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3 years ago

An auditorium has rows of seats with a seats in each row Kayla

Mathematics

1 answer:

Lelu [443]3 years ago

3 0

Step-by-step explanation:

Note: there is a typo, 'a' should be '8'

The number of seats in each row is 8 and the total number of seats is between 70 and 150.

Let x be the number of rows, then we have the inequality:

70 ≤ 8x < 156

Divide all sides by 8 to get:

70/8 ≤ x < 156/8
9 ≤ x ≤ 19 (taking closest integers)

So the number of rows is between 9 and 19 both inclusive.

All possible number of rows

9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

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Solve the equation sin2x = 3cos2x. The value of x that satisfies the equation if x lies in the second quadrant is °. The value o

faltersainse [42]

Answer:

$126\degree$

and

$126\degree$

respectively.

Step-by-step explanation:

The given trigonometric equation is

$\sin2x=3\cos2x$

We divide both sides by $\cos2x$ to get,

$\frac{\sin2x}{\cos2x}=3$

This implies that,

$\tan2x=3$

We take the inverse tangent of both sides to get,

$2x=\tan^{-1}(3)$

$\Rightarrow 2x=71.565$

$\Rightarrow x=35.7825$

$\Rightarrow x\approx 36\degree$

Since the tangent ratio has a period of $180\degree$ , another solution is

$x=180+36$

$x=216\degree$ to the nearest degree.

In the third quadrant,

$2x=180+71.565$

$\Rightarrow 2x=251.565$

$\Rightarrow x=125.7825$

$\Rightarrow x=126\degree$

The solutions are

$x=36\degree,126\degree,216\degree$

The value of x that satisfies the equation if x lies in the second quadrant is $126\degree$

The value of x that satisfies the equation if x lies in the third quadrant is $216\degree$

5 0

3 years ago

A charitable organization holds a canned food drive to benefit the local food bank. The number of cans collected by the voluntee

kirill115 [55]

Answer:

Step-by-step explanation:

Minimum: 2

Quartile Q1: 4.5

Median: 10

Quartile Q3: 15

Maximum: 19

8 0

2 years ago

−4x+7y+5=0 x−3y=−5 How many solutions does the system have?

xeze [42]

Solution:

Using Substitution Method:

-4x+7y=-5 (Equation 1)

x-3y=-5 (Equation 2)

get the value of x from Equation 2

x=3y-5 (Equation 3)

Put the value of x from Equation 3 in Equation 1

-4(3y-5)+7y=-5

-4(3y)+20+7y=-5

-12y+7y=-5-20

-5y=-25

Negative sign on both sides cancels each other

y=25/5

y=5

Putting value of y in equation 3

x=3(5)-5

x=15-5

x=10

Therefore, [x,y]=[10,5]

Using Elimination Method

-4x+7y=-5 (Equation 1)

x-3y=-5 (Equation 2)

Multiply equation 2 with -4 in order to eliminate the x term

-4(x-3y)=-5*4

-4x+12y=20 (Equation 3)

Adding Equation 1 and 3

-4x+7y=-5

-4x+12y=20

+ - = - (Change Of Sign with x and y terms)

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

0x-5y = -25

-5y=-25

y=5

Substituting y’s value is Equation 1

-4x+7(5)=-5

-4x+35=-5

-4x=-40

Cancellation of negative sign on both sides

x=40/4

x=10

[x,y]=[10,5]

3 0

3 years ago

Help me please !! i need the answer

madam [21]

Answer:

$PQ=22\\\\QR=7\\\\PR=29$

Step-by-step explanation:

To find the value of y, you can create an equation where two parts of the line are equal to the whole line:

$PQ+QR=PR$

Substitute given values:

$(8y+6)+(y+5)=(19y-9)$

Solve for y. Simplify parentheses:

$8y+6+y+5=19y-9$

Combine like terms to simplify the equation:

$8y+y+6+5=19y-9\\\\9y+11=19y-9$

Get the variable on one side of the equation and the constants on the other. Add 9 to both sides:

$9y+11+9=19y-9+9\\\\9y+20=19y$

Subtract 9y from both sides:

$9y-9y+20=19y-9y\\\\20=10y$

Isolate the variable. Divide both sides by 10:

$\frac{20}{10} =\frac{10y}{10} \\\\y=2$

The value of y is 2. Insert this value into each line segment value and solve:

$PQ=8(2)+6\\\\PQ=16+6\\\\PQ=22$

$QR=(2)+5\\\\QR=7$

$PR=19(2)-9\\\\PR=38-9\\\\PR=29$

:Done

You can check by using:

$PQ+QR=PR\\\\22+7=29$

This statement is true, so the values are correct.

7 0

3 years ago

Plz help quickly only I need the answer

Nastasia [14]

Answer:

the second one

Step-by-step explanation:

4 0

2 years ago