Equation of a line in the standard form that passes through the points (3, 0) and (0, -2) will be [y = (2/3)x - 2].
As per the question statement, a straight line passes through the points (3, 0) and (0, -2).
We are required to determine the equation of the above mentioned line in it's standard form.
To solve this question, we need to know the formula to write the standard equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as [tex][(y-y_{1})=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}(x-x_{1})][/tex].
Here, let (x₁, y₁) be (3, 0) and (x₂, y₂) be (0, -2).
Therefore, equation of our concerned line passing through the two points (3, 0) and (0, -2), by substituting [(x₁, y₁) = (3, 0)] and [(x₂, y₂) = (0, -2)] in the above mentioned formula, will be [(y - 0) = {(-2 - 0)/0₂ - 3)}(x - 3)]
Or, [y = {(-2)/(-3)}(x -3)]
Or, [y = (2/3)(x - 3)]
Or, [y = (2/3)x - 2]
Equation: In mathematics, an equation is a statement that expresses the relation of equality between two expressions, by connecting them with the "equal to" sign (=).Line: In geometry, a line is an infinitely long one-dimensional object or shape with no width, depth, or curvature.To learn more about Equations and lines, click on the link below.
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A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours.
a. What does the 65 tell us in this situation?
The car travels
miles in 1 hour.
b. How many miles does the car travel in 1.5 hours?
The car travels
miles in 1.5 hours.
c. How long does it take the car to travel 26 miles at this speed?
It takes the car
hours to travel 26 miles.
(a) 65 means the car will travel 65 miles in 1 hour .
(b) The car will travel 97.5 miles in 1.5 hours .
(c) The car will take 0.4 hours to travel 26 miles at his speed .
In the question ,
it is given that
the car is traveling down a highway at a constant speed
and the equation representing is d =65*t
Part(a)
On comparing , the given equation with the equation of speed , time and distance
which is , distance = speed × time
on comparing both the equations , we get speed = 65 mph .
hence , 65 means the car will travel 65 miles in 1 hour .
Part(b)
substituting the value t = 1.5 hours in the given equation , we get
d = 65×1.5
= 97.5
hence , The car will travel 97.5 miles in 1.5 hours
Part(c)
Substituting the value of d = 26 miles in the given equation , we get
26 = 65×t
t = 26/65
t = 0.4 hours
hence , It takes the car 0.4 hours to travel 26 miles.
Therefore , (a) 65 means the car will travel 65 miles in 1 hour .
(b) The car will travel 97.5 miles in 1.5 hours .
(c) The car will take 0.4 hours to travel 26 miles at his speed .
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Write an equation of the line passing through the point (2, -9) that is perpendicular to the line y=x+6.
Answer:
y = -x - 7
Step-by-step explanation:
Perpendicular to the slope m = 1 is the slope -1/m = -1.
y = m * (x - Px) + Py
y = -1 * (x - 2) + (-9)
y = -x + 2 - 9
y = -x - 7
A sequence is defined by f(0) = -3, f(n) = f(n-1) + 0.5 for n ≥ 1.
1.
Write the first five terms of this sequence, starting with term 0.
2.
Write the nth term definition of this sequence.
Answer:
1.
f(0) = -3
f(1) = f(0) + 0.5 = -3 + 0.5 = -2.5
f(2) = f(1) + 0.5 = -2.5 + 0.5 = -2
f(3) = f(2) + 0.5 = -2 + 0.5 = -1.5
f(4) = f(3) + 0.5 = -1.5 + 0.5 = -1
2.
f(n) = 0.5n - 3
This function is linear.
3/4 + 1/3 as a fraction
Answer:
Step-by-step explanation:
Answer:1 1/12
Step-by-step explanation: 3/4+1/3=13/12=1 1/12
hi helpppppppppppppppppppppppppppppppppppp
Answer:
with what?
Step-by-step explanation:
the value of y is directly proportional to the value of x. when x = 20, the value of y = 16/5. the value of y is incline choice 1 when x = 50 incline choice 1:
1. 312.5
2. 1160
3. 3
4. 3200
Since y is directly proportional to x then the value of y is 8
In a proportional relationship, one variable is always equal to the constant value of the other.
The "constant of proportionality" is the name of this constant.The ratio between the constant values of two proportional quantities is known as the proportionality constant.When the ratio or product of two fluctuating values results in a constant, we say that two values are in proportion.The Direct Variation and Inverse Variation types of proportions between the two provided values determine the value of the proportionality constant.It is clear that y increases in proportion to x by applying the direct proportionality formula, y = kx.
Given y is directly proportional to x.
Therefore y = kx
now at x = 20 , y = 16/5
∴16/5 = 20 k
or, k = 16 /100
Now at x = 50 ,
Y = 16 /100 × 50
or, y = 8
Therefore that value of y is 8.
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The personal assets and liabilities of a carpenter are listed below.
What is the carpenter's net worth?
$139,450
$145,228
$281,313
$284,678
$139,450
==========================================================
Explanation:
asset = an item that is either cash or can be turned into cash
liability = something that needs to be paid back (eg: truck loan)
A = total assets
A = (homeValue) + (workEquipment) + (carValue) + (investments)
A = ( $175,742 ) + ($3,365) + ($44,346) + ($61,225)
A = $284,678
B = total liabilities
B = (mortgage)+(credit card balance)+(truck loan)
B = ($76,765)+($2,055)+($66,408)
B = $145,228
C = net worth
C = A - B
C = ($284,678) - ($145,228)
C = $139,450 which points us to choice A as the final answer.
The net worth of the carpenter is $144,633.
Given that, Home value = $175,742, Mortgage = $76,765, Credit card balance = $2,055, Owned work equipment = $3,365 and Car value = $44,346.
What is the net worth?Net worth is the value of all the non-financial and financial assets owned by an individual or institution minus the value of all its outstanding liabilities.
Here,
Net worth = Financial assets - Liabilities
= (175,742+3,365+44,346) - (76,765+2,055)
= 223,453 - 78,820
= $144,633
Therefore, the net worth of the carpenter is $144,633.
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is (0,-4) a solution to the equation y = -10x + -4?
Yes, it is a solution
Explanation:y = -10x + - 4
The given point: (0, -4)
To know if it is a solution, we need to replace the y and x with the points given.
If the result on the left hand side is the same as the right hand side then, it is a solution
x =0, y = -4
-4 = -10(0) + -4
-4 = 0 + (-4)
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
-4 = 0 - 4
-4 = -4
The left hand side is the same as the right hand side. Hence, it is a solution
Answer:
Yes it is a solution
Step-by-step explanation:
y = -10x + - 4
Point: (0, -4)
MANUFACTURING At a factory, molten glass is poured into molds to make
paperweights. Each mold is a rectangular prism with a height 4 inches
greater than the length of each side of its square base. Each mold holds
63 cubic inches of molten glass. What are the dimensions of the mold?
The dimensions of the mold are a length and width of 3 inches and a height of 7 inches.
What is the volume of a rectangular prism?The volume of a rectangular prism is the space that it contains. We know that the volume of any prism is calculated by multiplying its base area by its height.
Given :
Let's assume that the length and the width of the "box" is x.
It is said that the height is 4 inches greater, so the height is x+4.
The volume of the mold is:
V = (x)(x)(x +4)
V = x²(x +4 ) using the Distributive Property.
V = x³ + 4x²
Since from the question we have Volume = 63 cubic inches
The equation we have is,
63 = x³ + 4x²
Subtracting 63 from both sides of the equation,
x³ + 4x²- 63 = 0
The cubic equation can be written as,
(x−3)(x²+7x+21) = 0
The solution of the quadratic equation (x²+7x+21) is,
x = -b ±√(b² - 4ac) / 2a
a = 1 , b =7 and c = 21
Substituting the values in the formula,
x = -7 ±√(7² - 4(1(21)) / 2(1)
x = -7 ±√-35 / 2
Hence,there are no real solutions to the quadratic equation.
There is only one real solution to the equation x = 3.
Therefore, the length and width of the rectangular prism are 3 inches and the height is x+4 = 3+4 = 7 inches.
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What is the probability of
spinning an A?
B B
A
B
A
[?]%
Answer:
I believe you have a 25% of spinning an A
Step-by-step explanation:
If there are two possible A's to land on and there are 8 different choices,
2/8 = 1/4 and 1/4 is equal to 25%
So the probability would be "not likely"
Hope this helps! Please have an amazing day! :)
1. How many ways can you flip a coin and roll four-sided tetrahedron dice?
Draw the tree diagram in the space provided below.
Answer:
Step-by-step explanation: I cant do the tree Diagram, however, I will help if you flip a coin (Heads or tails) The chances of it landing on heads will divide by 2 every time its heads or tails again and vise versa .
How to draw two equilateral triangles that are not congruent
No, it is not feasible to produce any two structuring elements that is not always congruent with one another. This is because equilateral triangles have no internal angles.
This is further explained below.
What is an equilateral triangle?Generally, In the field of geometry, a triangle is said to be equilateral if all three of its sides have the same length.
In the well-known geometry of Euclidean, an equilateral triangle is also an equiangular triangle. This means that all three of the triangle's interior angles are equivalent to each other and are each 60 degrees.
No, it is not possible to create any two equilateral triangles that are not always congruent with one another.
In conclusion, The logic for this is that while each angle in an equilateral triangle is 60 degrees, the sides of the triangle cannot always be identical.
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What is the equation of the line that passes through the point (8, 1) and has a slope of -3/4?
Answer:
y-1= -(3/4)(x-8)
Step-by-step explanation:
y -1 =(-3/4)(x-8)
Distribute
y -1= (-3/4)x+6
Get rid of -1 by adding 1 to both sides
y=(-3/4)x+7
Hope this helps :)
Find the height, if area is 24cm2 and the base is 6cm.
Answer:
4cm..............................
Step-by-step explanation:
24/6=4
4x6=24
Write the equation for the line that passes through the given point and is perpendicular to the given line (1,7); x - 4y = 8
The equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3
Given : x - 4y = 8
4y = x- 8
On dividing by 4 we get;
y= x/4 - 2
This is of the form y = mx + c
Thus m in this case on comparing we get m= 1/4
We know the formula of the slope ;
y - y₁ =m ( x - x₁ )
y - 1 = 1/4 ( x- 7)
On cross multiplying we get ;
x- 4y = 3
Thus the equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3 .
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Explore Part 2
Drag the number cards to create three points that represent a proportional relationship.
Use the sketch tool if it helps you with your thinking.
Please help I give 10 pt
Answer:
Step-by-step explanation:
1,3 2,6 4,8
I hope it helps, thank you!
Provide the missing reasons for the following proof:
(In the picture)
Options
- Transitive Property of
Congruence
- Subtraction Property of
Equality
- Vertical Angles Theorem
(VAT)
- Division Property of
Equality
- Given
- Angle Congruence
Postulate
- Substitution Property of
Equality
The missing reasons are for the given two triangles VXW and VYZ are found.
What is defined as the congruent triangles?The assessments of the sides and angles of two or so more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. Two triangles have been shown to be congruent if the pairs of their corresponding angles and sides are equal. They are the same size and shape.The missing reasons for the following proof are -
∠XVW ≅ ∠W ; - Given∠XVW ≅ ∠ZVY ; Vertical Angles Theorem (VAT)m ∠ZVY ≅ ∠W ; Transitive Property of Congruence80x + 13 = 75x + 28 ; Angle Congruence Postulate5x = 15 ; Substitution Property of Equalityx = 3 ; Division Property of EqualityThus, the missing reasons are for the given two triangles VXW and VYZ are found.
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1. consider a lottery with three possible outcomes: $125 will be received with probability 0.25, $100 will be received with probability 0.3 and $50 will be received with probability 0.45. a. what is the expected value of the lottery? b. what is the variance of the outcome? c. what would a risk-neutral person pay (at most) to play the lottery?
The lottery's anticipated worth is $80.
Given that,
The probability of receiving $125 is 0.25; the likelihood of receiving $100 is 0.3; and the likelihood of receiving $50 is 0.45.
A) EV=125*.2+100*.3+50*.5=$80
The lottery's anticipated worth is $80.
The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is what we have: ;;
125(0.2) + 100(0.3) + 50(0.5) (0.5)
= 25 + 30 + 25 = $80
B) This is the formula for variance is shown in figure :
So, we can calculate the variance as follows:
.2*(125-80)^2+.3*(100-80)^2+.5*(50-80)^2=975
C) A risk-neutral person would pay $80 or less to play the lottery.
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Answer:
Step-by-step explanation:
Expected value of the lottery is $83.75.
Variance of the outcome is 909.6.
A risk-neutral person would pay $83.75 or less to play the lottery.
a) The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is,
125(0.25) + 100(0.3) + 50(0.45)
= $83.75
b) we can calculate the variance as follows:
Variance=.25*(125-83.75)^2+.3*(100-83.75)^2+.45*(50-80)^2=909.6
c) A risk-neutral person would pay $83.75 or less to play the lottery.
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Alex, Cameron and Sam are all taking part in a 400 m race.
They are each running at a different constant speed.
Alex is running 12% faster than Cameron, whilst Sam is running 2% slower than Cameron.
When Alex crosses the finish line, how many metres is Sam from the finish line?
Answer:
A= C + 12%C = 1.12C
S=.C -2%C = .98C
A,C and S are the speeds of Alex, Cameron and Sam
400 meter race
how far is Sam from the finish line when Alex crosses the finish line?
distance = speed times time
400 = AT where T=Alex' finish time
400=1.12T
400=CU where U = Cameron's finish time
400=SV where V = Sam's finish time
T<U<V
Alex' finish time is less than Cameron's finish time is less than Sam's finish time
if Cameron runs at 20 meters per second, finishing in 20 seconds
then Sam is about 50 meters from the finish line when Alex finishes
sorry if i´m too late, hope this helps!
how does x equal y in three dimesional math
Step-by-step explanation:
in 3-dimensional math we have 3 dimensions, and not just 2.
we have
forwards - backwards
left- right
up- down
so, we have there x, y and z.
and the equations typically are
z = ax + by
or even more general
cz = ax + by
or more complex functions of x and y.
z = f(x, y).
I am not sure what else you could mean with that question.
Please help. quickly
The total surface area of the triangular prism is 756 meter²
Given,
A triangular prism and its net.
We have to find the surface area of the triangular prism.
First we can consider the right angled triangle.
Height = 9 meter
Base = 12 meter
Hypotenuse = 15 meter
Area of the right angled triangle = (1/2 bh)
Here,
Area = 2 × (1/2 bh) = 2 × (1/2 × 12 × 9) = 2 × 6 × 9 = 108 meter²
Now, area of right rectangle.
Area of rectangle = length × breadth
Here, the breadth of the rectangle is the height of the triangle = 9 meter
Length = 18 meter
Area = length × breadth = 9 × 18 = 162 meter²
Then, area of middle rectangle.
Length = 18 meter
Breadth = 12 meter
Area = length × breadth = 18 × 12 = 216 meter²
Next, area of left rectangle.
Length = 18 meter
Breadth = Hypotenuse of the triangle = 15 meter
Area = length × breadth = 18 × 15 = 270 meter²
Now, lets calculate the total surface area of the triangular prism.
Surface Area of triangular prism = 108 + 162 + 216 + 270 = 756 meter²
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Determine whether the given function is even, odd or neither. *(1 Point)f(x) = x3 - 2x
Given:
The function is,
[tex]f(x)=x^3-2x[/tex]Replace x by -x in the given function,
[tex]\begin{gathered} f(x)=x^3-2x \\ f(-x)=(-x)^3-2(-x) \\ =-x^3+2x \\ =-(x^3-2x) \\ =-f(x) \end{gathered}[/tex]It is observed that, when the x is replace by -x the function end up with exactly opposite of the given function.
Thus, the given function is odd.
Please only answer : The horizontal scale should be X-scale and The vertical scale should be Y-scale
Regarding the scales to plot the points on the table, we have that:
The horizontal goes from X-min = -7 to X-max = 6.The horizontal scale should be X-scale = 1.The vertical goes from Y-min = -1500 to Y-max = 1200.The vertical scale should be Y-scale = 200.What are the ideal scales for the graphs?To find the ideal scales, we have to verify which are the extrema values of each variable, that is, the minimum and maximum value of each x and y.
From the table, the minimum and maximum values of X are given as follows:
X-min = -7.X-max = 6.This is a small range of values, hence the horizontal scale should be of 1.
From the same table, second column, the minimum and maximum values of Y are given as follows:
Y-min: -1500.Y-max: 1200.This is a large range of values, hence an ideal vertical scale is of 200, as then the number of traces would be almost the same as the number of traces of x.
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I don’t get it I have to find the exterior angle (t+20)
Answer:
110
Step-by-step explanation:
To find the measure of the exterior angle we first need to find the value of t.
The sum of interior angles in a triangle is equal to 180° so we can write the following equation:
t + 10 + t + t + 20 = 180 add like terms
3t + 30 = 180 subtract 30 from both sides
3t = 150 divide both sides by 3
t = 50
The exterior angles and the angle represented with t + 20 make a straight line
and they are supplementary angles so their sum is equal to 180
t + 20 = 70 to complete this to 180 we need 110
Please help me with this question, if it’s wrong I will report you, thank you for your help!
IN THE ATTACHED PICTURE YOU CAN SEE THE YELLOW VERTICAL LINE TOUCHED THE GRAPH ONCE IT MEANS THE GRAPH ABOVE IS A FUNCTION.
THEREFORE THE LAST OPTION IS THE SOLUTION. THE GRAPH IS A FUNCTION BECAUSE IT PASSES THE VERTICAL LINE TEST .
HOPE THIS HELPS
Find the surface area and volume of the following solids , a cylinder with radius 5 m and height 0.5 m
The radius of the cylinder is 5 m and the height is 0.5 m.
Then, the total surface area is
[tex]\begin{gathered} A=2\pi r(r+h) \\ =2\pi(5)(5+0.5) \\ =55\pi\text{ squared meter} \end{gathered}[/tex]So, the surface area is
[tex]55\pi=172.79\text{ squared meter}[/tex]Now, the volume is
[tex]\begin{gathered} V=\pi(r^2)h \\ =\pi(5)^2(0.5) \\ =39.27\text{ cubic meter} \end{gathered}[/tex]So, the volume of the cylinder is 39.27 cubic meters.
100 times my number is 12.6 more than 5,000.
Answer:
50.126
Step-by-step explanation:
hope this helps
The solution is 50.126
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
100 times my number is 12.6 more than 5000
Let the number be x
100 times the number = 100x
Now, 100x is 12.6 more than 5000
100x = 5000 + 12.6
100x = 5012.6
Divide by 100 on both sides , we get
x = 50.126
Hence , the solution is 50.126
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1) Work out the area and the perimeter of the shape below.
10 cm
12 cm
4 cm
Diagram NOT
accurately dr
Answer: 10 cm
Step-by-step explanation: because i am alwauys right about your mom
a. Solve a³ = 11.
b. Solve c² = 27.
Answer: a = 2.2
C = 5.1,-5.1
3. If it costs $3.50 per pound of sliced ham at the
deli and Weylan spent $2.90, how many pounds
did he buy? Round to the nearest hundredth of a
pound.
The amount in pounds of sliced ham he can buy is 083 pounds.
How to find the number of pounds he bought?It costs $3.50 per pound of sliced ham at the deli and Weylan spent $2.90.
The number of pounds of sliced ham he bought can be calculated as follows:
Hence,
3.50 dollars = 1 pounds of sliced ham
2.90 dollars = ?
cross multiply
amount of pounds he bought = 2.90 × 1 / 3.50
amount of pounds he bought = 2.90 / 3.50
amount of pounds he bought = 0.82857142857
amount of pounds he bought = 0.83 pounds
Therefore, the amount of pounds bought to the nearest hundredth is 0.83 pounds.
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