Answer:
In an equilateral pentagon, all angles have equal degree measures, so to find the degree measure of one angle, we need to find the sum of the degree measures of the interior angles and then divide by the number of angles.
Step 1: Find the sum of the degree measures of the interior angles of the pentagon:
180 * (5 - 2) = 540 degrees
Step 2: Divide the sum by the number of angles:
540 degrees / 5 angles = 108 degrees
The degree measure of angle E is 108 degrees.
The degree measure of angle E is 108°.
We can use interior angels theorm.
The sum of the interior angles of a pentagon can be calculated using the formula:
Interior angle sum = (n - 2) × 180
where n is the number of sides of the polygon.
In this case, n = 5, so the sum of the interior angles of the pentagon is (5 - 2) × 180 = 540°.
Since angle A and angle B are both equal to 108°, we can say that:
angle A + angle B = 2 × 108 = 216°.
So, the sum of the remaining three interior angles (angles C, D, and E) is:
540 - 216 = 324°
Since each of these three angles is equal, the measure of each angle must be 324° divided by 3, or:
324 ÷ 3 = 108°
So, the degree measure of angle E is also 108°.
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A right rectangular prism is shown.
What is the length of DH¯¯¯¯¯¯ to the nearest tenth of an inch?
Drag and drop the answer into the box.
The length of DH (diagonal) in the rectangular prism is approximately 3.5 inches.
How to Find the Measure of the Diagonal of a Right Rectangular Prism?A rectangular prism has three dimensions: length, width, and height. The diagonal of a rectangular prism is the distance between two opposite corners of the prism.
To find the diagonal of a rectangular prism, you can use the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the length, width, and height.
In this case, the length is 1.5 inches, the width is 1 inch, and the height is 3 inches. So, you can use the formula:
d² = 1.5² + 1² + 3²
d² = 2.25 + 1 + 9
d² = 12.25
Then take the square root of the d²
d = √12.25
d ≈ 3.5 inches.
Therefore, the measure of the diagonal of the rectangular prism is approximately 3.49 inches.
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Answer:
3.5
Step-by-step explanation:
I took the quiz
Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. Y = 4 - 1/2x text(, ) y = 0 text(, ) x = 0 text(, ) x = 1 Find the volume V of this solid. V = Sketch the region, the solid, and a typical disk or washer. (Do this on paper. Your instructor may ask you to turn in this work. )
The volume of the solid is approximately 32π/3 cubic units.
The volume of the solid obtained by rotating the region bounded by the curves y = 4 - 1/2x, y = 0, x = 0, and x = 1 about the x-axis can be found using the method of disks/washers. The formula for the volume is given by:
V = π * ∫[a,b] (R^2 - r^2) dx
where R is the outer radius (4 - 1/2x), r is the inner radius (y = 0), a and b are the limits of x (x = 0 and x = 1), and dx represents a small slice of the solid.
Evaluating the definite integral:
V = π * ∫[0,1] (16 - x^2 - x^2) dx = π * ∫[0,1] (16 - 2x^2) dx = π * (16x - 4/3 x^3) evaluated at x = 1 - x = 0 = π * (16 - 4/3) = 32π/3 cubic units.
So the volume of the solid is approximately 32π/3 cubic units.
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The size length of a square is 5x-7. Find x if the perimeter is 125.
If the size length of a square is 5x-7 and the perimeter is 125, then the value of x is 7.65 units.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
The length of the square is given as a = (5x - 7) units
The formula for the perimeter of square is -
P = 4a
The value for perimeter of the square is 125 units.
Substitute the values in the equation -
P = 4a
125 = 4(5x - 7)
125 = 20x - 28
20x = 125 + 28
20x = 153
x = 153/20
x = 7.65
Therefore, the value of x is obtained as 7.65 units.
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Different between adding and subtracting linear
Therefore, the method (addition or subtraction) used to combine or separate the terms is the primary distinction between adding and subtracting linear expressions.
Another difference is that when we subtract linear expressions, we get a smaller expression, whereas when we add them, we get a larger one.
What exactly are linear expressions?A mathematical expression that results from the linear combination of variables and constants is known as a linear expression.
Linear expressions can be combined or separated using two distinct operations: adding and subtracting.
By keeping the same variable while adding the coefficients (the numerical part) to linear expressions, like terms are combined. If we wanted to add 2x and 3x, for instance, we would get 5x.
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Find the area of this circle. Use 3 for T. A = πr² [?] in² 26 in
The Area of the circle, A is 530.66 inch.
Define area of circle?An area of a circle is the amount of two-dimensional space within the boundaries of the circle. It is the region enclosed by a circle's circumference. The area of a circle can be found by using the formula A = πr2, where A denotes the area of the circle, r represents its radius, and π is equal to 3.1416. The radius of a circle is the distance from its center to its circumference. It can also be found by dividing the circumference by 2π.
Given,
Diameter, d = 26 inch
Radius, r = d/2 = 26/2 = 13 inch
π = 3.14 or 22/7
We apply all these above values in the formula, we get area of circle:
A = πr²
A = 3.14 x (13)²
A = 530.66 inch
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!!BRAINLIEST TO CORRECT ANSWERS!!
Let f(x) = 2x^2 + x - 3 and g(x) = x - 1. Perform the indicated operation, then find the domain. (f - g)(x)
A) x^2 - 4; domain: positive real numbers
B) 2x^2 - 4; domain: all real numbers
C) x^2 - 4; domain: all real numbers
D) 2x^2 - 2; domain; all real numbers
Let f(x) = 2x^2 + x - 3 and g(x) = x - 1. Perform the indicated operation, then find the domain. (f * g)(x)
A) 2x^3 - x^2 - 4x + 3; domain: all real numbers
B) 2x^3 + x^2 - 3x; domain: all real numbers
C) 2x^3 + x^2 + 4x - 3; domain: negative real numbers
D) 2x^2 + x - 3x + 3; domain: positive real numbers
=============================================
Work shown for problem 1
[tex](f - g)(\text{x}) = f(\text{x}) - g(\text{x})\\\\(f - g)(\text{x}) = (2\text{x}^2+\text{x}-3)-(\text{x}-1)\\\\(f - g)(\text{x}) = 2\text{x}^2+\text{x}-3-\text{x}+1 \\\\(f - g)(\text{x}) = 2\text{x}^2-2\\\\[/tex]
This leads to choice D as the final answer.
The domain is the set of all real numbers since the result is a polynomial. Any polynomial function has the domain "all real numbers". This is because we don't have anything like a division by zero error. We also don't have to worry about square roots of negative values.
------------------------
Work shown for problem 2
[tex](f * g)(\text{x}) = f(\text{x}) * g(\text{x})\\\\(f * g)(\text{x}) = (2\text{x}^2+\text{x}-3) * (\text{x}-1)\\\\(f * g)(\text{x}) = \text{x}(2\text{x}^2+\text{x}-3)-1(2\text{x}^2+\text{x}-3)\\\\(f * g)(\text{x}) = 2\text{x}^3+\text{x}^2-3\text{x}-2\text{x}^2-\text{x}+3\\\\(f * g)(\text{x}) = 2\text{x}^3-\text{x}^2-4\text{x}+3\\\\[/tex]
This leads to choice A as the final answer.
The domain is the set of all real numbers for the exact same reasoning as problem 1.
3. Find the value of h.
h
2h
60°
30°
120°
15°
2h
h
(1 point)
The value of the variable, h is 60 degrees
How to determine the value of hThe properties of a trapezium are expressed as;
It is a 2-Dimensional shapeThe bases of a trapezium are parallel to each otherLength of both the diagonals is equalDiagonals of a trapezium always intersect each otherAdjacent interior angles sum up to 180°Sum of all the interior angles in a trapezium is always 360°If the size of the angles of the trapezium are 2h, 2h, h and h
Then, it is represented as;
Add all the angles
2h + 2h + h + h
Equate the angles to the sum of the interior angles of a trapezium, we get
2h + 2h + h + h = 360
Now, add the like terms
6h = 260
Divide both sides by the coefficient of h, we get;
6h/6 = 630/6
h = 60 degrees
Hence, the value is 60 degrees
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After traveling 70 meters in its dive, the submarine is at a depth of 25 meters. About what will the submarine’s depth be if it continues its dive for another 110 meters? Round to the nearest whole number A) 40m
B) 64m
C) 18m
D) 4m
About 40 meters the submarine’s depth be if it continues its dive for another 110 meters. So the option A is correct.
Since it is essentially a ratio problem, we can use the information given and apply the Rule of Three assuming that the submarine is moving at a constant speed.
In this rule, the depth after 110 meters is obtained by simply multiplying the ratio's diagonal values and dividing by the last value.
70min = 25 m
110min = x m
x = (110 × 25)/70
x = 2750/70
x = 39.28
x = 40(approx)
We can see that at 110 minutes, the depth would have been approximately 40 meters, but since the submarine travelled further during this time, we must add this measurement to the original 25 meters to determine the submarine's total depth.
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d. tickets to the zoo cost $25 for adults and $10 for children. the total ticket sales one day were $47,750. the number of children, c, who visited the zoo was 270 more than 6 times the number of adults, a, who visited. write and solve a system of equations to find the total number of visitors to the zoo that day.
The total number of visitors to the zoo that day=3980.
Given:
cost of each ticket for an adult=$25
cost of each ticket for an adult=$10
Total ticket sales one day=$47,750.
⇒$25+$10=47,750
⇒25+10=47,750-----(1)
Also,
c=6a+270
6a-c=-270------(2)
multiplying eq(2) with 10 we get:
60a-10c=-2700----(3)
Adding eq(1) and eq(3) we get
25a+10c=47,750
60a-10c=-2700
--------------------------
85a=45050
--------------------
To calculate a value just divide 45050 by 85 we get
a=45050/85
a=530
Now to get the value of c substitutes a value.
c=60(530)+270
c=3450
Number of Adult visitors=530
Number of children visitors=3450
Total Number of visitors=3980.
Therefore, the total number of visitors to the zoo that day=3980.
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WILL GIVE BRAINLIEST AND 30 POINTS IF SOMEONE HELPS
The variables are x = 1/2 and y = 5/3
How to solve for the variable x and y?From the figure, we have been told 21x = 5x + 8. So let's solve for x.
21x = 5x + 8
21x - 5x = 8
16x = 8
x = 8/16
x = 1/2 = 0.5
Using the Basic Proportionality Theorem or Thales’s Theorem, which states that "If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally". We can say:
(20y-2)/(17y + 3) = (5x+8)/(21x)
Substitute x = 0.5 and solve for y:
(20y-2)/(17y + 3) = (5(0.5) + 8)/(21(0.5))
(20y-2)/(17y + 3) = (10.5)/(10.5)
(20y-2)/(17y + 3) = 1
20y-2 = 17y + 3
20y - 17y = 3 + 2
3y = 5
y = 5/3
Thus, the variables are x = 1/2 and y = 5/3
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If a jogger runs 84 laps in 28 minutes, what is the rate at which this jogger runs?
3 laps for every 12 minutes.
4 laps for every 3 minutes.
4 laps every 1 minute.
3 laps every 1 minute.
Answer:
3 laps every 12 minutes
Step-by-step explanation:
please help me with this problem!!
The details which describe the free African American who lived in the South is that they were counted as part of population statistics which is denoted as option D.
What is Population statistics?This is referred to an an entire set of items from which you draw data for a statistical study while on the other hand, population refers to the people who live in a particular area at a specific time.
From the passage we were told that there was about 225,964 free African americans of which only 6 percent were free black people which made them less than those found in the North. They were counted during census which means that they were part of the population statistics.
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Evaluate the expression.
(13+9)+37
=
Answer: 59
Step-by-step explanation:
(13 + 9) + 37
13 + 9 = 22
22 + 37
59
steven makes a base monthly salary of $2700. as a vendor, be must sell $17000 worth of items per month. he also makes a 10% commission on all sales beyond the monthly quota. there is also an additional 5% bonus on top of the normal commission rate for any sales beyond $25000. if steven made $4800 this month, how much did he sell to the nearest dollar?
If Steven made $4,800 this month, the value of his sales for the month is $51,000.
How the sales value is determined:Steven's base monthly salary on sales of $17,000 = $2,700
First sales commission above $17,000 sales = 10%
Second bonus commission above $25,000 sales = 5%
Total earnings for the month = $4,800
Commissions:First sales commission = $800 ($25,000 - $17,000 x 10%)
Additional bonus commission = $1,300 ($4,800 - $2,700 - $800)
$1,300 = 5%
Sales above $25,000 = $26,000 ($1,300/5%)
Sales value = $51,000 ($25,000 + $26,000)
Thus, we can assert that Steven generated Sales of $51,000 to earn a total of $4,800 for the month.
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A rectangular rug has a perimeter of 240 yards. The width of the rug is 2 yards more than two times the length. Find the length and the width
The length of a rectangular rug is 84 yards and the width is 36 yards
Let 'l' represents the length of the rectangular rug and 'w' represents the width of a rectangular rug.
The length of the rug is 12 yards more than two times the width.
So, we get an equation,
l = 12 + 2w
Also, a perimeter of a rectangular rug is 240 yards
We know that the formula for the perimeter of rectangle:
P = 2(w + l)
Using this formula the perimeter of a rectangular rug would be,
P = 2 × [w + (12 + 2w)]
240 = 2 (12 + 3w)
120 = 12 + 3w
108 = 3w
w = 118/3
w = 36
And the length would be,
l = 2 + 2( 36)
l = 84 yards
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The complete question is:
A rectangular rug has perimeter 240 yards. The length is 12 yards more than twice the width. Find the length and width of the rug.
In statistics, a population is a set of similar items or events which is of interest for some question or experiment and a sample is a set of data collected from a population by a defined procedure. In the following examples of statistical studies, identify the population of interest and the sample and provide the sample size.
An employee at the local ice cream parlor asks eight customers if they like unicorn ice cream.
Population:
Sample size:
The population of interest and the sample size include the following:
Population: all potential customers of the parlor.
Sample size: 8.
What is a population?In Statistics and science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.
What is a sample?In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.
In this scenario, we can logically deduce that sample is the eight customers that were selected and questioned by an employee at the local ice cream parlor.
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Which is a correct solution for the following system of Inequalities
The solution for the system of inequalities is (-0.43,4.15).
What is an inequality?
An inequality statement in algebra uses the inequality symbol to illustrate the relationship between two expressions. A symbol of inequality has non-equal expressions on both sides.
We are given a graph on which two inequalities are plotted
First, we need to frame the equations from the points.
For the blue line, we have points (0,2) and (-1,7)
So, using slope-intercept form, we get the equation as
y+5x>2
For the red line, we have points (0,4) and (3,3)
So, using slope-intercept form, we get the equation as
y+0.33x >4
Now, in order to find the solution, we will subtract both the equations
On subtracting, we get
⇒(y+5x) - (y+0.33x) = 2 - 4
⇒y+5x - y-0.33x = -2
⇒4.67x = -2
⇒x = -0.43
Substituting this value in the equation, we get
⇒y+5(-0.43) = 2
⇒y-2.15 = 2
⇒y = 4.15
Hence, the solution for the system of inequalities is (-0.43,4.15).
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How would paying off the lowest outstanding balance credit card first be beneficial over paying off the one with the highest?
Paying off the lowest outstanding balance credit card first will not be beneficial over paying off the one with the highest. Instead, it's beneficial to pay the highest outstanding balance first.
Actually, paying the one with the highest interest rate is logically the right thing to do because you can shorten the amount that you spend on interest or charges by month, but paying the lowest outstanding balance credit card first makes more sense if you could transfer the highest interest balance into a low or maybe no interest rate that is being offered to another card, only if you are so certain that you will pay the remaining balance or on before its due.
It should be remarked that paying off the lowest outstanding balance credit card first cannot be beneficial over paying off the one with the highest interest rate.
It's significant to pay the one that has the highest interest rate. This is because it'll assist in shortening the amount the person will pay as interest.
In conclusion, it's important to pay the highest Interest rate.
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The two tables give the number of pints of blue and yellow that are used to make different amounts of two shades of green dye. Green #1 is made by mixing blue and yellow in a ratio of 2:3 2:3 . Green #2 is made by mixing blue and yellow in a ratio of 1:2 1:2 . Use the drop-down menus to complete each sentence below.
In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2 and green #1 is bluer shade of green than Green # 2.
How to explain the table?It should be noted that there are two tables which give the number of pints of blue and yellow that are used to make different amounts of two shades of green dye.
Green #1 is made by mixing blue and yellow in a ratio of 2 : 3.
Green #2 is made by mixing blue and yellow in a ratio of 1 : 2.
The first one has 2 parts of blue at 3 parts of yellow. In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2.
In grade two the blue part is half of the yellow part. This means that green #1 is bluer shade of green than Green # 2.
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What is the range of h Choose 1 answer - 4 <= h(x) < 6 The x h(x)-vabuc5-4.0.2.and 4 The x h(x)- sqrt 3 locs-4-2 2,4,and l; - 5 <= h(x) < 4
The range of h include the following: A. -4 ≤ h(x) ≤ 6.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.
How to identify the range of this graph?Generally speaking, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown, we can reasonably and logically deduce the following:
Range = [-4, 6]
In mathematical notation, the range of this graph can be rewritten as -4 ≤ h(x) ≤ 6.
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Given:
f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2
Find:
(f- g)(x)
(g-f)(x)
(f + g)(x)
Polynomials
The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = 4 x² - x + 5
What is a function?A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.
The general mathematical representation of a function is y = f(x).
f(x)=x²- 5x+7
g(x)=3x² + 4x - 2
(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)
(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)
(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2
(f + g)(x) = 4 x² - x + 5
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proviion of a weekend tay in ydney valued at $1,000 which included flight to the value of $300, meal to the value of $200 and accommodation to the value of $500, a a chritma gift in december 2022. need to calculate the FBT liability
the total FBT liability for this benefit is $329 ($700 x 47% = $329).
Fringe Benefits Tax (FBT) is imposed by the Australian Taxation Office (ATO) on certain non-cash benefits provided to employees. If a company provides a weekend stay in Sydney valued at $1,000 as a Christmas gift in December 2022, the FBT liability is calculated as follows:
The taxable value of the benefit is calculated by deducting the expenses that are not subject to FBT, i.e. $300 (flight) from the total value of the gift, i.e. $1,000. This leaves a taxable value of $700 ($1,000 - $300 = $700).
The FBT liability is then calculated by multiplying the taxable value, i.e. $700, by the FBT rate which is currently 47% (as of 2021). This results in an FBT liability of $329.
Therefore, the total FBT liability for this benefit is $329 ($700 x 47% = $329).
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Aaron just accepted a job at a new company where he will make an annual salary of $52000. Aaron was told that for each year he stays with the company, he will be given a salary raise of $3500. How much would Aaron make as a salary after 6 years working for the company? What would be his salary after t years?
Aaron would make $73000 salary after 6 years. His salary after t years will be 52000 + 3500t. The solution has been obtained by using the linear expression.
What is a linear expression?
The expression with the highest degree of one is a linear expression. This demonstrates that there are no variables in a linear expression with an exponent bigger than one. Such an equation yields a straight line on the graph.
We are given that Aaron has just accepted a job at a new company where he will make an annual salary of $52000.
Also, for each year he stays with the company, he will be given a salary raise of $3500.
So, let's formulate a linear expression for the given situation.
The expression comes out to be
52000 + 3500t, where t denotes the number of years
Salary after 6 years will be
⇒52000 + 3500(6)
⇒52000 + 21000
⇒$73000
Hence, Aaron would make $73000 salary after 6 years and his salary after t years will be 52000 + 3500t.
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Ex4: Write a polynomial function in standard form with the given zeros then graph the function: ( 2 pts)
x=-1,-1, 2,3
After setting f (x) = 0, solve for to determine the intercept(s) of. Set y = f(0) and then find to determine the intercept of. Choose test points to establish the sign of each interval on the axis after using the intercept(s) to divide it into intervals. Determine the test points.
How do you graph a polynomial function with zeros?The Use of Zeros When Graphing Polynomials
You may graph a polynomial function using the steps below.
To assess how the graph will behave at its finish, use the leading-term test.
Choose the x− capture(s) of f(x) by putting f(x)=0 and then figuring up a solution for x .
Choose the y− a snare in f(x) by putting y=f(0) and discovering y.
Use the x− dividing intercept(s) x−
Divide the axis into intervals and then select test points to ascertain the sign of f(x) per interval.
the test points on a map.
To identify the general form of the graph, locate additional points as necessary.
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is f(x)=x+1/x+2 a function? Explain.
The equation represented as f(x) = x + 1/x + 2 is a function
How to determine if the equation is a functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x + 1/x + 2
The above equation is a rational equation whose numerator and denominator are linear functions
Equations with these properties are always functions
This is so because their x values do not have multiple y values
Hence, the equation f(x) = x + 1/x + 2 is a function
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Which of the following best describes the number shown below?
0.535353..
Answer:
Hi, I'm Za'Riah! I will gladly assist you with this problem. (see explanation)
Step-by-step explanation:
1. Repeating Decimal
2. Rational Number
This is all I can think of at the moment.
Lorena and Karla are creating an art project in the shape of a right triangle. They have a 92 cm long piece of wood, which is to be used for the hypotenuse. The two legs of the triangular support are of equal length. Approximately how many more centimeters of wood do they need to complete the supports?
The amount of wood that they need to complete the supports is given as follows:
130.10 cm.
How to obtain the amount of wood needed?First we must obtain the side lengths of the right triangle.
The equal side lengths of the right triangle are obtained applying the Pythagorean Theorem, hence:
x² + x² = 92²
2x² = 92²
x² = 4232
x = square root of 4232
x = 65.05 cm.
They have two sides of 65.05 cm, hence the amount of wood needed is obtained as follows:
2 x 65.05 = 130.10 cm.
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A card is drawn from a standard deck and a
letter is chosen from the word
INCREDIBLE. What is the probability of
drawing a king then getting an I?
The probability of drawing a king then getting an 1 is P = 0.006
How to find the probability?First we need to find the probability of randomly drawing a king from the deck, that is equal to the quotient between the number of kings on a deck and the total number of cards on the deck.
There are 4 kings and 52 cards, thus the probability is:
p = 4/52
Then we want to get a 1, the probability is computed in the same way, notice that now there are 51 cards on the deck because we already drawn one.
q = 4/51
The joint probability (first drawing a king and then a 1) is equal to the product between the individual ones.
P = (4/52)*(4/51) = 0.006
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Mia estimated 5/8 + 1/9 by replacing 5/8 with 1 and 1/9 with 0. Her
estimated sum was 1 + 0 = 1. Explain why Mia's estimate is Not accurate?
NOT accurate.
Estimation done by Mia is not accurate, as the accurate estimated sum of the given expression 5/8 + 1/9 is equal to ( 1/2).
Estimation done by Mia is not accurate:
Replaced 5 /8 with 1.
But accuracy represents:
0 < (1 /4 ) < ( 1 /2 ) < (5 /8 ) < ( 3 / 4 ) < 1
( 5 / 8 ) is more close to ( 1 /2 ).
Estimated value of ( 5 / 8 ) is ( 1 / 2 )
0 < ( 1 / 9 ) < ( 1 / 4 )
So , estimated value of ( 1 / 9 ) is 0
Estimated sum = ( 1 / 2 ) + 0
= ( 1 / 2 )
≠ 1
Therefore, accurate estimated sum of 5/8 + 1/9 is equal to ( 1 /2 ).
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Which descriptions and equations could be the function rule? Select all that apply.
The table in the attached image shows some of the input and output values for a function rule.
For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The table of input and output values are given for the function.
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-2 - (-11)]/[0 - (-3)]
(-2 + 11)/(0 + 3)
9/3
3
So, the slope point is obtained as m = 3.
The equation becomes - y =3x + b
To find the value of b substitute the values of x and y in the equation -
-11 = 3(-3) + b
-11 = -9 + b
b = -11 + 9
b = -2
So, the value for b is -2.
Now, the equation becomes -
y = 3x - 2
The graph is plotted for the function.
Therefore, the equation is y = y = 3x - 2.
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