Use the discriminant to determine how many real number solutions exist for the quadratic equation −4x2 + 3x

The hypotenuse of a right triangle is √18 units. what are the lengths of the legs of the triangle? How many different answers ca

storchak [24]

Since a right triangle has special rules to it such that the hypotenuse squared equals the sum of the squares of the other 2 sides. In other words, if the hypotenuse = c, and the 2 smaller sides are a and b, then:
${c}^{2} = {a}^{2} + {b}^{2}$
Solving for c (hypotenuse), we get:
$\sqrt{({c}^{2})} = \sqrt{({a}^{2}+{b}^{2} )} \\ c = \sqrt{({a}^{2}+{b}^{2} )}$
Therefore c is the root of the square of the other sides. So by having root18, it's like saying:
$\sqrt{18} = \sqrt{({a}^{2} + {b}^{2} )} \\ 18 = {a}^{2} + {b}^{2}$
Getting rid of the square root, so sides a and b must have their squares total 18:
the only squares < 18 are: 16 (4×4), 9 (3×3), 4 (2×2), and 1 (1×1)
of those above added in any order of two of them, only 16+4
$18 = 17 + 1 - - > \sqrt{17} \: and \: 1 \\ 18 = 16 + 2 - - > \sqrt{16} \: and \: \sqrt{2} \\ ... \: 4 \: and \: \sqrt{2} \\ 18 = 15 + 3 - - > \sqrt{15} \: and \: \sqrt{3}$
$18 = 14 + 4 - - > \sqrt{14} \: and \: \sqrt{4} \\ ... \sqrt{14} \: and \: 2 \\ 18 = 13 + 5 - - > \sqrt{13} \: and \: \sqrt{5} \\ 18 = 12+ 6 - - > \sqrt{12} \: and \: \sqrt{6}$
$18 = 11 + 7 - - > \sqrt{11} \: and \: \sqrt{7} \\ 18 = 10 + 8 - - > \sqrt{10} \: and \: \sqrt{8} \\ ... \sqrt{10} \: and \: 2 \sqrt{2} \\ 18 = 9 + 9 - - > \sqrt{9} = 3 \: and \: 3$
I HOPE THAT IS ALONG THE LINE THAT WAS ASKED FOR!!! :-D

7 0

2 years ago

Let w=width and 4 + w=

kozerog [31]

Answer:

Part 1 : $w^2+4w-60=0$

Part 2 :

w=6

l = 10

Step-by-step explanation:

Part 1:

Let the width of the rectangle = w

Length of the rectangle = w + 4

Area of the rectangle is given as

60 Sq Yrds

$60=w(w+4)$

$60=w^2+4w$

$w^2+4w-60=0$

Hence this expression represents the area of the rectangle. Solving which for w will give us the width of the rectangle.

Part 2:

(w+10)(w-6)= 0

either (w+10) = 0

or

(w-6)=0

or both are zero

(w+10) = 0 ⇒ w = -10

not possible as the dimension can not be 0

(w-6)=0 ⇒ w=6

Hence the width is 6 yards

And thus the length will be 6+4 = 10 yards

8 0

2 years ago

Rationalize the denominator please

GenaCL600 [577]

There is a video on khanacademy, search "rationalize the denominator." Then instead of getting the answer you will learn how to do it and be able to do it on other problems in the future.

7 0

3 years ago

Into the boxes:<br> 2x + 8 = 1x + 9<br> Solve the equation.

JulsSmile [24]

Answer:

x = 1

Step-by-step explanation:

Rearrange equation by making x's on one side and numbers on the other

2x - x = 9 - 8

x = 1

6 0

2 years ago

Read 2 more answers

how do you multiply binomials? Plz help! Will mark brainliest whoever answers first! Thank you for helping me, and have a good d

zepelin [54]

1. multiply the first term of each binomials together

2. multiply the out terms together.

3. multiply the inner terms together

4. multiply the last terms of each expression together

5. list the four results of FOIL in order

6. combine the like terms.

I hope this helps

6 0

2 years ago

Use the discriminant to determine how many real number solutions exist for the quadratic equation −4x2 + 3x –28 = 0.