In which choice is

Find values a and b that satisfy a∙〈5,-4,0〉+b∙〈2,2,-3〉=〈11,-16,-6〉.

WARRIOR [948]

The right hand side of the equation is 〈11 , -16 , 6〉

The values of a and b are a = 3 , b = -2

Step-by-step explanation:

If n . <a , b> + m . <c , d> = < x , y>, then

na + mc = x
nb + md = y

∵ a ∙〈5 , -4 , 0〉 + b ∙ 〈2 , 2 , -3〉 = 〈11 , -16 , 6〉

- By using the rule above

∴ a(5) + b(2) = 11 ⇒ (1)

∴ a(-4) + b(2) = -16 ⇒ (2)

∴ a(0) + b(-3) = 6 ⇒ (3)

Use equation (3) to find the value of b

∵ a(0) + b(-3) = 6

∴ 0 - 3b = 6

∴ -3b = 6

- Divide both sides by -3

∴ b = -2

Substitute b in equation (1) or equation (2) to find a

∵ a(5) + b(-2) = 11

∴ 5a - 2b = 11

∵ b = 2

∴ 5a - 2(2) = 11

∴ 5a - 4 = 11

- Add 4 to both sides

∴ 5a = 15

- Divide both sides by 5

∴ a = 3

To check your answer substitute a and b in equation (2)

∵ a(-4) + b(2) = -16

∴ -4a + 2b = -16

∵ a = 3 , b = -2

∵ The left hand side is -4a + 2b = -4(3) + 2(-2) = -12 - 4 = -16

∵ The right hand side is -16

∴ L.H.S = R.H.S

∴ The values of a and b are 3 , -2

The values of a and b are a = 3 , b = -2

Learn more:

You can learn more about the equations in brainly.com/question/11306893

#LearnwithBrainly

8 0

3 years ago

Step by step on how to solve this equation 2 x + 3 = x − 4 because I fogot how to do basic math

valentina_108 [34]

Answer:

-7

Step-by-step explanation:

2x +3 =x-4

2x - x =-4 - 7

x=-7

4 0

3 years ago

Help me I’m lost .-.

Anna11 [10]

Answer:

z=100

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

180-80=100

8 0

3 years ago

Read 2 more answers

The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of

Ipatiy [6.2K]

Answer:

a) 0.4121

b) $588

Step-by-step explanation:

Mean μ = $633

Standard deviation σ = $45.

Required:

a. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?

We solve using z score formula

= z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

For x = $646

z = 646 - 633/45

z = 0.22222

Probability value from Z-Table:

P(x<646) = 0.58793

P(x>646) = 1 - P(x<646) = 0.41207

≈ 0.4121

b. How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16? (Round your answer to the nearest dollar.)

Converting 0.16 to percentage = 0.16 × 100% = 16%

The z score of 16%

= -0.994

We are to find x

Using z score formula

z = (x-μ)/σ

-0.994 = x - 633/45

Cross Multiply

-0.994 × 45 = x - 633

-44.73 = x - 633

x = -44.73 + 633

x = $588.27

Approximately to the nearest dollar, the amount should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16

is $588

7 0

3 years ago

A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with ac

lina2011 [118]

Answer:

y = 2666.67

Step-by-step explanation:

Well to solve this we can make a system of equations.

x = cost of car alone

y = cost of accesories,

$\left \{ {{x+y=24000} \atop {x=8y}} \right.$

So now we plug in 8y for x in x + y = 24000.

(8y) + y = 24000

9y = 24000

Divide both sides by 9

y = 2666.666666

or 2666.67 rounded to the nearest hundredth.

Now that we have y we can plug that in for y in x=8y.

x = 8(2.666.67)

x = 21,333.33 rounded to the nearest hundredth.

Thus,

accessories "y" cost around 2666.67.

Hope this helps :)

6 0

3 years ago

Read 2 more answers