If there is a nonmathematical symbol in the preceding expression, then your browser doesn't have the math symbol font. Please follow the instructions on the WeBWorK front page to install the STIX math fonts. To get around this temporarily, (i) print a hardcopy (the symbols will be there), (ii) in the options box in the right column of this screen, check the formatted option and press the apply options button, or (iii) go to a UITS public cluster (e.g., the Library) and work there.) Find the following:
a. g(h(x))=_______
b. h(g(x))=_______
c. h(h(x))=_______
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]g(h(x)) = \sqrt[4]{x^2 + x +5} + 3[/tex]
b
[tex]h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17[/tex]
c
[tex]h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10[/tex]
Step-by-step explanation:
From the question we are told that
[tex]h(x) = x^2 + x + 5[/tex]
and
[tex]g(x) = \sqrt[4]{x} + 3[/tex]
Considering first question
Now we are told g(h(x))
i.e
[tex]g(h(x)) = [x^2 + x + 5 ]^{\frac{1}{4} } + 3[/tex]
=> [tex]g(h(x)) = \sqrt[4]{x^2 + x +5} + 3[/tex]
Considering second question
Now we are told h(g(x))
i.e
[tex]h(g(x)) = [x^{\frac{1}{4} } + 3]^2 + x^{\frac{1}{4} } + 3 + 5[/tex]
=> [tex]h(g(x)) = x^{\frac{1}{2} } + 6x^{\frac{1}{4} } + 9+ x^{\frac{1}{4}} + 8[/tex]
=> [tex]h(g(x)) = x^{\frac{1}{2}} + 7x^{\frac{1}{4}} + 17[/tex]
=> [tex]h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17[/tex]
Considering third question
[tex]h(h(x))= [x^2 + x + 5]^2 + [x^2 + x + 5 ] + 5[/tex]
=> [tex]h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10[/tex]
Related Questions
George used the diagram below to help determine 30% of 60. Which expression could George have used?
30% of 60
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
6
6
6
6
6
6
6
6
6
6
(0.10)(6)
(0.10)(60)
(3)(6)
(3)(60)
Answers
Answer:
(3)(6)
Step-by-step explanation:
I did the quiz
George could have used the expression (0.30)(60) to determine 30% of 60.
How to determine . Which expression could George have usedGeorge could have used the expression (0.10)(6)(0.10)(60) to determine 30% of 60.
(0.10) represents 10% or 0.10 as a decimal. Since 30% is three times 10%, George can use three instances of (0.10) to represent 30%.
(6) represents the value 6, which is the number being multiplied by the percentage.
(0.10)(60) represents 10% of 60, which is 6.
Multiplying (0.10)(6)(0.10)(60) gives us the result of 6, which is 30% of 60.
Therefore, George could have used the expression (0.10)(6)(0.10)(60) to calculate 30% of 60.
Learn more about expression at https://brainly.com/question/1859113
#SPJ2
The sum of twice a number and 1 is less than 5.
Answers
Answer:
2x + 5 ≤ x - 3
Step-by-step explanation:
Answer:
[tex]2x + 1 < 5[/tex]
0/4 06 Fill in the Blank Text The ratio of the number of people who own a smartphone to the number of people who own a flip phone is 6:4. If 200 more people own a smartphone than a flip phone, how many people own each type of phone?
Answers
9514 1404 393
Answer:
smart phone: 600flip phone: 400Step-by-step explanation:
The difference in ratio units is 6-4 = 2, which corresponds to 200 people. So, each ratio unit corresponds to 200/2 = 100 people. Then the ratio 6 : 4 corresponds to 600 : 400 = smart : flip owners.
The number of phone owners is ...
600 smart phone
400 flip phone
What is the domain and range of y= x⁴-1?
anyone help me quickly please!!!
Answers
What do the factors (x+2)(-8x+70)in the factored form represent?
Answers
Answer:
-2(x+2)(4x-35)
Step-by-step explanation:
i promise its easy ok
Answers
Answer:
1)1/3
2)3
Step-by-step explanation:
rise over run then reduce
wrong
Write an equation of the line in slope-intercept form.
Answers
Answer:
The answer would be y=-1/3x+1.
Step-by-step explanation:
To find the slope, you must use the formula y2-y1/x2-x1. That would make it 1-2/0-(-3) which the slope is -1/3. Now, using the formula y-y1=m(x-x1) which would be y-2=-1/3(x-(-3) if you plug it in. Solving the equation, you would get y=-1/3x+1.
Suppose you conduct a hypothesis test about a population mean when the standard deviation is unknown by calculating a t statistic and determining whether to reject the null hypothesis. Assume that your t statistic is a positive value and that you will reject the null hypothesis when t is very large. For each of the potential changes to the components of your study design or the results listed below, determine the change to the t statistic.
a. A switch from using a two-tailed test to a one-tailed test
b. An increase in the sample variance (s^2)
c. An increase In the significance level (such as using α= 0.05 instead of σ= 0.02)
d. A decrease in the sample Size (n)
Answers
Answer:
a. remain the same
b. decrease
c. remain the same
d. t decreases
the answers are in bold letters under each question. Thank you
Step-by-step explanation:
a. A switch from using a two-tailed test to a one-tailed test
A switch from 2 tailed test to one tailed test will have t statistic remain the same. This does not change the value of t statistic
b. An increase in the sample variance (s^2)
when sample variance s^2 is increased, we will have it that standard error has increased. therefore t statistic will decrease
c. An increase In the significance level (such as using α= 0.05 instead of σ= 0.02)
t statistics will remain the same. this is due to the fact that significance level is not a part of the t statistics formula.
d. A decrease in the sample Size (n)
when sample size is decreased, standard error will increase. therefore t statistic will decrease.
The use of student-test implies:
Normal distributionSample size below n < 30The solution is:
a) t(s) will be the same
b) t(s) will decrease
c) t(s) will be the same
d) t(s) will decrease
a) To calculate t(s), we use the equation:
t(s) = (μ - μ₀)/s/√n (1)
where:
μ is sample mean
μ₀ is the population mean
s is sample standard deviation
n sample size
As we can see, t(s) does not depend on the confidence level (α), therefore changing confidence level, would not affect t(s) value
b) Increasing s², will make t(s) decrease as from equation (1)
c) As explained in letter a), t(s) does not depend on α. Hence, changing α, would not affect the value of t(s)
d) If the sample size n decrease t(s) will decrease
Related Links: https://brainly.com/question/14004751
Find the asymptotes of the rational function 2x+2 / x^2+1
Show work please. Thank you!
Answers
Step-by-step explanation:
Enter a problem...
Calculus Examples
Popular Problems Calculus Find the Asymptotes f(x)=(2x^2)/(x^2-1)
f
(
x
)
=
2
x
2
x
2
−
1
Find where the expression
2
x
2
x
2
−
1
is undefined.
x
=
−
1
,
x
=
1
The vertical asymptotes occur at areas of infinite discontinuity.
x
=
−
1
,
1
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
where
n
is the degree of the numerator and
m
is the degree of the denominator.
1. If
n
<
m
, then the x-axis,
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
.
3. If
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
and
m
.
n
=
2
m
=
2
Since
n
=
m
, the horizontal asymptote is the line
y
=
a
b
where
a
=
2
and
b
=
1
.
y
=
2
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
1
,
1
Horizontal Asymptotes:
y
=
2
No Oblique Asymptotes
Due to inflation, prices have increased by 12% since 2012. If the current price of a car is $34,500, how much would it have cost in 2012? Round your answer to the nearest cent.
Answers
Answer:
that depends on the year. like round from 2020?
Step-by-step explanation:
Both the circles in the figure below have a radius of 5 cm. Find the area of the rectangle?Immersive Reader
(1 Point)
50 sq.cm
50π sq.cm
100 sq.cm
200 sq.cm
PLEASE HELP ME PLS!
Answers
Answer:10
Step-by-step explanation:
I guessed
The area of the rectangle is 200 square cm
The radius of the circle is given as:
[tex]r = 5cm[/tex]
The width of the rectangle is made by 2 circles (i.e. 4 radii).
So, we have:
[tex]Width = 4r[/tex]
The length of the rectangle is made by 1 circle (i.e. 2 radii).
So, we have:
[tex]Length = 4r[/tex]
The area of the rectangle is then calculated as:
[tex]Area =Length * Width[/tex]
This gives
[tex]Area = 2r * 4r[/tex]
[tex]Area = 8r^2[/tex]
Substitute 5 for r
[tex]Area = 8 * 5^2[/tex]
[tex]Area = 200[/tex]
Hence, the area of the rectangle is 200 square cm
Read more about areas at:
https://brainly.com/question/14137384
The gross domestic product is?
Answers
3x2 − 6x − 10 + 9x + 5x2 − 8
Answers
8x^(2)+3x-18, simplified,
Find the distance between the points (13,19) and (13,-14)
Answers
Answer:
[tex]d = 33[/tex]
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in the 2 coordinates into the distance formula to find distance d:
[tex]d = \sqrt{(13-13)^2+(-14-19)^2}[/tex]
[tex]d = \sqrt{(0)^2+(-33)^2}[/tex]
[tex]d = \sqrt{(-33)^2}[/tex]
[tex]d = 33[/tex]
Answer:
the distance between the two points is 33 units.
Step-by-step explanation:
because the two points have the same x value, we only need to consider the y values.
find the difference to solve for the distance.
[tex]19-(-14)\\19+14\\33[/tex]
the answer is 33 units.
hope this helps :)
Last week, Mrs. Grant purchased a 3-pound
package of strawberries for $6.84. This week
she paid $10.24 for a 4-pound package of
strawberries. What was the difference in the
unit cost per pound that Mrs. Grant paid this
week compared to last week?
Answers
Answer: 1.28
Step-by-step explanation:
$6.84 divided by 3 = 3.28
$10.24 divided by 4 = 4.56
3.28 - 4.56 = 1.28
Hope this helps!
(If you need me to explain more just comment)
What is the area of the shaded part in the figure shown here?Immersive Reader
(1 Point)
200 sq.cm
150 sq.cm
125 sq.cm
100 sq.cm
PLEASE HELP FAST!
Answers
Answer:
The area of the shaded part is 100 [tex]cm^2[/tex]
Step-by-step explanation:
Subtracting Areas:
We can find the shaded area by adding or subtracting areas.
We'll use the latter method.
The total shape is a rectangle of side lengths 15 cm and 10 cm. Thus its area is:
[tex]A_t=15\ cm\cdot 10\ cm=150\ cm^2[/tex]
The area of each non-shaded square is:
[tex]A_s=(5\ cm)^2=25\ cm^2[/tex]
The total non-shaded area is
[tex]2*A_s=50\ cm^2[/tex]
Thus, the shaded area is:[tex]A_{shaded}=A_t-2*A_s=150 - 50 = 100[/tex]
The area of the shaded part is 100 [tex]cm^2[/tex]
simplify this expression 3 to the power of -3
27
-27
1/27
-1/27
Answers
Ruchi had 2 1/2 litres of milk. She used 1/2 litre for curd, 3/5 litre for tea, 1/4 litre for coffee, and the remaining she gave to her children in the breakfast. How much milk was used by the children for breakfast?
Answers
Answer: 1 15/100
Step-by-step explanation: 2 1/2- 1/2 = 2 - 3/4 = 1 3/4 - 3/5 = 1 15/100
Given parameters:
Total volume of milk Ruchi has = [tex]2\frac{1}{2}[/tex] liters
Amount used for curd = [tex]\frac{1}{2}[/tex] liters
Amount used for tea = [tex]\frac{3}{5}[/tex] liters
Amount used for coffee = [tex]\frac{1}{4}[/tex] liters
Unknown:
Quantity of milk used by the children for break fast = ?
Since this quantity is the remaining volume;
Remaining volume = Total volume - (Amount used for curd + amount used for tea + amount used for coffee)
Remaining volume = [tex]\frac{5}{2} - (\frac{1}{2} + \frac{3}{5} + \frac{1}{4} )[/tex]
Remaining volume = [tex]\frac{23}{20}[/tex]
The remaining volume used by the children is [tex]\frac{23}{20}[/tex]
Adult tickets for the movies are $11.50 each and child tickets are $8.75 each. How much would a family with 3 adults and 5 children pay for their tickets? (Multi-Step)
Answers
Answer:
$78.25
Step-by-step explanation:
Each adult = $11.50
Each child = $8.75
3 adults and 5 children
(11.50 x 3) + (8.75 x 5)
34.5 + 43.75 = $78.25
11.50 x 3 = 34.50
8.75 x 5 = 43.75
34.50 + 43.75 = 78.23
$78.23
What is 3/5 times 6/5
Answers
Answer:
if its not simplified then 18/5 but if it has to be simplified then its 3 3/5
Y=-2(x+3)^2+26
what is the standard form
Answers
Answer:
Y = 2x^2+12x+44 (standard form / quadratic form)
Step-by-step explanation:
2(x+3)^2+26
2(x^2+6x+9) + 26
2x^2+12x+18+26
2x^2+12x+44
-3 • 2 • (-2)
HELP fast
Answers
Answer:
12
Step-by-step explanation:
-3 * 2 is -6
-6 * -2 is 12
because a negative times a negative is positive
Tell whether −5.236¯¯¯¯¯ is terminating or repeating.
Answers
Answer:
Terminating
Step-by-step explanation:
Just did it!
Answer:
-5.236 is a terminating decimal. I hope this helps you!
please help 15 points
x2≥−4
Answers
Answer:
Solve for
x
by simplifying both sides of the inequality, then isolating the variable.
Step-by-step explanation:
Answer:
Does the name, Josh, Sound familiar? Maybe that'll ring a bell of why I'm saying this.
Step-by-step explanation:
8. Three groups of 10 kids. The average weight of a kid in each
group is 35 kilograms. One more kid joined each group.
i) The average weight of a kid in the first group is still 35
kilograms.
The average weight of a kid in the second group is now
36 kilograms.
iii) The average weight of a kid in the third group is now
34 kilograms.
Compute the weight of the new kid in each group.
25
Answers
Answer: 385
Step-by-step explanation:
Mean the three groups of 10 kids=35
Total weight of 3 groups (10x35)=350
Mean weight of 3 groups and one boy ( 35 + 350)=385
If a circle has an area of 84π units then what is the measure of its
radius in exact units?
a. 2√21 units
b. √ 54 units
C 10.4 units
d. 108 units
Answer quickly please
Answers
a. 2√21 units
Step-by-step explanation:Hi there !
Area formula
A = π·r²
replace A84π = πr²
r² = 84π/π
r² = 84
r² = 2²×3×7
r = √2²×3×7
r = 2√3×7
r = 2√21
Good luck !
Find the measure of the following angles.
1) M
2) M
3) m
4) m
5) M
Answers
NEED HELP 20 points
Solve for x: −4x − 4 = −4(x + 2)
0
−4
All real numbers
No solution
Answers
Answer:
no solution
Step-by-step explanation:
Help please, if you know how to do it. Posting separate questions so you get more points,l thanks
Answers
9514 1404 393
Answer:
y = x^2 +x +1; (-1/2, 3/4)y = 3x^2 -15x +12; (-2, 54), (5, 12)y = -1/2x^2 +2x +5; (0, 5)Step-by-step explanation:
1. The graph looks like the vertex is at x = -1/2. So we can start with the equation y = (x +1/2)^2 +k. At x=0, this becomes 1 = 1/4 +k, or k = 3/4. The leading coefficient of 1 is consistent with the other points shown, so the equation is ...
y = (x +1/2)^2 +3/4 . . . . vertex is (-1/2, 3/4)
y = x^2 +x +1
__
2. The zeros appear to be at x=1 and x=4, so the factored form of the equation is ...
y = a(x -1)(x -4)
At x = 0, this is ...
12 = a(-1)(-4)
3 = a
So, the equation is ...
y = 3x^2 -15x +12
The values at the two points of interest are ...
y = 3(-2-1)(-2-4) = 54 . . . . point (-2, 54)
y = 3(5 -1)(5 -4) = 12 . . . . point (5, 12)
__
3. Using the vertex shown, the vertex form of the equation is ...
y = a(x -2)^2 +7
Filling in the point (-2, -1), we can find the value of a:
-1 = a(-2-2)^2 +7
-8 = 16a
a = -8/16 = -1/2
So, the equation is ...
y = -1/2x^2 +2x +5
For x=0, the y-value is 5. The y-intercept is (0, 5).
Answer:
9514 1404 393
y = x^2 +x +1; (-1/2, 3/4)
y = 3x^2 -15x +12; (-2, 54), (5, 12)
y = -1/2x^2 +2x +5; (0, 5)
1. The graph looks like the vertex is at x = -1/2. So we can start with the equation y = (x +1/2)^2 +k. At x=0, this becomes 1 = 1/4 +k, or k = 3/4. The leading coefficient of 1 is consistent with the other points shown, so the equation is ...
y = (x +1/2)^2 +3/4 . . . . vertex is (-1/2, 3/4)
y = x^2 +x +1
6m+5n when m =6 and n=4
Answers
Answer:
Step-by-step explanation:First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:
5m +5n+6m−4n
Next, group like terms:
5m+6m+5n−4n
Now, combine like terms:
(5+6)m+(5−4)n
11m+1n
11m+n