Understand Subtraction with Integers - Instruction

Order the numbers −7, 2, −4, 8 from least to greatest

Nutka1998 [239]

Answer: -7, -4, 2, 8

7 0

3 years ago

Read 2 more answers

Help anyone can help me do this question,I will mark brainlest.

postnew [5]

Answer:

Step-by-step explanation:

7 0

3 years ago

Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, âˆ’1), B(4, âˆ’3, 0), C(1

zavuch27 [327]

Answer:

Angle at vertex A : 59.2° B: 61.7° C : 59.1°

Step-by-step explanation:

1. First find the length of the vectors

AB = B-A = (4-1, 3-0, 0-1) = (3, 3, -1)

AC = C-A = (1-1, 4-0, 3-1) = (0, 4, 2)

BC = C-B = (1-4, 4-3, 3-0) = (-3, 1, 3)

2. Find magnitude of the vectors

|AB| = √(3^2+3^2+〖(-1)〗^2 )=√19

|AC| = √(0^2+4^2+2^2 )=2√5

|BC| = √(〖(-3)〗^2+1^2+3^2 )=√19

3. Find the angles between them

cos θ = (a.b)/(|a||b|) -----> θ = arc cos ((a.b)/(|a||b|))

AB, AC : θ =arc cos (AB.AC)/(|AB||AC|) = arc cos ( (3.0+3.4+ -1.2)/(√19 x 2√5)= 10/(2√95) ) =59.136, which is approximately 59.14°

AB, BC : θ =arc cos (AB.BC)/(|AB||BC|) = arc cos( (3.-3+3.1+ -1.3)/(√19 x √19)= (-9)/19 ) = 118.27°

Because of the direction of BC is pointing relative to AB this is the angle outside the triangle, and we should find the supplementary angle.

180-118.27 = 61.73°

If we used –(BC) = CB in the formula (just negate the numerator) we would have gotten the correct angle on first try.

The 3rd angle should be what’s left after subtracting from 180°;

180-61.73-59.14 = 59.13 °

You can confirm using the formula again :

AC, BC : θ =arc cos (AC.BC)/(|AC||BC|) = arc cos( (0.-3+4.1+ 2.3)/(√19 x 2√5)= 10/(2√95) = 59.13°

Rounding everything up so they add up to 180 degrees we have Angle at vertex A : 59.2° B: 61.7° C : 59.1°

7 0

3 years ago

Glenda and Fiero are at a restaurant eating meal that costs $30. They have a discount coupon that gets them 10% off the cost. If

yaroslaw [1]

The cost of meal = $$30$

The tip to the waiter = $8%$ %

Discount = $10%$ %

Cost = $30 + 0.08 * 30 - 0.1 * 30$

Cost = $30(1 + 0.08 - 0.1)$

Cost = $ $$29.4$ 0

8 0

2 years ago

Two payment options to rent a car: You can pay $20 a day plus 25¢ a mile (Option A) or pay $10 a day plus 50¢ a mile (Option B).

BaLLatris [955]

You must drive more than 40 miles to make option A the cheaper plan

Solution:

Two payment options to rent a car

Let "x" be the number of miles driven in one day

You can pay $20 a day plus 25¢ a mile (Option A)

25 cents is equal to 0.25 dollars

OPTION A : 20 + 0.25x

You pay $10 a day plus 50¢ a mile (Option B)

50 cents equal to 0.50 dollars

Option B: 10 + 0.50x

For what amount of daily miles will option A be the cheaper plan ?

For option A to be cheaper, Option A must be less than option B

Option A < Option B

$20 + 0.25x < 10 + 0.50x$

Solve the inequality

Add -0.50x on both sides

$20 +0.25x -0.50x < 10 + 0.50x - 0.50x\\\\20 - 0.25x < 10$

Add - 20 on both sides,

$20 - 0.25x - 20 < 10 - 20\\\\-0.25x < -10$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$

$0.25x > 10$

Divide both sides by 0.25

$x > 40$

Thus you must drive more than 40 miles to make option A the cheaper plan

7 0

3 years ago

Understand Subtraction with Integers - Instruction - Level G