Ask question

Ask question

All categories

3 years ago

10

18. Madison stayed 3 nights at a hotel that charged x dollars per night. The sales tax was 12.5%. Which expression represents th

e total cost Madison paid to stay 3 nights at the hotel?
A.3x+ 12.5 . C.3x+ 1.125
B.3x(12.5) . D.3x(1.125)

1 answer:

sdas [7]3 years ago

6 0

Answer:

D. 3x(1.125)

Step-by-step explanation:

You might be interested in

If sin(y°) = cos(x°), which of the following statements is true?

Firdavs [7]

Answer:

<u>y = w and ΔABC ~ ΔCDE</u>

Step-by-step explanation:

Given sin(y°) = cos(x°)

So, ∠y + ∠x = 90° ⇒(1)

And as shown at the graph:

ΔABC is aright triangle at B

So, ∠y + ∠z = 90° ⇒(2)

From (1) and (2)

<u>∴ ∠x = ∠z </u>

ΔCDE is aright triangle at D

So, ∠x + ∠w = 90° ⇒(3)

From (1) and (3)

<u>∴ ∠y = ∠w</u>

So, for the triangles ΔABC and ΔCDE

∠A = ∠C ⇒ proved by ∠y = ∠w
∠B = ∠D ⇒ Given ∠B and ∠D are right angles.
∠C = ∠E ⇒ proved by ∠x = ∠z

So, from the previous ΔABC ~ ΔCDE by AAA postulate.

So, the answer is <u>y = w and ΔABC ~ ΔCDE</u>

4 0

3 years ago

Read 2 more answers

The question is given in the picture.

lorasvet [3.4K]

This is a really interesting question! One thing that we can notice right off the bat is that each of the circles has the same amount of area swept out of it - namely, the amount swept out by one of the interior angles of the hexagon. Let’s call that interior angle θ. We know that the amount of area swept out in the circle is proportional to the angle swept out - mathematically

θ/360 = a/A

Where “a” is the area swept out by θ, and A is the area of the whole circle, which, given a radius of r, is πr^2. Substituting this in, we have

θ/360 = a/(πr^2)

Solving for “a”:

a = π(r^2)θ/360

So, we have the formula for the area of one of those sectors; all we need to do now is find θ and multiply our result by 6, since we have 6 circles. We can preempt this but just multiplying both sides of the formula by 6:

6a = 6π(r^2)θ/360

Which simplifies to

6a = π(r^2)θ/60

Now, how do we find θ? Let’s look first at the exterior angles of a hexagon. Imagine if you were taking a walk around a hexagon. At each corner, you turn some angle and keep walking. You make 6 turns in all, and in the end, you find yourself right back at the same place you started; you turned 360 degrees in total. On a regular hexagon, you’d turn by the same angle at each corner, which means that each of the six turns is 360/6 = 60 degrees. Since each interior and exterior angle pair up to make 180 degrees (a straight line), we can simply subtract that exterior angle from 180 to find θ, obtaining an angle of 180 - 60 = 120 degrees.

Finally, we substitute θ into our earlier formula to find that

6a = π(r^2)120/60

Or

6a = 2πr^2

So, the area of all six sectors is 2πr^2, or the area of two circles with radii r.

5 0

3 years ago

Identify the augmented matrix for the system of equations.

lord [1]

Answer:

The augmented matrix for the system of equations is $\left[\begin{array}{cccc}0&2&-3&1\\7&0&5&8\\4&1&-3&6\end{array}\right]$ .

Step-by-step explanation:

This system consists in three equations with three variables ( $x$ , $y$ , $z$ ).The augmented matrix of a system of equations is formed by the coefficients and constants of the system of linear equations. In this case, we conclude that the system of equations has the following matrix:

$\left[\begin{array}{cccc}0&2&-3&1\\7&0&5&8\\4&1&-3&6\end{array}\right]$

The augmented matrix for the system of equations is $\left[\begin{array}{cccc}0&2&-3&1\\7&0&5&8\\4&1&-3&6\end{array}\right]$ .

8 0

2 years ago

Simplify by dividing negative three over eight divided by five over nine.

goblinko [34]

Answer:

$\frac{-27}{40}$

Step-by-step explanation:

First we need to write in correct form :

$\frac{-3}{8}:\frac{5}{9}$

We know how to divide fractions. If we can divide numerator by numerator, denominator by denominator, we just do it. In this example we can not do that.

So, we rewrite first fraction and multiply by reciprocal second ( numerator and denominator change place)

$\frac{-3}{8} *\frac{9}{5}$

Now, multiply numerator by numerator, denominator by denominator :

$\frac{-27}{40}$

8 0

3 years ago

Read 2 more answers

Yolanda owns 4 rabbits. She expects the number of rabbits to double every year.

jok3333 [9.3K]

R=Number of rabbits

y=Years that have passed by { y ≥ 0 }

R=f(y) --> R is a function of y.
---------------------------------------------

Note that when:

y=0, R=4 ---> Point: (0, 4)

y=1, R=8 ---> Point (1, 8)

y=2, R=16 ---> Point (2, 16)

y=3, R=32 ---> Point (3, 32)

y=4, R=64 ---> Point (4, 64)

--------------------------------------------

So the equation you want is going to form a curved graph.

That equation is:

$R={ 2 }^{ y+2 }$

<em>*You can test out this function on any decent graphing software.</em>

7 0

3 years ago

Read 2 more answers