Complete the round to the nearest as needed

The number of seats in a row has been increased at a rectangular-shape movie theater after renovation so that it is now five mor

Damm [24]

Let the number of rows be = r

Let the number of seats per row be = s

we know that the number of seats is 126.

So, $s\times r=126$ ..... (1)

As given, there are five more seats per row than the number of rows, so we can say that:

$s=r+5$

Putting this in equation (1)

$(r+5)*r=126$

$r^{2}+5r=126$

$r^{2}+5r-126=0$

$r^{2}+14r-9r-126=0$

$(r+14)(r-9)=0$

r=-14 and r=9 (neglecting the negative value) we get r=9

And s=r+5

so, s =9+5=14

Hence, there are 5 rows and 14 seats per row.

4 0

4 years ago

What is the exact value of sin 45° ?<br><br>enter your answer, as a simplified fraction.

Ne4ueva [31]

Look at the picture.

Use the Pythagorean theorem:

$b^2=a^2+a^2\\\\b^2=2a^2\to b=\sqrt{2a^2}\\\\b=\sqrt{a^2}\cdot\sqrt2\\\\b=a\sqrt2$

$\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\theta=45^o,\ opposite=a,\ hypotenuse=a\sqrt2$

substitute

$\sin45^o=\dfrac{a}{a\sqrt2}=\dfrac{1}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}=\dfrac{\sqrt2}{2}$

Answer: $\sin45^o=\dfrac{\sqrt2}{2}$

7 0

3 years ago

Mark thinks the equation y= 4+6x will match the red solid graph. Mia thinks it will match the blue dotted graph.

Blizzard [7]

Answer:

Step-by-step explanation:

l

6 0

3 years ago

Read 2 more answers

What's is the answer to 15n-19n

Art [367]

Answer:

-4n

Step-by-step explanation:

8 0

3 years ago

Indicate the equation of the given line in standard form. Show all your work for full credit. the line containing the median of

alukav5142 [94]

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

- The standard form of the linear equation is Ax + BC = C, where

A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

parallel bases and which of them are the non-parallel bases

# The side RS

∵ $m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}$

# The side ST

∵ $m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}$

# The side TU

∵ $m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}$

# The side UR

∵ $m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}$

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

∵ The midpoint of RS = $(\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})$

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

midpoint of RS

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

7 0

4 years ago