a spinner with 7 equally sized slices is shown below. The dial is spun and stops on a slice at random. What are the odds in favo

Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR= 5 m and diagonal QS

svet-max [94.6K]

Answer:

Given the statement: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P.

Properties of Kite:

The diagonals are perpendicular

Two disjoint pairs of consecutive sides are congruent by definition of kite

One diagonal is the perpendicular bisector to the other diagonal.

It is given that: Side QR = 5m and diagonal QS = 6m.

Then, by properties of kite:

$QP = \frac{1}{2}QS$

Substitute the value of QS we get QP;

$QP = \frac{1}{2}(6)$ = 3 m

Now, in right angle $\triangle RPQ$

Using Pythagoras theorem:

$QR^2= RP^2 +QP^2$

Substitute the given values we get;

$(5)^2= RP^2 +(3)^2$

or

$25= RP^2 +9$

Subtract 9 from both sides we get;

$16= RP^2$

Simplify:

$RP = \sqrt{16} = 4 m$

Therefore, the length of segment RP is, 4m

5 0

2 years ago

Read 2 more answers

Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

Proved, because 7/6 is rational

<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>

8 0

3 years ago

Identify the independent and dependent variables!!

nikdorinn [45]

Age is the independent variable

8 0

3 years ago

Solve for x.<br> 5(x - 3) + 4(x + 3) = 3(x - 1)<br> What’s the answer ?

SSSSS [86.1K]

Answer:

x=0

Step-by-step explanation:

Solve for x.

5(x - 3) + 4(x + 3) = 3(x - 1)

Distribute

5x -15 +4x +12 = 3x-3

Combine like terms

9x -3 = 3x-3

Add 3 on each side

9x -3+3 = 3x-3

9x = 3x

Subtract 3x from each side

9x-3x = 3x-3x

6x =0

Divide by 6

6x/6 = 0/6

x=0

3 0

3 years ago

Read 2 more answers

Complete the equation...

Nimfa-mama [501]

Answer:

x^2 -14x +49

( x-7)^2

Step-by-step explanation:

x^2 -14x

We are completing the square

Take the coefficient of x

-14

Divide by 2

-14/2 = -7

Square it

(-7)^2 = 49

Add it

x^2 -14x +49

Take the -7

( x-7)^2

8 0

3 years ago

Read 2 more answers