The rule for the given set of data is y = 3x - 1.
What is rule in function?The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.
A function rule can be defined as the procedure that transforms an input value into an output in plain English.
Lets put two of the points in slope formula
y - y₁ = m(x - x₁)
29 - (-13) = m(10 - ( -4))
42 = m14
m = 42/14
m = 3
Now lets make the equation
y - 29 = m(x - 10)
y = 3x - 30 + 29
y = 3x - 1
Thus, the rule for the given set of data is y = 3x - 1.
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PLEASE HELP ASAP!!!!!
Answer:
Left triangle: 12.5 cm
Right triangle: 21 cm
Trapezoid: 50 cm
Total: 83.5
Step-by-step explanation:
Left triangle: The formula to find the area of a triangle is 1/2bh, in which b=base and h=height. The base of the left triangle is 5 cm and the height is 5 cm. 5*5=25. 25/2=12.5 cm.
Right triangle: Once again, use the area formula for a triangle. The base of the right triangle is 6 cm and the height is 5+2=7. 6*7=42. 42/2=21 cm.
Trapezoid: The formula to find the area of a trapezoid is a+b/2(h) in which a and b are the top and bottom of the trapezoid and h=height. In this case, a=9 cm and b=5+6=11 cm. The height is 5 cm. 9+11=20. 20/2=10. 10*5=50 cm.
Add all of the areas. 12.5+21+50=83.5. So, the total area is 83.5 cm.
HELP PLEASE!!
a swimmer takes a running jump off a pier. The path of the swimmer can be modeled by the equation h=-0.1d^2+0.1d+3, where H is the height in feet and d is the horizontal distance in feet. How far from the pier does the swimmer enters the water?
Answer: 5 ft
Step-by-step explanation:
Given
The path of the swimmer is given by
[tex]h=-0.1d^2+0.1d+3[/tex]
The swimmer can go horizontally depends upon the depth
So, find the maximum depth by taking derivative w.r.t height
[tex]h'=-0.2d+0.1[/tex]
Put derivative equal to 0
[tex]\Rightarrow -0.2d+1=0\\\\\Rightarrow d=\dfrac{1}{0.2}\\\\\Rightarrow d=5\ ft[/tex]
thus, the swimmer can go up to a distance of 5 ft.
Simplify the expression 6−2x+5+4x . Show or explain your reasoning.
Answer:
2x + 11 is your answer
Step-by-step explanation:
yeah just 2x + 11
find the area of the region enclosed by one loop of the curve. r = sin(6θ)
Area of the region enclosed by one loop of the curve is pi/288.
To find the area of the region enclosed by one loop of the curve, we can use the formula for the area of a polar region:
A = 1/2 * ∫(r^2)dθ
We can use this formula with the equation for r given:
A = 1/2 * ∫(sin^2(6θ))dθ
This integral can be simplified by noting that sin^2(x) = (1/2)(1 - cos(2x))
Thus,
A = 1/2 * ∫(1/2)(1 - cos(12θ))dθ
This integral can be solved by noting that the antiderivative of (1/2)(1 - cos(12θ)) is (1/24)(sin(12θ) + θ).
Therefore, the area enclosed by one loop of the curve is
A = 1/2 * ((1/24)(sin(12θ) + θ)) evaluated from 0 to pi/6
A = (1/48)(sin(2pi) + pi/6)
= (1/48)(0 + pi/6)
= pi/288
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Which equation represents a line that is perpendicular to the line with equation y = 2x - 8? Select all that apply.
Ay=1/2x+1
B. y=-1/2x+1
C. x + 2y = 5
D. -x + 2y = -3
E. -x-2y = 9
Step-by-step explanation:
credits are also on there
Tori spends $38.00 on coffee each month. About how much dose Tori spend on coffee over 9 months
Answer:
Tori spends $342.00 on coffee over 9 months
Step-by-step explanation:
38 x 9 = 342
= $342.00
What would be the explicit equation for the sequence 3, 9, 27, 81 
Answer:
times it by
Step-by-step explanation:
3×3=9, 9×3=27, 27×3=81, 81×3=243
sorry if this isn't the answer your looking for.
Yesenia buys water to make tea for all her friends. She buys 1 qurt of water and 1/2 gallon of water. How many cups of water does she buy
Answer:
12 cups of water
Step-by-step explanation:
This question has to do with conversion
We are told that she buy 1 quart and 1/2 gallon of water.
Hence,
1 quart of water = 4 cups of water
1 gallon of water = 16 cups of water
1/2 gallon of water = x
Cross Multiple
x = 1/2 × 16 cups of water
x = 8 cups of water.
Therefore, the total cups of water that she bought = 4 cups of water + 8 cups of water = 12 cups of water
what is the vertex and solutions for y=x^2+5x-7 and y=-x^2+3x+8
The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution to the equation is x = -5,7/1. Similarly , the vertex for the given equation [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].
What is parabola?The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).
What is vertex of a parabola?A parabola's vertex is the location where its symmetry line and parabola intersect.
The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:
[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]
For the first equation: [tex]y = x^2 + 5x - 7[/tex]
The vertex would be:
[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]
So the vertex is [tex](-2.5,-4.25)[/tex]
For the second equation:[tex]y = -x^2 + 3x + 8[/tex]
The vertex would be:
[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]
So the vertex is [tex](-3/2,1/4)[/tex]
To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.
[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]
Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4
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What is the volume of the following rectangular prism?
Answer:
Length * Height * Width, or V = L * H * W. Ex: V = 5 in.
Answer:
28
Step-by-step explanation:
We are given the area of a base and the width of the prism.
Volume = area of base * width
Volume = 8/3 * 21/2 = 28
helpppppppppp plst q
Answer:
9π units
Step-by-step explanation:
The arc length is calculated as
length = [tex]\frac{1}{2}[/tex] × 2πr ( r is the radius )
length = πr = π × 9 = 9π ← exact answer
PLEASE IM BEGGING FOR HELPP
Answer:
y ≥ 1
Step-by-step explanation:
According to the graph, the y values start at 1 and go to ∞. Therefore, the range of the function is y ≥ 1.
1) Iris' puppy is 2 1/5 feet long. Which
decimal represents Iris' puppy's length?
a) 2.15 feet
b) .215 feet
c) 2.2 feet
d) 2.02 feet
need an answer ASAP!
Answer:
c) 2.2 feet
Step-by-step explanation:
1) Iris' puppy is 2 1/5 feet long. Which
decimal represents Iris' puppy's length?
c) 2.2 feet
Help! NO LINKS!!!
I need an answer so if anyone can help,please do!
How to do elimination with 3 equations?
Elimination is a method of solving a system of equations using addition or subtraction to eliminate one of the variables.
Here we will use the elimination method to solve a system of three equations with three variables.
Let's say we have three equations with three variables x, y and z.
Equation 1: ax + by + cz = d
Equation 2: ex + fy + gz = h
Equation 3: ix + jy + kz = l
We will start by multiplying the first equation by a number that will make the coefficients of y in the two equations the same.
Let's say we choose to multiply the first equation by -f, so that we get:
-fax -fby -fcz = -fd
Now we add the two equations to eliminate y:
ax + by + cz + (-fax -fby -fcz) = d -fd
ax -fax + by -fby + cz -fcz = d -fd
(a -f)x + (b -f)y + (c -f)z = d -fd
Now we can multiply the second equation by a number that will make the coefficients of z in the two equations the same. Let's say we choose to multiply the second equation by -k, so that we get:
-kex -kfy -kgz = -kh
Now we add the two equations to eliminate z:
(a -f)x + (b -f)y + (c -f)z + (-kex -kfy -kgz) = d -fd -kh
(a -f)x + (b -f)y + (c -f)z -kex -kfy -kgz = d -fd -kh
(a -f -k)x + (b -f -k)y = d -fd -kh
We can now solve this equation for x:
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
Now we can substitute this expression for x in any of the original equations and solve for y:
Let's choose to substitute in the first equation:
ax + by + cz = d
(d -fd -kh - (b -f -k)y) / (a -f -k) + by + cz = d
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
Now we can substitute this expression for y in any of the original equations and solve for z:
Let's choose to substitute in the second equation:
ex + fy + gz = h
e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + gz = h
gz = h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
Now we have
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
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After Charlie ate 2/3 of the remaining cake, he divided the rest equally among his 3 friends. What fraction of the pan of cake did each friend get? Write an expression and show all of your work.
Answer: 1/9 of the cake
Step-by-step explanation:
Charlie ate 2/3 of the cake which means that what is left to give the friends is:
= 1 - 2/3
= 1/3 of the cake
This was divided equally amongst three friends so the expression would be:
= 1/3 ÷ 3
This can also be written as:
= 1/3 * 1/3
= 1/9
Each friend got 1/9 of the cake.
Answer:
1/9 of the cake
Step-by-step explanation:
1 - 2/3 = 1/3 left
(1/3) / 3 = 1/9 = what each friend got
In one fell swoop we have ( 1 - 2/3) / 3 = 1/9
Write the equation of the line in slope-intercept form that contains the points (4, -1) and (9, 9).
Answer:
y = 2x - 9
Step-by-step explanation:
y2 - y1 / x2 - x1
9 - (-1) / 9 - 4
10 / 5
= 2
y = 2x + b
-1 = 2(4) + b
-1 = 8 + b
-9 = b
Edgar has a fountain that holds 5 quarts of water. He only wants to fill it 3/4 full. How many 1-pint containers does it take to fill the fountain? How could he fill it with pint and cup containers? Explain.
Answer:
Step-by-step explanation:
1 quart = 2 pints = 4 cups
1 pint = 2 cups
1/2 pint = 1 cup .....so.....
First question
5 quarts = 10 pints
10 * (3/4) = 7.5 pint contianers will fill it 3/4 full
7.5 pints = 7 pints + 1 cup
Anyone know how to solve this?
What is 13^c^11?
O A. 91
OB. 105
C. 78
D. 120
Answer:
78
Step-by-step explanation:
13! / 11! · 2!
13 x 12 / 2
13 x 6 = 78
sketch if it helps you.
There is an amoeba (a single-celled animal) on a dish-
After one hour, the amoeba divides to form two
amoebas.
One hour later, each amoeba divides to form two mor
Every hour, each amoeba divides to form two more.
How many amoebas are there after 6 hours?
Answer:
64
Step-by-step explanation:
The x-coordinate of point P is positive, and the y-coordinate of point P is positive. In which quadrant is point P?
Quadrant I
Quadrant IV
Quadrant II
Quadrant III
Answer:
Quadrant I
Step-by-step explanation:
b/c both are on the right side that means they are positive
find the height of the two pillar with same height
Answer:
ED = AB = 25√3
Step-by-step explanation:
Let ED = AB = X
DC = 100 - BC
Tan 60 = [tex]\frac{\sqrt{3} }{1} = \frac{ED}{DC}[/tex] = [tex]\frac{X}{100-BC}[/tex]
[tex]\sqrt{3} (100-BC) = X[/tex]
Tan 30 = [tex]\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}[/tex]
[tex]\frac{BC}{\sqrt{3} } = X[/tex]
[tex]\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC[/tex]
X = [tex]\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\[/tex]
X = 25√3
Jai is 1. 45 meters tall. At 11 a. M. , he measures the length of a tree's shadow to be 39. 55 meters. He stands 34. 1 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter
The height of the tree to the nearest hundredth of a meter is 10.5 meters.
The length of Jai's shadow = length of tree's shadow - distance of standing of Jai
Length of Jai's shadow = 39.55 - 34.1
Performing subtraction on Right Hand Side of the equation
Length of Jai's shadow = 5.45 meters
Tan theta = height of tree/length of shadow = height of Jai/length of his shadow
height of tree/39.55 = 1.45/5.45
Keep the values in formula
Height of tree = 39.55×1.45/5.45
Performing multiplication
Height of tree = 57.35/5.45
Performing division
Height of tree = 10.5 meters
Thus, the height of tree is 10.5 meters.
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Hey guys so I NEEEEEED HELP ON THIS MATH QUESTION, so here it is please help me P.S: LIMITED TIME, P.P.S: LIKE IN 40-74 MINUTES!!! HELP
The approximate diameters of Uranus and Mars are listed below:
Uranus: 5.11×10^4
kilometers
Mars: 6.79×10^3
kilometers
How many times larger is the diameter of Uranus? Write your answer in standard notation, rounding to the nearest tenth.
The number of times the diameter of Uranus is larger than the diameter of Mars is 7.5 times
How to determine the number of times larger is the diameter of UranusFrom the question, we have the following parameters that can be used in our computation:
The diameters of Uranus and Mars
These diameters are given as
Diameter of Uranus: 5.11×10^4 kilometers
Diameter of Mars: 6.79×10^3 kilometers
Express the diameters properly
So, we have the following representation
Diameter of Uranus: 5.11 × 10⁴ kilometers
Diameter of Mars: 6.79 × 10³ kilometers
This means that
Number of times larger = Diameter of Uranus/Diameter of Mars
Substitute the known values in the above equation, so, we have the following representation
Number of times larger = 5.11 × 10⁴ kilometers/6.79 × 10³ kilometers
Evaluate the quotient
So, we have the following representation
Number of times larger = 7.5
Hence, the number of times is 7.5
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Julien's parents want $64,000 at the end of 3 years. They put their money in an account that yields 10% per year compounded monthly. Julien's parents should deposit $______. Round your answer to the nearest dollar.
Answer: [tex]\$47,471[/tex]
Step-by-step explanation:
Given
Julien's parents want $64,000 at the end of 3 years
The rate of interest is 10% annually
Suppose they invested P amount initially
So, compound interest, compounded monthly is
[tex]\Rightarrow A=P\left( 1+\frac{r}{n}\right)^{nt}\quad [\text{n=Numner of compounding periods}]\\\\\text{Insert the values}\\\Rightarrow 64,000=P\left( 1+\frac{0.10}{12}\right)^{12\times 3}\\\\\Rightarrow 64,000=P\left( 1+\frac{10}{12}\right)^{36}\\\\\Rightarrow P=\dfrac{64000}{1.3481}\\\\\Rightarrow P=\$\ 47,471.37\approx \$ 47,471[/tex]
There are 84 classes in a school. Two-thirds learned about the Holocaust. The rest did not. How many classes did not learn about the Holocaust?
Answer:
28 classes
Step-by-step explanation:
84/3 = 28 classes
Answer:
28 classes didn't learn about the Holocaust
Step-by-step explanation:
If there are 84 classes and two-thirds learned about the Holocaust that means that you have to divide by three.
84 ÷ 3 = 28
Then, you can check your answer by multiplying 28 × 3 = 84
If G-H-I, and if GH = 2x - 9 , HI = 14 , and GT = 3x - 8 , then find GI.
The value of GI, given that GH = 2x - 9 , HI = 14 , and GT = 3x - 8 will be 31.
What is the value of the variable?An algebraic equation is formed by comparing two algebraic expressions to one another.
In G-H-I, GH = 2x - 9, HI = 14 , and GT = 3x - 8
If G-H-I is a line and GH, HI and GT lies between G to I
To find G to I ⇒ GI = GH + HI = GT
GI = 2x - 9 + 14 = 3x - 8
2x + 5 = 3x - 8
2x - 3x = -8 - 5
-x = -13
x = 13
Substituting x in GT = 3x - 8; GI = GT
GI = 3(13) - 8
GI = 39 - 8
GI = 31
Using algebraic expressions, if x is 13 then, 3x - 8 or 2x - 9 will be GI = 31
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Necesito esta actividad hecha para mañana y no ne dieron explicación previa
Answer:
uhhugvtrctreex
Step-by-step explanation:
Erin is picking out some movies to rent, and he has narrowed down his selections to 5 documentaries, 5 mysteries, 5 dramas, and 7 action movies. How many different combinations of 9 movies can he rent if he wants all 5 mysteries
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
How are the various combinations determined?The following formula determines how many combinations of n objects can be taken r at a time: (n,r) = C(n,r)! .
She was a master of both wit and martial arts. The art and science of education blend beautifully. He saw slam poetry as the ideal synthesis of thought, writing, and theater. The desired mix is produced by the computer system (the perfect combination of arabica and robusta).
Five documentaries make up the total.
7 comedies total are available.
Four mysteries are present.
5 horror movies are there.
A total of 14 films, excluding comedies, are available.
If he wants to rent all 7 comedies, there are a total of 9 different combinations that he can do.
1 * (14*13)/2 = 91
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
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