A. Find the equation of the L line that intersects graph C at point A (2, -5). B. Find the line equation with the coefficient of direction equal to -10 and touch and graph C
Answers
Graph C has a function
[tex]f(x)=2x^3-16x+11[/tex]Since the line L intersects the graph at the point, A (2, -5)
To find the slope of the line we will differentiate the f(x) and substitute x by 2
[tex]\begin{gathered} f^{\prime}(x)=2(3)x^{3-1}-16x^{1-1}+0 \\ f^{\prime}(x)=6x^2-16 \\ m=6(2)^2-16 \\ m=24-16 \\ m=8 \end{gathered}[/tex]The slope of the line is 8, substitute it in the form of the linear equation
[tex]\begin{gathered} y=mx+b \\ y=8x+b \end{gathered}[/tex]To find b substitute x by 2 and y by -5
[tex]\begin{gathered} -5=8(2)+b \\ -5=16+b \end{gathered}[/tex]Subtract 16 from both sides to find b
[tex]\begin{gathered} -5-16=16-16+b \\ -21=b \end{gathered}[/tex]Then the equation of the line is
[tex]\begin{gathered} y=8x+(-21) \\ y=8x-21 \end{gathered}[/tex]Related Questions
Write the equation 2(x + 3 )= 2x + 6 as a system of equations
Answers
Answer:
y=2x+6
y=2x+6
Explanation:
Given the equation:
[tex]2\mleft(x+3\mright)=2x+6[/tex]The equation written as a system of equations is:
[tex]\begin{gathered} y=2\mleft(x+3\mright) \\ y=2x+6 \end{gathered}[/tex]Opening the bracket in the first equation gives:
[tex]\begin{gathered} y=2x+6 \\ y=2x+6 \end{gathered}[/tex]How do you solve this problem?
Answers
The area of the figure given below is 56.6 units² .
In the question ,
a figure is given
where there is one rectangle and two semicircles .
the length of the rectangle is given as 11 units
and the breadth of the rectangle is = 4 units
we know that the area of the rectangle is = length × breadth
on substituting the values ,
we get
area = 11 × 4
area = 44 units²
the radius of the semicircle = 2 units
the are of the semi circle = (1/2)*π*r²
since there are two semicircle , the area of the two semi circle will be
= 2 * (1/2)πr²
= π*r²
On substituting , the value of radius = 2 ,
we get the area is = 3.14*(2)² = 12.56 using π = 3.14
so the area of the complex figure is = 44 + 12.56 = 56.56
≈ 56.6
Therefore , The area of the figure given below is 56.6 units² .
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Help me please I don’t know the answer
Answers
Answer:
Classification by Angles: Obtuse
Classification by Sides: Scalene
Step-by-step explanation:
➜ This triangle has an obtuse angle, or an angle greater than 90°, so it is an obtuse triangle. This is the classification by angles.
➜ This triangle's sides are all different lengths, as shown by the three different angle measurements. This means this triangle is scalene, and scalene is the classification by sides.
An athlete swims at a constant rate. After 12 minutes, the swimmer swims 16 laps. A. Graph this relationship. B. Is this a proportional relationship? Explain.
Answers
Answer:
Step-by-step explanation:
i need help please help tysm
Answers
Answer:
(2, 3)
Step-by-step explanation:
the work is all in the pic go check it out I am so sorry if it's incorrect also have a nice day:)
Of the ice cream cones sold yesterday at Zeke's Ice Cream Shop, 3/10 were chocolate and another 3/10 were vanilla. What fraction of the ice cream cones sold were either chocolate or vanilla?
Answers
The fraction of ice cream cones sold that are either chocolate or vanilla is 3/5.
What is the fraction?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/5. 3 is the numerator and 5 is the denominator.
In order to determine the fraction of ice cream cones sold that are either chocolate or vanilla, add the fraction of chocolate cones sold and vanilla cones sold together. Addition is the process of determining the sum of two or more numbers.
Fraction of ice cream cones sold that are either chocolate or vanilla = 3/10 + 3/10 = 6/10 = 3/5.
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Find the smallest whole number bu which 512 must be multiplied in order to give a perfect square
Answers
Answer:
2
Step-by-step explanation:
512÷2=256
256÷2=128
128÷2=64
64÷2=32
32÷2=16
16÷2=8
8÷2=4
4÷2=2
2÷2=1
=(2^2)+(2^2)+(2^2)+(2^2)+2
When 2 is multiplied it will make it a perfect square.
512×2=1024
√1024
=32
A basketball player's shooting percentage was 0.425 at the end of the season. What does that mean? (1) He made 4.25% of the baskets he attempted. (2) He made 4 out of every 25 baskets he attempted. (3) He made 42.5% of the baskets he attempted. (4) He made 17 out of every 40 baskets he attempted
Answers
shooting percentage: 0.425 (decimal)
To express in percentage:
0.425 x 100 = 42.5%
(3) He made 42.5% of the baskets he attempted.
And also
17/40 = 0.425
(4) He made 17 out of every 40 baskets he attempted
What is the absolute value of the number plotted on the number line?.
A. -1.75
B. -1.25
C. 1.25
D. 1.75
Answers
Answer:
D. 1.75
Step-by-step explanation:
Absolute value cannot be negative, so that gets rid of A & B. The point is at -1.75 so it has to be D.
A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. Is it a right triangle?
Answers
If a triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. No it is not a right triangle.
Determining whether the triangle is a right triangleWe would be making use of converse of Pythagoras' theorem to determine whether the triangle is a right triangle.
In a situation were we have a right triangle the square on longest side will be the same with the sum of square of other sides
Longest side
45² = 2025
Other side
30 ² + 35 ²
900 + 1,225
= 2125
Hence,
2025 ≠ 2125
Based on the above it is not a right triangle because the longest side did not equate the other side.
Therefore it is not a right triangle.
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As 2125 ≠ 2025 therefore it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.
This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers.
∴ 30² + 35² = 45².
900 + 1225 = 2025.
2125 ≠ 2025.
It is not a right-angle triangle because it didn't satisfy the property of Pythagoras's theorem.
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pls help me super confused on inequality
Answers
40.50d - 400(0.12) ≤ 210
_____________________
Step 1:
40.50×d - 48 ≤ 210
Step 2:
40.50×d ≤ 210 + 48
Step 3:
40.50×d ≤ 258
Step 4:
d ≤ 258÷ 40.50
Final step:
d ≤ 6.37
Answer fast
Which of the following is used to identify outliers in a set of data?
1.5(IQR)
1.5(range)
2(mean)
2(median)
Answers
The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).
What is the Interquartile range (IQR)?We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.
To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.
Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.
Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.
Hence, the correct answer would be option (A).
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1 (Express 360° into centesimal system.)
Answers
Answer: 400 gradians
Reason:
100 gradians = 90 degrees
4*100 gradians = 4*90 degrees
400 gradians = 360 degrees
Pls help me. I'm struggling so bad
Answers
The formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
in the question ,
it is given that the
formula to find , "gravitational force" between two objects is
[tex]F_{g}[/tex] = (G*M₁*M₂)/r²
to express the formula in terms of M₁ ,
we first multiply both the sides by r² ,
on multiplying , we get
[tex]F_{g}[/tex]*r² = G * M₁ * M₂
On dividing both sides by G ,
we get
( [tex]F_{g}[/tex]*r² ) /G = M₁ * M₂
we have to find the formula for M₁ ,
we divide both sides by M₂,
So , on dividing both sides by M₂ , we get
( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) = M₁
hence M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ )
Therefore , the formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
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Solve the system of one linear- one Quadratic equations algebraically.
x-y=3
x^2-3y=19
Answers
Answer:
x=-2 y=-5
x=5 x=2
X=5 x=2
Cffccccf
What is the slope of -2,1 and 2,1
Answers
Is should be 50% slope
Answer:
m=0
Step-by-step explanation:
(-2,1) (2,1)
x1=-2,x2=2,y1=1,y2=1
Gradient/slope
m=y2-y1/x2-x1
m=1 - 1/2-(-2)
m=0/2+2
m=0/4
m=0
A machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate, in
pounds per hour, does the machine make nails? Show your work.
Answers
The rate of pounds per hour of the machine is 1.5 pounds per hour
How to determine the rate of pounds per hour?From the question, we have the following parameters:
Pounds of nails = 2 1/4 pounds of nail
Number of hours = 1 1/2 hour
From the above parameters, the rate of pounds per hour can be calculated using the following formula of constant of proportionality
The constant of proportionality is calculated as
Constant of proportionality = Pounds of nails/Number of hours
In this case, we have
Rate of pounds per hour = Pounds of nails/Number of hours
Substitute the known values in the above equation
Rate of pounds per hour = (2 1/4)/(1 1/2)
So, we have
Rate of pounds per hour = 1.5
Hence, the rate is 1.5 pounds per hour
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Answer:
1 1/2
Step-by-step explanation:
2 1/4 divide 1 1/2 is 1 6/12
1 6/12 simp —-> 1 1/2 (1.5)
which plan will result in the prive of feed reaching 12 faster
Answers
In plan B the price rises by 10%.
Thus the price rise is per week is $0.8
In plan A the price rise per week is $0.1
In plan C the price rise per week is
[tex]\frac{12-8}{8}=\frac{4}{8}=0.5[/tex]In plan D the price rise per week is $0.25
Considering all the plan the maximum price rise for each week is 0.8.
So the plan that would lead to $12 fastest is plan B.
The answer is plan B.
A house is bought for $75000 and then resold for $87000. Calculate the percentage profit
Answers
The selling price of the house = $87000
Profit = selling price - cost price
=> Profit made = $87000-$75000
=> Profit made = $12000
Profit Percentage is given by the formula , Profit % = [tex]\frac{profit X 100}{cost price}[/tex]
=> Profit % = [tex]\frac{12000 X 100}{75000}
=> Profit % = 16%
Hence the percentage of profit made by reselling the house is [tex]\fbox{16%}[/tex].
oan, omb, apb and mpn are straight lines and an = 3oa. m is the midpoint of ob. oa = a ов = b ap = kab where k is a scalar quantity. express ab and mn in terms of a and b. express mp in terms of a, b and k. finally, find the value of k.
Answers
The values of the vectors obtained from the vector diagram are;
[tex]\overrightarrow{AB} = - a + b[/tex]
[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]
[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
K = 2.5
What is a vector in geometry?A vector can be expressed as a line segment that has a direction.
The given parameters are;
The straight lines are; OAN, OMB, APB, and MPN
AN = 3•OA
The midpoint of OB = M
The vectors
[tex] \overrightarrow{OA} = a[/tex]
[tex] \overrightarrow{OB} = b[/tex]
[tex]\overrightarrow{AP} = K \cdot \overrightarrow{AB} [/tex]
From the question diagram, we have;
[tex]\overrightarrow{AB} = - a + b[/tex]
[tex]\overrightarrow{AP} = K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]
[tex]\overrightarrow{AN} [/tex] = 2•a
[tex]\overrightarrow{NP} = \overrightarrow{AP} - \overrightarrow{AN} [/tex]
[tex]\overrightarrow{NP} = -2\cdot a + K \cdot ( - a + b)[/tex]
[tex] \overrightarrow{MB} = 0.5 \cdot b[/tex]
[tex]\overrightarrow{PB} = -a + b - K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MP} =0.5 \cdot b - -a + b - K \cdot ( - a + b) = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
Given that we can write;
[tex]x \cdot \overrightarrow{NP} = \overrightarrow{NM}[/tex]
x × (-2•a + k•(-a + b)) = -3•a + 0.5•b
-2•x•a - k•x•a + x•k•b = -3•a + 0.5•b
Which gives;
-2•x - k•x = -3...(1), and x•k = 0.5...(2)
From (2), x = 0.5÷k
From (1), -2×(0.5÷k) - k×(0.5÷k) = 3
-k - 0.5 = -3
-k = -3 + 0.5 = -2.5
k = 2.5
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PLS HELP DUE NOWWWWWWWWWW
Answers
The correct statement will be:
A. The rate of change is the number of inches grown per month, and the initial value is the starting height.
We can form the following equation from the given data:
H(m) = 13 + 41m,
Where H ( Height ) is a function of the number of months ( m ).
We can see that the height changes with respect to months i.e. as the number of months increases, the height of the sunflower also increases.
The initial value or the initial height of the sunflower remains constant throughout and has less impact on its height.
So, option A will be the ultimate explanation for the data given.
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Answer:
Step-by-step explanation:
This is a linear function of time, as mentioned.
A linear function is always in the form of:
[tex]y=mx+b[/tex]
The 'sunflower's height is a linear function of time', so the [tex]x[/tex] variable represents the time (which is in terms of months here), and the [tex]y[/tex] would represent the sunflower's height after time has passed.
The initial value is when [tex]x=0[/tex].
[tex]x=0[/tex] means at the very beginning.
At the very beginning, the height would be the starting height, so the initial value would be the starting height.
The rate of change means the change in [tex]y[/tex] in respect to [tex]x[/tex].
Since [tex]y[/tex] represents the height after [tex]x[/tex] months, the rate of change would be the change in height per month.
You could also write it as the number of inches grown per month.
The initial value is the starting height, and the rate of change is the number of inches grown per month, so the correct answer is (A).
-20 greater than or equal to 5v
Answers
Write the inequality for the statement and solve for v
[tex]\begin{gathered} -20\ge5v \\ -\frac{20}{5}\ge v \\ -4\ge v \end{gathered}[/tex]It means that v is less than or equal to -4. The solution set for this inequality is:
[tex](-\infty,-4\rbrack[/tex]Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. The speed of the tennis ball is...
Answers
The speed of the tennis ball is 6.2 metres per seconds.
How to find the speed of the tennis?Speed is measured as the ratio of distance to the time in which the distance was covered.
Therefore, speed can be represented mathematically as follows;
speed = distance / time
Hence, the table tennis travels 12.4 metres south in 2 seconds.
The speed of the tennis can be computed as follows:
distance = 12. 4 metres
time = 2 seconds
Therefore,
speed = 12.4 / 2
speed = 6.2 meters per seconds.
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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s
What is Speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.
Given that,
Katie and her best friend Liam play tennis every Saturday morning.
When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.
The speed of the tennis can be found by using formula
speed=distance/time
distance = 12. 4 metres
time = 2 seconds
Now speed=12.4/2
speed=6.2
Hence speed of the tennis ball is 6.2m/s
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Write the equation in slope intercept form: -6x+4y=20
Answers
Answer:
[tex]y=\frac{3}{2}x+5[/tex]
Step-by-step explanation:
[tex]-6x+4y=20 \\ \\ 4y=6x+20 \\ \\ y=\frac{3}{2}x+5[/tex]
10. Evaluate (14-2)÷3(2-3) - 2²Mark only one oval.A. OB. 2C. 20D. 22
Answers
Order of the operations: parentheses, exponentials, division and multiplication, addition and subtraction.
1. Solve operations in parentheses:
[tex]=12\div3\cdot6-2^2[/tex]2. Solve exponentials:
[tex]=12\div3\cdot6-4[/tex]3. Solve division:
[tex]=4\cdot6-4[/tex]4. Solve multiplication:
[tex]=24-4[/tex]5. Solve subtraction:
[tex]=20[/tex]Then, the solution for the given expression is 20Answer: Answer is 20( please make me brainliest i just did this all in my head)
Step-by-step explanation: soo (14-2) =12 12divided by 3=4 so (2*3)= 6 so 4x6=24 24-2*2 =20 (2*2)=4 so 24-4=20 well this is confusing but i tried my best so hope my answer wasn't toooo confusing lol :)
Find the measure of each angle in the diagram
Answers
3y + 11 = 50
10y = 130
4x -22 = 50
7x + 4 = 130
First we solve for x and y
The two “x” variable angles are supplementary so combined they will equal 180 degrees
(4x -22)+ (7x + 4) = 180
Combine
11x -18 = 180
Add 18 to both sides to isolate variable
11x -18+ 18 = 180 + 18
11x = 198
Divide both sides by 11 to solve for x
11/11 x = 198/11
x = 18
The two “y” variable angles are supplementary so combined they will equal 180 degrees
(3y + 11)+ 10y = 180
Combine
13y + 11 = 180
Subtract 11 from both sides to isolate y
13y + 11 -11 = 180 - 11
13y = 169
Divide both sides by 13 to solve for y
13/13 y = 169/13
y = 13
Now we can solve the angles
3y + 11 =
3(13) + 11 = 50
10y =
10(13) = 130
4x -22 =
4(18) -22 = 50
7x + 4 =
7(18) + 4 = 130
The vertical angle measurement equals each other so it is correct
if it takes 3/4 of an hour to fill 3/5 of a pool how many hours will it take to fill the pool completely
Answers
The time taken to completely fill the pool is 5/4 hour
How to determine the time to fill the pool?From the question, the given parameters are:
Time =3/4 hour
Size of the pool = 3/5
The time to fill the pool is then calculated as
Time = Given time/Proportion of the pool
Substitute the known values in the above equation
So, we have the following equation
Time = 3/4 hour ÷ 3/5
Express the quotient as product
So, we have the following equation
Time = 3/4 hour x 5/3
Evaluate the products
Time = 5/4 hour
Hence, the time taken is 5/4 hour
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1. Jack buys small tins of tomatoes every week. They usually cost 50¢ each. Last week,
however, Jack saw that the shop was selling six large tins of tomatoes plus a bag of
pasta for $7.50. He worked out that the pasta was normally $2. Jack decided that he
could use one large tin of tomatoes instead of two small tins so he bought 18 large tins
of tomatoes together with three bags of pasta.
This week, however, the small tins of tomatoes are on offer at $1.60 for a pack of four.
How much more did Jack pay last week for tinned tomatoes than if he had bought them
this week?
Answer is in what unit?
Answers
Jack paid $ 2.10 more than last week for tinned tomatoes.
The answer is in dollars.
Given that:-
Price of small tomato tins = 50 cents
Price of pasta packet = $ 2
Price of large tomato tins = 2*50 cents = $ 1
Total price of 6 large tins and a pasta packet = $ 7.50
Price of 4 small tins of tomatoes this week = $ 1.60
Price paid by Jack last week for 18 large tins and 3 pasta packets = 7.50*3 = $ 22.50
Price of 18 large tins = 22.50 - 2*3 = 22.50 - 6 = $ 16.50
As 18 large tins equals 36 small tins, we can write,
Price Jack would have paid this week = 36*1.60/4 = $ 14.40
The amount Jack paid more for tinned tomatoes = 16.50 - 14.40 = $ 2.10
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If you write every whole number from I to
100. how many times will you write the digit
"2"?
Answers
Answer:
20 times
Step-by-step explanation:
Digit 2 appears 20 times in first 100 natural numbers
What is the value of x+ y in the system of equations below?
8x + 9y = 4.92
9x + 14y = 6.93
Answers
The value of x + y in the system of equations is 0.82125.
Given system of equations:-
8x + 9y = 4.92 ...(1)
9x + 14y = 6.93 ...(2)
We have to find the value of x + y in the system of equations.
Multiplying (1) by 9 and (2) by 8, we get,
72x + 81y = 44.28 ...(3)
72x + 112y = 55.44 ...(4)
(4) - (3), we get,
0x + 31y = 11.16
31y = 11.16
y = 11.16/31
y = 0.36
Putting the value of y in (1), we get
8x + 9*(0.36) = 6.93
8x + 3.24 = 6.93
8x = 6.93 - 3.24
8x = 3.69
x = 0.46125
Hence,
x + y = 0.46125 + 0.36 = 0.82125
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