Answers
Answer:
A) Gradient = -3
B) 3y - x = 7
Step-by-step explanation:
The curve has the equation;
y = x³ - 6x² + 9x + 1
We are given the pints it passes through as;
A(2,3) and P(3, 1)
A) to find the gradient, we will find the derivative of the given equation.
Thus;
Gradient = y' = 3x² - 12x + 9
At point A, x = 2. Thus;
Gradient = 3(2²) - 12(2) + 9
Gradient = 12 - 24 + 9
Gradient = -3
B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3
Thus, equation of the normal to the curve at point A will be;
(y - 3) = ⅓(x - 2)
Multiply both sides by 3 to get;
3y - 9 = x - 2
3y - x = 9 - 2
3y - x = 7
Related Questions
Find The values of ( d ,f ,e ) angles
Answers
Answer:
angle d =35, e=55, f=55.............
What is the volume of a cube with edge lengths of 2/3 units
Answers
Answer:
Step-by-step explanation:
8/27 because if you think about it 2/3 x 2/3 x 2/3 x 2/3 = 8/27
Pleas e help me 100 points and brainliest
Answers
Answer:
this is your answer. I think it is right.
Answer:
see the answersStep-by-step explanation:
to understand thisyou need to know about:factoringlCDPEMDAStips and formulas:L.C.D=lowest common denominatorlet's solve:[tex]1) \sf\frac{7}{m - 6} \: , \frac{1}{m} \\ [/tex]
denominators are m-6,m
therefore
the lowest common denominator is
(m-6)(m)[tex] \sf\frac{1}{n - 1} \: , \frac{1}{ {n}^{2} - 2n + 1 } [/tex]
denominators n-1,n²-2n+1
step-1
factor n²-2n+1 to find the lowest common denominator
use (a-b)²=a²-2ab+b to factor n²-2n+1therefore
(n)²-2.n.1+(1)²(n-1)²therefore
the L.C.D of the second expression is
(n-1)² alternative form(n-1)(n-1)[tex]3) \tt\frac{k}{ {h }^{2} - 5h + 6} \: , \frac{3}{h -3 } [/tex]
step-1
factor out h²-5h+6 to find L.C.D
rewrite -5h as -2h-3h: h²-2h-3h+6factor out h: h(h-2)-3h+6factor out -3: h(h-2)-3(h-2)group: (h-3)(h-2)therefore
the L.C.D of the third expression is
(h-3)(h-2)Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 4(m∠Y) − 210°. Find m∠Y.
Answers
Answer:
angle Y= 60 degrees
Step-by-step explanation:
angle S + angle Y = 90 degrees because they are complementary
Y = 90 - S
angle S = 4(Y)-210
substitute for Y
S = 4(90 - S) - 210
S = 360 - 4S - 210
reduce
5S = 150
S = 30
Y = 90 - 30 = 60
The volume of a cuboid is 189cm3.
The length is 7cm and the width is 9cm.
Work out the height of the cuboid.
Answers
Volume of cuboid:
Let h cm be the height of the cuboid.
7 x 9 x h = 189
63h = 189
h = 189/63
h = 3
The height of the cuboid is 3 cm.
Use the diagram below to find x and each missing angle. Please
Answers
Answer:
x=18
<1=34
<2=56
Step-by-step explanation:
A warehouse has 1,750 boxes of water bottles. A truck unloaded another 530 boxes at the warehouse. Each box holds 48 bottles of water. How many bottles of water are in the warehouse?
Answers
Answer:
109440
Step-by-step explanation:
1750 boxes of water bottles with 48 bottles of water each: 1750 x 48 = 84000
plus the other 530 boxes at the warehouse which alone are: 530 x 48 = 25440
adding up 84000 + 25440 = 109440
The total number of bottles of water in the warehouse will be 27,190.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A warehouse has 1,750 boxes of water bottles.
A truck unloaded another 530 boxes at the warehouse.
Each box holds 48 bottles of water.
Then the number of bottles that were unloaded by truck will be
⇒ 530 x 48
⇒ 25,440
Then the total number of bottles of water in the warehouse will be
⇒ 25,440 + 1,750
⇒ 27,190
The total number of bottles of water in the warehouse will be 27,190.
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PLZ HELY ILL MARK BRANILEST
Answers
Answer:
518
Step-by-step explanation:
14 x 74 = 1036 1036 / 2 = 518
( really need brainliest , hope it helps )
( first )
ou intend to draw a random sample in order to test a hypothesis about an unknown population mean. You will use a hypothesis test. A description of each of the steps of a hypothesis test follows, but they may be specified in the incorrect order. Specify the correct order of the steps. Determine the null and alternative hypotheses. Draw a conclusion about the unknown population using what is known about the sample. Determine the probability at which you will conclude that the sample outcome is very unlikely. Draw a random sample, and calculate the sample statistic.
Answers
Answer:
Determine the null and alternative hypotheses : STEP 1
Draw a conclusion about the unknown population using what is known about the sample : STEP 4
Determine the probability at which you will conclude that the sample outcome is very unlikely : STEP 2
Draw a random sample and calculate the sample statistic : STEP 3
Step-by-step explanation:
The correct order of the steps are :
Determine the null and alternative hypotheses : STEP 1
Draw a conclusion about the unknown population using what is known about the sample : STEP 4
Determine the probability at which you will conclude that the sample outcome is very unlikely : STEP 2
Draw a random sample and calculate the sample statistic : STEP 3
how many inches is 2 1/6 ft
Answers
Answer:
26 inches
Step-by-step explanation:
In the triangle below, which equation can be used to solve for x?
Answers
Answer:
triangle VUW
angle V=75 degrees
angle U= 50 degrees
side VU= 13 ft
Step-by-step explanation:
piete)
Decide whether the following statement makes sense or does not make sense. Explain your reasoning.
I drove at a speed of 35 miles for the entire trip.
Answers
Answer:
It doesn't make sense
Step-by-step explanation:
Given
Statement: .... at a speed of 35 miles .....
Required
Does it make sense?
In motion, speed is measured in km/h, m/s, miles per hour (depending on context) while distance is measured in km, m or miles.
However, the given statement mention the unit of speed to be miles which is incorrect.
Hence, we can conclude that the statement does not make sense.
A correct statement would be: I drove at a speed of 35 miles per hour .......
A lumber mill needs one more tree cut down that is at least 29 feet long. The person cutting down the tree is 6 feet 2 inches tall. Using shadows to determine whether a tree is tall enough, the person stands next to the tree and measures the length of his shadow as 32 inches. What is the length (to the nearest tenth of a foot) of the tree’s shadow that will allow the tree to be cut down?
Answers
Answer:
create a proportion 72/348 = 32/x
Step-by-step explanation:
x = 1682
1682 ÷ 12 = 140.1
The length of the tree’s shadow that will allow the tree to be cut down will be 150.5 inches.
What are ratio and proportion?
A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
A lumber mill needs one more tree cut down that is at least 29 feet long. The person cutting down the tree is 6 feet 2 inches tall.
29 feet = 348 inches
6 feet 2 inches = 74 inches
Using shadows to determine whether a tree is tall enough, the person stands next to the tree and measures the length of his shadow as 32 inches.
Then the length of the tree’s shadow that will allow the tree to be cut down will be
Let x be the tree’s shadow. Then we have
x / 348 = 32 / 74
x = 150.486
x ≅ 150.5 inches
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A quadrilateral ABCD has the given angle measures. Select all measurements which
could come from a cyclic quadrilateral.
A:
angle A is 90°, angle B is 90°, angle C is 90°, and angle D is 90°
B:
angle A is 80°, angle B is 80°, angle C is 100°, and angle C is 100°
C:
angle A is 70°, angle B is 110°, angle C is 70°, and angle D is 110°
D:
angle A is 60°, angle B is 50°, angleC is 120°, and angle D is 130°
E:
angle A is 50°, angle B is 40°, angle C is 120°, and angle D is 150°
Answers
Answer:
A: angle A is 90°, angle B is 90°, angle C is 90°, and angle D is 90°
B: angle A is 80°, angle B is 80°, angle C is 100°, and angle C is 100°
D: angle A is 60°, angle B is 50°, angle C is 120°, and angle D is 130°
Step-by-step explanation:
The sum of opposite angles of a cyclic quadrilateral is 180°
It must satisfy the following:
A+C=180° and B+D=180°
Only choice A and B and D satisfy.
The correct options are options A, B, and D.
What is a cyclic quadrilateral?A quadrilateral having all its corners on a circle plus opposite angles' sum is 180° called a cyclic quadrilateral.
A) ∠A =90°
∠B=90°
∠C =90°
∠D =90°
∠A + ∠C = 180°
∠B + ∠D =180°
So, this quadrilateral can come from a cyclic quadrilateral.
B) ∠A =80°
∠B=80°
∠C =100°
∠D =10 0°
∠A + ∠C = 180°
∠B + ∠D =180°
So, this quadrilateral can come from a cyclic quadrilateral.
Similarly, options C, D, and E also can be checked whether they can come from a cyclic quadrilateral or not.
C) Cannot come from a cyclic quadrilateral since ∠A + ∠C =140°≠180°.
D) ∠A + ∠C = 180°
∠B + ∠D =180°
So, this quadrilateral can come from a cyclic quadrilateral.
E)Cannot come from a cyclic quadrilateral since∠A + ∠C = 170°≠180°.
Therefore, The correct options are options A, B, and D.
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Three sets of data are given below. What is the
median of the ranges?
Data A: -3,2,-5,6,8
Data B: 4,9,6,2
Data C: 8,3,0,4
A) 2
B) 5
C) 7
D) 8
Answers
1.) take 8-(-3)
2.) 9-2
3.) 8-0
Then list the number in order least to greatest
-13 7 8
Find the middle number
Get 7
One winter day, the temperature in Houston is 8 Celsius. Find the temperatures in these other cities. Explain or show your reasoning.
In Orlando, it is 17 warmer than it is in Houston
In Salt Lake City, it is 18 colder than it is in Houston
In Minneapolis, it is 25 colder than it is in Houston
In Fairbanks, it is 12 colder than it is in Minneapolis
Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks.
Answers
Salt Lake city = -10° because 8-18
Minneapolis = -17° because 8-25
Fairbanks = -29° because -17-12
Houston = 8° - 37° = Fairbanks
Hence, the temperatures in these other cities are
Orlando is [tex]25[/tex] degree
Salt Lake is [tex]-10[/tex] degree
Minneapolis is [tex]-17[/tex] degree
Fairbanks is [tex]-29[/tex] degree
What is the degree?
A degree, usually denoted by °, is a measurement of a plane angle in which one full rotation is [tex]360[/tex] degrees.
Here given that,
One winter day, the temperature in Houston is [tex]8[/tex] Celsius.
In Orlando, it is [tex]17[/tex] warmer than it is in Houston.
In Salt Lake City, it is [tex]18[/tex] colder than it is in Houston.
In Minneapolis, it is [tex]25[/tex] colder than it is in Houston.
In Fairbanks, it is [tex]12[/tex] colder than it is in Minneapolis.
So, it would be
Orlando = [tex]25[/tex] degree
because [tex]17+8=25[/tex] degree
Salt Lake city [tex]= -10[/tex] degree
because [tex]8-18=-10[/tex] degree
Minneapolis [tex]= -17[/tex] degree
because [tex]8-25=-17[/tex] degree
Fairbanks [tex]= -29[/tex] degree
because [tex]-17-12=-29[/tex] degree
Hence, the temperatures in these other cities are
Orlando is [tex]25[/tex] degree
Salt Lake is [tex]-10[/tex] degree
Minneapolis is [tex]-17[/tex] degree
Fairbanks is [tex]-29[/tex] degree
To know more about the degree
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In right angle ABC, a = 12, b = 9, and c = 15. Find tan ∠B
Answers
Answer: 53.13010235
To go on a summer trip, Felipe borrows $200. He makes no payments until the end of 3 years, when he pays off the entire loan. The lender charges sim
Interest at an annual rate of 2%.
Answers
Answer:
Step-by-step explanation:
A=P(1+rt)
A=200(1+.02(3))
A=200(1.06)
A=$212
Simplify completely*****
Answers
Answer:
[tex]\displaystyle \frac{2(x + 4)}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{4x + 16}{6}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{4(x + 4)}{6}[/tex][Fraction] Reduce: [tex]\displaystyle \frac{2(x + 4)}{3}[/tex]Write a rule for a function with a parabolic graph that contains the x-intercepts (-20,0) and (40,0) and a maximum point whose y-coordinate is 30.
Answers
Step-by-step explanation:
Since the x-intercepts are -20 and 40, the line of symmetry is x = (-20 + 40)/2 = 10.
Now we have y = a(x - 10)² + 30, where a is an unknown constant. We can find a by using an x-intercept point.
=> (0) = a[(40) - 10]² + 30
=> 900a + 30 = 0, a = -1/30.
Hence the rule is y = -(x - 10)²/30 + 30.
a) Simplify
X - 2 / 7(x - 2)2
Answers
Answer:
3x/7 + 8/7
Step-by-step explanation:
There are 30 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in the dance recital?
Answers
females: 30/x = 5
x = 6
males: y/6 = 4
y = 24
there are 24 men in the dance recital.
Find the equation of the line that is perpendicular to the x-axis and passes through the point (-10,-1). Give the full equation as your answer. The equation is _______________
Answers
Answer:
x = -10
Step-by-step explanation:
First, determine the slope of the answer. The x-axis is a horizontal line, thus the new line must be vertical. All vertical lines are represented by the equation x = a number. That number represents the x-value of all the points the vertical line passes through.
So, since the line passes through (-10, -1), take the x-value of that point and put it into that equation. Thus, x = -10.
Let y = 5e5z
A. Find the differential dy
25e53
dy
B. Use part A. to find dy when x = - 3 and dir = 0.4.
Round your answer to 2 decimal(s).
dy =
Submit Question
Answers
Answer:
[tex]\displaystyle dy = 25e^{5x}dx\\dy = 3.27 \cdot 10^7[/tex]
General Formulas and Concepts:
Math
RoundingEuler's Number e - 2.71828Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightCalculus
Derivatives
Derivative Notation
Differentials
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹eˣ Derivative: [tex]\displaystyle \frac{dy}{dx}[e^u] = u'e^u[/tex]
Step-by-step explanation:
Part A
Step 1: Define
[tex]\displaystyle y = 5e^{5x}[/tex]
Step 2: Differentiate
[Function] eˣ Derivative: [tex]\displaystyle \frac{dy}{dx} = \frac{dy}{dx}[5x] \cdot 5e^{5x}[/tex][Derivative] Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 5x^{1 - 1} \cdot 5e^{5x}[/tex][Derivative] Simplify: [tex]\displaystyle \frac{dy}{dx} = 5 \cdot 5e^{5x}[/tex][Derivative] Multiply: [tex]\displaystyle \frac{dy}{dx} = 25e^{5x}[/tex][Derivative] [Multiplication Property of Equality] Isolate dy: [tex]\displaystyle dy = 25e^{5x}dx[/tex]Part B
Step 1: Define
[Differential] [tex]\displaystyle dy = 25e^{5x}dx[/tex]
[Given] x = 3, dx = 0.4
Step 2: Evaluate
Substitute in variables [Differential]: [tex]\displaystyle dy = 25e^{5(3)}(0.4)[/tex][Differential] [Exponents] Multiply: [tex]\displaystyle dy = 25e^{15}(0.4)[/tex][Differential] Evaluate exponents: [tex]\displaystyle dy = 25(3.26902 \cdot 10^6)(0.4)[/tex][Differential] Multiply: [tex]\displaystyle dy = (8.17254 \cdot 10^7)(0.4)[/tex][Differential] Multiply: [tex]\displaystyle dy = 3.26902 \cdot 10^7[/tex][Differential] Round: [tex]\displaystyle dy = 3.27 \cdot 10^7[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differentials
Book: College Calculus 10e
plz help with 24-28!!!!!!!!!!!!!!
Answers
Answer:
4
Step-by-step explanation:
The system of equations y = 2x + 5 and y = –3x – 15 is shown on the graph below.
On a coordinate plane, 2 lines intersect at (negative 4, negative 3).
According to the graph, what is the solution to this system of equations?
(–4, –3)
(–3, –4)
(–5, 5)
(5, –5)
Answers
Answer: A
Explanation:
Answer:
A. (–4, –3)
Step-by-step explanation:
This is in case any one else had the answer on a different letter.
Pls pls help with this math
Answers
Answer:
7, -1
Step-by-step explanation:
x^2 - 6x + 7 = 0
(x - 7)(x + 1) = 0
==> x = 7, x = -1
Answer:
The answer would be 7,-1
x³-5x²+2x-10 devided by x²+2
Answers
Answer:
x-5
Step-by-step explanation:
a department store sells a pair of shoes with an 87% markup, if the store bought the pair of shoes for 55.25, what is the selling price to the nearest dollar?
Answers
Answer:
$103
so 87% of $55.25 is 48.0675
48.0675+55.25 is 103.3175
103.3175 rounded to the nearest dollar is 103.
Pleeeeeeease help me! However helps me first gets brainliest points!
Simplify the following algebraic expressions:
a. - 6x + 5 + 12x -6
b. 2(x - 9) + 6(-x + 2) + 4x
c. 3x2 + 12 + 9x - 20 + 6x2 - x
d. (x + 2)(x + 4) + (x + 5)(-x - 1)
e. (x+8)(x+9)+(x+1)(-x-6)
Answers
Answer:
A) 6x-1
B) -6
C) 9x2+8x-8
D) 3
E) 10x+66
Step-by-step explanation: