Answers
The slope intercept form of the equation is y = [tex]\frac{1}{2}x+2[/tex].
What is slope intercept form of the equation?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.
Here the given line coordinates are [tex](x_1,y_1) = (2,3)[/tex] and [tex](x_2,y_2)=(-4,0)[/tex].
Now using slope formula , slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> m = [tex]\frac{0-3}{-4-2}=\frac{-3}{-6}=\frac{1}{2}[/tex]
Now using equation formula then [tex]y-y_1=m(x-x_1)[/tex]
=> y-3= [tex]\frac{1}{2}[/tex] (x - 2)
=> 2y-6 = x-2
=> 2y = x-2+6
=> 2y = x+4
=> y = [tex]\frac{1}{2}x+2[/tex]
Hence the slope intercept form of the equation is y = [tex]\frac{1}{2}x+2[/tex].
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Related Questions
the carrollton molding company molds plastic handles for certain southwire products. it cost them $0.30 for to make each handle plus $2082 per week to keep their molding machine operating. the company sales each handle for $1.30. how many handles must be sold weekly to break even?
Answers
To break even, Carrollton Molding Company needs to sell 1602 plastic handles per week.
Carrollton Molding Company molds plastic handles for certain Southwire products. It costs them $0.30 to make each handle plus $2082 per week to keep their molding machine operating.
The company sells each handle for $1.30.The break-even point (BEP) is defined as the point at which total revenues equal total costs. The company must sell enough units to cover all of its fixed and variable costs to reach the break-even point. The formula to calculate the break-even point is:
Break-even point = Fixed costs / (Selling price per unit - Variable costs per unit)Given, Fixed costs = $2082Selling price per unit = $1.30Variable costs per unit = $0.30Substituting these values in the formula to calculate the break-even point, Break-even point = $2082 / ($1.30 - $0.30)Break-even point = $2082 / $1.00Break-even point = 2082So, Carrollton Molding Company needs to sell 2082 units to break even.
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which statement about the graph is true?
Answers
The 1st statement is true about the graph. Here the graph is a function with domain {0≤x≤5} and the range {-6≤y≤0}.
What are graphs?An organised representation of the data is all that the graph is. It facilitates our understanding of the facts.
The Latin term datum, which means "something delivered," is where the word data originated.
The development of a research question is followed by the ongoing observational collection of data.
Here in the question,
The graph is a function with domain {0≤x≤5} and the range {-6≤y≤0}.
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Rewrite (5)/(6)x+2=(7)/(8) so that is doesn't have any fractions. Don't use decimals in the answer.
Answers
The equation (5)/(6)x+2=(7)/(8) when rewritten without fraction has a representation of 40x + 96 = 42
Rewriting the equation without fractionGiven that we have the following
(5)/(6)x+2=(7)/(8)
When the brackets are removed, we have the following equation
5/6x + 2 = 7/8
Multiplying through the equation by 6
So, we have
6 * (5/6x + 2 = 7/8)
When the products are evaluated, we have
5x + 12 = 6 * 7/8
Multiplying through the equation by 8
So, we have
8 * (5x + 12 = 6 * 7/8)
When the products are evaluated, we have
40x + 96 = 42
Hence, the solution is 40x + 96 = 42
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An electronics store placed an ad in the newspaper showing LED TVs for sale. The ad says " Our LED TV's average $700." The prices of the LED TVs are $1200, $1000, $1449, $899, $700, $1100, $1295, and $700.
Find the mean, median, and mode of the prices.
b. Which measure is the store using in their ad? Why did they choose to use it?
The store is using the ___ because it ____
Answers
Answer:
median, and mode
Step-by-step explanation:
Kiara bought a box of cereal that weighs 1 7/16 pounds. During one week, she user about 1/2 of a pound of the cereal. Which are two reasonable estimates for how much,in pounds,the box of cereal weighs now
Answers
The box of cereal now weighs approximately 0.9 pounds and 1.3 pounds.
To estimate the weight of the cereal in the box now, we must subtract the amount of cereal used during the week from the total weight of the box when Kiara bought it.
The total weight of the box when Kiara bought it is 1 7/16 pounds. To convert this fraction to a decimal, divide the numerator (7) by the denominator (16): 7/16 = 0.4375.
The amount of cereal used during the week is 1/2 of a pound. To convert this fraction to a decimal, divide the numerator (1) by the denominator (2): 1/2 = 0.5.
Subtract the amount of cereal used from the total weight of the box: 0.4375 - 0.5 = -0.0625.
Since the result is negative, we can approximate the weight of the cereal in the box now as 0.9 pounds. We can also round the result to the nearest hundredth: 0.4375 - 0.5 = -0.0625 = 0.94 pounds.
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What is the area of this composite shape?
Answers
Answer:
Step-by-step explanation:
firstly you have to cut the composite shape to rectangles and triangle or even more but the shape have already been calculated so if you cut it on the rectangle the area will be side × side which it is equal to 8 × 7≈ 56
while on that small triangle
In
Circle C,
the diameter is 30 units long,
CE= 6x, and m
Find x.
Answers
The diameter of circle C is [tex]x[/tex], which is [tex]5[/tex].
What in geometry is a circle?A circle is the collection of all points on a plane that are at a specified distance from another point (the radius) (the centre). A radius is any distance separating a point on a circle from its center. Any two radii are equal in length under the concept of a circle.
What do you call a half circle?A semicircle is a half circle produced by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends.
Since [tex]CE[/tex] is a radius of the circle and the diameter is [tex]30[/tex] units long, we know that [tex]CE[/tex]is half the length of the diameter:
[tex]CE = 1/2[/tex](diameter)[tex]= 1/2([/tex]30 units)[tex]= 15[/tex] units
We are given that [tex]CE = 6x[/tex], so we can solve for [tex]x[/tex]:
[tex]CE = 6x = 15[/tex]
[tex]x = 15/6[/tex]
[tex]x = 2.5[/tex]
Now, we can use the fact that angle [tex]CED[/tex], where [tex]D[/tex] is the center of the circle, is a central angle that intercepts arc [tex]CD[/tex], to find the measure of angle [tex]CED[/tex].
Since the diameter of the circle is a straight line, it forms a [tex]180[/tex] degree angle at its endpoints. Therefore, angle [tex]CED[/tex] is half of this angle, which is:
angle [tex]CED = 1/2(180 degrees) = 90[/tex]degrees
We are given that angle [tex]CED[/tex] is [tex]30[/tex] degrees, so we can set up an equation:
angle [tex]CED = 30 = 6x[/tex]
Simplifying and solving for [tex]x[/tex]:
[tex]6x = 30[/tex]
[tex]x = 30/6[/tex]
[tex]x = 5[/tex]
Therefore, [tex]x[/tex] is equal to [tex]5[/tex].
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Use point-slope form to write the equation of a line that passes through the point
(2,8) with slope - 1/3
Answers
Answer:
[tex]y - 8 = - \frac{1}{3} (x - 2)[/tex]
What is the solution set of this system of equations?
y = -x^2 + 2x + 4
x + y = 4
A. (7, -3) and (4, 0)
B. ( 7, -3) and (0, 4)
C. (0, 4) and (4, 0)
D. (0, 4) and (3, 1)
Answers
The solution set of this system of equations (C) (0, 4) and (4, 0).
Define simultaneous equationSimultaneous equations refer to a set of two or more equations that need to be solved together to determine the values of the variables that satisfy all the equations.
Given:
y = -x²+ 2x + 4
x + y = 4
We can substitute the first equation into the second equation to get:
x + (-x² + 2x + 4) = 4
Simplifying, we get:
-x² + 3x = 0
Factorizing, we get:
x(-x + 3) = 0
So the possible values of x are x = 0 and x = 3.
If x = 0, then y = 4 (from the second equation).
If x = 3, then y = -3 (using the first equation).
Therefore, the solution set of the system of equations is (0, 4) and (3, -3).
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what is the correct answer answer
Answers
Line segment BD is 12 units
Using the pythagorean theorem a^2 + b^2 = c^2
Find the total number of outcomes that are possible. Selecting a letter from the word TROPHY and a day from the month of May.
Answers
The total number of outcomes that are possible is 186.
There are different ways to solve the problem of finding the total number of outcomes when selecting a letter from the word TROPHY and a day from the month of May. One way is to use the Multiplication Rule of Counting, which states that if there are n1 ways to perform the first task and n2 ways to perform the second task, then there are n1 x n2 ways to perform both tasks.
Let's apply this rule to the given problem.
1. Selecting a letter from the word TROPHY: There are 6 letters in the word TROPHY. Therefore, there are 6 ways to select a letter from the word TROPHY.
2. Selecting a day from the month of May: There are 31 days in the month of May. Therefore, there are 31 ways to select a day from the month of May.
Using the Multiplication Rule of Counting, the total number of outcomes that are possible is the product of the number of ways to perform each task:
Total number of outcomes = 6 x 31 = 186.
Therefore, there are 186 possible outcomes when selecting a letter from the word TROPHY and a day from the month of May.
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Use a trigonometric ratio to solve for y. Round to two decimals places as necessary giving brainliest to whoever gets the correct answer. Image is below
Answers
The value of height of triangle is 12.3 units.
Define triangleA triangle is a polygon with three sides, three angles, and three vertices (or corners). It is one of the most fundamental shapes in geometry and has many unique properties that make it a useful tool in mathematics and science.
The sum of the three interior angles of a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the lengths of the other two sides.
Given;
Triangle is right angle
hypotenuse=18 units
Using trigonometric formula
sin43=y/18
.68=y/18
y=12.3
Value of height of triangle is 12.3 units.
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what number is 3.5% more than 26?
how do you solve this
txs for the help
Answers
what number is 3.5% more than 26?
Answer:
26.91Step-by-step explanation:
3.5%=0.035
0.035*26=0.91
26+0.91=
26.91
SOMEONE PLEASE HELP ME WITH QUESTION 22
Answers
Answer:
24pi
Step-by-step explanation:
WILL MARK BRRRRRRRRRRRRRRRRRRRAAAAAAAAAAAAAAAIIIIIIIIIIIIIIIIIIIINNNNNNNNNNNNNNNNLLLLLLLLLLLLLLLLLIIIIIIIIIIIIIIIEEEEEEEEEEEEEEEEEESSSSSSSSSSSSSSSSSSSSSTTTTTTTTTTTTTTTTTTTTTTT
I have a fair die with sides 1, 2, 3, 4, 5, 6. I throw the die three times. Determine the probability that the third roll is double the sum of the first two rolls.
Answers
The only way for each roll are {1,2,3,4,5,6}, and since the die is fair, each outcome is equally likely.
Now, we need to find the cases where X3 is double the sum of X1 and X2. This can happen in the following ways:
If X1+X2 = 1, then X3 must be 2.
If X1+X2 = 2, then there is no possible value of X3 that satisfies the condition.
If X1+X2 = 3, then there is no possible value of X3 that satisfies the condition.
If X1+X2 = 4, then X3 must be 8.
If X1+X2 = 5, then there is no possible value of X3 that satisfies the condition.
If X1+X2 = 6, then X3 must be 12.
If X1+X2 = 7, then there is no possible value of X3 that satisfies the condition.
If X1+X2 = 8, then X3 must be 16.
If X1+X2 = 9, then there is no possible value of X3 that satisfies the condition.
If X1+X2 = 10, then X3 must be 20.
If X1+X2 = 11, then there is no possible value of X3 that satisfies the condition.
If X1+X2 = 12, then X3 must be 24.
Therefore, there are 5 possible outcomes that satisfy the condition, out of a total of 6^3 = 216 possible outcomes (since each roll has 6 possible outcomes). So the probability of X3 being double the sum of X1 and X2 is:
P(X3 is double the sum of X1 and X2) = 5/216 ≈ 0.0231
So, the probability of the third roll being double the sum of the first two rolls is approximately 0.0231.
Which expression is equivalent to pq?
p + q
p - q
p Over q
qp
Answers
The expression pq represents the product of two variables p and q.only the expression qp is equivalent to pq. Thus, option D is correct.
What is the expression equivalent?Let's explore each of the given expressions and see if any of them are equivalent to pq.
p + q: This expression represents the sum of two variables, p and q. It is not equivalent to pq because addition represents combining two quantities, whereas multiplication (represented by pq) represents repeated addition of the same quantity.
p - q: This expression represents the difference between two variables p and q. It is also not equivalent to pq because subtraction represents taking away one quantity from another, whereas multiplication (represented by pq) represents repeated addition of the same quantity.
p / q: This expression represents the quotient of two variables p and q. It is not equivalent to pq because division represents splitting a quantity into equal parts, whereas multiplication (represented by pq) represents repeated addition of the same quantity.
qp: This expression also represents the product of two variables p and q, but the order of the variables is reversed.
However, the commutative property of multiplication states that the order of factors does not affect the result of the multiplication operation. Therefore, qp is equivalent to pq.
Therefore, only the expression qp is equivalent to pq.
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3. Susan picked a squash that weighed lb. Larry picked a 8/15 lb
squash that weighed 1/4 as much as Susan's squash. How
much did Larry's squash weigh?
Answers
Answer
8/60 = 2/15
Step-by-step explanation: to get 60 times it by 4 so 8/60 then simplify it by 4 to get 2/15
Find the area of the figure below. (Hint : Area = π•r^2)
Answers
Question 7 (Multiple Choice Worth 2 points)
(Equivalent Algebraic Expressions MC)
Which is an equivalent expression for
d1¹2
2
11d¹2
2
11d
00.2d¹2
4d-³
22d⁹
?
Answers
According to the given information, option (b) is the correct answer.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent quantities or values that can vary, depending on the values assigned to the variables in the expression. Algebraic expressions can be simple or complex, and they can have one or more variables.
b) 2/11d¹² is the equivalent expression for 4d⁻³ /22d⁹.
To simplify the expression, we can use the rule of negative exponents: d⁻ⁿ = 1/dⁿ
So, 4d⁻³ /22d⁹ = 4/22d¹² = 2/11d¹²
Therefore, option (b) is the correct answer.
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Please help me find the lengths!
Answers
The value of length OP is √65
The value of length PQ is √65
The value of length QR is √65
The value of length RO is √65
What is distance between two point ?Distance between two points is the length of the line segment that connects the two points in a plane.
The distance between two points is given as ;
d = √ (y2-y1)² + (x2-x1)²
The slope of a line = y2-y1)/x2-x1. This means the value of y2-y1 and x2-x1 have been calculated for each line.
Length OP = √ 4²+7²
= √ 16+49
= √ 65
length PQ = √8²+1²
= √ 64+1
= √65
length QR = √ 4²+7²
= √ 16+49
= √ 65
length RO = √8²+1²
= √ 64+1
= √65
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ajay decides to research the relationship between the length in inches and the weight of a certain species of catfish. he measures the length and weight of a number of specimens he catches then throws back into the water. after plotting all his data, he draws a line of best fit. what does the slope of the line represent?
Answers
The slope of the line of best fit represents the change in the average weight of the catfish for every one-unit change in the length of the catfish. It gives an indication of the strength and direction of the relationship between the length and weight of the catfish.
A positive slope indicates that as the length of the catfish increases, its weight tends to increase as well, while a negative slope indicates the opposite. The magnitude of the slope indicates how steeply the weight changes with respect to the length. A larger slope indicates a stronger relationship, while a smaller slope indicates a weaker relationship.
Thus, the slope of the line of best fit can provide valuable insights into the relationship between the length and weight of the catfish and can be used to make predictions about the weight of the catfish for a given length.
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The scale on the map is 1:25000
How many kilometres on the ground is represented by 6cm on the map?
Answers
Answer: 150,000 km
Step-by-step explanation: If every centimeter is equal to 25000 kilometers, than 6 x 25000 = 150,000.
Answer:
1.5 km
Step-by-step explanation:
1 kilometer = 1000 meters and 1 meter = 100 cm, so 1 km = 100,000cm
If the scale on the map is 1:25,000, 6cm on the map = 150,000 cm
Since 1 km = 100,000 cm, 1 km/100,000 cm = 1
150,000 cm x 1 km/100,000 cm = 1.5 x 1km = 1.5 km
Here is a graph of the equation 2x-y=1 are the points (0,1/2) and (-7,-3) solutions to the equation 
HELPPPP ASAP
Answers
Neither of the two points is a solution of the linear equation.
Are the points solutions of the linear equation?Here we have the linear equation.
2x - y = 1
And we have the graph of this line.
We want to check if the points (0, 1/2) and (-7, -3) are solutions.
You can do this in two ways, one is finding the points on the coordinate axis and check if the points lie on the line, the other is replace the values in the eequation and see if it becomes true.
Because the graph is really small in the image, I will do the second one.
For (0, 1/2) we have:
2*0 - 1/2 = 1
0 - 1/2 = 1
-1/2 = 1
This is false.
For the second (-7, -3) we have:
2*-7 - (-3) = 1
-14 + 3 = 1
-11 = 1
This is false.
Neither of the points is on the line.
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Is this a right triangle? 8 cm ,10cm with a base of 12cm
Answers
The equation is true, which means the given triangle is a right triangle.
What is triangle?A triangle is a geometric shape that is formed by connecting three non-collinear points with straight line segments. These points are called vertices of the triangle, and the line segments are called sides. The angles formed by the intersection of these sides are called interior angles of the triangle. Triangles are used in many areas of mathematics, including geometry, trigonometry, and calculus. They also have practical applications in fields such as engineering, physics, and architecture, where they are used to calculate measurements and solve problems involving angles and distances.
Here,
To determine whether the triangle is a right triangle or not, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the sides are given as 8 cm, 10 cm, and 12 cm. We can check if this triangle is a right triangle by verifying if the Pythagorean theorem holds true.
Let's label the sides as follows:
a = 8 cm (one of the legs)
b = 10 cm (the other leg)
c = 12 cm (the hypotenuse)
According to the Pythagorean theorem, we have:
c² = a² + b²
Substituting the given values, we get:
12² = 8² + 10²
144 = 64 + 100
144 = 144
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What is the value of 3x- (y / 2+ 5) when x=3.5 and y= 4?
Answers
Answer:
3.5
Step-by-step explanation:
3x -(y / 2+ 5) x = 3.5 and y = 4
= 3(3.5) -(4/2 + 5)
= 3(3.5) -(2 + 5)
= 10.5 -(2 + 5)
= 10.5 -(7)
= 10.5 - 7
= 3.5
A triangle has an area of 14.5 square feet. The base of the triangle is 8 feet. What is the height?
Answers
Step-by-step explanation:
Triangle Area = 1/2 base * height
14.5 = 1/2 8 * height
3.625 ft = height
The triangles are similar.
Answers
Answer:
AC = 16 units
Step-by-step explanation:
we can solve with an equation to find the value of x and then add 1 to find AC (work in attached drawing).
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each hypotenuse length with the leg lengths that will create a right triangle.
Hypotenuse
√6 units
√5 units
√8 units
√3 units
√5 units, √3 units
Legs
√1 unit, √2 units
√2 units, √3 units
√5 units, √3 units
√5 units, 2 units
√5 units, 1 unit
Answers
the completed pairs are - √5 units, 2 units
Starting with the first pair, we have √5 units on both tiles, so we can place them in the same box.
Moving on to the second pair, we have √3 units on one tile and √5 units on the other. We need to find a pair that matches √3 units. Since there is no tile with √3 units, we cannot place this pair in the same box.
Lastly, we have two tiles left - one with √5 units and another with 1 unit. We need to find a pair that matches 1 unit. Since there is no tile with 1 unit, we cannot place this pair in the same box either.
Therefore, the completed pairs are:
- √5 units, √5 units
- √5 units, 2 units
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A helicopter is landing, and the pilot monitors her altitude, A, in feet over a set number of time intervals, t . She records her data and all of her data points fit the equation below. A= 8,500 350t What does the slope of this equation represent?
Answers
The slope of the equation A = 8,500 + 350t represents the rate of change of altitude with respect to time. Specifically, it represents the vertical speed of the helicopter in feet per unit of time (in this case, per time interval t).
The slope of the equation is m = -350 and the helicopter is descending at a rate of 350 feet per unit time
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
A = 8,500 - 350t
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = -350
So , it indicates that the altitude is falling at a rate of 350 feet per unit of time (t). The helicopter is falling at a constant rate of 350 feet per unit of time, according to this negative slope
Hence , the slope of the line is m = -350
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The complete question is attached below :
A helicopter is landing, and the pilot monitors her altitude, A, in feet over a set number of time intervals, t . She records her data and all of her data points fit the equation below. A= 8,500 - 350t
What does the slope of this equation represent?
Ai Mi has a loyalty card good for a 13% discount at her local hardware store. What would her total in dollars and cents be, after the discount and before tax, if the total cost of all the items she wants to buy is $39? Round to the nearest cent.
Answers
Ai Mi's total cost after the discount but before tax would be $33.93. Rounded to the nearest cent, this is equal to $33.94.
What is cost?Cost refers to the total amount of money, time, effort, or resources that are required to produce or acquire a particular good or service. It can be expressed in monetary terms or other units of measurement depending on the context. Cost plays a crucial role in decision-making for individuals, businesses, and governments.
According to the given data:If Ai Mi has a 13% discount, it means that she will pay only 87% of the total cost of the items.
So, the cost after the discount can be calculated as:
$39 x 0.87 = $33.93
Therefore, Ai Mi's total cost after the discount but before tax would be $33.93. Rounded to the nearest cent, this is equal to $33.94.
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