Answer:
{x,y}={ 11 /69 ,− 11 /10 }
Step-by-step explanation:
1. A line with a slope of 2 passes through (3,-2). Write the equation in Point-Slope Form.
2. A line with a slope of 2 passes through (3,-2). Write the equation in Slope-Intercept Form.
If the US released 5.877 billion metric tons of carbon dioxide and 1 trillion pounds=0.4536 billion metric tons, how many trillions of pounds of carbon dioxide did the US release?
Answer: 12.96 trillion pounds
Step-by-step explanation:
From the question, we are informed that:
1 trillion pounds = 0.4536 billion metric tons
Therefore, if the US released 5.877 billion metric tons of carbon dioxide, the trillions of pounds of carbon dioxide that the US release will be:
= 5.877 / 0.4536
= 12.96 trillion pounds
A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form.
Answer:
Point-slope form: y + 5 = 13/-4 (x-1)
Slope-intercept form:
Step-by-step explanation:
Ok, so first to find the equation in point-slope form, you need to find the slope. So, the slope would be 7- (-5)/-3-1 , which is 13/-4. That is your slope, or m. Now, for point-slope form, you have the equation y - y1 = 13/-4 (x-x1). Now, you take one of your points, say (1, -5), and you put it into the equation. So your point-slope form equation would be y - (-5) = 13/-4 (x - 1). This would simplify to y + 5 = 13/-4(x - 1).
Now for slope-intercept form, you have m, the slope, which is 13/-4. Substituting that into the equation, you have y = 13/-4x + b. To find b, you substitute one of your coordinates into the equation. For example, (1, -5). Then you have -5 = (13/-4 * 1) +b. Simplify this, and you have b = -5+ 13/-4, which is -20/4 + 13/-4, which is -20/4 - 13/4 = -33/4. So your final equation is y = 13/-4x - 33/4.
Hope that helped.
Which of the following best explains the value of Sine StartFraction pi Over 3 EndFraction on the unit circle below?
A unit circle is shown. A radius with length 1 has an angle measure of StartFraction pi Over 3 EndFraction
sine StartFraction pi Over 3 EndFraction = StartFraction opposite Over hypotenuse EndFractionEquals StartFraction opposite Over 1 EndFraction Equals opposite
The length opposite the angle is the vertical distance from the x-axis on the graph.
sine StartFraction pi Over 3 EndFraction = StartFraction adjacent Over hypotenuse EndFraction = StartFraction adjacent Over 1 EndFraction Equals adjacent
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Sine StartFraction pi Over 3 EndFraction = StartFraction opposite Over hypotenuse EndFraction = StartFraction opposite Over 1 EndFraction Equals opposite
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Sine StartFraction pi Over 3 EndFraction = StartFraction adjacent Over hypotenuse EndFraction = StartFraction adjacent Over 1 EndFraction Equals adjacent
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Answer:
a. sine StartFraction pi Over 3 EndFraction = StartFraction opposite Over hypotenuse EndFractionEquals StartFraction opposite Over 1 EndFraction Equals opposite
The length opposite the angle is the vertical distance from the x-axis on the graph.
Step-by-step explanation:
sin (π/3) = opposite/hypotenuse = opposite/1; The length opposite the angle is the vertical distance from the x-axis on the graph.
What is the trigonometric ratio of unit circle?
Unit circle is a circle centered at the origin, (0,0) with radius(r) i.,e r= 1.
The angle π/3 forms an arc of length S and the x-axis and y-axis divide the coordinate plane and the unit circle as it is centered at (0.0).
Also, the terminal side intersect the circle at (x, y). Thus;
sin (π/3) = opposite/hypotenuse = opposite/1
Thus;
sin (π/3) = opposite
Also, the length opposite the angle is the vertical distance from the x-axis on the graph.
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What is the length of BC?
O 11
O 23
O 40
O 60
Plz help
Answer:
BC = 40
Step-by-step explanation:
Answer:
X=23
BC = 40
Step-by-step explanation:
the sum in the form a(b+c) such that the integers band chave no common factor.
99 +33
Answer:
33(3+1)
Step-by-step explanation:
Find the GCF of 99 and 33
99=3^2•1133=3•11So the GCF is 3•11=33Factor 33 out
33(3+1)Simplify: (2a)(-5b)
?
Answer:
-10ab
Step-by-step explanation:
(2a)(-5b)
Multiply the constants
2* -5 = -10
Multiply the variables
a*b = ab
Combine
-10ab
The expression -10ab represents the product of 2a and -5b
To simplify the expression (2a)(-5b), we can multiply the coefficients and combine the variables.
Multiplying the coefficients, 2 and -5, gives us -10.
For the variables, we multiply the like terms, which in this case are 'a' and 'b'. When we multiply 'a' and 'b', we simply write them side by side: ab.
Therefore, simplifying (2a)(-5b) results in -10ab.
The expression -10ab represents the product of 2a and -5b, combining the coefficients and variables into a single term. It is important to note that the order of the variables, 'a' and 'b', is maintained in the simplified form.
Learn more about expression here
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1) Albert has $200 in the bank. He would like to save $50 every month to buy Christmas
gifts. Which equation can be used to find y, the amount Albert will save for x days?
y = 50x + 200
y = 50 + 200x
y = 250x
y = 200 + 250x
Answer:
y = 50x + 200
Step-by-step explanation:
He has $200 at the bank. He is then adding 50 per month (that's why its 50x).
I need help this is my last question (math class)
Answer:
Step-by-step explanation:
5.00 for 2 loaves is $2.50 a loaf.
She wants 5 loaves for $12.50
5*2.50= $12.50 so she is correct.
What is the equation of the graphed line written in standard form?
Answer:
C. y = -2/3x -2
Step-by-step explanation:
We know the slope is negative. You can find slope using rise/run. The y-intercept is -2 because the line meets -2 at the y-intercept.
Answer:
The first answer (top)
Step-by-step explanation:
Standard form is ax+by=c
a and b are the coefficients
Take a point from the given line
I chose (0, -2)
Then, plug in the values of x and y
2*0+3*-2=-6
-6=-6
Since it works the standard form of the line is 2x+3y=-6
2. Now that you have the height of the cone, how can you solve for the
slant height, s?
Answer:
s^2 = r^2 + h^2.
Step-by-step explanation:
You need to know the radius of the base as well.
Then you use the Pythagoras theorem:
s^2 = r^2 + h^2 where r = radius and h = the height.
The mean age of five people in a room is 24. One of the people (age 40) leaves the
room. The mean age of the remaining four people is
Answer:
thxss for the points love
Step-by-step explanation:
kisses
Answer:
16
Step-by-step explanation:
The equation of the line in the graph is y= (blank) x+ (blank)
??????!?????????????????????!?!
Step-by-step explanation:
if the area of a box is 1 cm^2
then area of triangle is6 cm square
Graph the equation.
y-1 = -2(x-2)
Answer:
y-1 = -2(x-2) graph:
Answer:
Graph is below
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
2
y-intercept:
(
0
,
5
)
x
y
0
5
5
2
0
The amount a basketball coach spends at a sporting goods store depends on the number of basketballs the coach the coach buys. The situation is represented by the function rule a=16b.
Complete the following table of values.
Please Show Your Work All My Points Please Help Me!!!!! 6x^2+8x-6=2-2x-2
Answer:
6x^2+10x-6=0
Step-by-step explanation:
First, you need to add all like terms:
6x^2+8x-6=-2x
Now move the -2x to the other side:
6x^2+10x-6=0
Answer:
x =(-5+√61)/6= 0.468
or:
x =(-5-√61)/6=-2.135
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*x^2+8*x-6-(2-2*x-2)=0
Step by step solution :
STEP 1 :
The Equation at the end of step 1
(((2•3x2) + 8x) - 6) - -2x = 0
STEP 2 :
STEP 3 :
Pulling out like terms
3.1 Pull out like factors :
6x2 + 10x - 6 = 2 • (3x2 + 5x - 3)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 + 5x - 3
The first term is, 3x2 its coefficient is 3.
The middle term is, +5x its coefficient is 5.
The last term, "the constant", is -3
Step-1: Multiply the coefficient of the first term by the constant 3 • -3 = -9
Step-2: Find two factors of -9 whose sum equals the coefficient of the middle term, which is 5.
-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8
Observation: No two such factors can be found !!
Conclusion: Trinomial can not be factored
The Equation at the end of step 3 :
2 • (3x2 + 5x - 3) = 0
STEP 4 :
Equations which are never true:
4.1 Solve : 2 = 0
This equation has no solution.
A non-zero constant never equals zero.
Parabola, Finding the Vertex:
4.2 Find the Vertex of y = 3x2+5x-3
Parabolas have the highest or lowest point called the Vertex. Our parabola opens up and accordingly has the lowest point (AKA absolute minimum). We know this even before plotting "y" because the coefficient of the first term, 3, is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is if the parabola has indeed two real solutions.
Parabolas can model many real-life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that an object, thrown upwards, can reach. For this reason, we want to be able to find the coordinates of the vertex.
For any parabola, Ax2+Bx+C, the x -coordinate of the vertex is given by -B/(2A). In our case, the x coordinate is -0.8333
Plugging into the parabola formula -0.8333 for x we can calculate the y -coordinate :
y = 3.0 * -0.83 * -0.83 + 5.0 * -0.83 - 3.0
or y = -5.083
Parabola, Graphing Vertex, and X-Intercepts :
Root plot for : y = 3x2+5x-3
Axis of Symmetry (dashed) {x}={-0.83}
Vertex at {x,y} = {-0.83,-5.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.14, 0.00}
Root 2 at {x,y} = { 0.47, 0.00}
Solve Quadratic Equation by Completing The Square
4.3 Solving 3x2+5x-3 = 0 by Completing The Square.
Divide both sides of the equation by 3 to have 1 as the coefficient of the first term :
x2+(5/3)x-1 = 0
Add 1 to both side of the equation :
x2+(5/3)x = 1
Now the clever bit: Take the coefficient of x, which is 5/3, divide by two, giving 5/6, and finally square it giving 25/36
Add 25/36 to both sides of the equation :
On the right-hand side we have :
1 + 25/36 or, (1/1)+(25/36)
The common denominator of the two fractions is 36 Adding (36/36)+(25/36) gives 61/36
So adding to both sides we finally get :
x2+(5/3)x+(25/36) = 61/36
Adding 25/36 has completed the left-hand side into a perfect square :
x2+(5/3)x+(25/36) =
(x+(5/6)) • (x+(5/6)) =
(x+(5/6))2
Things which are equal to the same thing are also equal to one another. Since
x2+(5/3)x+(25/36) = 61/36 and
x2+(5/3)x+(25/36) = (x+(5/6))2
then, according to the law of transitivity,
(x+(5/6))2 = 61/36
We'll refer to this Equation as Eq. #4.3.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(5/6))2 is
(x+(5/6))2/2 =
(x+(5/6))1 =
x+(5/6)
Now, applying the Square Root Principle to Eq. #4.3.1 we get:
x+(5/6) = √ 61/36
Subtract 5/6 from both sides to obtain:
x = -5/6 + √ 61/36
Since a square root has two values, one positive and the other negative
x2 + (5/3)x - 1 = 0
has two solutions:
x = -5/6 + √ 61/36
or
x = -5/6 - √ 61/36
Note that √ 61/36 can be written as
√ 61 / √ 36 which is √ 61 / 6
Solve Quadratic Equation using the Quadratic Formula
4.4 Solving 3x2+5x-3 = 0 by the Quadratic Formula.
According to the Quadratic Formula, x, the solution for Ax2+Bx+C = 0, where A, B, and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = 5
C = -3
Accordingly, B2 - 4AC =
25 - (-36) =
61
Applying the quadratic formula :
-5 ± √ 61
x = —————
6
√ 61, rounded to 4 decimal digits, is 7.8102
So now we are looking at:
x = ( -5 ± 7.810 ) / 6
Two real solutions:
x =(-5+√61)/6= 0.468
or:
x =(-5-√61)/6=-2.135
HOPE THIS HELPS!
PLEASE MARK BRAINLIEST IF THIS HELPED YOU LEARN! :)
Can someone help me please
simplify the expression: 8x + 13 - 3x + 9=
Answer:
5x + 22=
Step-by-step explanation:
8x+13-3x+9
Combine like terms.
8x-3x=5x
13+9=22
Piece it back together.
5x+22
And there you have it. Hope it helps! :3
Do the organic prices vary directly with the conventional prices? If so, identify k. Does the total cost of organic apples vary directly with the number of pounds of organic apples purchased? If so, identify k.
THE RIGHT ANSWER IS (i just had to answer my own question so that other people can get it but just copy and paste this thanks :) )
no, this is not a direct variation
yes this is a direct variation with k=2.34
2
Answer:
1: No, this is not direct variation
2: Yes, this is direct variation with k= 2.34
Step-by-step explanation:
I’m Just Built Different
73 is what percent of 800
Answer:
0.09125%
Step-by-step explanation:
Divide 73 by 800 and you will get 0.09125
Answer:
It should be %9.75
Given m|n, find the value of x.
(8x+6) (9x-30)
Step-by-step explanation:
(8x+6) (9x-30)
=72x²-240x+54x-180
=72x²-186-180
Answer:
(8x+6) (9x-30)
=72x²-240x+54x-180
=72x²-186-180
Step-by-step explanation:
Can someone please find out what x is?
Answer: x = 2
Simplify and Distribute
(−5)(4x)+(−5)(−2)=(−2)(3)+(−2)(6x)
−20x+10=−6+−12x
−20x+10=−12x−6
Adding 12x both sides.
−20x+10+12x=−12x−6+12x
−8x+10=−6
Subtract 10 both sides
−8x+10−10=−6−10
-8x = -16
Then divide both sides by 8
-8x/8 = -16/8
x=2
In a survey of 2,200 people who owned a certain type of car, 880 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
*blank*% of the people surveyed were satisfied with the car.
Answer:
40%
Step-by-step explanation:
Given parameters:
Number of people surveyed = 2200
Number of people who said they would buy the car again = 880
Unknown:
The percentage of people satisfied with the car = ?
Solution:
The percentage of people satisfied with the car purchase can be determined using the expression below:
Percentage of people satisfied = [tex]\frac{Number of people who said they would buy the car again}{Number of people surveyed} x 100[/tex]
Percentage of people satisfied = [tex]\frac{880}{2200}[/tex] x 100 = 40%
f(0) = 3 and f(1) = 15.
Answer:
Step-by-step explanat
Given=F(0) = 3 and f(1) = 15.
So f(X)=12x+3
When X=0, f(0)=12x0+3=3
When X=1, f(1) = 12x1+3= 15
So f(X)=12x+3 is the solution o
Label the number that is on the numberline
Answer:
0.4
Step-by-step explanation:
Since there are 5 spaces between the 1 and 0, each tick represents [tex]\frac{1}{5}[/tex] or 0.2 units. Counting up from 0 you get 0.4
Answer:
0.4Step-by-step explanation:
1 divide by the number of lines: 1 / 5 = 0.20.2 multiply by the number of lines where the arrow is pointing at0.20 x 2 = 0.4
therefore, the answer is 0.4
how do you write 7,870 in scientific notations ?
Answer:
7.87X10^3
Step-by-step explanation:
^ means to the power of
8% of $40 is $
plzzz help
Answer:
$3.2
Step-by-step explanation:
so there's a strategy to do this its very helpful!
100%-$40
8%-x
~cross multiply~
100x=320
÷100 ÷100
________________
x=$3.2
Hope this helps :D
What would the equation be if my coordinates were, (-4,3) (2,6) ?
Answer:
y=1/2x+4
Step-by-step explanation:
change of x=2-(-4)=6
change of y=6-3=3
slope=3/6 or 1/2
y intercept=5
y=1/2x+5
what is positive 1 plus negative 6
Answer:
-5
Step-by-step explanation:
When answering these problems, I like to think of dirt stacks. (Weird, but it helps.)
Okay, so you have a stack of dirt one foot off the ground. Then you dig six feet down, including the stack. Because the stack will be 5 feet into the ground now, the answer is -5.