Answer:
[tex]90^\circ[/tex]
Step-by-step explanation:
Given two non zero vectors, [tex]\vec a, \vec b[/tex].
Let the angle between the two vectors = [tex]\theta[/tex]
Given that:
[tex]|\vec a+\vec b|=|\vec a-\vec b|[/tex]
Let us have a look at the formula for magnitude of addition of two vectors:
[tex]|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}[/tex]
Where [tex]\theta[/tex] is the angle between the two vectors.
formula for magnitude of subtraction of two vectors:
[tex]|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}[/tex]
As per the given condition:
[tex]\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}[/tex]
Squaring both sides:
[tex]a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ[/tex]
So, the angle between the two vectors is: [tex]90^\circ[/tex]
Ryan went to the store to buy some apples. The price per pound of the apples is $4.25
per pound and he has a coupon for $2 off the final amount. With the coupon, how
much would Ryan have to pay to buy 5 pounds of apples? Also, write an expression
for the cost to buy p pounds of apples, assuming at least one pound is purchased.
Answer:19.25
4.25p-2
Step-by-step explanation:
The sum of two numbers is eleven. One number is thirty-eight less than six times the other. Find the numbers.
Answer:
One of the number is 4 while the other is 7
Step-by-step explanation:
The sum of two numbers is eleven
Let the numbers be x and y
X+ y = 11
One number is thirty-eight less than six times the other
X= 6y-38
X+ y = 11
6y-38 +y= 11
6y+y= 11+38
7y=49
Y= 49/7
Y= 7
X+ y = 11
X+7= 11
X= 11-7
X= 4
Express the following vector in the form v=v1i+v2j+v3k. 3u - v if u=(4,7,-3) and v=(2,-7,5).3u - v = ____ i + ____ j + _____ k.(Simplify your answers.)
Answer:
5i+14j-7kStep-by-step explanation:
Given the vectors u = (4,7,-3) and v=(2,-7,5), both vectors are 3-dimensional in nature and can also be rewritten as;
u = 4i+7j-3k and v = 2i-7j+5k
To get 3u-v, we will substitute the given vectors into the expression;
3u-v = 3(4i+7j-3k) - (2i-7j+5k)
open the parenthesis
3u-v = 12i+21j-9k - 2i + 7j - 5k
collect like terms
3u-v = (12i - 2i) + (21j + 7j) (-9k-5k)
3u - v = 10i+28j-14k
To simplify the answer, we will divide through by 2
3u - v = 10i/2+28j/2-14k/2
3u - v = 5i+14j-7k
Hence the simplified form of the expression is 5i+14j-7k
Consider the positively charged particles seen here. The magnitude of their combined charges is represented by the vector arrow. If one charged particle is removed, what will be the result on the force field and how will it be illustrated? A) remain constant; no change in vector B) decreases by one; arrow length decreases by 1/3 C) decreases by one but arrow length remains constant D) decreases by a factor of 2; arrow changes direction
B)decreases by one; arrow length decreases by 1/3
Answer:
B)decreases by one; arrow length decreases by 1/3
Step-by-step explanation:
It is recommended that pregnant women over eighteen years old get 85 milligrams of vitamin C each day. A doctor is concerned that her pregnant patients are not getting enough vitamin C. So, she collects data on 45 of her patients and finds that the mean vitamin intake of these 45 patients is 81 milligrams per day with a standard deviation of 12 milligrams per day. Based on a level of significance of α = .02, test the hypothesis.H0 : u = 85H1 : u< 85n = 45sample mean = 81σ = 12z based on α = .02 = -2.05 ( if lessthan -2.05 we will reject the null hypothesis)Sample standard deviation = 12/√45 = 1.789z= x-u/σ(o sample) - 81-85/1.789 = -2.236-2.236is less than -2.05 so wereject the H0 : u = 85
Answer:
|Z| = 2.237 < 2.32 at 0.02 level of significance
Null hypothesis is accepted
Recommended that pregnant women not over eighteen years old get 85 milligrams of vitamin C each day
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 45
Mean of the Population 'μ' = 85
Mean of the sample 'x⁻' = 81
Standard deviation of the sample 'σ' = 12 milligrams
Null Hypothesis: H₀:μ=85
Alternative Hypothesis: H₁:μ≠ 85
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{81 -85}{\frac{12}{\sqrt{45} } }[/tex]
Z = -2.237
Level of significance = 0.02
Z₀.₀₂ = 2.32
|Z| = 2.237 < 2.32 at 0.02 level of significance
Conclusion:-
Null hypothesis is accepted
Recommended that pregnant women not over eighteen years old get 85 milligrams of vitamin C each day
Factor.
14y2 + 70y
14y2 + 70y=
Answer:
14y(y+5)
Hope this helps!
Answer:
the answer is 14y(y+5)
Step-by-step explanation:
Solve the equation. Check for extraneous solutions. |x−2|=6x+8 x=_____ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
Answer:
x= -0.857143 = -6/7
Step-by-step explanation:
Of the 10 contestants in a televised quiz competition, 2 were eliminated during this week's show, and 2 more will be eliminated during next week's show
How many groups of 6 remaining contestants are possible a week from now? Assume that the show airs on the same day every week.
28
210
20,160
151,200
Answer:a) 28
Step-by-step explanation:
10-2=8
8 objects currently 6 placements for next week = 28 combinations of people of who could stay or leave
Answer:
A
Step-by-step explanation:
The answer is the first one: 28 :) Have a good day everyone!
15+0= 15
O Communative Property
O Associative Property
O identity Property
O Distributive Property
First of all, let's take a look on the question.
[tex]\large{15 + 0 = 15}[/tex]
Here, 0 is added to 15 and the resultant is 15 only. So, we can say that 0 when added with any number gives the same number as the resultant.
So, the property is known as Identity property because 0 is added to get the identity of the same number.
The Correct Option:
[tex] \large{ \boxed{ \red{ \bf{Option \: C}}}}[/tex]
So, let's know more...
Commutative property ➝ a + b = b + aAssociative property ➝ a + (b + c) = (a + b) + cDistributive property ➝ a(b + c) = ab + acSo this is the general form of these properties which is general observed in the rational numbers.
━━━━━━━━━━━━━━━━━━━━
Which property is shown below 7n=22 then n=3
Answer:
Substitution property.
Step-by-step explanation:
You have to substitute n to get the answer therefore, substitution.
A certain lottery game, 32 numbers are randomly mixed and 7 are selected. A person must pick all 7 numbers to win. Order is not important. What is the probability of winning?
Answer:
Below.
Step-by-step explanation:
The number of combinations of 7 from 32 = 32! / 7! (32-7)!
= 3365856
So it is 1/ 3365856 = 0.000000297
or about 3 in 10,000,000.
One rule of thumb for estimating crowds is that each person occupies 2.5 square feet. Use
this rule to estimate the size of the crowd watching a concert in an area that is 150 feet long
and 240 feet wide
Answer:
The number of people that will occupy 36000 square feet= 14400 people
Step-by-step explanation:
each person occupies 2.5 square feet.
Area of concert in an area that is 150 feet long and 240 feet wide
Area=150*240
Area=36000 square feet
If one person occupies 2.5 square feet
The number of people that will occupy 36000 square feet
= 36000/2.5
= 14400 people
The number of people that will occupy 36000 square feet= 14400 people
What is the solution to this system:
4x+9y=28
- 4x-y=-28
Answer:
x = 7
y = 0
Step-by-step explanation:
→To solve this, you can use the elimination method. To do this, you must have one set of variables that can cancel each other out. In the problem given, we already have positive 4x and -4x, making them cancel out:
4x + 9y = 28
-4x - y = -28
__________
8y = 0
y = 0
→Plug in 0 for y, into an equation:
-4x - 0 = -28
-4x = -28
x = 7
The difference of the quotient of 5 and x and the product of 18 and y
Answer:
(5/x)-(18y)
Step-by-step explanation:
First write the expression (5/x) and then the second expression (18y) the write the difference, so basically a subtraction. (5/x)-(18y)
what is the solution to : 3(1/2 m - 3) =45
Answer:
[tex]m=36[/tex]
Step-by-step explanation:
We can solve for this equation by isolating [tex]m[/tex] on one side. To do this, we can "reverse" the equation.
[tex]3(\frac{1}{2}m - 3) = 45[/tex]
Let's divide both sides by 3.
[tex]3(\frac{1}{2}m-3)\div3 = 45\div3\\\\\frac{1}{2}m - 3 = 15[/tex]
Add 3 to both sides:
[tex]\frac{1}{2}m - 3 + 3 = 15 + 3\\\\\frac{1}{2}m = 18[/tex]
Multiply both sides by two (since [tex]\frac{1}{2}\cdot2=1[/tex])
[tex]\frac{1}{2}m \cdot 2 = 18 \cdot 2\\\\m = 36[/tex]
Hope this helped!
Answer:
m = 36
Step-by-step explanation:
Step 1:
3 ( 1/2m -3 ) = 45
Step 2:
3/2m - 9 = 45
Step 3:
3/2m = 54
Step 4:
54 ÷ 3/2
Step 5:
54/1 × 2/3
Answer:
m = 36
Hope This Helps :)
The perimeter of the rectangle is 48 inches. If the width of the rectangle is 11 inches what is the length?
Answer:
The length is 13 inches.
Step-by-step explanation:
Find the least common multiple of 4, 2, and 7
Answer:
28
Step-by-step explanation:
So we know that 2 is already a multiple of 4 so we can just find the least common multiple of 4 and 7. So we can do:
4, 8, 12, 16, 20, 24, 28
7, 14, 21, 28
So the least common multiple between 4, 2, and 7 is 28
Angie and Kenny play online video games. Angie buys 1 software and of game play. Kenny 2 buys software and 6 months of game play. Each software package costs $50. If their total cost is $295, what is the cost of one month of game play?
Answer:
The cost of one month of gameplay is $99.2
Step-by-step explanation:
295/6 + 50
49.2 + 50
99.2
(I rounded to the nearest tenth on multiple occasions)
Find the product of (5/16)(-2)(-4)(-4/5)
Answer:
It's -2
(5/16)(-4/5)=(-20/80)
(-2)(-4)=(8)
(8)(-20/80)= -160/80
-160/80=-2
Your team scores and -8 and -for on the first two rounds of a game how can you use addition to find your Teams total score
Answer:
-12
Step-by-step explanation:
-8-4=-12
because -×-=+
and -+-=-
why because when you add the highest number gives you the sign
1. Which inequality is true?
A.6 π > 18
B.6 π < 18
C.6 π = 18
D.18 > 6 π
Answer:
a
Step-by-step explanation:
a is the answer ..........
Without shipping costs, a helmet costs 28.86. If Jordan paid 38.02 for the helmet, including shipping, how much did the shipping costs?
Answer:
Jordan paid $9.16 for shipping.
Step-by-step explanation:
Is 10 greater than 10.1
Answer:
no
Step-by-step explanation: 10.1 is .1 higher
Answer:
yes
Step-by-step explanation:
mark as me brainlist
If h(x) = 6 - X, what is the value of (hom (10)?
Answer:
16
Step-by-step explanation:
which ordered pair would form a proportional relationship with the point graphed below
A.(-10, 30)
B.(30, -15)
C.(-30, 10)
D.(80, -30)
Answer:
d
Step-by-step explanation:
i took the test
15 POINTS
1.) name two planes that intersect in WX in the figure to the right
what is the midpoint of 3,7 and -2,3
Answer:
(1.5) (2.2)
Step-by-step explanation:
SHOULD BE CORRECT
I HAD THAT QUESTION YESTERDAY AND MY TEACHER SAID IT WAS RIGHT ♀️
Answer:
(1/2,5)
Step-by-step explanation:
Midpoint formula is (x1+x2)/2,(y1+y2)/2
(3-2)/2 , (7+3)/2
=(1/2,5)
Might be wrong, though.
v+8-6=10
Please help quick
pls help fast !!!!!????
Answer:
[tex]k=-\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]-\frac{1}{2} -\frac{3}{2} = \frac{3}{2} k[/tex]
[tex]-2= \frac{3}{2} k[/tex]
[tex]-\frac{4}{3}[/tex][tex]=k[/tex]
PIZZA CRUST Pepe’s Pizza makes 52 pizza crusts the fi rst week and 180 pizza crusts each subsequent week. Dianne’s Delicatessen makes 26 pizza crusts the fi rst week and 90 pizza crusts each subsequent week. In how many weeks will the total number of pizza crusts made by Pepe’s Pizza equal twice the total number of pizza crusts made by Dianne’s Delicatessen?
Answer:
Always.
Step-by-step explanation:
Let's write two equations.
Pepe's Pizza:
They made 52 pizza crusts the first week and 180 crusts each subsequent week. In other words, in x weeks after the first week, their total number of crusts made is modeled by the equation:
[tex]P=52+180x[/tex]
Dianne's Delicatessen:
They made 26 pizza crusts the first week and 90 crusts each subsequent week. So, in x weeks after the first week, their total number of crusts is modeled by:
[tex]D=26+90x[/tex]
And we want to find the number of weeks such that the number of crusts made by Pepe's Pizza is equivalent to twice the number of crusts made by Dianne's Delicatessen. In other words:
[tex]P=2D[/tex]
Substitute P and D for their equations:
[tex]52+180x=2(26+90x)[/tex]
Distribute the right:
[tex]52+180x=52+180x[/tex]
As we can see, the two equations turns out to be the same.
In other words, no matter what week it is (excluding the first week), the amount of crusts made by Pepe's Pizza will always be twice the crusts made by Dianne's Delicatessen.