Answer and step-by-step explanation:
We just have to apply one function in the other one. See:
→ f(g(x)):
[tex]f(x) = \dfrac{2x-3}{x+4}\\\\f(g(x)) = \dfrac{2g(x)-3}{g(x)+4} = \dfrac{2\cdot\dfrac{3+4x}{2-x}-3}{\dfrac{3+4x}{2-x}+4}\\\\f(g(x)) = \dfrac{\dfrac{6+8x}{2-x}-3}{\dfrac{3+4x}{2-x}+4}\\\\f(g(x)) = \dfrac{\dfrac{(6+8x)-3(2-x)}{2-x}}{\,\,\,\dfrac{(3+4x)+4(2-x)}{2-x}\,\,\,}=\dfrac{(6+8x)-3(2-x)}{(3+4x)+4(2-x)}\\\\f(g(x)) =\dfrac{6+8x-6+3x}{3+4x+8-4x}=\dfrac{11x}{11}\\\\\\\boxed{f(g(x)) = x}[/tex]
→ g(f(x)):
[tex]g(x) = \dfrac{3+4x}{2-x}\\\\g(f(x)) = \dfrac{3+4f(x)}{2-f(x)} = \dfrac{3+4\dfrac{2x-3}{x+4}}{2-\dfrac{2x-3}{x+4}}\\\\g(f(x)) = \dfrac{3+\dfrac{8x-12}{x+4}}{2-\dfrac{2x-3}{x+4}}\\\\g(f(x)) = \dfrac{\dfrac{3(x+4)+(8x-12)}{x+4}}{\,\,\,\dfrac{2(x+4)-(2x-3)}{x+4}\,\,\,}=\dfrac{3(x+4)+(8x-12)}{2(x+4)-(2x-3)}\\\\g(f(x)) =\dfrac{3x+12+8x-12}{2x+8-2x+3}=\dfrac{11x}{11}\\\\\\\boxed{g(f(x)) = x}[/tex]
What verifies that f and g are inverses of each other.
Q.E.D.
How many factors are in a B + CD + EF + GH
The given expression is
=ab+cd+ef+gh
The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction, Multiplication and Division.
→The expression consists of four terms which are, ab, cd, ef, and gh.
→Each term contains
Two factors.
plz mark as brainliest
1. Marsha used 2 cups of sugar to make 3 dozen
cookies. How much sugar would she use to make 9
dozen cookies?
I WILL GIVE YOU 20 POINTS AND THE BRAINLYEST
all of the points in the picture are on the same line.
Find the slope on the like exain or show your reasoning
write and equation for the line.
find the values for A and B. Explain your reasoning.
Answer:
Step-by-step explanation:
Find the slope and then the equation of line.
(x₁ , y₁) = (2 , 2) & (x₂, y₂) = (6 , 10)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{10 - 2}{6 - 2}\\\\= \frac{8}{4}\\\\= 2[/tex]
m = 2
Equation of the line: y - y₁ = m(x - x₁)
y - 2 = 2 (x - 2)
y - 2 = 2x - 4
y = 2x - 4 + 2
y = 2x - 2 --------------(I)
(a, 8)
Plug in x = a & y = 8 in (I)
8 = 2a - 2
8 + 2 = 2a
10 = 2a
a = 10/2
a = 5
(4 , b)
Plug in x = 4 & y = b in (I)
b = 2*4 - 2
b = 8 - 2
b = 6
Answer:
dog peas
Step-by-step explanation:
donkey peas
James says that 12 is a common factor of 3 and 4. June says that 12 is a common multiple of 3 and 4. Who is correct?
Answer:
June is correct.
Step-by-step explanation:
June is correct because Common Multiples are what we get after multiplying the number while common factors are what we can multiply to get the number.
The average of 5 quiz grades is 10. When the lowest grade is dropped and the new average is calculated, it turns out to be 11. What was the score of the dropped grade?
Answer:
The score of the dropped grade is 6
Step-by-step explanation:
To find the average of a set of numbers you need to add all the numbers and divide by how many numbers there are. The problem wants you to solve it in reverse. Let put this into an algebraic equation with a, b, c, d, and e being the variables of the test scores
(a+b+c+d+e)/5=10
Then we can multiply both sides by 5 and get
a+b+c+d+e=50
Lets assume that c is the lowest test score. To calculate the average of that we get
a+b+d+e/4=11
Doing the same thing, we know that a+b+d+e=44
Now compare the two:
a+b+c+d+e=50
a+b+d+e=44
We can now know that c=50-44=6
So, 6 is the score of the dropped quiz. Hope that helped!
Need help please please it due today at 4:50pm really need help please
Answer:
70
Step-by-step explanation:
Enter the number that makes the equation true
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
What is the value of s?
s = __°
Answer:
50 what
Step-by-step explanation:
at 4 pm charlie realizes he has half an hour to get to his grandmother's house for dinner? if his grandmother lives 40 miles away, how fast will charlie have to drive to get there on time?
Answer:
10 minutes
Step-by-step explanation:
Speed = distance ÷ time, so 40 ÷ 4 = 10
hope this helps :)
Determine the quotient of 1 and 1 over 3 divided by 3 over 5 . (2 points)
a
1 and 1 over 10
b
1 and 5 over 9
c
2 and 2 over 9
d
2 and 4 over 5
Answer:2 2/9
Step-by-step explanation: 4/3 x 5/3= 20/9= 2 2/9
Sammy saw a fish swimming at a constant rate toward the ocean floor. From a starting position of 7 meters below sea level, the fish is descending 3 meters per second. Sammy said the equation y= -7x - 3 can be used to represent the situation. Explain why Sammy is incorrect and how he could fix it.
Answer:
what grade is this lol
Step-by-step explanation:
Answer:
y = 3x - (-7)
Step-by-step explanation:
As the fish starts at -7 meters below sea level, and is descending 3 meters per second, Sammy needs to subtract -7, and then multiply 3 by x. (x being the time is takes)
Can someone help with this problem? ASAP
G(x)=(x-2)(3x+3) find the zeros of the function enter the solution from least to greatest
Hello i need help with that too
Answer: g (x)=(x -2)(3x +3)
lesser x = -1
greater x = 2
Step-by-step explanation:
ula for a Variable
The surface area of a cone is given by the formula
S = nil + n0r2 Solve the formula for l.
0 1=S - p2
O l=S+ p2
Ol= $ - p2
TT
01 = 5 +2.
1=
TT
Answer: 80 votes
Step-by-step explanation: Solve the formula for l. A) l ... 01/18/2017. Mathematics · High School. answered. The surface area of a cone is given by the formula S = πl + πr2. ... all of the 2's are to the power of R the 5/3.14's are fractions. 2 ... Incognit-oh-no… ... and 219 more users found this answer helpful. Thanks 140. 4.7. (80 votes).
The surface area of a cone is given by the formula S = πl + [tex]\pi r^2[/tex], the formula for I will be l = S/3.14 – [tex]r^2[/tex]. The correct option is C.
What is surface area?The surface area of a three-dimensional shape is the amount of space that surrounds it.
Starting with the given formula:
[tex]S = \pi l + \pi r^2[/tex]
We want to solve for l.
First, we can isolate the term with l on one side of the equation by subtracting [tex]\pi r^2[/tex] from both sides:
[tex]S - \pi r^2 = \pi l[/tex]
Then we can divide both sides by π to isolate l:
[tex]l = (S - \pi r^2) / \pi[/tex]
Therefore, the solution is:
[tex]l = (\frac{S}{\pi} - r^2)[/tex]
Thus, the correct option is C.
For more details regarding surface area, visit:
https://brainly.com/question/29298005
#SPJ7
Your question seems incomplete, the probable complete question is:
The surface area of a cone is given by the formula S = πl + πr2. Solve the formula for l.
A) l = S – r2
B) l = S + r2
C) l = 5/3.14 – r2
D) l = 5/3.14 + r2
all of the 2's are to the power of R
the 5/3.14's are fractions
1979 to 2020 is how many years
Could someone help a girl out?
Answer:
x = 19
Step-by-step explanation:
Trapezium area formula: [tex]\frac{a+b}{2} * h[/tex], where a & b are the two bases.
Now, if we plug in our known values, we can solve for the missing base.
[tex]\frac{5 + x}{2} * 4 = 48[/tex]
[tex]\frac{5 + x}{2} = 12\\\\5 + x = 24\\\\x = 19[/tex]
Answer:
Yes I would have to agree with Goliath, x = 19.
Step-by-step explanation:
You can mark Goliath Brainlest if you want they did the answer first.
Write an equation in slope-intercept form that goes through (12, 4) and (20,8).
Answer:
Equation in slope-intercept form that goes through (12, 4) and (20,8) is: [tex]y = \frac{1}{2}x-2[/tex]
Step-by-step explanation:
Given two points are:
[tex](x_1,y_1) = (12,4)\\(x_2,y_2) = (20,8)[/tex]
Slope intercept form of line is given as:
[tex]y = mx+b[/tex]
Here m is the slope of the line and b is the y-intercept.
Slope of a line is calculated by the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Putting the values
[tex]m = \frac{8-4}{20-12}\\m = \frac{4}{8}\\m=\frac{1}{2}[/tex]
Putting the value of slope in slope-intercept form we get
[tex]y = \frac{1}{2}x+b[/tex]
To find the value of b, any one point will be put in the equation
Putting the first point (12,4) in the equation
[tex]4 = \frac{1}{2}(12) + b\\4 = 6+b\\b = 4-6\\b = -2[/tex]
Putting the value of b
[tex]y = \frac{1}{2}x-2[/tex]
Hence,
Equation in slope-intercept form that goes through (12, 4) and (20,8) is: [tex]y = \frac{1}{2}x-2[/tex]
For many important processes that occur in the body, direct measurement of characteristics of the process is not possible. In many cases, however, we can measure a biomarker, a biochemical substance that is relatively easy to measure and is associated with the process of interest. Bone turnover is the net effect of two processes: the breaking down of old bone, called resorption, and the building of new bone, called formation. A biomarker for bone formation measured was osteocalcin (OC), measured in the blood. The units are nanograms per milliliter (ng/ml). For the 31 subjects in the study the mean was 33.4 ng/ml. Assume that the standard deviation is known to be 19.6 ng/ml.
Required:
Give the margin of error and find a 95% confidence interval for the mean TRAP amount in young women represented by this sample.
Answer:
The margin of error is [tex]E = 6.9 [/tex]
The 95% confidence interval is [tex] 26.5 < \mu < 40.3 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 31
The mean is [tex]\mu = 33.4 \ ng/ml[/tex]
The standard deviation is [tex]\sigma = 19.6 \ ng/ml[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{19.6 }{\sqrt{31 } }[/tex]
=> [tex]E = 6.9 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 33.4 - 6.9 < \mu < 33.4 + 6.9 [/tex]
=> [tex] 26.5 < \mu < 40.3 [/tex]
Which number line model represents the expression 3.5+(-5)
Answer:
it is -1.5.
Step-by-step explanation:
Answer:
the answer is A
Step-by-step explanation:
hope this helps
I really need help can someone please understand
sure what’s the problem
(34+ (9 x 2)) divide2 = _
Answer:
26
Step-by-step explanation:
9 x 2= 18
18+34= 52
52/2= 26
2. Carlo, a school varsity player, has 32 table tennis ball and 16 table
tennis paddles. He wants to sell packages of balls and paddles
together. What is the greatest number of packages he can sell with
no leftover balls or paddles?
Answer:
balls
Step-by-step explanation:
lol hahahahahahahahhahahahahahhahahahahahahahahhahah
Answer:
two balls for every one paddle
Step-by-step explanation:
In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the proportion of all students who read or watch the news on a daily basis. Interpret your results. If you wanted to develop a 95% confidence interval with a margin of error of .01, how many students would need to be surveyed?
Answer:
The 90% confidence interval is [tex]0.199 < p < 0.261 [/tex]
The sample size to develop a 95% confidence interval is [tex]n = 2032 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n =500
The sample proportion is [tex]\^ p = 0.23[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.23 (1- 0.23)}{500} } [/tex]
=> [tex]E = 0.03096 [/tex]
Generally 90% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.23 -0.03096 < p < 0.23 + 0.03096 [/tex]
=> [tex]0.199 < p < 0.261 [/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is given as [tex]E = 0.01[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.96 }{0.01} ]^2 *0.23 (1 - 0.23 ) [/tex]
=> [tex]n = 2032 [/tex]
help with number 1 & number 2 please !
Step-by-step explanation:
2vt= (ht²/2) - 2c - r
v= ((ht²/2) -2c -r) / 2t
v= ht/4 - c/t - r/2t
For f(x)=-5x+10, what is the value of x for which f(x) =35
X = 5
None are correct
X=3
X=-4
X=-5
Answer:
x=-5. -5x+10 replace the x with -5, multiply, add ten, and you'll get f(x)= 35
Answer:
-5
Step-by-step explanation:
f(x) =35
f(x) = -5x +10
equate the two equations:
-5x +10 =35
-5x =35-10
-5x =25
x = 25/-5
x = -5
What is the slope of a line perpendicular to the line passing through the points P (2,5) and Q (-3,7)?
Answer:
2/5
Step-by-step explanation:
perpendicular line means the two lines' slope when multiplied together gives a answer of -1.
hence, we just need to find the slopw of the line connecting the 2 points and form an equation with -1 to get the slope the question wants.
slope of the line PQ:
(7-5)/(-3-2) = -2/5 (slope formula)
slope of the perpendicular line:
-2/5 x slope = -1
slope = (-1)/(-2.5) = 2/5
Each square and figure DNE has a side length of one unit compare the area of the two figures which figure has more area how much more explain or show your reasoning
Answer:
✅Figure E has more area
✅Figure E has 5.14 units² much more than Figure D.
Step-by-step explanation:
The logic to solving this kind of problem is to decompose and each of the figure to find out how many squares and circles are there in each figure, them calculate the area of each figure using the formula for area of square and area of a circle.
✍️Figure D:
Figure D is composed of 2 squares and 4 semicircles (2 full circles).
Since side length of 1 square = 1 unit, therefore, radius of the semi-circle/circle = 1 unit.
Area of the 2 squares = 2(s²) = 2(1²) = 2 unit²
Area of the 2 full circles = 2(πr²) = 2(3.14*1²) = 6.28 unit²
Area of Figure D = 2 + 6.28 = 8.28 unit²
✍️Figure E:
Figure E is composed of 4 squares and 6 quarter circles (3 full circles).
Area of the 4 squares = 4(s²) = 4(1²) = 4 unit²
Area of the 3 full circles = 3(πr²) = 3(3.14*1²) = 9.42 units²
Area of figure E = 4 + 9.42 = 13.42 unit²
✅Therefore, we can conclude that Figure E has more area.
✅Figure E has 5.14 unit² more area than Figure D (13.42 - 8.28 = 5.14).
PLS Help! SHOW WORK ON IT
Answer:
Perimeter of Triangle ABC is 21
Step-by-step explanation:
According to the Midpoint Theorem, if the line segment adjoins midpoints of any of the sides of a triangle, then the line segment is said to be parallel to all the remaining sides, and it measures about half of the remaining sides.
In this case, since XY=7, then AZ+ZC will need to equal 14 as that's opposite of half. Since AZ=ZC given that they are congruent, then AZ=7. Therefore the perimeter is XA+XZ+AZ=5+9+7=21
A corporation is having a shareholders meeting to vote on a new issue. Not all shareholders are able to attend. In fact, most usually do not. The ownership of the corporation is represented by 2,351,00 shares of stock owned by 111,273 shareholders. Must all of the shareholders own more than one share of stock? If 3,411 shareholders attend the meeting, what percent of the shareholders attended the meeting? Round to the nearest percent. If the shareholders who do not attend own a combined 1.8 million shares of the corporation and the shareholders are voting on a particular issue, these shareholders can vote by proxy - an absentee ballot. If 100,000 of the shareholders vote by proxy, what percent of the shareholders did not vote at all?? Round to the nearest percent.
Answer:
a) The percentage of the shareholders who attended the meeting is 3%.
b) The percentage of the shareholders who did not vote at all is 7%.
Step-by-step explanation:
a) Data and Calculations:
Outstanding shares = 2,351,000
Number of shareholders = 111,273
Number of shareholders who attended the meeting = 3,411
The percentage of the shareholders who attended the meeting = 3,411/111,273 * 100
= 3.065
= 3%
Absent shareholders = 107,862 (111,273 - 3,411) and own 1.8 million shares
Proxy voters = 100,000
Non-voting shareholders 7,862
Therefore, the percentage of shareholders who did not vote at all
= 7,862/111,273*100
= 7.0655
= 7%
help please with #3
Answer: x = 2a over b + c
Step-by-step explanation:
1. Multiply both sides by two. This cancels out 2 and turns a into 2a. It should look like 2a = bx + cx
2) Since both b and c have x’s, we turn it into (b + c)x
3. Then divide both sides by b+c to get 2a over b + c = x