Answer:
using distance formula or graphing you can find your answer
Step-by-step explanation:
(7,0) from 4 to -3 is -7. Take the absolute vale of -7 and you get 7.
Hope i helped :)
Answer:
Distance from A to B = 7 units
Step-by-step explanation:
We are given the following two points and we are to find the distance between them:
A (4,2)
B (-3,2)
We will be using the distance formula for this:
Distance = [tex] \sqrt { ( x _ 2 - x _1)^ 2 + ( y _ 2 - y _ 1 ) ^ 2 } [/tex]
AB = [tex]\sqrt{(-3-4)^2+(2-2)^2} = \sqrt{49}[/tex] = 7 units
A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situation?
Answer:
A.
Step-by-step explanation:
NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.
"A number, y, is equal to twice the sum of a smaller number and 3."
This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.
[tex]y=2(x+3)[/tex]
"The larger number is also equal to 5 more than 3 times the smaller number."
This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.
[tex]y=3x+5[/tex]
Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.
This form calls for us to have our x term first, then our y term, then our constant.
[tex]y=2(x+3)\\y=2x+6\\-2x+y=6[/tex]
Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.
[tex]-2x+y=6\\2x-y=-6[/tex]
This makes the only possible answer choices (A) and (C).
Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.
[tex]y=3x+5\\-3x+y=5\\3x-y=-5[/tex]
This is only represented by choices (A) and (B).
Therefore, answer choice (A) is the only one which represents both equations.
PLEASES HELPPP !!!!
Which of the following is an equation of a line parallel to the equation y=1/2x+1?
a. y=-1/2x+1
b. y=-2x-5
c. y=1/2x-5
d. y=2x-5
Answer:
[tex]\large\boxed{C.\ y=\dfrac{1}{2}x-5}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff\ m_1m_2=-1\to m_2=\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]
Parallel line have the same slope.
Therefore a line parallel to the line [tex]y=\dfrac{1}{2}x+1[/tex] has equation
[tex]y=\dfrac{1}{2}x+b[/tex]
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
Answer:
I'm pretty sure its A
Step-by-step explanation:
To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
Option: A is the correct answer:
[tex]A.\ y=-3x[/tex]
Step-by-step explanation:The equation of a line passing through two points (a,b) and (c,d) is calculated with the help of a two-point formula:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Based on the graph we observe that the line passes through:
(0,0) and (3,-9)
i.e. we have: (a,b)=(0,0) and (c,d)=(3,-9)
i.e. the equation of line is given by:
[tex]y-0=\dfrac{-9-0}{3-0}\times (x-0)\\\\i.e.\\\\y=\dfrac{-9}{3}\times x\\\\i.e.\\\\y=-3x[/tex]
The answer is: Option: A
Jim Smith is a salesman who receives a $1,100 draw per week. He receives a 12% commission on all sales. Sales for Jim were $205,000 for the month. Assuming a four-week month. Jim's commission after the draw is
Answer:
$29,000
Step-by-step explanation:
Given:
Receivable draw per week= $11,00
Commission on all sales= 12%
Sale for the month= $205,000
weeks in a month= 4
Jim's commission after the draw=?
total draws= 11,00 (4)
= 44,00
Commission on the sale= 205000(0.12)
=24600
Jim's commission after the draw= 4400 +24600
=29,000 !
Jim Smith's commission after the draw is calculated by determining his total commission from sales and then subtracting the draw he receives weekly. For a month where he made $205,000 in sales, his commission after the draw is $20,200.
The subject of this question is Jim Smith's commission after the draw, who works as a salesman and receives a draw of $1,100 per week plus a 12% commission on all sales. Considering that Jim made $205,000 in sales for the month, we would first calculate his total commission by multiplying the sales amount by the commission percentage. Next, we deduct the total draw for the month from the total commission to find Jim's commission after the draw.
To calculate the total commission earned, you would use the formula: Commission = Sales x Commission Rate. Therefore, for a sales amount of $205,000 and a commission rate of 12%, the total commission would be $205,000 x 0.12, which equals $24,600. Since a month is considered to have four weeks, Jim's total draw for the month would be $1,100 x 4, totaling $4,400.
To find out how much commission Jim has after accounting for the draw, we subtract the draw from the total commission: Commission after Draw = Total Commission - Total Draw, or $24,600 - $4,400, which equals $20,200.
what is the slope of the line for y = 1/2x + 2 and what is the y intercept of the line
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
In this case m is 1/2 and b is 2.
This means that the slope of this line is 1/2 and the y-intercept is (0, 2) or simply 2
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 2 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = 2
Van was asked to add 46 to 37 and round the result to the nearest ten. He figured that since he was going to have to round anyway, he might as well do it before adding the numbers. He rounded 46 to 50 and 37 to 40, thus getting an answer of 50+40=90. This answer is not correct. What is the correct answer?
Answer:
80
Explanation:
46 + 37 = 83 so 83 rounded to the nearest 10 is 80
Answer:
80
Step-by-step explanation:
46+37 = 83
Rounding to the nearest ten
80
How to use substitution? (With picture) thanks!
Answer: x = 10 y = 6
Step-by-step explanation:
0.1X + 5 = y
0.2X + 4 = y
0.1X + 5 = 0.2X + 4
-0.1X - 4 = -0.1X - 4
1 = .1X
x = 10
0.1(10) + 5 = y
1 +5 = y
6 = y
Question 7
Answers:
Jane's Uber business has the function f(x) = 0.10x+5
Joe's Uber business has the function f(x) = 0.20x+4
x is the number of miles, f(x) is the total cost for the customer
-------------------------
Explanation:
Jane charges $5 no matter how many miles are driven. This is the base fee. On top of this base fee, an additional price is charged based on the number of miles driven. If Jane drives 1 mile, then an additional 0.10*1 = 0.10 dollars is added on. If 2 miles are driven, then 0.10*2 = 0.20 dollars is added on. And so on.
In general, an additional 0.10*x dollars is added on the base fee to get the total cost to be 5 + 0.10x which rearranges to 0.10x + 5. That's how I ended up with f(x) = 0.10x + 5
Joe's equation will be constructed in a similar way. His base fee is $4 and you add on 0.20x dollars (since it costs $0.20 per mile for Joe's company). Overall, we get f(x) = 0.20x + 4 for Joe's company.
Note how your teacher is not asking you to solve for x or f(x). If you want, you can replace f(x) with y; however, this isn't in function notation.
=============================================================
Question 8
Answers:
Function for Joseph's plan is: f(x) = 0.10x + 20
Function for Micki's plan is: f(x) = 0.15x + 10
The plans cost the same when 200 text messages are sent
-------------------------
Explanation:
We'll set up the equations in a similar way done in problem 7. We start with $20 as the base fee for Joseph's plan and then add on 0.10x dollars because $0.10 is charged per text message. We have x represent the number of text messages. Joseph's function is therefore f(x) = 0.10x + 20. Similarly, Micki's function is f(x) = 0.15x + 10
Let's replace f(x) with y and we have these two equations: y = 0.10x + 20 and y = 0.15x + 10
Now use substitution to solve for x and y
y = 0.10x + 20
0.15x + 10 = 0.10x + 20 ... y replaced with 0.15x+10
0.15x-0.10x = 20-10
0.05x = 10
x = 10/0.05
x = 200
This means that the two plans cost the same when 200 messages are sent.
Note plugging x = 200 into each f(x) function leads to
f(x) = 0.10x + 20
f(200) = 0.10*200 + 20
f(200) = 20 + 20
f(200) = 40 <<--- it costs Joseph $40 to send 200 messages
and
f(x) = 0.15x + 10
f(200) = 0.15*200 + 10
f(200) = 30 + 10
f(200) = 40 <<--- it costs Micki $40 to send 200 messages
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 20 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
The LARGEST angle has a measure of ____ degrees.
Answer:
LARGEST ANGLE= 96 DEGREES
Step-by-step explanation:
MEASURE OF LARGEST ANGLE= 3A
SMALLEST ANGLE= A
THIRD ANGLE= 20+A
3A+A+20+A=180(SUM OF INTERIOR ANGLES OF TRAINGLE IS 180 DEGREES)
TRANSPOSE 20 TO RHS.
5A=180-20=160
A=160/5
=32
MEASURE OF SMALLEST ANGLE=32
LARGEST ANGLE=3A=3*32=96 DEGREES
THIRD ANGLE=32+20=52 DEGREES
Answer:
The largest angle has a measure of 96 degrees.
Step-by-step explanation:
In order to solve this problem, we have to know the fact that the sumatory of the internal angles of any triangle is 180 degrees.
With this statement in mind, and looking at the image, we can say:
180 = A + B + C (eq. 1)
Before continue any further, let's affirmt that B is the smallest angle.
Now the enunciate says "One angle in a triangle has a measure that is three times as large as the smallest angle"; This can be express as:
A = 3B (eq. 2)
The other enunciate is "The measure of the third angle is 20 degrees more than that of the smallest angle" This can be express as:
C = B + 20 (eq. 3)
Now, replacing equations 2 and 3 into 1:
(eq. 1) 180 = 3B + B + B + 20
And clearing B:
B = 32.
By knowing B, we can clear A and C from equations 2 and 3 respectively:
(eq. 2) A = 3B, so A= 96
(eq. 3) C = B + 20, so C =52
The first term of a sequence is 4 and the common ratio is –2. What is the formula for the sequence based on term number
Answer:
its B and the next one is C
Step-by-step explanation:
Formula for the sequence based on term number is
[tex]a_{n} =(4)(2)^{n-1}[/tex].
What is geometric sequence?In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given
First term [tex]a[/tex] = 4
Common ratio r = -2
It is a geometric sequence because we have common ratio
Formula for the sequence based on term number is
[tex]a_{n} =ar^{n-1}[/tex]
[tex]a_{n} =(4)(2)^{n-1}[/tex]
Hence, Formula for the sequence based on term number is
[tex]a_{n} =(4)(2)^{n-1}[/tex].
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Which statements are always true regarding the diagram? Check all that apply. m∠3 + m∠4 = 180° m∠2 + m∠4 + m∠6 = 180° m∠2 + m∠4 = m∠5 m∠1 + m∠2 = 90° m∠4 + m∠6 = m∠2 m∠2 + m∠6 = m∠5
Answer:
The true statements are:
m∠ 3 + m∠ 4 = 180° ⇒ 1st
m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd
m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd
Step-by-step explanation:
* Look to the attached diagram to answer the question
# m∠ 3 + m∠ 4 = 180°
∵ ∠ 3 and ∠ 4 formed a straight angle
∵ The measure of the straight angle is 180°
∴ m∠ 3 + m∠ 4 = 180° ⇒ true
# m∠ 2 + m∠ 4 + m∠ 6 = 180°
∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle
∵ The sum of the measures of interior angles of any Δ is 180°
∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ true
# m∠ 2 + m∠ 4 = m∠ 5
∵ In any Δ, the measure of the exterior angle at one vertex of the
triangle equals the sum of the measures of the opposite interior
angles of this vertex
∵ ∠ 5 is the exterior angle of the vertex of ∠ 6
∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6
∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ true
# m∠1 + m∠2 = 90°
∵ ∠ 1 and ∠ 2 formed a straight angle
∵ The measure of the straight angle is 180°
∴ m∠1 + m∠2 = 90° ⇒ Not true
# m∠4 + m∠6 = m∠2
∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle
∵ There is no given about their measures
∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is
equal to the measure of ∠ 2
∴ m∠4 + m∠6 = m∠2 ⇒ Not true
# m∠2 + m∠6 = m∠5
∵ ∠ 5 is the exterior angle at the vertex of ∠ 6
∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ Not true
Answer: A,B,C. OR 1,2,3
Step-by-step explanation:
The sum of a number and twice its reciprocal is 27/5. Find
the number.
Answer:
x , reciprocal= 1/x
x+2(1/x)=27/5
x+2/x=27/5
x^2+2=27/5*x
x^2-27/5*x+2=0
(x-5)(x-2/5)=0
x=5, 2/5
76degrees faherheit = what in Celsius?
Answer:
24.4444
Step-by-step explanation:
76 degrees faherheit = 24.4444 degrees Celsius
(76°F − 32) × 5/9 = 24.444°C
Answer:
rjjj3krktkkrkrkektk4kgk4mgk3mrl3lfkwjkeoc
a rectangle has a width of 9 units and a length of 40 units.what is the length of a diagonal
Answer:
41 units
Step-by-step explanation:
In this question, you should remember that the diagonal drawn will represent the longest side of the triangle that will be formed .This is to say the triangle will have the two shorter sides (the length and width) and the longest side (diagonal).
Apply the Pythagorean relationship where
The width will be the shortest side aThe length will be the other side bThe diagonal will be the hypotenuse cThe formula to apply here will be
[tex]a^2+b^2=c^2\\\\\\a=9,b=40,c=?\\\\\\9^2+40^2=c^2\\\\\\81+1600=c^2\\\\\\c^2=1681\\\\\\c=\sqrt{1681} =41units[/tex]
Answer:
Diagonal = 41 units
Step-by-step explanation:
It is given that,a rectangle has a width of 9 units and a length of 40 units.
To find the diagonal of rectangle
We know that rectangle can be considered as combination of two right triangles.
Here length of right triangle = 40 units and height = 9 units
Hypotenuse = diagonal of rectangle.
Hypotenuse² = Length² + height
= 40² + 9²
= 1600 + 81
= 1681
Hypotenuse = √1681 = 41
Therefore diagonal of rectangle = 41 units
If the angle measure is the largest of the triangle, what do you know about the side opposite?
It is the length.
If a side is the shortest of the triangle, what do you know about the angle opposite that side?
It is the degree measure.
Answer:
A) the longest side
B) the smallest angle
Step-by-step explanation:
Relationship of sides to interior angles in a triangle
In a triangle:
The shortest side is always opposite the smallest interior angleThe longest side is always opposite the largest interior angleRecall that in a scalene triangle, all the sides have different lengths and all the interior angles have different measures. In such a triangle, the shortest side is always opposite the smallest angle. Similarly, the longest side is opposite the largest angle.
So,
A) the longest side
B) the smallest angle
Answer: the longest side
the smallest angle
Step-by-step explanation: the largest is longest
the smallest is shortest
1 Point
Which of the following equations represents a line that is parallel to y = 5x - 4
and passes through the point, (3, 4)?
Answer:
y = 5x - 11Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\==============================[/tex]
[tex]\text{We have the equation:}\ y=5x-4\to m_1=5.\\\\\text{Therefore}\ m_2=5.\\\\\text{We have the equation:}\ y=5x+b.\\\\\text{Put the coordinates of the given point (3, 4) to the equation:}\\\\4=5(3)+b\\\\4=15+b\qquad\text{subtract 15 from both sides}\\\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=5x-11[/tex]
The area of two rectangles is given by he functions: area of a rectangle A:f(x)= 4x2+6x area of rectangle B:g(x)=3x2-x Which function represents the difference? A.h(x)=7x2-5x B.h(x)=x2-7x C.h(x)=x2+5x D.h(x)=x2+7x
Answer:
x^2+7x if you are asked to find the difference of a function f and function g
Step-by-step explanation:
We are asked to A-B or f(x)-g(x).
(4x^2+6x)-(3x^2-x)
4x^2+6x-3x^2+x
The like terms I'm going to pair up.
4x^2-3x^2+6x+x
1x^2 +7x
x^2 +7x
The answer is x^2+7x
Answer:
OPTION D: [tex]h(x)=x^2+7x[/tex]
Step-by-step explanation:
You know that the area of Rectangle A is given by :
[tex]f(x)= 4x^2+6x[/tex]
And the area of Rectangle B is given by:
[tex]g(x)=3x^2-x[/tex]
Therefore, in otder to find the function that represents the difference, you need to subtract the functions f(x) and g(x).
Then, you get this function h(x):
[tex]h(x)=f(x)-g(x)\\\\h(x)= (4x^2+6x)-(3x^2-x)\\\\h(x)=4x^2+6x-3x^2+x\\\\h(x)=x^2+7x[/tex]
What is the value of x?
Answer:
x = 8
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Sum the exterior angles and equate to 360
62 + 66 + 77 + 59 + 12x = 360, that is
264 + 12x = 360 ( subtract 264 from both sides )
12x = 96 ( divide both sides by 12 )
x = 8
If p and q prime number greater than 2which of the following is not even integer ? a.p+q b.p×q c.p^2-q^2 d.p-q
B, because every prime number greater than 2 is odd, and the product of two odd numbers is odd.
Answer: I'm pretty sure its B
Step-by-step explanation:
..
Select the values that are solutions to the inequality x2 + 3x – 4 > 0.
Answer:
So any number in the following set is a solution:
[tex](-\infty,-4) \cup (1,\infty)[/tex]
given the inequality to solve was:
[tex]x^2+3x-4>0[/tex]
Step-by-step explanation:
The left hand side is a quadratic while the right hand side is 0.
Since this is a quadratic>0, I'm going to factor the quadratic if possible and then solve that quadratic=0 for x.
That is I'm going to solve:
[tex]x^2+3x-4=0[/tex]
Since a=1, I get to ask what multiplies to be c (-4) and add up to be b(3).
Those numbers are 4 and -1.
So the factored form for the equation is:
[tex](x+4)(x-1)=0[/tex]
Setting both factors equal to 0 since 0*anything=0:
x+4=0 and x-1=0
-4 -4 +1 +1
---------------------------------------------------
x=-4 and x=1
Ok so if this wasn't a quadratic I would make a number line and choose numbers to plug into the quadratic to see which intervals would give me positive results. I say positive due to the >0 part.
However since I know about the shapes of quadratics, I'm going to use that.
The quadratic function [tex]f(x)=x^2+3x-4[/tex] has x-intercepts (-4,0) and (1,0) and is open up.
I determine that it was opened up because the leading coefficient is 1 which is positive.
Now the left tail and right tail is what is above the x-axis so the solution set is:
[tex](-\infty,-4) \cup (1,\infty)[/tex]
Answer:
-6 and 5
Step-by-step explanation:
Sarah was 50 1/4 in tall and she was 12 years old she was 4 and 1/2 inches tall when she was 11 years old how much did she grow during the year
Nathan wanted to make a safe investment with decent returns. His financial advisor suggested a financial service that provided a higher rate of interest. However, he warned Nathan that he won’t be able to withdraw the money before the maturity date. Which financial service has Nathan’s financial advisor suggested?
A.
checking account
B.
certificates of deposit
C.
savings account
D.
stocks and bonds
Assemble the proof by dragging tiles to the statements HELLPPPPPP PLEASEEEE
Answer:
See explanation
Step-by-step explanation:
1. [tex]JK\cong LM[/tex] - given
2. [tex]JL\cong LN[/tex] - definition of midpoint (the midpoint of the segment divides the segment into two congruent segments)
3. [tex]\angle LJK\cong \angle NLM[/tex] - corresponding angles theorem (corresponding angles theorem states: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.)
4. [tex]\triangle JLK\cong \triangle LNM[/tex] - SAS (SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent).
Kelly has 11 markers in a backpack. One of them is pink and one is blue. Find the probability Kelly will reach into the backpack without looking and grab the pink marker and then reach in a second time and grab the blue marker. Express your answer as a fraction in simplest form.
Answer:
1/110
Step-by-step explanation:
Her chance of originally grabbing a pink marker is 1/11. Her chance of grabbing a blue marker after the pink marker is taken out is 1/10. When you multiply 1/11 by 1/10, you get a 1/110 chance of getting the colored markers in this series
Answer:
The probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]
Step-by-step explanation:
Hello, this is a great question and one that many people struggle with in school. Hopefully I can help you understand it more clearly. Kelly has 11 markers in total within her backpack and needs to randomly pick out the pink marker. since there is only 1 that would mean her probability of picking out the pink marker is 1/11 .
Now there are 10 markers inside the backpack and she needs to randomly pick out the blue marker. since there is only 1 blue marker that would mean her probability of picking that one out is 1/10.
So now we have the following probabilities
1/11 for the pink marker 1/10 for the blue markerNow if we want to find the probability of her getting the pink marker and the blue marker one after another we would need to multiply both fractions together
[tex]\frac{1}{11} * \frac{1}{10} = \frac{1}{110}[/tex]
So the probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]
Need help in number 20. Thanks for helping
Answer:
It is F
Step-by-step explanation:
if you plug in the y and x values that should get you the answer
Answer:
F.
Step-by-step explanation:
Find the area the sector
Answer:
A= 706.85m^2
Step-by-step explanation:
A= 4• Pi•r^2
= 4•Pi•15^2
=2827.43/4
=706.8575m^2
For this case we have that by definition, the area of a circular sector is given by:
[tex]A = \frac {a * r ^ 2} {2}[/tex]
Where:
r: It's the radio
a: It is the angle of the sector
We have to:
a = 90 degrees
[tex]90\ degrees = \frac {\pi} {2}[/tex]
Then, replacing:
[tex]A = \frac {\frac {\pi} {2} * 15 ^ 2} {2} = \frac {225 \pi} {4}[/tex]
Answer:
Option A
Explain the steps necessary to convert a quadratic function in standard form to vertex form
Answer:
Sample Response: A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.
Step-by-step explanation:
trust me
To prove a projectile's trajectory is parabolic, we start with the horizontal motion equation, solve for time, and substitute into the vertical motion equation, ending up with a quadratic equation in the form of y = ax + bx², showing parabolic motion.
Explanation:To prove that the trajectory of a projectile is parabolic, we start with the two separate equations for horizontal and vertical motion. The horizontal motion equation is given by x = Voxt, where Vox is the horizontal velocity component. We solve this for time t to get t = x / Vox. We then substitute this expression for t into the vertical motion equation y = Voyt - 1/2gt2, where Voy is the vertical velocity component and g is the acceleration due to gravity.
Substituting t = x / Vox into the vertical equation, we get y = Voy(x / Vox) - (1/2)g(x / Vox)2. This simplifies to y = (Voy/ Vox)x - (g / 2Vox2)x2, which is of the form y = ax + bx2, proving that the trajectory is parabolic with a and b as constants.
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which two quantities form a proportional relationship?
A.1/4 and 3/8
B.2/15 and 3/30
C.10/18 and 45/81
D.5/6 and 5/24
c.10/18 and 45/81
10/18=.5555555555555555555555
45/81=.5555555555555555555555
Answer:
D 5/6 and 5/24
step by step explanation :
when you multiply 6 times 4 it equals 24
If f(x) = -x^2 + 6x - 1 and g(x) = 3x^2 - 4x - 1, find (f + g)(x).
O A. (f+g)(x) = 2x2 + 2x - 2
B. (f+g)(x) = 4154x2 + 10x
O C. (f+g)(x) = 2x2 - 10x
O D. (f+g)(x) = 4x2 + 10x + 2
[tex]
f(x)=-x^2+6x-1 \\
g(x)=3x^2-4x-1 \\
f(x)+g(x)=-x^2+6x-1+3x^2-4x-1=\boxed{2x^2+2x-2}
[/tex]
The answer is A.
Hope this helps.
r3t40
Find the midpoint between (4,-1) and (3,2)
Midpoint has form of,
[tex]M(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
We can insert the data,
[tex]M(\dfrac{4+3}{2},\dfrac{-1+2}{2})[/tex]
Which simplifies to,
[tex]\boxed{M(3.5, 0.5)}[/tex]
Hope this helps.
r3t40
briana has earned the following test grades: 82%, 75% and 90%. She wants to maintain an 85% average for her test scores. what must she receive on the final test in order to acieve this goal?
Answer:
93%
Step-by-step explanation:
Formula for calculating average = sum of data/ total number of data
Step 1: Add all percentages
Let the percentage on the last test be x
82% + 75% + 90% + x = 247% + x
Step 2: Apply the formula
Average = sum of percentages/ total number of tests
85 = 247 + x /4
340 = 247 + x
x = 340 - 247
x = 93%
Therefore, Briana must receive 93% on her final test to maintain an average of 85%.
!!