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Find the angle between the vectors ????=????+???? and ????=−????+????. (Give an exact answer. Use symbolic notation and fractions where needed.)

Answers

Answer 1

Answer:

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

$a = 2i + j -3k$

$b = 3i - 2j -k$

Required

The angle between them

The cosine of the angle between them is:

$\cos(\theta) = (a\cdot b)/(|a|\cdot |b|)$

First, calculate a.b

$a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)$

Multiply the coefficients of like terms

$a \cdot b =2 * 3 - 1 * 2 - 3 * -1$

$a \cdot b =7$

Next, calculate |a| and |b|

$|a| = \sqrt{2^2 + 1^2 + (-3)^2$

$|a| = \sqrt{14$

$|b| = √(3^2 + (-2)^2 + (-1)^2)$

$|b| = √(14)$

Recall that:

$\cos(\theta) = (a\cdot b)/(|a|\cdot |b|)$

This gives:

$\cos(\theta) = (7)/(√(14) * √(14))$

$\cos(\theta) = (7)/(14)$

$\cos(\theta) = 0.5$

Take arccos of both sides

$\theta =\cos^(-1)(0.5)$

$\theta =60^o$

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1. Simplify each of the following fractionsleaving each as an improper fraction, not a wholenumber. Do not use your calculator!4.5053.28
Consider the statement p:x+9=10.which of the following is a equivalent statement

What does (2,7) look like on the coordinate plane.

Answers

Answer: from (0,0) (2,7) is 2 right from (0,0) and 7 up from (2,0)

Step-by-step explanation: go right 2 and 7 up

Answer:

okay so your coordiantes are in the form of (x,y) on a graph.You start at the origin and go to the right 2 units and up 7 units.

Step-by-step explanation:

Hope this helps!

At a concession stand, seven hot dogs and two hamburgers cost $16.25; two hot dogs and seven hamburgers cost $17.50. Find the cost of one hot dog and the cost of one hamburger.

Answers

The cost of 1 hot dog is $1.75 and the cost of 1 hamburger is $2.

Let x be the cost of one hot dog and y be the value of one hamburger. we will set up a system of linear equations to solve for x and y:

From the first statement, we recognize that:

7x + 2y = 16.25 ----(1)

From the second statement, we know that:

2x + 7y = 17.50 ----(2)

We will use both substitution or elimination method to solve this system of equations. let's use elimination method right here. we are able to multiply equation (1) through 7 and equation (2) by 2 to eliminate y:

49x + 14y = 113.75 ----(3)

4x + 14y = 35 ----(4)

Subtracting equation (4) from equation (3), we get:

45x = 78.75

Dividing each sides by using 45, we get:

x = 1.75

Substituting x = 1.75 into equation (1), we can solve for y:

7(1.75) + 2y = 16.25

12.25 + 2y = 16.25

2y = 4

y = 2

Consequently, the cost of 1 hot dog is $1.75 and the cost of 1 hamburger is $2.

Learn more about system of linear equations:-

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Write a formula that will compute the final grade for the course, using G to represent the final grade, H to represent the homework average, Q to represent the quiz average, P to represent the project grade, T to represent the test average, and F to represent the final exam grade. Note: Keep in mind how you must write the percentages that show the weighting of each category when doing computations!

Answers

Answer:

To calculate final grade we use the formula:

Final grade = H( the weight of h) + Q( the weight of q) + P (the weight of project) +T (the weight of test) + F(the weight of final exams).

This formula help us to calculate the grade we need to get.

Step-by-step explanation:

Solution:

Suppose grade breakdown for certain college course is as follow:

Homework = 15%

Quizzes = 20%

Project = 10%

Test = 40%

Final exam= 15%

Let G represent the final grade

H represents homework average,

Q represents quizzes and P represent project, T represent test average and F represent final exam.

To calculate final grade we use the formula:

Final grade = H( the weight of h) + Q( the weight of q) + P (the weight of project) +T (the weight of test) + F(the weight of final exams).

This formula help us to calculate the grade we need to get.

Final answer:

The final grade, G, can be computed by adding together the weighted values of the homework average, quiz average, project grade, test average, and final exam grade. This can be represented by the formula G = 0.20*H + 0.20*Q + 0.25*P + 0.15*T + 0.20*F.

Explanation:

To compute the final grade for the course, you will need to multiply each category by its weighting percentage, then add the results together. This can be represented as the following formula:

G = 0.20*H + 0.20*Q + 0.25*P + 0.15*T + 0.20*F

In this formula, G is the final grade, H is the homework average, Q is the quiz average, P is the project grade, T is the test average, and F is the final exam grade. The coefficients (0.20, 0.20, 0.25, 0.15, and 0.20) represent the weighting percentages in decimal form for each respective category.

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Rewrite the function by completing the square.
f(x) = x^2 – 10x—96

Answers

Answer:

$f(x) = (x - 5)^(2) - 121$ .

Step-by-step explanation:

The goal is to rewrite $f(x)$ in the vertex form $a\, (x - h)^(2) + k$ by completing the square (where $a$ , $h$ , and $k$ are constants.)

Expand the vertex form expression:

$\begin{aligned}& a\, (x - h)^(2) + k\n &= a\, (x - h)\, (x - h) + k \n &= a\, \left(x^2 - h\, x - h\, x + h^2\right) + k \n &= a\, \left(x^2 - 2\, h\, x + h^2\right) + k\n &= a\, x^2 - 2\, a\, h\, x + \left(a\, h^2 + k\right) \end{aligned}$ .

Compare this expression to $f(x) = x^2 - 10\, x - 96$ and solve for the constants $a$ , $h$ , and $k$ . Make sure that the coefficient of each term matches:

Coefficient for the $x^2$ term: $a$ in the expanded expression and $1$ in the expression for $f(x)$ . Hence, $a = 1$ .

Coefficient for the $x$ term: $(-2\, a\, h)$ in the expanded expression and $(-10)$ in the expression for $f(x)$ . Hence, $-2\, a\, h = -10$ .

Coefficient for the constant term: $\left(a\, h^2 + k\right)$ in the expanded expression and $(-96)$ in the expression for $f(x)$ . Hence, $a\, h^(2) + k = -96$ .

Substitute $a = 1$ into the second equation, $-2\, a\, h = -10$ , and solve for $h$ .

$-2 \, h = -10$ .

$h = 5$ .

Substitute both $a = 1$ and $h = 5$ into the third equation, $a\, h^(2) + k = -96$ , and solve for $k$ .

$5^2 + k = -96$ .

$k = -121$ .

Therefore, $a\, (x - h)^(2) + k$ becomes $(x - 5)^2 + (-121)$ .

Hence, the vertex form of the parabola $f(x)$ would be:

$f(x) = (x - 5)^(2) - 121$ .

Answer:

(x - 5)² -121 = 0

Step-by-step explanation:

if you need to find the roots you can take the square root of each side:

(x-5)² = 121

square root of (x-5)² is x-5

square root of 121 is ±11

first root: x-5 = 11

x = 16

second root: x-5 = -11

x = -6

Let x = 20. Which expression has a value greater than 4x−10 ? 5x−100 8(x−10) 5(2x−26) 5x−30

Answers

Answer:

8(x-10)

Step-by-step explanation:

When the calculation is repetitive, I like to let a calculator or spreadsheet do it. The value of the given function is

4·20 -10 = 70

Only the expression 8(x-10) = 8(20-10) = 80 has a larger value for x=20.

_____

Comment on this solution

It is actually fewer keystrokes to copy the numbers into a calculator, but getting a record of results can be difficult.

Answer:

Step-by-step explanation:

Help!!!
Find all solutions to the equation

7 sin^2x - 14 sin x + 2 = -5

Answers

7 sin^2(x) - 14 sin(x) + 2 = -5
Temporarily substitute y in for sin(x) to make it more readable
7y^2 - 14y + 2 = -5
Move the -5 over by adding to both sides
7y^2 - 14y + 7 = 0
Simplicity by dividing both sides by 7 to get
y^2 - 2y + 1 = 0
Factor to get
(y-1)(y-1) = 0
Or y-1 = 0
y = 1
Therefore
Sin(x) = 1
x = pi/2 + 2pi * n where n represents all whole numbers
Final answer:
x = pi/2 + 2pi * n
Hope I helped :)

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