Answers
The answer of the given question based on linear equations what is the y intercept of the line b =4.
What is y-intercept?In linear equation of form y = mx + b, where m is slope and b is y-intercept, the y-intercept is point at which line intersects the y-axis. It is value of y when x is equal to a zero.
To find the y-intercept of the line, we need to identify the point at which the line intersects with the y-axis. This is the point where x=0.
From the given graph, we can see that when x=0, the point on the line is (0, 4). Therefore, the y-intercept (b) of the line is 4.
So, the answer is:
b = 4
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Answer:
b=2
Step-by-step explanation:
its 2 not 4 the dot is located on 2 in between the first and second quadrant.
Related Questions
Find the Rate. (Round to the Nearest Tenth)
Principal = $900
Time = 1 year
Interest = $76.50
Answers
Answer:
$ 1,937.50.
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
Write equation to represent the new function Vertically stretched by a factor of 4, then translated 3 units right.
Answers
Answer:
Suppose the original function is denoted by f(x). To represent the new function that is vertically stretched by a factor of 4 and then translated 3 units to the right, we can use the following equation:
g(x) = 4 f(x - 3)
In this equation, f(x - 3) represents the original function f(x) translated 3 units to the right, and the multiplication by 4 stretches the function vertically by a factor of 4. Therefore, g(x) represents the new function that is vertically stretched by a factor of 4 and then translated 3 units to the right.
Step-by-step explanation:
The histogram represents data collected on the frequency of how far the tide rose, in feet, up the beach from the buoy.
A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 2, above 6 to 10 that stops at 6, above 11 to 15 that stops at 2, above 16 to 20 that stops at 5, and above 21 to 25 that stops at 1.
Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 21. This means that the tide frequently measured around 11 to 15 feet.
The data is skewed, with a maximum range of 24. This means that the tide was frequently very high in the 21 to 25 feet range.
The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.
The data is symmetric, with a maximum range of 20. This means that the tide frequently measured around 1 to 5 feet.
Answers
The correct statement regarding the histogram is given as follows:
The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
Hence the number of observations of each interval is:
1 to 5: 2 observations.6 to 10: 5 observations.11 to 15: 2 observations.16 to 20: 6 observations.21 to 25: 1 observations.Here are two similarly high bins, hence the distribution can be said to be bimodal, with maximum range given as follows:
25 - 5 = 21 - 1 = 20.
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Answer: its d
Step-by-step explanation:
Rocio is planning her holiday baking. She has three recipes that use butter and needs to make sure she buys enough at the store. One recipe calls for 2½ cups, one needs cup, and one needs 1 cup. Find the total amount of butter she needs. Simplify your answer and write it as a mixed number if necessary. 4½ cups 2½ cups 53/12cups 3/4/9cups
Answers
Rocio needs a total of 137/12 cups of butter for her holiday baking.
How to find the total amount of butter she needs.Rocio needs 4½ cups, 2½ cups, and 5⅓ cups of butter for her three recipes, respectively.
We can add these amounts of butter to find the total amount:
4½ cups + 2½ cups + 5⅓ cups
= 9/2 cups + 5/2 cups + 53/12 cups (converting mixed numbers to fractions)
= 54/12 cups + 30/12 cups + 53/12 cups (finding a common denominator)
= 137/12 cups
Therefore, Rocio needs a total of 137/12 cups of butter for her holiday baking.
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Can someone help me on this?
Answers
Answer:
X+15 is the answer..................
Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum of the given function for this region.
Answers
Using inequalities, Y(x=0) = -2 and X(y=0) = -2 in region 1.
To pick area 1, draw a line at the intersection of (-2,0) and (0, -2), then choose the right side. such as.
Region 2) To pick the region to the left or upwards in region 2, we must draw a line from (0,2) to (-2,4).
Y(x=0) = 2\sX(y=-2) = -4
Region 3) To pick the region to the right, we must draw a line connecting (-4,0) and (0,4), as I'll demonstrate.
What are inequalities?Inequalities in mathematics describe the relationship between two non-equal numbers. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, several inequalities are utilised to compare the numbers, whether it is less than or higher than.
The feasible area is now visible. Let's determine the vertices' coordinates.
Where the blue and green lines intersect is our first vertex.
3x + 2 = x + 4 and y = 3x + 2
3x - x = 4 - 2
y = 3× (1) + 2 = 3 + 2 = 5 when 2x = 2x = 1
(X, Y) = Vertex 1 (1,5)
The intersection of the red and green lines is at vertex #2:
y = -x -2; y = x + 4; y = x + 4 = -x - 2; and y = x + x = -2 - 4
2x = -6, x = -6/2, and y = (-3) + 4 = -3 + 4 = 1 are the results.
(X, Y) = Vertex 2 (-3,1)
The intersection of the red and blue lines is at vertex 3:
y = -x - 2, y = 3x + 2 -x - 2, and y = 2 + 2 -4 x = 4 x = -4 / 4 = -1;
So, y = 3×(-1) + 2 = -3 + 2 = -1
(X, Y) = Vertex 3 (-1, -1)
Let's now modify the graph by including the supplied equation.
The intercept where Y=0 is 0 is given by f(x,y) = -3x + 5y = 0 5y = 3x + 0 y = 3/5 × X + 0
the gradient m = 3/5
A line can be drawn from (0,0) to (-10, -6)
Let's now examine how it would appear in the area where it is practical.
We can see that the function intercepts the blue line or the line of the second section, which is where the largest value is located.
y = 3x + 2 3x + 2 (3/5 - 3) x = 2 -12/5 × x = 2 x = -5/6.
Hence, y = 3x + 2 3/5 × (-5/6) = -1/2.
The maximum is therefore found at (x,y) = (-5/6, -1/2).
The point where the function crosses the red line now marks the minimum.
y = 3/5 × x; y = -x -2
3/5 x = -x - 2\s (3/5 + 1) × x = -2\s8/5 x = - 2\sx = -2× (5/8) = -5/4.
y = 3/5 × (-5/4) = -3/4
The minimum is thus found at (x,y) = (-5/4, -3/4)
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The scale factor of two similar cylinders is 5:2.
The volume of the smaller cylinder is 28 m3.
What is the volume of the larger cylinder?
Question 8 options:
700 m3
350 m3
70 m3
437.5 m3
175 m3
Answers
Using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.
What is the scale factor?When a shape is magnified and each side is multiplied by the same number, this is known as a scale factor.
The scaling factor is this figure. Scale factors are used on maps to accurately depict distances between locations.
With a scale factor of 2, the new shape that results from scaling the old shape is twice as large.
So, get the volume of the larger cylinder as follows:
x/5 = 28/2
2x = 28*5
2x = 140
x = 70m³
Therefore, using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.
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Complete question:
The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?
Question 8 options:
A. 700 m3
B. 350 m3
C. 70 m3
D, 437.5 m3
E. 175 m3
Write the missing digits
Answers
Answer:
A
Step-by-step explanation:
step by step you will learn
Michael plants a circular garden with a diameter of 10 feet. What is the area of his garden
Answers
Answer:
The area of the garden is 78.5 square feet.
Step-by-step explanation:
need help with This Math
Answers
The perimeter of triangle QST is 32.
option D.
What is the perimeter of triangle QST?The perimeter of triangle QST is calculated by determining the value of x as shown below.
If length SQ = length ST, then angle STQ must be equal to angle SQT, so we will have the following equation.
Cos T = ( 3x - 1 ) / ( 5x + 1 )
Cos Q = ( 2x + 1 ) / (5x + 1 )
Cost T = Cos Q
( 3x - 1 ) / ( 5x + 1 ) = ( 2x +1 ) / ( 5x + 1 )
3x - 1 = 2x + 1
x = 2
The perimeter of triangle QST is calculated as;
= 5x + 1 + (3x -1 + 2x + 1 ) + 5x + 1
= 15x + 2
= 15 (2) + 2
= 32
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Following are the transactions in the books of a Khaptad Ltd: Issues 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 100. Issued 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 90 Issued 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 110 Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 100. Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 90 Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 110. Issued 4000, 12% debentures of Rs.100 each at Rs 90 and redeemable at Rs 100. Issued 4000, 12% debentures of Rs.100 each at Rs 90 redeemable at Rs 105. Issued 4000, 12% debentures of Rs.100 each at Rs 90 and redeemable Rs 95 Required: Journal entries: a. for the issue of debentures b. for the redemption of debentures
Answers
a. Journal entries for the issue of debentures:
Issues 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 100.
Debit: Cash/Bank Account (4000 x 100) = 400,000
Credit: Debentures Account (4000 x 100) = 400,000
Issued 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 90.
Debit: Cash/Bank Account (4000 x 100) = 400,000
Credit: Debentures Account (4000 x 90) = 360,000
Credit: Discount on Issue of Debentures Account (4000 x 10) = 40,000
Issued 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 110.
Debit: Cash/Bank Account (4000 x 100) = 400,000
Credit: Debentures Account (4000 x 110) = 440,000
Credit: Premium on Issue of Debentures Account (4000 x 10) = 40,000
Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 100.
Debit: Cash/Bank Account (4000 x 110) = 440,000
Credit: Debentures Account (4000 x 100) = 400,000
Credit: Loss on Issue of Debentures Account (4000 x 10) = 40,000
Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 90.
Debit: Cash/Bank Account (4000 x 110) = 440,000
Credit: Debentures Account (4000 x 90) = 360,000
Credit: Discount on Issue of Debentures Account (4000 x 20) = 80,000
Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 110.
Debit: Cash/Bank Account (4000 x 110) = 440,000
Credit: Debentures Account (4000 x 110) = 440,000
Issued 4000, 12% debentures of Rs.100 each at Rs 90 and redeemable at Rs 100.
Debit: Cash/Bank Account (4000 x 90) = 360,000
Credit: Debentures Account (4000 x 100) = 400,000
Credit: Discount on Issue of Debentures Account (4000 x 10) = 40,000
Issued 4000, 12% debentures of Rs.100 each at Rs 90 redeemable at Rs 105.
Debit: Cash/Bank Account (4000 x 90) = 360,000
Credit: Debentures Account (4000 x 105) = 420,000
Credit: Premium on Issue of Debentures Account (4000 x 15) = 60,000
b. for the redemption of debentures:
Redemption of debentures issued at Rs. 100 and redeemable at Rs. 100:
Debenture Redemption A/C Dr. 400,000
To Debentureholders A/C 400,000
(Being the debentures of Rs. 100 each redeemed at par)
Redemption of debentures issued at Rs. 100 and redeemable at Rs. 90:
Debenture Redemption A/C Dr. 360,000
Loss on Redemption A/C Dr. 40,000
To Debentureholders A/C 400,000
(Being the debentures of Rs. 100 each redeemed at a discount of Rs. 10)
Redemption of debentures issued at Rs. 100 and redeemable at Rs. 110:
Debenture Redemption A/C Dr. 440,000
Gain on Redemption A/C Dr. 40,000
To Debentureholders A/C 400,000
(Being the debentures of Rs. 100 each redeemed at a premium of Rs. 10)
Redemption of debentures issued at Rs. 110 and redeemable at Rs. 100:
Debenture Redemption A/C Dr. 400,000
To Debentureholders A/C 400,000
(Being the debentures of Rs. 110 each redeemed at par)
Redemption of debentures issued at Rs. 110 and redeemable at Rs. 90:
Debenture Redemption A/C Dr. 360,000
Loss on Redemption A/C Dr. 40,000
To Debentureholders A/C 400,000
(Being the debentures of Rs. 110 each redeemed at a discount of Rs. 20)
Redemption of debentures issued at Rs. 110 and redeemable at Rs. 110:
Debenture Redemption A/C Dr. 440,000
To Debentureholders A/C 400,000
Gain on Redemption A/C Cr. 40,000
(Being the debentures of Rs. 110 each redeemed at par with a premium of Rs. 10)
Redemption of debentures issued at Rs. 90 and redeemable at Rs. 100:
Debenture Redemption A/C Dr. 400,000
Loss on Redemption A/C Dr. 10,000
To Debentureholders A/C 390,000
To Securities Premium Reserve A/C 20,000
(Being the debentures of Rs. 90 each redeemed at a discount of Rs. 10 and Securities Premium Reserve credited with Rs. 2.50 per debenture redeemed)
Redemption of debentures issued at Rs. 90 and redeemable at Rs. 105:
Debenture Redemption A/C Dr. 420,000
Loss on Redemption A/C Dr. 30,000
To Debentureholders A/C 390,000
To Securities Premium Reserve A/C 30,000
(Being the debentures of Rs. 90 each redeemed at a discount of Rs. 15 and Securities Premium Reserve credited with Rs. 7.50 per debent
Which of these correctly expresses the system of equations in standard form
Answers
Equations that correctly expresses the system of equations in standard form are x + y = 22 and 3x + 4y = 76.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given,
Cost of blue sea shells = $3
Cost of pink sea shells = $4
Cost of 22 sea shells = $76
Let number of blue sea shells is x and number of pink sea shells is y
then number of total shells
x + y = 22
Cost of shells
3x + 4y = 76
Hence, x + y = 22 and 3x + 4y = 76 are the equations that correctly expresses the system of equations in standard form
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Which expression is equivalent to x1/2⋅x1/3 x1/2⋅x1/3, where the expression is defined?
Answers
[tex]x^{5/6}[/tex] is value of x in expression .
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself.
This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: The formula is (Number/Variable, Math Operator, Number/Variable).
expression = [tex]x^{1/2} . x^{1/3}[/tex]
= [tex]x^{1/2 + 1/3}[/tex]
= [tex]x^{5/6}[/tex]
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A register has 5376 business cards to give out the register gives out an equal number of business cards in 48 days until there are no more business cards live how many business cards does the register give out each day a 111 business cards be 112 business cards C1 130 business cards D1 114 business cards you have to divide 48÷5376
Answers
Answer: 112 business cards
Step-by-step explanation:
We will divide the number of business cards by the number of days cards were handed out to see how many cards were handed out per day.
5,376 cards / 48 days = 112 business cards
Eighteen cyclists were each asked the number of miles they biked last week. Their responses are given below.
Answers
Answer:
You didn't give the answers
Convert the following to Degrees: 5/18 Counter-Clockwise
Answers
5/18 counter-clockwise is equivalent to 100 degrees counter-clockwise.
What is Fraction ?
A fraction is a number that represents a part of a whole or a ratio between two quantities. It is expressed as a ratio of two integers, with the numerator (top number) representing the part or quantity being considered and the denominator (bottom number) representing the total or whole.
To convert a fraction of a full rotation to degrees, we can use the fact that a full rotation is equivalent to 360 degrees.
In this case, 5/18 represents a fraction of the full rotation, where the numerator (5) represents the number of counter-clockwise rotations and the denominator (18) represents the total number of rotations in a full circle.
To find the number of degrees, we can multiply the fraction by 360 degrees:
(5/18) * 360 = 100 degrees
Therefore, 5/18 counter-clockwise is equivalent to 100 degrees counter-clockwise.
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Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction and number of units if Z′(−1, 4). 4 units down 4 units up 4 units to the right 4 units to the left
Answers
The translatiοn directiοn is 4 units tο the left.
What is Triangle?A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.
A pοlygοn with three edges and three vertices is called a triangle. It is οne οf the fundamental geοmetric shapes. Triangle ABC is a triangle with vertices A, B, and C. In Euclidean geοmetry, any three nοn-cοllinear pοints give rise tο a distinct triangle and a distinct plane.
The translatiοn directiοn is 4 units tο the left because Z' has mοved frοm (3,4) tο (-1,4), and the x-cοοrdinate has decreased by 4.
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ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
Answers
Answer:ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
Step-by-step explanation:ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
if the size of the angles of a triangle are (x-35) ( x-25) and (1/2 x - 10) find value of x
Answers
Answer: x = 100
Step-by-step explanation:
The angles of a triangle add up to 180, meaning that (x-35)+(x-25)+(1/2 x - 10) = 180. Now you can solve for x
if tan(A) = 3/4 then sin(b) equals
Answers
The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.
What is trigοnοmetry?Relatiοnships between cubic splines and mathematics When the disciplines οf astrοphysics were cοmbined, it is thοught that the subject was bοrn in the third century B.C. Precise mathematical techniques can be used tο sοlve a large number οf geοmetric equatiοns οr tο identify the οutcοmes οf calculatiοns invοlving them. The study οf the six fundamental trigοnοmetric functiοns is knοwn as trigοnοmetry. They gο by many different names and abbreviatiοns, such as sine, dispersiοn, angle, οblique, etc (csc).
Here,
cοs(b) Plus sin(b) = 1
Using the equatiοn, we can find the sοlutiοn fοr cοs(b) in terms οf sin(b):
cοs(2b) = (1 - sin(2b)) (b)
Inputting this intο the fοrmula fοr tan(b), we οbtain:
Tan is equal tο sin(b)/√(1 - sin2(b)).
When we square bοth sides and multiply by the remainder, we get:
(Tan(b)) / (1 + (Tan(b))) Equals sin2(b)
By simplifying and substituting tan(b) = sin(A)/cοs(A), we οbtain:
the fοrmula fοr sin2(b) is (sin(A))/((cοs(A))² + (sin(A))²)
Inputting the numbers we previοusly discοvered fοr sin(A) and cοs(A), we οbtain:
=> sin²(b) = (3/5)
=> sin² / ((4/5)
=> sin² + (3/5)²)
=> sin²(b) = 9/25 / (16/25 + 9/25)
=> sin²(b) = 9/25 / 25/25
=> sin²(b) = 9/25 sin(b) = +/- 3/5
Sin(b), which is pοsitive in the first regiοn, results in:
sin(b) = 3/5
As a result, sin(b) = 3/5 if tan(A) = 3/4.
Therefοre, The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.
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Determine whether f(x)= x^2-2x-3/ x^2+3x+2 has any holes. If it does, give the coordinates.
Answers
To determine whether the function f(x) = (x^2-2x-3)/(x^2+3x+2) has any holes, we can factor the numerator and denominator and simplify the expression. The numerator can be factored as:
x^2 - 2x - 3 = (x - 3)(x + 1)
And the denominator can be factored as:
x^2 + 3x + 2 = (x + 1)(x + 2)
Therefore, we can simplify the function as:
f(x) = [(x - 3)(x + 1)]/[(x + 1)(x + 2)]
The factor of (x + 1) appears in both the numerator and denominator, so we can simplify further by canceling it out:
f(x) = (x - 3)/(x + 2)
Since (x + 1) was canceled out, we have a hole in the graph of the original function at x = -1. To find the coordinates of the hole, we can evaluate the simplified function at x = -1:
f(-1) = (-1 - 3)/(-1 + 2) = -4
Therefore, the hole in the graph of the original function is located at the point (-1, -4).
In an examination, Julius scored 5 more marks than John who in turn scored 4 marks less than Grace. If the total mark scored by the three students was 150. Find the mark of each student?
Answers
Making linear equations for given scores, Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.
What is a linear equation, exactly?
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable, with the degree of each variable being 1. In other words, a linear equation is an equation of a straight line, which can be expressed in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept of the line. Linear equations are used to model relationships between variables that have a constant rate of change, such as distance traveled over time or cost per item.
Now,
Let's assume that Grace's score is x.
Then, John's score will be x-4.
And, Julius's score will be x-4+5 = x+1.
The sum of their scores is given as 150. So, we can write an equation as:
x + (x-4) + (x+1) = 150
Simplifying the equation, we get:
3x - 3 = 150
Adding 3 to both sides, we get:
3x = 153
Dividing by 3 on both sides, we get:
x = 51
So, Grace's score is x = 51.
John's score is x-4 = 47.
And, Julius's score is x+1 = 52.
Therefore,
Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.
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A line passes through the point (2, -3) and has a slope of - 4.
Write an equation in slope-intercept form for this line.
Answers
hope it helps
the formula for equations like this is :
y - y1 = m (x - x1)
(Score for Question 3: of 5 points) 1. a). Find the inverse of the function, f(x) = (x - 2)3 - 3. Please show all work in finding the inverse Answer: b) Now graph the inverse function f-1 (x) using the equation you found as the answer to part a) No computer-generated graphs will be accepted. Remember to clearly indicate at least three (3) points on the graph
Answers
The inverse of function is (x + 3)^(1/3) + 2 and the graph is attached below
What is the inverse of the functiona) To find the inverse of the function f(x) = (x - 2)^3 - 3, we can follow these steps:
1. Replace f(x) with y: y = (x - 2)^3 - 3
Solve for x in terms of y:
a. Add 3 to both sides: y + 3 = (x - 2)^3
b. Take the cube root of both sides: (y + 3)^(1/3) = x - 2
c. Add 2 to both sides: x = (y + 3)^(1/3) + 2
Replace x with f^-1(x): f^-1(x) = (x + 3)^(1/3) + 2
b) To graph the inverse function f^-1(x), we can use the equation we found in part a) and plot some points:
When x = 0, f^-1(x) = (0 + 3)^(1/3) + 2 = 3^(1/3) + 2When x = 1, f^-1(x) = (1 + 3)^(1/3) + 2 = 2^(1/3) + 2When x = 3, f^-1(x) = (3 + 3)^(1/3) + 2 = 2 + 2 = 4So we have three points: (0, 3^(1/3) + 2), (1, 2^(1/3) + 2), and (3, 4).
To sketch the graph, we can also note that the function f(x) = (x - 2)^3 - 3 has a vertical asymptote at x = 2 and a local minimum at (2, -3). Therefore, the inverse function f^-1(x) will have a horizontal asymptote at y = 2 and a local maximum at (4, 2).
Combining all of this information, we can sketch the graph of f^-1(x) as shown below:
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the roots of the equation x²-5x+3=0 are α and β. form the quadratic equation whose roots are (2α-β) and (2β-α)
Answers
The quadratic equation whose roots are (2α-β) and (2β-α) is given as follows:
y = x² - 5x - 23.02.
How to define the quadratic equation?The quadratic equation for this problem is defined as follows:
x²-5x+3=0.
The coefficients of the equation are given as follows:
a = 1, b = -5, c = 3.
Hence the discriminant of the equation is of:
D = (-5)² - 4 x 1 x 3
D = 13.
Then the roots are given as follows:
x = (5 - sqrt(13))/2 = 0.697.x = (5 + sqrt(13))/2 = 4.303.Then the roots of the second equation are given as follows:
2 x 0.697 - 4.303 = -2.91.2 x 4.303 - 0.697 = 7.91.Applying the Factor Theorem, the quadratic function is defined as a product of it's linear factors, as follows:
y = (x + 2.91)(x - 7.91)
y = x² - 5x - 23.02.
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IfA+B+C = 180°, prove that:
1) cos² A + cos² B-cos² C=1-2sin A sin B sin C
Answers
Answer: We will start by using the identity cos² A + sin² A = 1 to replace sin² A with cos² A - 1 in the expression 1 - 2sin A sin B sin C:
1 - 2sin A sin B sin C = 1 - 2sin A (cos B cos C - sin B sin C) [Using the product-to-sum formula for sin (B + C)]
= 1 - 2sin A cos B cos C + 2sin A sin B sin C
Now, we will use the identity cos (180° - x) = -cos x to replace cos C with -cos (A + B):
cos² A + cos² B - cos² C = cos² A + cos² B - cos² (A + B)
= cos² A + cos² B - (cos² A cos² B - 2cos A cos B sin A sin B)
= cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B
= (cos² A)(1 - cos² B) + (cos² B)(1 - cos² A) + 2cos A cos B sin A sin B
= cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B
Now, we will use the identity sin (A + B) = sin A cos B + cos A sin B to rewrite the last term:
cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B
= cos² A + cos² B - cos² A cos² B + 2sin A sin B cos A cos B
= (cos² A)(1 - cos² B) + (cos² B)(1 - cos² A) + 2sin A sin B cos A cos B
= (cos² A + cos² B - 1) + (1 - cos² A)(1 - cos² B) + 2sin A sin B cos A cos B
= 2sin² A sin² B + 2sin A sin B cos A cos B
= 2sin A sin B (sin A cos B + cos A sin B)
= 2sin A sin B sin (A + B)
= 2sin A sin B sin (180° - C) [Using A + B + C = 180°]
= -2sin A sin B sin C
Substituting this expression back into the original equation, we get:
cos² A + cos² B - cos² C = 1 - 2sin A sin B sin C
Therefore, the expression is proved.
Step-by-step explanation:
Find the volume of the sphare.
Answers
The volume of the sphere is,
⇒ The volume of sphere = 14,130 cm³
What is Multiplication?The multiplication means to add a number to itself with a particular number of times. And, Multiplication can be viewed as a process of repeated addition.
Given that;
Radius of sphere = 15 cm
Now, We know that;
⇒ The volume of sphere = 4/3πr³
Substitute value of Radius = 15 cm
⇒ The volume of sphere = 4/3 × 3.14 × 15³
⇒ The volume of sphere = 14,130 cm³
Thus, The volume of the sphere is,
⇒ The volume of sphere = 14,130 cm³
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Find all the missing angles in the diagram below. Explain how you used two different angle theories to find at least two missing angles.
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Angles a and b are each measured at 97°, while angles c and d are each measured at 68°. Angles and lines were used to arrive at the solution.
What are lines and angles?Straight lines have careless depth and careless width. Other types of lines include those that are perpendicular, transverse, and intersecting other lines. A form is considered to have an angle if two of its rays originate from the same location.
According to the information:We are given two parallel lines so,
Angle a = 97° (Corresponding angles)
We know that angles on a straight line form a linear pair.
So,
⇒112° + d = 180°
⇒d = 68°
Angle c = 68° (Alternate interior angles)
Using angle sum property,
⇒ a + b + 68° = 180°
⇒ 97° + b + 68° = 180°
⇒ b = 15°
Hence, the missing values have been obtained.
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a restaurant had 13 lb of rice when they opened on Wednesday morning . they cooked and served 3 1/ 12 pounds of it at lunchtime. how much rice was left after lunch
Answers
After finding the difference, we found that the amount of rice left after lunch, written in mixed fraction form, is 9 11/12 lbs.
What are fractions?
Every number of equal parts is represented by a fraction, which also represents a portion of a whole. A single object or a collection of objects might be whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves. The number of parts into which the whole has been divided is shown by the denominator. How many sections of the fraction are displayed or chosen is shown in the numerator.
Given,
The amount of rice the restaurant had when they opened = 13 lbs
The amount of rice that was cooked and served = 3 1/12lbs
We are asked to find the amount of rice left.
This can be found by subtracting the amount of rice served from the total amount of rice.
Note that the amount of rice served is in fractions.
So we use fraction subtraction to solve this.
Then,
amount of rice left = 13 - 3 1/12
3 1/12 is a mixed fraction.
We should convert it into an improper fraction.
3 1/12 = (3*12 + 1 ) /12 = 37/12
Now solving,
amount of rice left = 13 - 3 1/12 = 13 - 37/12
Taking LCM to make a common denominator.
LCM = 12
amount of rice left = 13 - 37/12 = (13*12 - 37)/12 = 119/12 = 9 11/12 lbs.
Therefore after finding the difference, we found that the amount of rice left after lunch, written in mixed fraction form, is 9 11/12 lbs.
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Question 1-16
An equation is shown.
x² + 18x + 7 = 4
Enter a number in each box to rewrite the equation into an equation of the form (x − p)² = q.
1
(x-
²=0
Answers
Answer:
Step-by-step explanation:
To rewrite the equation x² + 18x + 7 = 4 in the form (x - p)² = q, we need to complete the square by adding and subtracting a constant term.
First, we subtract 4 from both sides of the equation:
x² + 18x + 7 - 4 = 0
Simplifying, we get:
x² + 18x + 3 = 0
To complete the square, we need to add and subtract the square of half the coefficient of x, which is (18/2)^2 = 81:
x² + 18x + 81 - 81 + 3 = 0
Simplifying, we get:
(x + 9)² - 78 = 0
Now, we can rewrite the equation in the desired form by adding 78 to both sides:
(x + 9)² = 78
Therefore, the values to be entered in the boxes are:
1: (x + 9)
2: 78