Based on the graph, what is the constant of variation?

Leonard and Liam each own a collection of vintage cars. Leonard has 7 cars more than Liam has. Three times the number of cars Le

dimulka [17.4K]

Answer: The answer is (22, 15).

Step-by-step explanation: Given that 'x' represents the number of cars Leonard has and 'y' represents the number of cars Liam has.

Then, according to the given information, we have

$x-y=7,\\\\3x+2y=96.$

Multiplying the first equation by 2 and adding to the second equation, we have

$2x+3x=14+96\\\\\Rightarrow 5x=110\\\\\Rightarrow x=22.$

So,

$y=x-7=22-7=15.$

Therefore, Leonard has 22 cars and Liam has 15 cars.

Thus, (22, 15) is the solution to the given system.

5 0

3 years ago

Read 2 more answers

Hey guys did you know Brainly has a very nice app with some cool camera features?

love history [14]

Yes, Brainly is a very useful app. I love helping people, and it allows me to gain some help from others when needed :)

6 0

3 years ago

Simplify the following

den301095 [7]

Answer:

1) 11 $\sqrt{3}$

2) 2 $\sqrt{2}$

3) $20\sqrt{3} + 15\sqrt{2}$

4) $53 + 12\sqrt{10}$

5) -2

6) $7\sqrt{2} - 5\sqrt{3}$

Step-by-step explanation:

1) 2 $\sqrt{12}$ + 3 $\sqrt{48}$ - $\sqrt{75}$

=(2 × 2 $\sqrt{3}$ )+ (3 × 4 $\sqrt{3}$ ) - 5 $\sqrt{3}$

= 4 $\sqrt{3}$ + 12 $\sqrt{3}$ - 5 $\sqrt{3}$

= 11 $\sqrt{3}$

2) 4 $\sqrt{8}$ -2 $\sqrt{98}$ + $\sqrt{128}$

= (4 × 2 $\sqrt{2}$ ) - (2 × 7 $\sqrt{2}$ ) + 8 $\sqrt{2}$

= 8 $\sqrt{2}$ - 14 $\sqrt{2}$ +8 $\sqrt{2}$

= 2 $\sqrt{2}$

3) 5 $\sqrt{12\\}$ - 3 $\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}$

= 5× $2\sqrt{3}$ - 3× $3\sqrt{2}$ + 4× $6\sqrt{2}$ + 2× $5\sqrt{3}$

= $10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}$

= $20\sqrt{3} + 15\sqrt{2}$

4) $(2\sqrt{2} + 3\sqrt{5} )^{2}$

= $8 + 12\sqrt{10} + 45$

= $53 + 12\sqrt{10}$

5) $(1+\sqrt{3} ) (1-\sqrt{3} )$

= $1 - 3$

= -2

6) $(2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )$

= $2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}$

= 2× $3\sqrt{2}$ - 2× $2\sqrt{3}$ - $\sqrt{3} + \sqrt{2}$

= $6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}$

= $7\sqrt{2} - 5\sqrt{3}$

Hope the working out is clear and will help you. :)

5 0

3 years ago

Read 2 more answers

PLEASE HELP IS THIS RIGHT??????????AND EXPLAIN PLZZ

Anit [1.1K]

Add like terms

-4x+x=-3x
6-2=4

So the simplified term is 4-3x

6 0

3 years ago

The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A ran

Artist 52 [7]

Answer:

We conclude that the residents of Wilmington, Delaware, have higher income than the national average

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $44,500

Sample mean, $\bar{x}$ = $52,500

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s = $9,500

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 44,500\text{ dollars}\\H_A: \mu > 44,500\text{ dollars}$

We use one-tailed(right) t test to perform this hypothesis.

c) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{52500 - 44500}{\frac{9500}{\sqrt{16}} } = 3.37$

b) Rejection rule

If the calculated t-statistic is greater than the t-critical value, we fail to accept the null hypothesis and reject it.

Now,

$t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. We conclude that the residents of Wilmington, Delaware, have higher income than the national average

5 0

3 years ago