Select all of the following that are linear functions.
x = 5
y
-2
4
0
1
2
-2.
4
5
x + 7 = 4y
Answers
A) x = 5 is not a linear function since it is a vertical line and does not have a slope. B) The table description does not provide enough information to determine if it is a linear function. C) x + 7 = 4y is a linear function in slope-intercept form (y = (1/4)x + 7/4).
A linear function is a mathematical function that can be represented by a straight line with a constant slope. The equation of a linear function can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Option A (x = 5) is not a linear function, as it is a vertical line with an undefined slope. Option B is a linear function, as the table describes points that can be plotted to form a straight line. Option C is also a linear function, but it is in a different form (x + 7 = 4y). This equation can be rearranged to y = (1/4)x + 7/4, which is in the standard form of a linear function.
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Answer: C.) x + 7 = 4y and D
Step-by-step explanation: i hope this helps
Related Questions
a) Find the approximations T8 and M8 for the integral Integral cos(x^2) dx between the limits 0 and 1. (b) Estimate the errors in the approximations of part (a). (C) How large do we have to choose n so that the approximation Tn and Mn to the integral in part (a) are accurate to within 0.0001?
Answers
(a) Using the Trapezoidal rule, T8 = (1/16)[cos(0) + 2cos(1/16) + 2cos(2/16) + ... + 2cos(7/16) + cos(1)].
Using the Midpoint rule, M8 = (1/8)[cos(1/16) + cos(3/16) + ... + cos(15/16)].
(b) The error in the Trapezoidal rule is bounded by (1/2880)(1-0)^3(max|f''(x)|), where f''(x) = -4x^2sin(x^2) and 0 <= x <= 1. Therefore, the error in T8 is approximately 0.00014. The error in the Midpoint rule is bounded by (1/1920)(1-0)^3(max|f''(x)|), which gives an approximate error of 0.00011 for M8.
(c) Let n be the number of intervals in the approximation.
Then, the error bound for the Trapezoidal rule is (1/2880)(1-0)^3(max|f''(x)|)(1/n^2), and the error bound for the Midpoint rule is (1/1920)(1-0)^3(max|f''(x)|)(1/n^2).
Setting these equal to 0.0001 and solving for n, we get n >= 129 and n >= 160 for the Trapezoidal and Midpoint rules, respectively. Therefore, we should choose n >= 160 to ensure that both approximations are accurate to within 0.0001.
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30 points please help me do this question
Answers
Answer:
the area of triangle OAP is 12 square units.
Step-by-step explanation:
First, we need to find the coordinates of the center of the circle, which is (0, 0), and the radius, which is √40 = 2√10.
Since line I is a tangent to the circle at point A, it is perpendicular to the radius OA at point A. Therefore, OA is perpendicular to line I and forms a right angle with it.
We can find the equation of line I using the point-slope form:
slope of radius OA = (0 - 6) / (0 - 2) = -3
slope of line I = 1 / 3 (because it is perpendicular to OA)
equation of line I: y - 6 = (1/3)(x - 2)
simplifying, we get: y = (1/3)x + 4
To find the x-coordinate of point P, we need to solve for x when y = 0:
0 = (1/3)x + 4
x = -12
Therefore, point P has coordinates (-12, 0).
Now, we can find the coordinates of point O, which is the origin (0, 0), and the coordinates of point A, which are given as (2, 6).
To find the area of triangle OAP, we can use the formula for the area of a triangle:
Area = (1/2) x base x height
We know that OA is the base of the triangle and its length is the radius of the circle, which is 2√10.
To find the height of the triangle, we need to find the distance from point A to line I, which is the perpendicular distance. We can use the formula for the distance between a point and a line:
distance = |ax + by + c| / √(a² + b²)
where a, b, and c are the coefficients of the equation of the line, and x and y are the coordinates of the point.
In this case, the equation of line I is y = (1/3)x + 4, so a = -1, b = 3, and c = -12.
Substituting the values, we get:
distance = |(-1)(2) + (3)(6) - 12| / √((-1)² + 3²)
distance = |6| / √10
distance = 3√10 / 5
Now we can substitute the values into the formula for the area of the triangle:
Area = (1/2) x base x height
Area = (1/2) x 2√10 x (3√10 / 5)
Area = 6/5 x 10
Area = 12
Therefore, the area of triangle OAP is 12 square units.
LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm, and
Answers
The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.
Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:
x² + (LV/2)² = DV²/4
y² + (OE/2)² = LE²/4
Simplifying each equation and substituting the given values, we get:
x² + (LV/2)² = 81/4
y² + (OE/2)² = 225/4
We also know that the diagonals bisect each other, so we can set up another equation:
LV/2 + OE/2 = LO = VE
Substituting the given value for LE, we get:
LV/2 + OE/2 = 15
Solving this equation for one of the variables, we get:
LV = 30 - OE
Substituting this expression into the first equation above, we get:
x² + ((30 - OE)/2)² = 81/4
Simplifying and rearranging, we get:
OE² - 60OE + 675 = 0
Using the quadratic formula, we get:
OE = (60 ± √(3600 - 2700)) / 2
OE = 15 or 45
If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:
x² + 7.5² = 81/4
y² + 7.5² = 225/4
Solving these equations, we get:
x = 3√7
y = 9/√7
If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:
LV = OE = 15
x = 3√7
y = 9/√7
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Complete question:
LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.
The location of the incenter of ABC is:
A. Point D
B. Point F
C. Point E
Answers
Storyboards are a helpful part of the design process because the storyboard develops
A) A pseudocode description of the algorithm being designed
B) The mathematical formulas required for computing a correct answer
C) What information is needed to solve the problem, and how to present that information
D) The amount of time and space it will require to find a solution
Answers
The correct option among the four options that are given in the question is option C. The storyboard is a helpful part of the design process because the storyboard develops what information is needed to solve the problem, and how to present that information.
What is a storyboard?
A storyboard is a graphic organizer that consists of illustrations or images shown in sequence for the purpose of pre-visualizing a motion picture, animation, motion graphic or interactive media sequence. A storyboard is created to provide a visual representation of how a story will unfold on a screen.Storyboards are important in the design process because they help designers understand the complexity of a particular problem and come up with a plan to solve it. The storyboard can be used to explain how the user will interact with the software, what functions are necessary, what data is required, and how the data will be displayed on the screen. Storyboards help designers visualize the user's experience and think through the design process. They are an essential tool for designers who want to create engaging, user-friendly software or interfaces.
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suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward a distance of 6 units. what are the coordinates of your position? (x, y, z)
Answers
The coordinates of your position If we start at the origin, we are moving only along the x-axis of a distance of 7 units in positive direction and then only in the negative y-axis direction and z-coordinate is zero are (7,-6,0).
The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.
The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).
The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).
Therefore, the coordinates of our position are (7, -6, 0)
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If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.
Answers
The required ratio of is (a + c) : c 11:8.
How to find ratio ?Given that a:b=1:4 and b:c=3:2.
We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.
To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:
[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]
Simplifying the expression inside the parentheses, we get:
[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]
Therefore, the ratio [tex]$(a+c):c$[/tex] is:
[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]
Hence, the required ratio is 11:8$.
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The triangle has a perimeter of 8x-2 what is the leangth of the missing side
Answers
The length of the missing side is 4x + 5 units
To find the length of the missing side of the triangle, we need to use the fact that the sum of the lengths of all three sides of a triangle is equal to its perimeter. So, we can write:
Perimeter = (length of first side) + (length of second side) + (length of missing side)
Substituting the given values, we get:
8x-2 = (x-7) + 3x + (length of missing side)
Simplifying and solving for the missing side, we get:
8x-2 = 4x-7 + (length of missing side)
Length of missing side = (8x-2) - (4x-7)
Length of missing side = 4x + 5 units
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The given question is incomplete, the complete question is:
The triangle has a perimeter of 8x-2. what is the length of the missing side?
An urn contains eight green balls and six red balls. Four balls are randomly selected from the urn in succession, with replacement. That is, after each draw the selected ball is returned. What is the probability that all four balls drawn are red. Round your answer to three decimal places
Answers
The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.
Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:
P(Red) = Number of Red Balls / Total Number of Balls
P(Red) = 6 / (8 + 6)
P(Red) = 0.4286
So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:
P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)
P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286
P(4 Red Balls) = 0.04 or 4%
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GEOMETRY:
a pile standing vertically casts a 19 ft shadow. At the same time, a 6 ft person near the beam casts a shadow 4’6’’. What is the height of the pole?
Answers
Answer:
X / 19 = 6 / 4.5 both person and pile have same ratio of shadow
X = 6 / 4.5 * 19 = 25.3 ft
Tiago sells sunflower oil in large tins and extra-large tins.
The large tin and the extra-large tin are mathematically similar.
The volume of the extra-large tin is 75% more than the volume of the large tin. Both tins are cylinders.
The radius of the large tin is 20 cm.
Calculate the radius of the extra-large tin.
Answers
Answer:
24 cm (to nearest cm)
Step-by-step explanation:
XLV = extra large tin volume (cm³)
LV = large tin volume (cm³)
XLR = extre large tin radius (cm)
LR = large tin radius (cm) = 20
XLV = 1.75 × LV
Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;
We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;
This means the volumetric scale factor or multiplier is ×1.75;
Subsequently, we know:
XLV = 1.75 × LV
Similarly, there is a relationship between the radii of the tins;
The relationship is, however, slightly different;
[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]
We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;
Easy way to figure this is radius is in cm, volume is in cm³;
So:
XLR = 1.205... × LR
XLR = 1.205... × 20
XLR = 24.101... --> 24 cm (to nearest cm)
5. If j(x) = x+8, find x such that
j(x)=10
Answers
J(x) is equal to two things meaning
X+8=j(x)=10
Meaning
X+8=10
10-8=2
X=2
Erica's bedroom is shaped like the letter L. One of the rectangles that makes up her room measures 10 feet by 8 feet. The other rectangle measures 12 feet by 8 feet. What is the area of her entire bedroom?
Answers
the area of her entire bedroom is 176 feet².
What is rectangle?A rectangle is a parallelogram with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equal edges.
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
Area of first rectangle = length * breadth= 10*8=80 feet²
Area of second rectangle = length * breadth= 12*8 = 96 feet²
Total area of bedroom= 80+96= 176 feet²
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solve the nonlinear system of equations for real solutions.
y = x² - 2
7x-y = 12
Answers
Answer: y=12
Step-by-step explanation: can't simplify
Picture Shown Below with question:
Answers
Answer: 23
Step-by-step explanation:
Vertical angles are congruent (equal) so you first make the equations for angle A and B equal to each other and solve for x.
x + 15 = 5x - 17
32 = 4x
x = 8
Plug the x value (8) back into either equation to find the measure of angle B.
x + 15
8 + 15 = 23
For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?
Answers
Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?
Step-by-step explanation:
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Answers
a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution. what type of probability distribution did the teacher use?
Answers
The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.
What is the Probability distribution?The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.
The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.
A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.
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BP = FC + VCM
The fixed costs associated with the fundraiser include: one-time charges of art ($45), screen and set-up ($60),
and advertising ($50 for a newspaper ad). In addition, the unit cost of the sweatshirt will be $16.50 per sweatshirt, with an additional charge of $.50 per shirt for shipping and individual plastic wrap. You plan to sell the sweatshirts for a retail price of $22.
A. Calculate breakeven in units.
B.calculate breakeven in dollars
Answers
1. The breakeven in units equals 31 units.
2. The dollar amount to breakeven is
What is the breakeven in units?The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:
= $16.50 + $0.50
= $17.00
The contribution margin per unit is:
= 22.00 - $17.00
= $5.00
The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:
= $45 + $60 + $50
= $155
Using the breakeven formula, we can calculate the number of units required to break even:
= Fixed costs / Contribution margin per unit
= $155 / $5.00
= 31 units
What is the breakeven in dollars?To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:
The breakeven in dollars equals to:
= Breakeven in units x Selling price per unit
= 31 x $22.00
= $682.00
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what is an equation of the line that passes through the points (5 -6) and (-5 -2)
Answers
Answer:
7
Step-by-step explanation:
A(-5,−2) , B(5,−6)
Equation of line AB⟹
(5-6), (-5-2) = 3+3 = 6+1= 7
There are 500 wrist watches in a box. Out of these 50 wrist watches are found defective. One
watch is drawn randomly from the box. Find the probability that wrist watch chosen is a
defective watch
Answers
The probability that wrist watch chosen is a defective watch is 1 / 10
Total number of watches n(S)=500
Number of watches defective n(A)=50
P(A)= n(A) / n(S)
⇒P(A)= 50 / 500
Probability of watches to be defective = 1 / 10 or 50 / 500
Probability is a branch of mathematics that deals with the study of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and making predictions about the outcome of a random process. The probability of an event is represented by a number between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.
Probability theory provides a set of rules and tools for analyzing and modeling the behavior of random phenomena, such as coin flips, dice rolls, or the occurrence of a disease in a population. These tools include probability distributions, which describe the likelihood of different outcomes, and statistical inference, which allows us to make predictions based on a sample of data.
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Help pls
I need three answers
Answers
The value οf x fοr the expressiοn must be simplified is 12,32,48.
What is expressiοn?Expressiοns in mathematics must cοntain a statement, at least οne arithmetic οperatiοn, at least twο numbers οr variables, οr bοth. With the help οf this mathematical οperatiοn, οne can multiply, divide, add, οr subtract.
Unknοwn variables, numbers, and arithmetic οperatοrs make up an algebraic expressiοn. There are nο symbοlic representatiοns οf equality οr inequality in it.
Here since 71 is a prime number , [tex]\sqrt{71}[/tex] cannot be simplified itself.
Then [tex]\sqrt{71x}[/tex] can only be further simplified if [tex]\sqrt{x}[/tex] itself can be simplified.
Here , amοng the given chοices,
=>12 = 4*3 [ 4 is perfect square] , sο it can be simplified.
=> 32 = 16*2 [16 is perfect square] , sο it can be simplified.
=> 48 = 16*3 [ 16 is perfect square] , sο it can be simplified.
Hence the value οf x fοr the expressiοn must be simplified is 12,32,48.
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3. Find the sine of angle in the triangle below.
8
7
Answers
Answer:
90 degrees then decreace that then turn that into a fraction
Step-by-step explanation:
Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2
Answers
No, the given value of h=2 is not a solution of the equation 1/3h=6.
1/3 h = 6
We need to determine whether h = 2 is a solution of this equation. To do this, we substitute h = 2 into the equation and see if it is true or not.
1/3 (2) = 6
2/3 = 6
This is not true, since 2/3 is not equal to 6. Therefore, h = 2 is not a solution of the equation 1/3 h = 6.
Aura builds model airplanes her first model airplane is 4 1/3 feet long she wants her next model airplane to be 1/4 as long as the first. How long will the next model airplane be
Answers
13/12 will be long the next airplane model. This will be because her next model is to be 1/4 as long as the first.
Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the per cent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form.
Given,
The length of her first model is in the fraction [tex]4\frac{1}{3}[/tex]
As her next model has to be 1/4 as long as the first model
Therefore,
Length of her new or next model
1/4 of [tex]4\frac{1}{3}[/tex]
so, 1/4 * 13 / 3
13/12
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Which expressions are completely factored? Select each correct answer.
A. 32y^10-24=8(4y^10-3)
B. 20y^7+10y^7=5y(4y^6+2y)
C. 18y^3-6y=3y(6y^2-2)
D. 16y^5+12y^3=4y^3(4y^2+3)
i have a tough time with math bc im a very easily distracted person, so i need a tad bit of help ^^"
Answers
Answer:
a, c and d
Step-by-step explanation:
a 20-volt electromotive force is applied to an lr-series circuit in which the inductance is 0.1 henry and the resistance is 40 ohms. find the current i(t) if i(0) = 0.
i(t) = ___
Determine the current as t → [infinity].
lim t→[infinity] i(t) =_____
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The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
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I need help please
Answers
Answer:
136
Step-by-step explanation:
35x2+7x6+12x2
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
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Answer:
Step-by-step explanation:
the second blank is wrongt
Complete the sequence in the grids so that starting
of a 2x2 board turned off by pressing one at a time on each
grid we reach all the lit squares.
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Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.
What is sequence?In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.
Here,
One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.
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