find the angle between the vectors u=i-9j and v=8i+5j
Answers
Answer: \(\cos^{-1} \left(\frac{-37}{\sqrt{7298}} \right) \approx 115.665^{\circ}\)
Step-by-step explanation:
\(u \cdot v=(1)(8)+(-9)(5)=-37\\\\|u|=\sqrt{1^{2}+(-9)^{2}}=\sqrt{82}\\\\|v|=\sqrt{8^{2}+5^{2}}=\sqrt{89}\\\\\cos \theta=\frac{-37}{\sqrt{82}\sqrt{89}}\\\\\theta=\cos^{-1} \left(\frac{-37}{\sqrt{82}\sqrt{89}} \right)\\\\\theta=\boxed{\cos^{-1} \left(\frac{-37}{\sqrt{7298}} \right) \approx 115.665^{\circ}}\)
Related Questions
food concession owner in a mall sold 120 beef, vegetable and pork sliders in 7 days. 20% of the sliders sold were beef and 15% were vegetable. How many pork sliders were sold?
Answers
The number of pork sliders sold is given as follows:
24 pork sliders.
How to obtain the number of pork sliders sold?The number of pork sliders sold is obtained applying the proportions in the context of the problem.
The total number of pork sliders is given as follows:
120 pork sliders.
The percentage of pork sliders sold is given as follows:
20%. (proportion of 0.2).
Hence the amount sold is given as follows:
0.2 x 120 = 24 pork sliders.
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Q7 PLEASE HELP ME !!!!!!!!!!!!!!!!!!!
Answers
The outcomes that are contained in the events are
X = 3 and 10 ⇒ P(X) = 1/5Not X =1, 2, 4, 5, 6, 7, 8 ⇒ P(Not X) = 4/51 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)
The outcomes contained in the eventsFrom the question, we have the following parameters that can be used in our computation:
X = gray colours
Given that
gray colours = 3 and 10
We have
X = 3 and 10
Not X =1, 2, 4, 5, 6, 7, 8
The probability is then calculated as
P(X) = 2/10 = 1/5
For P(Not X), we have
P(Not X) = 1 - 1/5 = 4/5
The equation of P(Not X)In (a), we have
P(Not X) = 1 - 1/5 = 4/5
This means that
P(Not X) = 1 - P(X)
So, the solution is
1 - P(X) = 4/5
The equivalent expressionUsing the above (a) and (b) as a guide, we have the following:
1 - P(X) is the same as P(Not X)
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2(2x−3)+4<6x+7−11 just need the answer for this !!!! helppp
Answers
Answer:
x>1
Step-by-step explanation:
Which function will cross the y-axis at (0, 7)?
Oy=x+7
Oy=x-7
0y=x+5
Oy=7x
Answers
The value of function which cross the y-axis at point (0, 7) will be;
⇒ y = x + 7
What is substitution method?To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The point which cross the function = (0, 7)
Now,
Since, The point which cross the function = (0, 7)
Hence, The point must be satisfy the function.
By option (1);
⇒ y = x + 7
Put (x, y) = (0, 7)
⇒ 7 = 0 + 7
⇒ 7 = 7
Thus, The correct function which passes through the point (0, 7) is,
⇒ y = x + 7
Option (i) is true.
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The diameter of the circle above is 12 cm. What is the circumference of the circle? (Use = 3.14.)
Answers
Answer:
37.68
Step-by-step explanation:
i had this one
find the image of A(-2,4) under a translation (x,y)->(x-2,y-3)
Answers
Answer:
Point A would be at the coordinates, (-4, 1). Hope this helps!
AC is 9.1 centimeters and BC is 4.2 centimeters. Find AB
Answers
Answer:
AB = 4.9cm
Step-by-step explanation:
We know
AC is 9.1 centimeters, and BC is 4.2 centimeters.
Find AB
We take
9.1 - 4.2 = 4.9cm
So, AB = 4.9cm
The radius of a circle is 3.9 in. Find the circumference to the nearest tenth.
Answers
Answer:
24.5
Step-by-step explanation:
Neil and Barry each bought a new phone plan. Neil bought a plan that costs $80 for a new phone and $3per minute of talk, text, or data. Barry bought a plan that costs $230 for a new phone and $2 per minuteof talk, text, or data.7. Write an equation to represent eachfriend's phone plan.8. How much will each friend pay if they eachuse 100 minutes?10. How many minutes would it take for bothplans to cost the same amount?chorar the
Answers
7.-
Equation for Neil P = 80 + 3m
Equation for Barry P = 230 + 2m
8.-
Neil P = 80 + 3(100)
P = 80 + 300
P = $380
Barry P = 230 + 2(100)
P = 230 + 200
P = $430
10.-
P = 80 + 3m
P = 230 + 2m
80 + 3m = 230 + 2m
3m + 2m = 230 - 80
m = 150
please help. i need to raise my grade so i can keep my kitten
Answers
1. Use the distributive property to remove parenthesis.
2. Combine constants which are like terms.
3. Subtract 10 from both sides of the equation.
4. Divide both sides by 4 to isolate the x.
5. The solution.
The equations of three lines are given below.
Line 1: =4y+3x2
Line 2: =+6x8y−8
Line 3: =y+43x8
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and 2
line 1 and 3
line 2 and 3
Answers
Answer:
parellel
Step-by-step explanation:
they are parellel to each other
The vertex form of a function is g(x) = (x-3)² + 9. How does the graph of g(x) compare to the graph of the function
f(x)=x²?
Og(x) is shifted 3 units left and 9 units up.
O g(x) is shifted 3 units right and 9 units up.
O g(x) is shifted 9 units left and 3 units down.
Og(x) is shifted 9 units right and 3 units down.
Answers
Answer:
(3,9)
Step-by-step explanation:
Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. The better deal is:
Multiple Choice
Four Rivers because she will earn about $6,442 more.
Four Rivers because she will earn about $6,523 more.
Four Rivers because she will earn about $4,000 more.
Four Rivers because she will earn about $20,000 more.
Answers
Answer:
The answer is option (C). Four Rivers Bank
Explanation:
a). The total amount Jane will receive after 5 years after investing $40,000 in the Mystic Bank can be expressed as follows;
A = P (1 + r/n) (nt)
where;
A = the future value of the initial investment
P = initial investment amount/principal amount
r = the annual interest rate
n = the number of times that interest is compounded per unit t
t = the time the money is invested for
In our case;
P=$40,000
r=12/100=0.12
n=interest is compounded quarterly which is four times a year=4
t=5 years
Replacing values in the formula;
A=40,000(1+0.12/4)^(4×5)
A=40,000(1+0.03)^20
A=40,000×1.806
A=72,244.45
The total amount Jane will receive after 5 years if she chooses to invest with the Mystic Bank is $72,244.45
b). The total amount Jane will receive after 5 years after investing $40,000 in the Four Rivers Bank can be expressed as follows;
A = P (1 + r/n) (nt)
where;
P=$40,000
r=14/100=0.14
n=interest is compounded semiannually which is two times a year=2
t=5 years
Replacing values in the formula;
A=40,000(1+0.14/2)^(2×5)
A=40,000(1+0.07)^10
A=40,000×1.967
A=78,686.05
The total amount Jane will receive after 5 years if she chooses to invest with the Four Rivers Bank is $78,686.05
c). The best deal would be to invest with Four Rivers Bank for 5 years since the total amount Jane will receive after 5 years will be $78,686.05 which is greater than $72,244.45, which is the total amount she will receive if she chooses to invest with Mystic Bank
you live halfway between you're school and the park. you're friend lives halfway you and the park. how far away does you're friend live from school if you live 1/4 mile from school
Answers
Your friend lives 1/2 mile away from the school or a distance of 1/2 mile away
Let's call the distance between your friend's home and the park "x" miles.
Since your friend lives halfway between you and the park, the distance between your home and your friend's home is also x miles.
Therefore, the distance between your friend's home and school is:
x + 1/4 miles
This is because your friend needs to travel x miles from their home to reach your home, and then an additional 1/4 mile to reach the school.
Since your friend lives halfway between you and the park, and the distance between your home and the park is 1/4 mile, we can write:
x = 1/4 mile
Substituting this value into the equation we derived earlier, we get:
x + 1/4 miles
= 1/4 miles + 1/4 miles
= 1/2 mile
Therefore, your friend lives 1/2 mile away from the school.
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Seven subtracted from seven times a number is 147. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is
B) Solve your equation in part [A] for
Answers
The translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.
What is the numerical value of x?Given the statement in the question?
"Seven subtracted from seven times a number is 147"
Translate the statement into an equation;
Let x represent the unknown number.
Seven times a number ⇒ 7 × x = 7xSeven subtracted from ⇒ -7Is 147 ⇒ = 147Now, combine
7x - 7 = 147
Therefore the translation of the statement is 7x - 7 = 147.
Next, we solve for x
7x - 7 = 147
Add 7 to both sides
7x - 7 + 7 = 147 + 7
7x = 154
x = 154/7
x = 22
Therefore, the translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.
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Five years from now peter age will be two plus three times his current age. Identify the equation representing this situation
Answers
Answer: 5=3x+2
Step-by-step explanation:
5=3x+2
5 years from now, he will be 3x+2 his current age
What will happen to the graph of f(x)=x, if the equation is changed to y=x-5?
Answers
Gregory rode his scooter 2 miles in 30 minutes. At this rate, how far would he ride in
45 minutes?
Answers
It would be 3 miles.
55/(4+1)+3-three cubed
Answers
Answer:38
Step-by-step explanation:
Answer: 14
Step-by-step explanation:
First you have to do 4+1=5, then you do 55/5 and get 11, once you do that you do 11+3=14.
I hope that this helps!!!
slope, y-intercept, and equation
Answers
Slope: 1/4
y-intercept: (0,3)
equation: y=1/4x+b
State YOUR thoughts/reactions
WRITE AT LEAST 4 COMPLETE SENTENCES IN PARAGRAPH FORMAT.
When Saul died, David was crowned king. David united the tribes and continued the fight against the Philistines and other enemies. He captured Jerusalem and made it his capital, starting its transformation into one of history’s most important cities.
David’s son Solomon inherited a peaceful kingdom. He built a great stone temple in Jerusalem. Solomon’sTemple became the focus of religious life. Solomon used trade and taxes to fund other huge building projects. However, most of the tax burden fell on the northern tribes, who came to resent Solomon’s
Answers
Answer:
All you have to do is write how you feel about this it's simple :|
Step-by-step explanation:
Suppose you invest $7500 at an annual interest rate of 4.2% compounded continuously. How much will you have in the account after 2 years? Round the solution to the nearest dollar.
$17,373
$8158
$8157
$17,372
Answers
Answer:
$ 8157
Step-by-step explanation:
7500 e^.042(2) = 8157.22 ~ 8157
Alan draws the two triangles below.
Alan claims that the two triangles are similar. Which of the following methods could he use to prove his claim? Select TWO that apply.
A
show that all pairs of corresponding sides are congruent.
B
show that the triangles are congruent, as well congruent triangles are similar
C
show that a sequence of rigid motions and dilations carries one triangle onto the other triangle
D
show that all pairs of corresponding angles are congruent and all corresponding sides are proportional
Answers
The method that could be used to prove the claim that the two triangles are similar is to show that all pairs of corresponding angles are congruent and all corresponding sides are proportional. That is option D.
What is a triangle?A triangle is defined as a polygon that has three sides that sums up to 180° and three edges.
A triangle that is congruent with another triangle means that the triangle is similar to the other triangle.
This means that the angles are equal and the sides are equal too.
Therefore, the given triangle can be said to be congruent.
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ALGEBRA Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%. During the monthly billing cycle, Ben charged $238.75, made a payment of $300.00, and had a finance charge of $7.99. Find his unpaid balance, previous balance, and new balance.
Answers
The new balance is a credit of $ 48.78.
Since Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%, and during the monthly billing cycle, Ben charged $ 238.75, made a payment of $ 300.00, and had a finance charge of $ 7.99, to find his new balance, the following calculations must be performed:
Finance charge + new purchases + previous balance - payments = X 238.75 x 1.01875 + 7.99 - 300 = X 243.22 + 7.99 - 300 = X 251.21 - 300 = X -48.78 = X
Therefore, the new balance is a credit of $ 48.78.
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Xavier is buying fencing to surround his garden if his garden has a perimeter of 30 yards and fencing cost six dollars a yard how much money will he need for the fencing
Answers
Answer:
$180
Step-by-step explanation:
If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180
bre
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What is the value of arctan (-13);
MA
OA. 60°
OB. 90°
OC -60°
OD. 0°
O E. 45°
Answers
Answer:
The answer to this question is 60degree
Austin and Dale earn money by painting fences over the summer. Working alone, Austin takes 3 hours longer than Dale to paint a fence. Working together, the two of them can paint a fence in 2 hours. How many hours would it take each of them working alone?
Answers
Answer:
Austin will take 9 hours to paint a room and dale with take 3 hours to paint a room
Step-by-step explanation:
A new car costs $28,000. It is expected to depreciate at an average rate of 8% per year.
Find the value of the car in 8 years.
Answers
Answer:
35
Step-by-step explanation:
In a triangle, the measure of one angle is five more than the first and the third angle is one more than four times the first.
Answers
Answer:
A= 29
B=34
C=117
Step-by-step explanation:
A triangle has three sides and a triangle always adds up to be 180
A + B + C = 180
B = A + 5
C = 4A + 1
Plug in.
A + A + 5 + 4A + 1 = 180
6A + 6 = 180
6A = 174
A = 29
Now since you found A, find the other two by plugging A in!
C = 4(29) + 1
C = 117
Plug in the B equation
B = 29 + 5
B=34
Check your answers
29 + 117 + 34 = 180
What is the explicit formula for this sequence?
40, 20, 10, 5,...
A. an= = (1)
B. an-40-2(n-1)
C. an = 40 (¹)
D. an = 40. (1)-0•40(n-1)
Answers
Answer:
D. an = 40. (1)-0•40(n-1)
Step-by-step explanation:
Simplifying the formula, we have:
an = 40 - 0 * 40 * (n-1)
an = 40 - 0
an = 40