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3 years ago

What is the principal square root of -4

Mathematics

1 answer:

devlian [24]3 years ago

6 0

Answer:

The principal square root of -4 is 2i.

Step-by-step explanation:

$\sqrt{-4}$ = 2i

We have the following steps to get the answer:

Applying radical rule $\sqrt{-a} =\sqrt{-1} \sqrt{a}$

We get $\sqrt{-4} =\sqrt{-1} \sqrt{4}$

As per imaginary rule we know that $\sqrt{-1}=i$

= $\sqrt{4} i$

Now $\sqrt{4} =2$

Hence, the answer is 2i.

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A pair of shoes was discounted 20% after the discount, the cost of the shoes is $100 what was the initial price

Lerok [7]

It is $80 dollars I think

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3 years ago

For what value of c does x^2−2x−c=4 have exactly one real solution?<br> PLEASE HELP!!!!!!!

Paul [167]

Answer:

-5

Step-by-step explanation:

Moving all terms of the quadratic to one side, we have

$x^2-2x-(c+4)=0$ .

A quadratic has one real solution when the discriminant is equal to 0. In a quadratic $ax^2+bx+d$ , the discriminant is $\sqrt{b^2-4ad}$ .

(The discriminant is more commonly known as $\sqrt{b^2-4ac}$ , but I changed the variable since we already have a $c$ in the quadratic given.)

In the quadratic above, we have $a=1$ , $b=-2$ , and $d=-(c+4)$ . Plugging this into the formula for the discriminant, we have

$\sqrt{(-2)^2-4(1)(-(c+4))$ .

Using the distributive property to expand and simplifying, the expression becomes

$\sqrt{4-4(-c-4)}=\sqrt{4+4c+16}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{20+4c}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{4}\cdot\sqrt{5+c}\\~~~~~~~~~~~~~~~~~~~~~~=2\sqrt{c+5}.$

Setting the discriminant equal to 0 gives

$2\sqrt{c+5}=0$ .

We can then solve the equation as usual: first, divide by 2 on both sides:

$\sqrt{c+5}=0$ .

Squaring both sides gives

$c+5=0$ ,

and subtracting 5 from both sides, we have

$\boxed{c=-5}.$

3 0

2 years ago

There are 65 children in the sixth grade. The ratio of boys to girls 3 to 2. A) how many girls are in the grade?

Akimi4 [234]

Given that,

Total number of children = 65

The ratio of boys to girls is 3 :2.

To find,

The number of girls in the grade.

Solution,

Let there are 3x girls and 2x boys.

ATQ,

3x + 2x = 65

5x = 65

x = 13

So, no of girls = 3x

= 3(13)

= 39

Hence, there are 39 girls in the grade.

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2 years ago

A box contains 4 oranges, 9 apples, and 3 pears. Liliana selects a piece of fruit from the box at random. What is the probabilit

valina [46]

Hello!

You first find out how many objects there are in total

4 + 9 + 3 = 16

Then you find the probability of Liliana picking a orange

Since there are 4 oranges and 16 things to pick she has a 4/16 chance of getting an orange

Next you find the probability of Liliana picking a pear

There are 3 pears and 16 items to pick so she has a 3/16 chance

Then you add them together to find the chance of either happening

4/16 + 3/16 = 7/16

So she has a 7 out of 16 chance of getting an orange or a pear

The answer is 7/16

Hope this helps!

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2 years ago

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a_sh-v [17]

Answer:

Step-by-step explanation:

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