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Sliva [168]
3 years ago
9

I need help on this problem

Mathematics
1 answer:
zhannawk [14.2K]3 years ago
3 0
We know the length and width. We're just  trying to find all of the area in between. To find area, we do length*width. Length is 11.5 and the width is 10.75. 11.5*10.75=123.625 ft^2
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there are 270 at Colfax Middle School, where the ratio of boys to girls is 5:4. there are 180 students at Winthrop Middle School
ruslelena [56]

Colfax:

Add the ratio numbers together:

5 + 4 = 9

Divide total students by that:

270 / 9 = 30

Multiply each ratio by 30:

Boys = 30 *5 = 150

Girls = 30 * 4 = 120


Do the same for Winthrop:

4 +5 = 9

180 /9 = 20

Boys = 20 * 4 = 80

Girls = 20 * 5 = 100


Total students = 270 + 180 = 450

Total Girls = 120 + 100 = 220


Fraction that are girls = 220 / 450 which reduces to 22/45

4 0
3 years ago
HEEELLLLPPP!!!! PLZZZZ!!!! THANK U!!!<br> (5 screenshots included)
IRISSAK [1]
1.=(2/3,0) 2.=(-3,0) 3.=-10 4.=need a graphing calc 5.=need a graphing calc
6 0
2 years ago
For 0 ≤ ϴ &lt; 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va
Black_prince [1.1K]

Answer:

3 solutions:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is tan(\frac{\theta}{2}) so let's focus on that part of the equation first.

We know that:

tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}

therefore:

cos(\frac{\theta}{2})\neq0

so we need to find the angles that will make the cos function equal to zero. So we get:

cos(\frac{\theta}{2})=0

\frac{\theta}{2}=cos^{-1}(0)

\frac{\theta}{2}=\frac{\pi}{2}+\pi n

or

\theta=\pi+2\pi n

we can now start plugging values in for n:

\theta=\pi+2\pi (0)=\pi

if we plugged any value greater than 0, we would end up with an angle that is greater than 2\pi so,  that's the only angle we cannot include in our answer set, so:

\theta\neq \pi

having said this, we can now start solving the equation:

tan(\frac{\theta}{2})=sin(\theta)

we can start solving this equation by using the half angle formula, such a formula tells us the following:

tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}

so we can substitute it into our equation:

\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)

we can now multiply both sides of the equation by sin(\theta)

so we get:

1-cos(\theta)=sin^{2}(\theta)

we can use the pythagorean identity to rewrite sin^{2}(\theta) in terms of cos:

sin^{2}(\theta)=1-cos^{2}(\theta)

so we get:

1-cos(\theta)=1-cos^{2}(\theta)

we can subtract a 1 from both sides of the equation so we end up with:

-cos(\theta)=-cos^{2}(\theta)

and we can now add cos^{2}(\theta)

to both sides of the equation so we get:

cos^{2}(\theta)-cos(\theta)=0

and we can solve this equation by factoring. We can factor cos(\theta) to get:

cos(\theta)(cos(\theta)-1)=0

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

cos(\theta)=0

\theta=cos^{-1}(0)

\theta={\frac{\pi}{2}, \frac{3\pi}{2}}

Equation 2:

cos(\theta)-1=0

we add a 1 to both sides of the equation so we get:

cos(\theta)=1

\theta=cos^{-1}(1)

\theta=0

so we end up with three answers to this equation:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

7 0
2 years ago
What is the first operation used to evaluate 5+7•6-2÷4
Kisachek [45]

Multiply 7x6 since when using pemdas, multiplication and division can be inverted, i.e. if multiplication is before division then you multiply and vice versa.


Hope this helps!

3 0
3 years ago
HELPPP
Bingel [31]

I'm not sure if it only wants you to find Equation 1 or go further and solve:

x = the number of 5c coins

y = the number of 10c coins

Equation 1: the total number of coins is 65

x + y = 65

total value of $3.80

0.05x + 0.1y = 3.8

<u>Simultaneous Equations</u>

Make one coefficient the same

10 * (0.05x + 0.1y = 3.80 = 0.5x + y = 38

x + y = 65

0.5x + y = 38

Subtract the equations

(x + y) - (0.5x + y)= 65 - 38

(x - 0.5x) + (y - y) = 65 - 38

0.5x = 27

x = 54

Substitute it into the original equation to find y.

x + y = 65

54 + y = 56

y = 65 - 54 = 11

Substitute it into the other equation to check it's right.

0.05x + 0.1y = 3.8

0.05(54) + 0.1(65) = 3.8

x = 54 5c coins

y = 11 10c coins

8 0
3 years ago
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