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4 years ago

Explain why the negation of “Some students in my class use e-mail” is not “Some students in my class do not use e-mail”.

Mathematics

1 answer:

Olenka [21]4 years ago

6 0

Answer with Step-by-step explanation:

Since we have given that

Some students in my class use e-mail.

It is a type of 'E' statements.

Its negation should be No students in my class use e-mail.

Because if we use "Some students in my class do not use e-mail”.

It also implies some students in my class still use e-mail.

But negation contains only opposite of given statement.

So, Some students in my class do not use e-mail” is not true.

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A 24ft flagpole has a shadow of 9ft. A soldier standing next to the flagpole has a shadow of 2.25 feet. How tall is the soldier?

natima [27]

Answer:

6 feet

Step-by-step explanation:

Let's form a proportion;

24 x

____ = _____ ,

9 2.25

24(2.25) = 9x,

54 = 9x,

x = height of soldier = 6 feet

4 0

4 years ago

Read 2 more answers

Help!! Which of the following best represents Z1 • Z2 select all that apply

AURORKA [14]

$z_1=\sqrt{3}\left(cos\:\frac{\pi }{4}+i\:sin\:\frac{\pi }{4}\right)$

$z_2=\sqrt{6}\left(cos\:\frac{3\pi \:}{4}+i\:sin\:\frac{3\pi \:}{4}\right)$

$\cos \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}$

$\sin \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}$

$\cos \left(\frac{3\pi }{4}\right)=-\frac{\sqrt{2}}{2}$

$\sin \left(\frac{3\pi }{4}\right)=\frac{\sqrt{2}}{2}\\$

$Z_1*Z_2=\sqrt{3}\left(cos\:\frac{\pi }{4}+i\:sin\:\frac{\pi }{4}\right)\cdot \sqrt{6}\left(cos\:\frac{3\pi \:}{4}+i\:sin\:\frac{3\pi \:}{4}\right)$

$=\sqrt{3}\left(\frac{\sqrt{2}}{2}+\:i\frac{\sqrt{2}}{2}\right)\cdot \sqrt{6}\left(\frac{-\sqrt{2}}{2}+\:i\frac{\sqrt{2}}{2}\right)$

On simplifying, we get

$Z_1* Z_2 =-3\sqrt{2}$

<h2>Therefore, correct option is 1st option.</h2>

3 0

3 years ago

Factor completely x^3 + 1/8

maksim [4K]

Answer:

((2 x + 1) (4 x^2 - 2 x + 1))/8

Step-by-step explanation:

Factor the following:

x^3 + 1/8

Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:

(8 x^3)/8 + 1/8

(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:

(8 x^3 + 1)/8

8 x^3 + 1 = (2 x)^3 + 1^3:

((2 x)^3 + 1^3)/8

Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):

((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8

1^2 = 1:

((2 x + 1) ((2 x)^2 - 2 x + 1))/8

Multiply each exponent in 2 x by 2:

((2 x + 1) (2^2 x^2 - 2 x + 1))/8

2^2 = 4:

Answer: ((2 x + 1) (4 x^2 - 2 x + 1))/8

5 0

3 years ago

Read 2 more answers

Simplify:<br> (4p3 + 6p2 – 7) – (8p? – 7 – 3p)

Kipish [7]

Answer:

4p3 + 6p2 - 8p - 7

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "p2" was replaced by "p^2". 1 more similar replacement(s).

STEP

Equation at the end of step 1

(((4 • (p3)) + (2•3p2)) - 7) - 8p

STEP

Equation at the end of step

((22p3 + (2•3p2)) - 7) - 8p

STEP

Checking for a perfect cube

3.1 4p3+6p2-8p-7 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 4p3+6p2-8p-7

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -8p-7

Group 2: 4p3+6p2

Pull out from each group separately :

Group 1: (8p+7) • (-1)

Group 2: (2p+3) • (2p2)

3.3 Find roots (zeroes) of : F(p) = 4p3+6p2-8p-7

Polynomial Roots Calculator is a set of methods aimed at finding values of p for which F(p)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers p which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 4 and the Trailing Constant is -7.

The factor(s) are:

of the Leading Coefficient : 1,2 ,4

of the Trailing Constant : 1 ,7

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 3.00

-1 2 -0.50 -2.00

-1 4 -0.25 -4.69

-7 1 -7.00 -1029.00

-7 2 -3.50 -77.00

-7 4 -1.75 3.94