The Cartesian equation will be;
⇒ (x - 3) / 1 = (y - 0)/2
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation is,
⇒ r = 3i + λ (i + 2j)
Where, 'λ' is a parameter.
Now,
Since, The equation is,
⇒ r = 3i + λ (i + 2j)
Where, 'λ' is a parameter.
Hence, The Cartesian equation is find as;
⇒ xi + yj = 3i + λi + 2λj
By compare, we get;
⇒ x = 3 + λ
⇒ y = 2λ
Thus, The Cartesian equation is;
⇒ (x - 3) / 1 = (y - 0)/2 = λ
Therefore, The Cartesian equation will be;
⇒ (x - 3) / 1 = (y - 0)/2
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2 = x
3 26
How do i solve this equation
Answer:
do the butterfly method if you don't know how to do that comment and I'll show you a screenshot
Find the smallest length that can be divided exactly into equal sections of length 5m,8m and 12m
As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.
What is an LCM example?The acronym LCM stands for the least common multiple or factor of any two or more specified integers. The least common multiple for the numbers 16 and 20 is 80, hence the LCM of those two numbers will be, for instance, 2 x 2 x 2 x 2 x 5 = 80.
What is the LCM of 4 and 8?8 is the LCM of 4 and 8. The LCM is the number that can be divided by the provided numbers equally. You can discover the least common multiple of 4 and 8 by looking at the common multiples. 4 is a multiple of 8, 12, 16, 20, 24, etc.
finding prime factors of the given numbers by repeated division method in order to find the LCM;
2 | 5,8,12
5 | 5,4,6
2 | 1,4,6
2 | 1,2,3
3 | 1,1,3
0 | 1,1,1
so we get 2x5x3x2=60
As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.
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The shortest length which can be split into equal segments of length 5 meters, 8 meters, or 12 meters is 120.
What does "section" signify in terms of forms and purposes?Your form may be divided into sections with the help of sections, as the name suggests. This enables your users to input responses that might be categorized. The fact that sections divide your form into distinct screens is another significant benefit. For instance, a first screen shows section 1. When concealed lines in external views cannot adequately represent a part's inner design, sections are employed. The internal components can be viewed more clearly by imagining cutting through the thing and removing a section of it.
Briefing:Finding the LCM by repeatedly dividing the supplied integers to get their prime components:
2 | 5,8,12
2 | 5,4,6
2 | 5,2,3
3 | 5,1,3
5 | 5,1,1
1 | 1,1,1
So we get 2*2*2*3*5*1 = 120
The lowest length that could be divided into precisely equal segments in lengths 5 m, 8 m, and 12 m is 120, which equals the LCM of 5, 8, & 12.
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"How do we transform System A into System B?
Equation [A1] → Equation [B1]
Equation [A2]→ Equation [B2]
Equation [A1]+Equation [A 2] → Equation [B 2]
Equation [A2]+ Equation [A 1] → Equation [B 1]"
The transformation of System A into System B is:
Equation [A2]+ Equation [A 1] → Equation [B 1]"
The correct answer choice is option D
How can we transform system A into System B ?To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].
System A:
-3x + 4y = -23 [A1]
7x - 2y = -5 [A2]
Multiply equation [A2] by 2
14x - 4y = -10
Add the equation to equation [A1]
14x - 4y = -10
-3x + 4y = -23 [A1]
11x = -33 [B1]
Multiply equation [A2] by 1
7x - 2y = -5 ....[B2]
So therefore, it can be deduced from the step by step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].
The complete image is attached.
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Solve for x. Leave your answer in simplest radical form.
Answer:
√122
Step-by-step explanation:
first we have to find the missing side with x on the 5 and 9 triangle by using the theorem
a^2+b^2=c^2
9^2+5^2=c^2
81+25=c^2
106=c^2
√106=c
and now we can use this as a side to find x
4^2+√106^2=x^2
16+106=x^2
122=x^2
√122=x
Hopes this helps please mark brainliest
Determine the equation of the parabola that opens up, has vertex (7, 7), and a focal
diameter of 16.
Answer:
Step-by-step explanation:
Question: Determine the equation of the parabola that opens up, has vertex (7,7), and a focal diameter of 16 . This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.
Answer: ((x2)−14x+87)/16
Step-by-step explanation:
focal diameter = 16,
4a=16;
a=4.
(h,v)=(7,7-a)
==> (h,v)=(7,3)
the equation of the parabola = ((x-7)^2)=16(y-3)
=> y = ((x^2)-14x+87)/16.
Find the Maclaurin series of the following functions. Step by Step Please
The Maclaurin series of xcos(-x) up to n = 3 is
[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
The function is given in the question as
m(x) = xcos(-x)
Taylor (Maclaurin) series of xcos(x) up to n=5
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) = xcos(x)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(f(0)(x))′=(xcos(x))′=−xsin(x)+cos(x)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(−xsin(x)+cos(x))′=−xcos(x)−2sin(x)
Evaluate the 2nd derivative at the given point: (f(0))′′=0
3rd derivative: f(3)(x)=(f(2)(x))′=(−xcos(x)−2sin(x))′=xsin(x)−3cos(x)
Evaluate the 3rd derivative at the given point: (f(0))′′′=−3
Now, use the calculated values to get a polynomial:
[tex]m(x)=0+\frac{1}{1!}x+\frac{0}{2!}x^2+\frac{-3}{3!}x^3+.....[/tex]
[tex]m(x)=x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
Thus, the Maclaurin series of xcos(-x) up to n = 3 is
[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]
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Suppose megan wants to run more sprints and laps. How many of each could she run so that her total sprints and total laps are in the ratio that the coach wanted?
Answer:
2
Step-by-step explanation:
After adding the two equations to eliminate x you are left with 4y=-8. Solve for y: y =
Answer: -2
Step-by-step explanation:
4y/4 = -8/4
y = -2
Answer:
Step-by-step explanation:
Answer is -2
The vertex angle of an isosceles triangle measures
15 degrees more than one of its base angles. How
many degrees are there in a base angle of the
triangle?
The required three angle is 55 , 55 and 70
What is an angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
Let each of the base angle of isosceles triangle = x
Vertex angle = (x+15)
Sum of the angle = 180
x + x + (x + 15) = 180
3x + 15 = 180
3x = 180 - 15
x = 165 / 3
x = 55
Each base angel = 55
Vertex angle = x + 15
= 55 + 15
= 70
Required three angles = 55 , 55 and 70
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If f(1)=7, f(5)=-3, f(11)=-9, g(7)=11, g(-3)=6 and g(-9)=1, then find g(f(11))
Answer:
1
Step-by-step explanation:
g(f(11))
It says in the problem that f(11) = -9
So:
g(-9)
It says again in the problem that g(-9) = 1
So the answer is 1
rotate (2,-3) 270 degree counterclockwise around (1,-2) then translate (x-2,y+5)
The image point of the transformation is (-1, 6)
How to determine the image of the transformation?The coordinate of the point is given as
(2, -3)
The transformations are given as
270 degree counterclockwise around (1,-2) Translation by (x-2,y+5)The rotation is around the point (1,-2)
So, the point becomes
Point = (2 - 1, -3 + 2)
Evaluate
Point = (1, -1)
The 270 degrees rotation has the algebraic rule of its rotation to be changed from (x, y) to (-y, x) i.e. (x, y) => (-y, x)
So, we have
(x, y) = (1, 1) after the rotation
The translation is given as
(x - 2, y + 5)
So, we have
(x, y) = (1 - 2, 1 + 5)
Evaluate
(x, y) = (-1, 6)
Hence, the coordinates of the image is (-1, 6)
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In a clothing store, 50% of the customers buy a shirt, 30% of the customers
buy a pair of pants, and 15% of the customers buy both a shirt and a pair of
pants.
If a customer is chosen at random, what is the probability that he or she buys
a shirt or a pair of pants?
A. 0.20
B. 0.18
C. 0.65
D. 0.80
Answer:
.20
Step-by-step explanation:
because customers are always right
help me with this you need to do associative property of addition, identity property of addition, associative property of multiplication, and identity of multiplication also tell what Properties are shown. due tomorrow morning
Answer:
12 x 12
Step-by-step explanation:
(12+0)=12
(12 x 1)= 12
using a slope formula find the slope pf the line theough the points (0,0) and (2,6)
Step-by-step explanation:
slope formula: (y2-y1)/(x2-x1)at the point (0,0), it is known that x=0 and y=0.at the point (2,6), it is known that x=2 and y=6.slope: (6-0)/(2-0) =6/2 =310 less than the product of 8 and b
Step-by-step explanation:
8b-10
hope it helps. please mark brainliest
Answer: The correct answer is (8*b) - 10
Step-by-step explanation:
When translating word problems into equations, the term "product" denotes multiplication, and "less than" denotes subtraction.
This wording "10 less than the product of 8 and b" tells us to multiply 8 and b, then subtract 10:
(8*b) - 10
Apply the distributive property to simplify the expression
8(12x – 20)
I believe the answer must be 96x-160
Because we have to multiply 8x12 which is 96. and there is x next to it. so keep the x as it is.
and next to it is minus ( - ) sign so keep it as it is.
now we have to multiply 8x20 which is 160.
so if we write it together it will be:
so if we write it together it will be:96x - 160.
Thank you
PLEASE IT DUE SOON!!! DONT EVEN KNOW WHERE TO START IM SO CONFUSED!!!
QUESTION DOWN BELOW!! ONLY HAVE 20MIN SO PLEASE SOMEONE!!
A test point which is in the solution set for the linear inequality is: C. (-2, 4).
How to determine the true test point?In order to determine which ordered pairs is a true solution based on the given linear inequality, we would have to test each of the ordered pairs by substituting their values into the linear inequality as follows;
For ordered pair (-2, -4), we have:
2x - 9y < 0
2(-2) - 9(-4) < 0
-4 + 36 < 0
32 < 0 (False).
For ordered pair (-1, -5), we have:
2x - 9y < 0
2(-1) - 9(-5) < 0
-2 + 45 < 0
43 < 0 (False).
For ordered pair (-2, 4), we have:
2x - 9y < 0
2(-2) - 9(4) < 0
-4 - 36 < 0
-40 < 0 (True).
For ordered pair (-1, -1), we have:
2x - 9y < 0
2(-1) - 9(-1) < 0
-2 + 9 < 0
7 < 0 (False).
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The function f(x) = 2x3 + 3x2 + 2x – 1 is divided by (x – 1) .
Step-by-step explanation:
here is your answer hope it helps you plaz mark me as brainlist
A marching band needs to raise $13,500 for a trip to the Rose Bowl. The director told the band members that one-third of the amount that has been raised so far is equal to half of the amount that is still needed. How much more money needs to be raised for the trip?
Answer: $5400
Step-by-step explanation:
x = amount raised so far
13500 - x = amt. still needed
x/3 = (13500 - x)/2
2x = 3(13500 - x)
2x = 40500 - 3x
5x = 40500
x = 40500/5 = 8100 (amt. raised so far)
13500 - 8100 = 5400 (amt. still needed)
What is the equation of the line that passes through the point (2,-6) and has a slope of -3?
5. Find the value of x. Round the length to the nearest tenth. 18 yd 309 2?.
By Trigonometric formula - Tan(∅) = [tex]\frac{opposite}{adjacent}[/tex] , we got that answer - x= 10.4 yard (On rounding to tenth place)
what are trigonometric equations?An equation containing one or more trigonometric ratios of unknown angles is known as a trigonometric equation. In terms of angles, it is written as ratios of the sine, cosine, tangent, secant, and cotangent angles. A trigonometric equation is, for instance, cos2 x + 5 sin x = 0.
For angle 30 degrees adjacent side is 18 yard and opposite side is x.
=> Tan(∅) = [tex]\frac{opposite}{adjacent}[/tex]
=> Tan(30) = [tex]\frac{x}{18}[/tex]
=> x=Tan 30 (18)
=> x= 10.39
=> x= 10.4 yard (On rounding to tenth place)
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An airplane cruises 1 kilometer in
1
12
of a minute. What is its cruising speed?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
kilometers per minute
Answer: It is 12 kilometers per minute
Step-by-step explanation:
in the problem that you'll need to simplify your answer and write it as a proper fraction, mixed number, or whole number so I can confirm this is 100% correct.
Step-by-step explanation:
You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase. How much is due the first month?
Find the probability of rolling a sum greater than 7 given that you rolled an odd number first.
Answer:
I think the answer is 1/2. Given the first die was odd, you rolled either a 1,3, or 5. Now on the second roll only a 6,4, or a 2 will give you a sum of 7. Given that is half of the sample space of the second die, it is 1/2?
Step-by-step explanation:
50 points! Which expression is equivalent to 7(y - 4)? * 1 point
7y - 28
7y - 4
3y
7y - 3
I have to explain also!
order the fraction to least to greatest 2/3 3/7 4/8
HELP PLEASE I NEED IT
Answer:=
Step-by-step explanation:
.............................
The answer is 1,200
First you need to add . + . to get 1.5M and then you need to subtract the rest ( 1.5M - one million four hundred ninety-eight thousand eight hundred )
So then you get 1,200
Hope this helped!
NEED ANSWERS ASAP PLEASE HELP!!! THE NUMBERS ARE THE QUESTION #
Area of the parallelogram is 882 square units
the solution of the inequality is plotted in the last number line
area o the glass window is 144π cm²
the second number line is the correct plot
the water left after the serving is 2 gallons 3 quart 1 pint
How to find the area of the parallelogramArea of a parallelogram is given by the formula
= base * height
= 63 * 14
= 882 square units
The solution of the number line is b/2 ≥ 4
= b ≥ 8
the last option is correct
Area of circle is solved by
= πd² / 4
= π * 24² / 4
= 144π cm²
The inequality 4 > -y
= -4 < y
The second option is correct
total fluid ounces used
= 68 * 4 = 272 ounces
272 ounces = 2.125gallons
5 - 2.125 = 2.825 gallons
2.875 gallons
0.875 gallons = 3.5 quart
2 gallons 3.5quart
0.5 quart = 1 pint
2 gallons 3 quart 1 pint
Water left in the cooler is 2 gallons 3 quart 1 pint
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Please help!!!!
Write an equation in point-slope form that passes through the points (2, 4) and (-3, -6).
Answer:
uh let's see
Step-by-step explanation:
2,4 and -3,-6
y2-y1/
x2-x1
-6-4
-3-2
-10/-5 = 2
slope is 2
u do the rest I'm tired