Answer:
The inclination of the through the points (5, 14) and (9, 18) is 45°
Step-by-step explanation:
The given point has coordinates (5, 14) and (9, 18)
To find the inclination, θ, of the line passing the two points, with point 1 having coordinates (x₁, y₁) and point 2, having coordinates (x₂, y₂), we have to look for the slope as follows;
The slope, m = Change in the y-coordinate ÷ Change in the x-coordinate
[tex]m = \dfrac{y_2 - y_1}{x_2-x_1}[/tex]
Where:
y₁ = The y-coordinate of point 1 = 14
x₁ = The x-coordinate of point 1 = 5
y₂ = The y-coordinate of point 2 = 18
x₂ = The x-coordinate of point 2 = 9
Substituting, we have;
[tex]m = \dfrac{18 - 14}{9-5} = \dfrac{4}{4} = 1[/tex]
The inclination of the line is the angle the line makes with x-axis
Since the slope gives the ratio of the opposite and adjacent segment to the angle of inclination, the arc-tangent of the slope will give the angle in degrees as follows;
[tex]tan^{-1}m = tan^{-1} \left (\dfrac{y_2 - y_1}{x_2-x_1} \right) = \theta[/tex]
given that m = 1, we have;
tan⁻¹(m) = θ = tan⁻¹(1) = 45°.
Please help...........
Answer:
315.1° (1 d.p.)
Step-by-step explanation:
Please see the attached picture for the full solution.
? Question
Type the correct answer in each box. Round your answers to one decimal place.
Use the function g(x) = 4(0.6)¥ to complete the table and find the y-intercept.
Answer:
-10=661.5
-1=6.7
0=4.0
1=2.4
2=1.4
8=0.1
(0,4)
Step-by-step explanation:
The y intercept is (0,4)
What is a Function?A function is a law that relates a dependent and an independent variable.
The function is g(x) = 4 (0.6)ˣ
The table shows the value of x
The value of g(x) at different value of x is
At x = -10
g(x) = 661.5
At x = -1
g(x) = 6.7
At x = 0
g(x) = 4
At x = 1
g(x) = 2.4
At x = 2
g(x) = 1.4
At x = 8
g(x) = 0.1
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PLEASE HELP I WILL MARK BRAINLIEST RIGHT AWAY!!!
Answer:
C
Step-by-step explanation:
The slope formula is y^2 - y^1 over x^2 - x^1
hope this helps!
also the answer is just the inverse of that answer
The sum of two numbers is 29. If the
larger number is 2 less than three times
the smaller number, what is the smaller
number.
Answer: 7
Step-by-step explanation:
The smaller number is 7.75.
What is an Equation?An equation is a mathematical statement formed when two expressions are equated using an equal sign.
The equations are useful in determination of unknown parameters.
The equations are of various types, such as Trigonometric equations, quadratic equations.
The system of equations are used to solve complex problems.
Let the smaller number is x.
The larger number is 2 less than three times the smaller number
Then the larger number is 3x -2
The sum of the two numbers is 29
The sum is the output of the mathematical operation, Addition.
The equation formed is :
3x -2 + x = 29
Grouping the variables and the constants
4x = 31
Dividing both side of the equation by 4
x = 7.75
The value of the smaller number is obtained.
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Which graph represents this function, f(x)=1/2x-5
Answer:
If I'm not mistaken your graph is supposed to be like this
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
If ∆ABC ≅ ∆DEF, which one of these is a pair of corresponding parts
Answer:
AB = DE
BC = EF
AC = DF
∠ABC = ∠ DEF
∠BAC = ∠EDF
∠BCA = ∠EFD
Step-by-step explanation:
As its congruent all the corresponding parts will be equal
Bella's back garden deck cost ₹5,391.47 per square metre to build. The deck is 11 metres wide and 12 metres long. How much did it cost to build the deck ...? brainliest as well as thanks also pleaase
Answer:
₹711,674.04
Step-by-step explanation:
1.firstly we need to solve for the total area of Bella's back garden deck.
2. Then we need to estimate mate the total cost of the garden given that a square metre cost ₹5,391.47 to build.
Given
length of garden = 12 metres
width of garden = 11 metres
Hence the area of the garden is given as
[tex]Area= length* width[/tex]
[tex]Area = 12*11= 132m^2[/tex]
if a square metre cost ₹5,391.47 to build.
132 square metre will cost= ₹5,391.47*132= ₹711,674.04
find x3 -y3,if x-y=5 and xy=14
Answer:
335
Step-by-step explanation:
Factor the given binomial:
x - y = 5
xy = 14
x = y + 5
(y + 5)y = 14
y^2 + 5y - 14 = 0
(y + 7)(y - 2) = 0
y = -7 or y = 2
y = -7
xy = 14
-7x = 14
x = -2
y = 2
2x = 14
x = 7
Solutions:
x = -2, y = -7
x = 7, y = 2
For x = -2, y = 7
x^3 - y^3 =
= (-2)^3 - (-7)^3
= -8 - (-343)
= 335
For x = 7, y = 2
x^3 - y^3 =
= 7^3 - 2^3
= 343 - 8
= 335
The table below shows the students in an Algebra 1 class. What is the probability that a randomly chosen student will be a girl GIVEN that the student does NOT own a graphing calculator? (Note: If your fraction will reduce, you need to reduce it.)
Answer:
6/13
Step-by-step explanation:
Of the 13 students who do not own a graphing calculator, 6 are girls. The probability is 6/13.
The area of a rectangular community garden is 200 square feet. The length of a rectangular garden is twice it’s width. Find the length and width of the garden.
PLEASE HELP!!!
Answer:
The length is 20 ft, and the width is 10 ft.
Step-by-step explanation:
area = length * width
Let the width = w
length = 2w
A = LW
A = 2w * w = 200
2w^2 = 200
w^2 = 100
w = 10
L = 2w = 20
The length is 20 ft, and the width is 10 ft.
the length of diagonal of a rectangular field is 23.7 m and one of its sides is 18.8 m. find the perimeter of the field.
Answer:
Approximately 66.4 Meters
Step-by-step explanation:
So we have a rectangle with a width of 18.8 meters and a diagonal with 23.7 meters. To find the perimeter, we need to find the length first. Since a rectangle has four right angles, we can use the Pythagorean Theorem, where the diagonal is the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
Plug in 18.8 for either a or b. Plug in the diagonal 23.7 for c.
[tex](18.8)^2+b^2=23.7^2\\b^2=23.7^2-18.8^2\\b=\sqrt{23.7^2-18.8^2} \\b\approx14.4 \text{ meters}[/tex]
Therefore, the length is 14.4 meters. Now, find the perimeter:
[tex]P=2l+2w\\P=2(14.4)+2(18.8)\\P=66.4\text{ meters}[/tex]
A doctor recommends a two-step process to treat a rare form of pancreatic cancer. The first method is successful 80% of the time. If the first method is successful, the second method is successful 90% of the time. If the first treatment is not a success, the second is 25% of the time. What is the probability that both treatments are unsuccessful?
Answer:
The answer is 15%.
Step-by-step explanation:
The probability that:
Both treatments are successful:80% x 90% = 72%
The first method is a success, but the second one is not:80% x (1 - 90%) = 8%
The first method is not successful, but the second one is:(1 - 80%) x 25% = 5%
Both treatments are unsuccessful:1 - (72% + 8% + 5%) = 15%
what is the value of 3cubed
Answer:
27
Step-by-step explanation:
3 cubed=3✖️3✖️3=27
Answer:
3³ = 3 × 3 × 3 = 9 × 3 = 27
Hope this helps you
Bella is going back to school shopping and her favorite store is having a sale. She sees there are 4 packages of 15 tops for $18 and 5 packages of 10 tops for $16 which is the better deal? How do you know
Answer:
The 4 packages of 15 tops for $18 is a better deal
Step-by-step explanation:
We can see which set of tops have the lowest unit price.
4 packages of 15 tops for $18:
4*15=60
There is a total of 60 tops for $18, which means each top costs 18/60 dollars, or $0.30.
5 packages of 10 tops for $16
5*10=50
There is a total of 50 tops for $16, which means that each top costs 16/50 dollars, or $0.32.
0.32>0.3
The 4 packages of 15 tops for $18 is a better deal :)
Have a great day
Use zero product property to solve.
F(x)=3x(2x-6)
Answer:
x=0 x=3
Step-by-step explanation:
F(x)=3x(2x-6)
Set equal to zero
0 =3x(2x-6)
Using the zero product property
3x =0 2x-6 =0
x =0 2x = 6
x = 6/2
x = 3
Answer:
x = 0 or x = 3
Step-by-step explanation:
Set the output to 0
0 = 3x(2x-6)
Set factors equal to 0.
3x = 0
x = 0
2x - 6 = 0
2x = 6
x = 3
Find the other endpoint of the line segment with the given endpoint
and midpoint
Endpoint 1: (9,1)
Midpoint: (1,6)
Endpoint 2= (
Step-by-step explanation:
Let the other endpoint be (x,y)
Since, (1,6) is the midpoint between (9,1) and (x,y)
Therefore,
1=(9+x)/2
=> 2=9+x
=> x= -7
and,
6=(1+y)/2
=>12= 1+y
=> y=11
So, the other endpoint is ( -7, 11)
Answer:
( - 7 , 11)Step-by-step explanation:
Let the coordinates of Endpoint 2 be
(x ,y)
The midpoint of the endpoints is given by
[tex](1,6) = ( \frac{9 + x}{2} , \frac{1 + y}{2} )[/tex]
Where x and y are coordinates of Endpoint 2
Comparing with the midpoint we have
[tex]1 = \frac{9 + x}{2} \\ 2 = 9 + x \\ \\ x = 2 - 9 \\ \\ x = - 7[/tex]
[tex]6 = \frac{1 + y}{2} \\ 12 = 1 + y \\ \\ y = 12 - 1 \\ \\ y = 11[/tex]
Therefore x = - 7 and y = 11
The coordinates of Endpoint 2 are
( - 7 , 11)Hope this helps you
Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).
Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
[tex]|u|=\sqrt{14^2+9^2}[/tex] which is [tex]\sqrt{277}[/tex]
[tex]|v|=\sqrt{3^2+6^2}[/tex] which is [tex]\sqrt{45}[/tex]
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
[tex]cos\theta=\frac{uv}{|u||v|}[/tex] where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
[tex]cos^{-1}\theta=\frac{96}{111.64676}[/tex] which returns an angle measure of 30.7. Plugging that all into the dot product formula:
[tex]u*v=\sqrt{277}*\sqrt{45}cos(30.7)[/tex] gives you a dot product of 96
(Tough day dividing polynomials and I'm still lost!) Please help me my hands are legit numb:)
Answer:
Option D. 9
Step-by-step explanation:
There are two ways to obtain the answer to the question.
Method 1:
Let 2x + 1 = 0
Making x the subject, we have
2x + 1 = 0
Collect like terms
2x = –1
Divide both side by 2
x = –1/2
Now, put the value of x into the expression 4x³ – 6x² – 8x + 7, we have:
4x³ – 6x² – 8x + 7
x = –1/2
4(–1/2)³ – 6(–1/2)² – 8(–1/2) + 7
4(–1/8) – 6(1/4) – 8(–1/2) + 7
–1/2 – 3/2 + 4 +7
– 4/2 + 4 + 7
– 2 + 4 + 7
= 9
Method 2:
Divide 4x³ – 6x² – 8x + 7 by 2x + 1
Please see attached photo for explanation.
4. You work for an advertising company and have been hired to place a blimp above a football stadium. The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line. a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line? b. How high above the ground is the blimp? c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet. Will the fans be able to read the advertisement? If not, what possible angle of elevation could we use? d. What is the exact angle if the blimp is at 150 feet?
Answer:
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
The height of the blimp above the ground is h = 153.884 yard
No, the fans will not be able to read the advertisement.
The exact angle if the blimp is at 150 feet is 45.74°
Step-by-step explanation:
From the summary of the information given :
The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line.
That statement above being illustrated in the attached diagram below for better understanding.
a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line?
The trigonometric ratio that can be used to calculate how high the blimp will be above the 50 yard line is :
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
b. How high above the ground is the blimp?
Using the above derived trigonometric ratio,
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
[tex]tan \ 72^0 = \dfrac{h}{50}[/tex]
[tex]h =tan \ 72^0 \times {50}[/tex]
[tex]h =3.07768 \times {50}[/tex]
h = 153.884 yard
The height of the blimp above the ground is h = 153.884 yard
c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet.
Will the fans be able to read the advertisement?
No, the fans will not be able to read the advertisement.
This is because, 153.884 yard to feet
= 153.884 × 3
= 461.652 feet which is more than the maximum given 150 feet.
If not, what possible angle of elevation could we use?
The possible angle of elevation can be determined by taking the tangent of the trigonometric ratio.
SO
tan θ = [tex]\dfrac{h}{150}[/tex]
tan θ = [tex]\dfrac{153.884}{150 \ feet}[/tex]
tan θ = 1.026
θ = tan ⁻¹ (1.026)
θ = 45.74°
d. What is the exact angle if the blimp is at 150 feet?
The exact angle if the blimp is at 150 feet is 45.74°
Write as an equation: Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara? (Let b = Barbara)
a+b+c=68
b-3=a
c-5=b
now just solve the system of equations, substitue so that there are only b's in the equation:
a+b+c=68
(b-3) + b + (b+5) = 68
3b=66
b=22
Therefore Barbara is 22
The required age of barbar is 22 years.
Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Alice, Barbara and Carol are a, b and c.
Age Alice is 3 years younger than Barbara,
a = b - 3 - - - -(1)
Age Barbara is 5 years younger than Carol
b = c - 5
c = b + 5 - - - -(2)
Together the sisters are 68 years old i.e.
a + b +c =68
From equation 1 and 2
b - 3 + b + b +5 = 68
3b + 2 = 68
3b = 66
b = 33
Thus, the required age of barbar is 22 years.
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what is the value of the digit 6 in the number 48.061?
Answer:
The hundredths place.
Step-by-step explanation:
48 is the whole number, and .061 is the decimals. As you probably know, this is the whole numbers place value.
ones, tens, hundreds, thousand, 10 thousand, 100 thousand, million...ect.
The decimal places are different
in this case the 0 is the tenths
the 6 is the hundredths
and the 1 is the thousandths.
Mostly, the decimal points are just with added ths to the end.
Hope this helped :D
As per the given number, the place value of 6 is that it is at hundredths place.
What is Place Value?Place value is the value assigned to each digit in a number. Depending on its location, each digit in such a number has a unique value. Because a digit's value relies on where it appears in an integer, it is possible for an amount to have two equivalent digits with different values.
The decimal equivalent of 48 is .061. The entire number is 48. This is the entire integer's place value, as you are surely aware.
The decimal places are different
In the given question, the 0 is at tenths place ,6 is the hundredths place and 1 is the thousandths place.
The decimal points are typically only inserted at the end.
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Helppppppppp I need answer❤️❤️❤️
Answer:
c. (3x^2-1)(x-7)
Step-by-step explanation:
=(3x^3-21x^2)+(-x+7)
=-(x-7)+3x^2(x-7)
=(3x^2-1)(x-7)
-4______1 what symbol makes this sentence true
Answer:
<
Step-by-step explanation:
Kini and Duke are each working during the summer to earn money in addition to their weekly allowance, and they are saving all of their money. Kini earns $9 an hour at her job, and her allowance is $8 per week. Duke earns $7.50 an hour, and his allowance is $17 per week. How many hours do Kini and Duke need to work in order to save the same amount of money in one week?
Answer:
Step-by-step explanation:
9x + 8 = 7.5x + 17
1.5x = 9
x = 6 hours
The world's tallest building is the Burj Khalifa in Dubai at 828 m tall. The CN Tower in Toronto is 553 m tall. Ryan wants to compare the Burj Khalifa and the CN Tower by creating rectangular prism models on a 10 cm by 10 cm square base. He has decided to represent the Burj Khalifa with a rectangular prism that has a height of 40 cm. What is the volume of each rectangular prism? Round your answer to the nearest cubic centimetre. Show your work for full marks.
Answer:
Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]
Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]
Step-by-step explanation:
Given
Height of Burj Khalifa = 828 m
Height of CN Tower in Toronto = 553 m
Base of rectangular prism is a square with sides 10 cm [tex]\times[/tex] 10 cm.
Height of Burj Khalifa prism = 40 cm
828 m is represented as 40 cm
[tex]\Rightarrow 553 m[/tex] is represented as [tex]\frac{40}{828 } \times 553 = 26.71\ cm[/tex]
So, height of rectangular prism of CN Tower = 26.71 cm
Volume of a Prism is given by the Formula:
[tex]V=Area\ of\ Base \times Height[/tex]
Base is a square, so Area of base = [tex]Side^2[/tex]
Volume of Burj Khalifa Prism:
[tex]V_B=10^2 \times 40 = 4000\ cm^2[/tex]
Volume of CN Tower Prism:
[tex]V_C=10^2 \times 26.71 = 2671\ cm^2[/tex]
So, the answer is:
Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]
Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]
pleaseer❤️❤️ help me
Answer:
1)D 2)C 3)A 4)B 5) A
Step-by-step explanation:
1) The area rectangle is 36x^2 -1
We know ,
A= l*b
=36x^2 -1
=(6x)^2 -1
=(6x+1) (6x-2)
This the value of l,b respectively.
So, Perimeter of rectangle is 2(l+b)
P=2(6x+1) + 2(6x-1)
=24x
2)The area of square is 4(x+5)^2
We know,
A=l^2
=4(x+5)^2
=4(x^2 + 10x + 25)
=(2x+10)^2
This is the value of l=2x+10.
So, Perimeter of square is 4l
P=4(2x+10)
=8x+40
3)The fully factorized form is
= -2x^2 + 10x +12
= -2x^2 + 12x -2x +12
= -2x(x-6) -2(x-6)
= -2(x-6) (x+1)
4)The fully factorized form is
=x^4 -81
=(x^2)^2 -9^2
=(x^2 + 9) (x^2 - 9)
=(x^2 + 9) (x^2 - 3^2)
=(x^2 + 9) (x + 3) (x - 3)
5)The fully factorized form is
= 5x^4 - 320
= 5(x^4 - 64)
= 5((x^2)^2 - 8^2)
= 5(x^2 + 8) (x^2-8)
A square has side length x and a triangle has a base (3x - 2) and height (2x + 4). At what value of x will the two figures have the same area?
Show work and explain all steps.
Answer:
0.73
Step-by-step explanation:
Data obtained from the question include the following:
Length (L) of square = x
Base (b) of triangle = (3x – 2)
Height (h) of triangle = (2x + 4)
Area of square = L²
Area of square = x²
Area of triangle = ½bh
Area of triangle = ½(3x – 2) (2x + 4)
Expand
½ [3x(2x + 4) –2(2x + 4)]
½[6x² + 12x – 4x – 8]
½[6x² + 8x – 8]
3x² + 4x – 4
Area of triangle = 3x² + 4x – 4
Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:
Area of triangle = area of square
Area of triangle = 3x² + 4x – 4
Area of square = x²
Area of triangle = area of square
3x² + 4x – 4 = x²
Rearrange
3x² – x² + 4x – 4 = 0
2x² + 4x – 4 = 0
Solving by formula method
a = 2, b = 4, c = –4
x = – b ± √(b² – 4ac) / 2a
x = – 4 ± √(4² – 4×2×–4) / 2×2
x = – 4 ± √(16 + 32) / 4
x = – 4 ± √(48) / 4
x = (– 4 ± 6.93)4
x = (– 4 + 6.93)4 or (– 4 – 6.93)4
x = 0.73 or –2.73
Since the measurement can not be negative, the value of x is 0.73.
Identify the expression equivalent to 4(x+ x + 7) - 2x+8 - 4 by substituting x = 1 and x = 2.
O A.
6x + 11
OB.
3(x + 7)
OC. 2(3x + 16)
OD.
3x + 16
Answer:
C. 2(3x + 16)
Step-by-step explanation:
If we replace x by 1 in the expression, we get:
4(1+ 1 + 7) - 2(1) + 8 - 4 = 4(9) - 2 + 8 - 4 = 38
If we replace x by 2 in the expression, we get:
4(2+ 2 + 7) - 2(2) + 8 - 4 = 4(11) - 4 + 8 - 4 = 44
Then, if we replace x=1 and x=2 on expression A, we get:
6x+11 = 6(1) + 11 = 17
6x + 11 = 6(2) + 11 =23
if we replace x=1 and x=2 on expression B, we get:
3(x + 7) = 3(1 + 7) = 24
3(x + 7) = 3(2 + 7) = 27
if we replace x=1 and x=2 on expression C, we get:
2(3x + 16) = 2(3(1) + 16) = 38
2(3x + 16) = 2(3(2) + 16) = 44
if we replace x=1 and x=2 on expression D, we get:
3x + 16 = 3(1) + 16 = 19
3x + 16 = 3(2) + 16 = 22
Finally, the answer is C, because we get the same answers as in the initial equation
The total volume of a tree increases 6% each year. What will its volume be after 7 years if its volume is 5 cubic meters now? A. 5(0.06)7 B. 5(7)(0.06) C. 5(1.06)7 D. 5(7)(1.06)
Complete Question:
The total volume of a tree increases 6% each year. What will its volume be after 7 years if its volume is 5 cubic meters now? A. 5(0.06)^7 B. 5(7)(0.06) C. 5(1.06)^7 D. 5(7)(1.06)
Answer:
C. 5(1.06)^7
Step-by-step explanation:
The volume of a tree increases by 7% every year
The formula we would be using is
V(t) = Vo (1 + r)t
Where V(t) = Volume after t years
Vo = Present of initial volume
r = rate of increase
t = time
From the question,
V(t) = Volume after t years = unknown
Vo = Present of initial volume = 5m³
r = rate of increase = 6% = 0.06
t = time = 7 in years
V(t) = 5 × ( 1 + 0.06)^ 7
V(t) =(5)(1.06)^7
Therefore, its volume be after 7 years if its volume is 5 cubic meters now is
Option C: (5)(1.06)^7
The graph of h(x) is a translation of f (x) = RootIndex 3 StartRoot x EndRoot. On a coordinate plane, a cube root function goes through (negative 3, negative 1), has an inflection point at (negative 2, 0), and goes through (negative 1, 1). Which equation represents h(x)?
Answer:
The correct option is;
[tex]h(x) = \sqrt[3]{x + 2}[/tex]
Step-by-step explanation:
Given that h(x) is a translation of f(x) = ∛x
From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;
When x = -1, h(x) = 1
When x = -3, h(x) = -1
h''(x) = (-2, 0)
Which gives
d²(∛(x + a))/dx²= [tex]-\left ( \dfrac{2}{9} \cdot \left (x + a \right )^{\dfrac{-5}{3}}\right )[/tex], have coordinates (-2, 0)
When h(x) = 0, x = -2 which gives;
[tex]-\left ( \dfrac{2}{9} \cdot \left (-2 + a \right )^{\dfrac{-5}{3}}\right ) = 0[/tex]
Therefore, a = (0/(-2/9))^(-3/5) + 2
a = 2
The translation is h(x) = [tex]\sqrt[3]{x + 2}[/tex]
We check, that when, x = -1, y = 1 which gives;
h(x) = [tex]\sqrt[3]{-1 + 2} = \sqrt[3]{1} = 1[/tex] which satisfies the condition that h(x) passes through the point (-1, 1)
For the point (-3, -1), we have;
h(x) = [tex]\sqrt[3]{-3 + 2} = \sqrt[3]{-1} = -1[/tex]
Therefore, the equation, h(x) = [tex]\sqrt[3]{x + 2}[/tex] passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).
Answer: B
Step-by-step explanation: