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horsena [70]
3 years ago
8

You drive 351.6 miles using 16.4 gallons of gasoline. At this rate, how many gallons of gasoline would you need to drive 1000 mi

les? Round your answer to the tenth place (one place after the decimal).
Mathematics
1 answer:
liberstina [14]3 years ago
3 0

Answer:

46.6 gallons

Step-by-step explanation:

351.6 miles = 16.4 gallons

1000 miles = x gallons

simply cross multiply

351.6 × x = 1000× 16.4 gallons

351.6x = 16400 gallons

x = 16400÷ 351.6

x= 46.643913538

x = 46.6 gallons (rounded to the tenth place)

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At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A
alexgriva [62]

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) =  128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) =  128°(0.989)^22.3 + 72 = 172°

8 0
3 years ago
Find the value of b. Then find the angle measures of the pentagon.
melamori03 [73]

Answer:

b = 90

Step-by-step explanation:

Sum the interior angles of the pentagon and equate to 540

Starting from the top and going clockwise

b + b + 45 + 90 + 2b - 90 + \frac{3}{2} b = 540 ← simplify left side

\frac{11}{2} b + 45 = 540 ( multiply through by 2 to clear the fraction )

11b + 90 = 1080 ( subtract 90 from both sides )

11b = 990 ( divide both sides by 11 )

b = 90

Thus

b + 45 = 90 + 45 = 135

2b - 90 = 2(90) - 90 = 180 - 90 = 90

\frac{3}{2} b = \frac{3}{2} × 90 = 135

The angle measure from the top clockwise are

90°, 135°, 90°, 90°, 135°

7 0
2 years ago
Solve for &lt;1.<br> &lt;1<br> &lt;1 = [?]<br> &lt;2<br> &lt;4=123°<br> 57°
aleksandr82 [10.1K]

Answer:

Angle 1=66

Step-by-step explanation:

Step 1, solve for angle 2

<2+123=180 degrees

Angle 2=57 degrees

Step 2, solve for angle 1

Since this is an isosceles triangle, to solve for angle 1, the equation is 2(57)+x=180

Angle 1=66 degrees

4 0
3 years ago
Read 2 more answers
Given the values in the table on the left come from
schepotkina [342]

–3.2 < x < –2.4

1.6 < x < 2.4

7 0
3 years ago
Translate the following word sentence into a numerical expression: When you square five times a number, you get three more than
8090 [49]
“Square five times a number” with “a number” being x is the same as saying:

5x²

“three more than the number” is the same as saying:

3 + x

Therefore the sentence “When you square five times a number, you get three more than the number.” is the same as:

5x² = 3 + x

Hope this helps, have a great day! :)
4 0
2 years ago
Read 2 more answers
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