4xpower of 2 + 9 when x = 2

Triangle ABC has vertices A(- 3, - 4), B(16, - 2) and C(13, - 10) . Show algebraically that ABC is a right angled triangle.

8_murik_8 [283]

Given:

The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).

To show:

That the triangle ABC is a right angled triangle.

Solution:

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).

Using the distance formula, we get

$AB=\sqrt{(16-(-3))^2+(-2-(-4))^2}$

$AB=\sqrt{(19)^2+(2)^2}$

$AB=\sqrt{361+4}$

$AB=\sqrt{365}$

Similarly,

$BC=\sqrt{\left(13-16\right)^2+\left(-10-\left(-2\right)\right)^2}$

$BC=\sqrt{73}$

And,

$AC=\sqrt{\left(13-\left(-3\right)\right)^2+\left(-10-\left(-4\right)\right)^2}$

$AC=\sqrt{292}$

Now, add the square of two smaller sides.

$BC^2+AC^2=(\sqrt{73})^2+(\sqrt{292})^2$

$BC^2+AC^2=73+292$

$BC^2+AC^2=365$

$BC^2+AC^2=(AB)^2$

Since the sum of the square of two smaller sides is equal to the square of the largest side, therefore the given triangle is a right angle triangle by using Pythagoras theorem.

Hence proved.

7 0

3 years ago

A package of 2 fancy plastic hats costs $8. What is the unit price of a hat?

snow_tiger [21]

Each hat price cost $4

7 0

3 years ago

Read 2 more answers

2. What are all the possible rational roots of the polynomial P(x) = 5* + 2003 + 2x2 +4?

Crank

Step-by-step explanation:

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 7" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">77.

Find its factors (with the plus sign and the minus sign): ±1" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">±1±1, ±7" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">±7±7.

These are the possible values for p" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">pp.

The leading coefficient (the coefficient of the term with the highest degree) is 2" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal;

7 0

2 years ago

Solve. 5m+72=−2m+52 Drag and drop the answer into the box.

olasank [31]

5m + 72 = -2m + 52
5m + 72 + 2m = -2m + 52 + 2m
7m + 72 = 52
7m + 72 - 72 = 52 - 72
7m = -20

7m/7 = -20/7
m = -20/7

5 0

3 years ago

Select the correct answer.

katen-ka-za [31]

Answer:

d

Step-by-step explanation: bc ik

7 0

3 years ago