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2 years ago

Given ∠A and ∠B are vertical angles with m∠A=20x+10 and m∠B=30x−10 .

Mathematics

1 answer:

snow_tiger [21]2 years ago

6 0

Answer:

x = 2

Step-by-step explanation:

Vertical angles are equal to each other. It means that,

∠A = ∠B

So,

20x+10 = 30x−10

Taking like terms together, we get :

20x-30x=-10-10

-10x=-20

x=2

So, the value of x is 2.

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Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2

Aleksandr [31]

Given that the x-axis represented the number of small tanks and the y-axis represented the number of large tanks.

Given that his small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner and there are a total of 72 oz of water conditioners available.

The line representing the various combinations of tanks he could put the water conditioner into is given by 2x + 6y = 72.

Since, the manager labeled only the intercepts.

The x-intercept is the value of x when y = 0 and is given by

2x + 6(0) = 72

x = 72 / 2 = 36

Thus, the x-intercept is (36, 0)


The y-intercept is the value of y when x = 0 and is given by

2(0) + 6y = 72

y = 72 / 6 = 12

Thus, the x-intercept is (0, 12)

Therefore, the points labeled by the manager are: (0, 12) and (36, 0)

4 0

2 years ago

Find a ⋅ b. a = 8i + 6j, b = 4i + 5j

frutty [35]

You could rewrite this as double brackets, as you are multiplying together two sets of two terms. It would then look like:
(8i + 6j)(4i + 5j)
and you can expand by multiplying together all of the terms

8i × 4i = 32i²
8i × 5j = 40ij
6j × 4i = 24ij
6j × 5j = 30j²

To get your final answer, you then just need to add together all of the like terms, and get 32i² + 30j² + 64ij

I hope this helps!

7 0

2 years ago

Read 2 more answers

A cell phone company charges a $10 flat fee plus $0.05 per minute for minutes up to 600. For minutes over 600, the company

mash [69]

Answer:

In both the cases, the given total amount is given as:

T = 10 + 0.05 m (when minutes talked m < 600)

T = 40 + 0.15 k (when minutes talked k > 600)

Step-by-step explanation:

Here, the flat fee by the phone company = $10

The charge for each minute for first 600 minutes = $0.05

The per minute cost after 600 minutes = $0.15

Let us assume the number of minutes talked = m

Case 1: when the minutes talked is less than 600 minutes.

Total Charges = Flat Fee + 0.05 x ( the minutes talked)

or, T = $10 + m ($0.05)

or T = 10 + 0.05 m (when m < 600)

Case 2: when the minutes talked is more than 600 minutes.

Let us assume the minutes talked over 600 = k minutes

Total Charges = Flat Fee + Charges for 600 minutes + 0.15 x ( the minutes talked over 600)

or, T = $10 + 600 ($0.05) + k($0.15)

or T = 10 + $30 + 0.15 k (when k > 600)

⇒ T = 40 + 0.15 k (when k > 600)

Hence, in both the cases, the given total amount is given as:

T = 10 + 0.05 m (when m < 600)

T = T = 40 + 0.15 k (when k > 600)

7 0

2 years ago

A nationwide survey of 100 boys and 50 girls in the first grade found that the daily average number of boys who are absent from

dusya [7]

Te difference of 2 standard deviation of a population n1 & n2 is given by the formula:
sigma (difference)=√(sigma1/n1 + sigma2/n2), Plug:

sigma(d)= √(49/100 + 36/50)

Sigma(d=difference) =1.1

6 0

2 years ago

Read 2 more answers

RESTAURANTS In 2012, a popular pizza franchise had 2483 restaurants. In 2017, there were 2606 franchised

lisabon 2012 [21]

y - 2483 = 24.6(x - 2)

Let x represent the number of years after 2010

Let y represents the number of restaurants in x years

2012 is 2 years after 2010

2017 is 7 years after 2010

Number of restaurants owned by RESTAURANTS in 2012 = 2483

This can be represented in coordinate form as (2, 2483)