there are 65 children in the sixth grade. there are 15 more boys than girls. what is the ratio of boys to girls

Given:

[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex].

To find:

The expression, which is equivalent to the given expression.

Solution:

We have,

[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex]

[tex]=\dfrac{\sin (x)}{1^2-\cos ^2 (x)}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex]         [tex][\because \tan \left(\dfrac{x}{2}\right)=\dfrac{1-\cos (x)}{\sin (x)}][/tex]

[tex]=\dfrac{\sin (x)}{(1-\cos (x))(1+\cos (x))}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex]         [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

Cancel out the common factors.

[tex]=\dfrac{1}{1+\cos (x)}[/tex]

Therefore, the correct option is C.

    Given question is incomplete; find the complete question in the attachment.

    Simplified form of the given trigonometric expression will be represented by Option C.

Given expression is,

[tex][\frac{\text{sin(x)}}{1-\text{cos}^2(x)}]\tan(\frac{x}{2} )=\frac{\text{sin(x)}}{1-\text{cos}^2(x)}\times \frac{1-\text{cos}x}{\text{sinx}}[/tex] [Since. [tex]\text{tan}\frac{x}{2} =\frac{1-\text{cosx}}{sinx}[/tex]]

                          [tex]=\frac{1-\text{cos}x}{(1-\text{cosx})(1+\text{cosx})}[/tex]

                          [tex]=\frac{1}{1+\text{cosx}}[/tex]

   Therefore, Option C will be the correct option.

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Answer:

0

Step-by-step explanation:

4x + 10 - 30

4 × 5 + 10 - 30

20 +10 - 30

30 - 30

0

Answer:

[tex]y-1=-3(x+2)[/tex]

Step-by-step explanation:

The equation of the given line:

[tex]y-1=\frac{1}{3}(x+2)[/tex]

This equation is in the form [tex]y-y_{1}=m(x-x_{1})[/tex].  Therefore, 1/3 is the slope.

To find a perpendicular line, take the opposite reciprocal of the slope (-1/old slope).  Therefore, the slope of the perpendicular line is -3.

The equation of the perpendicular line: [tex]y-1=-3(x+2)[/tex]

Answer:

Step-by-step explanation:

Find the variable in the expression and see what has been done to it. Here, 'a' has been multiplied by c, and b has been subtracted from the product. Undo those operations in reverse order.

Undo the subtraction of b by adding b to both sides.

  g +b = ca -b +b

  g +b = ca . . . . . note b is no longer subtracted from the product

Undo the multiplication by dividing both sides by c.

  (g +b)/c = (ca)/c

  (g +b)/c = a

  a = (g +b)/c

__

The second problem is worked exactly the same way.

  u = 2x -2

  u +2 = 2x . . . . . add 2 to both sides

  (u +2)/2 = x . . . . divide both sides by 2

  x = (u +2)/2

Answer:

f, x, 7, -2

Step-by-step explanation:

Answer:

If I had to guess... I think it would be Y

Step-by-step explanation:

The reason why I think its Y is because the line on the graph seems to go constant till it gets to the tip. As you can see the line is less slanted meaning that she is going slower. (If you know what I mean.. I tend to be bad at explaining things hehe..)

Step-by-step explanation:

*Syntax Error*

just consult with your teacher

Answer:

Please explain your question better.

Step-by-step explanation:

60 - 720 = 660

660 divided by 12 = 55

Answer:

60

Step-by-step explanation:

$720 divided by $12 is 60.

I don't think I did this right.

Nope prolly not

Answer:

the conclusion is not valid

Answer: The conclusion is valid by the law of syllogism

The law of syllogism follows the basic form:

If P, then Q

If Q, then R

Therefore, if P then R

We can write it like this

[tex]P \to Q \\\\Q \to R\\\\\therefore P \to R[/tex]

We can think of it like starting at town P, moving to Q, then to R. Or we could go from P directly to R if we aren't worried about the town in the middle (town Q).

The period of a function is the horizontal length of one complete cycle. The period may also be described as the distance from one "peak" (max) to the next "peak" (max). This sine curve, y = sin x, has a period of 2π, the horizontal length of one complete cycle.

Answer: B period

Step-by-step explanation:

EDGE 2020

Answer:

w=1

Step-by-step explanation:

6(1-4w)=-18

(6*1)-(6*4w)=-18

6-24w=-18

-24w=-24

w=1

Will u mark me brainliest plz!!!!???!!!

w=1

Step-by-step explanation:

Answer:

each x point should be mapped to a y point

Step-by-step explanation:

Answer:

A.11

Step-by-step explanation:

i think 11 hours is the minimum number of hours that a car share needs to be used per year because it might also make Company B a more stabilized deal.

Answer:

A, 11

Step-by-step explanation:

Explanation: if you ignore the annual and just multiply both hourly by 10 and add the annually after they are both equivalent to 190 and since B costs less from 11 hours and beyond B will cost less.

Answer: 7x^2 + 2x + 7

Step-by-step explanation:

Combine likes terms that have alike variables and alike exponents.

(3x^2 + 4x^2) + (2x) + (2 + 5)

7x^2 + 2x + 7

Answer:

2 4 6

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

You can rewrite the equation into slope intercept form and you get Y=10-5x/2 (The whole problem is being divided by 2).

You can leave -5/2 as it is because it's a lot easier to plot the point using Rise over Run or Rise/Run.

Hope this helps! :)

Answer: y - 3 = -1/5(x+5)

Step-by-step explanation:

Hope this helps

Answer:

When you plug in the coordinate into the equation, the equation becomes false.

Step-by-step explanation:

Step 1: Define

y = 3x + 1

(4, 1)

Step 2: Substitute and Evaluate

1 = 3(4) + 1

1 = 12 + 1

1 ≠ 13

Answer: plus x and y into the formula

Step-by-step explanation:

Answer:

I’m. Not really good at math but I think its b

Step-by-step explanation:

Answer:

h(3) = 18

Step-by-step explanation:

Step 1: Define

h(t) = -3t + 6 + 7t

h(3) is x = 3

Step 2: Simplify

h(t) = 4t + 6

Step 3: Substitute and Evaluate

h(3) = 4(3) + 6

h(3) = 12 + 6

h(3) = 18

Answer:

y = 65 degrees

Step-by-step explanation:

(this is what i remember from geometry at least so let me know if i got anything wrong)

2x+25 and 3x-10 are opposites which means they are equal to each other.

2x+25 = 3x-20 get the x values on the same side by subtracting 2 from both sides

25 = x-20 to get the x value alone add 20 to both sides

45 = x

now you can plug in x to either equation to find out what their degree is

2(45)+25 = 115 degrees

and since this equation and y are on the same line you can subtract 115 from 180 (a line is equal to 180 degrees) to find y

180-115 = 65 degrees

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle. The value of the variables x and y are 35 and 85, respectively.

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.

The angle measuring (2x+25)° and (3x-10)° are vertical angles. Therefore, we can write,

(2x + 25) = (3x - 10)

2x + 25 = 3x - 10

25 + 10 = 3x - 2x

x = 35

Also, in the given image the angle measuring (2x + 25)° and y° are supplementary angles, therefore, we can write,

(2x + 25)° + y° = 180°

2x + 25 + y = 180°

Substitute the value of x,

2(35) + 25 + y = 180

70 + 25 + y = 180

95 + y = 180

y = 85°

Hence, the value of the variables x and y are 35 and 85, respectively.

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Answer:

80 machines

Step-by-step explanation:

If a machine makes 20 gadgets every fourth (1/4) of an hour, it makes 80 machines every hour (20*4).

80 machines gadgets are made every hour.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

A factory makes 20 gadgets every 1/4 hour.

So, in an hour made = 20÷1/4 machines

                                  =20×4

                                  =80

i.e. If a machine makes 20 gadgets every fourth (1/4) of an hour,

it makes 80 machines every hour (20*4).

Hence, 80 machines gadgets are made every hour.

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Answer:

54°

Step-by-step explanation:

Since m<2 + m<1 is equal to 180, we can set up the equation to find m<1.

plug in 126 as m<2, so we get

126 + m<1 = 180

-126              -126

m<1 = 54.

From this knowledge, we know that

7.) 54°

8.) 126°

9.) 54°

10.) 126°

11.) 54°

12.) 126°

13.) 54°

14.) 126°

The average rate of change of [tex]f(x)[/tex] over 3 ≤ x ≤ 5 is

[tex]\dfrac{f(5)-f(3)}{5-3}=15[/tex]

Solve for [tex]f(5)[/tex]:

[tex]\dfrac{f(5)-10}2=15[/tex]

[tex]f(5)-10=30[/tex]

[tex]\boxed{f(5)=40}[/tex]

Looks like f(x, y) = cot⁻¹(xy), as in the inverse cotangent.

If you're like me and you don't remember the derivative of the inverse trig functions, we can derive it as follows. Let y = cot⁻¹(x), so that for appropriate x we can write cot(y) = x. By the chain rule, differentiating both sides gives

-csc²(y) y' = 1

y' = -sin²(y) = -sin²(cot⁻¹(x)) = - 1 / (x² + 1)

Next, recall that the derivative of a function f(x, y) at a point (a, b) in the direction of a vector v is given by

∇ f(a, b) • v

Compute the gradient ∇ f(x, y) :

∇ f(x, y) = - y / ((xy)² + 1) i - x / ((xy)² + 1) j

At the point P, we have

∇ f(x, y) = - 8/17 i - 8/17 j

So, the derivative of f at P along v = - 4 i + 5 j is

(- 8/17 i - 8/17 j) • (- 4 i + 5 j) = - 8/17

The new cost of the Xbox is $165.60

1.00 - 0.28 = 0.72

0.72 * 230 = 165.60