Step-by-step explanation:
[tex] - 1 > - 2(x - 4) - 5(4x - 7) \\ - 1 > - 2x + 8 - 20x + 35 \\ - 1 > - 2x - 20x + 8 + 35 \\ - 1 > - 22x + 43 \\ 22x > 43 + 1 \\ 22x > 44 \\ \frac{22x}{22} > \frac{44}{22} \\ x > 2[/tex]
Given the function f'(x)=x^{5}-5x^{3}, determine all intervals on which f is decreasing.
The function f'(x) is decreasing on the interval (-√5, 0) and (0, √5)
What is a function?A function is a mathematical equation that shows the relationship between two variables.
How to find the interval on which the function is increasing?Givenj the function f'(x) = x⁵ - 5x³, to find the points at which the function is increasing, we find its critical points by equating it to zero.
So, f'(x) = x⁵ - 5x³
x⁵ - 5x³ = 0
x³(x² - 5) = 0
⇒ x³ = 0 and x² - 5 = 0
⇒ x = 0 and x² = 5
⇒ x = 0 and x = ±√5
To determine the points at which f'(x) is decreasing, we differentiate f'(x) with respect to x and substitute the values of x into it.
So, we have
f'(x) = x⁵ - 5x³
df'(x)/dx = d(x⁵ - 5x³)/dx
f"(x) = 5x⁴ - 15x²
So, f'(x) is decreasing when f"(x) > 0.
So, substituting x = 0 into the equation, we have that
f"(x) = 5x⁴ - 15x²
f"(x) = 0⁴ - 15(0)²
= 0 - 0
= 0
Since f"(x) = 0. This is a point of inflection
Substituting x = √5 into the equation, we have that
f"(x) = 5x⁴ - 15x²
f"(x) = 5(√5)⁴ - 15(√5)²
= 5 (25) - 15 (5)
= 125 - 75
= 50
Since f"(x) = 50 > 0, f'(x) is decreasing
Substituting x = -√5 into the equation, we have that
f"(x) = 5x⁴ - 15x²
f"(x) = 5(-√5)⁴ - 15(-√5)²
= 5 (25) - 15 (5)
= 125 - 75
= 50
Since f"(x) = 50 > 0, f'(x) is decreasing
So, f'(x) is decreasing on the interval (-√5, 0) and (0, √5)
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1) Rick had to borrow $35,000 to buy a brand new
car. He has to pay 10% interest for 5 years. How
much interest will he have to pay?
80
On solving the provided question we can say that the total interest he pay in 5 year is = $17500.
How much is interest?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money. The basic interest formula is as follows: Interest is equal to P, R, and T. P is the principal sum (the beginning balance). Interest rate, R (usually per year, expressed as a decimal). T = Number of intervals of time (generally one-year time periods).
Money required to borrow new car is $35,000.
and Rick pay 10% interest per year
so, interest he pay in one year = $35000 x 10% = $3500
total interest he pay in 5 year is = $17500
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What hour should each influencer post to get exactly 64,500 likes?
Rihanna: L(t) = -1² +13t-20
Drake: L (t) = -2t² + 17.5t - 10
YoungBoy: L (t)=-² +30t-150
Answer should be in hours
Rihanna
Drake
Young Boy
A :: Hour 13 (1:00pm)
B :: Likes won't reach exactly 64,500
C :: Hour 18.24 (6:14pm)
Match with them
Answer:young boy
Step-by-step explanation:
The camp director is putting 85 sack lunches
The meaning of the situation involving the camp director and the sack lunches, is D. The number of lunches left over after packing the boxes.
What does the remainder show ?The remainder in this instance, shows the number of lunches that the camp director will not be able to fit in boxes and so will be left over after the boxes have been packed.
There are 85 sack lunches and yet only 3 lunches can go into a single box. The number of boxes would be:
= 85 / 10
= 10 boxes remainder 5 lunches
10 boxes will be filled with lunch sacks and 5 lunches will be leftover.
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The full question is:
The camp director is putting 85 sack lunches in boxes for a picnic. She can fit 8 lunches in each box. She does the division problem shown to find out how many boxes she will need. 85 divided 8 = 10 remainder 5
What is the meaning of the remainder in this situation?
A. The number of extra boxes needed.
B. The number of extra lunches needed.
C. The number of boxes left over after packing the lunches.
D. The number of lunches left over after packing the boxes.
What is the sum of the exterior angles for each of the parallelogram and the hexagon?
A) 90°
B) The answer depends on the number of sides of the polygon
C) 180°
D) 360°
Very confused, if you could please explain it to me, that would be great!!
The sum of the exterior angles for a parallelogram is 360°.
What is exterior angle?Exterior angles are angles that are formed outside two lines when they intersect. They are located outside the two lines, on the outside of the shape. They can be found by adding the two interior angles together, whose measurements are always equal to 180 degrees. Exterior angles are also supplementary angles, meaning that the sum of their measurements is always equal to 360 degrees.
This is because the four angles on the outside of the parallelogram are all right angles, and the sum of four right angles is 360°.
Similarly, the sum of the exterior angles for a hexagon is also 360°.
This is because the six angles on the outside of the hexagon are all 120° angles, and the sum of six 120° angles is 360°.
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SALE
50% OFF!
During the sale, Wanda pays $3 for a spinach salad. What was the original price?
Submit
Answer:
$6
Step-by-step explanation:
50% x 2 = 100%
3 x 2 = $6
Sketch the graph of the function f(x, y) x2
The graph of the function f(x, y) = [tex]x^2[/tex] is a three-dimensional parabolic surface that opens upwards.
It is symmetric around the x-axis. This means that the shape of the surface is the same on both the positive and negative x-values. It is also a concave-up function, which means the graph is curved upwards.
Its vertex is located at the origin (0,0) and the equation of the parabola is y =[tex]x^2[/tex]. This means that the x-values of the graph can be any real number, while the y-values will always be non-negative as the square of any real number is always non-negative.
As x-values increase or decrease, the y-values will also increase, resulting in a smooth and continuous surface. Overall, the graph represents the upward parabolic shape of x squared.
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17. Which expression is a factor of 6x² + 7x-5?
A 3x + 5
B 2x + 1
C 6x +1
D x + 5
Answer:
A
Step-by-step explanation:
6x² + 7x - 5
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 6 × - 5 = - 30 and sum = + 7
the factors are - 3 and + 10
use these factors to split the x- term
6x² - 3x + 10x - 5 ( factor the first/second and third/fourth terms )
= 3x(2x - 1) + 5(2x - 1) ← factor out (2x - 1) from each term
= (2x - 1)(3x + 5) ← in factored form
with 3x + 5 being a factor
help …………… me please
The value of x is 10 the answer being ten is because the smaller triangle is half the size of the bigger one.
What is a formula for a triangle?
To find a triangle's area, use the formula area = 1/2 * base * height. Choose a side to use for the base, and find the height of the triangle from that base. Then, plug in the measurements you have for the base and height into the formulaThe basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle. However, there are other formulas that are used to find the area of a triangle which depend upon the type of triangle and the known dimensions.The area of a triangle is the space enclosed within the three sides of a triangle. It is calculated with the help of various formulas depending on the type of triangle and is expressed in square units like, cm2, inches2, and so on.To learn more about formula for a triangle refers to:
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
Answer: There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9). ✅
PLEASEEEE GIVE BRANLIEST
Step-by-step explanation:
There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9). One statement that could be true for g is:
g(x) = 2x + 8
This function has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45. It also satisfies the values of g(0) = -2 and g(-9) = 6.
It's important to note that this is only one possible function that satisfies the given information and there are many other functions that could also work such as:
g(x) = 3x -2
g(x) = -2x +10
g(x) = x+5
So the statement that could be true for g is that "There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9)."
*Keep in mind you didn't specify a specifc statement to verify false or true*
PART B
Tim's upcoming move will span 250 miles. Which company should he hire? Explain how you found your
answer.
For upcoming trip. Tim should hire company A
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
Given,
Distance to cover = 250 miles
For company A
By the graph line passes through
(200, 200) , (0,150)
equation of the line,
y-150 = [(200-150)/(200-0)](x-0)
y-150 = [50/200] x
y = x/4 + 150
y = 0.25 x + 150
No. of miles = 250
y = 0.25×250 + 150
y = 62.5 + 150
y = $212.5
Price for company B
y' = 0.75x + 50
where x is number of miles
for 250 miles price of company B
y' = 0.75 × 250 + 50
y' = 187.5 + 50
y' = $237.5
∵ y < y'
∴Price of trip with company A is less than company B
Hence, Tim should hire Company A for upcoming trip.
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help me please i will give brainest
Answer:
b=2a+
Step-by-step explanation:
a=1/2(b-c)
a=1/2b-1/2c
a + 1/2c=1/2b
2/1(a+1/2c)=(1/2b)2/
2a+c=
b=2a+
PLEASE ANSWER FAST FOR TEST
Represent the following scenario as a rate and a unit rate.
Write your Unsimplfied Rates as unsimplified fractions.
Write your Simplified Unit Rates as whole numbers or decimals rounded to two decimal places.
Form
Representing Rates and Unit Rates in Multiple Ways
Unsimplified Rate
Simplfied Unit Rate
"per language"
Dawn spent $32.2 on 14 gallons of gas.
Rate of Dollars to Gallons
dollars
gallons
dollars per gallon
Rate of Gallons to Dollars
gallons
dollars
gallons per dollar
The amount per gallon that Dawn will spend is $2.3 per gallon.
How to calculate the value in the word problem?It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In the information given, it was stated that Dawn spent $32.2 in 14 gallons of gas. The amount per gallon will be:
= Total amount / Number of gallons
= $32.2 / 14
= $2.3
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how many groups of 5/3 are in 1
The number of groups of 5/3 are in 1 would be equal to 3/5
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
Division of fraction
Given that groups of 5/3 are in 1
= 1 ÷ 5/3
Then Multiply by the reciprocal of 5/3
The reciprocal of 5/3 is 3/5
1 ÷ 5/3
= 1 × 3/5
= 3/5
Therefore, the number of groups of 5/3 are in 1 is; 3/5
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(URGENT) lWhich pair of functions are inverses of each other?
If the two graphs are mirror images of one another across the line y = x, then they are inverse functions.[tex]$f(x)=\frac{x}{3}+10$ \\[/tex] and [tex]$g(x)=3 x-10$[/tex]
How do you find a pair of inverse functions?As for looking at the graphs, we already knew that. You should keep in mind that inverse functions are represented by two graphs that are mirror images of one another over the line y = x. The broadest definition of an inverse function is one that "reverses" another function.
The inverse, for instance, must take b to an if a function goes from a to b. When the first and second elements of each pair in the original function are switched, a set of ordered pairs is obtained that is known as the inverse of the function. The act of switching the x and y coordinates is known as obtaining an inverse. They aren't opposites. The output of the first function is sent through an inverse function, which then generates an output whose input was the first function.
So, option A) [tex]$f(x)=\frac{x}{3}+10$ \\[/tex] and [tex]$g(x)=3 x-10$[/tex] is the appropriate response.
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The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. About what percentage of the men are over 70.5 inches tall?
a ----2.5
b-----68
c-----16
d----5
e-----32
Answer:
Step-by-step explanation:
To find the percentage of men who are over 70.5 inches tall, we need to use the standard normal distribution table, which gives the proportion of observations that fall within a given range of standard deviation from the mean.
We first need to standardize the height of 70.5 inches by subtracting the mean (68 inches) and dividing by the standard deviation (2.5 inches) to get (70.5 - 68) / 2.5 = 0.8
This tells us that 70.5 inches is 0.8 standard deviations above the mean.
We can then look up the proportion of observations that fall within this range in the standard normal distribution table, which is approximately 0.1587 or 15.87%. So, the answer is (1-0.1587) = 84.13 or 84.13%.
So the answer is 84.13%
For the function below, write the differential. f(x) = ln(1 + x2) dy = Calculate dy for the given values of x and dx. x = 2 and dx = 0.2 dy = How accurate is dy in approximating ?y (i.e., what is their difference) to the nearest thousandth?
The dy for the given values of x and dx. x = 2 and dx = 0.2 dy is 0.16
The given function f(x) = ln(1 + x2) dy
In differentiation, we have a formula where f(x) is calculated:
d/dx ln=1/u.du/dx
Apply this formula for the given function:
f(x) = ln(1 + x2) dy
f'(x)= 1/x²+1*2x dx
f'(x)=2x/x²+1 dx
To calculate the dy for the given values of x and dx. x = 2 and dx = 0.2 dy
substitute these values into f'(x) we get:
f'(x)=2x/x²+1 dx
f'(x)=2(2)/2²+1 (0.2)
f'(x)=4/5(0.2)
f'(x)=0.16
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One-fifth per cent of the blades produced by a blade manufacturing factory turn out to be defective. The blades are supplied in packets of 10.Use Poisson distribution to calculate the approximate number of packets containing no defective in a consignment of1,00,000 packets.
Probability of defect per blade = 1/500 = 0.002
Poisson distribution :
Pₓ (k) = (x ^k)/k × e⁻ˣ
Where k = The number of defective blades in a packet.
For a packet of 10 blades the mean number of defect x = 0.002 × 10 = 0.02
1.) When k = 0
Pₓ(0) = (0.02⁰ / 0!) × e - 0.02 = 0.980199
The approximate number of packets containing blades with no defective is :
10000 × 0.980199 = 9802
2.) When k = 1
Pₓ(1) = (0.02 / 1!) × e-0.02 = 0.019604
Approximate number containing one defective is :
10000 × 0.019604 = 196
3.) When k = 2
Pₓ(2) = (0.02² / 2!) × e - 0.02 = 0.000196
Approximate number containing 2 defective :
0.000196 × 10000 = 1.9 = 2
4.) When k = 3
Pₓ(3) = (0.02³ / 3!) × e-0.02 = 0.000013
Approximate number containing 3 defective is :
0.000013 × 10000 = 0.13 = 0
Answer:
no defective blades in a consignment of 1,00,000 packets is 99837.
Step-by-step explanation:
we first need to find the mean number of packets containing no defective blades. This mean is equal to the total number of packets (1,00,000) multiplied by the probability of a packet containing no defective blades.
The probability of a blade being defective is given as 0.002 (or 2/1000) or 2/100 or 1/50 or 2%.
Since a packet contains 10 blades. So the probability of a packet containing no defective blades is (1 - 0.002)^10 = 0.999936 or (1-0.02)^10 = 0.99837
So the mean number of packets containing no defective blades is (1,00,000 * 0.99837) = 99837
Could someone please help me with this?
Answer:
b = 10
Step-by-step explanation:
[tex]y=(x-h)^2+k\\y=(x-(-5))^2+9\\y=(x+5)^2+9\\y=x^2+10x+25+9\\y=x^2+10x+34[/tex]
Please Help!!
Simplify -|-7+4|
Answer: 7-4
Step-by-step explanation:
So basically multiply (-1) to -7 and 4
-7(-1)=7 4(-1)=-4
then, 7-4
HELPPPP
Which of the following graphs represents a function?
A Th graph showing a circle intercepting the x-axis at 5 and -5 and the y-axis also at 5 and -5.
B The graph shows a parabola open to the top and touching the base at (0, 0).
C The graph shows a s- shaped curved line starting from (10, 2) and taking the curve at points (0, 1), (-1, 0), (0, -1), and (0, -3) and ending at (-10, -4).
D The graph shows a parabola open to the left and touching the base at (0, 0).
The graph that represents a function is:
The graph shows a parabola open to the top and touching the base at
(0, 0).
The graph shows a parabola open to the left and touching the base at
(0, 0).
Options B and D is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function can have many-to-one but not one-to-many.
A
The graph shows a circle intercepting the x-axis at 5 and -5 and the y-axis also at 5 and -5.
This means,
If the center of the circle is (h, k).
The coordinates of the circle are:
(5, k), (-5, k), (h, 5), and (h, -5)
(h, 5) and (h, -5) indicate one-to-many.
This is not a function.
B.
The graph shows a parabola open to the top and touching the base at
(0, 0).
The equation of the parabola is y = x².
For x = 1, y = 1
For x= -1, y = 1
This indicates many-to-one only.
This is a function.
C.
The graph shows an s-shaped curved line starting from (10, 2) and taking the curve at points (0, 1), (-1, 0), (0, -1), and (0, -3) and ending at (-10, -4).
The points (0, 1), (0, -1), and (0, -3) indicate one-to-many.
This is not a function.
D
The graph shows a parabola open to the left and touching the base at
(0, 0).
The equation of the parabola is y² = 4px.
This equation is a function.
Thus,
The graph that represents a function is a parabola open to the top and a parabola open to the left.
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For the following function f(x)=x-3/5 Find f^-1(x)
Answer:
the having of the record is that
What is t equal to 30+6t=11t
If 30+6t=11t then the value of t is: 6
How to solve the given equation?This is a simple algebraic equation. To solve for t, we can start by isolating t on one side of the equation.
The equation is 30 + 6t = 11t
First we can subtract 11t from both sides:
30 + 6t - 11t = 11t - 11t
This gives:
30 - 5t = 0
Next, we can add 5t to both sides:
30 - 5t + 5t = 0 + 5t
This gives:
30 = 5t
Finally, we can divide both sides by 5:
30 / 5 = 5t / 5
This gives:
t = 6
So, t is equal to 6.
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Use the division or the multiplication property of equality to 927/y = 309 solve . What is the result?
Maria makes a fruit salad. The table shows the amounts of different kinds of fruit that she uses. Kind of Fruit Amount Grapes 3 2/3 cups Melon 2 1/4 cups Pineapple 23/4 cups Strawberries? The amount of strawberries that Maria uses is 3/8 times the amount of the other fruits combined. How many cups of strawberries does Maria use?
Proportionately, the number of cups of strawberries that Maria needs to use is 3¹/₈ cups.
What is proportion?Proportion refers to a part of a whole.
Proportion is a ratio of one value to another.
Proportions are depicted as decimals, fractions, or percentages.
In this situation, we know that the amount of strawberries is a fractional value of the combined fruits.
Thus, we can multiply the fraction of strawberries against the combined value of the other fruits to determine the number of cups of strawberries needed.
Kind of Fruit Amount
Grapes 3²/₃ cups
Melon 2¹/₄ cups
Pineapple 2³/₄ cups
Total of other fruits = 8²/₃ cups
Strawberries ?
Strawberries = 3¹/₈ (8²/₃ x ³/₈)
Thus, Maria needs 3¹/₈ cups of strawberries.
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Find the sum of 458 and 342. Use place value and find the sums of the hundreds, tens, and ones.
Estimated total is equal to (500 + 300) = 800.
What are place value ?In mathematics, place value refers to the relative importance of each digit in a number.
These locations begin at the unit's location (ones place).
The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located.
The value of a digit depends on its position in the number, which might result in a number having two comparable digits with distinct values.
Using place value diagrams, we can check that the digits are positioned correctly.
The right place for each digit in a number is shown on a place value chart. In order to precisely determine the positional values or worth of the various digits in a number, we must first write the.
According to our question -
to the next hundreds of 458 = 500, the estimated value
to the nearest hundreds of 324, the estimated value is 300.
Estimated total is equal to (500 + 300) = 800.
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(Factoring Algebraic Expressions LC)
Rewrite 8a + 32ab using a common factor.
A: 8ab(1 + 32ab)
B: 8ab(0 + 4)
C: 8a(1 + 4b)
D: 8a(0 + 4b)
Answer:
The answer is option c.
Please could you give me brainliest
How do the interior and exterior angles of a polygon relate? *
They are congruent
O They are supplementary
O They are complementary
There is no relationsh
The function f(x) = 4x + 9 represents the number of animals adopted at one shelter, where x is the number of months.
The function g(x) = x + 2 represents the number of animals adopted at another shelter, where x is the number of months.
Part A: What is (f + g)(x)? Show all necessary steps. (2 points)
Part B: Evaluate (f + g)(5). Show your work. (2 points)
Part C: Explain what your answer represents in terms of the scenario. (2 points)
a. The function, (f + g)(x), is evaluated as: (f + g)(x) = 5x + 11
b. The function (f + g)(5) = 36
c. (f + g)(5) = 36 means in 5 months, the total number of animals adopted at the two shelters is 36.
How to Evaluate Functions?We can evaluate functions just as we solve normal algebraic equations when we plug in the given value of a variable.
Given the following:
f(x) = 4x + 9 [number of animals at one shelter]
g(x) = x + 2 [number of animals at another shelter
Part A: Find (f + g)(x)
(f + g)(x) = f(x) + g(x) = 4x + 9 + x + 2
Combine like terms:
(f + g)(x) = 5x + 11
Part B: Find (f + g)(5)
Substitute the x = 5 into the function (f + g)(x)
(f + g)(5) = 5(5) + 11
(f + g)(5) = 25 + 11
(f + g)(5) = 36
Part C: It means in 5 months, the total number of animals adopted at the two shelters is 36.
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Please answer this question quickly for me
Answer:
Step-by-step explanation:
The inverse of the statement "If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent" is "If two triangles are not congruent, then the two sides and the included angle of a triangle are not congruent to two sides and the included angle of another triangle."