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2 years ago

13

A hotel is designing a new lobby. The lobby shape is a rectangle with two congruent right triangles on either side, as shown bel

ow.
What is the total area, in square feet, of the lobby?

2 answers:

SashulF [63]2 years ago

6 0

Answer:620

Step-by-step explanation:

FromTheMoon [43]2 years ago

3 0

Answer:

kokomo John's Sunday on Sundays and Mondays I have to me I just ask that wat just got home so we got a mirror with it but how

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Given: cos θ=-4/5, sin x = -12/13, θ is in the third quadrant,

USPshnik [31]

By definition of tangent,

tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)

Recall the double angle identities:

sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)

cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1

where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):

sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))

and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.

<em />

We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get

sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5

Then

tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)

tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)

tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)

tan(2<em>θ</em>) = 24/7

4 0

3 years ago

Order the numbers from least to greatest: -6, 5, -5, 6, 0

Arturiano [62]

-6,-5,0,5,6 that is the order from least to greatest

3 0

3 years ago

What is 4 ( 2x + 5) - 2x

sashaice [31]

Answer:

(8x + 20)-2x

Step-by-step explanation:

We don't know what x is, so we use the Distributive Property to do 4 x 2x, then 4x5. We put parentheses around it, and then do - 2x

7 0

3 years ago

Calculate the allele frequencies in this population of palm trees. A model consisting of a box containing fourteen, randomly arr

bogdanovich [222]

Answer:

The correct answer is

0.5 F, 0.5 f

Step-by-step explanation:

We note the following

Number of colored circles in the box = 14

Number of red circles in the box = 4

Number of purple circles in the box = 6

Number of blue circles in the box = 4

The allele frequency are as follows

Where the frequency is given as

Genotype Frequency Relative frequency

FF = Red 4 4/14 (0.29≈0.3)

Ff = Purple 6 6/14 (0.43≈0.4)

ff = Blue 4 4/14(0.29≈0.3)

Within this population,

We however have 4 FF = 8 F

6 Ff = 6 F + 6 f and

4 ff = 8 f

Total allele = 8+6+6+8 = 28

Relative frequency of F = (8+6)/28 = 14/28 = 0.5

relative frequency of f = (8+6)/28 = 0.5

Therefore the allele frequencies in the palm tree population is

0.5 F, 0.5 f

When in equilibrium we have

However the FF has the product of F×F which is = F² = 0.29 so the frequency of F = √(0.29) = 0.535≈ 0.5

The frequency of Ff is Ff or fF = 0.43 since there is equal number of each allele in Ff we have fF or Ff = Ff = 0.43

Which hives 0.43/2 = F =f ≈ 0.2

To

and ff = 0.29 so that f = 0.535 ≈ 0.5

Therefore f = F = 0.5 + 0.2 = 0.7

5 0

3 years ago

Can somebody help me with this?

icang [17]

We are given polynomial: $5x^3+8x^2-7x-6$ .

We need to explain why the binomial (x + 2) IS a factor of this polynomial expression and why the binomial (x + 1) IS NOT a factor of this polynomial expression.

Let us set first factor equal to 0 and solve for x.

x+2=0

x=-2.

Plugging x=-2 in given polynomial, we get

$5(-2)^3+8(-2)^2-7(-2)-6 = 5(-8) +8(4)+14-6$

$= -40 +32+14-6$

$=0$

<em>Because x=-2 gives 0 on plugging in given polynomial, so it's factor of given polynomial expression.</em>

Now, let us check second factor x+1=0

x=-1.

Plugging x=-1 in given polynomial, we get

$5(-1)^3+8(-1)^2-7(-1)-6 = 5(-1) +8(1)+7-6$

=-5+8+7-6.

= -4.

<em>Because x=-1 doesn't gives 0 on plugging in given polynomial, so it's not a factor of given polynomial expression.</em>

7 0

3 years ago