In a class of 80 students, 45 are good in math,15 are good in both math and english,13 are good in both math and psychology,16 are good in both english &physchology ,20are good in physchology and 9 are good in all of the three .how many of them are good in mathematics

Explanation:

Use the identity [tex]\sin{\theta} = 1 - \cos^2{\theta}[/tex] so we can write our equation as

[tex]6(1 - \cos^2{\theta}) - \cos{\theta} - 5 = 0[/tex]

or

[tex]6\cos^2{\theta} + \cos{\theta} - 1 = 0[/tex]

Let [tex]x = \cos{\theta}[/tex] so our equation becomes

[tex]6x^2 + x - 1 = 0[/tex]

Using the quadratic equation, we find that its roots are

[tex]x = \dfrac{-1 \pm \sqrt{(1)^2 - 4(6)(-1)}}{2(6)} = \dfrac{1}{3},\:-\dfrac{1}{2}[/tex]

which gives us

[tex]\cos{\theta} = \dfrac{1}{3} \Rightarrow \theta = 70.53°[/tex]

[tex]\cos{\theta} = -\dfrac{1}{2} \Rightarrow \theta = 120°[/tex]

Answer:

answer is 2. thank you. have a nice day

Answer:

what happened are you OK

Answer:

-3x + 6

Step-by-step explanation:

-3(x - 2) to find the equivalent of this expression, we need to multiply inside the parenthesis with -3 (with both x and -2)

-3(x - 2 = -3x + 6 (two negative expressions multiplied results in positive)

Answer:

16 miles per hour (mph)

Step-by-step explanation:

Okay, so the beginning of the question states that Tamara rode her bicycle 8 miles in 0.5 hours.

0.5 is equivalent to 1/2 (one-half).

This means that she rode 8 miles in just half of an hour (30 minutes).

If she continues at this rate, she will have rode another 8 miles in the next 30 minutes.

And, 8 + 8 = 16.

Therefore, the average rate that she rode her bicycle is 16 miles per hour (mph).

Let me know if you have any questions.

Answer:

the rational numbers is 3

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Answer: 30, 45, 60, 75, 90

Step-by-step explanation: you will use multiples of 15 to find the answer. Detail given below:

1. if parking lot have 2 rows then 30 spaces

2. if parking lot have 3 rows then 45 spaces

3. if parking lot have 4 rows then 60 spaces

4. if parking lot have 5 rows then 75 spaces

5. if parking lot have 6 rows then 90 spaces

Answer:

Inequality

2x > 14

Solution

x > 7

Step-by-step explanation:

Twice of a number = 2x or 2 * x

Is more than 14 = > 14

Put these 2 descriptions together

2x > 14

Then divide each side by the coefficient

2x / 2 = x > 14 / 2 = x > 7

Answer:

2x > 14

Any number above 7.

Step-by-step explanation:

"Twice a number (x) is more than 14." can be written as 2x > 14.

Breakdown:

2x > 14 for Twice a number (x) is more than 14.

2x > 14 for Twice a number (x) is more than 14.

2x > 14 for Twice a number (x) is more than 14.

The solution to the inequality is any number above 7.

Answer:

Length = 14 yd

Width = 5.5 yd

Step-by-step explanation:

Let width = x and length = 2x + 3

The formula for area is length x width.

(2x + 3) ( x ) = 77

2x² + 3x - 77 = 0

-77 x 2 = -154

What two numbers multiply to -154 and add to 3?

2x² + 14x - 11x - 77 = 0

2x (x + 7) - 11 (x + 7) = 0

(2x - 11) (x + 7) = 0

x = -7 (this isn't possible so ignore it)

x = 5.5 (width)

Now insert 5.5 into the initial equation.

2 (5.5) + 3 =

11 + 3 = 14

Answer:

Length is 3

width is 25•66

Step-by-step explanation:

Hope it helps!

Thanks.

Answer:

7725

Step-by-step explanation:

h=75ft

b1=125ft

b2=81ft

A=75((125+81)/2)

Answer:

47.2

Step-by-step explanation:

Hi

to solve you must transcrive every word in math terms correctly.

so let's first give a name to our mysterious number. As you know, in math we generally call unknown by letter. " X"

so let's now play the detective.

what do we know on " X" ?

we add 3 to X so we have : X+3

then we multiply by 5. so. ( X+3) *5 .

if we do that we have twice X , so 2X

so ( X+3) * 5 = 2 X

now that we have translatted our data in math term, let's unmask. " X"

( X+3) *5 = 2X

5*X +3*5 = 2X

5X +15 = 2X

5X-2X = -15

3X = -15

X = -15/3

X = -5

So is " -5" is our guy.

let's check it out to be sure .

-5 +3 = -2

-2*5 = -10

-10 is twice -5. so -5 is the correct answer.

Ps : some operation are commonly implied. if you do not. know how I could write some line in the calculus, dont hesitate to ask in comments.

There is no mysteries in math everything is done according to rules and can be explained. So don't hesitate !

9514 1404 393

Answer:

  4 in 3492 is 100 times 4 in 704

Step-by-step explanation:

To find the value of a particular digit, set the other digits to zero.

  4 in 3492 = 400

  4 in 704 = 4

The first 4 is 100 times the value of the second 4.

Answer:

7

Step-by-step explanation:

Let's say our sum is s.

s = 10 right angles

a right angle is 90 degrees

s = 10 (90)

s= 900

Given the amount of sides in a polygon (n), the sum of the interior angles is equal to

(n-2) * 180

Therefore, the sum of the interior angles is equal to

(n-2) * 180 = 900

divide both sides by 180 to help isolate n

n-2 = 5

add 2 to both sides to isolate n

n = 7

Answer:

0.17

Step-by-step explanation:

find the area of both circles:

then find the ration of the area of the small circle to the area of the large circle: 100pi/576pi (you can cancel out the pi here to get 100/576) -> 0.1736

round to the nearest hundredth and you get 0.17

Answer:

H-12=6

H−12+12=6+12

h=18

Answer:

h=18

Step-by-step explanation:

h-12=6

is the normal eqaution, you need to determine the value of h, on the left side of the eqaution you have negative twelve we must get the h on its own by moving the 12 to the right side using of basic math rules you must know that when you have a negative and want to move it to the right hand side it must become a positive

so in formula it wil look like this

h = 6 + 12

Add up 6 with 12 that wil give you 18

so the value of h is then 18

h = 18

Answer:

4.16 m/s

Step-by-step explanation:

Speed = Distance/Time

           = 10/2.4

           = 4.16 m/s

Answer:

the number of pink would be 112 because 224 divided by 2 is 112 then the red and white are 56 cuz 112 divided by 2 is 56

Step-by-step explanation:

Answer:

32 cm²

Step-by-step explanation:

Area of rectangle

= length × breadth

= 8 cm × 4 cm

= 32 cm²

Answer:

6 angles.

Step-by-step explanation:

This shape is a hexagon, since it has 6 sides. And because it has 6 sides, it has 6 vertexes, also known as angles.

Hope this helps!

Answer:

between 15.5 and 16

Step-by-step explanation:

which std

Answer:

Step-by-step explanation:

Given data:

The 5-number summary is:

Answer:

x = 2

Step-by-step explanation:

x + 1.5 = 3.5

  -1.5      -1.5                   minus 1.5 from both sides

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

x = 2

Work Shown:

(f o g)(x) = f(g(x))

f(x) = x + 7

f( g(x) ) = g(x) + 7 ... replace every x with g(x)

f( g(x) ) = x^2-1 + 7 .... plug in g(x) = x^2-1

f( g(x) ) = x^2 + 6

(f o g)(x) = x^2 + 6

Answer:

[tex]0.3[/tex]

Step-by-step explanation:

[tex]3 \div 10 = 0.3[/tex]

Answer: 0.3

Step-by-step explanation:

Answer:

parallel: -1/2

perpendicular: 2

Step-by-step explanation:

lines that are parallel have the same slope because they never intersect

lines that perpendicular, have the opposite reciprocal slope.

y = mx + b

where m is the slope

y = -1/2x + 6

-1/2 is the slope.

the slope in the equation given: -1/2

the slope parallel to the line given : -1/2

the slope perpendicular : opposite reciprocal, so the opposite of -1/2 is 1/2 and the reciprocal of 1/2 is 2.

Answer:

x < -√3/2, x > √3/2, or -√1/2 < x < √1/2

Step-by-step explanation:

|1 - x^2| > 1/2

~Apply absolute value rule

​1 - x^2 < -1/2 or 1 - x^2 > 1/2

~Simplify

x < -√3/2, x > √3/2, or -√1/2 < x < √1/2

Best of Luck!