The sequence 5, 9, 13, 17 is the ariphmetic progression where a(1)=5 is the first member of the progression and the diference is d=9-5=4 (the distance between the neighboring members)
For ariphmetic progression is known that n- term is equal to
a(n)=a(1)+d*(n-1)
So for our case
a(n)=5+4(n-1)=5+4n-4=4n+1
a(n+1)= 5+4(n+1-1)= 5+4n