Answer: Velocity is a vector, so it has a magnitude and direction.
Speed is its magnitude, which is obtained from
|〈-3, 4〉 m/s| = √((-3 m/s)² + (4 m/s)²) = √(25 m²/s²) = 5 m/s
Its direction is an angle θ made with the positive horizontal axis, satisfying
tan(θ) = (4 m/s) / (-3 m/s) = -4/3 → θ = arctan(-4/3) + 180°n
where n is any integer. Now you have to consider that the x coordinate is negative and the y coordinate is positive, so 〈-3, 4〉 points into the second quadrant, and we get an angle there for n = 1 of about
θ ≈ 126.87°
Alternatively, you can use the vector 〈1, 0〉 in place of the axis, then compute the angle by relating it to the dot product, so θ is such that
〈-3, 4〉 • 〈1, 0〉 = |〈-3, 4〉| |〈1, 0〉| cos(θ)
(-3)•1 + 4•0 = √((-3)² + 4²) • √(1² + 0²) cos(θ)
-3/5 = cos(θ) → θ = arccos(-3/5) + 360°n
where again, n is any integer, and we get the same solution θ ≈ 126.87° in the second quadrant when n = 0.
Step-by-step explanation:
Ian's car can go 195 miles on 5 gallons of gas. During a drive last weekend, Ian used 4 gallons of gas. How far did he drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas he used.
Justify the congruence between each of the following pairs of triangle.
Answer:
Refer to the attachment for the labelling of the triangles.
In △ABC & △DEC,
∠C = ∠C [common angles → vertically opposite angles]
AC = CE [equal pair of sides]
BC = DC [equal pair of sides]
•°• △ABC ≅ △EDC (Single-Angle-Side congruence rule → SAS congruence rule.....the angle is included between the 2 equal sides).
Hope it helps ⚜
Solve for x:
8x^2−3=2
Please provide a step-by-step answer.
Answer:
[tex]\rf x=\frac{\sqrt{10}}{4},\:x=-\frac{\sqrt{10}}{4}[/tex]
step wise explanation:
[tex]\rf 8x^2 - 3=2[/tex]change sides:
[tex]\rf 8x^2 =2+3[/tex]simplify
[tex]\sf 8x^2 = 5[/tex]change sides:
[tex]\sf x^2 = \frac{5}{8}[/tex]changing square to square root:
[tex]x = \pm \sqrt{\frac{5}{8} }[/tex]normal answer:
[tex]\rf \sqrt{\frac{5}{8} } \ \ or -\sqrt{\frac{5}{8} }[/tex]apply radical rule of
[tex]\rf \frac{\sqrt{5} }{\sqrt{8} } } \ \ or \rf -\frac{\sqrt{5} }{\sqrt{8} } }[/tex][tex]\sf \frac{\sqrt{5}}{2\sqrt{2}} \ \ or \ \ \sf -\frac{\sqrt{5}}{2\sqrt{2}}[/tex]rationalise:
[tex]\frac{\sqrt{5}\sqrt{2}}{2\sqrt{2}\sqrt{2}} \ \ or \ - \frac{\sqrt{5}\sqrt{2}}{2\sqrt{2}\sqrt{2}}[/tex]final answer, simplified:
[tex]\rf x=\frac{\sqrt{10}}{4},\:x=-\frac{\sqrt{10}}{4}[/tex]Answer:
[tex]x = \boxed{ \frac{\sqrt{10}}{4} , - \frac{\sqrt{10}}{4} }[/tex]
Step-by-step explanation:
We can solve this question by using the method of finding the square root.
The given equation is:
[tex]8x ^ { 2 } -3=2[/tex]
Add 3 to both the sides of the equation.
[tex]8x^{2}=2+3[/tex]
Now, add 2 & 3 to get 5.
[tex]8x^{2}=5[/tex]
Dividing both the sides of the equation by 8, we get...
[tex]x^{2}=\frac{5}{8}[/tex]
Now, take the square root of both the sides of the equation...
[tex]x =\sqrt{ \frac{ 5 }{ 8 } } \\x = \frac{\sqrt{5}}{\sqrt{8}} \\[/tex]
Rationalize the denominator.
[tex]x = \frac{\sqrt{5}}{2\sqrt{2}} \\x = \frac{\sqrt{5}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}} \\x = \frac{\sqrt{5}\sqrt{2}}{2\times 2} \\x = \frac{\sqrt{10}}{2\times 2} \\x = \boxed{ \frac{\sqrt{10}}{4} , - \frac{\sqrt{10}}{4} }[/tex]
[tex]\rule{200}{3}[/tex]
The value of x = [tex]\boxed{ \frac{\sqrt{10}}{4} , - \frac{\sqrt{10}}{4} }[/tex][tex]\rule{200}{3}[/tex]
Hope this helps!
Pls help me pls pls pls
Answer:
1.) 163
2.) 56
3.) 94
Step-by-step explanation
Because the angles are supplementary, it means they equal 180 degrees. Therefore, just use this equation to found the unknown angle.
180-(The Number you are given) = (The angle you want)
For Example,
180-86=94
Which comparison is not correct?
-8<1-41
1-21 <1-91
1-7]>-9
|81 > 1-91
Answer:
I'm pretty sure it is C
Step-by-step explanation:
Please solve this question
Answer:
a = [tex]\frac{-7}{3}[/tex] (because point P is 7 units away from line x = 0, so point P' must also be 7 units away from the line in the other direction)
b = 2
A soccer league has $630 to buy new soccer
balls. If each ball costs $6, how many balls can the
league buy?
soccer balls
Answer:
The soccer league can buy 105 soccer balls.
Step-by-step explanation:
I did $630 divided by $6 and got 105! :)
you are paid $60 per week plus $5 per sale. At least how many sales do you need to make in order to have over $350? which inquelity best represent this
Solve the measurement conversion problem. 1 km = 1,000m Add all amounts then convert
During the camp relay race , the campers had to canoe 500 meters, hike 200 meters, run the trail for 20 meters, and swim for 50 meters . How many kilometers was the relay race?
A) 7.7 kilometers
B) 7,700 kilometers
C) 0.77 kilometers
D) 770 kilometers
Answer:
The answer is C.) In order to get one kilometer, you have to have 1,000 meters.
Step-by-step explanation:
Hope this helped.
A brainliest is always appreciated.
VI) You finally purchased a backup oxygen tank needed for the base which originally cost
$50,000 on sale for $18,000. (3 points)
a) How much did you save?
b) What fraction of the original price was this?
c) What % of the original price was this?
Answer:
a) $32,000
b) 9/25
c) 36%
Step-by-step explanation:
Hello!
A) How much did you save?
Let's see. In order to find the savings, we must subtract the new price from the original.
50,000 - 18,000 = 32,000You saved $32,000 (a pretty good deal!)
B) What fraction of the original price was this?
To find the fraction, we must divide the new price from the original.
18,000/50,0009,000/25,000 => SImplify9/25 => SimplifyIt's 9 twenty-fifths of the original price.
C) What fraction of the original price was this?
Convert the fraction to percent
9/259*4/25*4 => Denominator of 10036/10036%factor the following x^2+4x+2
Answer:
Find out the factors of 3x² + 4x - 4.
To prove
As given in the question
= 3x² + 4x - 4
simplify the above
= 3x² + 6x - 2x - 4
= 3x(x +2) -2(x + 2)
= (3x - 2) ( x - 2)
The factors of the 3x² + 4x - 4 are (3x - 2) ( x - 2) .
and from the option given in the question (3x -2 ) is the factor of the 3x² + 4x - 4.
Step-by-step explanation:
have a great day
Write the function whose graph is the graph of y=x^3 but is shifted down 1 unit.
Check the template in the picture below.
[tex]y = x^3\implies y=\stackrel{A}{1}(\stackrel{B}{1}x+\stackrel{C}{0})^3 +\stackrel{D}{0}\qquad \qquad \underset{\textit{shifted down by 1 unit}}{y=\stackrel{A}{1}(\stackrel{B}{1}x+\stackrel{C}{0})^3 \stackrel{D}{-1}}\implies y=x^3-1[/tex]
Dana is given the total surface area of a rectangular pyramid. She is asked for the lateral surface area. Describe how Dana can use the given information to determine the lateral surface area.
To get the lateral surface area, dana will subtract the two base area from the total surface area.
Total surface area of rectangular prism
The total surface area of a rectangular prism is the sum of the areas of all of the faces or surfaces that enclose the solid. Therefore,
2lw + 2wh + 2lhwhere
l = length
w = width
h = height
Lateral surface area of a rectangular prismThe lateral surface area of a rectangular prism is the surface area of the solid without the bases.
Therefore,
LA = 2 ( l + w ) hTotal surface area = Lateral surface area + 2 (Base Area)
Total surface area = 2 (l + w) h + 2 (l x w) = 2lh + 2wh + 2lw
Therefore,
Lateral surface area = Total surface area - 2 (Base Area)
To get the lateral surface area, dana will subtract the two base area from the total surface area.
learn more on rectangular pyramid here: https://brainly.com/question/3096481
There are 93 children at a summer camp. Each camp cabin has 8 beds for 8 children. How many cabins are for all 93 children? How many empty beds will remain? Select the true statement.
Answer:
12 cabins with 3 empty beds
Step-by-step explanation:
Closest multiple of 8 to 93 is 8*12=96
96-93=3 empty beds
Answer:
There will be 11 cabins with 5 extra beds.
Step-by-step explanation:
Kindly answer it thanks
Onion; Self-propagation
yeast; budding
starfish; fussion
potato; tubers
ginger; Self-propagation
i don't understand this question please help
Answer:
LM = 22
Step-by-step explanation:
11(44) = (LM)^2
484 = (LM)^2
LM = √484 = 22
Answer:
LM = 22
Step-by-step explanation:
If a tangent segment and a secant segment are drawn from an exterior point to a circle, then the square of the measure of the tangent segment is equal to the product of the measures of the external secant segment and the secant segment.
So for this circle,
point of intersection = Mtangent segment = LMexternal secant segment = NMsecant segment = OMSo LM² = NM · OM
Given:
NM = 11OM = 44LM² = 11 · 44 = 484
⇒ LM = √484 = 22
An internet company randomly selected 50 of its
customers and asked them how many hours per
week they use the internet. Of those surveyed, 28
use the internet more than 15 hours per week.
Based on the data, if the company has 800
subscribers how many watch more than 10 hours
per week?
Answer:
448 subscribers
Step-by-step explanation:
First, find the percentage of people that use the internet more than 15 hours per week.
[tex]\%=\frac{28}{50}=0.56=56\%[/tex]
Now, we can use this information to find 56% of 800.
[tex]56\%*800[/tex]
Note that percentages can also be written as that number over 100.
[tex]\frac{56}{100}*800=\frac{44800}{100}=448\text{ subscribers}[/tex]
Can what of you kind men or women help me with this question?
Answer:
The area is 48 square units.
Step-by-step explanation:
Split up the shape into 2 shapes a rectangle and a Triangle.
Rectangle:
[tex]6*4=24[/tex]
Triangle:
[tex]6*4=24[/tex]
Add them up:
[tex]24+24=48[/tex]
~Kandy~
Hope this Helped!
Brainliest Please!
3/8×1/3×3/4=?
What is is the answer???
The exact form is: 3/32
And the decimal form is: 0.09375
Helen says the sum of two prime numbers is always even. patty disagrees who is correct? Explain your answer
Answer:
Patty
Step-by-step explanation:
The sum of 2 + 3 is 5 so it is not always a even number
Milan tutors history. For each hour that he tutors, he earns 50 dollars. His earnings, (in dollars), after tutoring for hours is given by the following function.
Total pay = (50dollars/hour) * (h hours)
Hope that helps!
There is a pair of parallel sides in the following shape.
What is the area of the shape?
Answer:
21
Step-by-step explanation:
It is a Trapezium so the formula will be 1/2 * (base 1 + base 2) * height
so 1/2 * ( 9+5) * 3
= 1/2 * 14 * 3
= 1/2 * 42
= 21
This is my first time answering someones' question as I am new to Blainly...So please mark me Brainlist.
Thank You!
:)
Answer: 21
Step-by-step explanation:
Graph the line that represents the equation
y=-30 +1
11%, 1/8, 2/25 least your greatest
Answer:
2/25, 11%, 1/8
Step-by-step explanation:
Hopefully this is correct
Answer:
Turn them into decimals
Step-by-step explanation:
11% = 0.11
1/8 = 0.125
2/25= 0.08
0.08, 0.11, 0.125 I believe is the correct order.
Dylan made 15 out of 35 free throws. What's his experimental probability as a simplified fraction?
I need explanation helppp only to people who knows no spamming
Answer:
I believe the answer is either B or D.
Step-by-step explanation:
if I had to choose I think your best choice would be B. But if you draw it on a graph there is a possibility it could be D. But I think your best choice is B.
So, what you need to do here is to first plot all the points on the coordinate plane. When you plot all the points, and connect them all together, you should be able to see a shape. When I plotted all your points, I got a parallelogram or a rectangle, which is most likely the correct answer here because it is more specific than saying a parallelogram. A parallelogram can be a square, rhombus, or any other shape that fits the characteristics of one, so saying "rectangle" is better.
Hector paid $12 for 6 pastries. He wants to create an equation in the form c- Dp, to represent the total cost, c, to buy p
pastries.
What number should Hector put in the square to complete his equation?
Find the cost of one pastry:
$12 / 6 pastries = $2 per pastry
the answer would be $2
NO LINKS!! Please help me with this problem
Part (a)
x = number of adults
y = number of students
5x = amount all of the adults paid ($5 each)
2y = amount the students paid ($2 each)
5x+2y = total amount of money for adults and students combined
The total amount (5x+2y) must be more than $150
So we end up with 5x+2y > 150 as the inequality.
This inequality involves the boundary line 5x+2y = 150 which goes through the y and x intercepts of (0,75) and (30,0) respectively. We use a dashed line for the boundary to mean that points on the boundary are not included as solution points.
We shade above the dashed boundary line to finish off the graph.
Refer to figure (a) shown below.
========================================================
Part (b)
x = number of adults
y = number of students
x+y = total number of people
120 seats is the max capacity so x+y cannot exceed this value.
x+y = 120 or x+y < 120
Or in short x+y ≤ 120 is the inequality
This involves the boundary line x+y = 120 which goes through the y and x intercepts of (0,120) and (120,0). We shade below the solid boundary line.
Refer to figure (b) shown below.
========================================================
Part (c)
Now imagine we overlapped the blue region from part (a) and the red region from part (b)
We'll get the purple region shown in figure (c). At this point, I'm only considering cases when x ≥ 0 and when y ≥ 0. It's not possible to have a negative number of people, so that's why we focus on the upper right quadrant of the xy grid.
This purple region consists of all (x,y) points that make ALL of the inequalities to be true. Exclude any points on the dashed boundary.
For example, if we picked the point (x,y) = (50,40) then this point is in the purple region. We can confirm its a solution by checking each inequality.
5x+2y > 150
5*50+2*40 > 150
250+80 > 150
330 > 150 .... which is true
and,
x+y ≤ 120
50+40 ≤ 120
90 ≤ 120 ... which is also true
Furthermore, both x and y are nonnegative making x ≥ 0 and y ≥ 0 to be true as well. Every inequality mentioned is true for (x,y) = (50,40) to fully confirm the solution point. There are other possible solutions such as (40,60) and (80,20) which I'll let you verify.
If we stick to the (50,40) from earlier, then this means 50 adults and 40 students went to the concert.
Answer: 50 adults and 40 studentsOther answers are possible
Dante will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $63.96 and costs an additional $0.10 per mile driven. The second plan has an initial fee of $51.96 and costs an additional $0.15 per mile driven. How many miles would Dante need to drive for the two plans to cost the same?
answer: 240 miles
Answer:
Sir it says the answer at the bottom of the question
Step-by-step explanation:
It is 240 and I also did the math (.10 * 240 = 24 + $63.96 = 87.96)
and (.15 * 240 = 36 + 51.96 = 87.96) the answer is 240!
Which best describes a trapezoid?
A) 4 angles, 1 set of parallel sides
B) 4 angles, 2 sets of parallel sides
C) 4 right angles, 4 unequal sides
D) 4 equal angles, 4 equal sides
please help.....
