the linear equation tangent at x = -2 is:
y = 123.33*x + 226.74
How to find the equation of the tangent line?To get the slope of the line we need to evaluate the first derivative in x = -2, we get:
f'(x) = 3√(2 - 4x) + (-12/2)*3x*(2 - 4x)^(-1/2)
Evaluating in x = -2 we get:
f'(-2) = 3√(2 - 4*-2) + (-12/2)*3*-2*(2 - 4*-2)^(-1/2) = 123.33
Then the line is something like:
y = 123.33*x + b
And the line must pass through:
f(-2) = 3*(-2)*√(2 - 4*(-2)) = -18.97
So the line must pass through the point (-2, -18.97)
Replacing that in the linear equation:
-18.97 = 123.33*2 + b
-19.92 + 123.33*2 = b = 226.74
Then we conclude that the linear equation tangent at x = -2 is:
y = 123.33*x + 226.74
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
PLS HELP!! ILL GIVE BRAINLYEST!!
The school cafeteria serves portions of fried rice that are 140 grams each.
A. If 64 portions of rice are served, how many grams of rice would that be?
B. Write an expression for the total weight in grams of rice needed for p portions.
C. One day, the total weight of rice served was 11,340 grams. How many portions were served that day?
D. Write an expression for the number of portions served if the total rice weighed t grams.
Answer:
A: 8,960
B: 140 x 64 = p
C: 81
D: im sorry but im confused on that one
Step-by-step explanation:
A: 140 x 64 = 8,960
C: 11,340 / 140 = 81 ( / = divided)
if a number is written as 3x3x5x3x7x7 find the smallest number by which this is to be multiplied to get a perfect cube
Answer:
175,
Step-by-step explanation:
perfect cube needs an extra 7 and two 5s.When u put these numbers you will see
What do you call two lines in 3-space that never meet, but are not parallel.
An example:
Look where two walls meet. They meet at a vertical line. Let's call that line A.
Now look at where the ceiling and another wall meet (this wall is not the same as the previous two walls mentioned). The ceiling and this new wall meet at line B
Lines A and B are skew lines since they'll never cross even if you extend them out forever. They aren't parallel lines either because they don't point in the same 3D direction.
Check out the diagram below.
First try was incorrect
Tarzan played a game in which he could either lose or gain points
each round. At the end of 3 rounds, he had -8 points. After one more
round, he had 12 points. Express the change in points in the most
recent round as an integer.
Answer:
20
Step-by-step explanation:
|-8 - 12| = 20
The absolute value of -8 minus 12 will show us the difference, or the change in points as in this problem
|-8 - 12| = 20
12. A DJ for the school dance plans to play
dance music for two hours. She has 20
requests for songs, and each song plays 31/2 minutes. If she playa all of the requests, how much time will she have to play other songs?
Answer:
50
Step-by-step explanation:
So, put 2 hours into minutes. You get 120. Now, seeing how you have 20 song requests, and each one takes 3.5 minutes, multiply those two values. Now you have 70. After doing that, just subtract 70 from 120 and get 50.
Question content area top Part 1 You are running a fuel economy study. One of the cars you find is blue. It can travel 38 1/2 miles on 1 1/4 gallons of gasoline. Another car is red. It can travel 22/5 miles on 4/5 gallons of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
Based on the miles that each car can travel on, the unit rate of miles per gallon for each car is:
Blue car - 30.8 miles per gallonRed car - 5.5 miles per gallonThe car that can therefore travel the greater distance on 1 gallon of gasoline is the Blue car.
What is the unit rate for the miles per gallon?The blue car can travel 38.5 miles on 1.25 gallons of gasoline. The unit rate is:
= 38.5 / 1.25
= 30.8 miles per gallon
The red car can travel 22/5 miles on 0.80 gallons of gasoline so the unit rate is:
= 22/5 ÷ 0.80
= 5.5 miles per gallon
The blue car can therefore travel the greater distance on 1 gallon of gasoline.
Find out more questions on the unit rate at https://brainly.com/question/28505127
#SPJ1
Multiply and simply the resulting expression with positive exponents.
(2−4−4) · (−74−2)
Please show all of the steps for your solution.
two different points on a number line are both 3 units from the point with coordinate -4. The solution to which equation gives the coordinates of both points
Two different points on the number line both at 3 units from the point, x=-4 are x= -1 and x= -7 and these two points are solution to the quadratic equation : x²+8x + 7 = 0.
What is an quadratic equation and how to frame quadratic equations using its solutions?Quadratic solution in one variable x is ax²+ bx + c = 0 ,where a, b, c are constants
If two solutions x = a and x=b are given, then the quadratic equation which can give solution as x = a and x = b can be written as:
(x-a)(x-b) = 0
Given that the two different points are at 3 units from x = -4
One point will be x = -4-3 = -7
Another point will be x = -4 +3 = -1
For more explanation please look at the attached image.
Given two solutions are x= -1 and x = -7
Then the corresponding equation will be (x-(-1)) (x-(-7))=0
(x+1)(x+7) = 0
x²+8x + 7 = 0.
Also, Learn more about quadratic equations from here:
https://brainly.com/question/1863222
#SPJ1
what is the value of the expression x^2+9/x^2 when x=0
(50 points) if L||M, solve for x and y
#11 but u can try #12 too
ignore my writing i didn’t know what to do
Check the picture below.
I’d UV = 32 and TV = 40, what is TU?
Answer: TU=8
Step-by-step explanation:
TV=TU+UV
40=TU+32
40-32=TU+32-32
TU=40-32
TU=8
Take the equation as,
→ TV = TU + UV
→ TU = TV - UV
Let's find the value of TU,
→ TU = TV - UV
→ TU = 40 - 32
→ [ TU = 8 ]
Hence, the value is 8.
Select all the correct figures.
Which figures have rotational symmetry?
PLS HELP! (math) Ill give you a brainliest and 10 points. :)
Answer: [tex]-\frac{43}{6}d - \frac{1}{8}[/tex]
Step-by-step explanation:
Convert everything to improper fractions:
[tex](-\frac{10}{3}d+\frac{3}{4}) - (\frac{23}{6}d-\frac{7}{8}) \\[/tex]
Multiply right side by two to get common denominator and distribute negative sign on to both terms in the second set of parenthesis:
[tex]-\frac{20}{6}d+\frac{6}{8}-\frac{23}{6}d-\frac{7}{8}[/tex]
Combine like terms:
[tex]= -\frac{43}{6}d-\frac{1}{8}[/tex]
please just find the values of a and b , I can do the rest.
Step-by-step explanation:
1×1+1×1/100
1+1/100
2/100
0.02 It might be the answer
Let us consider ab as 8
(8÷1/8)^2
(8/8)^2
(8/1)
8 ANS
HELP ITS URGENTGKHJLKGFHHB
Which are correct representations of the inequality 6x ≥ 3+ 4(2x - 1)? Select three options.
According to the given statement
Option 1 . 6x ≥ 3 + 8x - 4
2. 1 ≥ 2x
3. Option C represents the inequality drawn on the number line.
are the correct options.
What is Inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
According to the given values;
Inequality has been given as 6x ≥ 3 + 4(2x - 1)
By solving it further,
6x ≥ 3 + 8x - 4 [Option B is the correct option]
6x ≥ 8x - 1
6x - 8x ≥ 8x - 1 - 8x
-2x ≥ -1
2x ≤ 1
1 ≥ 2x [Option A is the correct option]
x ≤ ¹/₂
Option C represents the inequality drawn on the number line.
Therefore, Options A, B and C are the correct options.
To know more about Inequality, visit;
https://brainly.com/question/23575974
#SPJ9
The triangle below is reflected about the y-axis and then translated 4 units to the left.
The resulting triangle isA A'B'C' . What is the measure of angle C'?
1. 35°
2. 55°
3. 63°
4. 125°
Answer:
55⁰
Step-by-step explanation:
a + b + c = 180⁰
35⁰ + 90⁰ + c⁰ = 180⁰
125⁰ + c⁰ = 180⁰
180⁰ - 125⁰ = 55⁰
c = 55⁰
Explain why 0+a=a. ?
Answer:
any number or letter added to zero results in the number itself
Step-by-step explanation:
Darren is copying abc first,he constructs de as a copy of ab.next he constructs d as a copy of a,using de as one of the sides.
The discussion is shown below:
What is Construction?Geometric constructions help us to draw lines, angles, and shapes with simple tools.
Given:
A copy of triangle ABC is drawn
He has constructed an angle D and side DE. All he needs to do is constructed another edge.
The process for constructing is to start with point D and create a ray with angle D to point DE.
In order to cross the ray at point F, draw a line parallel to AB.
Learn more about construction here:
https://brainly.com/question/12990797
#SPJ2
Two trains leave stations 396 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other travels
at 100 miles per hour. How long will it take for the two trains to meet?
Answer:
It will take 2.2 hours for the trains to meet.
Step-by-step explanation:
Given,
Distance between two trains = 396 miles
Speed of one train = 95 mph
Speed of other train = 85 mph
Combined speed of trains = 95+85 = 180 mph
Distance = Speed * Time
Time =
Time =
Time = 2.2 hours
It will take 2.2 hours for the trains to meet.
Keywords: speed, distance
Learn more about distance at:
brainly.com/question/13219835
brainly.com/question/1836777
#LearnwithBrainly
Step-by-step explanation:
P ( A ) = 0.67 , P(A∪B)=0.89 and ( B ) = 0.54 . Find P(A∪B′) P ( A ∪ B ′ ) . Give an exact answer as a decimal
The value of the probability P(A u B') is 0.8218
How to determine the probability?The given parameters are
P(A) = 0.67
P(B) = 0.54
P(A u B) = 0.89
From the above parameters, we have
P(B') = 1 - P(B)
P(B') = 1 - 0.54
P(B') = 0.46
So, we have
P(A u B') = P(A) + P(B') - [P(A) * P(B')]
This gives
P(A u B') = 0.67 + 0.46 - (0.67 * 0.46)
Evaluate
P(A u B') = 0.8218
Hence, the value of the probability P(A u B') is 0.8218
Read more about probability at
https://brainly.com/question/24756209
#SPJ1
(8x-14) what is the solution of x?
Answer: [ x = 2 ] is the solution to the equation.
Step-by-step explanation: (8x-14) what is the solution of x?
Range of hx = 2r^2 + 20r +42
Answer: Range: hx>=-8
Step-by-step explanation:
Find the vertex first:
2r^2 + 20r +42=
2(r^2 + 20r/2 +42/2)=
2(r^2 + 10r +21)=
2(r^2 + 10r +25-4)=
2(r^2 + 5r+5r +25-4)=
2(r(r+5)+r(r+5)-4)=
2((r+5)^2-4)=
2(r+5)^2-4*2=2(r+5)^2-8 ==> Vertex: (-(5), -8) ==> (-5, -8)
-8 is when the range starts
Range: hx>=-8
In which set of number would you fibe the number
-153 would lie in the sets of real number which is option (A) .
A real number is a number that includes both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as √3 and π(22/7) are all real numbers.We have given a number -153 which is an integer and it can be written in the form of [tex]\frac{p}{q}[/tex] where q is not equal to 0 .Hence , it is an rational number also and integer and rational number constitute together to form real numbers.
Learn more about real number here :
https://brainly.com/question/2600240
#SPJ9
The complete question is mention below :
In which set of number would you find the number -153
(A) real number
(B) natural number
(C) whole number
(D) irrational number
(E) integer
(F) rational number
2.) How should $90 be divided into two parts so that the second part is $30
less than twice the first part?
In a year, Ivan earns $10,000 in taxable income from his part-time job. Using the above table, how much
federal income tax does Ivan owe?
O $1006
O $1500
O $970
O $1000
Question 2
1 pt
Answer:970
Step-by-step explanation:
The height of an object off the ground, h (in feet) t seconds after it is launched into the air is given by
h(t) = −16t2 + 96t, 0 ≤ t ≤ 6.
Find the average rate of change of h over the interval
[3, 6].
( ) feet per second
Interpret your result.
During the last three seconds of the objects's time in the air, it is
falling at an average rate of (. )feet per second.
The average rate of change of h over the interval is -48 feet per second.
Given,
The height of an object off the ground, h (in feet) t seconds after it is launched into the air is given by
h(t) = −16t2 + 96t, 0 ≤ t ≤ 6.
We need to find the average rate of change of h over the interval [3, 6].
How do we find the average rate of change of a function over an interval?If we have an interval [a, b] and a function f(x).
The rate of change is given by:
= f(b) - f(a) / b - a
We have,
h(t) = −16t² + 96t and [3, 6].
h(6) = -16 x 6² + 96 x 6 = -576 + 576 = 0
h(3) = -16 x 3² + 96 x 3 = -144 + 288 = 144
The average rate of change of h is:
= h(6) - h(3) / 6 - 3
= 0 - 144 / 3
= -144 / 3
= -48
Thus the average rate of change of h over the interval is -48 feet per second.
Learn more about the average rate of change here:
https://brainly.com/question/23780823
#SPJ1
How many squares are in the
Answer:
10
Step-by-step explanation:
What is the value of x in the equation , 7x+y=48 when y = 3?
Answer:
x =[tex] \frac{45}{7} [/tex]
Step-by-step explanation:
7x + y = 48
substitute y with 3 as given so,
7x + 3 = 48
7x = 48 - 3
7x = 45
x = 45 ÷ 7
x = [tex] \frac{45}{7} [/tex]
hope this helps
graph the line that passes through (0,3) and has slope 2/3
Answer:
(0,3) (3,5)
Step-by-step explanation:
You already have a point of (0,3) so graph that point and then using the slope go up 2 and right 3 so the other point you'll have is (3,5).
Equation: y = 2/3x + 3
Perpendicular slope is opposite sign reciprocal i.e. -3/2
Equation: y = -3/2x + 3
points on graph (0,3) (2,0)
