All categories

3 years ago

Alan drove 260 miles using 12 gallons of gas. At this rate, how many gallons of gas would he need to drive 286 miles?

Mathematics

1 answer:

jekas [21]3 years ago

6 0

Answer:

Alan would need 13.2 gallons of gas to drive 286 miles.

Step-by-step explanation:

This question can be solved in a number of ways. First, you can find the unit rate, or the approximate amount of miles that Alan can drive per gallon of gas. Since we know that Alan drove 260 miles using 12 gallons of gas, we can divide the number of miles by the number of gallons to get the amount of miles per gallon: 260 ÷12 = 21.67miles per gallon. In order to find the amount of gas needed to drive 286, we take the total mileage divided by the unit rate: 286 ÷ 21.67 = 13.2 gallons. The other way to solve is using a proportion with a variable, for example: 260/12 = 286/x. Using cross-multiplication and divide, we get 260x = 3432, divide both sides of our equation by 260 to isolate the variable and solve for x = 13.2 Either method will result in the same answer.

You might be interested in

1. y-23=55 2. x-14= -8

leva [86]

Answer:

1. y = 32

2. x = 6

3. -33 = n

4. a = -15.6

Step-by-step explanation:

y-23=55

+23 +23 (23 cancels)

y = 32

x - 14 = -8

+14 +14 (-14 cancels)

x = 6

-15 = n + 18

-18 -18 (18 cancels)

-33 = n

18.3 + a = 2.7

-18.3 -18.3 (18.3 cancels)

a = -15.6

8 0

3 years ago

A bag contains 6 yellow marbles and 18 red. If a representative sample contains 2 yellow marbles, then how many red would you ex

kramer

Answer:

6 red marbles

Step-by-step explanation:

We must first find our multiplier since a sample represents a population (the whole thing).

6/2 = 3, so 3 * 2 = 6.

I will use the value of 6/2, aka 3 and use that as my divisor.

18/3 = 6.

Therefore, you would expect to have 6 red marbles.

3 0

3 years ago

Help please, also explain

olga55 [171]

Firstly, It says that the two triangles are similar .

The scale factor is 2 as 12 / 6 = 2

25 + 85 = 110

180 - 110 = 70.

70 degrees

8 0

3 years ago

Read 2 more answers

What's the next number in the series. 65536, 256, 16..?

Artemon [7]

Hi there!

Since
$65536 = {256}^{2}$
and
$256 = {16}^{2}$
, we would need to find
$\sqrt{16}$
, which is 4.

So, the answer is 4.

Hope this helps!

5 0

3 years ago

1) Determine the discriminant of the 2nd degree equation below:

Aleksandr-060686 [28]

$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}$

❒ p(x) = x^2 + 2x + 1 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}$

❒ p(x) = x^2 - x - 20 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}$

❒ p(x) = x^2 - 3x - 4 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}$

<u>━━━━━━━━━━━━━━━━━━━━</u>

5 0

3 years ago

Read 2 more answers