Answer:
Slope of the Curve: [tex]f'(x)=\frac{-6}{x^2}[/tex]
Equation of Tangent Line: y + 3 = -3/2(x + 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeCalculus
The definition of a derivative is the slope of the tangent line.
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]f(x)=\frac{6}{x}[/tex]
Step 2: Take Derivative
Quotient Rule: [tex]f'(x)=\frac{0(x)-6(1)}{x^2}[/tex]Multiply: [tex]f'(x)=\frac{0-6}{x^2}[/tex]Subtract: [tex]f'(x)=\frac{-6}{x^2}[/tex]Step 3: Find Instantaneous Derivative
Substitute in x: [tex]f'(x)=\frac{-6}{(-2)^2}[/tex]Exponents: [tex]f'(x)=\frac{-6}{4}[/tex]Simplify: [tex]f'(x)=\frac{-3}{2}[/tex]This value shows the slope of the tangent line at the exact value of x = 2.
Substitute: y + 3 = -3/2(x + 2)Use the coordinates J(7, 8), K(1, 2) and L(5, 2) for △JKL.
The centroid for △JKL is at point M. What is JM rounded to the nearest tenth?
prolly D
..............................
The distance between the point JM will be 4.81 units.
What is the centroid of the triangle?In science and math, the centroid of a planar figure or firm figure, also known as the point of intersection or center of the figure, is the mean absolute position of all of the other points on the subject's surface.
The centroid of the triangle is given as,
(x, y) = [(x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃) / 3]
Use the coordinates J(7, 8), K(1, 2) and L(5, 2) for △JKL. Then the centroid for △JKL is at point M is given as,
(x, y) = [(7 + 1 + 5) / 3, (8 + 2 + 2) / 3]
(x, y) = (13/3, 12/3)
(x, y) = (13/3, 4)
Then the distance between the point JM is calculated as,
D² = (13/3 - 7)² + (4 - 8)²
D² = 7.1111 + 16
D² = 23.11
D = √23.11
D = 4.81 units
The distance between the point JM will be 4.81 units.
More about the centroid of the triangle link is given below.
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Math, Stumped me once more
Answer:
[tex]B.Alternate\ Exterior\ Angles[/tex]
Step-by-step explanation:
[tex]As\ the\ exterior\ angles\ lie\ on\ the\ opposite\ sides\ of\ the\ transversal,\\that\ cuts\ two\ parallel\ lines,\ the\ set\ of\ 'Alternate\ Exterior\ Angles'\ formed\\are\ equal.[/tex]
can anyone help me ?
Answer: m∠T = 48°
ΔMAT has MA = MT
=> ΔMAT is a isosceles triangle at M
=> ∠A = ∠T = (180° - ∠M)/2
=> x + 20 = (180 - 3x)/2
⇔ 2x + 40 = 180 - 3x
⇔ 5x = 140
⇔ x = 140/5
⇔ x = 28
=> ∠A = ∠T = 28 + 20 = 48°
Step-by-step explanation:
Which calculation will give the best estimate of the result of 23 x 4.8?
0 20 0.5
0 30 x 0.5
O 20 x 5
O 30 x 5
Answer:
20x5
Step-by-step explanation:
Im desperate, please help asapp!!
Answer:
A: Quadrant IV
B. Quadrant III
Step-by-step explanation:
Quadrant IV is the bottom right
Quadrant III is the bottom left
−x + (−3) = x + 3
plz hurry
Answer:
X= -3
Step-by-step explanation:
please help!!
What is the experimental probability of drawing a red marble, given the following results?
blue: 8
green: 5
red: 7
a. 7/13
b. 13/20
c. 7/20
d. 7/8
Answer:C
Step-by-step explanation: You want to add up all the marbles, and then take the red marbles and divide by all the marbles 7/20
Categorize each triangle by both sides and angles. Choose two for each question below.
Answer:
Obtuse
Step-by-step explanation:
Answer: scalene, and obtuse
Step-by-step explanation: All of the sides are different lengths so that makes it a scalene triangle. On the picture it also shows that one of the angles is 107 degrees. Since 107 is larger than 90, it is an obtuse triangle.
Graph the line with a slope of 3/5 and goes through the point (1,2).
Answer:
The answer is y= 3/5x+7/5
6
Julie bought a 5-lb bag of potatoes for
$2.70. The bag contained 10 potatoes.
If each potato weighs and costs about
the same, which is the most reasonable
estimate of the unit rate per potato?
A $0.27
C $2.70
B $0.50
D $3.70
Answer: a
Step-by-step explanation:
multiply each answer by 10
What is the slope of the line 3x – 9y = 4?
Answer:
Slope = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Write the equation in y =mx + c form
3x - 9y = 4
-9y = -3x + 4
[tex]y = \frac{-3x}{-9}+ \frac{4}{-9}\\\\y =\frac{x}{3} - \frac{4}{9}\\m = \frac{1}{3}[/tex]
x - 15 = -25
plz help
Answer:
x=-10
Step-by-step explanation:
How do I solve this inequality?
Answer:
x is the element of {-4,-3,-2,-1,0,1,2,3,4}
Suppose a cylinder has a diameter of 18 feet and a height of h feet. Which equation can be used to find V, the volume of the cylinder in cubic feet?
Answer:
Volume of a cylinder, V = πr^2h
but r= d/2
therefore, Vol = π(d/2)^2h
from the parameters given,
Vol = π(18/2)^2h
=81πh
SOMEBODY PLEASE HELP ASAP!!! WILL GIVE BRAINLIEST
In parallelogram KLMN, KN = 10, MN = 7 and mK = 50°
Find the measures of the remaining angles of parallelogram KLMN. Justify each of the measures with a theorem.
Find the measures of the remaining side lengths of parallelogram KLMN. Justify each of the measures with a theorem.
Answer:
a- 130, 130, and 50
b- 7 and 10
Answer:
a- 130, 130, and 50
b- 7 and 10
Step-by-step explanation:
A squirrel burrowed 6 holes in 2 minutes. How many holes could the squirrel burrow in 7 minutes
Answer:
He burrows 6 holes in 2 minutes which means that he can burrow 3 holes in 1 minute.
To determine how many he can burrow in 7 minutes, you would multiply the
unit rate of 3 holes in 1 minute by 7.
He would burrow 21 holes in 7 minutes.
Step-by-step explanation:
brainliest pls?
Answer:
He burrows 6 holes in 2 minutes which means that he can burrow 3 holes in 1 minute.
therfore your answer would be 21 holes in 7 minutes
Step-by-step explanation:
Jeremey performs the same operations on four values of x. He records each resulting y-value in a table, as shown below. Which equation shows the operations Jermey performs on x to get to y
Answer:
Y=4x-3
Explanation: If we look 2 = 5 We can do 4(2)= 8 -3 = 5 So that the answer and 4(4)= 16-3 = 13 so these are the Y so this is the answer!
Compute: (√2 )^5−( √2 )^4+( √2 )^3−(√2 )^2+√2 −(√2 )^0
Answer:
2.89949493661
Step-by-step explanation:
Hope i helped! Have a wondeful weekend! :)
Answer: 2.899494936610
Step-by-step explanation:
what is the cube root of 262144
Answer:
the cube root of 262144 is 512
Answer:
64
Step-by-step explanation:
The cube root of 262144 is 64
write y= -x +3 in standard form. then graph the function
Answer:
x+y=3; graph is in word doc
Step-by-step explanation:
hi ! if you come across this can you please help me out?:) tysm
Answer: y=4x-2
Step-by-step explanation:
Since you are looking for y-intercept, the point has to be on the vertical line and the slope is 4 so it has to go up 4 to the right 1
#15, what is this answer ?
Answer:
43.39
Step-by-step explanation:
It's easy division/
x = 4x + 3 "explain your thinking"
Answer:
x equals to -1
Step-by-step explanation:
x-4x :3
-3x : 3
so x: -1
Which point is located at (2,-5)?
Answer:
B.
Hope this helps!
For any rectangle ABCD, determine whether each statement is always, sometimes, or never true. ∠a≅∠b
Answer:
always
Step-by-step explanation:
no matter what the angles of a rectangle will be 90 degrees so the answer is always
Answer:
Step-by-step explanation:
Consecutive angles are equal only when dealing with a square or a rectangle. All other 4 sided figures do not have this property.
So the answer is sometimes.
Find the volume of a pyramid with a square base, where the side length of the base is
14.4 m and the height of the pyramid is 15.3 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:
Volume of pyramid with square base is 1057.54 m³
Step-by-step explanation:
We are given:
Length of base of pyramid = 14.4 m
Height of pyramid = 15.3 m
We need to find:
Volume of pyramid with square base
The formula used is: [tex]Volume=\frac{1}{3}\times a^2 \times h[/tex]
Where a = base of pyramid and h is height
Putting values and finding volume
[tex]Volume=\frac{1}{3}\times a^2 \times h\\Volume=\frac{1}{3}\times (14.4)^2 \times (15.3)\\Volume=\frac{1}{3}\times 207.36 \times 15.3\\Volume=1057.54 \ m^3[/tex]
So, Volume of pyramid with square base is 1057.54 m³
Answer:
1057.5
Step-by-step explanation:
Ray earns $15 an hour for up to 40 hours a week. If he works more than 40 hours a week, he is paid time and a half. That means Ray is paid 150% of his hourly wage for every hour he works over 40 hours.
How much additional money does Ray earn for every hour he works over 40 hours?
Last week, Ray worked 46 hours. He incorrectly calculated he earned $45 of additional pay. What was Ray’s error when he miscalculated his overtime pay? Explain your answer.
How much was Ray’s paycheck for working 46 hours? Show your work.
Would Ray make more money working 40 hours a week for two weeks or working 32 hours one week and 46 hours the next? Justify your solution.
For every hour he works over 40 hours, he is paid an additional $7.50.
Ray’s error when he miscalculated his overtime pay is +$45.
How to calculate the error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
His normal pay is $15/h
150%/100 = 1.5
Multiply his normal pay by the rate in decimal form;
$15 X 1.5 = $22.5
His OT pay is $22.5/h.
Additional money = (OT pay) - (Normal pay)
= $22.5 - $15
= $7.5
Or $7.5 = $7.50
Thus, For every hour he works over 40 hours, he is paid an additional $7.50.
Ray actual pay for the week was $100 then from the question he incorrectly calculated it as {$100 + $45} = $145 which is $45 above his actual pay.
Error = measured value - actual value.
Error = $145 -$100 =$45.
Since the value $145 is greater than his actual pay $100, we have to include a positive sign to the error $45.
Therefore, Error = +$45.
Learn more about this concept here;
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Find the gradients of lines A and B. NEED ASAP
Step-by-step explanation:
The line A, the slope is +2
And line B the slope is n-1
Answer:
For A;
x1 = -2, y1 = -3, x2 = 3, y2 = 7
Gradient = (y2 - y1)/(x2 - x1)
= (7 - (-3))/(3 - (-2))
= 10/5 = 2.
For B;
x1 = 7, y1 = -2, x2 = -2, y2 = 7
Gradient = (y2 - y1)/(x2 - x1)
= (7 - (-2))/(-2 - 7)
= 9/-9 = -1.
please help me :)
2)
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper.
part A. Use the graph below to justify the lead executive’s statement.
part B. Determine the approximate year that the two ad revenues were equal.
Answer:
Part B= (7.5 years, 2.25ish dollars) or about (7,2)
Step-by-step explanation:
im sorry i couldn't answer part b
identify the slope and write the equation of the line .
Answer:
y=-2x+5; slope is -2
Step-by-step explanation:
slope is rise/run. we can see it rises 2 and goes left one which would give us rise/run=2/-1=-2. that is our slope.
using y=mx+b to write the equation, m is slope and b is the y-int.. we can see that the y-int. is (0,5). we can plug 5 into b.
plugging b and m in we can get the equation: y=-2x+5