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4 years ago

Simplify as far as possible without a calculator. (7+2√2)(7−2√2)

Mathematics

1 answer:

bogdanovich [222]4 years ago

5 0

Answer:

Step-by-step explanation:

Given

(7 + 2 $\sqrt{2}$ )(7 - 2 $\sqrt{2}$ ) ← expand factors using FOIL

= 7² - 2 $\sqrt{2}$ + 2 $\sqrt{2}$ - (2 $\sqrt{2}$ )² ← collect like terms

= 49 - 8

= 41

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The weights of boxes of candies produced in a factory are normally distributed with a mean weight of 16 oz and a standard deviat

JulijaS [17]

Let the required weight be X, then
z = (X - mean)/standard deviation
2 = (X - 16)/1
X - 16 = 2
X = 2 + 16
X = 18 oz.

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3 years ago

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The point (–3, –4) is reflected across the x-axis. What quadrant is the reflected point located? A. Quadrant I B. Quadrant II C.

Natali5045456 [20]

Answer:

Step-by-step explanation:

Since (-3, -4) is in Quadrant III and the reflected point will be "flipped" vertically the answer is Quadrant II.

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4 years ago

There is an unknown number •it is a four digit number •the tens are double the ones •the thousands are double the tens •the sum

oksano4ka [1.4K]

Answer:

8542

Statement

1.It is a four digit number

2.The tens are double the ones

3.The thousands are double the tens

4.The sum of the digits is nineteen

Step-by-step explanation:

It is a four digit number

lets take 4 digit number-ABCD

The tens are double the ones

$C=2D$ -----------------------------1

The thousands are double the tens

$A=2C$ -------------------------------2

According to equation 1 and 2

$A=4D$

If we take

$D=1,2$

Possible number

$4B21$ OR $8B42$

The sum of the digits is nineteen

I use hit and trial method

$4B21$ - If I take B is maximum

$4+9+2+1\neq 19$

$8B42$ - If, i try to find value of B

$8+B+4+2=19$ ---------------------3

$14+B=19\\B=19-14\\B=5$

So the unknown number is- 8542

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4 years ago

Problem1 a right square frustum is formed by cutting a right square pyramid with a plane parallel to its base. Suppose the origi

timama [110]

Answer:

Volume of the frustum is 76 unit³

Step-by-step explanation:

From the figure attached we have to calculate the volume of the frustum formed by cutting off a square pyramid from the top.

Volume of the frustum = $\frac{1}{3}\text{(area of the base with side 6 units)(height)}-\frac{1}{3}\text{(area of the base with side MN)}(Height)$

Since ΔAPO' and ΔAOQ are similar so

$\frac{AO}{AO'}= \frac{OQ}{O'P}$

$\frac{9}{6}= \frac{3}{O'P}$

O'P = $\frac{3\times6}{9}=2$ units

Therefore, side MN = 2× O'P = 4 units

Now we put these values in the formula

Volume of the frustum = $\frac{1}{3}(6\times6)(9)}-\frac{1}{3}(4\times4)(6)$

= $\frac{1}{3}(324)-(\frac{1}{3}\times96)$

= $\frac{324}{3}-\frac{96}{3}$

= $\frac{324-96}{3}=\frac{228}{3}$

= 76 unit³

8 0

3 years ago

Is there a difference between calculating a 30% discount and calculating the sale price of 30% off? If so, explain what the diff

Nesterboy [21]

Nope! they’re the same because for both you would find 30% of the original price and then subtract whatever 30% is from the original price

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3 years ago

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