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3 years ago

Find distance formula between (-9, 1) & (-5, -2)

1 answer:

5 0

The "distance formula" is a result of the Pythagorean Theorem:

h^2=x^2+y^2, where h is the hypotenuse of a right triangle and x and y are the side lengths.

The distance formula then becomes:

d^2=((x2-x1)^2+(y2-y1)^2

In this case:

d^2=(-5--9)^2+(-2-1)^2

d^2=4^2+(-3)^2

d^2=16+9

d^2=25

d=√25

d=5 units

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Find the value of x. O is the center of the circle. Round your answer to the nearest hundredth.

katrin [286]

$x=5.38$ . Correct option C)5.38

<u>Step-by-step explanation:</u>

Here we have , Find the value of x. O is the center of the circle. Round your answer to the nearest hundredth. picture is attached . Let's find out:

In the given figure , Let's draw a line from center to the point where cord of length 8 unit is touching the circle or intersecting or , where this chord finishes . This line is radius of circle and is denoted by x , So now we have a right angle triangle with dimensions as :

$Perpendicular =3.6\\Base=\frac{8}{2}=4\\Hypotenuse=x$

By Pythagoras Theorem ,

$Hypotenuse^2=Perpendicular^2+base^2$

⇒ $x^2=(3.6)^2+(4)^2$

⇒ $x=\sqrt{(3.6)^2+(4)^2}$

⇒ $x=\sqrt{12.96+16}$

⇒ $x=\sqrt{28.96}$

⇒ $x=5.38$

Therefore , $x=5.38$ . Correct option C)5.38

6 0

3 years ago

How do you check the answer of -6 = x/3

viktelen [127]

Answer:

-6 = x / 3 -Multiply both sides by 3

-6 * 3 = x / 3 * 3

-18 = x

Now, you can check your answer:

-6 = -18 / 3

-6 = -6

Hope this helps!

8 0

3 years ago

the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

-BARSIC- [3]

Length and width of rectangle is 15 inches and 6 inches respectively

<h3><u>Solution:</u></h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

<em><u>The formula for area of rectangle is given as:</u></em>

$\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}$

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

$\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}$

On solving the above expression for x we get

$\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}$

$\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}$

Hence length and width of rectangle is 15 inches and 6 inches.

4 0

3 years ago

1-25. Given f(x) =- 2/3x +3 and g(x) = 2x2 - 5, complete parts (a) through (f).

Korolek [52]

Answer:

When f or g are equivalent to a number you are solving for x. For example b, d, e, f. In the equation g(x) =2x2-5 I assumed 2 was a typo. So, if it's incorrect, please use same steps and just adjust the solution.

Step-by-step explanation:

$f(x)=-\frac{2}{3x}+3$