The equation of a line parallel to x - 4y = 36 is x - 4y = 16.
If the two lines are parallel then their slope must be equal. Two parallels lines have different intercepts but same slope. The slope intercept form of a line is y = mx + c. Where m is the slope and c is the intercept.
Now, writing the given equation in slope-intercept form,
x - 4y = 36
4y = x - 36
[tex]y=\frac{1}{4}x-9[/tex]
By comparing it with slope-intercept form, we get
[tex]m=\frac{1}{4}[/tex]
c = -9
Now, Finding the equation of line passing through (-4,-5) with slope as [tex]\frac{1}{4}[/tex],
[tex]m=\frac{y-y_1}{x-x_1} \\\\\frac{1}{4}=\frac{y-(-5)}{x-(-4)}\\\\ \frac{1}{4}=\frac{y+5}{x+4}\\x+4=4y+20\\x-4y=16[/tex]
The equation of parallel line is x - 4y = 16.
Hence, the equation of a line parallel to x - 4y = 36 is x - 4y = 16.
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Solve the following:
2x -7 /4= x + 3/3
Answer:
[tex]\frac{11}{4}[/tex] or 2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Here is one way to solve this problem
2x - [tex]\frac{7}{4}[/tex] = x + 1 (3/3 is another way to write one) Multiply all the way through by 4
4(2x - [tex]\frac{7}{4}[/tex]) = 4(x + 1) Distributive property
8x -7 = 4x +4 Subtract 4x from both sides
4x - 7 = 4 Add 11 to both sides
4x = 11 Divide both sides by 4
x = [tex]\frac{11}{4}[/tex]
Allie is playing basketball. She takes a shot 17 ft away from the basket. When the ball is 2 ft away from her, it is at a height of 10 ft above the floor. The ball reaches its highest height of 17 ft above the
floor when it is 9 feet away from her.
a. Find the value of a.
b. If the hoop is 10 ft high, how close would Allie have to be in order to make the basket?
a. The value of a is
(Simplify your answer.)
According to the vertex form of the parabola,
a) The value of a is -1/7.
b) And If the hoop is 10 ft high, the distance close to Allie have to be in order to make the basket should be 16 feet.
Vertex form of the parabola
The vertex form of the parabola can be given as,
y = a(x - h)² + k
Where
h,k are the coordinates of the vertex.
Given,
Allie is playing basketball. She takes a shot 17 ft away from the basket. When the ball is 2 ft away from her, it is at a height of 10 ft above the floor. The ball reaches its highest height of 17 ft above the floor when it is 9 feet away from her.
Here we need to find the following:
a. The value of a
b. If the hoop is 10 ft high, how close would Allie have to be in order to make the basket?
We know that, Allie takes a shot of 17 ft away and at the distance of 2 feet the ball achieve the height of 10 feet from the ground.
And the greatest height achieved by the ball is 17 ft above the floor.
Then the value of a is calculated by using the point that is obtained thorough the given details is,
=> (2, 10)
And the vertex of the equation are (9, 17)
When we apply these on the vertex form, then we get,
10 = a(2 - 9)² + 17
-7 = a(-7)²
49a = -7
a = -1/7
Therefore, the value of a is 1/7.
Now we have to find if the hoop is 10 ft high, The distance close to Allie have to be in order to make the basket-
Here the value of y is 10 and x is not known.
Now, we have to put these values on the equation then we get,
=> 10 = -1/7 (x - 9)² + 17
=> -7 = -1/7 (x -9)²
=> 49 = (x - 9)²
=>√49 = x - 9
=> x = 16
Therefore, if the hoop is 10 ft high, the distance close to Allie have to be in order to make the basket should be 16 feet.
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F(x,y) = x^2 + y^2 - 2x, D is the closed triangular region with vertices (0,0), (0,2), and (0,-2). Find the absolute maximum and minimum values of f on the set D. I know the maximum and minimum are f(0,+-2) = 4, minimum f(1,0) = -1. I need a step by step process on how to get to this answer
The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.
The given function is F(x,y) = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex] → 1
D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).
Differentiate 1 partially with respect to x:
df/dx = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](x) = 2x - 2
Differentiate 1 partially with respect to y:
df/dy = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](y) = 2y
Consider [tex]f^{'}[/tex](x) = 0 and [tex]f^{'}[/tex](y) = 0 to find the critical points.
[tex]f^{'}[/tex](x) ⇒ 2x -2 =0
x = 1
[tex]f^{'}[/tex](y) ⇒ 2y
y = 0
Thus, the critical point is (x,y) = (1,0).
Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).
At (x,y) = (0,0)
f(0,0) ⇒ 0 + 0 - 0 = 0
At (x,y) = (0,2)
f(0,2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (0,-2)
f(0,-2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (1,0)
f(1,0) ⇒ 1 + 0 - 2 = -1
Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.
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NSPECTIONS Mrs. Sanchez is inspecting a shed to determine if it is safe to use for storing football equipment. Mrs. Sanchez mapped the top view of the ceiling walls of the shed on a coordinate plane. If one of the walls lies from (–6, 11.5) to (2, 9.5) and the second wall lies from (–1, –2.5) to (2, 9.5), are the walls perpendicular? Explain your reasoning.
Answer:
Step-by-step explanation:
Answer:Yes, because the line that represents the first wall has a slope of -.25 and the line that represents the second wall has a slope of 4
Step-by-step explanation:
check the slope of both points
(-6,11.5) to (2, 9.5)
11.5-9.5= 2
-6-2=-8
2/-8
m=-1/4
(-1, -2.5) to (2,9.5)
-2.5=9.5=-12
-1-2=3
-12/-3
m=4
Yes, because the line that represents the first wall has a slope of -.25 and the line that represents the second wall has a slope of 4
What are the x and y intercepts? What do they mean in terms of the graph?
Step-by-step explanation:
these intercepts are the points where the graph intersects with the coordinate axes (x and y).
the x-intercept is a point on the x-axis, meaning when y = 0.
the y-intercept is a point on the y-axis, meaning when x = 0.
so, the x-intercept here is 14 at the point (14, 0).
the y- intercept is 7 at the point (0, 7).
that means the object started falling from a height of 7 meters and hit the ground after 14 seconds.
the falling speed was then
7 meters / 14 seconds = 0.5 meters / second
what are we talking about ? an asteroid with very little gravity ?
Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
However, the graph has no maximum or minimum
This means that there is absence of a vertex in the graph
The transformationHere, we have:
The graph is translated 4 units to the left of the origin The graph is translated 2 units below the originThis transformation can be represented as (x - 4, y - 2)
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Does the point (-2, 7) lie on the graph of y = -2x+1
The point (-2, 7) is not on the graph of y = -2x + 1
How to determine if the point is on the graph?From the question, we have the following equation
y = -2x + 1
This equation represents the equation of the graph
Also, we have the following points
(-2, 7)
This point implies that
(x, y) = (-2, 7)
Substitute (x, y) = (-2, 7) in the equation y = -2x + 1
So, we have
7 = -2 x -2 + 1
Evaluate
7 = 5
This is false
Hence, the point is not on the graph
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How many kilometres is 6.5cm
Answer:
0.000065 km
Step-by-step explanation:
To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km
Noah runs a farm stand that sells bananas and raspberries. Each pound of bananas
sells for $3 and each pound of raspberries sells for $2.25. Noah made $72 from
selling a total of 28 pounds of bananas and raspberries. Graphically solve a system of
equations in order to determine the number of pounds of bananas sold, a, and the
number of pounds of raspberries sold, y.
There is no possible solution for the weight of raspberries sold, given that 28 pounds of banana were sold.
What is Co-ordinate Geometry?
Graphs and coordinates are utilised in coordinate geometry to discover information about various geometric figures. A description of the coordinate plane must be included in a definition of coordinate geometry. A coordinate plane, also known as a coordinate graph, is a grid system formed by the intersection of two number lines known as axes. The x-axis is the horizontal number line, and the y-axis is the vertical number line. These axes meet at a position known as the origin.
Solution:
let, the total weight of banana sold be x pounds
and total weight of raspberries soldd be y pounds.
From the data given in the question, the equation formed is
3x + 2.25y = 72
(See Graph)
at x = 28 we will get the value of y as -5.34
which is not a possible solution
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if the 90% confidence limits for the population mean are 45 and 55, which of the following could be the 99% confidence limits a) [48, 55] b) [49, 53] c) [42, 58] d) [46, 51] e) [49, 51] f) none of the above
The 99% confidence limit will be option B which is (45, 55)
90% confidence limits for the population mean are (46,54)
mean = 46+54 / 2 = 50.
the margin of error E = 54-46/2 = 4
For 90% Confidence Z- Critical value is = 1.645
But the margin of error
E = ZS/√n
4=(1.645)S/√n
S/√n = 4 / 1.645
= 2.4316
For 95% confidence Z-critical value is 1.96
A 95% confidence interval is = mean ± E
(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316
= 50+ 4.7660
= 45.2340, 54.7660
= (45, 55)
Hence the correct option is B which is (45, 55) as the 99% confidence limit.
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help
How many terms are in the following
expression:
5x + 3 - x +2x + 2/3x
Help please
74°
94°
100°
106°
Answer:
106
Step-by-step explanation:
180-74=106
You can find x by looking at the corresponding angle under it and we know a straight line is 180 degrees and the other side of the x is 74 degrees then we just subtract to find the x angle
Hopes this helps please mark brainliest
Use the number line to find the difference of 2 - (-4.5)
The value after solving the expression will be equal to 6.5.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtracting, multiplying, and dividing two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
From the data in the question,
The expression is,
2 - (-4.5)
⇒ 2 + 4.5
= 6.5
Therefore, the result for the expression is 6.5.
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omg !!! please help so much !
Answer:
75
Step-by-step explanation:
15*3=45
6*5=30
45+30=75
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Capital social 2.000.000 banco caixa 20.000 imovel 1.000.000 50% a vista 50% a prazo moveis 90.000 a vista transferencia bancaria veiculo 150.000 a prazo mercadoria a prazo 200.000
30% of the tickets sold at a school carnival were early-admission tickets. If the school sold 100 tickets in all, how many early-admission tickets did it sell?
The number of early-admission tickets that it sells is 30.
How to calculate the number of early admission?From the information, 30% of the tickets sold at a school carnival were early-admission tickets and the school sold 100 tickets in all.
Therefore, the number of early admission will be:
= Percentage for early admission × Total number of tickets
= 30% × 100
= 0.3 × 100
= 30
Therefore, there are 30 early admission.
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pls help me with algebra
Which equation represents a line which is perpendicular to the line y=-4x-5?
A. x+4y=-32
B.4x+y=3
C.4x−y=−4
D.4y−x=4
Answer:
D.4y−x=4
Step-by-step explanation:
Perpendicual lines have a slope that is the negative inverse of the referenced line. The reference here is:
y = -4x-5
The slope is -4
The negative inverse of -4 would be +(1/4). Any line that has a slope of +(1/4) will be perpendicular to y=-4x+5.
The equations in the answer options are not arranged according to the standard format of y=mx+b, where m is the slope and b the y-intercept.
We could graph all the equations and look for the one(s) that are perpendicualr, but it might be safer, and faster, to rearrange them in the standard format, and then note the slope:
Slope =+(1/4)?
A. x+4y=-32
4y= -x-32
y = -(1/4)x-8 -(1/4) NO
B.4x+y=3
y = -4x + 3 -4 NO
C.4x−y=−4
y = 4x + 4 4 NO
D.4y−x=4
4y=x+4 +(1/4) <==YES
y=(1/4)x+1 [Option D has a slope of +(1/4). It will be perpendicular]
See the attached graph.
A 7-meter roll of blue ribbon costs $12.04. What is the unit price?
The unit price for a 7-meter roll of blue ribbon costs $12.04 is $1.72.
What is unit price?The unit price is simply used to calculate the price that's paid for each good.
In this case, the 7 -meter roll of blue ribbon costs $12.04. Therefore, to get the unit price goes thus:
= Total amount paid / Number of meters
= $12.04 / 7
= $1.72
The unit price is $1.72.
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5 The table shows the weights of different packages.
What is the approximate total mass of packages A, B,
and D? (Hint: 1 lb ≈ 0.45 kg)
Package | Weight (lb)
A | 0.25
B | 0.8
C | 1
D | 1.75
answers:
F 1.26 g
G 2.8 g
H 280 g
J 1260 g
Answer:
1710 grams (not on the answer list)
Step-by-step explanation:
The total weight of the 4 packages is 3.8 pounds (lbs). The conversion factor is (0.45 kg/lb).
(3.8 lbs)*((0.45 kg/lb) = 1.71 kg or 1710 grams. Pease check the numbers provided.
The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72
Answer:
y=2·6^2
Step-by-step explanation:
Use formula y=a[tex]b^x[/tex], plug in two different points.
72=ab^2
12=ab^1
isolate one so that a is on one side
a=[tex]\frac{12}{b}[/tex]
plug in a into the other equation
72=[tex]\frac{12}{b}[/tex][tex]b^2[/tex]
72=[tex]\frac{12b^2}{b}[/tex]
72=12b
b=6
complete solving for a now
a=2
now put it back into [tex]y=ab^x[/tex]
y=2·6^2
Please help!! Asap screenshot below.
Help pls I'll give you brainliest and 15 points asap.
How does the graph of g(x)=4⌊x⌋ differ from the graph of f(x)=⌊x⌋?
1. Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ up 4 units.
2.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ down 4 units.
3.Multiplying by 4 stretches the graph of g(x)=4⌊x⌋ vertically by a factor of 4.
4.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ right 4 units.
Question 2
How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?
1.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units.
2.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.
3.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units.
4.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.
Answer:
Question 1: #3 is correct.
Question 2: #4 is correct.
Brad had a small gathering at a local steakhouse. The steakhouse offers three dinner platters which vary by size and price. They ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters.
Steak Platter Prices
• 6-ounce $9.95
• 8-ounce $12.95
• 11-ounce $15.95
If a gratuity of 18% was added to the bill, which of the following is closest to the total of the steak platters and gratuity, ignoring sales tax?
Hello!
If Brad had a small gathering at a local steakhouse where they ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters. After adding an 18% gratuity their total before sales tax should have been $130.45
Step-by-step explanation:
[tex]4[/tex] x [tex]9.95=39.80[/tex]
[tex]3[/tex] x [tex]12.95=38.85[/tex]
[tex]2[/tex] x [tex]15.95=31.90[/tex]
[tex]31.90+[/tex][tex]38.85+[/tex][tex]39.80=[/tex][tex]110.55[/tex]
[tex]110.55[/tex] x [tex]0.18[/tex] [tex]=19.899[/tex]
[tex]110.55+19.90[/tex][tex]=130.45[/tex]
0.00097 in standard form
Answer:
9.7x10^-4
Step-by-step explanation:
If f(x) = x, when g(x) = f(x) - 10 is graphed on the same coordinate grid, which statement describes the relationship of the graphs of f and g?
The graph g(x) is graph of f(x) translated down 10 units.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that changes over time is represented by a line graph.
Given:
f(x) = x, when g(x) = f(x) - 10
As, from the graph we can see that both function f(x) and g(x) shows a parallel relation.
Also, the function f(x) is subtracted from 10 then the function is translated down by 10 units.
Hence, g(x) is graph of f(x) translated down 10 units.
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3/8=15/5x-2 please help me find x
Answer x = 19/24
Step-by-step explanation:
f(x) = x +4
g(x) = 3x
What is the value of fg(7)?
Answer: 105 (altough im not entirely sure sry...)
Step-by-step explanation:
I believe since it is "fg" then only the g gets the 7 (g(7)) and the f is just f(1)
This is quite difficult so you this may not be correct
I hope
\frac{2x^3t^3}{xt^2}\:\cdot \frac{\left(3xt\right)^3}{9x^2t}
Answer:
[tex]6x^{3}t^{3}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{\left(3xt\right)^3}{9x^2t}[/tex]
[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^c \cdot b^c:[/tex]
[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{3^3x^3t^3}{9x^2t}[/tex]
[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{27x^3t^3}{9x^2t}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]
[tex]\implies \dfrac{2x^3t^327x^3t^3}{xt^29x^2t}[/tex]
Collect like terms:
[tex]\implies \dfrac{2 \cdot 27x^3x^3t^3t^3}{9x^2xt^2t}[/tex]
Multiply the numbers 2 and 27:
[tex]\implies \dfrac{54x^3x^3t^3t^3}{9x^2xt^2t}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{54x^{3+3}t^{3+3}}{9x^{2+1}t^{2+1}}[/tex]
[tex]\implies \dfrac{54x^6t^6}{9x^3t^3}[/tex]
Separate like terms:
[tex]\implies \dfrac{54}{9} \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]
Divide the numbers 54 and 9:
[tex]\implies 6 \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 6 \cdot x^{6-3}\cdot t^{6-3}[/tex]
[tex]\implies 6 \cdot x^{3}\cdot t^{3}[/tex]
[tex]\implies 6x^{3}t^{3}[/tex]
The internal radius of a cylindrical bucket of height 50 cm is 21 cm. It is filled with water completely. If the water is poured into a rectangular vessel with internal length 63 cm and breadth 44 cm and it is completely filled with water, find the height of the vessel.
The height of the rectangular vessel into which the volume of water that completely fills the cylindrical bucket is poured is approximately 25 centimeters
What is the relation between height and volume of a cylinder?
The volume of a cylinder is the product of the base area of the cylinder and the height of the cylinder.
Height of the cylindrical bucket, h = 50 cm
Radius of the bucket, r = 21 cm
The level of water in the cylindrical container = The container is filled completely with water
The shape of the vessel into which the water is poured = Rectangular vessel
Length of the rectangular vessel into which the water in the cylinder is poured, L = 63 cm
Breadth of the rectangular vessel, B = 44 cm
Level to which the water fills the rectangular vessel = The rectangular vessel is completely filled with the water poured in from the cylinder
Volume of water in the cylinder, V = Volume of the cylinder = π·r²×h
Therefore;
V = π × 21² × 50 = 22050·π
The volume of water transferred from the cylinder = 22050·π cm³
Volume of the rectangular vessel, [tex]V_s[/tex] = L × B × H
[tex]V_s[/tex] = V = 22050·π cm³
Therefore;
The height of the rectangular vessel, H = [tex]V_s[/tex]/(L × B)
H = 22050·π/(63 × 44) = 24.9899415626 ≈ 25
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