Answer:
f(x) = √7x
g(x) = 1/x -8
To find the domain of f º g we must first find f o g(x)
To find f o g(x) wherever you see x in f(x) replace it by g(x)
That's
f o g = √7(1/x-8)
= √7 / √x - 8
To find the domain equate the denominator to zero
That's
√x - 8 = 0
Square both sides
(√x - 8)² = 0²
x - 8 = 0
x = 8
The domain of f o g is x E R except 8
Hope this helps
What is the solution to (5m)² - (2n-3m)³ if m=-3 and n=5
Answer:
-6634
Step-by-step explanation:
all we have to do is plug in -3 everywhere m is and 5 where n is:
(5(-3))² - (2(5)-3(-3))³
(-15)² - (10+9)³
225 - 6859
-6634
Factorise
(a + c)2- 62
AWARDING BRANLIEST FOR FIRST CORRECT ANSWER
ΔHFG is dilated by a scale factor of 2 with the center of dilation at point F. Then, it is reflected over line a to create ΔEFI. Based on these transformations, which statement is true? Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F. segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI segment FG = segment FI, segment FH = segment FE, and segment HG = segment EI; ΔHFG ~ ΔEFI segment FG = one half segment FE, segment FH = one half segment FI, and segment HG = one halfsegment EI; ΔHFG ~ ΔIFE segment FG = segment FE, segment FH = segment FI and segment HG = segment EI; ΔHFG ~ ΔIFE
Answer:
segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI
Step-by-step explanation:
In the picture attached, the triangles are shown.
After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG and segment EI. More specifically:
FG = 1/2*FIFH = 1/2*FEHG = 1/2*EIAnswer:
segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI
Step-by-step explanation:
In the picture attached, the triangles are shown.
After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG and segment EI. More specifically:
FG = 1/2*FI
FH = 1/2*FE
HG = 1/2*EI
This answer is right! took the test on FLVS and confirmed it :)
Origami is the Japanese art of paper folding. The diagram below represents an unfolded paper kabuto, a samurai warriors helmet. From the kabuto below, which of the following are pairs of congruent angles? Check all that apply.
Answer:
A,C,&D
Step-by-step explanation:any funny bur cute romance anime recommendations?
What is the volume of the rectangular prism below/described? (Don't forget to label your answer!)

Length= 4 1/2 in. Width= 5 in. Height= 3 3/4 in.
The volume of the prism is ___.
(hint: in2 is inches squared; in3 is inches cubed)
Answer:
Step-by-step explanation:
Volume = Length times width times height.
Here,
Volume = (4.5 in)(5 in)(3.75 in), which, when evaluated by calculator, comes out to 84.375 cubic inches.
This is equivalent to 84 3/8 cubic inches.
Answer:
[tex]84\frac{3}{8}in^3[/tex]
Step-by-step explanation:
V = L * W * H
V = 4 1/2 * 5 * 3 3/4
V = 9/2 * 5/1 * 15/4
V = 675/8
V = 84 3/8
10 tolas gold bought from American market at $ 553 per tola is sold in Nepal at 20% customs duty charge and 13% VAT. At what price should it be sold ?
Answer: $735.49
Step-by-step explanation:
Given, the price of 10 tolas gold bought from American market = $553
Custom duty charge = 20%
VAT = 13%
Custom duty charge = 20% of $553
= 0.20 x 553 [we divide a perecntage to convet it into decimal]
= $110.6
VAT = 13% of $553
= 0.13 x 553
= $71.89
Selling price = Original price +Custom duty charge + VAT
= $553+$110.6+ $71.89
= $735.49
Hence, it should be sold at $735.49 .
Optimize the equation P = 4x + 3y using the constraints x > 0, x < 4, y <
5. What is the maximum?
a. 13
b. 15
c. -3
d. 31
Answer:
Option D is correct
Step-by-step explanation:
With x < 4 and y < 5:
P = 4x + 3y < 4(4) + 3(5) = 16 + 15 = 31
=> Option D is correct
Given the equation P = 4x + 3y With constraints x > 0, x < 4 and y < 5:
Option D is correct that is 31.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given the equation P = 4x + 3y
With constraints x > 0, x < 4 and y < 5:
The maximum value is
P = 4x + 3y < 4(4) + 3(5)
P = 16 + 15
P = 31
Hence, the Option D is correct.
Learn more about equations here;
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a store bought a vacuum cleaner for $120. the overhead is 5% of the cost. the store wants to make a profit of 10% over the cost plus overhead. find the selling price of the cleaner.
Answer:
The selling price of the cleaner is:
$138.6Step-by-step explanation:
First, we have the base of the value that is $120, now we know that the overhead is 5%, so we must calculate this value in dollars, the 5% of $120 is:
$120 * 5% = $6This value you must add to the base ($120), so the cost with the overhead is $126. How the store wants to make a profit of 10%, you must calculate this 10% of the total cost obtained ($126):
$126 * 10% = $12.6And you must add this value to obtain the final price in the store:
$126 + $12.6 = $138.6Using the digits 1 to 9, at most one time each, fill in the boxes so that the points
make a parallelogram. Mathematically, use parallel line or congruent sides to
explain your answer. if there are calculations, include those in your explanation.
Answer:
(4, 7) (8, 9)
(2, 3) (6, 5)
Step-by-step explanation:
The definition of a parallelogram is a quadrilateral that has two pairs of opposite equal length parallel sides, including equal opposite angle measurements
To simplify the task, we plot the points on a graph paper for the parallelogram ABCD to get the following points;
B (4, 7) A (8, 9)
C (2, 3) D (6, 5)
The length of the opposite sides AB and CD are;
Length AB = √((9 - 7)² + (8 - 4)²) = √20 = 2·√5
Length CD = √((3 - 5)² + (2 - 6)²) = √20 = 2·√5
The length of the opposite sides AC and BD are;
Length AD = √((9 - 5)² + (8 - 6)²) = √20 = 2·√5
Length BC = √((7 - 3)² + (4 - 2)²) = √20 = 2·√5
The slope of segment AB is (9 - 7)/(8 - 4) = 2/4 =1/2
The slope of segment CD is (5 - 3)/(6 - 2) = 2/4 =1/2
Therefore, since the slopes of segments AB and CD are equal, segments AB and CD are parallel
Similarly, we have;
For segment AD, slope = (9 - 5)/8 - 6) = 4/2 = 2
For segment BC, slope = (7 - 3)/4 - 2) = 4/2 = 2
Therefore, the slopes of segments AD and BC are equal, segments AC and BD are parallel.
what is the answer to...[tex]-\frac{2}{3} (4x-6)+\frac{1}{3}(x-5)[/tex]
please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
2000 ft x 2= 4000 ft
So the answer is 4000 ft
Find the area ratio of a cube with volume 125m3 to a cube with volume 64m3.
Answer:
25:16
Step-by-step explanation:
i think its right
With reference to the figure, sin x =
Answer:
0.894
Step-by-step explanation:
Data provided in the question
BC length = 17.89 unit
DC length = 16 unit.
Now, we have to compute the angle y with the help of the cosine function;
Cosine defines the ratio between the right angle adjacent side and the hypotenuse
[tex]\cos = \frac{Adjacent side}{Hpotenuse}[/tex]
As per the triangle BDC;
Hypotenuse = BC =17.89 unit
And, the Adjacent side = 16 units
So;
[tex]\cos y =\frac{16}{17.89} =0.894354388[/tex]
[tex]y =\cos^{-1} (0.894354388) = 26.57^{\circ} (nearest\ to\ hundredths\ place)[/tex]
Now, determine the value of angle x
In right angle ΔABC;
As we know that
The three angles sum is 180 degrees
So,
[tex]\angle A + \angle B +\angle C =180^{\circ} ....(1)[/tex]
According to the given figure
[tex]\angle B=90^{\circ}, \angle A =x^{\circ}[/tex]
and
[tex]\angle C =y=26.57^{\circ}[/tex]
Now Substitute these in (1) for solving the angle x;
[tex]x^{\circ}+90^{\circ}+y^{\circ} =180^{\circ}[/tex]
or
[tex]x^{\circ}+90^{\circ}+26.57^{\circ} =180^{\circ}[/tex]
or
[tex]x^{\circ}+116.57^{\circ} =180^{\circ}[/tex]
[tex]x^{\circ}=180^{\circ} - 116.57^{\circ}=63.43^{\circ}[/tex]
Finally we have to determine the value of sin x;
Hence,
The value of [tex]\sin 63.43 =0.89438856[/tex]
or
= 0.894
Answer:
sin x = 0.894
Step-by-step explanation:
I hope you are refering to this figure:
When Reshard was born, his uncle bought him a $200 savings bond. When Reshard turns 20 years old, the bond will have earned 130% interest. How much will the bond be worth when Reshard turns 20?
Answer: 260
Step-by-step explanation: When we 200 times 130% we will get 260.
please help me and hurry
Answer:
median: 90
mode: 91
mean: 84.2 or round it to 84
Step-by-step explanation:
Let me know if this helps! have a great day! :)
Answer:
a) Median = 91
b) mode = 91
c)Mean 84.2
Step-by-step explanation:
a) Median is the middle term. So, 6th term
Median = 91
b) Mode is the score which occurs more number of times
91 occurs 3 times
Mode = 91
c) Mean= sum of all data's/Number of data's
= 85 + 91 + 48 +98 + 99 /5
= 421/5
Mean = 84.2
if a(x) = 2x - 4 and b(x) = x + 2, which of the following expressions produces a quadratic function?
(ab))
O (a - b)^)
O (a + b)(x)
Answer:
[tex](ab)(x)[/tex]
Step-by-step explanation:
Data provided in the question
a(x) = 2x - 4
b(x) = x + 2
Now we go through each options
First option
[tex](ab)(x)=(2x-4)(x+2)[/tex]
[tex]=2(x-2)(x+2)[/tex]
[tex]=2(x^2-4)[/tex]
[tex]=2x^2-8[/tex]
Second option
[tex]\dfrac{a}{b}(x)=\dfrac{2x-4}{x+2}[/tex]
Third option
[tex](a-b)(x)=(2x-4)-(x+2)[/tex]
[tex]=2x-4-x-2[/tex]
= x - 6
Fourth option
[tex](a+b)(x)=(2x-4)+(x+2)[/tex]
[tex]=2x-4+x+2[/tex]
= 3x - 2
As we can see from the above options only option A is correct i.e it only produced a quadric function
kamal has 6 cans of regular soda and 15 cans of diet soda. He wants to create some identical refreshment tables during the American football game. He also does not want to have any sodas left over. what is the greatest number of refreshment tables that Kamal can stock
Answer: 3
Step-by-step explanation:
This problem is looking for the Greatest Common Factor (GCF) of 6 and 15.
Draw a factor tree for each number and see what they have in common.
Reg Diet
6 15
∧ ∧
2 3 3 5
The GCF of 6 and 15 = 3
Each table will contain 2 cans of regular soda and 5 cans of diet soda.
five sixths of a number equals 4,375. What is the number
Answer:
The number is 5250
Step-by-step explanation:
5/6 * x = 4375
Multiply each side by 6/5 to isolate x
6/5 * 5/6 x = 4375 * 6/5
x =5250
Answer:
5250
Step-by-step explanation:
5/6x= 4375
x= 4375*6/5
x= 5250
1 Point
Which of the following best describes a random event?
A. The number of doctor visits a person makes in a year
B. The winner of an election
C. The age at which a baby will get her first tooth
D. The age at which a person is legally allowed to drive in the state of
California
SEBNI
Answer: B
Step-by-step explanation:
Makes the most sense out of all the options because it’s the most random or unpredictable
Please help with this
Answer:
I think it's D because the line AC looks like it is splitting the rectangle in half. I think this is right since the angles are congruent. (Angle BAC and Angle ACD)
When you need to convert from one system of measurement to another, you should convert to the
A. metric system.
B. system that will have the highest number.
C. system that will have the smallest number
D. system used on the medication label.
I need help on these questions pls answer asap 1.) A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the train to clear the tunnel? 2.)The two top NBA players played a basketball game against the RSM team. Together the NBA players made 85 baskets, scoring one point for free throws and two or three points for field goals. They scored a total of 184 points during the game. If they made 22 free throws, how many three-point field goals did they make?
Answer:
1. The train is will cross the tunnel in 2 minutes.
The train is traveling at 30 km every hour or 60 minutes, so it will move 1 km every 60/30 minutes, or every 2 minutes.
2. Explanation here first: 22 free throws means 22 points and 22 field goals.
184-22=162 points they still needed to get, and
85-22=63 goals they still needed to score
We can now use a system of equations, (where x is 3-point goals, and y is 2-point goals) to solve the problem:
3x+2y=162
x+y=63 (-2)
-------------------------------------------------------------
3x+2y=162
-2x-2y= -126
-------------------------------------------------------------
x=36, and y=27 so the NBA players got 36 3-point goals, and 27 2-point goals
We can check this:
(36*3) + (27*2) + 22 = 108+54+22 = 184 total points
Step-by-step explanation:
Hope this helps!
Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5. Pls help ASAP btw, the answer isn't -12/19 or 12/19
Answer:
The found values are:
A = 1/3
B = -8/3
Step-by-step explanation:
We know that general equation is given by:
y = mx + c
where m is the slope and c is a constant.
x + 3y = -5
y = -(1/3)x - 1/3(5)
Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:
Ax + By = 3
By = -Ax - 3
By = (1/3)x - 3
Hence, A = 1/3
Substitute point (-7,2) into the equation:
B(2) = (1/3)(-7) -3
B(2) = -7/3 - 3
B(2) = -16/3
B = -16/6
B = -8/3
of the methods for solving systems of equations, which is the least accurate and may only give an approximate answer?
a. Graphing
b. Substitution
c. Elimination
d. None, they are all exact.
Graphing is the least accurate method for solving systems of equations, and it may only give an approximate answer. Hence, option A is the right choice.
What is the system of equations?A system of equations is made up of two or more equations that are solved at the same time.
What are the different ways of solving systems of equations?There are three ways to solve a system of equations:
Graphing: All equations are graphed and the point of intersections are the solutions for the system of equations.Substitution: One variable is isolated in one equation, and its value is substituted in the other equation to solve the system of equations.Elimination: Operations are done on all equations to eliminate one variable and then solve for the system of equations.How to solve the question?In the question, we are asked which method for solving systems of equations is the least accurate and may only give an approximate answer.
We have discussed all methods above.
Of these methods, when solving manually, as the degree of the equation gets bigger and bigger, the graphing of equations will become difficult, and thus the graphing method will be the least accurate.
Thus, graphing is the least accurate method for solving systems of equations, and it may only give an approximate answer. Hence, option A is the right choice.
Learn more about solving a system of equations at
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What is the smallest number that is divisible by 1,2,3,4,5,6,7,8,9 and 10? How do you know? (explain) hurry pls
Answer:
The smallest number that is divisible by 1,2,3,4,5,6,7,8,9 and 10 is 2,520.
Step-by-step explanation:
2520/1 = 2520
2520/2 = 1260
2520/3 = 840
2520/4 = 630
2520/5 = 504
2520/6 = 420
2520/7 = 360
2520/8 = 315
2520/9 = 280
2520/10 = 252
Billy has three times as many llamas as lambs.
Milly has twice as many lambs as llamas.
They have 17 animals in total.
How many of the animals are llamas?
Answer:
There are 9 llamas.
Step-by-step explanation:
For Billy, we have to find a number that is divisible by four, because he has one group of lambs, and 3 times as many llamas, which gives us 4 groups altogether. The number must be below 10 in order to not go above 17 when Milly's number of animals are included, but above 4 itself in order to reach the target of 17 in the first place.
As you can guess, the only number that fits all the criteria is 8. It's divisible by 4 and below 10, but above 4 itself.
If Billy has three times as many llamas as lambs, then he must have 2 lambs, and 6 llamas, as 2 × 3 = 6.
If we know that Billy has 8 animals, then we also know that Milly must have 9 animals, as 17 - 8 = 9.
We also know that Milly has 3 groups of animals; one group of llamas, and two groups of lambs, meaning we divide the number of animals she has by 3.
9 ÷ 3 = 3.
This tells us Milly has just 3 llamas, because 3 is one group of 9, and 3 × 2 = 6, because she has twice the amount of lambs.
Billy has 2 lambs and 6 llamas.
Milly has 6 lambs and 3 llamas.
The amount of lambs is irrelevant to our final answer, so we can disregard them and do a final sum of 6 + 3 = 9, which gives us our answer.
Answer:
Billy: Has 4 lots of animals
Milly: Has 3 lots of animals
17 animals in total means that Billy must have 4 lots of 2 (8 animals) and Milly must have 3 lots of 3 (9 animals) So Billy has 6 llamas and Milly has 3, giving 9 llamas in total
What is the equation of the line that passes through the point (-2,14) and is perpendicular to the line with the following equation?
y = -x-1
OA
y =
OB
y =
- + 9
o + 16
1 - 12
Oc.
y =
OD.
y =
+ 19
Answer:
y = x + 16
Step-by-step explanation:
Step 1: Find slope of perpendicular line
Take the negative reciprocal of the 1st line
m = 1
Step 2: Find b
y = x + b
14 = -2 + b
b = 16
Step 3: Write equation
y = x + 16
Answer:
y = x + 16
Step-by-step explanation:
Given the equation y = -x - 1, we see that the slope (the coefficient of the x term) is -1. A line perpendicular to this one has a slope which is the negative reciprocal of the given equation: +1.
Using the point-slope formula for the equation of a straight line, we get:
y - 14 = +1(x + 2), or y - 14 = x + 2, or y = x + 16
Help plz with this question. Needed fast. I will mark brainliest.
Answer:
≈ 68.2°
Step-by-step explanation:
tan X= 20/8
tan X= 2.5
x= tan ⁻¹ 2.5
x ≈ 68.2°
Answer:
Step-by-step explanation:
To find the size of YXZ we should use some trigonometry but first let's find the length of YZ
The Pythagorian theorem :(XZ)²+(ZY)²=(YX)²
YX=[tex]\sqrt{20^{2}+8^{2} }[/tex]
=4[tex]\sqrt{29}[/tex]
We khow that sin(YXZ)=(YZ)/(YX) = 20/(4[tex]\sqrt{29}[/tex]) = 5/[tex]\sqrt{29}[/tex]using a calculator we get (YXZ)= 68°
Given the function f(x)=-3x^2+4x+6 find f(2) and f(3)
Answer:
f(2)= 2, f(3)= -9
Step-by-step explanation:
To find f(2) o f(3), you simply plug the respective number into the function, substituting it for x:
f(2)= -3(2)^2 + 4(2) + 6
f(2)= -12 + 8 + 6
f(2)= 2
f(3)= -3(3)^2 + 4(3) + 6
f(3)= -27 + 12 + 6
f(3)= -9
Find the equation of the line passing
through the points (3,-2) and (4, 6).
y = [? ]x + [ ]
Answer:
y = 8x - 26
Step-by-step explanation:
Since we already have the ending equation in slope intercept form, all we need to do is fill in the blanks. We do that by putting it in point slope form which is [tex]y-y_{1}=m(x-x_{1})[/tex]
(You can plug either point in and get the same result but I'm going to use the first one)
[tex]y-(-2)=8(x-3)[/tex]
Distribute the [tex]m(x-x_{3})[/tex]
[tex]y-(-2)=8x-24[/tex]
Isolate the [tex]y[/tex]
[tex]y-(-2)=y+2[/tex]
[tex]y+2(-2)=8x-24(-2)[/tex]
[tex]y=8x-26[/tex]
And that's your answer!