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3 years ago

6 • (4 + 2)2 – 32 answer.

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

4 0

This is a classic order of operations question

I always remember order of operations as PEMDAS, or

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

That is the order to do items, from left to right. Multiplication and decision take place at the same time, as do addition and subtraction

So lets look at your problem: 6 • (4 + 2)² – 32

The first thing to do is what is in the parentheses, the 4 + 2

6 • (6)² – 32

The 2nd thing is the exponent

6 • 36 – 32

Next we do the multiplication

216 - 32

And finally the subtraction, leaving us with

184

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A recipe calls for 14cup of brown sugar for every 23cup of white sugar. How many cups of brown sugar are required for every cup

photoshop1234 [79]

Note: Consider all the numeric values are in the fraction form. Like $14\to \dfrac{1}{4}$ , $23\to \dfrac{2}{3}$ etc.

Given:

A recipe calls for $\dfrac{1}{4}$ cup of brown sugar for every $\dfrac{2}{3}$ cup of white sugar.

To find:

The number of cups of brown sugar that are required for every cup of white sugar.

Solution:

We know that,

Required brown sugar for $\dfrac{2}{3}$ cup of white sugar = $\dfrac{1}{4}$ cup

Using this, we get

Required brown sugar for 1 cup of white sugar = $\dfrac{\dfrac{1}{4}}{\dfrac{2}{3}}$ cup

$=\dfrac{1}{4}\times \dfrac{3}{2}$ cup

$=\dfrac{3}{8}$ cup

So, $\dfrac{3}{8}$ cup of brown sugar is required for every cup of white sugar.

Therefore, the correct option is B.

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2 years ago

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2 years ago

15 points!!! GEOMETRY help please!!<br> Questions attached!

dolphi86 [110]

3. Look at the picture.

We have the right angle triangle. We know the sum of measures of angles in triangle is equal 180°. Therefore:

$x^o+90^o+43^o=180^o\\\\x^o+133^o=180^o\ \ \ |-133^o\\\\x^o=47^o$

$Answer:\ \boxed{47^o}$

4.
Look at the picture.

Use Pythagorean theorem:

$x^2+14^2=(10+x)^2\\\\x^2+196=10^2+2\cdot10\cdot x+x^2\ \ \ \ |-x^2\\\\196=100+20x\ \ \ |-100\\\\20x=96\ \ \ |:20\\\\x=4.8$

$Used:\ (a+b)^2=a^2+2ab+b^2$

$Answer:\ \boxed{4.8\ units}$

5.
TRUE: 1; 2; 4

6.
We find a slope of the line OP:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\O(2;\ 6)\to x_1=2;\ y_1=6\\\\P(4;\ 3)\to x_2=4;\ y_2=3\\\\m=\dfrac{3-6}{4-2}=\dfrac{-3}{2}$

We have: $OP:\ y=-\dfrac{3}{2}x+b$

Now, we must find the slope of the line perpendicular to the line OP.
We know:

$k:y=m_1x+b;\ l:y=m_2x+c\\\\k\ \perp\ l\iff m_1m_2=-1$

therefore

$-\dfrac{3}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{3}\right)\\\\m_2=\dfrac{2}{3}$

So. We have the answer! :)

$Answer:\ \boxed{y=\dfrac{2}{3}x+\dfrac{1}{3}}$