Answer:
FALSE.
Step-by-step explanation:
Given:
h(x)=x^2/f(x) f(3) = 2 f'(3) = 4To Find:
Whether h'(3) = -12 or not.Formula used:
For a function y = f(x)/g(x), the differentiation of y is defined as y' = [f'(x)*g(x) - g'(x)*f(x)]/(g(x))^2. This is know as quotient rule of differentiation.Using the above formula, we have
h'(x) = [2x*f(x) - f'(x)*x^2]/(f(x))^2
So, h'(3) = [2*3*2 - 4*(3)^2]/(2)^2
h'(3) = (12-36)/4
h'(3) = -24/4 = -6
So, h'(3) = -6 and not -12.
So, the given value is FALSE.
1) The compound interest of a sum of money is Rs 13310 and in 4 years is Rs 14641. Find the rate of interest and sum.
The rate of interest is 10% and the sum is Rs 10,1000.
What is compound interest?The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.
The compound interest formula is given by
Compound Interest = Amount – Principal
Here, the amount is
[tex]A=P(1+\frac{r}{100} )^{n}[/tex] where,
A = amount
P = principal
r = rate of interest
n = time (in years)
Given:
C.I. of a sum of money in 3 years = Rs 13310
C.I. of a sum of money in 4 years = Rs 14641
Let the principal be P and the rate of interest be r%
Then, according to the question,
For 3 years:
[tex]13310=P(1+\frac{r}{100} )^{3}[/tex] ..... (1)
For 4 years:
[tex]14641=P(1+\frac{r}{100} )^{4}[/tex] ..... (2)
Dividing equation (2) by (1), we obtain
[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]
⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]
⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]
⇒[tex]r=\frac{100}{10}[/tex]
⇒ r = 10%
Now, substituting r in equation (1),
[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]
⇒[tex]13310=P(\frac{1331}{1000} )[/tex]
⇒P = Rs 10,000
Therefore, the rate of interest is 10% and the sum is Rs 10,1000.
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help i don’t get it
answers pls
Answer: 13
Step-by-step explanation:
As the sum of the angles of a triangle is 180, we have that 39 + 90 + 3x+12 = 180.
3x = 180 - 39 - 90 - 12
3x = 39
x = 13
You cut a 90-foot rope into 6 pieces of equal length. What is the length of
each piece?
Answer:
Length = 15
Step-by-step explanation:
The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation
90 feet / 6 pieces
Which equals
90 feet / 6 pieces = 15 feet/piece (15 feet per peice)
Hope this helps :)
the ratio of 26,000 bytes to 48,000 bytes can be written in fractional form as
Answer:
26000:48000
26000/48000
26/48(cancel the zeros)
13/24
fractional form=13/24
find the number of sides of a regular polygonwhose exterior angle measure 18°
Answer:
20
Step-by-step explanation:
The sum of the exterior angles of a polygon add to 360. 360 divided by 18 is 20.
(ANSWER AT THE BOTTOM)A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular container costs the company $16, while the cylindrical container costs the company $15. If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs? Explain.
How many rectangular containers will be necessary to package 6,400 candles?
How many cylindrical containers will be necessary to package 6,400 candles?
Which container should the company use to minimize costs? Explain.
143,157,the rectangular containers,because it will cost the company $67 more to use the cylinder containers.
The number of rectangular containers will be necessary to package 6,400 candles is 143
The number of cylindrical containers will be necessary to package 6,400 candles is 157.
The container that would minimise cost is the rectangular container because it would $67 less to use the rectangular container.
Which container minimises costs?The first step is to determine the total cost of packing 6400 candles using the rectangular container.
Total cost = number of containers needed x cost of one rectangular container
Number of containers needed = total number of candles to be packages / number of candles the container can hold
6400 / 45 = 142.22 = 143 rectangular containers
Total cost = $16 x 143 = $2,288
The next step is to determine the total cost of packing 6400 candles using the cylindrical container.
Total cost = number of containers needed x cost of one cylindrical container
Number of containers needed = total number of candles to be packages / number of candles the container can hold
6400 / 41 = 156.1 = 157 cylindrical containers
Total cost = $15 x 157 = $2,355
Difference in costs = $2,355 - $2,288 = $67
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7. If Antonio makes x dollars per regular hours, and his boss tells him that he is
going to get paid over time at double time, write an equation to find his hourly
rate if he makes $1578.5 working 55 hours this week.
The equation for the hourly rate is 55x = 1578.5
For double hourly rate for overtime, it is 55 x 2x= 1578.5
Given
Antonia makes X dollars for regular hours
And 2x dollars for over time
Since he works 55 hours this week he works 8 hours a day
Hence the equation is as follows
55x = 1578.5
x= $28.7
In case of double payment during overtime
He gets double amount as following equation
55 x 2x
55 x 2(28.7) = $3157
Hence the equation to find his hourly rate is 55x = 157.85
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for a sequence of events in which the first event can occur n 1 ways, the second event can occur n 2 ways, the third event can occur n 3 ways, and so on, the events together can occur a total of n 1 times n 2 times n 3 times ... ways. this is called .
The most appropriate choice for Independent event and multiplicative counting rule will be given by
This is known as multiplicative counting rule.
What is Independent event and multiplicative counting rule?
Event that is not dependent on any other event is called independent event.
Let A and B be two independent events.
P(A∩B) = P(A) [tex]\times[/tex] P(B)
If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.
Here,
Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on
Also assuming that the events are independent
The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways
This is known as multiplicative counting rule.
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pls pls help whoever gets it right gets marked brainliest
Answer:
13 units
Step-by-step explanation:
[tex]d=√((x_2-x_1)²+(y_2-y_1)²) [/tex]
[tex] \sqrt{( - 2 - ( -14)^{2} } + ( - 4 - 1) {}^{2} [/tex]
[tex] \sqrt{12 {}^{2} } + ( - 5) {}^{2} [/tex]
[tex] \sqrt{169} [/tex]
= 13 UnitsThe equation y = 0.43x + 50 models the cost y of renting a car if the car is driven x
miles.
According to the model, what is the best estimate of the cost for renting a car if you
plan to drive 489 miles? Please round your answer to the nearest dollar.
By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.
What do we mean by equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.
Now, solve for y when the value of x is 489.
y = 0.43x + 5y = 0.43(489) + 5y = 210.27 + 5y = $215.27Rounding off: y = $215
Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.
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A store sells small notebooks for $6 and large notebooks for $10. If a student buys 6 notebooks and spends $48, how many of each size did he buy?
They could buy 8 small notebooks or 3 large notebooks and 3 small notebooks.
Answer: just one way to do it. You can buy 3, large books and 3 small books
Step-by-step explanation:
10x3=30
48-30=18
18 divided by 3 = 6
How is the graph of each equation related to
standard form Ax + By = C?
Answer:
When A = 0 and y = 1 and C = 2
0x + 1y = 2
y = 2 No matter what x is, y will always be 2 and this will create a horizontal line.
Step-by-step explanation:
Please answer the question in the photo
Answer:
u= 30
Step-by-step explanation:
the sum of all angles on a triangle is 180* so u add the others (120+30)
that brings it to 150 then 180-150=30*
help asap please and thank u
Answer:
y = 5, 3
x = 155, 171
(y = 5, x = 155)
(y = 3, x = 171)
Step-by-step explanation:
(8y - 15) = (y²)
-8y + 15 -8y + 15
--------------------------------
y² - 8y + 15 = 0
(y - 5) (y - 3) = 0
--------------
y = 5, 3
----------------------------------------------------------------------------------------------------------
y² + x = 180
(5)² + x = 180
25 + x = 180
-25 -25
--------------------
x = 155
(3)² + x = 180
9 + x = 180
-9 -9
------------------
x = 171
----------------------------------------------------------------------------------------------------------
I really hope this helps!
Find the area of the pool. Write as a polynomial.
Pool
6x
3x-5
If f(x) = 4x6 + x² + 4, then what is the remainder when f(x) is divided by x -1?
Answer:
9
Step-by-step explanation:
[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]
You purchase a home for $200,000 which appreciates at 2.5%. How much is it worth in 7 years?
Answer: The answer I came up with is: $237,737
Please help me please
F(4) if f(x) = 3 x -1
Answer:
f(4) = 11
Step-by-step explanation:
f(x) = 3 x -1
Let x = 4
f(4) = 3*4 -1
= 12-1
= 11
f (x) = 3x - 1
f (4) = 3 × 4 - 1
f (4) = 12 - 1
f (4) = 11
Hope Helpful :-;
Use proof by contradiciton to prove that the sum of the squares of two odd integers cannot be a perfect square. HINT: you can use the fact that the sum of two odd numbers must be even without proof
Assume to contrary that the sum of the squares of two odd integers can be the square of an integer. Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
What is a square?A quadrilateral with four equal sides is called a square. There are the numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about square's characteristics, mathematics, and design.
A square has four corners and is closed, two-dimensional (2D) object.
Assume to contrary that the sum of the squares of two odd integers can be the square of an integer.
Suppose that x,y,z∈Z such that [tex]x^{2} +y^{2} =z^{2}[/tex], and x and y are odd.
Let, x=2m+1 and y=2n+1.
Hence,
[tex]x^{2} +y^{2} =(2m+1)^{2} + (2n+1)^{2}[/tex]
=[tex]4m^{2}+4m+1+4n^{2}+4n+1[/tex]
=[tex]4(m^{2}+n^{2}) + 4(m+n)+2[/tex]
=[tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex]
Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.
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PLEASE HELP!: I'm so confused about what equations to write for the problem. All I need is the equations and I can solve it alone! I'll give brainly!
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal, and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
Using simple interest, the amounts invested into each account are given as follows:
Paper returns: $3,500.Metal returns: $1,500.Glass returns: $3,000.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = P(1 + rt)
In which:
P is the initial amount.r is the interest rate, as a decimal.The amount of interest after t years is given by:
I(t) = Prt
You invest $8,000 in 3 investment accounts, hence:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
From the rates of the account, we have that:
[tex]I_1 = 0.02P_1[/tex][tex]I_2 = 0.04P_2[/tex][tex]I_3 = 0.05P_3[/tex]The amount invested in the glass account was double the amount invested in the metal account, hence:
[tex]P_3 = 2P_2[/tex]
The yield was a total of $280 at the end of one year, hence:
[tex]I_1 + I_2 + I_3 = 280[/tex]
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
From the first and the third equations, we have that:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
[tex]P_1 + 3P_2 = 8000[/tex]
[tex]P_1 = 8000 - 3P_2[/tex]
Hence the amount of the metal investment can be found as follows:
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]
[tex]0.08P_2 = 120[/tex]
[tex]P_2 = \frac{120}{0.08}[/tex]
[tex]P_2 = 1500[/tex]
Hence the other investments are given as follows:
Paper: 8000 - 3 x 1500 = $3,500.Glass: 2 x 1500 = $3,000.More can be learned about simple interest at https://brainly.com/question/20690803
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8. Which best describes the relationship between the line that passes through (-1, -8) and (4,-4) and the line
that passes through (2, -9) and (7,-5)?
a. parallel
b. perpendicular
C.
same line
d. neither perpendicular nor parallel
Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Relationship between lines in this caseIn this case, you can calculated in this case:
Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:
m= (-4 - (-8))÷ (4 - (-1))
m= (-4 + 8)÷ (4 + 1)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-8= 4/5× (-1) + b
-8= -4/5 +b
-8 + 4/5= b
-36/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.
Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:
m= (-5 - (-9))÷ (7 - 2)
m= (-5 + 9)÷ (5)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-9= 4/5× (-2) + b
-9= -8/5 +b
-9 + 8/5= b
-37/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.
You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.
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Which expression is equivalent to t
3(x+24)?
A-2/3x+24
B-2/3x+16
C -2/3x-16
D 2/3x-16
Someone please help me!!! ( I'll mark brainliest )
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
Divide
-36
-8
Enter your answer as a mixed number, in simplified form, in the box.
the answer is this
4 4/8.
What is the smallest possible degree that the polynomial can have and why?
Check the picture below.
round to the underlined digit:
Answer:
c because if the number next to the underlined is above 5 u round up under 4 u round down
Step-by-step explanation:
Answer: c. 76
Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.
Write the definition as a biconditional statement:
An equilateral triangle is a triangle with three congruent sides.
The term "if and only if" makes the sentence bi-conditional. A triangle is equilateral if and only if it has three congruent sides.
A conditional statement with its opposite expressed in the form of "if and only if," collectively known as a bi-conditional statement. Bi-conditional logic is the theory behind bi-conditional assertions.
This can be compared to the conditional sentence, "if this, then that." Due to the lack of a "if and only if," it is not bi-conditional. The reversal of a conditional statement's ability to produce a bi-conditional depends on whether it is also true.
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( Please help + Will mark brainliest )
Answer the question in photo.
Answer: 1/4
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that A'D'=2 and AD=8, so the scale factor is 2/8 = 1/4.
Mrs. argueta needed to fill up her gas tank. gas cost $3.66 per gallon and she needed 9 1 2 gallons. how much did it cost mrs. argueta to fill up her tank?
Answer:
$3337.92
Step-by-step explanation:
$3.66 x 912 = $3337.92