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3 years ago

You're making deliveries and can travel 484 miles on 22 gallons of gas. How far can

Mathematics

1 answer:

baherus [9]3 years ago

3 0

836, because 484 divided by 22 is 22, so each gallon can do 22 miles. 38 times 22 is 836.

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Sixteen is divided by the sum of a number q and 1

atroni [7]

No context. If you want us to write an expression:

16 / (q+1)

4 0

3 years ago

Given the points (5, 2) and (7, 10) find the slope of the line going through the two points . Now write the point-slope form of

drek231 [11]

Step-by-step explanation:

the slope of a line is specified as the ratio y/x. that indicates how many units y changes, when x changes a certain amount of units.

so, going e.g. from (5, 2) to (7, 10), x changes from 5 to 7 = +2 units. and y changes from 2 to 10 = +8 units.

so, the slope y/x = m = 8/2 = 4

the point-slope form is

y - y1 = m(x - x1)

m = slope

(x1, y1) = coordinates of one point on the line. let's pick the first point (5, 2).

y - 2 = 4(x - 5)

or then fully simplified (leading to the slope- intercept form) :

y - 2 = 4x - 20

y = 4x - 18

for question 2 we do the same thing for (4, -2) and (0, -5).

x changes from 4 to 0, so, -4 units.

y changes from -2 to -5, so, -3 units.

slope = y/x = m = -3/-4 = 3/4

since there is a 0 included, let's use (0, -5) as point for the point-slope form

y - -5 = 3/4(x - 0)

y + 5 = 3/4 x

so, the last option is correct.

3 0

3 years ago

A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

3 years ago

An angle measures 156° less than the measure of its supplementary angle. What is the measure of each angle?

Advocard [28]

Answer:

Angle 1: 168

Angle 2: 12

Explanation:

I did the math! basically, i did 168-156, and got 12. Then i added, 168+12, and got 180. So i know that both angles together make 180 degrees, which is the definition of supplementary angles.

7 0

4 years ago

Which could be the measures of the three angles of an acute triangle.

slavikrds [6]

D
An acute angle is less than 90 degrees

5 0

4 years ago

Read 2 more answers