Perform the indicated operation. 22 6/11 ∙ 1 1/2

When calculating the circumference of a circle, sometimes the radius is given instead of the diameter. What is the relationship

Gwar [14]

The diameter is equal to the radius multiplied by 2.

3 0

2 years ago

Jack is packing snacks for him and his three brothers. He bought 10 1/2 ounces of pretzels. He wants to put the pretzels into ba

Llana [10]

Answer:

3.5

Step-by-step explanation:

total pretzel=10 1/2 or10.5

no. of brother = 3

now,

10.5 pretzel for each borther= 10.5/3

=3.5 ans

3 0

2 years ago

Calculate the length of sides triangle pqr and determine weather or not triangle is a right angled. P(-4,6) q(6,1) r(2,9)

Tom [10]

$\bold{\huge{\underline{ Solution }}}$

<h3>Given :-</h3>

We have given the coordinates of the triangle PQR that is P(-4,6) , Q(6,1) and R(2,9)

We have to calculate the length of the sides of given triangle and also we have to determine whether it is right angled triangle or not

<h3>Let's Begin :-</h3>

Here, we have 

Coordinates of P =( x1 = -4 , y1 = 6)
Coordinates of Q = ( x2 = 6 , y2 = 1 )
Coordinates of R = ( x3 = 2 , y3 = 9 )

By using distance formula 

$\pink{\bigstar}\boxed{\sf{Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}$

Subsitute the required values in the above formula :-

Length of side PQ

$\sf{ = }{\sf\sqrt{ (6 - (-4))^{2} + (1 - 6)^{2}}}$

$\sf{ = }{\sf\sqrt{ (6 + 4 )^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ (10)^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ 100 + 25 }}$

$\sf{ = }{\sf\sqrt{ 125 }}$

$\sf{ = 5 }{\sf\sqrt{ 5 }}$

Length of QR

$\sf{ = }{\sf\sqrt{(2 - 6)^{2} + (9 - 1)^{2}}}$

$\sf{ = }{\sf\sqrt{(- 4 )^{2} + (8)^{2}}}$

$\sf{ = }{\sf\sqrt{16 + 64 }}$

$\sf{ = }{\sf\sqrt{80 }}$

$\sf{ = 4 }{\sf\sqrt{5 }}$

Length of RP

$\sf{ = }{\sf\sqrt{ (-4 - 2 )^{2} + (6 - 9)^{2}}}$

$\sf{ = }{\sf\sqrt{ (-6 )^{2} + (-3)^{2}}}$

$\sf{ = }{\sf\sqrt{ 36 + 9 }}$

$\sf{ = }{\sf\sqrt{ 45 }}$

$\sf{ = 3}{\sf\sqrt{ 5 }}$

We have to determine whether the triangle PQR is right angled triangle

<h3>Therefore, </h3>

By using Pythagoras theorem :-

Pythagoras theorem states that the sum of squares of two sides that is sum of squares of 2 smaller sides of triangle is equal to the square of hypotenuse that is square of longest side of triangle

That is,

$\bold{ PQ^{2} + QR^{2} = PR^{2}}$

Subsitute the required values,

$\bold{ 125 + 80 = 45 }$

$\bold{ 205 = 45 }$

From above we can conclude that,

The triangle PQR is not a right angled triangle because 205 ≠ 45 .

6 0

2 years ago

Find the solution of (x+2)^2 +2=6 by using square roots method

kogti [31]

Answer:

(x + 2)² +2 = 6
(x + 2)² = 4
√(x + 2)² = √4
x + 2 = ± 2
x = -2 ± 2
x = -4, x = 0

4 0

2 years ago

The perimeter of an equilateral triangle is at most 72, what would this be as an inequality?

Reptile [31]

at most is either that number or less

so x<=72 would be the inequality

6 0

3 years ago