The equation of the line is y = (-2/3)x + 8/3
What is a perpendicular line?
Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular line can be used to graphically depict the condition of perpendicularity. It can be defined between any pair of lines, any pair of planes, or any pair of lines and planes.
The slope-intercept form of a line is written in the form:
y = mx + b
where:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept
Here, We have
y= 3/2x + 1/2 that passes through the point (-2,4)
But we do not know the value of b.
We can do this by substituting the point(-2,4), into the equation and we get
y = mx + b
4 = (-2/3)(-2) + b
b = 8/3
Now that you know all your values, rewrite the equation in slope-intercept form:
y = (-2/3)x + 8/3
Hence, the equation of the line is y = (-2/3)x + 8/3
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Find the dimensions of the rectangle with the largest area; it has two vertices on the x-axis and two vertices above the x-axis on the graph of
y = 5 − x^2.
Answer:
(2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333
Step-by-step explanation:
You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.
DimensionsThe graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².
AreaThe area will be the product of the width and height:
A = WH
A = (2x)(5 -x²) = 10x -2x³
Maximum areaThe area will be a maximum where the derivative of the area function is zero.
dA/dx = 10 -6x² = 0
x² = 10/6
x = (√15)/3
The corresponding rectangle dimensions are ...
width = 2x = (2/3)√15
height = 5 -x² = 5 -5/3 = 10/3
The rectangle with largest area is (2/3)√15 wide by 10/3 tall.
How many numbers are there from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4?
For example 15 and 51, where 5 – 1 = 4.
There are 9 numbers from the range with the difference of 4 in the digits
How to determine the frequency of the numbers with the properties?The properties of the numbers are given as
Difference: Largest - Smallest = 4
Range: 10 to 99
The numbers with above properties are as follows
15, 26, 37, 48, 59, 62, 73, 84 and 95
When these numbers are counted, we have
Frequency = 9
This means that there are 9 of such numbers from 10 to 99
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Una grúa está elevando 5 /7 de los 224 kg que puede elevar como máximo ¿Cuántos kilos está elevando?
The number of kilograms that the crane is lifting, based on the maximum it can lift and the proportion being lifted is 160 kilos
How to find the number of kilos?The number of kilos that the crane is lifting can be found by the formula :
= Maximum kilogram capacity x Proportion of maximum being lifted
Maximum kilogram capacity = 224 kg
Proportion of maximum being lifted = 5 / 7
The kilos being lifted by the crane is therefore :
= 224 x 5/7
= 1, 120 / 7
= 160 kilos
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A number line going from negative 20 to positive 20.
What is the absolute value of –20?
Use the number line to answer the question.
–20
0
20
40
Answer:
20
Step-by-step explanation:
Absolute value is the distance from zero. Absolute value is always positive.
| -20 | is positive. It is 20 units from 0. So it is 20.
| -20 | = 20
(Be careful, absolute value doesn't just flip the sign to the opposite.
| 20 | = 20 also because the distance from 0 to 20 is also 20.)
Factor the given number 102 Input the number's prime factors in ascending order.
(-2,6), m = 4 !!!!!!!!!!!!
Answer:
y=4x+14
Step-by-step explanation:
Kalia’s parents give her simple interest on any money she saves for college. Which equation and solution represents the total interest, T, earned when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10?
T = 100 • (10 + 0.1); $1,010
T = 100 • (10 + 0.01); $1,001
T = 100 • 0.1 • 10; $100
T = 100 • 0.01 • 10; $10
The equation and solution representing the total interest, T, earned by Kalia when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10, is D. T = 100 • 0.01 • 10; $10.
What is the simple interest?Simple interest is interest that does not compound.
Simple interest does not accumulate interest, unlike compound interest, which is added to the principal for subsequent interest.
Principal = $100
Simple interest rate = 1%
Period of savings = 10 years
The simple interest in dollars = T
T = 100 x 0.01 x 10
T = $10
Thus, Option D correctly represents the total interest earned by Kalia.
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What is 624×8 please answer this
Write the fraction 45/54 in simplest form
Answer:5/6
Step-by-step explanation:
If f(x) = 4x² and g(x)=3x, what is (fg)(x)?
(fg)(x)=
(Simplify your answer.)
The multiplication of the given function is (fg)(x) = 12[tex]x^3[/tex]
What is operations of the function ?
Similar to how a function's constituent terms can be added, subtracted, multiplied, and divided, so can functions. These are to be noted as follows:
Addition f( x ) + g ( x ) means to combine two functions, and it may alternatively be expressed as ( f + g ) ( x )
It is possible to write ( f g ) ( x ) to represent the operation of subtracting the g(x) function from the f(x) function.
The two functions are multiplied together when you multiply f (x ) g (x), which can also be represented as (f g ) (x).
Division f (x)/g (x) means to split the two functions in half, and it can alternatively be expressed as (f/g)(x).
Here the given function ,
=> f(x) = 4[tex]x^2[/tex]
=> g(x)= 3x
Now (fg)(x) = f(x)*g(x)
=> (fg)(x)= 4[tex]x^2[/tex]*3x
=> (fg)(x) = 12[tex]x^3[/tex]
Hence the (fg)(x) = 12[tex]x^3[/tex].
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please help someone its the last question :((((((((((((((((((
Answer:
x = 11
Step-by-step explanation:
(7x - 4) and 73 are alternate exterior angles and are congruent , then
7x - 4 = 73 ( add 4 to both sides )
7x = 77 ( divide both sides by 7 )
x = 11
Answer:
[tex]x = 11[/tex]
Step-by-step explanation:
two angles are congruent for the parallelism of the two horizontal lines (external alternates). thus
[tex]7x - 4 = 73 \\ 7x = 77 \rightarrow x = 11[/tex]
Mary Granola consumes tomatoes and nectarines. Mary's indifference curves are kinky. When she is consuming more tomatoes than nectarines, she is just willing to trade 3 tomatoes for 1 nectarines. When she is consuming more nectarines than tomatoes, she is just willing to trade 4 nectarines for 1 tomatoes. Let P₁ be the price of nectarines and P₂ the price of tomatoes. Mary maximizes her utility subject to her budget constraint. Which is true? (Hint: Sketch one of her indifference curves.)
When P₁ >3P₂ she must consume only tomatoes.
What are indifference curves ?
An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.
Mary do trading 3 tomatoes for 1 nectarine.
So, MRS=3
P₁ >3P₂
P₁/P₂ > 3
P₁/P₂ < -3
This satisfies MRS=3
P₁ >3P₂ shows budget constraint
consumer specializes in tomatoes consumption.
if P₂ > 4 P₁ , consumer specializes in nectarine consumption. option is not there.
So, When P₁ >3P₂ she must consume only tomatoes.
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The sum of four positive integers is 125. If you increase the first number by 4, decrease the second by 4, multiply the third by 4, and divide the fourth by 4, you produce four equal numbers. What is the smallest of the original numbers
Step-by-step explanation:
a + b + c + d = 125
a + 4 = b - 4 = 4c = d/4
a + 8 = b
a = b - 8
16c = d
b = 4c + 4
4a + 16 = d
b - 8 + 4c + 4 + c + 16c = 125
4c + 4 - 8 + 4c + 4 + c + 16c = 125
25c = 125
c = 5
d = 16c = 80
4a + 16 = d = 80
4a = 64
a = 16
b = a + 8 = 16 + 8 = 24
so, the numbers are
16, 24, 5, 80
The measurements of two sides of a triangle are 12cm and 17cm Which side length could be the measurement of the third side of the triangle
Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.
In the given question,
The measurements of two sides of a triangle are 12 cm and 17 cm.
We have to find which side length could be the measurement of the third side of the triangle.
We know that,
The sum of the length of any two sides is always greater than the third side.
The given sides of triangles are 12 cm and 17 cm.
Hence, the length of the third side should be shorter than the total of the other two sides,
12 + 17 = 29 cm.
Considering that the third side must be less than the difference between the first two sides,
17 – 12 = 5 cm
So, the length of the third side falls between 5 cm and 29 cm.
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India's hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Step-by-step explanation:
10 hours per week: $10.50 x 10 = $105.00
20 hours per week: $105.00 x 2 = $210.00
40 hours per week: $210.00 x 2 = $420.00
A few more don't let me down :l
The division that can match the model is that 6 ÷ 1/5 = 30.
What is division?Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. It is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.
It is a process of repeated subtraction. It is the inverse operation of multiplication. It is defined as the formation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of those smaller numbers equals the larger number taken.
In this case, the division will be:
= 6 ÷ 1/5
= 6 × 5
= 30
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find the missing number of each unit rate 24/8=?/1 40/20 = ?/1
Answer:
24/8 = 3/1
40/20 = 20/1
Step-by-step explanation:
I hope this helps!
Created a painting with an area of 48 in.² and a length of 6 inches they create a second painting with an area of 64 in.² it has the same width as the first painting what is the length of the second painting
The length of the second rectangle is 8 in
How to find the length of the second painting?Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where
L = length of rectangle = 6 in and W = width of rectangleSo, making Wsubject of the formula, we have
W = A/L
Since
A = 48 in² and L = 6 inSubstituting these into the equation, we have
W = A/L
W = 48 in²/6 in
W = 8 in
Now, since the second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where
L = length of rectangle and W = width of rectangleSo, making L subject of the formula, we have
L = A/W
Since
A = 64 in² and W = 8 inSubstituting these into the equation, we have
L = A/W
L = 64 in²/8 in
L = 8 in
So, the length of the second rectangle is 8 in
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Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 22 1 4 cm 22 4 1 cm22, start fraction, 1, divided by, 4, end fraction, start text, c, m, end text tall. It has a rectangular shape and an area of 890 cm 2 890cm 2 890, start text, c, m, end text, squared. How wide across is Keala's book cover? cm
The width across Keala book cover is 40cm
What is a rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees
From the question,
The length of the cover
= 22 1/4
= 89/4
The area of the cover
=890 cm²
From the formula
Area of a Rectangle = Length x Breadth
890=89/4×Breadth
Breadth = 890×4/89
Breadth=40cm
Hence, the width of the book cover is 40cm
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On April 1, 2022 the balance in inventory is 220 units at $50 each
April 5, 2022 purchased 100 units at $60 each
Purchased 50 units at $45 each on April 10, 2022
Sold 300 units at $80 each on April 16, 2022
Sold 20 units at $95 each on April 25, 2022
Purchased 200 units at $40 each on April 30, 2022
The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:
FIFO LIFO
Ending inventory $10,250 $12,800
Cost of goods sold $17,000 $14,450
How does FIFO differ from LIFO?FIFO (First-in, First-out) assumes that the physical flow of goods sold depends on the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
Date Description Units Unit Costs Total Cost
April 1 Beginning inventory 220 $50 $11,000
April 5 Purchases 100 $60 6,000
April 10 Purchases 50 $45 2,250
April 16 Sales -300 $80
April 25 Sales -20 $95
April 30 Purchases 200 $40 8,000
Total 570 $27,250
Units sold 320
Ending inventory 250
FIFO:
Ending Inventory = $10,250 (200 x $40 + 50 x $45)
Cost of goods sold = $17,000 ($27,250 - $10,250)
LIFO:
Ending Inventory = $12,800 (220 x $50 + 30 x $60)
Cost of goods sold = $14,450 ($27,250 - $12,800)
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Question Completion:Calculate Ending Inventory And COGS Using FIFO And LIFO Methods For ABC Inc.
5x-3(x-3)=-5+4x+6 x=?????????
Answer:
[tex]\frac{7}{4}[/tex] or 1 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
I am not sure if you meant 6x or 6+x at the end of the equation. I went with what was written.
5x -3(x-3) = -5 +4x +6x Distribute the -3
5x -3x + 9 = -5 + 4x + 6x Combine like terms
2x + 9 = -5 + 10x Subtract 2x from both sides
9 = -5 + 8x Add 5 to both sides
14 = 8x Divide both sides by 5
[tex]\frac{14}{8}[/tex] = x
[tex]\frac{7}{4}[/tex] o r 1 [tex]\frac{3}{4}[/tex]
create an x and y table of all 5 points in the picture (graphing)
The x and y table of all 5 points in this graph include the following:
x y
1 1
2 2
3 3
4 4
5 5
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 on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Additionally, the graph of any proportional relationship is always modeled by a straight line with the data points passing through the origin (0, 0).
In this scenario, we can reasonably and logically deduce that all of the data points in this graph are represented by the red symbols.
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can somone help me with this will mark u brainliest
Answer:
686 cm^2
Step-by-step explanation:
First find the sides
7f = 49
4f = 28
To find a triangle area (right triangle), multiply each side like a rectangle, but divide it by two.
(49*28)/2 = 686
Answer:
67
Step-by-step explanation:
solve 4x + 2=(1/8)x-2
Answer:
x = -32/31
Step-by-step explanation:
4x - 1/8 x = -2 -2
(32 - 1)/8 x = -4
31/8 x = -4
x = -4 * 8/31
x = -32/31
help plss? i dont know what this means so answer would be great.
Answer:
(e) b h a k
Step-by-step explanation:
You want the order of operations involved in the transformation ...
g(x) = a(bx -h) +k
Order of operationsThe Order of Operations tells you that multiplication takes precedence over addition, and expressions inside parentheses are evaluated first.
EvaluationWe note there is an expression in parentheses here: (bx -h). In that expression is a multiplication operation (bx) and an addition operation (_-h).
The multiplication is done first, so evaluating this expression in parentheses, we ...
multiply by bsubtract hOnce the parenthetical expression is evaluated, we proceed to the main event. Again, multiplication and addition are required. That means the next two steps are ...
multiply (the value of the parentheses) by aadd kIn summary, the operations we perform during evaluation of the transformation successively apply the parameters ...
b h a k
what is the sum of 3x and -3x + 4?
The dimensions of the old stage at the concert hall were 30 feet wide and 15 feet deep. The new stage has a total area of 1000 square feet. The
dimensions of the new stage were created by adding the same distance x to the width and the length of the old stage. What deepth of the new stage?
The 30 feet by 15 feet dimension of the old stage and the 1,000 square feet of the new stage generates equations that gives the depth of the new stage;
The depth of the new stage is 25 feetWhat is an equation?An equation states the relationships between two expressions as being of the same value.
The width and depth of the concert hall for the old stage are 30 feet and 15 feet respectively
Area of the new stage = 1000 ft.²
The dimensions of the new stage are;
Width = 30 + x
Depth = 15 + x
Which gives;
(30 + x) × (15 + x) = 1,000
(30 + x) × (15 + x) - 1,000 = 0
x² + 45·x - 550 = 0
(x + 55)·(x - 10) = 0
The distance added to the width and length of the old stage, x = 10
The width of the new stage = 30 feet + 10 feet = 40 feet
The depth of the new stage = 15 feet + 10 feet = 25 feet
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What is the equation of the line that passes through the point (2,-7) and has a slope of -4
Answer: y+7=-4(x-2)
Step-by-step explanation:Point slope form is: y - y1 = m(x-x1)2 = x1-7 = y1 substituteAnswer: y+7=-4(x-2)
I need help with number 2...
For isosceles triangle RST the measure of angle T is 34 degree
In this question, we have been given a isosceles triangle RST with RS = RT.
So, by isosceles triangle theorem,
angle S = angle T
So, angle T = (3x - 2)°
We know that the sum of all angles of triangle is 180°
∠R + ∠S + ∠T = 180°
9x + 4 + 3x - 2 + 3x - 2 = 180°
15x + 4 - 4 = 180°
15x = 180°
x = 12
So, 3x - 2 = 3(12) - 2
= 34°
Therefore, for triangle RST the measure of angle T is 34 degree
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Find the slope of the line
Answer:
-3
Step-by-step explanation:
we sure y2-y1/x2-x1 to find slope
6+6/-4+0
12/-4
-3 is the slope
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