The sum of 12 and P can be written as 12 + P
Then, f decreased by the sum of 12 and P can be written as:
f - (12 + P)
Answer: it isn't correct, the correct answer is f - (12 + P)
Find the derivatives of the following using increment method.1.y = 6x² +10x - 3
Given
[tex]y=6x²+10x-3[/tex]Find
derivatives using increment method.
Explanation
Given
[tex]y=6x²+10x-3[/tex]replace x and y by
[tex]\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}[/tex]so ,
[tex]\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}[/tex]now divide by
[tex]\Delta x[/tex]so ,
[tex]\begin{gathered} y^{\prime}=\frac{12\Delta x^2+10\Delta x+6\Delta^2x^2}{\Delta x} \\ \\ y^{\prime}=12x+10+6\Delta x \end{gathered}[/tex]now taking limit
[tex]\begin{gathered} \lim_{\Delta x\to0}y^{\prime}=\lim_{\Delta x\to0}(12x+10+6\Delta x) \\ \\ y^{\prime}=12x+10 \end{gathered}[/tex]Final Answer
Therefore , the derivative of the function using increment method is 12x + 10
Rectangles ABCD and DEFG are congruent
AB=7cm
AD=17cm
Work out the length of CE
The length of CE is 7cm
How to determine the lengthTo determine the length, we need to consider the properties of a rectangle, we have;
It is a quadrilateralOpposite sides are known to be parallel and congruent to each otherThe interior angles are equal to 90 degreesDiagonals bisect each other at right anglesThe two diagonals have the same lengthRectangle having side lengths of x and y has the perimeter as 2x+2y unitsA rectangle with side lengths x and y has its area as: xy sin 90 = xy square unitsA diagonal of a rectangle is said to be the diameter of its circumcircleFrom the information given, we have that;
AB = 7cm
AD = 17cm
Then, line CE = line AB
But line AB = 7cm
CE = 7cm
Hence, the length is 7cm
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Which system of linear inequalities is represented by the graph? O y=x-2 and x-2y 4 O y=x + 2 and x + 2y = 4 O y=x-2 and x + 2y = 4 O y =x-2 and x + 2y =-4
The two inequalities are (option c) y > x - 2 and2y + x < 4
Given,
Let's start by locating the red-hued area.
If the shadow is visible to be over the line, then the situation will be as follows:
y > ax + b
Hence the equation for the line is ax + b.
The slope is a, and the y-intercept is b.
The line in the graph intersects the y-axis at y = -2, which results in:
b = -2
Two points on the line are required to determine the slope; these points are (0, -2), and (2, 0)
We are aware of the slope for a line passing through the points (x1, y1) and (x2, y2) as follows:
a = (y2 - y1)/(x2 - x1) (x2 - x1)
The slope for this line will then be:
a = (0 - (-2))/(2 - 0) = 2/2 = 1
Then this line's equation is:
1x - 2
And here's the inequality:
y > x - 2.
The shaded area of the blue one is below the line, thus we will have:
y < ax + b
The y-intercept in this situation is y = 2.
This line crosses through the points (0, 2) and, as can be seen (4, 0)
The slope is then:
a = (0 - 2)/(4 - 0) (4 - 0) = -2/4 = -1/2
This inequality is then:
y < (-1/2)x + 2
If we rewrite this using the choices, we get the following:
y < (-1/2)x + 2
2y < -x + 2 ×2
2y + x < 4
The two inequalities are (option c) y > x - 2 and2y + x < 4
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Answer: C
Step-by-step explanation:
A recent math test had an average score of 75, with a standard deviation of 10. What percentage of people scored an 85 or higher?16%34%50%, 13.5%
Answer:
16%.
Explanation:
In a recent math test:
• The average score = 75
,• Standard Deviation = 10
To find: The percentage of people who scored an 85 or higher, P(X>85).
First, find the z-score when X=85.
[tex]z-score=\frac{X-\mu}{\sigma}[/tex]Substitute the given values:
[tex]z=\frac{85-75}{10}=\frac{10}{10}=1[/tex]The people who scored an 85 or higher are 1 standard deviation away from the mean.
[tex]13.5\%+2.35\%+0.15\%=16\%[/tex]The percentage of people who scored an 85 or higher is 16%.
32+40+…+120=? Someone help PLEASE
Answer:
912
Step-by-step explanation:
the assumption is that this is an arithmetic progression
the nth term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
use this to find which term 120 is in the sequence
with a₁ = 32 and d = a₂ - a₁ = 40 - 32 = 8 , then
32 + 8(n - 1) = 120 ( subtract 32 from both sides )
8(n - 1) = 88 ( divide both sides by 8 )
n - 1 = 11 ( add 1 to both sides )
n = 12
given the first and last terms in the sequence then sum is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last)
S₁₂ = [tex]\frac{12}{2}[/tex] (32 + 120) = 6 × 152 = 912
What is the equation of a line that passes through the point (5, −3) and is parallel to 6x+3y=−12?
Enter your answer in the box.
Answer: Slope= -2.000
x-intercept= -2
y-intercept= -4.000
Hope this helps !
400 x 600x 800x150x120
Answer:
3.456e+12
or
3,456,000,000,000
Step-by-step explanation:
400 x 600 = 240,000
240,000 x 800 = 192,000,000
192,000,000 x 150 = 28,800,000,000
28,800,000,000 x 120 = 3,456,000,000,000
hope this helps you :D
-
у
0
1
1
3
2
9
3
27
y=−3x+9
3y=−9x+9 how many solutions
The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.
What is the solution to the equation?The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a consequence.
A connection between two or more factors results in a linear model when displayed on a graph. The variable will have a degree of one.
The linear equations are given below.
y = -3x + 9 ...1
3y = -9x + 9 ...2
Divide the equation 2 by 3, then the equation will become.
y = -3x + 3
The slope of the lines is the same but the lines are separated by a distance.
The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.
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find the 2 points if the (x,-1) which are 4 units from the pooint (3,2)
The possible coordinates of the other points are (3 + √7, -1) and (3 - √7, -1)
How to calculate the coordinates of the two points?From the question, we have
Points = (3, 2) and (x, -1)Distance = 4 unitsWhere (x, -1) represents the other points
The distance between the points is the number of units between them
It is calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y represent the coordinates of the given points
Substitute the known values in d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
So, we have
d = √[(3 - x)²+ (2 + 1)²]
Evaluate the expression
d = √[(3 - x)²+ 9]
Recall that d = 4
So, we have
√[(3 - x)²+ 9] = 4
Square both sides
(3 - x)²+ 9 = 16
This gives
(3 - x)² = 7
So, we have
3 - x = ±√7
Solve for x
x = 3 ± √7
Hence, the coordinates are (3 + √7, -1) and (3 - √7, -1)
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Susie has a part-time job at the video store. She makes between $41.89 and $47.91 a day. Which is a reasonable amount of money that Susie makes for working 7 days?
The amount of money that Susie makes for 7 working days will be;
⇒ $314.3
What is mean by Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Susie has a part-time job at the video store and she makes between $41.89 and $47.91 a day.
Now,
The amount of money for a day = ($41.89 + $47.91) / 2
The amount of money for a day = $89.8 / 2
The amount of money for a day = $44.9
Thus, The amount of money that Susie makes for 7 working days is;
= 7 x $44.9
= $314.3
Hence,
The amount of money that Susie makes for 7 working days will be;
⇒ $314.3
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60 points help will give brainliest
Answer:
(g o f)(8)
Step-by-step explanation:
First we find f(8).
f(8) = 8 - 1 or 7.
We now find g(f(8)), which means g(7).
g(7) = 7^3 or 343
What is the slope of a line that is perpendicular to a line represented by the equation 6y=−7x+4?
Enter your answer, as a fraction in simplest form, in the box.
The slope of the line that is perpendicular 6y=−7x+4 is: 6/7.
What are the Slopes of Perpendicular Lines?If one line has a slope of a/b, the slope of the line that is perpendicular to the line would be the negative reciprocal of a/b, which is -b/a.
If the slopes of perpendicular lines are multiplied together, for example (a/b)(-b/a), we would always have a result of -1.
Rewrite the equation 6y = −7x + 4 in slope-intercept form as y = mx + b, in other to determine the value of m = slope.
6y/6 = −7x/6 + 4/6
y = −7/6x + 2/3
The slope of 6y = −7x + 4 is -7/6. 6/7 is the negative reciprocal of -7/6. Therefore, the slope of the perpendicular line is: 6/7.
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When the internet first launched, it was slow, clogged up phone lines and was most certainly not cheap. In fact, most Internet service providers (ISP) charged a flat rate access fee that included 20 hours a month of internet time. After twenty-hours of use, the ISP’s charged an additional per-hour fee. Suppose in 1995, Charter charged a flat rate of $39.95 for the first twenty hours of service and an additional per-hour charge of $5.99.a. How much would a Charter bill for 18 hours of internet used be in 1995? b. How much would a Charter bill for 28 hours of internet used be in 1995?
from the question, we were told in 1995, Charter charged a flat rate of
$39.95 for the first twenty hours.
and an additional per hour charge of $5.99
if,
for 20 hours = 39.95
therefore for 1 hour = 39.95/20
so for 18 hours = 39.95/20 X 18.95/20
so for 18 hours = 9
so,
to get the amount Charter bill for 18 hours in 1995 is,
39.95 x 18/20
= 39.95 x 0.9
= $35.955
so Charter bill for 18 hours of internet used in 1995 is $35.955
ould bill for 28 hours is
so, what Charter would
question allistair throws a biased six-sided dice. the probability of getting a 6 with this dice is 0.4. the other numbers are equally probable. if he throws the dice 3 times, what is the probability that he gets 5, 3, and 2 in this order?
The probability that he gets 5, 3, and 2 in this order is 0.92, 0.52, and 0.32 respectively.
The possibility of rolling a 6 with these dice is 0.4, according to the question. The possibility of rolling a 1 through 5 on the dice is also the probability of not obtaining a 6.
a) Chance of receiving 5:
P(6) + Q(6) = 5
Q(6) = 5 - P(6)
Q(6) = 5 - 0.4
Q(6) = 4.6
The probability of obtaining 5 to 5 is 4.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 4.6
The first five numbers have an equally likely probability.
P(1) = 4.6 ÷ 5
P(1) = 0.92
b) Probability of getting 3:
P(6) + Q(6) = 3
Q(6) = 3 - P(6)
Q(6) = 3 - 0.4
Q(6) = 2.6
The probability of obtaining 3 to 5 is 2.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 2.6
The first five numbers have an equally likely probability.
P(1) = 2.6 ÷ 5
P(1) = 0.52
c) Probability of getting 2:
P(6) + Q(6) = 2
Q(6) = 2 - P(6)
Q(6) = 2 - 0.4
Q(6) = 1.6
The probability of obtaining 2 to 5 is 1.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 1.6
The first five numbers have an equally likely probability.
P(1) = 1.6 ÷ 5
P(1) = 0.32
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Determine whether the table of values represents a linear function. If so, write the function.
PLEASE HELP!!
Help help please please help help I need help 30 POINTS
Write an equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
Please help and Thank you.
h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
What is Translation?Translation is the process of reworking text from one language into another to maintain the original message and communication.
The parent function is: g(x)=|x|
we stretch the parent function y = |x| by a factor of 3.
h= |x/3|
If the constant is between 0 and 1, we get a horizontal stretch
if the constant is greater than 1, we get a horizontal compression of the function.
Hence h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
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Let h(x) = x+3−−−−−−√ and k(x) = 2x + 7. Find the value h(k(3)).
The value of the given function h(k(3)) when h(x) =√ x+3 and k(x) = 2x +7 is equal to 4.
As given in the question,
Given functions are :
h(x) =√ x+3 and k(x) = 2x +7
To find the value of the composite function h(k(3)) :
First calculate for k(3) we get,
k(x) = 2x+ 7
Substitute x =3 in k(x) we get,
k(3) = 2(3) +7
⇒ k(3) = 13
Now, Substitute the value of k(3) in the composite function h(k(3)) we get,
h(k(3))
= h(13)
= √ 13 +3
=√16
= 4
Therefore, the value of the given function h(k(3)) when h(x) =√ x+3 and k(x) = 2x +7 is equal to 4.
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Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of d days that have passed. A. Write an equation for the situation.B. Find the a amount of money he began with.C. How much money does Marty have after 9 days?
Given:
Amount Marty spent per day = $3
Number of days = 14
Remaining amount = $68
Since the amount left depends on the number
In a quadrilateral, two angles are x°, two angles are (3x+8)°. What is x and the measures of the angles?
Step-by-step explanation:
the sum of all angles in any quadrilateral is 360°.
so,
x + x + 3x + 8 + 3x + 8 = 360
8x + 16 = 360
8x = 344
x = 344/8 = 43°
3x + 8 = 3×43 + 8 = 129 + 8 = 137°
so, the angles are
43°
137°
43°
137°
Can someone help me quickly please ill give brainlist
Ms. Zhou was sketching out a new wooden toy design. One of the designs had the instructions to sketch
points at the following locations and then draw lines to connect the points in order
A (2,2); B (4,-4); C (-3,-4); and D (-1,2).
(a) Use the graph below (or a snip of the graph) to plot and label the points. Then connect the points in
order: A to B, B to C, C to D, and then D back to A to create her shape. (You must include a drawing
for credit)
Answer:
I've included a visual representation
Step-by-step explanation:
i did the assigment yesterday
Suppose Juan places $6000 in an account that pays 12% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.(b) Find the amount in the account at the end of 2 years.su
1) Since this investment has been in an account with 12% compound interest per year, then we can write out the following:
a) Note that there was no withdrawal during this first year.
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ F=6000(1+\frac{0.12}{1})^{1\cdot1} \\ F=6000(1.12)^1 \\ F=6720 \end{gathered}[/tex]b) To find out the amount of money over a course of this time 2 years, then we can write out the following:
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ F=6000(1+\frac{0.12}{1})^{1\cdot2} \\ F=7526.4 \end{gathered}[/tex]In this case, it is also compounded per year. Just the period (t) is greater than the other one.
So, we can tell the following about the earnings of this investment:
[tex]a)\$6720,b)\$7526.40[/tex]the slop of (10,8) and (1,9)
Answer:
slope = -1/9
Step-by-step explanation:
Hope this helps!!!
2/7×7/10 reduced to the smallest fraction
Answer:
1/5
Step-by-step explanation:
I multiplied 2 * 7, which is 14. Then, I multiplied 7 * 10 which equals 70. Then, I divided 14/70 by 14. The answer is 1/5.
Mei Mei is younger than Xin. Their ages are consecutive integers. Find Mei Mei's age if the sum of Mei Mei's age and 5 times Xin's age is 143.
Mei Mei's age if the sum of Mei Mei's age and 5 times Xin's age is 143. is 23 years.
Let the ages be x and x+1 since they're consecutive numbers.
In this case the sum of Mei Mei's age and 5 times Xin's age is 143. This will be:
x + 5(x + 1) = 143
x + 5x + 5 = 143
Collect like terms
6x + 5 = 143
6x = 143 - 5
6x = 138
Divide
x = 138 / 6
x= 23
Mei Mei is 23 years.
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(1 point) the shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 8 years and a standard deviation of 0.3 years. what value of shelf life do 16% of the battery shelf lives fall below? round your answer to one decimal place.
8.27 is the normally distributed value of the shelf life which falls under 16% of the battery shelf life.
Because the shelf life of a battery manufactured by one big business is known to be regularly distributed, we would use the normal distribution formula, which is stated as
z = (x - µ) ÷ σ
Where
x = shelf life of a battery in years.
µ = mean shell life
σ = standard deviation
Based on the facts provided,
µ = 8 years
σ = 0.3 years
The z score corresponds to a p-value of 16% in the normal distribution table,
(16 ÷ 100 = 0.16) is - 0.9.
Therefore,
- 0.9 = (x - 9) ÷ 0.3
0.3 × (- 0.9) = x - 8
0.27 = x - 8
x = 0.27 + 8
x = 8.27
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O EQUATIONS AND INEQUALITIESSolving a word problem with two unknowns using a linear...
Given:
Total number of hamburgers and cheeseburgers sold = 439
There were 61 fewer cheeseburgers than hamburgers sold.
Let's determine the number of hamburgers sold.
Let C represent the number of cheeseburgers
Let H represent the number of hamburgers sold.
We have the system of equations:
• H + C = 439
,• C = H - 61
Now, let's solve the equations simultaneously using the substitution method.
Substitute (H - 61) for C in the first equation.
We have:
H + (H - 61) = 439
H + H - 61 = 439
2H - 61 = 439
Add 61 to both sides:
2H - 61 + 61 = 439 + 61
2H = 500
Divide both sides by 2:
[tex]\begin{gathered} \frac{2H}{2}=\frac{500}{2} \\ \\ H=250 \end{gathered}[/tex]Therefore, they sold 250 hamburgers on Friday.
ANSWER:
250 hamburgers
Find the radius of a cylinder whose height is 10 cm and the total surface area is 352 cm².
Answer: the radius of a cylinder is 4 cm
Step-by-step explanation:
[tex]S_{ts}=352\ cm\ \ \ \ H=10\ cm\ \ \ \ \ r=?[/tex]
The total surface area:
[tex]\displaystyle\\ S_{ts}= 2\pi r^2+2\pi rH\\\\S_{ts}=2\pi (r^2+rH)\\\\352=2\pi (r^2+10r)\\\\[/tex]
Divide both parts of the equation by 2π:
[tex]\displaystyle\\56=r^2+10r\\\\56-56=r^2+10r-56\\\\0=r^2+10r-56\\\\Thus,\\\\ r^2+10r-56=0\\\\D=(-10)^2-4(1)(-56)\\\\D=100+224\\\\D=324\\\\\sqrt{D}=\sqrt{324} \\\\\sqrt{D}=18\\\\ r=\frac{-10б18}{2(1)} \\\\r=-14\notin\ (r > 0)\\\\r=4\ cm[/tex]
Answer:
r ≈ 4 cm
Step-by-step explanation:
Total Surface Area of a cylinder
A = Base Area x 2 + Lateral Surface Area
A = 2(πr²) + 2πrh
where r = radius of base and h = height of cylinder
Solving for r we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{h^2 + 2 \dfrac{A}{\pi} }-\dfrac{h}{2}\\\\[/tex]
Given h = 10 cm and A = 325 we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{10^2 + 2 \dfrac{352}{\pi} }-\dfrac{10}{2}\\\\\\[/tex]
[tex]\sqrt{10^2 + 2 \dfrac{352}{\pi} } =\sqrt{100+\dfrac{704}{\pi }}\\\\= \sqrt{100 + 224.09}\\\\\\[/tex]
= [tex]\sqrt{324.09}[/tex]
= 18.0025
1/2 x 18.0025 ≈ 9
So r ≈ 9 - 10/2 = 9 -5 = 4
r ≈ 4 cm
Determine whether there is enough information to conclude that the triangles are congruent. If so, select the theorem
you used.
Given: TR intersects NP, TU RU, NU - PU
Is ATUN ARUP?
N
No. There is not enough information to conclude that the triangles are congruent.
SAS
Yes. There is enough information to conclude that the triangles are congruent.
ASA
SSS
Previous
Answer:
SAS
Step-by-step explanation:
