x+21 is the length of GH from the given figure.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
A triangle GHJ, M is the intersection of the three medians.
Given that GJ is twenty one.
GJ=21
We need to find the length of GH.
Let the length of HJ is x.
Now GH=HJ+GJ
GH=x+21
Hence, x+21 is the length of GH from the given figure.
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______. a measurable part of a line that consists of two points, called endpoints, and all of the points between them.
Line segment is a a measurable part of a line that consists of two points, called endpoints.
What is coordinate Geometry?a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Given that measurable part of a line that consists of two points, called endpoints is a line segment.
A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.
Hence, line segment is a a measurable part of a line that consists of two points, called endpoints.
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b. What is the area of the rectangle in square units? Explain how you found your answer.
3. Each is 1 square unit. Which rectangle has the largest area? How do you know?
Rectangle A
Rectangle C
Rectangle B
The solution is, Rectangle A has the largest area.
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
from the given figure we get,
Each square is 1 square unit.
now, Rectangle A has 18 square
Rectangle C has 10 squares
Rectangle B has 8 squares
So, area of Rectangle A is 18 sq. unit
Rectangle C is 10 sq. unit
Rectangle B is 8 sq. unit
i.e. 18>10>8
Hence, Rectangle A has the largest area.
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Does the table below represent a linear function? Why or why not?
Answer:
yes
Step-by-step explanation:
because everytime you add 2 for x you add 1.8 for y
that means the difference is constant and the function is linear
Please help ASAP!
In which quadrant is (−11, −21) located?
I
II
III
IV
Answer:
3rd quadrant
since the x and the y co-ordinates are negative ,it can only fit in the third since
1st=positive, positive
2nd=negative, positive
3rd=negative, negative
4th=positve, negative
logan works as a chashier. today, he has given out 50% more nickels than dimes. if he has given out a tatal of 6.65 in nickels and dimes, how many dimes has he given out
If Logan has given out a total of 6.65 in nickels and dimes , then the number of dimes he has given out is 38 .
Let the number of nickels that Logan gave out be = n , and
the number of dimes that Logan gave out be = d ;
From the information , we know that Logan gave out 50% more nickels than dimes,
that means ; n = d + 0.5d = 1.5d ...equation(1) ;
We also know that the total amount given out in nickels and dimes is $6.65, and each nickel is worth of $0.05 and each dime is worth of $0.10,
So , n×0.05 + d×0.10 = 6.65 ;
Substituting the expression for n from the first equation into the second:
⇒ (1.5d)×0.05 + d×0.10 = 6.65 ;
Expanding and solving for d ;
we get ;
⇒ 0.075d + 0.10d = 6.65 ;
⇒ 0.175d = 6.65 ;
⇒ d = 6.65/0.175 = 38 ;
Therefore , Logan gave out 38 dimes.
The given question is incomplete , the complete question is
Logan works as a cashier. Today, he has given out 50% more nickels than dimes. if he has given out a total of 6.65 in nickels and dimes, How many dimes has he given out ?
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correct justification 2(y-5)+4=4 2y-10+4=4
The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
2(y - 5) + 4 = 4
Apply distributive property of addition. Then the equation is written as,
2(y - 5) + 4 = 4
2y - 10 + 4 = 4
Simplify the equation further, then we have
2y - 10 + 4 = 4
2y - 6 = 4
2y = 10
y = 5
The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.
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The line representing the equation part of the constraint 7x1 + 4x2 s 28 goes through the following two points (4,0) and (7,0) (0, 4) and (7,0) (4,0) and (0,7) (0, 4) and (0,7) none of the above
( 0, 7 ) and ( 0,4 ) are two points of the equation .
What Is an Equation, exactly?
An equation is a mathematical expression with two equal sides and an equal sign in between.
An equation is, for instance, 4 + 6 = 10. 4 + 6 is visible on the equal sign's left side, and 4 + 6 is visible on the equal sign's right side.
( 4,0) & ( 0,7 )
Given constraint is
7x₁ + 4x₂ ≤ 28
IF x₁ = 0
4x₂ = 28
x₂ = 7
( 0, 7 )
If x₂ = 0
7x₁ = = 28
x₁ = 4
( 4 ,0 )
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what is the volume of a round metal washer with an outer radius of 8 cm and an inner radius of 2 cm, and a thickness of 0.5 cm
The volume of the round metal washer is 94.25 cm cube.
As inferred from the question, the shape of the round metal washer is that of a hollow cylinder with:
outer radius= 8 cm
inner radius =2 cm
thickness = 0.5 cm
we know that the formula for calculating the volume of a hollow cylinder is as follows:
V = π ( [tex]R^{2}[/tex]-[tex]r^{2}[/tex])h cubic units
[ where R = outer radius, r= inner radius]
Putting the values in the above formula gives:
V= π ( 8 - 2) X 0.5
-> V= π (64-4) X 0.5 = 94.25 cm cube
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I need help please hurry I am timed on this!!!!
The factors of the polynomial are (x + 1)(x - 3).
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
The upper side of the tiles shows the expression (x + 1), and the left side shows the expression (x - 3).
In both cases, you have to consider how many + x or - x is (one +x in one case and three -x in the other case).
If you multiply the factors, you get,
(x + 1)(x - 3) = x² - 3x + x - 3
(x + 1)(x - 3) = x² - 2x - 3 .
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the statistical procedure that researchers use to identify underlying components that may exist in test without first proposing a formal model?
The statistical procedure that researchers use to identify underlying components that may exist in test without first proposing a formal model is exploratory factor analysis.
How to perform Functional Statistical AnalysisIn order to carry out a statistical analysis, we need to collect and review a sample of the data available in the research results for analysis.
While there is no single way to perform interpretive analysis, there are practices that can be replicated in any research if done in a way that is appropriate to the information provided.
These tips will allow us to carry out useful statistical analysis.
Give a clear and realistic picture of the data we have. Analyze how the data is related to the research subject. Designing a model that considers and describes the relationship between data and research subjects. Evaluate the model to determine its validity. Consider scenarios and tests using predictive analytics.Learn more about statistical analysis at https://brainly.com/question/11969248.
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a rectangular board is 1300 millimeters long and 800 millimeters wide. what is the area of the board in square meters? do not round your answer.
A rectangular board is 1300 millimeters long and 800 millimeters wide. Then, the area of the board in square meters is 104 m².
Determine the area of the boardThese are the specified parameters:
Length of the board (l) = 1300 mm
Breadth of the board (b) = 800 mm
The area of a rectangular board
A = l × b
= 1300 mm × 800 mm
= 1040000 mm²
The area of the board in square meters
To convert mm² to m², divide mm² by 10000.
Therefore
A = 1040000 mm²
= 1040000 : 10000 m²
= 104 m²
So, the area of the board in square meters is 104 m².
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At a community barbecue, Mrs. Hammond and Mr. Weber are buying dinner for their families. Mrs. Hammond purchases 1 hot dog meal and 3 hamburger meals, paying a total of $30. Mr. Weber buys 3 hot dog meals and 3 hamburger meals, spending $42 in all. How much do the meals cost?
The required cost of the meal given as a hot dog is of $6 and the hamburger is of $8.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Let's call the cost of a hot dog meal "x" and the cost of a hamburger meal "y".
From Mrs. Hammond's purchase, we know that:
x + 3y = 30 -- - - - - -(1)
From Mr. Weber's purchase, we know that:
3x + 3y = 42 - - - - - -(2)
We can use substitution to solve for one of the variables in terms of the other. If we substitute the first equation into the second equation:
3x + 3y = 42
3x + 3(30 - x)/3 = 42
3x + 30 - x = 42
2x = 12
x = 6
now,
6 + 3y = 30
3y = 24
y = 8
Thus, the required cost of the meal given as a hot dog is of $6 and a hamburger is $8.
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A water park has pools, slides, and rides that, in total, make use of 2.1 x
107 gallons
of water. They plan to add a ride that would make use of an additional 4.9 × 10³
gallons of water. Use scientific notation to express the total gallons of water made use
of in the park after the new ride is installed.
The total gallons of water made use of in the park after the new ride is installed is,
⇒ 21.0049 × 10⁶ gallons of water
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
A water park has pools, slides, and rides that, in total, make use of
2.1 × 10⁷ gallons of water.
And, They plan to add a ride that would make use of an additional 4.9 × 10³ gallons of water.
Hence, The total gallons of water made use of in the park after the new ride is installed is,
⇒ 2.1 × 10⁷ + 4.9 × 10³
⇒ 21000 × 10³ + 4.9 × 10³
⇒ (21,000 + 4.9) × 10³
⇒ 21,004.9 × 10³
⇒ 21.0049 × 10⁶ gallons of water
Thus, The total gallons of water made use of in the park after the new ride is installed is,
⇒ 21.0049 × 10⁶ gallons of water
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NEED HELP ASAP PLS! given the circle below. provide the following information.
-radius
-center
-equation
The features of the circle in this problem are given as follows:
Radius: 5 units.Center: (2,-1).Equation: (x - 2)² + (y + 1)² = 25.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center for this circle has the coordinates given as follows:
(2,-1).
The radius is the distance of any point on the circumference of the circle from the center, hence, tracing a horizontal line at y = -1, we have that:
r = 7 - 2
r = 5.
Hence the equation is given as follows:
(x - 2)² + (y + 1)² = 25.
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Please answer the questions and number them correspondingly. (Click all the screenshots and try to get all answers done please & thank you in advance.) The ones that need to be done are the questions with red boxes around them
Based on the given angles, the missing answers of the sequences uploaded screenshots are:
The vertex is ∠R; the sides are QR and RS; the angles name are ∠QRS, ∠R, and ∠SRQ; the angle is classified as right angleSupplementary VerticalSupplementaryx = 35°z = 37°∠H = 129°∠2 = 128°∠J = 17°Adjacent supplementaryVerical Adjacentx = 107°x = 38°Corresponding angles and congruentAlternate interior angles and congruentConsecutive interior angles and supplementaryAlternate exterior angles and congruentThe following answers are constructed based on the sequences of each problems not as the sequences of the uploaded screenshots.
Example 2Name of the vertex of the angle is ∠RThe sides of the angle are QR and RSThe three ways to name the angle is ∠QRS, ∠R, and ∠SRQThe angle is classified as a right angle (90°)Classifying Angles:3. Since ∠1 + ∠2 = 180°; then both are supplementary angles
4. Both ∠1 and ∠2 have equal size of angle and share no adjacent side; then both are vertical angles
5. 116° + 64° = 180°; then both are supplementary angle
8. Angles ∠3 and ∠4 are adjacent supplementary because it shares an adjacent side and its sum is 180°.
10. Angles ∠3 and ∠5 are vertical since they share no adjacent side but have equals size of angle.
12. Angles ∠1 and ∠5 are adjacent but neither complementary or supplementary because it sums are not 90° either 180°.
Finding Angle Measures:13. x and 107° are vertical angles; then:
x = 107°
15. x and 142° are supplementary angles; then:
x + 142° = 180°
x = 38°
17. ∠RST = 112°
∠RST = x + 87° = 112°
x = 35°
19. It is given that:
x and 127° are supplementary anglesx and y are vertical angles z and y are complementary angles; then:x + 127 = 180°
x = 53°
x = y = 53°
y + z = 90°
53° + z = 90°
z = 37°
Word Problems21. ∠G + ∠H = 180°
51° + ∠H = 180°
∠H = 129°
22. ∠1 = ∠2
∠2 = 128°
23. ∠J + ∠K = 90°
∠J + 73° = 90°
∠J = 17°
Practice Classifying:2. Corresponding angles and congruent
4. Alternate interior angles and congruent
6. Consecutive interior angles and supplementary
8. Alternate exterior angles and congruent
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a manufacturer of piston rings for automobile engines frequently tests the width of the rings for quality control. last week, a random sample of 15 rings were measured, and the mean and standard deviation of the sample were used to construct a 95 percent confidence interval for the population mean width of the rings. when all other things remain the same, which of the following conditions would have resulted in a wider interval than the one constructed? i. a sample size of 20 with 95 percent confidence ii. a sample size of 15 with 99 percent confidence iii. a sample size of 12 with 95 percent confidence responses
Answer:
II and III only
Step-by-step explanation:
HELP?!! PLEASE THANK U ITS DUE IN 3 MINS
what action changes the actual number of decimal places excel stores instead of just changing what is displayed? decrease decimal setting increase decimal setting round function decimal function
The correct answer is option (C). The answer is round function.
Given that,
Instead of just altering what is presented, Excel changes the amount of decimal places it really keeps.
To find : Something alters the real number of decimal places?
Number is rounded using ROUND function to a given number of digits. You can use the following formula, for instance, to round the value 23.7825 in cell A1 to two decimal places: =ROUND(A1,2) (A1,2) is 23.78 is the output of the function
Therefore, option is the right response (C). Round function is the solution.
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christoper wants to create a right trangle on a coordinate plane. he has already graphed points at (3,6) and (8,-2) and connected them with lines segment. which point could christopher place on the graph to create a right triangle
The point that creates a right triangle with the points (3, 6) and (8, -2), which Christopher could place on the graph to create a right triangle is the point (8, 7.25)
What is a right triangle?A right triangle is a triangle with one ninety degrees (90°) interior angle.
The points on the right triangle Christopher already graphed (3, 6), and (8, -2)
The property of a right triangle is one of the interior angles is 90°, therefore, the legs or two of the sides of a right triangle are perpendicular.
The slope of the line joining the specified two points is found as follows;
Slope = (-2 - 6)/(8 - 3) = -8/5
The slope of the line perpendicular to the line segment Christopher used to join the points (3, 6), and (8, -6) is 5/8
The equation of the perpendicular line is therefore;
y - 6 = (5/8)·(x - 6)
y = (5/8)·(x - 6) + 6 = 5·x/8 + 18/8
y = 5·x/8 + 18/8
When x = 8, we get; y = 5 × 8/8 + 18/8 = 7.25
Therefore, the point (8, 7.25), forms a right triangle with the points (3, 6) and (8, -2)
A point Christopher can place on the graph to create a right triangle is (8, 7.25)
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What is a reasonable product of 3 9/10 x 4 1/5
Answer:
16 19/50
Step-by-step explanation:
first make improper fractions of both 3 9/10 and 4 1/5
mutltiply the denomiator (the number on the bottom) by the whole number, add the numerator (the number on the top) and put that number over the denomiator. 3 9/10 = 39/10 and 4 1/5 = 21/5. Multiply the improper fractions. numerator x numerator and write that on the top with a line under it. Multiply the denomiators and write that on the bottom. 39*21= 819. 10*5=50. your number would be 819/50. Then divide 819 by 50. You get 16 19/50
The circle graph shows how a family budgets its annual income. If the total annual income is $100,000, what amount is budgeted for Auto expenses?
Savings
8%
Insurance
9%
Auto
14%
Clothing
15%
Food
19%
Leisure
13%
Housing
22%
Answer:
The amount budgeted for Auto expenses is $100,000 * 14% = $14,000.
Step-by-step explanation:
suppose a stick of length 1 is broken into two pieces uniformly randomly. what is the expected length of the smaller piece?
Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.
The random variable L (the length for the shorter stick) has a uniform distribution.
Thus the probability density function for L is as follows:
L = [tex]\frac{1}{0.5-0} = 2[/tex]This means 2 for all length in the range 0 - 0.5
Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.
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Use the general slicing method to find the volume of the following solid
The solid with a semicircular base of radius 15 whose cross sections perpendicular to the base and parallel to the diameter are squares The volume of the solid is __ cubic units.
(Type an exact answer)
The volume of the solid is approximately 807.08 cubic units.
Volume of Semicircular Solid w/Squared Cross-SectionsTo determine the volume of the solid, we can use the method of cylindrical shells.
Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.
The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:
r² = x² + (15-x)²
Solving for x, we get:
x = 15 * √(1 - (r/15)²)
The volume of the slice is then given by:
V = x² * (15 - x)
To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.
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calculate the value of x
The value of x considering the mean is two will be equivalent to 7.
What is the mean?The mean also known as the average is obtained by adding the data and then dividing it by the number of values. Here is an example: 3+6+4 = 13 / 3 = 4.3.
What is the missing number in this case?We know the mean is 2, based on this let's calculate the missing number:
The current number of cats: is 0+ 8 + 12 +3 =23 Based on this, the missing number would be 7, which would lead to a total of 8+12+24 = 44 cats divided by a total of 22, which means there are 2 cats per family.
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How is the sum expressed in sigma notation
Sigma notation for the sum is ∑5ⁿ⁻⁴ (where n = 1 to 5)
What is sigma notation?Sigma notation is the most easiest way of writing a very large sum of elements of a sequence in a simple manner.
∑ is the symbol that is pronounced as "sigma".
"i" or "n" is called the index of summation
Given sum,
1/125 + 1/25 + 1/5 + 1 + 5
First term a is 1/125
Common ratio r = 1/25/1/125 = 5
Sequence can be written as
aⁿ = a.rⁿ⁻¹
aⁿ = 1/125 . 5ⁿ⁻¹
aⁿ = 5⁻³. 5ⁿ⁻¹
aⁿ = 5ⁿ⁻⁴
Sigma notation can be written as
∑5ⁿ⁻⁴ where n = 1 to 5.
Hence, Sum expressed as Sigma notation ∑5ⁿ⁻⁴ (where n = 1 to 5).
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working alone, allen can build a fence in 8 hours, and danny can build the same fence in 16 hours. if after working alone for 2 hours, allen is joined by danny, how many more hours
Working alone, Allen can build 1/8 of the fence in 1 hour and working together, Allen and Danny can build 1/X of the fence in 1 hour, where X is their combined rate.
Let's say the total time required to build the fence is T hours.
After 2 hours, Allen has completed 1/8 * 2 = 1/4 of the fence.
So, the remaining work to be done is T - 1/4.
When Allen and Danny work together, their combined rate is X = 1 / (1/8 + 1/16) = 4/7.
The total time taken by them to finish the remaining work is (T - 1/4) / (4/7) = (7/4) * (T - 1/4) = 7T/28 - 7/28.
So, the total time taken to build the fence is 2 + (7T/28 - 7/28) = 2 + 7T/28 = T.
Therefore, T = 2 + 7T/28 = 2 + 7 * (8 hours) / 28 = 2 + 4 hours = 6 hours.
So, Allen and Danny took 6 - 2 = 4 hours to build the fence after working together.
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what central angle (in radians) corresponds to an arc length of 2 yd and a radius of 7 yd? round to the nearest hundredth of a radian.
The central angle corresponds to an arc length of 2 yd and a radius of 7 yd is 0.09 pi
Central angle is the angle subtended by an arc of a circle at the center of a circle. The radius vectors form the arms of the central angle. In other words, it is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle. When these two points are joined they form an arc. Central angle is the angle subtended by this arc at the center of the circle
The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.
Central angle =(s*360)/(2pir)
=we have s=2 yd
radius = 7 yd
angle = 16.5 degree = 0.09 pi
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HELP pls will mark you the brainliest
Answer:
#9 (x, y) = (6, 32)
#10 The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same and is $32
Step-by-step explanation:
The legend is missing so by looking at the graph alone we are unable to determine which color line corresponds to which kind of kite(Kites-R-Fun or Windy Kites)
However the associated table will help us determine this
The linear equation for a line is expressed as
y = mx + c
where m = slope of the line and b = y-intercept which is the y-value for the point where the line crosses the y-axis(at x = 0)
Slope m = rise/run = Δy/Δx = (y2 - y1)/(x2 - x1) for any two points (x1, y1) and (x2, y2) on the line
Let's take the two x values as x1=0 and x2=1 and use the table
For Kites-R Fun
x1 = 0 ==> y1 = 8. This is also the y-intercept, b
We see that the red line corresponds to x = 0, y = 8
x2 = 1 ==> y2 = 12
y2 - y1 = rise = Δy =12 - 8 = 4
x2 - x1 = Δx = 1 - 0 =1
Slope m = 4/1 = 4
Equation of Kites-R Fun is 4x + 8
For Windy Kites
x1 = 0 ==> y1 = 20
y-intercept = 20 or b = 20
x2 = 1 ==> y2 = 22
Rise = Δy =22 - 20 = 2
Run = Δx = 1 - 0 = 1
Slope = m, b = 20
Equation of blue line is
y = 2x + 20
The two equations are:
y = 4x + 8
y = 2x + 20
Equating right sides:
4x + 8 = 2x + 20
Move 2x to the left side and 8 to the right side:
4x + 2x + 8 - 8 = 2x - 2x + 20 -8
2x = 12
x = 6
For x = 6 the costs are the same
Plugging x = 6into equation y = 4x + 8:
y = 4(6) + 8 = 24 + 8 = 32
So the solution set is
(6, 32)
Looking at the graph we see the two lines intersect at this point
(Heck, we could have avoided all this work and just looked at the graph but I don't expect that was what they intended. You can add this as a side note)
On the second part
For Kites-R-US, each kite costs $4
The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same.
What is the surface area of the rectangular prism shown below?
The surface area of the rectangle prism is 52.05 in²
What is surface area of a prism?The total surface area of a prism is the sum of the areas of its lateral faces and its two bases.
The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
l = 7.2 in
b = 1 1/2 = 3/2
h = 1 3/4 = 7/4
SA = 2( 7.2×1.5+ 7.2 × 1.75 + 1.75×1.5)
SA = 2( 10.8 + 12.6 + 2.625)
SA = 2 ( 26.025)
SA = 52.05 in²
therefore the surface area of the rectangle prism is 52.05 in²
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Graph the line with the equation y = 1/3x + 7
Answer:
I Don.t really know the answer