The tangent to the given curve at the point (1,0) is: y=6x-6.
What is tangent?The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.When you ride a bicycle, every point on the wheel's circumference forms a tangent with the road, providing a practical illustration of a tangent.When you ride a bicycle, every point on the wheel's circumference forms a tangent with the road, providing a practical illustration of a tangent.A straight line that only touches a circle once is said to be tangent to it. The term "point of tangency" refers to this location.The first derivative f'(x), the slope (tangent) of the original curve, may be obtained at every point (x,y) on the curve because the supplied curve is a continuous function, making Eq. 1 differetiable at every x.
The slope of the tangent at x=1 is given by the first derivative of Eq. 1: f'(1)=9(1)2-3=6.
A line that passes through the point (x1, y1) and has a slope of m has the equation:
(y-y1)=m(x-x1) ··· Eq.2 (the point- slope form of linear function)
Here, x1=1, y1=0, and m=f'(x1)=6. Add these numbers to Eq. 2. It is possible to repeat and simplify Eq. 2 as follows: y-0=6(x-1) ⇒ y=6x-6
Consequently, y=6x-6 is the tangent to the given curve at position (1, 0).
To learn more about the tangent, refer to:
https://brainly.com/question/14790856
#SPJ4
The average weight of an apple is normally distributed with a mean of 0.33 of a pound with a standard deviation of 0.07. Michael went to the store and found an apple that weighted 0.50. What percent of the apples weigh less than the one Michael found?
Step-by-step explanation:
MEAN:0.33
STANDARD DEVIATION:0.07
WEIGHTED:0.50
0.33×0.07=0.0231÷0.50=0.0462
URGENT!!!!! ILL GIVE BRAINLIEST! AND 100 POINTS
Put the numbers in order from smallest to largest.
Answer:
(from smallest to largest)
1. 3.24 × 10^-5
2. 5.48 × 10 ^-2
3. 1.2 × 10¹
4. 4.68 × 10⁶
5. 8.34 × 10⁶
Step-by-step explanation:
We can put these in order through the exponents.
Hope this helps!
Which is an equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity? 88 over d raised to the twelfth power 2 over quantity 11 times d raised to the twelfth power end quantity negative 2 over quantity 11 times d raised to the sixth power end quantity 0.2d12
The expression "4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity" or 4d^(-3)/(22d^9) is equivalent to "2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity" or simply 4d^(-3)/(22d^9), combine all like terms and perform the necessary operations.
Using the following rules of exponents:
Quotient Rule for Exponents : a^m/a^n = a^(m - n)
Negative Exponent Rule : a^-m = 1/a^m
Simplify the expression.
4d^(-3)/(22d^9)
⇒ (4/22) [d^(-3)/d^9]
⇒ (2/11) [d^(-3 - 9)]
⇒ (2/11) d^-12
⇒ 2/(11d^12)
Hence, the equivalent expression is "2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
Learn more about algebraic expression here: https://brainly.com/question/723406
#SPJ4
Answer:
2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
Step-by-step explanation:
if someone solves this there are 4 more of the same question! Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
It is estimated that the annual cost of driving a certain new car is given by the formula
C = 0.39m + 2800
where m represents the number of miles driven per year and C is the cost in dollars. Jane has purchased such a car and decides to budget between $7480 and $8260 for next year's driving costs. What is the corresponding range of miles that she can drive her new car? (Enter your answer using interval notation.)
Answer:
[11000, 11600]
Step-by-step explanation:
Give me Brainliest if that helped! :)
Adelaide is the employee of the month at her job. Her reward is to select at random from 4 gift cards, 6 coffee mugs, 7 DVDs, 10 CDs, and 3 gift baskets. What is the probability that an employee receives a gift card, coffee mug, or CD?
According to the question, Adelaide is the employee and she has to select a reward from four gifts. And those are 6 coffee mugs, 7 DVDs, 10 CDs and 3 gift baskets.
Now, calculate the probability that the gift is either a coffee mug or CD.
Let us assume, ‘G’ represents the gift card, ‘C’ represents the coffee mug and ‘D’ represents the CD.
The total number of items are [tex]4+6+7+10+3 = 30[/tex] items
P(G or C or D) = P(G) + P(C) + P(D)
[tex]= \frac{4}{30} + \frac{6}{30} + \frac{10}{30} = \frac{20}{30} = \frac{2}{3} = 67%[/tex]
Therefore , the probability to receive either a gift card or coffee mug or CD is [tex]67[/tex] percent.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
To learn more about the Probability from the given link:
https://brainly.com/question/13604758
#SPJ4
Factorise 56w – 48.
Answer:8(7w+
Step-by-step explanation:
Let h(x) be the reflection of f(x)=3 x+3 in the x -axis. What is a function rule for h(x) ?
The function rule for h(x) = -3x -3.
In mathematics, functions can be manipulated algebraically to obtain graphs of functions through certain transformations. Such transformations are reflections of the x-axis or the y-axis. To flip a function f(x) on the x-axis, multiply the whole function by a negative value to get -f(x), and to flip a function f(x) on the y axis, f(-x ), specify the x variable with a negative value. If it is reflected around the y-axis, it will stay the same, which gives h(x) = 3x + 3. Flipping around the x-axis (assuming y = 0) has the y-axis as the axis of symmetry, but it is concave down.
The function rule around the x-axis gives a complementary sign of the value of the function, so
h(x) =-3x-3 will be reflection of f(x) =3x+3
More problems related to the graph transformation and Function rule are given in the link below.
https://brainly.com/question/10059147?referrer=searchResults
#SPJ4
ANSWER ASAP WILL MARK AS. BRAINLYST (Only if answer is correct)
Look at the photo and answer broth questions
Step-by-step explanation:
2 + 3 = 5
the sign of the sum is "-", because the temperature dropped (in both cases).
the total change in temperature is -5°.
the sum of 2 positive integers ... is always positive.
both numbers have a positive sign. the sum means "+", so we are adding 2 positive numbers.
nowhere in the operation are we going in the negative direction or bring a negative sign in.
so, where would a "-" sign come from ?
if I have something on the plus side, and I put something positive on top of it, the resulting pile will still be positive.
Determine whether ΔA B C ≅ ΔX Y Z . Explain. A(5,2), B(1,5), C(0,0), X(-3,3), Y(-7,6), Z(-8,1)
The given triangles are congruent its that ΔA B C ≅ ΔX Y Z.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
If ΔA B C ≅ ΔX Y Z then the corresponding sides will be the same.
Its that AB = XY , BC = YZ
The distance associated with two points (x₁, y₁) and (x₂, y₂) is given by
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So,
(AB) = [tex]\sqrt {\left( {5 - 1 } \right)^2 + \left( {2 - 5 } \right)^2 }[/tex]
AB = 5
(XY) = [tex]\sqrt {\left( {-3 + 7 } \right)^2 + \left( {3 - 6 } \right)^2 }[/tex]
XY = 5
Similarly BC = YZ and CA = ZX.
Hence "The given triangles are congruent its that ΔA B C ≅ ΔX Y Z".
For more about triangles,
https://brainly.com/question/2773823
#SPJ4
Here are 2 polygons. Select all sequences of translations, rotations, and reflections below that would take polygon Pto polygon Q
The required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.
What is translation?Translation means the displacement of a figure or a shape from one place to another. In translation a figure can move upward, downward, vertical and horizontal.
Some of the Translation are,
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Rotation means the circular movement of an object around a centre. It is possible to rotate different shapes by an angle around the centre point.
Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system.
Thus, the required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.
To learn more about translation :
brainly.com/question/1761538
#SPJ1
The complete question image is attached.
Write a two-column proof for each case of Theorem 10.6 Case 3
Given: P lies outside
Prove: m< ABC = 1/2m AC
The measure of an inscribed angle is one-half the measure of the central angle.
What is the inscribed angle and the circumscribed angle?An inscribed angle in geometry is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle formed by two given points on a circle at a given point on the circle.
The measure of an inscribed angle is one-half the measure of the central angle. The measure of a circumscribed angle is 180 degrees minus the measure of the central angle.
Given: P lies outside
m ∠ABC = m ∠DBC – m ∠DBA ( Addition Postulate, Subtraction Property of Equality)
m ∠DBC = m 1/2(arc DC)
m ∠DBA = m 1/2(arc DA) (The measure of an inscribed ∠ whose side diameter is half the measure of the intercepted arc (Case 1)).
m ∠ABC = m 1/2 (arc DC) – m 1/2(arc DA) (Substitution)
m ∠ABC = 1/2 [m(arc DC) – m(arc DA)] (Factor)
m(arc DA) + m(arc AC) = m(arc DC) (Arc Addition Postulate)
m(arc AC) = m(arc DC) – m(arc DA) (Subtraction Property of Equality)
m ∠ABC = m 1/2 (arc AC) (Substitution)
To learn more about inscribed angle refer to:
brainly.com/question/13110384
#SPJ4
Katherine is very interested in cryogenics (the science of very low temperatures).
With the help of her science teacher she is doing an experiment on the affect of low
temperatures on bacteria. She cools one sample of bacteria to temperature of -51°C
and another to -76°C. What was the temperature difference in the two experiments?
Temperature difference of experiments is -25°C.
Step-by-step explanation:
Given that
Katherine is very interested in cryogenics (the science of very low temperatures).With the help of her science teacher she is doing an experiment on the affect of low temperatures on bacteria.She cools one sample of bacteria to temperature of -51°C and another to -76°C.To find
Temperature difference in the two experimentsSo, according to the question
we have,
Temperature of 1st experiment = -51°C, andTemperature of 2nd experiment = -76°CWe have to find Temperature difference of experiments
So, we can say that
Temperature difference of experiments
= Temperature of 2nd experiment - Temperature of 1st experiment
Now, putting the all given values,
We, will get
Temperature difference of experiments = -76 - (-51)
= -76+51
= -25°C,
Answer:
So, Temperature will fall 25°C,To learn more about Temperature difference, please click on the link:
https://brainly.com/question/17864807
#SPJ9
What is summation notation for the series?
a. -5+2+9+16+ . . . . . . . +261+268
The arithmetic series -5+2+9+16+ . . . . . . . +261+268 can be written using the summation notation as
[tex]7\sum\limits^{40}_{n=1} {n} -480[/tex]
Let
a(1) + a(2) + a(3) + ... + a(n)
be an arithmetic series.
Then, the nth term will follow the formula:
a(n) = a(1) + (n-1) . d
where d = the common difference.
The value of d is:
d = a(2) - a(1) = a(n) - a(n-1).
The series given is:
-5+2+9+16+ . . . . . . . +261+268
This is an arithmetic series with a(1) = -5 and
d = 2 - (-5) = 7
Substitute these parameters into the formula of the nth term:
a(n) = a(1) + (n-1) . d
a(n) = -5 + (n-1) . 7
a(n) = 7n - 12
Let a(n) = 268, then:
268 = 7n - 12
7n = 280
n = 40
The series can, then, be expressed as:
-5+2+9+16+ . . . . . . . +261+268
[tex]=\sum\limits^{40}_{n=1} {a(n)}[/tex]
[tex]=\sum\limits^{40}_{n=1} {(7n-12)}[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -\sum\limits^{40}_{n=1} {12}[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -40\times12[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -480[/tex]
Learn more about the summation notation here:
https://brainly.com/question/10577562
#SPJ4
Mr. Delgado gets paid $40 per breaking
gig. If he has $120 saved, how many
breaking gigs will it take him to have
$400 if he doesn't spend any money?
Write AND Solve the Equation.
Answer:
7
Step-by-step explanation:
→ Write the equation
40x + 120 = 400
→ Minus 120 from both sides
40x = 280
→ Divide by 40 on both sides
x = 7
The number of breaking gigs that it takes him to have is $400 will be 7 breaking gigs.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Mr. Delgado gets paid $40 per breaking gig. If he has $120 saved. If he doesn't spend any money.
Then the number of breaking gigs that it takes him to have is $400 will be
40x + 120 = 400
Simplify the equation then we have
40x = 280
x = 280/40
x = 7
The number of breaking gigs that it takes him to have is $400 will be 7 breaking gigs.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
n=c-s solve for c, can anyone solve this?
Answer: sure ummm...
r
=
1
d
cs
Step-by-step explanation:
Answer: n+s=c
Step-by-step explanation:
n=c-s
+s +s
n+s=c
add s to both sides to get c by itself, and you end up with n+s=c
A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year.
Write an exponential function that models the value
of the car over
years.
To the nearest cent, what will be the value of the car after eight years?
Answer:
after 8 years the value of the car would be $8,173.42
Step-by-step explanation:
the given P=15250
r=7.5/100=0.075
t=x
y = 15250*(1 - 0.075)^x
after 8 years we would have
x = 8
y = 15250*(1 - 0.075)^8
y = $8,173.42
after 8 years the value of the car would be $8,173.42
Answer:
8173.42
Step-by-step explanation:
I just know it's correct
what property is 0x = 0
Answer:
Additive Identity Property of 0
Step-by-step explanation:
It means that additive identity is "0," as adding 0 to any number gives the sum as the number itself.
a box of brownie mix calls for 2 eggs and 1/2 cups of oil how many eggs and how much oil would you need for 2 boxes of brownie mix
Answer:
1 box of brownie mix= 2 eggs and 1/2 cups of oil
ans=
2 boxes of brownie mix= (2 eggs ×2)(1/2 cups of oil × 2)
=4 eggs and 1 cup of oil
Answer:
4 eggs and 1 cup of oil.
Step-by-step explanation:
2x2=4 1/2x2=1
Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) − 5?
The graph shifts 5 units up.
The graph shifts 5 units down.
The graph shifts 5 units left.
The graph shifts 5 units right.
The statement which describes the effect of replacing the graph of f(x) with the graph of f(x) - 5 is : (b) the graph shifts 5 units down.
What is Transformation?
Transformation :- The transformations of functions define how to graph a function is moving and how its shape is being changed. There are basically three types of function transformations: translation, dilation, and reflection.
f(x) = f(x) + k
This is a translation transformation that shifts the original function f(x) either k units up or k units down. If k is more than 0 then k shifts up. If k is less than 0 then k shifts down.
Here, k = -5<0
Hence, the shift is 5 units down.
To learn more about transformations of graphs visit :- brainly.com/question/10059147
# SPJ1
Find the percent of the given number. 79 % of 623
A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.
The percent of the given number 79 % of 623 is 492.17.
What is meant by percentage?A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.
Let the equation be 79 % of 623
Percentage = (value/total value) × 100 %.
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
79 % of 623 = 79/100 of 82
79/100 × 623 = 492.17
Therefore, the percent of the given number 79 % of 623 is 492.17.
To learn more about the percentage refer to:
brainly.com/question/24877689
#SPJ4
A soccer team brings a 4.5 -gallon cooler of water to their games. How many 4 -ounce cups can the team drink per game?
The number of 4 -ounce cups that the team can the team drink per game is 144.
It is given in the question that the soccer team brings a 4.5 gallon cooler of water to their games.
We have to find the number of 4 -ounce cups that the team can drink per game.
We know that,
1 gallon = 128 ounces
Hence, we can write,
4.5 gallon = 128*4.5 = 576 ounces
Hence, by using unitary method, we can write,
Number of 4 ounce cups the team can fill per game = ounces in 4.5 gallons/ounces in a cup = 576/4 = 144 cups.
To learn more about unitary method, here:-
https://brainly.com/question/22056199
#SPJ4
Four hamburgers cost 13.95. Find the unit rate
Answer:
$3.48
Step-by-step explanation:
Divide the number of hamburgers by the total cost:
13.95 / 4 =
3.4875
$3.48
Write an equation of the line passing through the points (3,8) and (-1,-16).
Answer:
here ya go !
Step-by-step explanation:
What is the difference in height between a rose bush that is 3'9” tall and Emma who is 5½ feet tall?
28. SAND A home improvement store sells bags of sand, which are labeled as weighing . The equipment used to package the sand produces bags with a weight that is within of the labeled weight. a. Write an absolute value equation to represent the maximum and minimum weight for the bags of sand. b. Solve the equation and interpret the result.
From the situation described, we have that:
a. The absolute value equation is: |w - 35| = 8.
b. The solutions are w = 27 and w = 43, meaning that the minimum weight is of 27 pounds and the maximum weight is of 43 pounds.
What is the missing information?A home improvement store sells bags of sand, which are labeled as weighing 35 pounds. The equipment used to package the sand produces bags with a weight that is within 8 pounds of the labeled weight.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
For this problem, the difference between the weight w and 35 pounds is of 8 pounds, hence the equation is:
|w - 35| = 8.
From the definition, the solutions are given as follows:
w - 35 = -8 -> w = 27.w - 35 = 8 -> w = 43.The solutions are w = 27 and w = 43, meaning that the minimum weight is of 27 pounds and the maximum weight is of 43 pounds.
More can be learned about the absolute value equation at https://brainly.com/question/5012769
#SPJ1
Take has a square-shaped garage with 32 square meters of floor space. she plans to build an addition that will increase the floor space by 50%. what will be the length of one side of the new garage?
The length of one side of the new square-shaped garage is 4√3 meters.
A square is a two dimensional figure that has 4 equal sides. The area of a square can be solved by multiplying the length of its side by itself.
A = s^2
where s = side length
If the initial square-shaped garage has an area of 32 square meters and will be increased by 50%, then the new area should be 50% more than the initial area.
new floor area = 50% initial area + initial area
new floor area = 50%(32) + 32
new floor area = 16 + 32
new floor area = 48 square meters
If the new garage has a floor area of 48 square meters, using the formula for the area of a square, solve for the length of its side.
A = s^2
48 = s^2
s = 4√3 meters
Learn more about squares here: https://brainly.com/question/24487155
#SPJ4
What is the mass of gasoline (density = 0.680 g/cm3 ) in a 94.6 l gasoline tank?
A 94.6 L gasoline with a density of 0.680 g/cm^3 has a mass of 64328 g.
Density is defined as the ratio between the mass of a substance and the volume it occupies. Denoted by ρ, density is mass per unit volume and the formula is given below:
ρ = mass / volume
Converting first the volume from L to cm^3.
1 L = 1000 cm^3
94.6 L = 94.6(1000 cm^3)
94.6 L = 94,600 cm^3
Given the density of the gasoline and its volume, solve for the mass of the gasoline using the formula for the density.
ρ = mass / volume
0.680 g/cm^3 = mass / 94,600 cm^3
mass = 0.680 g/cm^3 (94,600 cm^3)
mass = 64328 g
mass = 64.328 kg
Learn more about density here: https://brainly.com/question/1354972
#SPJ4
What is the difference between −125 anThe Japan Trench is 9 km below sea level. The Peru-Chile Trench is 8 km below sea level. What is the difference of depths between them, and which trench is deeper?
−17 km, and the Japan Trench is deeper
−1 km, and the Peru-Chile Trench is deeper
1 km, and the Japan Trench is deeper
17 km, and the Peru-Chile Trench is deeperd 18?
Based on the distance below sea level of the Japan Trench and the Peru-Chile Trench, the difference and the deeper trench is 1 km, and the Japan Trench is deeper.
Which is the deeper trench?The deeper trench is the one that is further down sea level. In other words, it is the one that is a larger distance below sea level.
The Japan Trench is 9 km below sea level while the Peru-Chile trench is 8 km below sea level. This means that the Japan Trench is deeper.
The difference is:
= 9 - 8
= 1 km
In conclusion, the Japan trench is deeper by 1 km.
Find out more on distance below sea level at https://brainly.com/question/27858424
#SPJ1
solve for x. 4x-30=2x
