The equation y = 2(kx - 1)^5 represents a curve. To find the equation of the curve, we need to determine the value of the constant k. To do this, we can use the two points given, (0,1) and (1,8), to find two equations and solve for k.
First, we'll substitute the x-coordinate and y-coordinate of the first point, (0,1), into the equation:
1 = 2(k * 0 - 1)^5
Expanding the right-hand side:
1 = 2(-1)^5
1 = -32
This equation is clearly false, so the point (0,1) does not lie on the curve represented by y = 2(kx - 1)^5.
Next, we'll substitute the x-coordinate and y-coordinate of the second point, (1,8), into the equation:
8 = 2(k * 1 - 1)^5
Expanding the right-hand side:
8 = 2(k - 1)^5
Dividing both sides by 2:
4 = (k - 1)^5
Taking the fifth root of both sides:
2 = k - 1
Adding 1 to both sides:
3 = k
Now that we have the value of k, we can write the equation of the curve:
y = 2(kx - 1)^5
= 2(3x - 1)^5
This is the equation of the curve that passes through the points (0,1) and (1,8).
It's important to note that the original equation y = 2(kx - 1)^5 is only one of an infinite number of curves that can pass through the points (0,1) and (1,8). The process of finding the equation of a curve that passes through specific points is known as curve fitting. The specific equation found in this case is just one possible representation of the curve that passes through the given points.
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7.4 big ideas question
Consider the series.
1000+200+40+8+8/5
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The Given Series 1000+200+40+8+8/5 is Convergent.
What is Convergent and divergent Series?If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on increasing or dropping as the terms of the series tend to infinity, it is said to be divergent.
Given:
The series is given as 1000+200+40+8+8/5
The common ratio is
200/1000
= 1/5
Then,40/200
= 1/5
= 0.2
Now, As the common ratio is < 1 so the series is convergent.
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Gary takes a suitcase and backpack on an airplane. The suitcase weighs 4 times as much as the backpack. The suitcase and the backpack together weigh 40 lb. HURRY!!! PLS :( Thank You, too!
I can't remember what to do
The solution of the inequalities is (0.67, 3.33)
How to make the solution of the inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y >= 2
x + y <= 4
y <= 2x + 2
Next, we plot the graph of the inequalities
Using the above as a guide, we have the following:
The solution is (0.67, 3.33)
This is so because the lines intersect at (0.67, 3.33) for y >= 2
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For a moving object, the force on the object varies directly with the objects acceleration. When a force of 30 N acts on a certain object, the acceleration of the object is 10 m/s^2. If the force is changed to 9 N, what will be the acceleration of the object?
Answer: The force on an object is directly proportional to its acceleration, which means that if the force is increased, the acceleration will also increase, and if the force is decreased, the acceleration will decrease. This can be expressed mathematically as:
F = k * a
where F is the force, a is the acceleration, and k is a constant of proportionality.
We can use the given information to find the value of k:
30 N = k * 10 m/s^2
k = 3 N*s^2/m
Now we can use this value of k to find the acceleration when the force is 9 N:
9 N = 3 Ns^2/m * a
a = 3 Ns^2/m / 9 N
a = 1/3 m/s^2
Therefore, the acceleration of the object when the force is 9 N is 1/3 m/s^2.
whats the expression (2x+3)(2x-4)
Answer:
[tex] {4x}^{2} - 2x - 12[/tex]
Step-by-step explanation:
To complete this problem, use FOIL. First, Outer, Inner, Last.
(2x + 3)(2x - 4)
First, multiply 2x by 2x.
[tex] {4x}^{2} [/tex]
Now, multiply the outer numbers, 2x and -4.
[tex] - 8x[/tex]
Third, multiply the inner numbers, 3 and 2x.
[tex]6x[/tex]
Lastly, multiply the last numbers, 3 and -4.
[tex] - 12[/tex]
Now, put it all together.
[tex] {4x}^{2} - 8x + 6x - 12[/tex]
The final step is to combine like, or similar terms.
The only ones that can be combined are -8x and 6x.
[tex] {4x}^{2} - 2x - 12[/tex]
WILL GIVE BRAINILEST
Step-by-step explanation:
5 × -8a = -40a
5 × -9 = -45
-40a - 45 = 5(-8a - 9)
5 × -8a = -40a
5 × -9 = -45
-40a - 45 = 5(-8a - 9)
Help me. Pls. Cuz. Am. Gonn. Die if I didn't solve this!!
Answer:
See the picture
Step-by-step explanation:
The 1 tells us where to start. This is our y-intercept. We start when x =0 and y =1. The y intercept is 1 (0,1). You see it in green.
From that point (0,1) you go up 1 and 2 to the right. This is the slope. You see it in pink.
Once you have the begin part in pink. You join it to the pink points and draw your line.
Chelsea is making a quilt and she has determined she needs 1472 square inches of burgundy fabric and 399 square inches of yellow. How many square yards of each material will she need? Round your answers up to the nearest quarter yard.
The burgundy fabric:
Incorrect square yards
The yellow fabric:
How many total yards of fabric will she have to buy?
square yards
The burgundy fabric:1.135 square yards
The yellow fabric: 0.307 square yards
The total yards of fabric will she have to buy 1.442 square yards.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement.
For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
Chelsea needs 1472 square inches of burgundy fabric and 399 square inches of yellow.
As, 1 yards= 36 inches
and, 1 square yards= 1296 inches
Then, 1472 square inches of burgundy fabric
= 1472/ 1296
= 1.135 square yards
and, 399 square inches of yellow.
= 399/ 1296
= 0.307 square yards
Thus, the total yards of fabric will she have to buy
= 1.135 + 0.307
= 1.442 square yards
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Hi, its me again. Find angle AOB
Answer:
AOC=360-130 = 230
ABC= 230/2=115
Answer:
∠ABC = 115∘
Step-by-step explanation:
∠ABC = 1/2 ∠AOC
(Angle subtended by a chord on major area is half of that subtended on center)
∴ ∠ABC = 1/2 x 130 = 65
ABCD is a cyclic quadrilateral
Sum of opposite angles = 180∘
∴ ∠ABC + ∠AOC = 180∘
∠ABC + 65 = 180∘
∠ABC = 115∘
find missing side lengths, leave your answers as radicals in simplest form
HELPP W THESE PROBLEMS
Answer:
u have to put lenght ×weight =volume
A wall is separated into two sections, A and B. The function A(x) = 4x − 1 represents the length of section A. The function B(x) = 8x − 3 represents the length of section B. What is the total length of the wall in terms of x?
1. (A + B)(x) = 12x2 − 20x − 4
2. (A + B)(x) = 32x2 − 20x + 3
3. (A + B)(x) = 32x + 4
4. (A + B)(x) = 12x − 4
Answer: 4 is correct
Step-by-step explanation:
A(x) + B(x) = (4x - 1) + (8x - 3)
= 12x - 4
someone ate 3 out of 5 bagels in the bag what percent of the bagels r left
Answer:
40%
Step-by-step explanation:
If someone ate 3 out of 5 bagels, then there are 5 - 3 = 2 bagels left.
To find the percentage of the bagels that are left, you need to divide the number of bagels left by the total number of bagels and multiply by 100.
So, the percentage of the bagels that are left is (2 / 5) * 100 = 40%.
Find the circumference of a circle with the diameter of 3 yd
Answer:
Step-by-step explanation:
Circumference = 2piR or piD
pi(3) = 9.42
Here are the ingredients needed to make 16 chocolate biscuits.
-chocolate biscuits
makes 16 chocolate biscuits
100g of butter
50g of caster suger
120g of flour
15g of cocoa
sabrina wants to make chocolate biscuits for 24 people
how much of each ingredients will she need?
Compare the volume and surface area of a sphere with a radius of 5 in. with that of a cube that has sides measuring 8.06 in.
1: The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.
2: The volume of the sphere is approximately equal to the volume of the cube, but the cube has a greater surface area.
3:The volume of the cube is greater than the volume of the sphere, but the sphere has a greater surface area.
4:The sphere and the cube have approximately the same volume and surface area.
The correct statement is : The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.
What are the surface area and volume of a sphere?Surface Area of a Sphere. A = 4 π r². The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle.
Given here: A sphere with 5 in. radius and a cube with side measuring 8.06 in.
Volume of the sphere is
V=4/3πr³
=4/3·π·5³≈523.59878 in³
Surface area of the sphere is
A=4πr²
=4·π·5²≈314.15927 in²
Now volume of the cube
a³=8.06³
≈523.60662 in³
Surface area of the cube
A=6a²
=6×8.06²
≈389.7816 in²
Thus The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.
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200 students chose one language to study.
Each student chose one language from French or Spanish or German.
Of the 200 students,
90 are boys and the rest of the students are girls
70 chose Spanish
60 of the 104 students who chose French are boys
18 girls chose German.
Work out how many boys chose Spanish.
The number of boys chosen Spanish are 59.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
let Girls are G, Boys are B, Spanish choose S, French chosen F and German Chosen Ge.
Total = 200
Girls = 200 - 90 = 110
P(S) = 70 (B+ G)
P(F) = 60 (B)
P(B) + P(G) = 70
S + F = 92
So, 70- G + 44 - G = 92
114 - 2G = 92
-2G = -22
G = 11
So, number of Boys choose Spanish
= 70- 11
= 59
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find the value of x , please show how you did it
The value of x in the figure is 15 degrees
How to find the value of xThe value of x in the figure is solved using the concept of sum of exterior angles in a polygon
The sum of exterior angles in a polygon is 360
7x + 83 + 33 + 6x + 49 = 360
collecting like terms
7x + 6x = 360 - 83 - 33 - 49
13x = 195
isolating x
x = 15 degrees
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Jake is traveling 12 mph in his boat. After 3 hours. How far will he have traveled?.
Suppose a is nn and the equation ax0 has only the trivial solution. Explain why a has n pivot columns and a is row equivalent to
The equation Ax = 0 has no free variables, so A has n pivot columns. Since A is square, the pivots must be on the main diagonal, so A is row equivalent to the n x n identity matrix Iₙ.
In order for the equation Ax = 0 to have only the trivial solution, there must be no free variables. This means that the matrix A must have n pivot columns. Since A is square, the n pivot positions must be in different rows, which means that the pivots must be on the main diagonal. This means that A is row equivalent to the n x n identity matrix Iₙ. To make it row equivalent, we can perform elementary row operations, such as adding or subtracting rows, or multiplying or dividing a row by a non-zero constant. Once we have done this, the matrix will be in echelon form and the main diagonal will be composed of all 1s. This means that A is row equivalent to Iₙ.
The complete question: Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to Iₙ
Choose the correct answer below.
A. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix, Iₙ.
B. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nˣn identity matrix, Iₙ.
C. Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix, Iₙ
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T
50 cm
√ 8 S
120 cm
100%
100% 21%
150 cm
100%
21%
21%
Calculate #2
x Each new rectangle is 21% longer than the original.
Complete the table with the length of each new
rectangle.
Original Rectangle Length
(cm)
120
50
150
Length After 21% Increase
(cm)
Original Rectangle Length (cm) | Length After 21% Increase (cm)
120 | 144
50 | 61
150 | 180
How did we get these values?Each new rectangle is 21% longer than the original, so to calculate the length after a 21% increase, we need to multiply the original length by 1 + 21%.
For the first rectangle (120 cm):
1.21 * 120 cm = 144.4 cm (rounded to 144 cm)
For the second rectangle (50 cm):
1.21 * 50 cm = 60.5 cm (rounded to 61 cm)
For the third rectangle (150 cm):
1.21 * 150 cm = 180.15 cm (rounded to 180 cm)
So the table with the length of each new rectangle would be:
Original Rectangle Length (cm) | Length After 21% Increase (cm)
120 | 144
50 | 61
150 | 180
The rounded values were used in this table.
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Identify the graph of the system of linear inequalities.
x+y<1
5x + y > 4
The graph of the system has been attached below. The solution has been obtained by using linear inequality.
What is linear inequality?
If the equals relation were used in its place, a linear inequality would produce a linear equation.
We are given two inequalities as x+y < 1 and 5x + y > 4
For plotting the points, we need to find x and y
1. x+y < 1
So, let y be 0, then
⇒x < 1
This gives us the point as (1,0).
Now, let x=0, then
⇒y < 1
This gives us the point as (0,1).
From these two points, the graph for the inequality is drawn and represented by red line.
2. 5x + y > 4
So, let y be -1, then
⇒5x > 5
⇒x > 1
This gives us the point as (1,-1).
Now, let x=0, then
⇒y > 4
This gives us the point as (0,4).
From these two points, the graph for the inequality is drawn and represented by green line.
Hence, the graph of the system of linear inequalities is obtained.
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PLS ASAP!! WILL GIVE BRAINLEST
The sides and angle of the right triangle are as follows:
b = 57.2 unitsc = 57.4 unitsB = 85 degreesHow to find the side and angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of the triangle can be found using trigonometric ratios as follows:
Hence,
tan 5 = opposite / adjacent
tan 5 = 5 / b
b = 5 / tan 5
b = 57.1506949525
Hence,
b = 57.2 units
sin 5 = opposite / hypotenuse
sin 5 = 5 / c
c = 5 / sin 5
c = 57.3685943662
c = 57.4 units
B = 180 - 90 - 5
B = 85 degrees
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determine the equation of the line that passes through the point (-9, -30) and is parallel to the line y=4x+1
Answer: This is the answer
Step-by-step explanation:
Use synthetic division and the remainder Theorem to find the indicated function value.
f(x) = 5x³-13x² + 4x-2: f(2)
To find f(2) using synthetic division, we set up the synthetic division table with the coefficients of the polynomial:
What is synthetic division?Synthetic division is a shorthand method of dividing a polynomial by a linear factor of the form (x - a), where a is a constant. The method is used to simplify the long division process and is particularly useful for finding the roots of a polynomial.The basic idea behind synthetic division is to use the coefficients of the polynomial and the constant a to create a condensed division table that eliminates the need for writing out all the intermediate steps of the division process.2 │ 5 -13 4 -2
│ 10 -6 -2
└───────────
5 -3 -2 0
The last entry in the bottom row of the table gives the remainder of the division, which is f(2). Therefore, we have:
f(2) = 5(2)³ - 13(2)² + 4(2) - 2 = 40 - 52 + 8 - 2 = -6
So, the value of the function f(x) = 5x³-13x² + 4x-2 at x = 2 is f(2) = -6.
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Lauren has a coin collection. She keeps 3 of the coins in her box, which is 4% of the collection. How many total coins are in her collection?
The total coins in Lauren's coin collection = 75
Let us assume that there are 'n' total coins in Lauren's coin collection.
She keeps 3 of the coins in her box, which is 4% of the collection.
This means that 4 percent of 'n' is equal to 3.
Using the percentage formula,
4 % of m = 3
m × (4/100) = 3
We solve above equation for m.
⇒ m × 4 = 3 × 100 ..........(multiply both the sides by 100)
⇒ m × 4 = 300
⇒ m = 300/4 ..........(divide both the sides by 4)
⇒ m = 75
Therefore, she has 75 coins in her collection.
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in each part, determine the fundamental group up to isomorphism by showing it is homotopy equivalent to a space whose fundamental group is already known. which of the spaces are contractible?
If a map f:X→Y between connected CW complexes induces isomorphisms f∗:πn(X)→πn(Y) for all n, then f is a homotopy equivalence. In case f
is the inclusion of a subcomplex X↪Y , the conclusion is stronger: X is a deformation retract of Y.
A fairly generic notion called isomorphism can be found in many branches of mathematics. The word is derived from the Greek words morphosis, which means "to form" or "to shape," and iso, which means "equal." An isomorphism is a bijective morphism in formal terms. An isomorphism, as used informally, is a map that maintains sets and relationships between elements.
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Overview
b)
Question Progress
a)
2
4
ܠ
5
6
7
Solve the equation.
8
10
Homework Progress
I think of a number, multiply it by three, and add four. I get twenty two
20/23 Marks
Using the statement above, form an equation.
Use the letter 'x' for the unknown number.
+
Answer:
Step-by-step explanation:
a) Just work backwards!
Instead of adding 4, subtract by 4
Instead of multiplying by 3, divide by 3
22 - 4 / 3 = x
b)
22 - 4 = 18
18 / 3 = 6
Therefore, x = 6
help me on this question please
Answer:
62
Step-by-step explanation:
you have to work out the surface area of a cuboid by:
3×2=6
5×3=15
5×2=10
sum of all the areas is 31
then times it by 2 which is 62
you don t really have to pay attention to the net, apart from the 2cm because you don t want to use it twice in the calculation.
Put the equation in
slope-intercept form.
y - 4x = 17
y = 4x + [?]
Enter
Answer: To put the equation y - 4x = 17 in slope-intercept form, we need to isolate the y variable on one side of the equation and have the coefficient of x be the slope of the line and the constant term be the y-intercept.
Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.
Starting with the equation y - 4x = 17, we can isolate y by adding 4x to both sides:
y - 4x + 4x = 17 + 4x
y = 4x + 17
So, the equation in slope-intercept form is y = 4x + 17, where the slope (m) is 4 and the y-intercept (b) is 17.
Step-by-step explanation:
y-4x = 17
slope intercept= y= 4x + 17