How do I write an equation for this relationship (where y represents the number of blocks and x represents the stage number).
Answers
The equation of the line is y = 4x + 1 , where the slope of the line is m = 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the number of blocks be y
Let the stage number be x
Let the first point be represented as P = P ( 1 , 5 )
Let the second point be represented as Q = Q ( 2 , 9 )
Now , the slope of the line between the points be
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 5 ) / ( 2 - 1 )
Slope m = 4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = 4 ( x - 1 )
On simplifying the equation , we get
y - 5 = 4x - 4
Adding 5 on both sides of the equation , we get
y = 4x + 1
Therefore , the value of A is y = 4x + 1
Hence , the equation of line is y = 4x + 1
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Related Questions
1) If 6y + 12 = 30, then what does 23 + 7 - 5y =
2) If x + 3x - 2x = 14, then what does 4x + 1 =
3) If d - 9 + 16 = 57 then what does 2d =
4) If p -11 + 3p = 77 then what does 2p / p + 2 =
Answers
Step-by-step explanation:
1. you must first find the value of y
[tex]6y + 12 = 30 \\ 6y = 30 - 12 \\ 6y = 18 \\ y = 3 \\ 23 + 7 - 5y \\ 23 + 7 - 5(3) = 15[/tex]
In ΔWXY, w = 4.8 inches, x = 7.2 inches and y=9.3 inches. Find the measure of ∠W to the nearest degree.
Answers
PLEASE HELPPPP MEEEEEEEE
Answers
Answer:
y = 3x + 9
Step-by-step explanation:
The initial equation would be y = mx + b where m is the slope and b is the y-intercept. Then you would use the equation y^2 - y^1 / x^2 - x^1 to get the slope. Substituting the factors in it would be, 15 - 12 / 2 - 1 having a slope of 3. Then seeing as x is 0 y is 9, 9 must be the y-intercept.
Find the area of the square below.
if im correct, its 9. But I want to double check since I haven't done this in a while!
Answers
Answer:
its 9 only
Step-by-step explanation:
cuz the formula of area of square is side²
Answer:
Yeah it's 9. Bcs the area of the square is *side × side*
Jamie and Hanna are 288 miles apart, traveling towards each other. If Hanna travels 22 mph and Jamie travels 14 mph how long until they meet?
Answers
Answer:
It will take them 8 hours to meet
Step-by-step explanation:
If Hanna travels 22 mph towards Jamie and Jamie travels 14 mph towards Hanna that means that the speed with which the close up equals...
22 + 14 = 36 mph
Now divide the distance between them by the speed with which they get closer to each other, and get...
288 miles / 36 mph = 8h
2 alien spaceships are traveling toward each other from space stations that are 7100 km apart at speed of 110000 km
Answers
It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:
Speed = distance / time
Distance = Speed * time
The spaceships are moving at 110000 km/h
The distance covered by each in x hours is:
Distance = 110000 * x = 110000x
Since they are 7100 km apart, hence:
110000x + 110000x = 7100
220000x = 7100
x = 0.03227 hours = 116.18 seconds
It would take 116.18 seconds for the spaceships to meet.
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Select the two values of x that are roots of this equation.
x2 - – 5x + 5 = 0
Answers
Answer:
Using the Quadratic Formula
x=-b ± √b²-4ac/[2a]
x= -(-5) ± √5² - 4(1)(5)/(2)
x= 5 ± √25-20 /(2)
x= 5 ± √5 /(2)
x= 5 + √5/(2) and 5 - √5/(2)
Answer
B and C
A family buys a studio apartment for $140,000 They pay a down payment of $35,000
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $7,000 down payment be?
Answers
Answer:
a. Their down payment is 25% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$35,000 ÷ $140,000 = 0.25 = 25%
b. A $7,000 down payment would be 5% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$7,000 ÷ $140,000 = 0.05 = 5%
plz help me i'm so confused :/
Answers
Answer:
Diameter = 14 yd
Step-by-step explanation:
Given:
Area of semicircle = 76.97 yd²
Required:
Diameter of semicircle
Solution:
Area of a semicircle = ½(πr²)
Area = 76.97 yd²
Plug in the values
Thus:
½(π*r²) = 76.97
Multiply both sides by 2
πr² = 2*76.97
πr² = 153.94
Divide both sides by π
r² = 153.94/π
r² = 49.0
Take the square root of both sides
r = √49.0
r = 7 yd
Diameter = 2(r)
Diameter = 2(7) = 14 yd
Hurry help me rq I need an answer fast its for 45 points
Answers
Answer:
A) I’m 100% sure it’s correct!
Step-by-step explanation:
Answer:
A. 7
Step-by-step explanation:
[tex]82 - 75 \\ = 7[/tex]
2 in
Ben uses clay to make the rectangular prism to the left. Naomi
uses cardboard to make the triangular prism to the right. Compare
the volumes of the prisms. Use pencil and paper. Describe two
(The figures are not to scale) different methods by which you can compare the volumes.
11 in
5 in
in
18 in
5 in
Which statement best compares the volumes of the two prisms?
O A. Naomi's prism has the greater volume.
OB. Ben's prism has the greater volume.
OC. The prisms have the same volume.
Answers
Answer:
A
Step-by-step explanation:
Ben uses clay to make the rectangular prism to the left. Naomi uses cardboard to make the triangular prism to the right. Therefore, Naomi's prism has a greater volume.
What is the volume of the rectangular prism?The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.
Volume of rectangular prism = (length x width x height)
Ben uses clay to make the rectangular prism to the left.
Volume of rectangular prism = (length x width x height)
= 11 x 5 x 2
= 110 cubic in
Naomi uses cardboard to make the triangular prism to the right.
The volume of a right triangular prism = ( height× Base Area)
= 4 x 18 x 4
= 288 cubic in
Therefore, Naomi's prism has a greater volume.
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. Solve the following
1. Jane had 4 apples
. She divided them so that she had just enough
fourths of an apple for each friend and herself. How many of them
were there?
20
2. Four-eighths of the class built a diorama while
of them built a
wishing well. Which activity had more members?
15
3. Renee Ann has a rope
that is
6/4 meters long. Baby has one that is 15/10 meters long. Who has a long rope?
Answers
Answer:
Step-by-step explanation:
1. If there are 4 apples, each apple has 4 fourths x 4 apples =16 fourths
2. Something is missing???
3. 6/4 x 5/5=30/20, 15/10 x 2/2=30/20 so both are same length
What is the growth factor of the following example? Assume time is measured in the units given.
A city grows by 28% per decade
a. 0.28 per decade c. 128 per decade
b. 28 per decade d. 1.28 per decade
Please select the best answer from the choices provided
Answers
Answer:
D. 1.28 per decade
Step-by-step explanation:
I calculated it logically
HELP! aaa 5,6,7,8 bonus
Answers
1. The height of a right triangular prism is 1 5/6 inches. Each side of the triangular base measures 10 inches, and the height of the base is 8 2/3 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.
What is the surface area of the solid formed?
100 POINTS!!! IF YOU DRAW AN ACCURATE DIAGRAM TOO, YOU WILL BE AUTOMTIC BRAINLIEST!!!!!!
Answers
If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
First step:-
Right triangular prism=1⁵/₆ inches= 11/6 inches
Height of the base=8²/₃ inches = 26/3 inches
Second step:-
Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)
Surface area = 5(100) +43.33+ 3(18.33)
Surface area = 500) +43.33 + 55
Surface area = 598.33 in²
Therefore the surface area of the solid formed is about 598.33 in²
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HELP ME NO LINKS I REALLY NEED HELP
Answers
Answer:
Mode
Step-by-step explanation:
If you have an outlier, the best way to measure a set of data is the mode, or the number that occurs the most.
Please answer the following question, AND NO LINKS OR YOU WILL GET REPORTED.
A parallelogram is cut from a piece of fabric. The parallelogram has a height of 8 inches and an area of 120 square inches. What is the length of the base of the parallelogram?
Answers
Answer:
The length is 15 inches squared
Step-by-step explanation:
total area / height = length
120 / 8 = 15
Which is the graph of f(x) =
4(3)?
y
y
7
6
5
5
4
4
3
3
3
2
2
2
-1
1
+
-3 -2 -14
1
2
3
4
5
8
-3 -2 -1
1
2
3
4
5
8
-3 -2 -2
1
2
3
4
5
6
2
2
ܕܝܚ.
جسمة
Answers
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
Answer: To solve the quadratic equation 8x^2 + 16x + 3 = 0, Patel could use the following steps:
Divide both sides of the equation by 8 to obtain x^2 + 2x + 3/8 = 0.
Rewrite the equation in the form (x + a)^2 = b by completing the square: x^2 + 2x + (1/2)^2 = (1/2)^2 - (3/8).
Rewrite the equation as (x + a)^2 - b = 0. In this case, a = 1/2 and b = -3/8.
Use the quadratic formula to solve for x:
x = (-1/2) +/- sqrt((1/2)^2 - (-3/8))
= (-1/2) +/- sqrt(5/8)
= (-1/2) +/- sqrt(40/64)
= (-1/2) +/- sqrt(10/16)
= (-1/2) +/- (5/8)
= -1 +/- 5/8
= -1 + 5/8 or -1 - 5/8
= -7/8 or 1/8
Therefore, the solutions to the quadratic equation are x = -7/8 or x = 1/8.
Step-by-step explanation:
Use the Parabola tool to graph the quadratic function.
f(x) = 2x2 + 8x + 10
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola
Answers
Step-by-step explanation:
f(x) = 2x²+8x+10
vertex point :
x = -8/2(2)= -8/4
=> x = -2 <= this is a symetry axis
f(-2)= 2(-2)²+8(-2)+10=8-16+10=2
the vertex point : (-2, 2)
intercept with y-axis :
f(0) = 0+0+10 = 10
the point : (0, 10)
the drawing as attached
X coordinate of vertex
-8/2(2)-8/4-2y coordinate
y=2(4)-16+10y=-8+10y=2Vertex is at (-2,2)
Put x=0
y=10Graph attached
Billy ran 3 miles on his first day of training. The next day he ran 2/3 that distance. How far did he run the second day?
Answers
Solve: -7(3x - 7) + 21x > 50
Answers
Answer: Option 2
Step-by-step explanation:
[tex]-7(3x-7)+21x \geq 50\\\\-21x+49+21x \geq 50 \\\\49\geq 50[/tex]
This is false, so there are no solutions.
solve the following 4x-3=2x+7
Answers
Answer: x=5 (simplified)
Answer:
4x-3=2x+7
4x-2x=7+3
2x=10
2x/2x=10/2
x=5
Brenda has $450 in her checking
account. She withdraws $15 a day for
lunch. Which equation can be used to
find
y, the total in Brenda's checking
account, if x represents the number of
days she bought lunch?
A. y = 450x + 15
B. y = 450 + 15x
C. y = 450 - 15x
D. y = 450x - 15
Need H
Answers
Answer:
the answer is B.450 +15x
Answer:
B
Step-by-step explanation:
Determine the center and radius of the following circle equation:
x^2 + y^2 + 12x + 16y + 19 = 0
Answers
Answer:
radius: 9
center: (-6, -8)
Step-by-step explanation:
First, you may wan to rearrange the equation so it is easier to sole, like:
x^2 + 12x + y^2 + 16y + 19 =0
Next, we need to complete the square. x^2 + 12x is the start of the square of x + 6, which ends in 36, and y^2 + 16y is the start of the square of x + 8, which ends in 64. We can start to write in the squares like:
x^2 + 12x + 36 - 36 + y^2 + 16y + 64 - 64 + 19 = 0
(36 & 64 are subtracted so the equation stays the same)
You can factor getting:
(x + 6)^2 - 36 + (y + 8)^2 - 64 + 19 = 0
You can combine the constants to get -36 - 64 + 19 = -81 and we can add 81 to both sides to get:
(x + 6)^2 + (y + 8)^2 = 81
The standard form of a circle equation is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center and r is the radius.
In this case, by substituting, we get the center is (-6, -8) and the radius is 9.
You decide to take a hot air balloon ride and remember to take binoculars to look around while you are airborne. As the balloon rises, you use a GPS to determine your height in meters, h, and the distance in kilometers, d, to the farthest object that you can see. The table below shows the two measurements.
Height in meters 15 30 45 60 75 90 105
Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598
1. Determine a function that could be used to model the data in the table.
Make sure to use h for height and d for distance.
2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round answer to the nearest whole number
3. What type of function best models the data in the table?
4. A building is 16km away. What height does the balloon have to rise for the building to be visible. Round the answer to nearest whole number.
Answers
Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex..
Explain trigonometry.Trigonometry is a discipline of mathematics that examines relationships between triangles' degrees and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.
Here,
Angle of elevation to the balloon's peak: = 28°
When the balloon is erect, a right triangle is formed by the horizontal distance to the balloon, l, the height of the balloon, h, and the distance to the top of the balloon, d.
Aside from the hypotenuse
l = The leg next to the provided reference angle
,h = The leg perpendicular to the specified angle,
Trigonometric ratios give us;
Cosx is equal to the product of the hypotenuse and adjacent lengths.
where we obtain;
Cos x equals l/d
=>Cos 28 = 30 m /d
=> d = 30m/Cos 28 ≈ 33.977
Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Solve this quadratic equation using the quadratic formula.
x^2 - 6x + 6 = 0
Answers
Answer:
x1=3+√3
x2=3-√3
Step-by-step explanation:
caiso calculator
mode 5 --> 3
then
1 = -6 =6
then hit =
you will get
x1=3+√3
x2=3-√3++99+
If there are estimated to be 10 ^ 11 galaxies in the known universe and 10 ^ 11 stars in each galaxy, how many stars are estimated to be in the universe?
Answers
Answer: We can use the information given to find the number of stars in the universe by multiplying the number of galaxies by the number of stars per galaxy:
number of stars = (10 ^ 11 galaxies) x (10 ^ 11 stars per galaxy)
This is a simple arithmetic problem and we can find the solution by multiplying the numbers 10^11 and 10^11
10^11 * 10^11 = (10101010101010101010)(101010101010101010*10) = 10^(11+11) = 10^22
So, there are estimated to be 10 ^ 22 stars in the known universe.
Step-by-step explanation:
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x - 1.
Answers
Answer:
You are correct. The answer is the blue point marked
Step-by-step explanation:
alex, beverly and carl live on the same straight road. alex lives 12 miles from beverly and carl 4 mies from berve,y, how far does alex live from carl?
Answers
Carl to Beverly = 4 miles
So it’s 12 + 4 = 16 miles