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2 years ago

Find the equation of the line shown. y 4 3 2 1 Х -2 -3 4

Mathematics

1 answer:

MakcuM [25]2 years ago

8 0

Answer:

y = 1/2x + 0.5

y = 1/2x + 1/2

Step-by-step explanation:

y = mx + b

b is y-intercept:

when x = 0, y = 0.5 (when the line cross the vertical (y) axis of the graph)

the point is (0, 0.5) so b = 0.5

m is slope:

slope = rise / run

rise = 1

run = 2

for every 2 x values, y increase by 1

slope (m) = 1/2

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A glass is 1/2 full. Then 65cm^3 of orange juice is poured in. The glass is now 6/7 full. What is the total volume of the glass?

ikadub [295]

Answer:

182 cm³

Step-by-step explanation:

Let x cm³ be the total volume of the glass.

1/2 x + 65 = 6/7 x

by multiplying both sides by 2, we have

x + 130 = 12/7 x

5/7 x = 130

x = 182

4 0

3 years ago

3. The profit for a company is given by the equation y = -0.0002x 2 + 140x – 250,000 where x is the number of units sold and y i

nirvana33 [79]

9514 1404 393

Answer:

350,000

Step-by-step explanation:

The vertex of the quadratic ax²+bx+c is located at x=-b/(2a). For the given profit function, the number of units (x) that will produce maximum profit is ...

x = -(140)/(2(-0.0002)) = 1,400,000/4

x = 350,000

350,000 units should be sold to maximize profit.

3 0

3 years ago

After spending $43 on groceries and $19 on a book,Mrs Groom had $16 left How much did Mrs.Groom have to begin with?

zzz [600]

Ok so you add 43 plus 19 and then you get the answer of 62 dollars answer 62$

7 0

3 years ago

Read 2 more answers

Suppose an unknown radioactive substance produces 8000 counts per minute on a Geiger counter at a certain time, and only 500 cou

mariarad [96]

Answer:

The half-life of the radioactive substance is of 3.25 days.

Step-by-step explanation:

The amount of radioactive substance is proportional to the number of counts per minute:

This means that the amount is given by the following differential equation:

$\frac{dQ}{dt} = -kQ$

In which k is the decay rate.

The solution is:

$Q(t) = Q(0)e^{-kt}$

In which Q(0) is the initial amount:

8000 counts per minute on a Geiger counter at a certain time

This means that $Q(0) = 8000$

500 counts per minute 13 days later.

This means that $Q(13) = 500$ . We use this to find k.

$Q(t) = Q(0)e^{-kt}$

$500 = 8000e^{-13k}$

$e^{-13k} = \frac{500}{8000}$

$\ln{e^{-13k}} = \ln{\frac{500}{8000}}$

$-13k = \ln{\frac{500}{8000}}$

$k = -\frac{\ln{\frac{500}{8000}}}{13}$

$k = 0.2133$

$Q(t) = Q(0)e^{-0.2133t}$

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.2133t}$

$0.5Q(0) = Q(0)e^{-0.2133t}$

$e^{-0.2133t} = 0.5$

$\ln{e^{-0.2133t}} = \ln{0.5}$

$-0.2133t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.2133}$

$t = 3.25$

The half-life of the radioactive substance is of 3.25 days.

7 0

3 years ago

Write a function rule for the area, a, of a triangle whose base, b, is 2 cm less than seven times the height, h. what is the are

sesenic [268]

B=7h-2
When h=14 b=96
a=(1/2)b*h
Therefor a=(96*14)/2
a=672cm^2

6 0

3 years ago

Find the equation of the line shown. y 4 3 2 1 Х -2 -3 4​

Find the equation of the line shown. y 4 3 2 1 Х -2 -3 4