The required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
As per the question we have to determine the derivative of the f(x) = (x⁴ + 9x² − 5)⁴.
What is derivative?A derivative is defined as the rate of change of the function with respect to the respective variables.
Here,
According to the question,
f(x) = (x⁴ + 9x² − 5)⁴
Differentiate both sides with respect to x.
f'(x) = d[(x⁴ + 9x² − 5)⁴] / dx
f'(x) = 4 (x⁴ + 9x² − 5)³ × (4x³ + 9×2x)
f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x)
Thus, the required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
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The velocity of an object fired directly upwards given v=96-48t, where t is in seconds. When will the velocity be between 48 and 80 feet per second
Write two numbers, neither of which is 8, whose GCF is 8.
To find two numbers whose GCF is 8 but neither is 8, choose multiples of 8 that are not equal to 8 itself.
Explanation:To find two numbers whose GCF is 8 and neither of which is 8, we need to find two numbers that have 8 as their largest common factor.
The easiest way to do this is to select a number that is a multiple of 8, such as 16, and then choose another number that is also a multiple of 8, but not equal to 8 itself, such as 24.
So, the two numbers whose GCF is 8 and neither of which is 8 are 16 and 24.
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Convert decimal 305 to binary. show your work. how many bytes will it take to store the number
Find the three consecutive integers whose sum is 171
171 / 3 = 57
56 + 57 +58 = 171
the 3 numbers are 56, 57 & 58
Think of a number, divide it by 5 and then add 27 to the result. The resulting number is half of the original number. What was the original number?
(Answer with work please)
a car cost $25000 plus $675 for tax, title, and license fees. Ari finances the car by putting down $2,500 in cash and taking out a 3-year, 4% loan. what will his monthly payments be (if figured across all 3 years rather than annually)?
Carla and Ross competed in the long-jump at a track meet. Carla jumped 3.5 meters. Ross jumped 99 inches. Who jumped farther and by approximately how many feet? Use 1 m = 3.27 ft. Explain how you solved this problem.
A basketball court is shaped like a rectangle. It has a perimeter of 288 feet. The width of the court is 50 feet. What is the length of the court? Use the following formula to help you decide: Pr = 2l + 2w where Pr is the perimeter of a rectangle, l is the length, and w is the width
using the given formula, fill in the numbers where they belong
perimeter = 288
width = 50
so Pr = 2l + 2w becomes
288 = 2l +2(50)
288 = 2l +100
subtract 100 from each side
188 =2l
divide both sides by 2
l = 188 /2
l = 94
length = 94 feet
Z varies inversely with the product of x and y. When x=2 and y =4 z=0.5 what is the value of x=4 and y=9
The perimeter of parallelogram WXYZ is 50 millimeters. What is WZ?
identify the function rule shown in the table.
n 3 4 5 6
y 2 1 0 -1
a. y = 2 + n
b. y = 5n
c. y = 5 -n
d. not enough information
3+2 = 5
4+1 = 5
5+0 = 5
6-1 =5
so answer would be C. y=5-n
check:
5-3 = 2
5-4 =1
5-5 =0
5-6 = -1
Your sister has x dollars. You have 3 times the amount she does
Pleasssssseeeee hellppppppppppppppppppppppppppppp
what is the vertex of the quadratic function: y=-3(x+5)^2-4
thomas earned $80 plus 10% of his sales for a net of $132. How much were his sales?
subtract base pay ( $80) from total pay
132-80 = 52
divide 52 by 10% for total sales = 52/0.1 = 520
his sales were $520
Answer:
Sales amount is $520 .
Step-by-step explanation:
Let us assume that the sales amount be x .
As given
Thomas earned $80 plus 10% of his sales for a net of $132.
10% is written in the decimal form
[tex]= \frac{10}{100}[/tex]
= 0.10
Thus
Total Earned amount = Earned amount + 0.10 × Sales amount
Put all the values in the above
132 = 80 + 0.10 × x
132 - 80 = 0.10x
52 = 0.10x
[tex]x = \frac{52}{0.10}[/tex]
x = $520
Therefore the sales amount is $520 .
bo has 23 video games for sale he plans to donate the money he makes from each sale to a local charity what is the least amount of money in whole dollars bo should charge for each game in order to raise 100$
Answer: $5
Step-by-step explanation:
Let x be the least charge for each video game.
Given : Total games for sale =23
The required minimum amount needed to raise by selling video games =$100
Then the required inequality:
Total games × x ≥ Required minimum amount
i.e. [tex]23x\geq100[/tex]
Divide 23 from both sides , we get
[tex]x\geq 4.34782608696\approx5[/tex]
Hence, Bo should Charge $5 for each game in order to raise 100$.
Solve |a| = -6
{-6}
{-6, 6}
Ø
Mathematically, the absolute value of a number is always non-negative, which means it can never be equal to a negative number. Hence, there's no possible value for 'a' in the equation |a| = -6, making the correct answer Ø.
Explanation:To solve |a| = -6, it’s important to understand the concept of absolute values. The absolute value of a number is its distance from zero on the number line. Therefore, it's always non-negative, because distances cannot be negative. Thus, there are no values of 'a' that would make |a| = -6, because absolute values cannot be negative.
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The equation x2 – 1x – 90 = 0 has solutions {a, b}. What is a + b
Answer:
Step-by-step explanation:
Alright, let get started.
The given equation is : [tex]x^2-1x-90=0[/tex]
This is a quadratic equation.
The standard form of a quadratic equation is : [tex]AX^2+BX+C=0[/tex]
Comparing the given equation with standard one, the values of A ,B and C are :
A is 1
B is -1
C is -90
Since a and b are the roots of the equation, so the formula for sum of roots a+b will be = [tex]\frac{-B}{A}[/tex]
a+b=[tex]-\frac{-1}{1} =1[/tex]
hence a+b will be 1 : Answer
Hope it will help :)
There is an average of 3.5 x 10^−2 kilograms of dissolved salt in each liter of seawater. The South China Sea contains approximately 9.88 x 10^18 liters of seawater. About how many kilograms of dissolved salt are in south china sea Enter your answer, in scientific notation, in the boxes. __×10__ kg
Answer:
[tex]3.458\times10^{17}[/tex] kg
Step-by-step explanation:
It has been given that in 1 liter of seawater, the amount of dissolved salt is [tex]3.5\times10^{-2}[/tex]kg
Let x kg of salt is dissolved in [tex]9.88\times10^{18}[/tex] liters of seawater.
Thus, we have
[tex]\frac{1}{3.5\times10^{-2}}=\frac{9.88\times10^{18}}{x}[/tex]
On cross multiplying, we get
[tex]x=3.5\times10^{-2}\times9.88\times10^{18}\\\\x=34.58\times10^{16}[/tex]
In scientific notation,
[tex]x=3.458\times10^{17}[/tex]
Thus, [tex]3.458\times10^{17}[/tex] kg of salt is dissolved.
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations. graph of line going through ordered pairs (0, 300) and (450, 0)
Which of these r-value represent the strongest correlation-0.7, -0.6, -0.5, -0.8
Cassie has 1/2 pound of sugar in her cabinet. Her cake recipe calls for 2/10 of a pound of sugar. How many cakes can she make?
P (1.23 < z < 3.24) =
The value of the P (1.23 < z < 3.24) is 0.49 after using the Z table and concept of the probability.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
P (1.23 < z < 3.24)
As we know, from the normal distribution, It's the probability curve of a continuous distribution that's most likely symmetric around the mean.
On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
From the Z curve:
P (1.23 < z < 3.24) = 0.49
Thus, the value of the P (1.23 < z < 3.24) is 0.49 after using the Z table and concept of the probability.
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What number is 30% of 150
The percentages can also be represented in decimal or fraction form. In academics the marks obtained in any subject are calculated in terms of the percentage. Here 30% of 150 is 45.
What is percentage?In mathematics, the percentage is defined as a number or ratio which can be expressed as a fraction of 100. If we have to calculate the percentage of a number, divide the number by the whole and it should be multiplied by 100.
So percentage means a part per hundred. The word percent means per 100. It is represented by the symbol %. For example 10% is equal to 1/10 fraction. Percentage have no dimension.
The formula used to calculate the percentage is:
Percentage = Value / Total value × 100
30% of 150 is:
150 × 30 /100 = 45
Thus 30% of 150 is 45.
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A number is one seventh of another number the difference of the number is 18 assume u are subtracting the smaller number from the other number
Sarah only knows the diameter of a circle. What should she do to find the radius?
Multiply the diameter by 2.
Divide the diameter by 2.
Multiply the diameter by pi
Divide the diameter by pi
Answer:
Therefore. The correct option is B. Divide the diameter by 2.
Step-by-step explanation:
Diameter of the circle : It is defined a line segment joining two points on the circumference of circles provided the segment passes through the center of the circle.
Radius of the circle : It is defined as a line segment joining any point on the circle to the center of the circle.
So, it can be illustrated that the radius is half of the diameter of the circle.
If we are given the diameter of the circle and we need to find the radius of the circle.
So, we will divide the given diameter of the circle by 2 to obtain the required radius of the circle.
Therefore. The correct option is B. Divide the diameter by 2.
Elle wanted to order candy online. Company A is offering 2 1/2 pounds of chocolate for $32.50, while Company B is offering 2 3/4 pounds of the same chocolate for $35.00. Which company is offering the lowest price per pound. Justify your answer.
Based on the price offered per company, we can infer that the cheaper company is Company B.
The cheaper company is the one that is selling a pound of chocolate for a lower price than the other company.
First convert the mixed fractions to decimals for easier calculation:
Company A = 2 ¹/₂ = 2.5 pounds
Company B = 2 ³/₄ = 2 + (3/4) = 2.75 pounds
The cost per pound is:
= Cost of chocolate / Number of pounds
Company A: Company B:
= 32.50 / 2.5 = 35 / 2.75
= $13 per pound = $12.73
In conclusion, Company B is cheaper for selling at $12.73.
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Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceeds of $400. Determine if Elly made a profit or loss, and how much per share.
Answer:
She made a profit of $ 2 on each share of stock
Step-by-step explanation:
Elly buys 75 shares of stock in a mutual fund for a total investment of $450.
cost of 1 share of stock= $ 450/75
= $ 6
She sells 50 shares of her stock for total proceeds of $400.
selling price of 1 share of stock=$ 400/50
= $ 8
Hence, She made a profit of $ 2 on each share of stock ($8-$6=$2)
5c + 2a − b; a = 5, b = 11, and c = 3
The value of the expression 5c + 2a − b at a = 5, b = 11, and c = 3 will be 14.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5c + 2a − b
The value of the expression 5c + 2a − b at a = 5, b = 11, and c = 3 will be given as,
⇒ 5c + 2a − b
⇒ 5 x 3 + 2 x 5 − 11
Simplify the expression, then we have
⇒ 5 x 3 + 2 x 5 − 11
⇒ 15 + 10 − 11
⇒ 25 − 11
⇒ 14
The worth of the articulation 5c + 2a − b at a = 5, b = 11, and c = 3 will be 14.
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Use cross products to determine whether the points a, b, and c are collinear.