Answers
The equation that represent the data in the table shown is y = -2x + 3.
How to know if the system is linear?Linear systems are sets of equations associated with each other and that have two or more variables. In linear systems, only linear equations are entered, that is, expressions where the greatest exponent of the unknowns is equal to 1.
A linear equation is in the form:
y = mx + b
Where:
m is the slope b is the y interceptFrom the table, using the point (0, 3) and (1, 1):
y - 3 = [(1 - 3)/(1 - 0)](x - 0)
y - 3 = -2xy = -2x + 3
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Related Questions
Calculate the cone: 1) volume; 2) the area of the lateral surface; 3) the total surface area;for AB = 14, SO = 24.
Answers
Given:
AB = 14
SO = 24
To find:
a) the volume
b) the area of the lateral surface
c) the total surface area
a) To find the volume of the cone, we will use the formula:
[tex]Volume\text{ of a cone = }\frac{1}{3}πr²h[/tex]r = radius
diameter = AB = 14
diameter = 2(radius)
radius = diameter/2 = 14/2
radius = 7
height = SO = 24
let π= 3.14
[tex]\begin{gathered} Volume\text{ of the cone = }\frac{1}{3}\times3.14\times7^2\times24 \\ Volume\text{ of the cone = 1230.88 unit}^3 \end{gathered}[/tex]b) To get the lateral surface, we will apply the formula:
[tex]\begin{gathered} lateral\text{ surface of the cone = \pi rl} \\ where\text{ l = }\sqrt{h^2+r^2} \end{gathered}[/tex][tex]\begin{gathered} Lateral\text{ surface of the cone = 3.14 }\times7\times\sqrt{7^2+24^2} \\ \\ Lateral\text{ surface area of the cone = 549.5 units}^2 \end{gathered}[/tex]c) The total surface area formula:
[tex]\begin{gathered} Total\text{ surface area of cone = Area of base + lateral surface area} \\ \\ Total\text{ surface area = \pi r}^2\text{ + \pi rl} \\ \\ Total\text{ surface area = \lparen3.14 }\times\text{ 7}^2)\text{ + 549.5} \end{gathered}[/tex][tex]Total\text{ surface area of cone = 703.36 unit}^2[/tex]Question 1 (1 point)Given the graph below, is this relation a function?MathMLXBlarSubmit
Answers
To be a function, a relation can't have more than 1 value of 'y' for the same value of 'x'
For example, if you have points (3,7) and (3,-6) does not represent a function but points (3,7) and (-3,7) does.
In this problem, none of the graphed pairs have 2 or more values of 'y' for a single value of 'x'. They are all different, so yes, this relation is a function
For
f(x) = 4x
and
g(x) = x10,
find the following.
(a)
(f + g)(x)
(b)
(f − g)(x)
(c)
(f · g)(x)
(d)
(f/g)(x)
,
x ≠ 0
Answers
The addition, subtraction, multiplication and division of the two functions are 4 · x + x¹⁰, 4 · x - x¹⁰, 4 · x¹¹ and 4 / x⁹, respectively.
How to determine the expression resulting from operations between functions
In functions there are two fundamental operations (addition, multiplication) and two derivate operations (subtraction, division). In this problem we must look for the following definitions:
Addition
(f + g)(x) = f(x) + g(x)
Subtraction
(f - g)(x) = f(x) - g(x)
Multiplication
(f · g)(x) = f(x) · g(x)
Division
(f / g)(x) = f(x) / g(x), for x ≠ 0.
If we know that f(x) = 4 · x and g(x) = x¹⁰, then the expression behind the operations are, respectively:
Addition
(f + g)(x) = 4 · x + x¹⁰
Subtraction
(f - g)(x) = 4 · x - x¹⁰
Multiplication
(f · g)(x) = (4 · x) · x¹⁰ = 4 · x¹¹
Division
(f / g)(x) = (4 · x) / x¹⁰ = 4 / x⁹
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Betsy's Bakery packages muffins in boxes of one dozen. If Besty bakes 1,152 muffins on Saturdays, how many boxes are ready to sell?
Answers
Answer:
96 boxes of muffins
Step-by-step explanation:
so how you would get to this answer would be 1152÷12
12 is equal to a dozen and so that is why you divide it by 12
the answer would be 96
During a sleepover, Carissa played karaoke with her friends. Her song was 6 minutes long. She had already sung for 4 minutes. Which equation could be used to see how much longer she will have to sing?
x + 2 = 6
x + 4 = 10
x + 4 = 6
x − 4 = 6
Brett has a box of colored pencils. He uses 78 pencils and has 120 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
78 + p = 120
p − 78 = 120
120 + p = 78
p = 120 − 78
Answers
Answer:
for the first one it is x + 4 = 6
for the second one it is 78 + p = 120
Step-by-step explanation:
i hoped this helped!!!
Answer:
x+4=6
Step-by-step explanation:
x represents the missing number 4 represents the time she had already sang and 6 is the total
Round all answers to 4 decimal places.
a. A bag contains 4 white marbles, 10 blue marbles, and 3 red marbles. If a marble is drawn from
the bag, replaced, and another marble is drawn, what is the probability of drawing first a white
marble and then a red marble?
b. A bag contains 10 green marbles, 3 red marbles, and 4 blue marbles. If two different marbles
are drawn from the bag, what is the probability of drawing first a green marble and then a blue
marble?
Answers
The probabilities are (a) 0.4228, and (b) 0.8382
Define probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
(a) probability of drawing first a white marble and then a red marble
= 4/(4+10+3) x 3(3+10+3) = 4/17 + 3/16 = 0.4228
(b) probability of drawing first a green marble and then a blue marble
= 10/(10+3+4) x 4(9+3+4) = 10/17 + 4/16 = 0.8382
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Julie is solving the equation 3x² + 5x + 15 = 0 and notices that the discriminant b^2 - 4ac has a value of -155. This
tells her that the equation has
A one real roots.
B one imaginary root.
C two real roots.
D two imaginary roots
Answers
Answer: i think b
Step-by-step explanation:
Gavin has a smart phone data plan that costs $20 per month that includes 6
GB of data, but will charge an extra $10 per GB over the included amount.
How much would Gavin have to pay in a month where he used 2 GB over the
limit? How much would Gavin have to pay in a month where he used went
over by x GB?
Total cost when over by 2 GB:
Total cost when over by x GB:
Answers
Total cost is given by the function $(20 + 10x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is referred to as the function's domain, and the set Y is referred to as the function's codomain. Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest known treatment of the concept of function. Initially, functions represented the idealised relationship between two varying quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).
Total cost is given by the function $(20 + 10x)
Total cost when over by 2 GB = $(20 + 10x2) = $(20+20) = $40
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The number f of miles a helicopter is from its destination x minutes after takeoff is given by f(x)=60−1.5x. The number f of miles a commercial jet is from its destination x minutes after takeoff is shown in the graph below.
Answers
The distance of each flight is 60 miles and the time taken is 40 minutes.
Distance is the total path covered by an object or species in a particular time period.
At x = 0 minutes after takeoff,
f(x)=60−1.5x (given)
= 60-1.5*0 (at 0 minutes)
= 60 miles (distance between the helicopter and destination)
So, the distance of the flight is 60 miles.
When the helicopter reaches the destination, distance left is 0 miles
Thus, f(x) = 0 in x minutes.
Putting the above data in the equation, we get
0 = 60 - 1.5x
1.5x = 60 (bringing unlike terms on different sides)
x = 60/1.5
x = 40 minutes
Therefore, the distance of each flight is 60 miles and the time taken is 40 minutes.
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Conscider this absolute value function.f(x) = (x – 5)How can function fbe written as a piecewise function?
Answers
f(x) = lx – 5l
x-5, if x-5 ≥ 0, x ≥5
-(x-5) = -x + 5 if x-5<0, x < 5
Write the sentence as an inequality.
A number r is no less than -1.5 and fewer than 9.5
Inequality:
Answers
Answer:
-1.5 ≤ r < 9.5
Step-by-step explanation:
All you have to do is just insert the numbers
we use ≤ as it says in the question "no less"
Based on the information below, what are the values of x and y of the solution to the system of equations used to
create the information?
38
141-14 |Ax|- 2141-
26
x = -5, y = 2
x = -0.2, y = 0.5
x=0.5, y = -0.2
x = 2, y = -5
38
8 26
Answers
The values of x and y of the solution to the system of equations are 2 and -5, respectively.
We are given three matrices. The matrices are A, Ax, and Ay.
The determinant of the matrix A is [(4*-2)-(-6*8)] = 40.
The determinant of the matrix Ax is [(38*-2)-(-6*26)] = 80.
The determinant of the matrix Ay is [(4*26)-(38*8)] = -200.
We need to find the values of x and y of the solution to the system of equations.
The value of x is |Ax|/|A| = 80/40 = 2.
Hence, the value of "x" is 2.
The value of y is |Ay|/|A| = -200/40 = -5.
Hence, the value of "y" is -5.
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If an object is shot upward with an initial velocity, vo, in feet per second (ft/s), the velocity, v, in ft/s is given by the
formula
v = vo -32t, where t is time in seconds. Find the initial velocity of an object if the velocity after 4 seconds is 41 ft/s.
-
Answers
= 170 ft/s
Explanation:
• given equation is v=Vo-32t
.. (i)
an initial velocity, Vo, in feet per second
(ft/s)
vin ft/s = 42 ft/s
† is time in seconds = 4 seconds
Putting the values in (i) , we get
42 = Vo - 32 x 4
multiply
42 = Vo - 128
add 128 to both sides
42 + 128 = Vo - 128 + 128
Simplify and add
170= Vo
Hence, the initial velocity of an object = 170
ft/s
Consider the following function.
f(x) = (x − 3)2, x ≥ 3
Find the inverse function
f −1.
Answers
The inverse equation of the function is f'1(x) = 3 + √x
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x)
How to determine the inverse function?The function f(x) is given as
f(x) = (x - 3)^2, x ≥ 3
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = (x - 3)^2
The next step is to switch/swap the positions of x and y in the equation
The equation becomes
x = (y - 3)^2
Make y the subject of the formula in the equation
The equation becomes
y = 3 + √x
Express as an inverse function
f'1(x) = 3 + √x
Hence, the equation of the inverse function is f'1(x) = 3 + √x
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I’m begging help me out with this, please
Answers
For given function f(x)=8/(x+2) , g(x)=4x² +2 then evaluation of the composition of function (fog)(-1) =1.
As given in the question,
Given function:
f(x) = 8 / (x+2)
g(x) = 4x² +2
Evaluation of the composition of function f(x) and g(x) we get,
(fog)(x)
= f(g(x))
Substitute g(x) = 4x² + 2
= f(4x² +2)
= 8/(4x² +2+2)
= 8/(4x²+4)
= 2/(x²+1)
Substitute x =-1 in the above function
(fog)(-1) = 2/ ((-1)² +1)
= 2/ 2
=1
Therefore, for given function f(x) = 8/ (x+2) , g(x) = 4x² +2 then evaluation of the composition of function (fog)(-1) =1.
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Suppose that the relation S is defined as follows.
s={(3, 0), (1, 2), (4, -1), (3, 9)}
Give the domain and range of S.
Write your answers using set notation.
Answers
The most appropriate choice for relation, domain and range will be given by-
Domain of S = {3, 1, 4}
Range of S = {0 , 2, -1, 9}
What is relation, domain and range?
A relation over set A and B is the subset of the cartesian product A x B.
Domain of a relation is the set of values for which the relation is defined.
Range is the set of solution obtained on putting the values of domain.
The relation S is defined as follows
S = {(3, 0), (1, 2), (4, -1), (3, 9)}
Now the set of values for which the relation is defined is the domain of the relation
For each ordered pair, the first number gives the values to be put in S. So the first number of every ordered pair is the domain.
So domain of S = {3, 1, 4}
Now, the second number gives the solution after putting the numbers in S.
So the second number of every ordered pair represents the range.
So, range of S = {0 , 2, -1, 9}
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Whats the solution to this formula?Tan^-1 ( 7 / 420) =
Answers
Okay, here we have this:
Considering the provided expression, we are going to solve it, so we obtain the following:
[tex]\begin{gathered} tan^{-1}(\frac{7}{420}) \\ =arctan(\frac{7}{420}) \\ =arctan(\frac{1}{60}) \\ =0.95° \end{gathered}[/tex]Finally we obtain that the expression is equal to 0.95°.
What are the coordinates of the vertices of the image triangle after a 90 clockwise rotation about the origin? :
A'(1, 3) B'(-3, 4) C'(-2,-3)
A'(3, 1) B'(4,-3) C'(-3,-2)
A'(3,-1) B'(4, 3) C'(-3, 2)
A'(1,-3) B'(-3,-4) C'(-2, 3)
A'(-3, 1) B'(-4,-3) C'(3,-2)
Answers
Before carrying out rotation transformation, the coordinates of the vertices of the pre-image are;
A (3, -6)
B(1, 2)
C (7, -1).
What is the effect of clockwise rotation transformation?We are given the coordinates of the transformed image as:
A'(6, 3),
B'(–2, 1),
C'(1, 7).
We need to find the coordinates of the pre-image A, B and C.
The rule for rotation of 90° about the origin is (x,y) ---> (-y,x).
But we need to find the coordinates of the vertices of the pre-image.
So, we need to apply rule (-y,x) ---->(x,y).
Applying the 90 degrees clockwise rotation rule,
A'(6, 3) -----> A (3, -6)
B'(–2, 1) -----> B(1, 2)
C'(1,7) -----> C (7, -1).
Therefore, coordinates of the vertices of the pre-image are
A (3, -6)
B(1, 2)
C (7, -1).
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Complete question is;
After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
he figure on the left represents a scale drawing of the figure on the right.
pls help its due in 10 min
Answers
The scale of the drawing is expressed as, 1 inch : 2.5 yards.
What is a Scale Factor?A scale factor describes to what size an original image has been reduced or enlarged. If the scale factor of an enlargement is 2, it means every side lengths of the original image is increased times two to get the new image after enlargement.
On the other hand, if the reduction was done using a scale factor of 0.5 or 1/2, it means the size of the original image was reduced by half to get the new side lengths of the new image.
How to Find the Scale Factor of a Scale Drawing?The scale factor of a scale drawing = dimension of new image/corresponding dimension of original image.
The figure by the right is the original figure, while the one on the left is the scale drawing which is the new figure.
Scale of the drawing = 1 inches to 5/2 yards
Scale = 1 inch : 2.5 yards.
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my aunt's food budget is R 3500 . She save 1/5 of her budget. How much money did she save?
Answers
The money she saved is 700.
What are fractions?Simply put, a fraction shows us how many pieces of a whole we have. The slash that is printed between the two numbers indicates that the numbers are a fraction. We have two numbers: the numerator at the top and the denominator at the bottom. The number is represented mathematically as a quotient, where the numerator and denominator are split.Given:
Aunt's food budget = 3500
Fraction of the budget she saved = 1/5
So, the total money she saved = 1/5 of the food budget
= 1/5 × 3500
= 700
Therefore, the money she saved is 700.
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Estimate the product of 653.2×4.6
Answers
Answer: 3004.72
Step-by-step explanation: i used a calculator
Which of the following linear equations represents the data chart?
Answers
Answer:
y = -x + 7
Step-by-step explanation:
let's use the first numbers as an example.
x=1 and y=6
now to get this we need to find the difference between the two numbers and we can do this by simply doing - 1 + 7 = 5
therefore making the answer y = -x + 7
Scatter Graphs
The best description of a scatter graph does the following:
“tells the story” of the graph from left to right giving specific values and dates for the first data point, the last data point, any relevant high points and low points
explains the overall trend seen on the graph
includes at least one relevant calculation (absolute change, percent change, ratio, etc) to better describe the data, the trends, or changes in the data
ends with some meaningful conclusion or “take away”
uses terminology correctly
1. Write a thorough description of this scatter graph using the guidelines above. [3 pts]
Answers
A specific type of graphic or mathematical diagram known as a "scatter plot" employs Cartesian coordinates to display values for typically two variables for a group of data.
A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.
If the points are color-, shape-, or size-coded, a second variable can be displayed. Each point's location on the horizontal axis is determined by the value of one variable, while its location on the vertical axis is determined by the value of the other. The data is shown as a series of dots.A scatter plot can be used when both continuous variables are independent of one another or when one continuous variable is in the researcher's control and the other one depends on it.The scatter graph can be represented by the line of best fit which is calculated by taking the average of all the x -coordinates and the y-coordinates.
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Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.-the equation is in the photo
Answers
As given by the question
There are given that expression:
[tex]4a^2\times3a^5[/tex]Now,
First, multiply the numbers:
[tex]4a^2\times3a^5=(4\times3)a^{2+5}[/tex]In the given solution of the question, there are perform addition, so this is the first error.
Now,
[tex](4\times3)a^{2+5}=12a^7[/tex]Hence, the correct answer is :
[tex]12a^7[/tex]What is the solution to this equation?
x+8 = -3
OA. x = -5
OB. x = 5
OC. x = 11
OD. x=-11
Answers
[tex]x + 8 = - 3 \\ x = -3 - 8 \\ x = - 11[/tex]
OPTION (D) SUITS ..IT IS THE SOLUTION.
help plssssss I really need help genuinly
Answers
hi can you please help me
Answers
The area of the kitchen will be:
[tex]\begin{gathered} A=w\cdot l \\ \text{where:} \\ w=\text{width}=36-24=12ft \\ l=\text{length}=8ft \\ A=12\cdot8 \\ A=96ft^2 \end{gathered}[/tex]What is the surface area of the prism?
77.25 cm2
154.5 cm2
225 cm2
309 cm2
Answers
The surface area of the prism represented by the net diagram is 154.5 cm^2
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the surface area of the prism?The given parameter is in the figure
In the figure, we have the net of a rectangular prism
From the net of a rectangular prism, we have the following dimensions
Length = 8 1/2 cm
Width = 4 1/2 cm
Height = 3 cm
The surface area of the prism is then calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation
So, we have the following equation
Surface area = 2 * (8 1/2 * 4 1/2 + 8 1/2 * 3 + 4 1/2 * 3)
Evaluate the products
So, we have the following equation
Surface area = 2 * (38 1/4 + 25 1/2 + 13 1/2)
Evaluate the sum
So, we have the following equation
Surface area = 2 * 77 1/4
Evaluate the products
So, we have the following equation
Surface area = 154.5
Hence, the surface area of the prism is 154.5 cm^2
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Pls answer also
Indicate which property is illustrated in Step 2.
Answers
Distributive property is illustrated in Step 2.
What is a distributive property ?The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.A, B, and C are the operands in the formula for the distributive property, which is written as a (b + c) = (a b) + (a c). Here, each phrase included in a bracket multiplies the number outside of it, and the results are added.According to the associative property, any three terms in an expression can be combined together to solve it. The arrangement of the numbers will never alter the outcome of their computation. For addition and multiplication, the associative property holds true.To learn more about : Distributive law
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What is the horizontal shift of y = cos(0 – ³7) + 3?4A. noneOB.-37OC. 3rD. 3Reset Selection
Answers
The horizontal shift will be the term that is subtracting the angle, in this case: -3pi/4= B .