Answer: y=-2x²-6x
Step-by-step explanation:
Its x-intercepts are 0 and -3, and the graph goes through the point (-1,4)
Hence we have three coordinates of the equation y=ax²+bx+c (1):
(0,0) (-3,0) (-1,4)
Let's substitute these coordinates into formula (1):
[tex]0=a(0)^2+b(0)+c\\0=a(-3)^2+b(-3)+c\\4=a(-1)^2+b(-1)+c\\\\0=0+0+c\\0=9a-3b+c\\4=a-b+c\\\\0=c\\0=9a-3b+0\\0=a-b+0\\\\c=0\\9a-3b=0\ \ (1)\\a-b=4\ \ \ \ \ (2)\\\\c=0\\\\[/tex]
Divide both parts of the equation (1) by 3 and multiply both parts of the equation (2) by -1: :
[tex]3a-b=0\\-a+b=-4\\\\[/tex]
Sum these equations:
[tex]2a=-4[/tex]
Divide both parts of the equation by 2:
[tex]a=-2[/tex]
We substitute the value of a=-2 into equation (2):
[tex]-2-b=4\\[/tex]
Divide both parts of the equation by -1:
[tex]2+b=-4\\\\2+b-2=-4-2\\\\b=-6[/tex]
[tex]Thus, \\\\y=-2x^2-6x+0\\\\y=-2x^2-6x[/tex]
A college football game is played to a sell-out crowd of 20,500 people. Student tickets are $7 while general admission tickets are $12. A
total of $176,000 was collected from ticket sales. How many people purchased student tickets? How many people purchased general
admission tickets?
people purchased student tickets and people purchased general admission tickets.
14000 student tickets and 6500 general admission tickets were purchased during the football game
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers.
Let x represent the amount of students tickets and y represent the amount of general admission tickets.
A total of $176,000 was collected from ticket sales. Hence:
7x + 12y = 176000 (1)
A college football game is played to a sell-out crowd of 20,500 people. Hence:
x + y = 20500 (2)
From the two equations:
x = 14000, y = 6500
14000 student tickets and 6500 general admission tickets
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An engineer is interested in the relationship between
the weight of a car (measured in pounds) and the fuel
economy (measured in miles per gallon of gas). To
investigate the relationship, she collects a simple
random sample of 10 cars and records their weight
and fuel efficiency. She finds the equation of the least-
squares regression line to be y=69-0.0114x, where
y is the fuel efficiency (mpg) and x is the weight (in
pounds). The residual plot is shown.
Based on the residual plot, is the linear model
appropriate?
O No, the residuals are relatively large.
O No, there is a clear pattern in the residual plot
O Yes, there is no clear pattern in the residual plot
Based on the residual plot, the linear model is appropriate as C. Yes, there is no clear pattern in the residual plot.
What is a linear model?A continuous response variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complex systems, as well as analyzing experimental, financial, and biological data. Linear regression is a statistical technique for developing a linear model.
The residual plot depicts the difference between the observed and fitted response values. The ideal residual plot, also known as the null residual plot, depicts a random scatter of points forming a band.
In this case, no clear pattern was detected.
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Answer:
it seems like the person above me is correct.
Step-by-step explanation:
Jessica found that the perimeter of her kitchen table was 18 feet she found the area of her kitchen table to be 18 ft.² what are the links and width of Jessica‘s kitchen table 
The length and width of Jessica's kitchen table are 6 ft and 3 ft or 3ft and 6 ft.
According to the question,
We have the following information:
Jessica found that the perimeter of her kitchen table was 18 feet she found the area of her kitchen table to be 18 ft.²
Now, let's take the length of the table to x ft and the width of the table to be y ft.
So, we know that following formulas are used to find the perimeter and area of rectangle:
Perimeter = 2(length+width)
2(x+y) = 18 ...(1)
Area = length*width
xy = 18
x = 18/y
Putting this value of x in equation 1:
2(18/y+y) = 18
18/y + y = 9
([tex]y^{2}[/tex]+18) = 9y
[tex]y^{2}[/tex]-9y+18 = 0
[tex]y^{2}[/tex]-6y-3y+18 = 0
y(y-6)-3(y-6) = 0
(y-6)(y-3) = 0
y-6 = 0 and y-3 = 0
y = 6 ft and y = 3 ft
Now, putting this value of y in x = 18/y:
x = 18/6
x = 3 ft
x = 18/3
x = 6 ft
Hence, the length and width of Jessica's kitchen table are 6 ft and 3 ft or 3ft and 6 ft.
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The following inequalities represent a system.
y ≥ −5x + 2
y > 3x − 1.5
Which of the following graphs represents the system?
The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.
The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.
The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.
The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.
A graph which represents the system of inequalities is: B. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
The rules for writing an inequality.In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality plotted on a graph and these include the following:
The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).Additionally, the y-value for this inequality graph intersects the x-axis at -1.5 and the boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be represented with the greater than (>) inequality symbol.
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An assistant is in charge of ordering lunch for the monthly office meeting. For the first month, she orders five Falafel wraps, fifteen Turkey BLT sandwiches, and twenty hot Ham and Swiss paninis for a total of $260. The next month, she orders eight Falafel wraps, eighteen Turkey BLT sandwiches, and 14 hot Ham and Swiss paninis for a total of $263. For the third month, she orders twelve Falafel wraps, 16 Turkey BLT sandwiches, and twelve hot Ham and Swiss paninis for a total of $258. How much does each sandwich cost?
The cost of Falafel wraps is $5.5, the cost of Turkey BLT sandwiches is $7.5, and the cost of hot Ham and Swiss paninis is $6.
How much does each sandwich cost?In order to determine the cost of each sandwich, we would assign variables to the cost of sandwiches ordered, and then translate the word problem into algebraic expression as follows:
Let the variable f represent the cost of Falafel wraps.Let the variable t represent the cost of Turkey BLT sandwiches. Let the variable h represent the cost of hot Ham and Swiss paninis.Therefore, translating the word problem into an algebraic expression, we have the following;
For the first month ⇒ 5f + 15t + 20h = 260 ......equation 1.
The next month ⇒ 8f + 18t + 14h = 263 ......equation 2.
For the third month ⇒ 12f + 16t + 12h = 258 ......equation 3.
Next, we would solve the system of algebraic expressions simultaneously.
Multiplying equation 1 by 12/5 and subtracting it from equation 3, we have:
6.25t - 24h = -366 ......equation 4.
Multiplying equation 2 by 5/8 and subtracting it from equation 1, we have:
3.75t + 11.25h = 95.625 ......equation 5.
Solving equation 4 and equation 5, we have:
Falafel wraps, f = $5.5
Turkey BLT sandwiches, t = $7.5
Hot Ham and Swiss paninis, h = $6.
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Points G (-5,-8) and H (3,7) are plotted on a coordinate grid. What is the distance between points G and H?
The distance between the points is 17
A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes are defined as coordinates. The x- and y-values are commonly represented by (x,y).
Given that
Points G (-5,-8) and H (3,7) are plotted on a coordinate grid
We have to find the distance between points G and H
The formula for calculating the distance between two points is given by
= √((3-(-5))2 + (7-(-8)2)
= √((3+5)2 + (7+8)2)
= √((8)2 + (15)2)
= √(64 + 225)
= √289
=17
Therefore the distance between the points is 17
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Simplify 16^3/4
Note: I understand the next part is to break it down as (^4√16)^3 but I am confused how you continue from there
The simplified form of the expression; 16^¾ as given in the task content is; 8.
What is the simplified form of the expression given in the task content?It follows from the task content that the simplified form of the expression as given in the task content is to be determined.
Since the given expression is; 16 ^ ¾.
It follows from the rational exponents law of indices that we have;
⁴√16³
where 16³ = 4096
Therefore, we have; ⁴√4096
The result is therefore; ⁴√4096
= 8.
On this note, the simplified form of the expression 16^¾ is; 8.
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Need help asap with these 4 quiestions. will give brainliest.
all are linked as pictures, one has the figure and question and another picture for the answers to choose from
Answer:
Question 1: We need to know whether Angles P and N are congruent or not.
Question 2: Cannot be proven congruent
Question 3: AAS Congruence Theorem
Question 4: ASA Congruence Postulate
Step-by-step explanation:
Background info: The information (congruence lines on sides and angles) is read counterclockwise (starting from the very left to right).
Question 1: In order to prove the triangles congruent with the AAS, we need two pairs of congruent angles and one pair of congruent sides. We still need one more pair of congruent angles. Since the triangle is read counterclockwise, the angle to the left of the current congruent angle given needs to be given to us. This is angles P and N.
Question 2: For this answer, the triangles cannot be proven congruent because we are only given three congruent angle pairs. This means that it should be the "AAA" Theorem, however, it doesn's exist due to the fact that the triangles could still be two different sizes despite the fact that the angles are the same. In order to prove this congruent, we would need info on congruent sides.
Question 3: Reading the triangle left to right, we see a congruent angle pair (A), another congruent angle pair (A), and a congruent side pair (S). Putting this together, we get AAS.
Question 4: Reading the triangle left to right, we see an angle pair (A), a side pair (S), and an angle pair (A). Putting this together, we get ASA.
Hope this helps! (No guarantees it's 100% correct)
Jane has $5.00. she purchased a biscuit which cost $0.79 and she purchased a soda for $1.30. How much would she receive as change? Your answer
Since Jane has $5.00 and purchased a biscuit and soda for $1.30. The amount that she receive as change is $ 2.91.
What does math subtraction mean?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.
Note that An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol is used to denote subtraction,
So 5.00 - 0.79 - 1.30
= 2.91
Therefore, one can say her reminder as change is 2.91 dollars.
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Triangle ABC is shown with exterior ∠z.
triangle ABC with angle A labeled 97 degrees, angle B labeled 34 degrees, and side AC extended with angle z labeled as exterior angle to angle C
Determine m∠z.
49°
97°
131°
146°
The value of angle z in the triangle illustrated is C. 131°.
What is the value of angle z?It should be noted that the value of the total angles in a triangle is 180°. In this case, the other two angles are given as 97° and 34°.
The other angle will be:
= 180° - (97° + 34°)
= 180° - 131°
= 49°
Therefore, the value of the angle z will be:
= 180° - 49° (angle on a straight line)
= 131°
Therefore, the correct option is C.
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Answer: C 131
Step-by-step explanation:
Describe the transformations of the graph y = (x - 3)³-2
Use the graph of y=h'(x) below, to estimate point(s) of inflection for the function h(x) , as
well as the intervals on which h(x) is concave up and concave down. Explain your reasoning.
Answer:
At x = 0 and at x = 2 there are points of inflections. In the intervals of
(negative infinity, 0) and (2, positive infinity) it is concave up.
In the intervals of (0, 2) it is concave down.
Step-by-step explanation:
Inflection points are point where h'(x) changes from increasing to decreasing and vise versa.
When a graph is concave up, h'(x) is increasing.
When a graph is concave down, h'(x) is decreasing.
r marks in percent. other earns Rs 27,000 and spends Rs 10,800 every month. Express her expenditure in percent. (ii) Calculate her saving
The expenditure of the man in percent is 40% and his savings is Rs16200 .
In the question ,
it is given that ,
amount earned by the man = Rs 27000
amount spend by the man = Rs 10800
So , the expenditure in percent can be calculated using the formula ,
we get ,
= (expenditure)/(total earning) × 100
= 10800/27000 × 100
= 0.4 × 100
= 40%
the savings = earning - expenditure
savings = 27000 - 10800
= 16200
Therefore , The expenditure of the man in percent is 40% and his savings is Rs16200 .
The given question is incomplete , the complete question is
A man earns Rs 27,000 and spends Rs 10,800 every month. Express her expenditure in percent also calculate his savings .
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Solve the equation −15 + x = −18 for x.
A. -3
B. 3
C. 33
C. -33
Answer:
-3
Step-by-step explanation:
x= -18 + 15 = -3
Peter plans to start his own business selling T-shirts each T-shirt costs him $2.50 to make he plans on selling each T-shirt for $14.50 What percent does Peter plan to mark up his shirts?
Peter plans to 480 percent increase for his shirts.
According to the question,
We have the following information:
Peter plans to start his own business selling T-shirts. Each T-shirt costs him $2.50 to make. He plans on selling each T-shirt for $14.50.
We know that the following formula is used to find the percent increase when the final price and initial price is given:
Percent increase = 100*(final-initial)/initial
(More to know: the same formula can be used to find the percent decrease for a product.)
Percent increase = 100*(14.50-2.50)/2.50
Percent increase = 100(12)/2.50
Percent increase = 480%
Hence, Peter plans 480% of increase for his shirts.
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Last week, Lisa sold 20 hand-engraved watch bands, earning a total profit of $105.00. She plans to make 50 engraved watch bands to sell at the community art fair. If she sells all 50 watch bands, how much profit can Lisa expect to earn?
$
Answer:
$262.50
Step-by-step explanation:
20 : 105 = 50 : x
x = (50 * 105)/20
x = (5 * 105)/2
x = 525/2
x = 262.50
Answer: $262.50
Step-by-step explanation:
What I did was divide the $105 by 20 and got $5.25. I then multiplied $5.25 by 50 since that's how many she's going to sell and got $262.50.
two people X and Y are finishing some job together in 8 hours. First person X would the same job finished 12 hours faster then the person Y.
For how many hours would each person alone finished this job.?
Answer:
4
Step-by-step explanation:
Welcome to Gboard clipboard, any text you copy will be saved here.
Given the triangle below, what is the value of y?
50°
50%
3y-10
y+20
Answer:
y = 15
Step-by-step explanation:
the triangle has congruent base angles of 50°
This means the triangle is isosceles with the 2 legs being congruent, so
3y - 10 = y + 20 ( subtract y from both sides )
2y - 10 = 20 ( add 10 to both sides )
2y = 30 ( divide both sides by 2 )
y = 15
5. Given the right triangle JKL, identify the locations of sides j, k, and I in relation to angle L
in terms of opposite, adjacent, and hypotenuse.
HELP
In relation to the angle L of the right triangle the sides are as follows:
l = opposite sidek = hypotenusej = adjacentHow to name the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.
The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.
Let's identify the sides j, k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.
Therefore,
l = opposite sidek = hypotenusej = adjacentThe hypotenuse side is the longest side of a right triangle.
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Answer the following questions for the function, please see attached picture
Answer:
concave down: ( negative infinity, 0)
concave up: (0, positive infinity)
minimum: x = 4
maximum: x=-6
Step-by-step explanation:
At a livestock market, one customer purchased 4 sheep and 2 cows for a total of $1660. Another customer purchased 3 sheep and 5 cows for a total of $2925. Create a system of equations and solve it with substitution or elimination, and find the price of a sheep, and the price of a cow.
Answer:
[tex]s \approx \$182.14[/tex]
[tex]c \approx \$435.72[/tex]
Step-by-step explanation:
Set up a system of equations, where s is the cost of a sheep and c is the cost of a cow:
[tex]4s + 2c = \$ 1660[/tex], [tex]3s + 5c = \$ 2925[/tex]
First, isolate c in the first equation.
[tex]4s + 2c = \$ 1660[/tex]
[tex]2c = \$ 1660 - 4s[/tex]
[tex]c = \$ 840 - 2s[/tex]
Next, substitute this value into the second equation:
[tex]3s + 5c = \$2925[/tex]
[tex]3s + 5(\$840 - 2s) = \$2925[/tex]
and simplify.
[tex]3s + \$4200 - 10s = \$2925[/tex]
[tex]-7s = -\$1275[/tex]
[tex]7s = \$1275[/tex]
[tex]s \approx \$182.14[/tex]
Finally, plug this value into the first equation to get the value of c:
[tex]4(\$182.14) + 2c = \$1660[/tex]
[tex]2c = \$1600 - \$728.57[/tex]
[tex]c \approx \$435.72[/tex]
So, a sheep costs about $184.14, and a cow costs about $435.72.
10. Find point W on the y-axis so that VW + XW is a minimum given V(2, 3) and
X(-2,-1).
10. The coordinates of the point W on the y-axis that makes VW + XW a minimum which is on the straight line joining V and X is W(0, 1)
What is a straight line in mathematics?A straight line is a line without a curve, and the equation of a straight line in mathematics is y = m·x + c
10. The given points are V(2, 3) and X(-2, -1)
The location of the point W is on the y-axis
The shortest distance between two points is a straight line.
When VW + XW is a minimum, W is on the straight line joining V and X, such that by the segment addition postulate, VX = VW + XW
The slope of the line joining V and X, m, is found as follows;'
[tex]m=\dfrac{-1- 3}{-2 - 2} =1[/tex]
The equation of the line in point and slope form is therefore;
y - 3 = 1 × (x - 2) = x - 2
y = x - 2 + 3 = x + 1
The equation of the line VW in the slope and intercept form, y = m·x + c is y = x + 1
The y-intercept is therefore, c = 1
The x-coordinates of a point on the y-axis is x = 0
The x-coordinate of W is 0
The y-coordinate of the point W on the line VX is given by the y-intercept of the line VX
The y-intercept of the line VX = 1 = The y-coordinate of the point W
The coordinate point W so that VW + XW is a minimum is W = (0, 1)
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I need help with this math problem
⇒Perimeter is the summation of all the sides of a shape
⇒Note for some sides I will not be able to explain because I cannot draw to show you.
P=S+S+S+S+S+S
P=4+8+12+2+8+4
P=38
⇒For the Area Divide the shape into two shapes Note it will results into two rectangles with the 1st rectangle having measurements L=12 and W=2
and the 2nd rectangle having L=8 and W=4 After finding the areas of both these rectangles ADD the areas for they will give you the area of the whole shape
[tex]1^{st} _{rectangle area} =L*W\\1^{st} _{rectangle area}=12*2\\\\\\1^{st} _{rectangle area}=24[/tex]
⇒[tex]2^{nd} _{rectangle area}=L*B\\2^{nd} _{rectangle area}=8*4\\2^{nd} _{rectangle area}=32\\\\total_{shape \\area}=24+32\\[/tex]
The Area of the shape is 56
note if you were to insert the unit of measurement you were going to put in the square measurement.
Please do not hesitate to ask failure to understand.
NO LINKS!! Use the diagram below to answer the following questions.
Answer:
a) WS, ZV, YU
b) VU
c) ZW
d) WXY
e) None
f) TU, TV, UV, XY, XZ, YZ
g) SW, VX, VZ, WX, WZ, YZ
Step-by-step explanation:
A prism is a polyhedron that has:
Two bases that are congruent and parallel to each other.Lateral sides that are parallelograms and link the two bases.Height that is the distance between the two bases.From inspection of the give diagram, the figure appears to be a quadrilateral prism with bases STUV and WXYZ.
Parallel line segments
Parallel line segments lie on parallel lines. Parallel lines are lines on a plane that never meet and are the same distance apart.a) Segments parallel to XT:
WS, ZV, YUb) Segments parallel to ZY:
VUc) Segments parallel to VS:
ZWPlanes
A plane is a flat, two-dimensional surface that extends into infinity. A plane can be named by the letters naming three non-collinear points in the plane.Parallel planes are planes that never intersect.d) Planes parallel to plane STU:
WXYe) Planes parallel to plane UVZ:
NoneSkew lines
Skew lines are a pair of non-coplanar lines that:
Do not intersect.Are not parallel to each other.f) Segments skew to SW:
TU, TV, UV, XY, XZ, YZg) Segments skew to UT:
SW, VX, VZ, WX, WZ, YZHow many proper subsets does the set Z, Roman numerals, have? Z={ I, V, X, L, C, D, M, MD }.
The number of proper subsets of Z = 255.
What is a subset ?Subsets are a subset of the mathematical idea known as Sets. A set is a group of items or components that are enclosed in curly braces, such as "a,b,c,d." Set B is said to be a subset of A if set A is a collection of even numbers and set B contains the numbers 2, 4, and 6. B is designated as BA and A is the superset of B.
The number of proper subsets can be calculated by the formula 2 raise ti the power n where n represents the number of elements in the set
Here, n = 8
thus [tex]2^{n} = 2^{8}[/tex]
which is equal to 256
However since one of the subsets of Z is itself it is not a proper subset
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Find the percent increase from 50 to 54.
A friend has given you left-over landscaping bricks. You decide to make a garden bed and surround it with the bricks. There are 74 bricks, and each brick is 8 inches long. You would like the garden bed to be slightly more than twice as long as it is wide, as shown in the diagram below. You have also given yourself a budget of $150 for additional materials should you need them. Your local home improvement store sells the same bricks for $1.98 per brick. The displayed sides present the number of bricks on each side, where x is a number of bricks.
The equation representing the perimeter is 6x + 2
The number of bricks for the width is 12 the number of bricks for the length is 25
The length would be 200 inches, the width would 96 inches
How to solve for the perimeter1. The perimeter of the garden bed is the perimeter of a rectangle
= 2( L + B)
where L = 2x + 1
B = x
we have to put the values in the formula
2((2x + 1) + (x))
2(3x + 1)
= 6x + 2
2. To get the length of each side we have
total bricks = 6x + 2
74 = 6x + 2
72 = 6x
x = 72 / 6
x = 12
length = 2x + 1
= 2 * 12 + 1
= 25 bricks
hence the width = 12 bricks
length = 25
c. The length would be 25 bricks x 8 inches
= 200 inches
The width = 12 x 8
= 96 inches
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complete question
(Image: Rectangle with one side equaling x and the other side equaling 2x+1)
Assessment Instructions Show and explain all steps in your responses to the following parts of the assignment.
Part 1: Write an equation representing the perimeter of the garden bed.
Part 2: Calculate how many bricks are used on each side.
Part 3: Determine the length of each side.
Justin is designing a drink container in the shape of a rectangular prism.
The container must be made out of 254 cm² of plastic.
Will the container be large enough to hold 1 cup of liquid? Justify your answer.
(1 cup = 236 cm³)
The container is large enough to hold 1 cup of liquid.
Will the container be large enough?From the information, Justin is designing a drink container in the shape of a rectangular prism and the container must be made out of 254 cm² of plastic.
In this case, since 1 cup = 236cm², it can be seen that 254cm² is more than 236cm².
Therefore, the container is large enough.
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Solve the equation for V.
P = IV
Enter the value that belongs in the
green box.
V
v = 8
The value of of V in the equation is P / I.
How to make a variable the subject of the formula?The equation given is P = IV and we were asked to solve for V. This means we should make V the subject of the formula in the equation.
The subject of a formula is the variable which is expressed in terms of the other variables.
Therefore, we have to express V in terms of other variables.
Hence,
P = IV
divide both sides by I
[tex]\frac{P}{I} = \frac{IV}{I}[/tex]
Hence,
V = p / I
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Please help its urgent!
Applying the midsegment theorem:
a. x = 17; y = 2
b. Length of DF is: 20 units.
How to Apply the Midsegment Theorem?According to the midsegment theorem:
Length of GH = half the length of EF
Given the following:
GH = x - 3EF = 28GH = 1/2(EF)
Substitute:
x - 3 = 1/2(28)
x - 3 = 14
x - 3 + 3 = 14 + 3
x = 17
DH = HF
DH = y + 8
HF = x - 7
Therefore:
y + 8 = x - 7
Plug in the value of x
y + 8 = 17 - 7
y + 8 = 10
y = 10 - 8
y = 2
Length of DF = y + 8 + x - 7
Plug in the values of x and y:
Length of DF = 2 + 8 + 17 - 7
Length of DF = 20 units.
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