A square has a perimeter of 40 feet. Find the length of the
diagonal of the square.

Answer:

See below

Step-by-step explanation:

sin ( 60 + 45) = sin60 cos 45  + cos45 sin60

                      = sqrt3 / 2 * sqrt2/2   + sqrt2/2 * 1/ 2

                        sqrt6/4    + sqrt 2/ 4

                          (sqrt6 + sqrt 2) / 4

1. a. No, g(x) is not a function because f(x) is not invertible. This is because it's not a monotonic function, which we gather from the table. On the interval [-2, 3], f(x) decreases from 7 to -2, but on the following interval [3, 4], f(x) increases to 3 and becomes positive once more. At best, f(x) is locally invertible.

1. b. This is impossible to determine... We can't know g(4) without knowing for which x we have f(x) = 4, but that's not included in the table.

1. c. The slope of the tangent line to f(x) at x = -2 is f'(-2) = -4.5. Then the equation of the tangent to f(x) at x = -2 - which means it passes through the point (-2, f(-2)) = (-2, 7) - is

y - 7 = -4.5 (x - (-2))   ⇒   y = -4.5x + 16

2. Given f(x) = arctan(3x) - ln(1 + 9x²), compute the derivative:

f'(x) = 3/(1 + (3x)²) - 18x/(1 + 9x²)

f'(x) = (3 - 18x)/(1 + 9x²)

Find the critical points of f(x), where f'(x) = 0 or doesn't exist. Only the first case can happen since the denominator is never zero. So

3 - 18x = 0   ⇒   x = 1/6

is the only critical point.

Also compute the second derivative, then check its sign at the critical point:

f''(x) = (-18 - 54x + 162x²) / (1 + 9x²)²

f''(1/6) = -72/5 < 0

The negative sign indicates that x = 1/6 is the site of a local maximum of

f(1/6) = arctan(1/2) - ln(5/4) ≈ 0.241

Also check the values of f(x) at the endpoints of the interval [0, 1]:

f(0) = 0

f(1) = arctan(3) - ln(10) ≈ -1.054

So, the maximum value of f(x) on [0, 1] is f(1/6) ≈ 0.241.

Using the table of values, the probability of selecting a girl that likes Michigan is 0.11

The table is given as:

           Ohio State   Michigan    NC State   Total

Boys        56                14                20           90

Girls         50               22               38            110

Total       106              36                58          200

In the above table, 22 girls out of the total sample size of 200 like Michigan.

This means that the required probability is:

P = 22/200

Evaluate the quotient

P = 0.11

Hence, the probability of selecting a girl that likes Michigan is 0.11

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The  Indication of the position of port Q on the drawing is shown by using the example of the image attached.

To Indicate the position of port Q on the drawing (use the x tool).

12 * 5  = 60km

Note that S=  VT

Because 1cm represent 3km

1/3 =x/60

3x = 60

x= 60/3

x= 20

So therefore, 60km needs 20cm.

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Answer:

60

Step-by-step explanation:

10 x sqrt64 - 5 x 4

10 x 8 - 5 x 4

80 - 20

60

Answer:

hr

Step-by-step explanation:

Ajay wraps a gift box in the shape of a triangular pyramid. The amount

of wrapping paper he uses is 173.2 square inches.

The formula for calculating the total surface area is expressed as:

Area = 4(area of triangle)

The area of the triangle

A = 0.5(8.66)(10)

A = 43.3 square inches

The total surface area will be

TSA = 4(43.3)

TSA = 173.2 square inches

Hence the amount of wrapping paper Ajay uses is 173.2 square inches

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Step-by-step explanation:

[tex] = \frac{2}{9} \times \frac{3}{5} \\ [/tex]

[tex] = \frac{6}{45} \\ [/tex]

Change into lowest term...

[tex] = \frac{2}{15} \\ [/tex]

Answer:

Step-by-step explanation:

Because a square must be positive no matter what the sign of x is.

(-2)^2 = 4

2^2 = 4

C+

if you get a C+ in term three and four then I don't think you will pass if you get a C+ in term three but get your grade up to B+ A- or A+ i term four you will and if you get in the B range for term 3 at least and keep it up in term four you will pass you just have to study and pay attention in class i believe in you. you can do it

Answer:

The measure of its complementary angle is 3.

Step-by-step explanation:

Answer:

D. (17,-1)

Step-by-step explanation:

We'll start by canceling out x. To do so, multiple the first equation by -1

-1( x - 2y)=( 19 )(-1)

This gives us:

-x +2y = -19

x + 3y = 14

Add the equations together:

→ 5y = -15

→ y = -1

Plug in y = -1 into an equation:

→ x + 3(-1) = 14

→ x - 3 = 14

→ x = 17

(17,-1)

Hope this helps!

Answer:

Step-by-step explanation:

The domain are all the x values

(-7,-3), (-4,1), (1,-4), (6,3)

x here is from -7 to 6

domain ∈ [-7, 6]

The range are all the y values

(1,-4), (-7,-3), (-4,1), (6,3)

y here is from -4 to 3

range ∈ [-4, 3]

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b² + c² - a²)/2bc

cos B= (a² + c²- b²)/2ac

cos C = (a²+ b²- c²)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s² + s² - s²)/(2s×s)

cos A = (s² )/(2s²)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s² + s² - s²)/(2s×s)

cos B = (s²)/(2s²)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s² + s² - s²)/(2s×s)

cos C = (s² )/(2s²)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

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Answer:

D: humor.

Step-by-step explanation:

it's just common sense. I am not a gen z so I should know.

Answer:

Kite

Step-by-step explanation:

Kite. A kite has one line of symmetry

Answer:

One solution

Step-by-step explanation:

The only solution is x = 2/3

Answer:

The third box model

Step-by-step explanation:

Since she earns 162 from babysitting and got a total of $810, it would eman that (x represents the amount of money she got from mowing lawns) 810-162=x

x=648 so the third box model is correct

Answer

24*9= the answer

Step-by-step explanation:

Answer:

H - 5 hours

Step-by-step explanation:

We can setup an equation to solve the question.

Let [tex]h[/tex] be the number of hours Mary must work.

[tex]250 = 160 + 3(6h)[/tex]

250 - the amount of money Mary needs

160 - the amount of money Mary has saved already

3 - How many days she works

6h - How much she gets paid per day

[tex]250 = 160 + 3(6h)\\90 = 3(6h)\\90=18h\\5=h[/tex]

This means Mary must work 5 hours each day to pay her rent.

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

Answer:

10

Step-by-step explanation:

it is 10 I jus did it 120 =12 x x =12 10

Answer:

180

Step-by-step explanation:

bcoz it's a straight angle

Answer:

The equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x+y=-5 is 2x+y=4

Answer:

The angles are vertical, and the value of x is 128 degrees

Step-by-step explanation:

You can tell vertical angles apart from adjacent by looking at their position. Adjacent angles are side by side, right next to each other. Vertical angles are directly across from each other, with their points touching.

Since the angle measures of vertical angles are equal, the value of x is 128

i hope this helps

Answer:

y = (x + 1)(x - 2)(x -3)

Step-by-step explanation:

Looking at the graph we see our zeros which is on the x-axis is -1 , 2, 3.

Thus create an equation.

y = (x + 1)(x - 2)(x -3)

The area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The length of the rectangle = [tex]64\dfrac{5}{7}[/tex]  m = 453/7 m

The breadth of the rectangle = [tex]23\dfrac{3}{8}[/tex] m = 187/8 m

The area of the rectangle hall:

= (453/7)(187/8)  = 1512.69 ≈ 1512.7square m

Thus, the area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

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