The equation of the line is y=x+12.
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The points are
(-3,9)=[tex](x_{1} ,y_{1} )[/tex] and (-9,3)=[tex](x_{2} ,y_{2} )[/tex]
The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
We have to Write the equation of the line.
According to given question we have,
Equation of line passing through the point (-3,9) and (-9,3).
Slope of the line=
[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\\=\frac{3-9}{-9+3} \\\\=\frac{-6}{-6} \\\\=1[/tex]
⇒y−9=1(x+3)
⇒y-9=x+3
Add 9 on both sides we get,
y=x+12
∴ y=x+12 which is in the form y=mx +c is the required equation.
Therefore, the equation of the line is y=x+12.
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y = x + 12
What is equation of a line?
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.
y-y₁=m(x-x₁)
mm₁=-1
Points (-3,9) and (−9,3).
Slope of the line m = (y₂ - y₁)/(x₂ - x₁)
m = (3-9)/(-9+3)
m = 1
Now equation of line passing through two points
(y - y₁)/(y₂ - y₁) = m*(x - x₁)/(x₂ - x₁)
(y - 9)/(3-9) = 1*(x - 3)/(-9+3)
y - 9 = x + 3
y = x + 12
Therefore, the equation of line is y = x + 12
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The width of a rectangle is 3 less than its length find the width of the rectangle if its perimeter is 26ft
The width of rectangle is 5 feet.
Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).
Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -
Perimeter = 2 × (length + width)
Keep the values in formula to find the value of width
26 = 2 × (x + x - 3)
Performing addition of variables inside the bracket
26 = 2 × (2x - 3)
Shifting 2 to other side of equation to find the value of x
2x - 3 = [tex]\frac{26}{2}[/tex]
Performing division to find the value of x
2x - 3 = 13
Shifting 3 to other side of equation to find the value of x
2x = 13 + 3
Performing addition to find the value of x
2x = 16
Shifting 2 as denominator to other side of equation to find the value of x
x = [tex]\frac{16}{2}[/tex]
Performing division to find the value of x
x = 8
So, length of rectangle is 8 feet
Width of rectangle = x - 3
Width of rectangle = 8 - 3
Width of rectangle = 5 feet
Hence, the width of rectangle is 5 feet.
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If cos(t) = 2/9 and t is in the 1st quadrant, find sin(t)
Answer:
Step-by-step explanation:
We can start by solving for t using the fact that [tex]cos(t) = \frac{2}{9}[/tex].
[tex]t = cos^{-1}(\frac{2}{9}) = 77.16\\[/tex]
then using that value of t solve for sin(t)
sin(t) = 0.975
As cos(t) is given and t is in the first quadrant then sin(t) will be equal to 8.77/9.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the information in the question,
cos(t) = 2/9
As we know that cos θ = B/H
B = 2 and H = 9
Now, use Pythagoras's theorem,
H² = P² + B²
P² = 9² - 2²
P = √77
P = 8.77
We also know that sin θ = P/H
So, sin(t) = 8.77/9
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IF YOU JUST SIMPLY ANSWER!!!! 100 points!!!!
Answer:
hi loll
Step-by-step explanation:
8. Two straight lengths of wire are placed on the ground, forming vertical angles. If the measure (3 points)
of one of the angles formed is 72°, what are the measures of the other three angles? Explain
your answer.
Given the matrices A and B shown below, find -2A + 2B.
A = [0 -6] B = [-8 -1]
Answer:
The and is –6
Step-by-step explanation:
–2A= –2[0 , –6]
2B= 2[–8 , –1]
–2A= –2 [0 , +12]
2B= 2[–16 , –2]
–2A + 2B=[0 ,12] + [–16 ,–2]
=[0+(–16) + 12+(–2)]
=[0–16+12–2]
= –16+10
= –6.
Hope it was helpful
help me i rlly need help this is do in few mins
Answer:
Step-by-step explanation:
first we can turn these mixed fractions into normal numbers so
1.42<.336 FALSE
.54>1.357 false
.615>.96 false
1.16>1.83 TRUE
10.) The height of a tree trunk is 20 meters, and the base has a diameter of 1 meter. If the tree has the mass
420, what is the density of the tree?
26.27 kgm⁻³
Density is the ratio of mass to volume
Density = Mass / Volume
Let us assume tree is a cylinder,
d= 1
r = d/2 = 0.5 m
h= 20 m
m= 420kg
Volume = π r²h
= 22/7 x o.25 x 20
Density = mass / volume
= 420 / 22/7 x o.25 x 20
= 26.27 kgm⁻³
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The first term of arithmetic sequence is 2 and 10th term is 39 find the 30th term
One batch of brown paint uses 8 of yellow paint and 3 cups of purple paint Tyler made a large amount of brown paint using 40 cups of yellow paint
Answer:
not sure what you were asking, but its 15 cups of purple paint
Cross braces help keep the deck posts straight. Find the measure of each angle.
Angle 5 = 180 - 146 = 34
Angle 6 = 146 since vertical angles are congruent
Angle 7 = 34 since vertical angles are congruent, or you could say 180-146 = 34 again. Any pair of adjacent angles add to 180. All four angles add to 360.
The diagram shows a solid triangular prism with a cylindrical hole of radius r cm drilled through it. (i) The ratio of the volume of solid removed : volume of remaining solid is 1 : 6. Find the value of r. Using your answer in part (i), find the total surface area of the solid shown.
The value of the radius r is 9.35 cm.
The dimensions of the triangular prism is 62 cm × 62 cm × 85 cm.
The volume of the prism will be:
Volume = (1/2) × 62 × 62 × 85
Volume = 163370 cm³
Now,
The volume of solid removed: The volume of remaining solid = 1 : 6
Therefore,
The solid removed = ( 1 / 7 ) of the total volume
Solid removed = ( 1 / 7 ) × 163370
Solid removed = 23338.57 cm³ which is the volume of the cylindrical hole.
Now, the volume of the cylinder is:
V = π (r)² h
23338.57 = π (r)² × (85)
23338.57 = (3.142) × (r)² × (85)
23338.57 = 267.1 r²
r² = 87.38
r = √(87.38)
r = 9.35 cm
The surface area of the triangular prism:
A = (1/2) (b) (h)
A = (1/2) (85)(62)
A = 2653 cm²
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The length of a rectangle is seven more than triple the width. if the permiter is 134 inches, find the dimensions
The dimensions of the rectangle that has the perimeter 134 inches is, 52 x 15 inches.
Perimeter of the Rectangle:
Perimeter of the rectangle is defined as the total distance covered by its boundaries or the sides.
The formula for the perimeter of a rectangle,
P = 2 (a + b) units
where
“a” is the length of the rectangle
“b” is the breadth of the rectangle
Given,
The length of a rectangle is seven more than triple the width.
Perimeter of the rectangle = 134inches.
Now we need to find the dimensions of the rectangle.
First, let's define the length of the rectangle as l and the width of the rectangle as w.
Next, we can write the relationship between the length and width as:
l = 3w + 7
We also know the formula for the perimeter of a rectangle is:
=> p = 2(l + w)
So, apply the given values on it,
=> 134 = 2 (3w + 7 + w)
=> 134/2 = 4w + 7
=> 67 = 4w + 7
=> 67 -7 = 4w
=> 4w = 60
=> w = 60/4
=> w = 15
So, the length is,
=> l = 3(15) + 7
=> l = 45 +7
=> l = 52.
Therefore, the dimensions of the rectangle is 52 x 15 inches.
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Jorge, sandra, danny, and valeria each mowed lawns after school and on the
weekends for a month. sandra mowed one-third of the number of lawns as jorge
and danny mowed half as many lawns as jorge. if valeria mowed 16 lawns and
the group mowed a total of 49 lawns in the month, how many did jorge mow?
Jorge mowed 18 lawns.
Let the number of lawns mowed by Jorge =x
So according to the question
Number of lawns mowed by sandra = x/3
Number of lawns mowed by Danny =x/2
Number of lawns mowed by Valeria =16
sum of total lawns mowed = lawns mowed by Jorge + lawns mowed by sandra + lawns mowed by Danny + lawns mowed by Valeria.
[tex]x+\frac{x}{3} +\frac{x}{2} +16=49[/tex]
taking LCM as 6 and solving further we get
[tex]\frac{6x+2x+3x+96}{6} =49[/tex]
By cross Multiplying we get
11x+96=294
11x=198
Solving further for x,
x=198/11
x=18
Therefore, the number of lawns mowed by Jorge is 18 .
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Consider this solution to a problem. what is the number of the step where the mistake is made? question 4 options: step 1 step 2 step 3 step 4
In step 1 mistake has been made because negative multiplication gives a positive result but is written negative.
What is the equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.
Given that,
−4(6−y) + 4 = −4
By using distribution property
-24 + 4y + 4 = -4
But in the question +4y is written as -4y which is wrong.
Hence In step 1 negative multiplication gives a positive result but is written negative so in step 1 mistake has been made".
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The given question is not complete.
Consider this solution to a problem.
Problem: −4(6−y)+4=−4
Step 1: −24−4y+4=−4
Step 2: −20−4y=−4
Step 3: −4y=16
Step 4: y=−4
In the first response box, enter the number of the step where the mistake is made.
Given the quantities a=3.7m, b=3.7s, c=80m/s, what is the value of the quantity d=a^3/cb^2?
The value of the quantity d is 0.0462 m^2/s.
Here,
The quantities a=3.7m, b=3.7s, c=80m/s.
We have to find the value of d = a^3/cb^2
What is quantity?
A quantity is an amount, number, or measurement that answers the question 'how much?' Quantities can be expressed in numbers or non-standard units.
Now,
The quantities a=3.7m, b=3.7s, c=80m/s.
The value of d;
[tex]d = \frac{a^{3} }{cb^{2} }[/tex]
[tex]d = \frac{3.7*3.7*3.7 }{80 * 3.7^{2} }[/tex]
[tex]d = \frac{3.7}{80}[/tex]
[tex]d = 0.0462[/tex]
Hence, The value of the quantity d is 0.0462 m^2/s.
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Use prime factorization to determine the greatest common factor of 180 and 504
Answer: 36
Step-by-step explanation:
First you plot down all the factors of 180.*
*180 1, 90 2, 60 3, etc.
Then you do the same for 504.*
*504 1, 252 2, etc.
Once you do that you look through and find the common factor, and you'll find that 180/5=36, and 504/14=36, finding you your GCF.
I would like the answers to one and two bit the bottom ones
The numeric values for the functions are given as follows:
6 - a) f(-2) = -13.
6 - b) g(4) = 11.
How to find the numeric value of a function?To find the numeric value of a function, we replace each instance of the variable by the desired value.
At item 6a, the function is given by:
f(x) = 5x - 3.
The numeric value at x = -2 is:
f(-2) = 5(-2) - 3 = -10 -3 = -13.
Hence f(-2) = -13.
At item 6b, the function is given by:
g(x) = 0.5x² + 3.
The numeric value at x = 4 is:
g(4) = 0.5(4)² + 3 = 8 + 3 = 11.
Hence g(4) = 11.
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Samra's guardians invested money for her into a 529 College Savings Plan, which compounds annually. The growth of the savings plan per year, x, can be represented by the exponential function f(x) = 500(1.03)x. What is the meaning of the y-intercept in the context of the problem?
The percent rate of change is 500%.
The initial value of the investment is $500.
The principal amount put into the savings plan is $1.03.
The average rate of change that is occurring is 1.03.
The y-intercept of the given exponential function would be represents the initial value of the investment is $500 which is the correct option (B).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The given exponential function f(x) = 500(1.03)ˣ
Here x would be represented growth of the savings plan per year
To determine the y-intercept of the function
We have to substitute the value of x = 0 in the given function,
⇒ f(x) = 500(1.03)⁰
⇒ f(x) = 500(1)
⇒ f(x) = 500
Therefore, the y-intercept of the given exponential function would be represents the initial value of the investment is $500.
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X(2x-5) = 12
How to solve for x?
Answer:
[tex]x=4,\:x=-\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]x\left(2x-5\right)[/tex]
Apply the distributive law.
[tex]=x\cdot \:2x-x\cdot \:5[/tex]
[tex]=2x^2-5x[/tex]
[tex]2x^2-5x=12[/tex]
Subtract 12 from both sides.
[tex]2x^2-5x-12=12-12[/tex]
[tex]2x^2-5x-12=0[/tex]
Now, apply the quadratic formula.
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:2\left(-12\right)}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \:11}{2\cdot \:2}[/tex]
Separate the solutions.
[tex]x_1=\frac{-\left(-5\right)+11}{2\cdot \:2},\:x_2=\frac{-\left(-5\right)-11}{2\cdot \:2}[/tex]
Simplify.
[tex]x=4,\:x=-\frac{3}{2}[/tex]
Please Help I Do Not Understand. 20+ Points!
5.69 ÷ 7
Please help I'm desperate
Show your work
Answer:0.81285714285
Step-by-step explanation: bc you are deviding by a desimal
What is the value of the absolute value expression |−134| + |4| − |−35|?
Answer:
174
Step-by-step explanation:
absolute value means the distance from zero. Distance is always measured with a positive number. If you asked me how far I lived from my work, I would never say -12 miles away. If I was going or coming to work, the distance would be the same 12 miles.
134 + 4 + 35 = 174
surface area of composite figures
Answer:
mark me brainliest hope your day goes wellStep-by-step explanation:
The area of the composite figures is the area of one or more simple polygons and circles combined. We can add the areas of all the basic figures together to calculate the area of the composite figures. Find the area of each shape and add them together to find the area of the composite figure.Answer:
The surface area is the sum of all the faces (or surfaces) of a 3D shape. Composite figures are 2 figures put together. (There is an example of a composite figure below) You find an area of both shapes and then add them together, to find the area of the full figure.
Step-by-step explanation:
If g(x) =4x²+2x-24,what is g(2)?
Answer:
-4
Step-by-step explanation:
x is a variable, so to do g(2) you have to write g(x), but substitute 2 in place of x:
g(2) = 4*2² + 2*2 - 24 = 16 + 4 - 24 = -4
Find the equation of the line shown.
Answer: y=0.5x+0.5
Step-by-step explanation:
[tex]\displaystyle\\(1,1)\ \ \ \ (-3,-1)\\\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }\\\\x_1=1\ \ \ \ x_2=-3\ \ \ \ y_1=1\ \ \ \ y_2=-1\\\\\frac{x-1}{-3-1}=\frac{y-1}{-1-1} \\\\\frac{x-1}{-4}=\frac{y-1}{-2} \\[/tex]
Multiply both parts of the equation by -2:
[tex]\displaystyle\\\frac{x-1}{2} =y-1\\\\\frac{x}{2}-\frac{1}{2} =y-1\\\\\frac{x}{2}-\frac{1}{2}+1 =y-1+1\\\\\frac{x}{2}+\frac{1}{2} =y \\[/tex]
Thus,
y=0.5x+0.5
solving factors finding answers for a b c and d
Step-by-step explanation:
a is 5, b is 24, c is 2 and d is 2
Nate and Maya are building model cars. Maya's car is 3 inches less than 2 times the length of Nate's car. The sum of the lengths of both cars is 26 inches. Write an equation to determine the lengths of Nate's and Maya's cars.
x + 3 − 2x = 26
x + 2x = 26
2x − 3 = 26
x + 2x − 3 = 26
Answer:
x + 2x - 3 = 26
Step-by-step explanation:
Define the variables:
Let x = length of Nate's car.Let y = length of Maya's car.If Maya's car is 3 inches less than 2 times the length of Nate's car, then:
⇒ y = 2x - 3
If the sum of the lengths of both cars is 26 inches, then:
⇒ x + y = 26
Substitute the found expression for y into the equation:
⇒ x + y = 26
⇒ x + (2x - 3) = 26
⇒ x + 2x - 3 = 26
Therefore, the equation to determine the lengths of Nate'a and Maya's cars is:
[tex]\boxed{x + 2x - 3 = 26}[/tex]
Solving the equation for x
⇒ x + 2x - 3 = 26
⇒ 3x - 3 = 26
⇒ 3x - 3 + 3 = 26 + 3
⇒ 3x = 29
⇒ 3x ÷ 3 = 29 ÷ 3
⇒ x = 9.7 in (nearest tenth)
Therefore, Nate's car is 9.7 in (nearest tenth).
To find the length of Maya's car, subtract the length of Nate's car from 26:
⇒ 26 - 9.7 = 16.3 in (nearest tenth).
Therefore, Maya's car is 16.3 in (nearest tenth).
Answer:
d) x + 2x - 3 = 26
Step-by-step explanation:
Given that,
→ Maya's car is 3 inches less than 2 times the length of Nate's car.
→ The sum of the lengths of both cars is 26 inches.
Now the equation will be,
→ x - 3 + 2x = 26
→ x + 2x - 3 = 26
→ 3x = 29
Hence, option (d) is correct answer.
A commuter train travels 50 kilometers in 43 minutesWhat is speed in kilometers per hour?
Answer:
70.42 kilometers.
Step-by-step explanation:
43 minutes/60 minutes (1 hour is 60 minutes) = 0.71 hours.
Now we set up a problem here.
50 kilometers/0.71 hours = x kilometers/1 hour
We multiply out 1 hour and cancel out from both sides.
50/0.71 kilometers = 70.42 kilometers.
Therefore, the train was traveling at 70.42 kilometers per hour.
What is walmart's ebit for the year of 2018 (round it to 3 numbers after the decimal point -> 0.581)?
Walmart's EBIT for the year 2018 is $17,101.
What is EBIT?Earnings before interest and taxes (EBIT) is a measure of a company's profit that includes all income and expenses (operating and non-operating) except interest and income tax expenses (for individuals).When a company does not have non-operating income or non-operating expenses, operating income and operating profit are sometimes used as synonyms for EBIT.To find Walmart's EBIT:
9,862 + 661+ 4,600 + (1,826 + 152) = $17,101Therefore, Walmart's EBIT for the year 2018 is $17,101.
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The correct question is given below:
What is Walmart's EBIT for the year of 2018 (round it to 3 numbers after the decimal point -> 0.581)?
EBIT= net income (Listed as "Net IncomeAvail to Common, GAAP" in Statement) + net income attributable to noncontrolling interest ("Listed as Income Loss Incl. MI Minority Interest" on Statement) + income taxes + interest expense (Interest Expense Net + "Interest Income" from the Statement ) (A financial statement would be provided).
1. Draw the graph of y = 3 – x/2 using a table of points from x = -3 to 3.
Answer:
Step-by-step explanation:
x = -3 to 3
means that they are asking for the graph from -3 to 3 on the x-axis
gradient is (-1/2) which means rise is -1 when run is 2
y-intercept is 3.
go to 3 on the y axis which means the coordinate (0,3) go downwards by 1 and to the right by 2. This will lead you to coordinate (2,-1). Now connect both points by a straight line.