The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12 so option (B) is correct.
What is a function?The function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
9x + 3y = 12
Subtract 9x both sides,
9x - 9x + 3y = 12 - 9x
3y = 12 - 9x
Divide by 3 into both sides,
y = 12/3 - 9x/3
y = -3x + 4
Since,y = f(x)
f(x) = -3x + 4 .Here -3 is the slope while 4 is the y-intercept.
Hence "The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12".
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The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units.
A solid oblique pyramid has an equilateral triangle base with a base edge length of 14 units. The base triangle is triangle A C D. The apex is point B. The angles formed with the lateral sides are 45 degrees.
What is BC, the height of the pyramid?
7 units
7StartRoot 2 EndRoot units
14 units
14StartRoot 2 EndRoot units
The height of the pyramid = BC = 14 units
What is a pyramid?It is a three-dimensional shape that has a polygonal base and flat triangular faces which joins at the apex at the top of the pyramid.
We have,
Base edge length = 14 units
From the figure below,
The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units so,
We get,
AC = CD = AD = 14 units _____(1)
All sides in an equilateral triangle are equal.
In the right triangle ABC,
tan 45° = BC / AC
tan 45° = 1
1 = BC / AC _____(2)
From (1) and (2) we get,
1 = BC / 14
BC = 14 units
The height of the pyramid = BC = 14 units
Thus,
The height of the pyramid is 14 units.
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Answer: C 14 UNITS
Step-by-step explanation:
Sara hiked up a mountain on a steep 3-mile trail. Then she hiked downhill on a less
steep 5-mile trail. She hiked 0.5 mph faster downhill than uphill.
If Sara hiked uphill at a rate of r mph, how fast was she hiking downhill?
Answer:
wait, its r + 0.5
Step-by-step explanation:
Apply the Strategy Solve each problem by making a table. 5. 1. A page from Dana's album is shown. Dana puts the same number of stickers on each page. She has 30 pages of stickers. How many stickers does she have in all? Dana has stickers in all. MOPPOPPG-BUDG
Step 1:
First count the number of stickers on a page
There are 12 stickers in a page
Step 2
There are 30 pages,
Hence, the number of stickers in 30 pages = 30 x 12 = 360
Final answer
Dana has 360 stickers in all
(d^2+4)b=g
Solve for b
Answer:
b = [tex]\frac{g}{(d^{2}+4) }[/tex]
Step-by-step explanation:
([tex]d^{2}[/tex] + 4)b = g Divide both sides by ([tex]d^{2}[/tex] + 4)
b = [tex]\frac{g}{(d^{2}+4) }[/tex]
Round 2.629 to the nearest tenth.
Answer:
2.6
Step-by-step explanation:
cause it is 2.6299999999
2.629 to the nearest tenth is 2.6.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Given:
A decimal number,
2.629.
Here, 2 is the whole number component and 0.629 is the fractional component part.
To round the number to the nearest tenth:
The number in tenth place is 6.
And the value right next to 6 is 2.
6 > 2.
So, the number will stay the same.
2.629 = 2.63
Then 2.63 = 2.6 to the nearest tenth.
Therefore, 2.6 is the required decimal.
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Need help finding the perimeter
13 + √85/3 is the perimeter of triangle .
Explain what a triangle is.
A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.The points P ( - 3 , -8 ) Q ( - 3, - 1) R ( -9,-8)
Distance between PQ = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( - 1 + 8)^{2} + ( -3 + 3)^{2} }[/tex]
= [tex]\sqrt{( -7 )^{2} +0 }[/tex]
= √49 ⇒ 7
Distance between QR = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( -9 + 3 )^{2} + ( -8 + 1)^{2} }[/tex]
= [tex]\sqrt{(- 6)^{2} + ( - 7)^{2} }[/tex]
= [tex]\sqrt{36 + 49}[/tex]
= √85
Distance between RP = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( - 3 + 9)^{2} + ( -8 + 8)^{2} }[/tex]
= [tex]\sqrt{(6)^{2} }[/tex]
= √36
= 6
perimeter = PQ + QR+RP/3
= 7 + √85 + 6/3
= 13 + √85/3
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Please help. The problem is attatched!
The equation is 15 + 0.5x = 25 + 0.25x and number of miles is 40.
While writing the equation for green and blue cars, one time fee will be added with cost of driving for miles. Let us assume the number of miles to be x.
Firstly writing the equation for green car -
Cost = 15 + 0.5×x
Now writing the equation for blue car -
Cost = 25 + 0.25×x
The number of miles for same cost will be calculated by equating the expressions.
15 + 0.5x = 25 + 0.25x
0.5x - 0.25x = 25 - 15
Performing subtraction on Left Hand Side and Right Hand Side of the equation
0.25x = 10
Shifting 0.25 to Right Hand Side of the equation
x = 10 ÷ 0.25
Performing division on Right Hand Side of the equation
x = 40
So, if both the cars travel 40 miles, the rental cost will be same. The correct equation for calculation is 15 + 0.5x = 25 + 0.25x.
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If the point (2, – 3) lies on the graph of the equation 2y = ax – 7, then the value of a is
Answer:
a = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
since (2, - 3 ) lies on the graph then it makes the equation true.
substitute x = 2 and y = - 3 into the equation and solve for a
2(- 3) = a(2) - 7 , that is
- 6 = 2a - 7 ( add 7 to both sides )
1 = 2a ( divide both sides by 2 )
[tex]\frac{1}{2}[/tex] = a
The perimeter of the flag is 2260 ft Determine the flag's width and length if the length is 350 ft greater than the width.
The length is 780 feet and the width is 430 feet.
Distance is measured in length.
The dimension of distance is a property of length in the International System of Quantities.
The majority of measurement systems have a base unit for length from which all other units are derived. The meter is the primary unit of length in the International System of Units (SI) system.The term "length" is usually considered to refer to an object's longest dimension.Nevertheless, depending on the position of the object, this isn't always the case.There are several terms used to describe the length of a fixed object, including height, which is also known as vertical length or vertical extension, and width, breadth, or depth.Let the length be x
Width = x - 350
Perimeter = 2260 feet
Now : 2(x + x +350) = 2260
or, 2 x + 700 = 2260
or, 2x = 1560
or, x = 780 feet
So length is 780 feet
Width = 780 -350 = 430 feet
Therefore the length is 780 feet and the width is 430 feet.
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Miranda is making bracelets. She already has 15 and she can make 3
per day. Determine the slope and the y-intercept.
Answer:
y=3x+15
Step-by-step explanation:
she can make 3 a day so 3x and she already has 15 so the line crosses the y-axis at 15
Jamal is constructing the bisector of angle ABC. He has a list of steps for the construction, but they are not in
order.
If the breadth of a rectangle is reduced by 4cm it's are would be reduced by 240 cm². How long is the rectangle?
Answer:
Let the length be x. The breadth be y Area=xy. On reducing breadth by 4 new breadth will be (y-4). X(y-4)=xy-240. Xy-4x=xy-240. -4x=-240. X=60. Hence rectangle is 60cm long
Step-by-step explanation:
hope it will help
y=-5(-4)-17
please add an explanation
Answer:
y = 3
Step-by-step explanation:
y = -5(-4) - 17
multiply first
y = (-5*-4) - 17
y = +20 -17
y = 3
A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.
Inequality is 32.50x + $10.50 ≤ $160 and 4 people can go to the amusement park.
What is an inequality?inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Given that,
$160 = Amount of money they have
$10.50 = Parking Cost
$32.50 = Cost of tickets per person
Because they only have $160, they can't spend more than that amount.
Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:
32.50x + $10.50 ≤ $160
Solve the equation
$160 - $10.50 = $149.50 (149.50 is how much is left for tickets after subtracting the parking cost)
$32.50 x 4 = $130 (4 tickets can be bought for the price of $32.50)
$149.50 - $130 = $19.50 (19.50 isn't enough for another person)
So, the solution to the inequality is 4 people can go to the amusement park.
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The value of y varies directly with x. If y = 8, when x = 4, what is y when x = 48?
A function is defined as a relation between a set of inputs having one output each.
The value of y when x = 48 is 96.
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
The value of y varies directly with x.
y = 8, when x = 4.
Domain = input = 4
Range = output = 8
Now,
We can say that y is a function.
i.e y = 2x.
Where x = input = domain and y = range = output.
The value of y when x = 48:
y = 2x
y = 2 x 48
y = 96
Thus,
The value of y when x = 48 is 96.
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The formula h 16t² describes the time t in seconds that it takes for an object to fall from a height of h feet. An object is dropped from
height of 1,600 feet. How many seconds does it take to reach the ground?
seconds
A solution set exists the set of values that satisfy a given set of equations or inequalities.
Its position must be 1600 then It takes 10s to get to the ground.
What is a solution set of an equation?A solution set exists the set of values that satisfy a given set of equations or inequalities. For instance, for a set of polynomials over a ring , the solution set exists the subset of on which the polynomials all vanish (evaluate to 0), formally.
The formula,
h = 16t²
where h is height and t is time.
You want to see how long it will take an object to fall 1600 feet down to the ground. These means its position must be 1600.
By setting the equation equal to this value,
we get:
1600 = 16t²
To estimate the value of t.
First, divide both side by 16, getting:
100 = t²
Now taking the square root of both sides, we get:
√(100) = 10 seconds.
It takes 10s to get to the ground.
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You are holding a kite string in your hand. The angle of elevation from your hand to the kite is 66 degree and the distance to the kite is 303 feet. Your hand is 4 feet above the ground. How high is the kite? Round your answer to the nearest tenth of a foot.
For given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.
As given,
Shown in diagram attached,
Angle of elevation ∠AEB=66°
Distance to the kite AE=303 feet
Hand above the ground DE=4feet
DE=BC
BC=4feet
Let 'h' be height of AB
Height of the kite=(h +4)feet
In ΔABE,
sin66°=h/303
⇒h=sin66° ×303
=0.9135 ×303
=276.7905
≈276.8 feet
Height of kite=(h +4) feet
=276.8 +4
=280.8 feet
Therefore, for given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.
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1. Write a matrix to represent the following system.
[tex]\left \{ {{-9x+4y =1} \atop {7x-9=5}} \right.[/tex]
Complete the matrix below.
[ _ _ | _ ]
[ _ _ | _ ]
[ _ _ | _ ]
2. Write a matrix to represent the following system.
[tex]\left \{ {{-5x+6y=1} \atop {5x-2y=9}} \right.[/tex]
Complete the matrix below.
[ _ _ | _ ]
[ _ _ | _ ]
[ _ _ | _ ]
The augmented matrices for each system are given as follows:
1.
[ -9 4 | 1 ]
[ 7 0 | 14]
2.
[ -5 6 | 1 ]
[ 5 -2 | 9]
How to build the augmented matrix of a system of equations?For a system of n variables, the first n columns of the matrix are composed by the coefficients of the variable of the system.
The two systems in this problem have variables x and y, hence:
The first column is composed by the coefficients of x.The second column is composed by the coefficients of y.Then the last column is composed by the values on the right side of the equations, that is, the results of the operations.
The second equation of the first system is:
7x - 9 = 5 -> 7x + 0y = 14 (this format is needed to build the augment matrix.
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Which relation represents a function?
In the given relations , the relation (B) represents a function, others are not function. To become a function each input should have only one output. Since others does not satisfy this criteria they are not functions.
How to check the relation is function or not ?Determine the input values. Determine the output values. If each input value results in only one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.To determine whether a graph represents a function, use the vertical line test. If a vertical line is moved across the graph and only touches the graph at one point at any time, the graph is a function. The graph is not a function, if the vertical line intersects it more than once.To learn more about relations refer to :
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How do I find the slope?
Answer:
Find the slope by putting your rise over your run. Make sure to label your points.
Step-by-step explanation:
Starting with the number 0, build a sequence of 5 numbers.
Answer:
How about:
0, 1, 2, 3, 4..............
lol jk here:
0, 66, 132, 198, 264
Step-by-step explanation:
Guess what it is! ;p
Solve for y 10x -5y=30
Answer:
y=2(x−3)
Step-by-step explanation:
The area of a square is 150 square feet. What is the side length of the square?
Answer:37.5
Step-by-step explanation:
so basically a square has four sides so 150 divided by 4
A (2,-4), B (3, 3) and C (-1,5) are the vertices of ΔABC . Find the equation of the altitude of the triangle through C.
Answer:
x + 7y = 34
Step-by-step explanation:
the altitude through C meets the opposite side AB at right angles
calculate the slope of AB using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (2, - 4 ) and (x₂, y₂ ) = B (3, 3 )
[tex]m_{AB}[/tex] = [tex]\frac{3-(-4)}{3-2}[/tex] = [tex]\frac{3+4}{1}[/tex] = [tex]\frac{7}{1}[/tex] = 7
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{7}[/tex] , then
y = - [tex]\frac{1}{7}[/tex] x + c ← partial equation of the altitude
to find c substitute C (- 1, 5 ) into the partial equation
5 = [tex]\frac{1}{7}[/tex] + c ⇒ c = 5 - [tex]\frac{1}{7}[/tex] = [tex]\frac{35}{7}[/tex] - [tex]\frac{1}{7}[/tex] = [tex]\frac{34}{7}[/tex]
y = - [tex]\frac{1}{7}[/tex] x + [tex]\frac{34}{7}[/tex] ( multiply through by 7 )
7y = - x + 34 ( add x to both sides )
x + 7y = 34 ← equation of altitude in standard form
Anyone please help me this all and have solutions
Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
What is a solution?
A designation of values to that same unknown variables that establishes the equality inside this equation is referred to as a solution.To put it another way, a solution is a figure or set of values one for every unknown) that, when used to replace the unknowns, cause the equation to equal itself.Equations or networks of equations can have just one unique solution when they are solved mathematically.Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
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carly has a job that pays 35 a week plus 2 for each sale she makes. how many sales dose she need to make to earn more than 100 this week?
Carly needs to perform 33 additional sales to earn 100 this week.
Firstly forming the expression as per the weekly earning and individual payment on extra sale. Writing the expression -
Amount earned = 35 + 2×number of sales
Keep the value of amount earned in mentioned formula to find the number of sales.
100 = 35 + 2×number of sales
2×Number of sales = 100 - 35
Performing subtraction on Right Hand Side of the equation
2×Number of sales = 65
Shifting 2 to Right Hand Side of the equation
Number of sales = 65/2
Performing division on Right Hand Side of the equation
Number of sales = 32.5
Round off the number
Number of sales = 33
Therefore, she needs to make 33 additional sales.
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What is the equation of the parabola with the vertex of (1,-8) that passes through (2,-6)
Hello!
What is the standard form of the parabola:
[tex]\hookrightarrow y=(x-h)^2+k[/tex]
(h,k): vertex's coordinate=> h: x-coordinate of vertex
=> k: y-coordinate of vertex
Since our vertex is (1,-8)
[tex]\hookrightarrow \text{Our equation is }y=(x-1)^2}-8[/tex] <== Answer
Hope that helps!
The sum of three numbers is 23. The third number one more than the sum of the first and second numbers. The first number is ten less than the third number. Find the numbers.
Answer:
2, 9, 12
Step-by-step explanation:
We know that the first number is ten less than the third number and that the third number is one more than the first number and second number combined. Because of this, our third number has to be one away than the combination of the first two numbers. Now, we just have to see the numbers of the first two values and the first number is 10 less than the third number. You can mostly guess the numbers once you understand. I hope that this didn't confuse you more. Hope this helps!
The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, find the mass of one the bodies, if the mass of the other is 2050kg (G=6.7by 10^-11Nm^2kg^2
The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, then the mass of one the bodies is
[tex]m_{1} = 1.88(10)^{-7}[/tex]
What is mass ?The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. The mass of a thing determines whether it is light or heavy.
Given that : The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m
F=[tex]G\frac{m_{1} .m_{2} }{r^{2} }[/tex]
[tex]m_{1} =\frac{F.r^{2} }{Gm_{2} }\\ m_{1} =\frac{745.(70.3)^{2} }{6.7(10)^{-11}.2050 }\\\\[/tex]
[tex]m_{1} =\frac{26881.3(10^{7} )}{13735}[/tex]
[tex]m_{1} = 1.88(10)^{-7}[/tex]
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I’m failing geometry pls help. Why did my teacher mark me wrong on this problem and what are the correct answers?
Step-by-step explanation:
it is a bit difficult to read the handwriting (and even the printed original texts) in this diffuse picture.
let's go through the 3 problems as I could decipher them.
1)
from what I can see you made a calculation mistake for y.
but you were right with your approaches.
12x - 8 = 15x - 23
15 = 3x
x = 5
therefore,
12x - 8 = 12×5 - 8 = 60 - 8 = 52°
and the large angle up there is
52 + 70 = 122°
and now
6y + 96 = (12x - 8) + 70 = 122
6y = 26
y = 26/6 = 13/3
by the way, x and y are not angles (and degrees). they are just factors in the expressions to calculate some angles.
12, 15 and 6 are not ° either. all are calculation factors or terms, that then together define the ° of angles.
2)
you made a mistake with the identification of what angles the linear pair is.
3x = 5x - 20
20 = 2x
x = 10 (again, not °, just a number)
3x = 3×10 = 30° (this is then an angle)
= 5x - 20
for y we could then use 2 different approaches
a) your linear pair approach.
4y is one angle, true, but the other is (2y + 3x) !
so,
4y + 2y + 30 = 180
6y = 150
y = 25 (again, not °, just a number)
2y = 50°
4y = 100°
3)
I hope you are right with (11x + 19) and (12y - 24). I would have read this in the picture as (11x + 18). and it could be (12y + 24).
assuming you are right :
11x + 19 = 7x + 47
4x = 28
x = 7 (again, not °, just a number)
11x + 19 = 7x + 47 = 96°
7z + 17 = 87
7z = 70
z = 10 (again, not °, just a number)
and yes, for y we are using the linear pair again. the two combining angles are (12y - 24) and (11x + 19).
(12y - 24) + (11x + 19) = 12y - 24 + 96 = 180
12y + 72 = 180
12y = 108
y = 9 (again, not °, just a number)
12y - 24 = 12×9 - 24 = 108 - 24 = 84°