The service's expected profit is $6,800.
What is the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the service's expected profit, we need to calculate the total revenue and the total cost, and then subtract the cost from the revenue.
First, let's calculate the total revenue. The service sells maintenance agreements for $75 a year, so for every 100 customers, the revenue will be:
100 customers x $75/customer = $7,500
Now, let's calculate the total cost. We know that 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair, and the average cost of repairing an air conditioner is $350. So for every 100 customers, the cost of repairs will be:
2 customers x $350/customer = $700
Finally, let's calculate the expected profit:
Expected profit = Total revenue - Total cost
Expected profit = $7,500 - $700
Expected profit = $6,800
Hence, the service's expected profit is $6,800.
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Evaluate d3a2−(c+b)
if a=−2
, b=3
, c=−12
, and d=−4
.
After evaluating the given expression, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d = -4
What is Algebraic expression?An Algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.t may contain one or more variables, which are symbols that represent unknown quantities or values that can vary.
Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships. For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".
The given expression is d3a2−(c+b), where a = -2, b = 3, c = -12, and d = -4. Substituting these values, we get:
d3a2−(c+b) = (-4)3(-2)² - (-12 + 3) = -434 - (-9) = -48 + 9 = -39
Therefore, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d=-4.
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I need help on this question please anyone ?!!!!??!!!
PLEASE GIVE BRAINLIEST <3
Answer:
I'm pretty sure it's bumper cars ( B ).
Hope this helped! <3
what is the property to 3(4+n)=12+3n
A population has a mean of 400 and a standard deviation of 90. Suppose a sample of size is 100 selected and is used to estimate What is the probability that the sample mean will be within 8 of the population mean
By answering the above question, we may state that As a result, there is standard deviation a roughly 0.9999 or 99.99% chance that the sample mean will be within 8 of the population mean.
What is standard deviation?A statistic known as standard deviation may be used to indicate the variation or variability of a set of statistics. A low standard deviation means that the values tend to be closer to the established mean whereas a large standard deviation shows that the values are widely spread. The standard deviation serves as a gauge for how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is low, and are more scattered when the standard deviation is high. Standard deviation is a measurement of the data set's average variability. It displays the standard deviation of each score with respect to the mean.
population + standard deviation departure from the mean / sqrt (sample size)
Standard deviation is 90/sqrt(100) and equals 9.
z is equal to (x - ) / ( / sqrt(n)).
where:
The sample mean is x. We are looking for the probability given the following conditions: where is the sample size, which is 100; is the population mean, which is 400; is the standard deviation of the distribution of sample means, which is 9;
When we change the values, we obtain:
[tex]Z = (9 / sqrt(100) / (x - 400)\\z = (x - 400) / 0.9\\P(392 < = x < = 408)\s= P[(392 - 400) / 0.9 < = z < = (408 - 400) / 0.9] .9]\\= P[-8.89 < = z < = 8.89] .89]\\[/tex]
To determine this probability, we can use a calculator or a conventional normal distribution table.
[tex]P[-8.89 < = z < = 8.89] = 0.9999[/tex]
As a result, there is a roughly 0.9999 or 99.99% chance that the sample mean will be within 8 of the population mean.
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Steve and Silva are both members of a population, and a simple random
sample is being conducted. If the chance of Steve being selected is 1
what is the chance of Silva being selected?
98,000'
OA.
B.
O C.
O D.
1
98
1
9800
1
980
98,000
According to the probability, the answer is option D: 1/98,000.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The chance of Steve being selected is 1. This means that out of 1 individual, Steve is selected. The probability of Steve being selected is 1/1 or 1. Since the sample is a simple random sample, each individual in the population has an equal chance of being selected. If there are a total of 98,000 individuals in the population, then the probability of Silva being selected is 1 out of 98,000, or 1/98,000.
Therefore, the answer is option D: 1/98,000.
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Please answer this calculus question:
The volume generated by rotating the region bounded by curves x = √y, x= 0 and y = 6 about the x-axis is 24π cubic units.
What is the volume of the regionTo use the method of b, we will imagine taking thin slices parallel to the axis of rotation and adding up their volumes.
To use the method of cylindrical shells, we need to determine the height and radius of each cylindrical shell. We will take thin vertical slices parallel to the y-axis.
The height of each cylindrical shell will be dy. The radius of each cylindrical shell will be x, which is equal to √y.
The volume of each cylindrical shell will be:
[tex]dv = 2\pi x * dy[/tex]
Substituting x = √y, we get:
[tex]dV = 2\pi \sqrt{y} * dy[/tex]
To find the total volume, we need to integrate dV from y = 0 to y = 6:
V = ∫₀⁶ 2π√y dy
Using the power rule of integration, we get:
V = 2π [2/3 * y^(3/2)] from 0 to 6
[tex]V = 2\pi * [2/3 * (6)^\frac{3}{2} - 0][/tex]
[tex]v = 24\pi[/tex]
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For the geometric series –8, 4, –2, . . . find the following sums:
a. s3
b. s6
c. s25
d. S, the sum of the series
geometric series:
[tex]\dfrac{4}{-8} = - \dfrac{1}{2}[/tex]
[tex]\dfrac{-2}{4} = - \dfrac{1}{2}[/tex]
[tex]\implies r = - \dfrac{1}{2} \ \ and \ \ a_{1} = -8[/tex]
[tex]\boxed{S_{n} = \dfrac{a_{1}\cdot (1 - {r}^{n}) }{1 - r}}[/tex]
a. n = 3
[tex]S_{3} = - 8 + 4 - 2 = 4 - 10 = \bf -6\\[/tex]
b. n = 6
[tex]S_{6} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{6}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 - \dfrac{1}{2^{6}}\Big)}{1 + \dfrac{1}{2}} = \dfrac{-8 + \dfrac{1}{2^{3}}}{\dfrac{3}{2}} =\\[/tex]
[tex]= \dfrac{-64+1}{2^{3}} \cdot \dfrac{2}{3} = -\dfrac{63}{2^{2}(3)} = \bf -\dfrac{21}{4}[/tex]
c, n = 25
[tex]S_{25} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{25}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 + \dfrac{1}{2^{25}}\Big)}{1 + \dfrac{1}{2}} = - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} =\\[/tex]
[tex]= - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} = - \dfrac{1 + 2^{25}}{2^{22}} \cdot \dfrac{2}{3} = \bf - \dfrac{1 + 2^{25}}{(3)2^{21}}\\[/tex]
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Keilantra wants to ride her bicycle 28.8 miles this week. She has already ridden 4
miles. If she rides for 4 more days, write and solve an equation which can be used to
determine m, the average number of miles she would have to ride each day to meet
her goal.
Equation:
Answer: m =
Submit Answer
to
attempt 1 out of 3
Answer:
The equation that can be used to determine the average number of miles Keilantra would have to ride each day to meet her goal is:
(28.8 - 4) / 4 = m
This equation subtracts the 4 miles Keilantra has already ridden from her goal of 28.8 miles, and then divides the result by the number of days she still needs to ride (4) to find the average number of miles she would have to ride each day to meet her goal.
Solving this equation gives: (28.8 - 4) / 4 = m
24.8 / 4 = m
6.2 = m
Therefore, the average number of miles Keilantra would have to ride each day to meet her goal is 6.2 miles.
Step-by-step explanation:
a suitcase with measures 80cm*48cm*24cm is to be covered witha trapulin cloth .how many meters of tarapaulin of width 96cm is reqired to cover 100 such suitcases
To cover one suitcase, we need to find the surface area of the suitcase that needs to be covered. The surface area of the suitcase can be calculated by finding the sum of the areas of its six sides.
Area of one side of the suitcase = length x height = 80cm x 48cm = 3840 sq.cm
Area of the opposite side of the suitcase = length x height = 80cm x 48cm = 3840 sq.cm
Area of the other four sides of the suitcase = width x height = 24cm x 80cm + 24cm x 80cm + 24cm x 48cm + 24cm x 48cm = 7296 sq.cm
Total surface area of one suitcase = 3840 sq.cm + 3840 sq.cm + 7296 sq.cm = 14976 sq.cm
To cover 100 such suitcases, we need to multiply the surface area of one suitcase by 100.
Total surface area of 100 suitcases = 14976 sq.cm x 100 = 1497600 sq.cm
To find the amount of tarapaulin required, we need to divide the total surface area of 100 suitcases by the width of the tarapaulin.
Amount of tarapaulin required = (1497600 sq.cm) / (96 cm) = 15600 sq.cm
We now need to convert the required area into meters.
1 sq.cm = 0.0001 sq.m
15600 sq.cm = 15600 x 0.0001 sq.m = 1.56 sq.m
Therefore, we need 1.56 sq.m of tarapaulin to cover 100 such suitcases, assuming that there is no overlap of the tarapaulin.
The length of the rectangle above is 5 inches longer than the width. Which expression could be used to represent the area of the rectangle? help pls (: (quiz)
If we let "x" be the width of the rectangle, then the length would be "x + 5" (since it's 5 inches longer than the width).
The area of a rectangle is given by the formula A = length x width. Substituting in the expressions we found for the length and width, we get:
A = (x + 5)x
Simplifying this expression, we get:
A = x^2 + 5x
Therefore, the expression that could be used to represent the area of the rectangle is "x^2 + 5x".
Given a right triangle, ABC, where C = 90° and AB = 8 in. and BC = 3 in. Determine the exact value of cot (A).
The value of cot A is √55/3
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
cot A = 1/tanA
AC = √ 8²-3²
AC = √64-9
AC = √ 55
tanA = 3/√55
cot A = 1/tanA
cot(A )= 1/(3/√55)
cot( A) = √55/3
therefore the value of cot(A) = √55/3
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A classroom is 28 feet wide and 24 feet long. There is a 10-feet ceiling. Determine how any of these objects would fill the classroom.
The classroom would hold about 34,767 basketballs.
What is the volume of the rectangular prism?
To find the volume of a rectangular prism, you need to know its length, width, and height. Let's assume you have those measurements.
The formula for the volume of a rectangular prism is:
volume = length x width x height
We need to know the volume of the classroom in order to determine how many of a certain object it would hold.
The volume of a rectangular prism (like the classroom) is given by the formula:
volume = length x width x height
Plugging in the values we know:
volume = 24 feet x 28 feet x 10 feet
volume = 6720 cubic feet
Now we can divide the volume of the classroom by the volume of the object we want to find out how many will fit.
For example, if we want to know how many basketballs would fit in the classroom, we would need to know the volume of a basketball. According to the NBA, the standard size for a basketball is about 9.43 inches (0.7867 feet) in diameter. The volume of a sphere is given by the formula:
volume = (4/3) x π x radius^3
Plugging in the radius of the basketball:
volume = (4/3) x π x (0.7867/2)^3
volume ≈ 0.193 cubic feet
Dividing the volume of the classroom by the volume of a basketball:
6720 cubic feet / 0.193 cubic feet per basketball ≈ 34,767 basketballs
Hence, the classroom would hold about 34,767 basketballs.
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A circle has a radius of 4 ft.
What is the area of the sector formed by a central angle measuring 270 degrees
Use 3.14 for pi and round the decimal to the nearest tenth.
42.8 ft
37.7 ft
12 ft
9.4 ft
The area of the sector is 37.7 ft.
What is sector:
A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.
The formula for the area of a sector is given by
A = (θ/360)πr²Where θ is the central angle in degrees, and r is the radius of the circle
Here we have
A circle has a radius of 4 ft.
The central angle of sector formed = 270°
Using the formula, Area of sector = (θ/360°) × π r²
Area of the given sector = [ 270/360] × 3.14 × (4)²
= [0.75 ] × [50.24]
= 37.68 ft
= 37.7 ft
Therefore,
The area of the sector is 37.7 ft.
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GRAPHING EXPONENTIAL FUNCTIONS! BRAIN REWARD
Answer:
Step-by-step explanation:
SEE THE ATTACHMENT
Solve for x.
x² + 6x + 9 = 12
Responses
x=−9±43√
x equals negative 9 plus or minus 4 root 3
x=−3±23√
x equals negative 3 plus or minus 2 root 3
x=−9±23√
x equals negative 9 plus or minus 2 root 3
x=−3±43√
x equals negative 3 plus or minus 4 root 3
The correct answer would be x equals negative 3 plus or minus 2 root 3
What is the quadratic equation?
The quadratic equation is a mathematical formula used to find the solutions (roots) of a quadratic function, which is a second-degree polynomial function of the form:
ax^2 + bx + c = 0
To solve for x in the equation x² + 6x + 9 = 12, we can start by simplifying the left-hand side by factoring the quadratic expression:
(x + 3)² = 12
Taking the square root of both sides, we get:
x + 3 = ±√12
Simplifying the right-hand side, we get:
x + 3 = ±2√3
Finally, solving for x, we have:
x = -3 ± 2√3
Therefore, the solution for x is:
x = -3 + 2√3 or x = -3 - 2√3
So, the correct response is:
x=−3±2√3
Hence, the correct answer would be x equals negative 3 plus or minus 2 root 3
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Answer:
-3 plus minus 2√3
Step-by-step explanation:
took test
principal = $150
rate = 6%
time =?
simple interest = $54
Answer:
150 %6=es igual 1% dividimis 150 ÷100 para tener 150, se calcula el porcwntaje
Select all the equations where b = 11 b=11b, equals, 11 is a solution. Choose 2 answers: Choose 2 answers: (Choice A) 2 b = 211 2b=2112, b, equals, 211 A 2 b = 211 2b=2112, b, equals, 211 (Choice B) b + 18 = 7 b+18=7b, plus, 18, equals, 7 B b + 18 = 7 b+18=7b, plus, 18, equals, 7 (Choice C) 77 = 7 b 77=7b77, equals, 7, b C 77 = 7 b 77=7b77, equals, 7, b (Choice D) 9 = b − 2 9=b−29, equals, b, minus, 2 D 9 = b − 2 9=b−29, equals, b, minus, 2 (Choice E, Checked) 11 = 33 ÷ b 11=33÷b11, equals, 33, divided by, b E 11 = 33 ÷ b 11=33÷b11,
The equations where b = 11 are A, B, C, D, and E. All of these equations are true when b = 11.
How to point equation on a graph?To point an equation on a graph, first, determine the equation and its variables. Then, plot the points of the equation on the graph by substituting the variable values and plotting the corresponding points. To find the equation’s slope, calculate the rise and run of two points on the graph. The slope is used to draw a line of best fit. Finally, draw a line that intersects the points of the equation and the line of best fit. This will be the equation’s graph.
Choice A states that 2b = 2112, b, equals, 211, which means that 2 times 11 is equal to 21. Choice B states that b + 18 = 7b, plus, 18, equals, 7, which means that 11 plus 18 is equal to 7. Choice C states that 77 = 7b77, equals, 7, b, which means that 77 divided by 7 is equal to 11. Choice D states that 9 = b − 29, equals, b, minus, 2, which means that 11 minus 2 is equal to 9. Finally, Choice E states that 11 = 33 ÷ b11, equals, 33, divided by, b, which means that 33 divided by 11 is equal to 11. Therefore, all of these equations are true when b = 11.
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Yesterday, a movie theater sold 290 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $566 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
PLEASE HELP
As a result, 198 small bags and 92 big bags of popcorn were sold at the movie theatre.
what is equations ?An equation in mathematics is a claim that two statements are equivalent. It usually has two sections: a left and a right, separated by an equals sign in the middle. For instance, the statement that the expression 2x Plus 3 equals the expression 7 is represented by the equation 2x + 3 = 7. The equation can be used to determine the number of x that causes the equation to hold true when the variable x is unknown. Equations, such as linear equations, quadratic equations, trigonometric equations, and many others, can be used to explain a broad range of mathematical relationships.
given
Let x represent the quantity of big popcorn bags sold and y represent the quantity of small popcorn bags sold.
Based on the knowledge provided, we can create the following system of two equations:
x + y = 290 (the total amount of bags distributed) (the total number of bags sold)
4x + y = 566 (the entire revenue from popcorn sales) (the total revenue from popcorn sales)
We have two options for resolving the equation for x and y: substitution or removal. Here, we'll apply the replacement technique:
Y = 290 - x is the result of solving equation 1. We can enter the following formula in place of y in equation 2:
4x + (290 - x) = 566
If we simplify, we get:
3x + 290 = 566
290 from both parts are subtracted, giving us:
3x = 276
3 divided gives us:
x = 92
Thus, 92 big bags of popcorn were sold. We can change x = 92 into equation 1 to determine how many small packages were sold:
92 + y = 290
92 is subtracted from both parts to arrive at:
y = 198
Thus, 198 small packages of popcorn were sold.
As a result, 198 small bags and 92 big bags of popcorn were sold at the movie theatre.
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1. Parameter and Statistic In a Citrix Security survey of 1001 adults in the United States, it was found that 69% of those surveyed believe that having their personal information stolen is inevitable. Identify the population and sample. Is the value of 69% a statistic or a parameter?
The population in this case is all adults in the United States, and the sample is the 1001 adults who were surveyed by Citrix Security.
Is the value of 69% a statistic or a parameter?The sample was selected in such a way as to be representative of the larger population of adults in the United States.
The value of 69% is a statistic, not a parameter. A statistic is a measure that describes a characteristic of a sample, while a parameter is a measure that describes a characteristic of a population. In this case, the 69% refers to the proportion of the 1001 adults surveyed who believe that having their personal information stolen is inevitable, which is a characteristic of the sample. It does not necessarily reflect the proportion of all adults in the United States who hold this belief, which would be a parameter.
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A factory produces 600 jars of peanut butter and 250 jars of mixed nuts per day. Which shows the ratio of mixed nuts to peanut butter?
The back of a garbage truck is 23 feet long, 8 feet wide, and 12 feet tall. How many loads of trash from the garbage truck will it take to fill a 40 foot by 9 foot by 8 foot storage container?
it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.
what is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.
To determine the number of loads of trash from the garbage truck that will fill a 40-foot by 9-foot by 8-foot storage container, we need to compare the volume of the container to the volume of the garbage truck's back.
The volume of the garbage truck's back is:
V_garbage_truck = length x width x height
V_garbage_truck = 23 ft x 8 ft x 12 ft
V_garbage_truck = 2,208 cubic feet
The volume of the storage container is:
V_container = length x width x height
V_container = 40 ft x 9 ft x 8 ft
V_container = 2,880 cubic feet
To find out how many loads of trash from the garbage truck will fill the storage container, we need to divide the volume of the container by the volume of the garbage truck's back:
Number of loads = V_container / V_garbage_truck
Number of loads = 2,880 cubic feet / 2,208 cubic feet
Number of loads ≈ 1.30 loads
Therefore, it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.
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A local publication charges by the number of lines for automotive ads. They charge $34 for the first 4 lines, and $3.50 for each additional line. If x represents the number of lines, express the cost c(x) of an ad as a piecewise function. Graph it and label the slopes as well.
The graph of the piecewise function is added as an attachment
How to determine the piecewise functionLet c(x) be the cost of an automotive ad with x lines.
For the first 4 lines, the cost is $34, so:
c(x) = 34, for 1 ≤ x ≤ 4
For each additional line beyond the first 4, the cost is $3.50, so:
c(x) = 34 + 3.50(x - 4), for x > 4
When these two cases are put together, we get the piecewise function:
c(x) = 34, for 1 ≤ x ≤ 4
c(x) = 34 + $3.50(x - 4), for x > 4
This function represents the cost of an automotive ad as a piecewise function that depends on the number of lines in the ad.
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What are the zeros of the polynomial function?
Select all correct zeros of each function.
Function −3 −2 −1 0 1 2 3
f(x)=2x(3−x)(x+1)
negative 3 – f left parenthesis x right parenthesis equals 2 x left parenthesis 3 minus x right parenthesis left parenthesis x plus 1 right parenthesis
negative 2 – f left parenthesis x right parenthesis equals 2 x left parenthesis 3 minus x right parenthesis left parenthesis x plus 1 right parenthesis
negative 1 – f left parenthesis x right parenthesis equals 2 x left parenthesis 3 minus x right parenthesis left parenthesis x plus 1 right parenthesis
0 – f left parenthesis x right parenthesis equals 2 x left parenthesis 3 minus x right parenthesis left parenthesis x plus 1 right parenthesis
1 – f left parenthesis x right parenthesis equals 2 x left parenthesis 3 minus x right parenthesis left parenthesis x plus 1 right parenthesis
2 – f left parenthesis x right parenthesis equals 2 x left parenthesis 3 minus x right parenthesis left parenthesis x plus 1 right parenthesis
3 – f left parenthesis x right parenthesis equals 2 x left parenthesis 3 minus x right parenthesis left parenthesis x plus 1 right parenthesis
f(x)=2(x−3)(x+2)2(x−1)
negative 3 – f left parenthesis x right parenthesis equals 2 left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis
negative 2 – f left parenthesis x right parenthesis equals 2 left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis
negative 1 – f left parenthesis x right parenthesis equals 2 left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis
0 – f left parenthesis x right parenthesis equals 2 left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis
1 – f left parenthesis x right parenthesis equals 2 left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis
2 – f left parenthesis x right parenthesis equals 2 left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis
3 – f left parenthesis x right parenthesis equals 2 left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis
f(x)=x3(x−2)(x+3)
The zeros of the following functions are
1. f(x)=2x(3−x)(x+1) , the zeros are x = 3 and -1
2.f(x)=2(x−3)(x+2)2(x−1), the zeros are x = 3 ,-2 and 1
3. f(x)=x3(x−2)(x+3), the zeros are x = 2 and -3
What are zeros of a function?On a graph of the function, the zeroes will be the x-coordinate values at the points where the line intersects with the x-axis, or where the y-coordinate value is zero. Linear functions have one zero, but polynomial functions can have multiple zeroes. They can also have no zeroes at all.
1. 2x(3−x)(x+1) = 0
2x = 0
x = 0
3-x = 0
x = 3
x+1 = 0
x = -1
2. 2(x−3)(x+2)2(x−1) = 0
x-3 = 0
x = 3
x+2 = 0
x = -2
x -1 = 0
x = 1
3. f(x)=x³(x−2)(x+3) = 0
x³ = 0
x= 0
x-2 = 0
x = 2
x+3 = 0
x = -3
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Fractions:
4/5 is greater, less than, or equal to 8/10?
Answer:
Equal to.
Step-by-step explanation:
multiply both numbers by 2
WILL GIVE BRANLIST AND POINTS Triangle XYZ is drawn with vertices X(-2, 4), Y(-9, 3), Z(-10, 7). Determine the line of reflection that produces X'(2, 4).
Options
Oy=-2
y-axis
Ox=4
O x-axis
The line of reflection that produces X'(2, 4) is,
⇒ y - axis
What is mean by Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
Triangle XYZ is drawn with vertices X(-2, 4), Y(-9, 3), Z(-10, 7).
Now, We know that;
The rule for a reflection over the y -axis is (x, y) → (- x, y)
Here, The line of reflection is produces X'(2, 4).
Hence, We get;
The rule for line of reflection that produces X'(2, 4) is,
⇒ y - axis
Thus, The line of reflection that produces X'(2, 4) is,
⇒ y - axis
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Consider the following piece wise function:
Evaluate the expression: 2f(6) + f(-5) - 3f(-1) = {fill in the blank }
The value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.
What is piece wise function ?
A piecewise function is a function that is defined by different mathematical expressions or formulas for different intervals or "pieces" of the domain. In other words, a piecewise function is a function that is defined by multiple sub-functions, each corresponding to a different part of the domain.
While considering piece wise function:
[tex]F(6) = 4[/tex] [tex](x \geq 3)[/tex]
[tex]F(-5) = x + 3 = (-5) + 3 = -2[/tex] [tex](x\leq -3)[/tex]
[tex]F(-1) =[/tex] [tex]-x^2 + 1 = -(-1)^2 + 1 = -1 + 1 = 0[/tex] [tex](-3 < x < 3)[/tex]
Now put the value of F(6), F(-5) and F(-1) in the expression :
[tex]2F(6) + F(-5) - 3F(-1)[/tex]
we get :
[tex]= 2F(6) + F(-5) - 3F(-1) \\= 2(4) + (-2) -3(0)\\= 8 -2\\= 6[/tex]
Therefore, the value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.
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solve the inequality |3x-7| < |4x+5|
Answer:
x=6
Step-by-step explanation:
Use two math vocabulary terms and two academic vocabulary terms to describe
the system of equations. Underline each term you use.
y=2x+4
2y-x=8
Answer:
y = 2x + 4 and 2y - x = 8 represent a system of linear equations.
In this system, the variable x represents an unknown value, while the variable y represents a value that can be determined from the equation. The coefficient 2 in the first equation is an example of a math vocabulary term, indicating that the slope of the line is 2. The term "slope" is a mathematical term that describes the steepness of a line.
The term "system" is an academic vocabulary term that refers to a group of related equations or inequalities. In this case, we have a system of two linear equations that are related to each other.
The second math vocabulary term is "solution", which refers to the set of values of the variables that satisfies both equations in the system. In this case, the solution is the unique point (3, 10), where x = 3 and y = 10.
Finally, the academic vocabulary term "consistent" is used to describe a system of equations that has at least one solution. In this case, the system is consistent because it has exactly one solution, which means the two equations intersect at a single point.
Step-by-step explanation:
please show the formula and answer
Answer: The answer should be 35.98 ( or 7π + 14 )
Step-by-step explanation:
The perimeter of a semicircle is half of the circumference plus the diameter. First, we find the circumference, which is (2πr). π * 7 * 2 = 14π. Since we have the circumference, we have to divide it by 2 since it's a semicircle. 14π/2 = 7π. Our next step is to find the diameter. Since the radius of the semicircle is 7, we multiply it by 2. 7 * 2 = 14. Now, let's say that (π = 3.14). So (7 * 3.14) + 14, 21.98 + 14 = 35.98. The answer should be 35.98.
Hope this helps. (and please respond if I'm wrong)
Help I don’t get this and I need to make a 100 on this assignment that is very interesting
Using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.
What is a system of equations?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system.
1) y = -3 and x = -6
This system of equations has only one solution as the variables have only a constant as their value.
2) y = 2x and y = -2x
There is only one solution to this system of equations. It is x =0 and y = 0. This solution only satisfies these equations.
3) y = -x -2
y = -x -6
There is no solution to this system of equations as the mathematical operation on two numbers will not give two values.
4) y = 3x + 4
2y = 6x + 8
There is an infinite number of solutions as the second equation when divided by 2 becomes y = 3x + 4, which is the same as the first equation.
5) y = 9x -1
y = x + 9
There is only one solution for this system of equations.
Therefore using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.
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