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2 years ago

Harley ate 3 Oreos each day of the week. If Ceire eats 2 Oreos each day of the week,

Mathematics

1 answer:

aliina [53]2 years ago

8 0

Answer:

Step-by-step explanation:

You take 3 times 7 and that's 21. Then 2 times 7 and that's 14. So, 21+14=35

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Students in a math class recorded the number of text messages they received the previous day. how many students received at leas

kirill [66]

Answer:

14 students

Step-by-step explanation:

You didn't include a graph, so I looked up the question to find the graph you are likely talking about.

If this graph does not match, ignore my answer (although the question is exactly the same so I'm guessing it might be the same)

{even if different , conceptually, here is what you do: }

Receiving at least 10 messages includes those who receive 10 messages.

Each X represents 1 student. So, 3 students received exactly 10 messages.

3 (who received 10)

2 (who received 15)

4 (who received 20)

5 (who received 25)

+________

14 students

14 students received ≥ 10 messages

(≥ means greater than or equal to,

< is less than (less < more)

> is greater than (more > less)

the line under includes the value _ (same or more ≥ than this value ; same or less ≤ than this value)

hope this helps you !!

6 0

2 years ago

Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.

Naya [18.7K]

Answer: $\boldsymbol{-25+18\sqrt{2}}$

The expression is in the form $a+b\sqrt{2}$ where a = -25 and b = 18

==========================================================

Work Shown:

Let $x = 3\sqrt{2}$ and then square both sides

$x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\$

We'll use both x and x^2 later on.

---------------------

The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

$\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\$

$\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}$

Therefore,

$\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}$

-------------------------------------

Checking the answer:

Use a calculator to find that,

$\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571$

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

3 0

2 years ago

Find the area enclosed by the graphs of y = sin x, y = cos x, x = 0, and x = 2. Sketch a graph.

mars1129 [50]

Answer:

1.34 (3 sf)

Step-by-step explanation:

To find the area between 2 curves:

$\int\limits^a_b {(top-bottom)} \, dx$

As these 2 curves intersect, we have to first calculate where they intersect, then work out the area between the curves BEFORE and AFTER the point of intersection, as the "top" and "bottom" curves change after the point of intersection (see attached graph).

sin(x) = cos(x)

⇒ tan(x) = 1

⇒ x = $\frac{1}{4} \pi$