# Evaluate the expression a=2, b=-3, c=-4 | b+1 | +8

## Answers

1. C

2. A

3. D

4. A

5. C

1. Find a ⋅ b.

a = <7, 4>, b = <3, 5> (2 points)

41 < right answer

<10, 9>

-1

<21, 20>

Explanation:

a . b means the dot or scalar product of the vectors a and b.

The scalar product of vectorr <x1,y2> and <x2,y2> is (x1)*(y1) + (x2)*(y2)

So, a . b = 7*3 + 4*5 = 21 + 20 = 41 < answer

2. Find a ⋅ b

a = 10i + 9j, b = 4i + 3j (2 points)

<40, 27>

<14, 12>

67 < answer

-13

Explanation:

Again you are required to find the dot product of two vectors. In this case the vectors are given using the representation with the unit vectors i and j.

The dot product of the vectors (x1 i + y1 j) . (x2 i + y2 j) is x1*x2 + y1*y2

So, (10i + 9j) . (4i + 3j) = 10*4 + 9*3 = 40 + 27 = 67

67

3. Find the angle between the given vectors to the nearest tenth of a degree.

u = <6, -1>, v = <7, -4> (2 points)

20.3° < answer

10.2°

0.2°

30.3°

Explanation:

You can use the dot product to find the angle between two vectors.

This is the formula:

cos(α) = [ <a> dot <b. ] / [|a| |b| ]

where α is the angle between the vector a and b.

<a> is the vector a, <b> is the vector b, <a> dot <b> is the dot product, |a| is the magnitude of vector a, and |b| is the magnitude of vector b.

<u> dot <v> = (6)(7) + (-1)(-4) = 42 + 4 = 46

|u| = √ (6^2 + 1^2) = √37

|v| = √ (7^2 + 4^2) = √65

=> cos(α) = [46] / [√37 * √65] = 0.938

=> α = arccos(0.938) = 20.3°

4. Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <10, 6>, v = <9, 5> (2 points)

Orthogonal

Parallel

Neither < answer

Explanation:

At sight they are neither orthogonal nor parallel. You can put the points in a graph and you will realize inmediately.

Let's calculate the angle, with the formula given in the above problem.

cos(α) = [<u> dot< >v] / [ |u| |v| ]

<u> dot <v> = 10*9 + 6*5 = 90 + 30 = 120

|u| = √(10^2 + 6^2) = √136

|v| = √(9^2 + 5^2) = √106

cos(α) = 120 / (√136 * √106] = 0,999

α = arctan(0,999) = 1,9°

Which confirms that they are neither orthogonal nor parallel

5. Evaluate the expression:

v ⋅ w

Given the vectors:

r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6> (2 points)

Solution:

v . w = v dot w = (3)(-4) + (-8)(-2) + (-3)(-6) = -12 + 16 + 18 = 22

22

1 C

2 A

3 D

4 D

5 B

here is the answers and i hope i helped

9, 7,-8.3,>

Step-by-step explanation:

5)-3 is marked exactly 3 units to the left of origin 0.

(since negative sign we mark on left of 0)

6) |-9| = absolute value of 9 = 9

7) y-11=-4

Add 11 to both the sides

WE get y =7 is the solution

8) a + b when a = 2.5 and b = -10.8.

= 2.5+(-10.8) = -(10.8-2.5) = -8.3

9) 0.4 is positive hence lies to the right of origin.

Partition the space between 0 and 1 into 10 equal subparts and mark 4th subdivision to get 0.4

10) -1.8>-2.5

Question 1:

Assume that the number is x

Two times a number is 2x and 9 more means that we will add 9

This gives us : 2x + 9 > option B

Question 2:

We are given the expression: 3m-5. To find the value of the expression at m = 7, all we have to do is substitute in the expression with the given value.

This gives us: 3(7) - 5 = 21 - 5 = 16 > option B

Question 3:

The given expression is 4x+8y-3x+2y. To simplify the expression, we will group the like terms (terms having the same variable raised to the same degree)

This gives us: x(4-3) + y(8+2) = x + 10y > option D

Question 4:

The given expression is: 24p + 64. To factor the expression, we will need to take out the common factor from both numbers and then use distributive property. We can note that both numbers are divisible by 8.

This gives us: 8() = 8(3p+8) > option C

Question 6:

We are given that W-8=-12. To isolate the W we will simply add 8 to both sides.

This gives us: W-8+8 = -12+8 > W = -4 > option B

Question 7:

We are given that 3q=12. To isolate q, we will simply divide both sides by 3.

This gives us: > q=4 > option A

Question 8:

We are given that . To get the value of q, we will simply multiply both sides by 6.

This gives us: > q=144 > option D

Question 9:

We are given that: 3b-9=15. To get the value of b, we will first add 9 to both sides of the equation and then divide both sides by 3.

This gives us: 3b-9+9=15+9 > 3b=24 > b= > option A

Question 10:

The given is: . To get the value of y, we will first subtract 10 from both sides and then multiply both sides by 5.

This gives us: > y = -25*5 = -125 > option A

Question 11:

The given is: -3(4-a=6). To get the value of a, we will first divide both sides by -3, then subtract 4 from both sides and finally multiply both sides by -1

This gives us: 4-a = > -a=-2-4=-6 > a=6 > option D

Question 12:

The given is: 5(x+6)=45. To get the value of x, first we will divide both sides of the equation by 5 and then subtract 6 from both sides.

This gives us: x+6 = > x = 9-6 = 3 > option B

Question 13:

Assume that the number of bottles is x.

He has 4 full bags of bottles. This means that number of bottles in bags = 4x

He has additional 8 bottles.

The total number of bottles is 104

This means that total number of bottles is 4x+8 = 104

Now, we solve the equation:

4x+8-8 = 104-8 > 4x=96 > x= > option C

Question 14:

Note that on the negative axis, the number decreases as its value increases (this is opposite to the positive counting). In other words: -1 > -2 and -2>-3 and so on.

This means that for h>-6 > h could be -4 > option D

Question 15 & 16:

The given is: Z-4>9. To get the value of Z, Add 4 to both sides of the equation.

This gives us: Z-4+4 > 9+4 > Z>13 > option D

Question 17:

The given is: Q+7 < -15. To get the value of Q, subtract 7 from both sides.

This gives us: Q+7-7 < -15-7 > Q < -22

Question 18:

The given is: -3y>9. To get the value of y, we will divide both sides by -3. Remember that when we divide by a negative number, we flip the inequality sign. This means that the > will be flipped to <

This gives us: > option C

Question 19:

The given is: -4. " class="latex-formula" id="TexFormula12" src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bk%7D%7B5%7D%20%3E%20-4.%20" title=" \frac{k}{5} > -4. "> To get the value of k, we will multiply both sides of the equation by 5.

This gives us: k > -4(5) > k > -20 > option A

Question 20:

The given is: 4g-8<20. To get the value of g, we will first add 8 to both sides of the equation and then divide both sides by 4.

This gives us: 4g<28 > g< > g<7 > option D

Question 21:

The given is: . To get the value of v, first we will subtract 12 from both sides of the equation, then we will multiply both sides by -2 (remember to flip the inequality sign since we are multiplying by a negative number)

This gives us: > option A

Hope this helps :)

The correct answers are:

#1) B - 2x+9

#2) B - 16

#3) D - x+10y

#4) C - 8(3p+8)

#5) No equation, cannot be done

#6) B - w = -4

#7) A - q = 4

#8) D - q = 144

#9) A - b = 8

#10) A - y = -125

#11) D - a = 6

#12) B - x = 3

#13) C - x = 24

#14) D - -4

#15) D - Z>13

#16) same as 15

#17) Not listed; Q < -22

#18) C - y < -3

#19) A - K>-20

#20) D - g< 7

#21) A - V > 8

Explanation:

#1) "Nine more than" means something plus 9. "Two times a number" means 2x. Together, this gives us 2x+9.

#2) For 3m-5 if m=7, substitute 7 for m. 3(7)-5 = 21-5 = 16.

#3) To simplify 4x+8y-3x+2y, combine like terms. We can use the commutative property to rewrite the like terms together: 4x-3x+8y+2y. Combining like terms, we have x+10y.

#4) To factor, we pull out the GCF. To find the GCF, we find the prime factorization of 24 and 64:

24 = 2(12) = 2(4)(3) = 2(2)(2)(3)

64 = 2(32) = 2(4)(8) = 2(2)(2)(2)(4) = 2(2)(2)(2)(2)(2)

They have 3 2's in common, so the GCF is 2(2)(2) = 8. Pulling this out of our expression, we have:

24p+64 = 8(3p+8)

#5) We have no equation to solve.

#6) We add 8 to each side:

w-8+8 = -12+8; w = -4

#7) We divide both sides by 3:

3q/3 = 12/3; q = 4

#8) We multiply both sides by 6:

(q/6)(6) = 24(6); q = 144

#9) 3b-9 = 15

First, add 9 to each side:

3b-9+9 = 15+9; 3b = 24

Now divide both sides by 3:

3b/3 = 24/3; b = 8

#10) y/5 + 10 = -15

First subtract 10 from both sides:

y/5+10-10 = -15-10; y/5 = -25

Now multiply both sides by 5:

(y/5)(5) = -25(5); y = -125

#11) -3(4-a) = 6

First use the distributive property:

-3(4) - -3(a) = 6; -12+3a = 6

Add 12 to each side:

-12+3a+12 = 6+12; 3a = 18

Divide both sides by 3:

3a/3 = 18/3; a = 6

#12) 5(x+6) = 45

Use the distributive property:

5(x)+5(6) = 45; 5x+30=45

Subtract 30 from each side:

5x+30-30 = 45-30; 5x=15

Divide both sides by 5:

5x/5 = 15/5; x = 3

#13) 4x+8=104

Subtract 8 from each side:

4x+8-8 = 104-8; 4x=96

Divide both sides by 4:

4x/4 = 96/4; x = 24

#14) We want a number larger than -6. For negative numbers, this means a number closer to 0; the number closest to 0 is -4.

#15) Add 4 to each side: z-4+4 > 9+4; z > 13

#16) Same as 15

#17) Subtract 7 from each side: q+7-7<-15-7; q<-22

#18) Divide both sides by -3 (remember, when you multiply or divide an inequality by a negative number, you must flip the inequality symbol): -3y/-3>9/-3; y<-3

#19) Multiply both sides by 5: (k/5)(5)>-4(5); k>-20

#20) 4g-8<20

First add 8 to each side: 4g-8+8<20+8; 4g<28

Divide both sides by 4: 4g/4<28/4; g<7

#21) v/-2 +12 < 8

First subtract 12 from each side: (v/-2)+12-12<8-12; (v/-2)<-4

Multiply both sides by -2 (remember to flip the inequality symbol): (v/-2)(-2)<-4(-2); v>8

12

Step-by-step explanation:

3+1=4

4+8=12

*| | -these are absolute value lines. Absolute value causes a negetive number to automatically have a positive value. For example, |-3| becomes 3.