I need help to find w =

Answer:

Step-by-step explanation:

Answer:

25%.

Step-by-step explanation:

First, let's find the area of both circles. The area of a circle is given by:

[tex]\displaystyle A = \pi r^2[/tex]

The radius of the smaller circle is one. Thus, its area is:

[tex]\displaystyle A = \pi (1)^2 = \pi[/tex]

The radius of the larger circle is two. Thus, its area is:

[tex]\displaystyle A = pi (2)^2 = 4\pi[/tex]

The probability that a random point chosen will be inside the small circle will be the area of the small circle over the total area. Hence:

[tex]\displaystyle P= \frac{\pi }{4\pi}=\frac{1}{4}= 25\%[/tex]

The probability of a random point being in the small circle is 25%.

Step-by-step explanation:

sec²x + cosec²x = sec²x.cosec²x

1/cos²x + 1/sin²x = 1/cos²x.1/sin²x

or, (sin²x+cos²x)/sin²x.cos²x = 1/(sin²x.cos²x)

or, 1/(sin²x.cos²x) = 1/(sin²x.cos²x)

Hence,

sec²x + cosec²x = sec²x.cosec²x proved!!

Answer:

[tex]\int\limits {{(sin \ x})^{-1} } \, dx = \text{ln}\left |{tan\, \left (\dfrac{x}{2} \right)} \right |[/tex]

Step-by-step explanation:

[tex]\int\limits {(sin \ x)^{-1}} \, dx = \int\limits {\dfrac{1}{sin \ x} } \, dx[/tex]

We have the following relationships;

[tex]\dfrac{1}{sin \ x } = csc \, x[/tex]

We can write;

[tex]csc \, x = csc \, x \times \dfrac{csc \, x + cot \, x}{csc \, x + cot \, x} = \dfrac{csc^2 \, x + csc \, x \cdot cot \, x}{csc \, x + cot \, x}[/tex]

We note that the numerator of [tex]\dfrac{csc^2 \, x + csc \, x \cdot cot \, x}{csc \, x + cot \, x}[/tex] , which is [tex]{csc^2 \, x + csc \, x \cdot cot \, x}[/tex] is the derivative of the denominator, [tex]{csc \, x + cot \, x}[/tex], therefore, we can use integration by substitution method and write;

[tex]{csc \, x + cot \, x} = u[/tex], from which we get;

[tex]({csc^2 \, x + csc \, x \cdot cot \, x}) \cdot dx = (-1)du[/tex]

Therefore, we can write;

[tex]\int\limits {\dfrac{1}{sin \ x} } \, dx = \int\limits {\dfrac{{csc^2 \, x + csc \, x \cdot cot \, x}}{{csc \, x + cot \, x}} } \, dx \Rightarrow -\int\limits {\dfrac{1}{u} } \, du = -ln \left |u \right |[/tex]

[tex]\text{-ln} \left |u \right | = \text{-ln}\left |{csc \, x + cot \, x} \right |[/tex]

Therefore;

[tex]\int\limits {\dfrac{1}{sin \ x} } \, dx = \text{-ln}\left |{csc \, x + cot \, x} \right |[/tex]

csc x + cot x = (1/sin x) + ((cos x)/(sin x)) = (1 + cos x)/(sin x)

(1 + cos x)/(sin x) = (cos²(x/2) + sin²(x/2) + cos²(x/2) - sin²(x/2))/(2sin(x/2)·cos(x/2)) = (2·cos²(x/2))/((2sin(x/2)·cos(x/2)) =  cos(x/2)/sin(x/2) = cot(x/2)

Therefore;

[tex]\text{-ln}\left |{csc \, x + cot \, x} \right | = \text{-ln}\left |{cot \, \left (\dfrac{x}{2} \right) } \right | = \text{ln}\left |{cot \, \left (\dfrac{x}{2} \right)} \right | ^{-1} = \text{ln}\left |{tan\, \left (\dfrac{x}{2} \right)} \right |[/tex]

Therefore;

[tex]\int\limits {{(sin \ x})^{-1} } \, dx = \int\limits {\dfrac{1}{sin \ x} } \, dx = \text{ln}\left |{tan\, \left (\dfrac{x}{2} \right)} \right |[/tex]

Answer:

Cost of Turkey per pound is $ 1.25 and Ham is $ 1.65.  

Step-by-step explanation:

Cindy:

cost of 12.3 pound Turkey and 11.7 pound Ham = $ 34.68

Samantha:

cost of 10.7 pound Turkey and 9.5 pound Ham = $ 29.05

Let the cost of one pound of Turkey is T and one pound of Ham is H.

So,

12.3 T + 11.7 H = 34.68 ..... (1)

10.7 T + 9.5 H = 29.05 ......(2)

Solve both these equations, we get

T = $ 1.25 and H =  $ 1.65

Answer:

6x+8+4x+2=180

so!! 10x+10=180

10x=170

x=17

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

The two angles labelled [tex]6x+8[/tex] and [tex]4x+2[/tex] are co-interior angles. When two parallel lines are cut by a traversal, co-interior angles are supplementary, meaning they add up to 180 degrees. Therefore, if line L is parallel to line M, [tex]6x+8[/tex] and [tex]4x+2[/tex] must be supplementary:

[tex]6x+8+4x+2=180[/tex]

Combine like terms:

[tex]10x+10=180[/tex]

Subtract 10 from both sides:

[tex]10x=170[/tex]

Divide both sides by 10:

[tex]x=\frac{170}{10}=\boxed{17}[/tex]

Answer:

The first one.

Step-by-step explanation:

Graph lines as if the inequalities were equal signs.

X = -3 is a vertical line at x = -3, because it's less than we shade to the left. All numbers less than -3 are to the left. The line is dashed because there is no equal to. Only less than. The line is not included in the solution set.

y = -x - 1 is a line with a y-intercept of -1 and a slope of -1. All values that are less that y are below the line. Because it's less than or equal to the line is solid.

Answer:

A

Step-by-step explanation:

The vertical line  is dotted at -3 and shaded to the left

x < -3

This gives us two choices left

A and C

The other line has a y intercept at -1 and is solid and shaded to the left

It is of the form

y ≤ mx+1  

We know the slope is negative since is goes down from left to right

The only Choice is A

Answer:

Step-by-step explanation:

Answer:

√74

Step-by-step explanation:

Answer:

For the First Question:

x = 61

y = 61

For the Second Question:

x = 12

y  = 7

Step-by-step explanation:

Second question:

96 = 11y + 19

11y = 77

y = 7

96 = 8x

x = 12

Answer:

(-3,-6) and (-3,2)

Step-by-step explanation:

A line with an undefined slope is vertical. In this case it must have x coordinates equal to -3

Answer:

(36+22+19)=77

then add red and yellow

=(36+22)

=58

then the probability will be

58/77

HOPE IT HELP YOU.......

Answer:

= -2i + 3

Step-by-step explanation:

3+i/2-i * 4+i/2+i

Group like terms

= i/2 + i/2 - 4i + i + 3

Combine the fractions i/2 + i/2: i

= i - 4i + i + 3

Add similar elements: i - 4i + i = -2i

= -2i + 3

Answer:

(12xy-6x -12y)

12xy-18xy

6xy

Answer:

- xy - x + 2y

Step-by-step explanation:

5x - 13xy + 14y + 12xy - 6x - 12y ← collect like terms

= (- 13xy + 12xy) + (5x - 6x) + (14y - 12y)

= - xy - x + 2y

Answer:

126,000

Step-by-step explanation:

150,000 * .15 = 22,500

150,000 - 22,500= 127,000

127,000 - 1500 = 126,000

Answer:

18/4

After simplification

9/2

Step-by-step explanation:

3/4 ÷ 1/6

Copy dot flip

3/4 * 6/1

18/4

If we simplify

Divide the top and bottom by 2

9/2

Answer:

Solution given

Cos[tex]\displaystyle \theta_{1}=\frac{3}{5}[/tex]

consider Pythagorean theorem

[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]

Subtracting [tex]Cos²\theta[/tex]both side

[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]

doing square root on both side we get

[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]

Similarly

[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]

Substituting value of [tex]Cos\theta_{1}[/tex]

we get

[tex]Sin\theta_{1}=\sqrt{1-(\frac{3}{5})²}[/tex]

[tex]Sin\theta_{1}=\sqrt{1-(\frac{9}{25})}[/tex]

[tex]Sin\theta_{1}=\sqrt{\frac{16}{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{2*2*2*2}}{\sqrt{5*5}}[/tex]

[tex]Sin\theta_{1}=\frac{4}{5}[/tex]

Since

In IVquadrant sin angle is negative

[tex]\bold{Sin\theta_{1}=-\frac{4}{5}}[/tex]

Answer:

[tex]\sin(\theta_1)=-\frac{4}{5}[/tex]

Step-by-step explanation:

We'll use the Pythagorean Identity [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex] to solve this problem.

Subtract [tex]\cos^2(\theta)[/tex] from both sides to isolate [tex]\sin^2(\theta)[/tex]:

[tex]\sin^2(\theta)=1-\cos^2(\theta)[/tex]

Substitute [tex]\cos(\theta)=\frac{3}{5}[/tex] as given in the problem:

[tex]\sin^2(\theta_1)=1-(\frac{3}{5}^2)[/tex]

Simplify:

[tex]\sin^2\theta_1=1-\frac{9}{25}[/tex]

Combine like terms:

[tex]\sin^2\theta_1=\frac{16}{25}[/tex]

For [tex]a^2=b[/tex], we have two solutions [tex]a=\pm \sqrt{b}[/tex]:

[tex]\sin\theta_1=\pm \sqrt{\frac{16}{25}},\\\begin{cases}\sin \theta_1=\frac{4}{5},\\\sin \theta_1=\boxed{-\frac{4}{5}}\end{cases}[/tex]

Since the sine of all angles in quadrant four return a negative output, [tex]\frac{4}{5}[/tex] is extraneous and our answer is [tex]\boxed{\sin(\theta_1)=-\frac{4}{5}}[/tex]

Answer:

16

having a hunch ig

Answer:

[tex](x+6) (x^2-6x+36)[/tex]

Step-by-step explanation:

Use the identity  [tex]a^3+b^3[/tex] × [tex](a^2-ab+b^2)[/tex]  and the fact that [tex]216=6^3[/tex]

we have that,

[tex]x^3+6^3=(x+6)(x^2-6x+36)[/tex]

Answer:

[tex]  B.  (x + 6)(x^2 - 6x + 36) [/tex]

Step-by-step explanation:

x^3 + 216

x^3 is the cube of x.

216 is the cube of 6.

This is the same as x^3 + 6^3 and follows the pattern

[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex]

[tex] x^3 + 216 = (x + 6)(x^2 - 6x + 36) [/tex]

Not enough information to solve..... Please make your question more clear

Answer:

y = + 1/2x -3

Step-by-step explanation:

x - 2y = 6

slope intercept form: y = mx + b

In order to put the given equation in slope intercept form we will need to isolate ( we can do this by solving algebraically ) y as seen in the equation shown above.

x - 2y = 6

Solve for y

Subtract x from both sides

x - x - 2y = 6 - x

-2y = 6 - x

Divide both sides by -2

-2y/-2 = (6 - x)/-2

y = -3 + 1/2x

* Swap -3 and 1/2x *

The equation in slope intercept form would be y = 1/2x - 3

Answer:

y = + x/2 +( - 3)

Step-by-step explanation:

make y the subject of the formula by placing x on the opposite side of y, which is right in this case, then divide every by negative two, then you'll get the answer that I've written.

Answer:

Tanya will get approximately $0.07 per square foot.

This can be solved by creating a ratio between the amount she is paid and the amount of square feet she cleans.

(1500)/(107)=(1)/(x) = 0.0713

Answer:

0.0713

Step-by-step explanation:

Tanya will get approximately $0.07 per square foot.

This can be solved by creating a ratio between the amount she is paid and the amount of square feet she cleans.

(1500)/(107)=(1)/(x) = 0.0713

Answer:

4 = x

Step-by-step explanation:

f(x) =2x

Let f(x) = 8

8 =2x

Divide each side by 2

8/2 = 2x/2

4 = x

Answer:

4

Step-by-step explanation:

f(x) = 2x

When f(x) = 8, x = 8/2 = 4.

Hope this helped,

~cloud

Answer:

1

Step-by-step explanation:

The given equation of the function is y = -a·(x - h)² + 1

The positive constants of the equation = a, and h

The points the function crosses the x-axis = 2, and 4

Where the function crosses the x-axis, y = 0, and x = 2, and 4, therefore, when x = 2, we have;

y = 0 = -a·(2 - h)² + 1

When x = 4, we have;

0 = -a·(4 - h)² + 1

-a·(2 - h)² + 1 = -a·(4 - h)² + 1

-a·(2 - h)² = -a·(4 - h)²

(2 - h)² = (4 - h)²

±(2 - h) = +#±(4 - h)

When

(2 - h) is negative, and (4 - h) is positive, but the same magnitude, we have';

-(2 - h) = +(4 - h)

2·h = 4 + 2 = 6

h = 3

0 = -a·(4 - h)² + 1 = -a·(4 - 3)² + 1 = -a + 1

Therefore, a = 1

Answer:

I don't know how to solve this mathematics

Step-by-step explanation:

......................

Answer:

[tex]-\frac{5}{2} x^{3} +\frac{17}{8} x^{2} -15[/tex]

Step-by-step explanation:

First combine like terms so for numbers with x^3 you have one:

-[tex]\frac{5}{2} x^{3}[/tex]

Then x^ 2

[tex]\frac{9}{8}x^{2} +x^{2}[/tex]

(4/4x^2 is just x^2 because 4/4 is 1)

So

[tex]\frac{17}{8} x^{2}[/tex]

Then all numbers with x cancel out because

2x+3x-5x is 0.

Then you just have -15.

So put them back together to get what I wrote in the answer.

Hope that helps lmk if I calculated that wrong!

Answer:

Talking 65 minutes, $ 6.50 must be paid.  

Step-by-step explanation:

Since your cell phone plan is by the minute, and each minute of use cost $ 0.10, to create a relation that represents the amount spent, A, per minute, m, of call time, and then use the relation to find the amount spent if you talk 65 minutes, the following calculations must be performed:

0.10 x M = A

0.10 x 65 = A

6.50 = A

Answer:

Let s be the son’s current age and d be the daughter’s current age. The system of equations is:

s - 10 = 2(d - 10)

s = 3 + d

Since s is already set to an equation, we can use the substitution method for s in the other equation:

s = 3 + d

s - 10 = 2(d - 10)

3 + d - 10 = 2(d - 10)

Simplify and solve for d:

3 + d - 10 = 2(d - 10)

-7 + d = 2d - 20

-7 = d - 20

13 = d

The daughter is 13 years old. To solve for the son’s age, we will plug in the solution for d into one of the equations. The second one is simpler so we will use that:

s = 3 + d

s = 3 + 13

s = 16

The son is 16 years old. Let us use the other equation to check our solutions:

s - 10 = 2(d - 10)

16 - 10 = 2(13 - 10)

6 = 2(3)

6 = 6

It checks out. The son is 16 years old, and the daughter is 13 years old.

The present age of the daughter and son are 14 and 10 years respectively.

Let the age of the daughter be x

Let the age of the son be y

If the daughter's age is 4 years more than the son's age now, then,

x = y + 4 ............. 1

If Eight years ago, the daughters' age was thrice the son's age, then;

Daughter = x - 8

Son  = y - 8

Hence, x - 8 =3(y - 8).................. 2

Substitute equation 1 into 2 to have:

x - 8 =3(y - 8).

y + 4 - 8 = 3(y - 8)

y - 4 = 3y - 24

y - 3y = -20

-2y = -20

y = 10

Recall that x = y + 4

x = 10 + 4

x = 14

Hence the present age of the daughter and son are 14 and 10 years respectively.

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