By chain rule, the first derivative of the composite function f(x) = [tex]4^{5\cdot x - 9}[/tex] is equal to [tex]4^{u}[/tex] · 5 · ㏑ 4.
How to determine the derivative of a composite function
Herein we have the case of a composite function, that is, a function of the form f[u(x)]. Chain rule is a derivative rule used to find the derivative of composite functions, which is now defined:
df / dx = (df / du) · (du / dx)
If we know that u(x) = 5 · x - 9 and f(u) = [tex]4^{u}[/tex], then the derivative of the compond function is:
df / du = [tex]4^{u}[/tex] · ㏑ 4
du / dx = 5
Then, by chain rule:
df / dx = [tex]4^{u}[/tex] · 5 · ㏑ 4
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Harry took a 5-hour trip on which he averaged 40 miles per hour. What distance did he travel?
Answer:
200 miles
Step-by-step explanation:
if its 40 miles per hour then multiply 5 with 40 and you'll end up with 200 miles
What is the slope of the line?
Write the slope as a fraction.
Answer: the slope is 1/4
Step-by-step explanation:
(2,0.5) (4,1)
Use the formula for finding the slope:
[tex]\boxed {The\ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]
[tex]x_1=2\ \ \ \ x_2=4\ \ \ \ y_1=0.5\ \ \ \ y_2=1\\[/tex]
Hence,
[tex]\displaystyle\\The\ slope=\frac{1-0.5}{4-2}\\\\The\ slope=\frac{0.5}{2}\\\\The\ slope=0.25\\\\The\ slope=\frac{1}{4}[/tex]
Which is greater -2/5 or -3/8 ?
Answer:-2/5
Step-by-step explanation: due to them being negative we are using the simple thing of which number is closer to zero. -2/5 is closer which means that is it greater. -2/5 would be ahead on number line if you need a visualization
Answer:
-3/8
Step-by-step explanation:
1) Work out the options you are given
-2/5 = -0.4-3/8 = -0.3752) Find which one is greater
As the numbers are decimal the 'seemingly greater number' might actually be the smaller one.
To find out which decimal is greater you can easily plot them into a number line.
The number that is further to the left is smaller and the number closer to the right is higher!
If we were to plot the numbers one a number line the -0.375 would be closer to the right meaning it is greater.
HINTS:
To make it easier to divide minus numbers, at first completely forget about the minus (you can plug it back in at the end).
For example, if you were given -2/5 get rid of the minus to get 2/5 and from this we can easily figure out 2 ÷ 5 which would give us 0.4.
At the point where you have your final number you can add the - back in making it -0.4
Hope this helps, have a great day!
In 2021, Sally Morris, a single taxpayer, pays $3,000 of interest on qualified student loans. Her AGI is $40,000. What is her qualified student loan interest deduction in 2021?
The qualified student loan interest deduction in 2021 is $37500.
What is adjusted gross income?Adjusted gross income is an individual's total gross income less specific deductions in the United States income tax system. It is used to compute taxable income, which is AGI minus personal exemption and itemized deduction allowances. AGI is more important than gross income for most individual tax purposes.
AGI is calculated by taking your gross income and subtracting certain "above the line" deductions. 401(k) contributions, health savings account contributions, and educator expenses are common examples of deductions
As per Law, a maximum of $2,500 will be allowed to be deducted from the Income. Thus the following would be the solution.
Income of Sally Morris = $40,000
Less: Qualified student loan interest $2,500
Modified Adjusted Gross Income $37,500
The deduction is $37500.
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If shown,
AB
and
CD
are straight lines. Find x in each case.
WILL MARK BRAINLISIT
Answer:
4x+x+x+90=360
6x+90=360
6x=270
x=45
good luck!
4x+x+x+90=360
6x+90=360
6x=270
x=45
Bob’s employer covers 23% of his family’s annual health insurance premium. The balance of the premium is deducted in equal amounts from bob’s paycheck 26 times over the calendar year. If $185. 30 is withheld from each of bob’s paychecks, what is his family’s annual health insurance premium? a. $805. 65 b. $4,817. 80 c. $6,256. 88 d. $20,946. 96.
If $185.30 is withheld from each of Bob's paychecks, then his family's annual health insurance premium is $4817.80.
From the given information,
It was stated that the balance of the premium is deducted in equal amounts from Bob’s paycheck 26 times over the calendar year and $185.30 is withheld from each of Bob’s paychecks.
Therefore, the family’s annual health insurance premium will be calculated :
= $185.30 × 26
= $4,817.80
In conclusion, the correct option is $4,817.80.
therefore, his family's annual health insurance premium is $4817.80
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The owner of a bookstore buys used books from customers for $1. 50 each. The owner then resells the used books for 400% of the amount he paid for them. What is the price of a used book in this bookstore?.
Answer:
$7.50
Step-by-step explanation:
Which does point A represent in this box plot?
A box plot is used to study the distribution and level of a set of a set of numbers. A box plot is made up of two lines and a box. The two lines are known as whiskers.
The end of the first whisker represents the minimum number. The minimum number is the smallest number in the dataset. The end of the second whisker represents the maximum number. The maximum number is the largest number in the dataset.
The first line to the left represents the lower (first) quartile. The second line on the box represents the median. The third line on the box represents the upper (third) quartile.
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Write the correct function and online represented in the table below
HELP ASAP
Answer:
y = 5x -2
Step-by-step explanation:
The 5 is the slope. It is the change in y over the change in x. As the x changes by 1, the y changes by 5.
The -2 is the y intercept. This is at the point (0,-2) The -2 is the y intercept.
need help, please and thank you
The length of the chord of the circle CD is 3.2.
What is a chord of the circle?A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension.
Given that the vertical length from the centre to the chord is 2.1 and the length up to the circle is 1.7.
Radius = 1.7 +2.4 = 4.1.
The chord length will be calculated as,
CD = √(4.1² - 2.4²)
CD = √(16.81 - 5.76)
CD = 3.2
Therefore, the length of the chord of the circle CD is 3.2.
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1. Is the game fair? We are flipping a coin twice. The first player wins if we get 2 tails, and the second player wins if we get 1 head and 1 tail. 2. Is the game fair? we are tossing two dice and the first player wins if the sum on the dice is 9 and the second player wins if the sum on the dice is 5.
- Pls help due tomorrow !
Graph the piecewise function.
(6 points - 2 points for each piece)
Points of interval A (-1,-3) and (-2,-6)
Points of interval B is (1,1) and (2,-1)
How to find Piecewise function?
Determine which of the following intervals (or inequalities) the input belongs to before evaluating a piecewise function at any given input. The function specification for that specific interval can then simply be updated to reflect the new input.
[tex]f(x)=\left \{ {{3x, if x\leq -1} \atop {-2x+3, if 0 < x < 4}}\atop {2, if x\geq 4}\right.[/tex]
lets take 3x as Interval A
-2x+3 as interval B
and 2 as interval C
Now lets calculate the interval A
f(x)=3x
as x≤-1
∴f(-1) = 3(-1)
=(-3)
∴ point is (-1,-3)
∴f(-2) = 3(-2)
=(-6)
∴ point is (-2,-6)
Now lets calculate the interval B
f(x)=-2x+3
as 0<x<4
∴f(1) = -2(1)+3
=-2+3
=1
∴ point is (1,1)
∴f(2) = -2(2)+3
=-4+3
= -1
∴ point is (2,-1)
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the equation of the curve is y = x^2 + ax + b. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.
The turning point of the parabola is the point (2, - 9).
What is the turning point of a quadratic equation?
Quadratic equations represents parabolae and the vertex of the parabola represents the turning point as the slope of the curve changes its sign, from positive to negative or viceversa. The vertex can be derived by the vertex form of the equation of the parabola:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantSince the quadratic equation has two real coefficients, we need the location of two points on Cartesian plane to find one solution. First, create the system of linear equations:
b = - 5 (1)
5 · a + b = - 25 (2)
Second, substitute b in (2) and clear a:
5 · a - 5 = - 25
5 · a = - 20
a = - 4
Third, write the quadratic equation:
y = x² - 4 · x - 5
Fourth, transform the equation into vertex form by completing the square:
y + 9 = x² - 4 · x + 4
y + 9 = (x - 2)²
Fifth, write the vertex of the parabola:
(h, k) = (2, - 9)
The point (2, - 9) represents the turning point of the parabola.
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Find each probability if you spin the spinner and roll the number cube.
10. P(blue, 2)
12. P(not blue, 5)
11. P(red, even)
13. P(yellow, not 4)
red
blue
yellow
red
4
6
5
Find the equation of the line passing through the given point and parallel to the given line.
( 7,-3) , 3y = 12x + 5
(-5, -2), y + 3x = 10
The equation of the lines passing the points and parallel to the equations ( 7,-3) , 3y = 12x + 5 (-5, -2), y + 3x = 10 is as follows:
y = 4x - 31y = -3x - 17.How to find the equation of a line?The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form. Therefore, let's represent the line in slope intercept form.
The equation of a line in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptParallel line shave the same slope.
Hence,
( 7,-3) , 3y = 12x + 5
y = 4x + 5 / 3
slope is 4
The equation of the line is y = 4x + b. let's find the y-intercept using (7, -3).
-3 = 4(7) + b
b = -3 - 28
b = - 31
Hence, y = 4x - 31
(-5, -2), y + 3x = 10
y = -3x + 10
slope = -3
Therefore, let's find y-intercept using (-5, -2)
-2 = -3(-5) + b
-2 = 15 + b
b = -2 -15
b = - 17
Therefore, y = -3x - 17.
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Eve play baketball. She make 4 free throw for every 3 free throw that he mie. If he mied 27 free throw at her lat practice, how many free throw did he make?
Using this probability, he would have to make 42.18% or 42 free throws, thus avoiding 27 free throws.
Averaged over 3 out of 4 free throws, the probability of a successful free throw is 0.75 and the probability of a missed free throw is 0.25.
There are several ways to score 3 of the 4 free throws.
Miss Hit Hit Hit
Hit Miss Hit Hit
Hit Hit Hit Hit Hit
So to calculate this probability we need to multiply the probability of each shot. Because when it comes to multiplication, the order of multiplication doesn't matter, it's just the numbers that matter, only her 4-day probability that the shot will be taken. be the same.
So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875
Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18% shot will be taken.
So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875
Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18%.
Hence, Eve had to make 42 free throws for getting 27 throws are mied.
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Which fractions are equivalent to 0.63 repeating?
===============================================
Work Shown:
[tex]\text{x} = 0.\overline{63}[/tex]
x = 0.63636363...
100x = 63.63636363...
100x - x = (63.63636363...) - (0.63636363...)
99x = 63
x = 63/99
x = (7*9)/(11*9)
x = 7/11
This table shows a few fractions equivalent to 7/11
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Multiply top} & \\ \text{and bottom by} & \text{Equivalent fraction}\\\cline{1-2}2 & 14/22\\\cline{1-2}3 & \boldsymbol{21/33}\\\cline{1-2}4 & \boldsymbol{28/44}\\\cline{1-2}5 & 35/55\\\cline{1-2}6 & 42/66\\\cline{1-2}\end{array}[/tex]
The terms in bold are the two answers
In other words, 7/11 = 21/33 when multiplying top and bottom by 3.
Also, 7/11 = 28/44 when multiplying top and bottom by 4.
To confirm those answers, use a calculator to find that
7/11 = 0.636363...
21/33 = 0.636363...
28/44 = 0.636363...
To rule out the non-answers, use the calculator to find that
14/21 = 0.667 approximately
7/12 = 0.5833 approximately
hi i was wondering if somebody can help me with this question. Given the inequality 4x ≤ 28, determine the value of x.
S:{7}
S:{9}
S:{12}
S:{38}
Answer:
Step-by-step explanation:
OK:
1. Isolate the x on the left side of inequality. Always remember if a number or variable crosses inequality, it becomes opposite!
4x ≤28
x ≤28/4
x ≤7
2. Double Check!
4*7 ≤28
28 ≤28 TRUE
x=7(s) or Choice A
Without calculating, order the quotients smallest to largest.
The order of the quotient from smallest to largest is given as follows:
42.6/70, 426/70, 42.6/0.07, 42.6/0.07.
What is a quotient?A quotient is given by the division of two terms a and b, that is:
a / b.
From this, we have that the dividend a and divisor b are inverse proportional, that is:
A large quotient is achieved when a is large and b is small.A small quotient is achieved when a is small and b is large.There are three divisions with the same term a, hence they are ordered, from smallest to largest, as follows:
42.6/70, 42.6/0.07, 42.6/0.07.
(the smallest the value of b, the largest the quotient).
The final quotient is:
426/70.
Dividing by 10 to have an equivalent value of a, we have that:
426/70 = 42.6/7.
Which is the second largest value of b, hence the second smallest quotient.
Missing InformationThe problem is given by the image shown at the end of the answer.
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The cost of endless chicken wings at Restaurant X is $4. The cost of chicken wings at Restaurant Z is 20 cent per wing plus a $1.60 charge for sauce. The total cost, c, of n chicken wings at either restaurant can be represented by an equation. Write and graph a system to find how many chicken wings you have to have for the cost to be the same at both restaurants.
Answer:
Step-by-step explanation:
Equation: $4 = 0.2x + $1.60
1. Subtract $1.60 from both sides to get $2.4 = 0.2x
2. Divide both sides by 0.2 to get the value of x. 12 = x.
ANSWER: You need to buy 12 chicken wings at restaurant Z for the cost to be the same. Hope this helped
What is the classification for this polynomial?
-6uv - 3u - 2v.
Click on the correct answer.
monomial
binomial
trinomial
5.
The area of a circle is 40 mm²,
determine the circumference.
Answer: the formula to find circumference is C=2times pie which is 3.14 times the radius. Radius is half of the diameter which in this case I believe would be 20 times that by 3.14 and get 62.8 then times that by two which gives you the answer of 125.6
Step-by-step explanation: correct me if I’m wrong
. The ratio of cups of almonds to cups of peanuts in a mixed nuts snack is 4 to 3.
How many cups of peanuts would be needed to make 49 cups of the mixed nuts
snack?
Number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups
The ratio of cups of almonds to cups of peanuts in a mixed snack = 4 : 3
Number of of cups of almonds = 4x
Number of cups of peanuts = 3x
Total number of cups of mixed nuts snack = 49 cups
Then the equation will be
4x + 3x = 49
Add the like terms
7x = 49
x = 49 / 7
x = 7
Number of cups of almonds needed = 4x
= 4×7
= 28 cups
Number of cups of peanuts needed = 3x
= 3×7
= 21 cups
Hence, number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups
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I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS
Answer:
third and last, can't promise that's right
What is another way to write (a6)(a²)?
a4
a8
a12
a36
If u can solve both the blanks that would be great
11/12+7/12 in simplest form
Answer:
The answer to your question could be either 3/2 (improper fraction), 1.5 (decimal), or 1 1/2 (mixed fraction).
Step-by-step explanation:
11/12 + 7/12 = 18/12
18/12 = 9/6
9/6 = 3/2
Alice changes size several times. The ratio of her orginal height to her second height is 24 to 5. The ratio of her second height ot he rthird height is 1 to 12. The ratio of her orginal height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is her shortest height?
Answer:
3 inches
Step-by-step explanation:
Let's call the heights H1 thru H4.
So we have
H1/H2 = 24/5
H2/H3 = 1/12
Therefore if we multiply these, we have
H1/H3 = 2/5
Finally we are given
H1/H4 = 16/1.
By logic we can see that H3 is the tallest.
Thus if H3 = 10 feet, H1 = 4 feet
And from that,
H2 = 1/12 (10 feet) = 5/6 feet = 10 inches
and finally
H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot =
3 inches
Answer:
3 inches
Step-by-step explanation:
Let's call the heights H1 - H4
Here, we have
H1/H2 = 24/5
H2/H3 = 1/12
And so, we have
H1/H3 = 2/5
Finally
H1/H4 = 16/1.
Thus if H3 = 10 feet, H1 = 4 feet
And from that,
H2 = 1/12 (10 feet) = 5/6 feet = 10 inches
And last,
H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot = 3 inches
What is the end behavior of the function f(x) = -5x³ + 2x² - 4x+6?
O down to the left, up to the right
O up to the left, down to the right
O up to the left, up to the right
Odown to the left, down to the right
Answer:
O up to the left, down to the right
Step-by-step explanation:
The function in your question will do the same thing that
f(x) = -x³ does.
Actually, even simpler, it will have the same end behavior as
f(x) = -x
which is just a line with negative slope, going down from left to right. The way end behavior is described: up to the left and down to the right.
In fact, all the functions with odd power as the biggest exponent will have the same end behavior.
(If the highest exponent is even, it acts like a parabola up+up or down+down.)