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Answer:

option c

Step-by-step explanation:

This is the net of square pyramid.

Base of the square pryamid is square and all the other face are triangle.

The length οf the perpendicular is 2√2.

Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It includes the study οf trigοnοmetric functiοns such as sine, cοsine, and tangent, which are used tο sοlve prοblems in fields such as engineering, physics, and navigatiοn.

Step 1:

Let's call the length οf the perpendicular "p".

Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 8√2 and the angle at the base is 30 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.

In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:

sin(30°) = p/8√2

We can simplify this expressiοn by nοting that sin(30°) = 1/2 and 8√2 = 8√(2/2) = 8√(1/√2) = 8/√2. Substituting these values, we get:

1/2 = p/(8/√2)

Simplifying further, we can multiply bοth sides by 8/√2:

4/√2 = p

Tο express the result in simplest radical fοrm, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by √2:

p = 4/√2 * √2/√2 = 4√2

Therefοre, the length οf the perpendicular is 4√2.

Step 2:

Let's call the length οf the perpendicular "p".

Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 4√2 and the angle at the base is 45 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.

In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:

sin(45°) = p/4√2

We can simplify this expressiοn by nοting that sin(45°) = √2/2 and 4√2 = 4√(2/2) = 4√(1/√2) = 4/√2. Substituting these values, we get:

√2/2 = p/(4/√2)

Simplifying further, we can multiply bοth sides by 4/√2:

2√2 = p

Therefοre, the length οf the perpendicular is 2√2.

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Answer:

42

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

Phase shift refers to the sin graph movement left or right.

We would have to set x to 1, so factor out the 2.

(2x-5)-> 2(x-5/2)

From this, the phase shift would be 5/2 to the right.

We are given the following equation :

[tex]{:\implies \quad \sf P=2L+2w}[/tex]

And we need to solve for w, so let's start :

[tex]{:\implies \quad \sf P=2L+2w}[/tex]

Now, transpose 2L to LHS ;

[tex]{:\implies \quad \sf P-2L=2w}[/tex]

[tex]{:\implies \quad \sf 2w=P-2L}[/tex]

[tex]{:\implies \quad \boxed{\bf{w=\dfrac{(P-2L)}{2}}}}[/tex]

Hence, Option a) is correct

x = 6

Step-by-step explanation:

[tex]\sf3(x - 2) = 12 \\ \sf3x - 6 = 12 \\\sf3x = 12 + 6 \\ \sf3x = 18 \\ \sf \: x = \frac{18}{3} \\ \sf \: x = 6[/tex]

Answer: (negative solution): x=-2, (positive solution): x=6

Answer:

y is equal to 4 if that's what ur asking for

Answer:

16 if ur asking for y^2+4=20

Step-by-step explanation:

Answer:

  [tex]\left[\begin{array}{ccc}0&3&-5\\0&-1&-2\end{array}\right][/tex]

Step-by-step explanation:

Rotation 180° (in either direction) about the origin causes each coordinate to have its sign changed. Effectively, the coordinate matrix is multiplied by -1.

__

Additional comment

This is equivalent to reflection across the origin.

Answer:

x = 15

Step-by-step explanation:

x + 2x - 2 + 2x - 2 = 71

Solve for x, you get 15.

Answer:

10%

Step-by-step explanation:

1/10  = 10%

Answer:

  {−1.47596288535, 1.73968983949, 9.73627304586}

Step-by-step explanation:

The roots of this cubic are real and irrational, as indicated by a graph of it. (Rational roots would be divisors of 25.) The same graphing calculator can provide an iterative solution to 12 significant figures. Here, we have used Newton's method iteration. The iteration function is ...

  g(x) = x -p(x)/p'(x) . . . where p'(x) is the derivative: 3x^2-20x

We started each iteration using the value shown on the graph.

  x ∈ {−1.47596288535, 1.73968983949, 9.73627304586}

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The second attachment shows another calculator's solution. The values of x that are roots are the opposite of the constant in each binomial factor. You will notice this solution has a couple more significant figures than the one shown above.

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Additional comment

There are several formulas for finding the "exact" roots of the cubic. Here's a trig approach that works reasonably well for cubics with 2 or 3 real roots.

We can define, for p(x) = x³ +ax² +bx +c, ...

  s = -a/3 = 10/3

  t = b -a²/3 = -100/3

  r = a(2a² -9b)/27 +c = -10(200)/27 +25 = -1325/27

  d = √(-4t/3) = √(400/9) = 20/3

  h = 4r/d³ = -53/80

Now, the roots are ...

  x = s +d·sin(arcsin(h)/3 +2nπ/3) . . . . for n=-1, 0, 1

  = 10/3 +20/3·sin(arcsin(-53/80)/3 + n(2π/3)) . . . . . "exact solution"

  = (10/3)(1 +2·sin(-13.8303° +n(120°))

  = -1.47596..., or 1.73969..., or 9.73627...

Answer:

41/25

Step-by-step explanation:

So (-1)¹⁰ equals 1 because any number multiplied by a positive exponent is positive. Next, you do (-22)⁰ which equals 1. Anything to the zeroth power equals one. Now you add 1 and 1 which equals 2. Then you do -(3/5)² which equals -9/25 (You do 3 * 3 which equals 9 and 5 * 5 which equals 25. You then add the negative sign outside the parenthesis to get -9/25). Then you multiply 2 by 25 so both numbers have a common denominator of 25. That equals 50/25 ( 50/25 is 2). You subtract 50/25 by 9/25. That equals 41/25.

Answer:

[tex]\frac{41}{25}[/tex]

Step-by-step explanation:

[tex](-1)^{10} + ( -22)^{0} - (\frac{3}{5})[/tex]

[tex]1 + (-22)^{0} - (\frac{3}{5})^{2}[/tex]

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

[tex]1 + 1- \frac{9}{25}[/tex]

add the numbers

[tex]2 -\frac{9}{25}[/tex]

Calculate the difference

[tex]\frac{41}{25}[/tex] ← Final answer! ~ Hope this helps~

Answer:

Ron owns 1.25% of shares.

Step-by-step explanation:

400/50000 comes out to 0.0125 which can be converted into a decimal by moving the decimal two places to the right.

The measure of the arc of the sinkhole that falls within the restaurants property is -21°

Let x be the angle at the dollar store at the intersection

Now the angle of the grocery store at the intersection, y is 2/3 that of the dollar store. So, y = 2x/3

Since both x and y are supplementary,

x + y = 180°

x + 2x/3 = 180°

5x/3 = 180°

x = 180° × 3/5

x = 36° × 3

x = 108°

The gas station has the same angle at the intersection but has 88° more of the sinkhole edge to stabilize. So, the angle the gas station store subtends at the sinkhole is z = x + 88°

Also, since the grocery stores property has 2/3 of the angle in the intersection at the dollar store has, but has 5° more of the sinkhole edge to stabilize. The angle the grocery store subtends at the sinkhole is k = y + 5° = 2x/3 + 5°

Let k' be the angle subtended by the restuarant at the sinkhole.

Since the sinkhole is a circle, we have that

x + z + k + k' = 360°

x + x + 88° + 2x/3 + 5° + k' = 360°

8x/3 + 93° + k' = 360°

8x/3 + k' = 360° - 93°

8x/3 + k' = 267°

So, making k' subject of the formula, we have

k' = 267° - 8x/3

Substituting the values of the variables into the equation, we have

k' = 267° -  8 × 108°/3

k' = 267° - 288°

k' = -21°

So, the measure of the arc of the sinkhole that falls within the restaurants property is -21°

Learn more about measure of arc here:

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Answer:

6.0

Step-by-step explanation:

practice many times

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]

By theorem : Angle made by an arc at the centre is double the angle made by the same arc on the circumference part of the circle.

Therefore~

[tex]\qquad \sf  \dashrightarrow \: 2 \times \angle ABC = 160[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle ABC = 160 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle ABC = 80 \degree[/tex]

I hope you understood ~

Answer:

16 triangles I am pretty sure.

Step-by-step explanation:

Answer:

m<BAC = 85°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc.

m<BAC = 170°/2

m<BAC = 85°

Answer:

he spent 12 dollars on each book

Step-by-step explanation:

minus 13 from 85 you get 72 and then divide 72 by 6

Answer:

12$ each

Step-by-step explanation:

Tim had 85$ to spend on 6 books.

After buying them he had 13$.

How much did each book cost.

Answer:

20 years time

Step-by-step explanation:

Answer:

R80625

Step-by-step explanation:

Total Cost : 60000 + 4500 = 64500

To make 25% profit: 64500 X 1.25 = 80625

Answer:

(5, -43)

Step-by-step explanation:

The value of the x-coordinate of the vertex of a function in standard form is given by -b/2a.  The value of a is the coefficient of the x^2 term.  The value of b is the coefficient of the x term.  In this problem, a = 2 and b = -20.  When you evaluate -b/2a you would replace the b with -20 and replace the a with 2 so you get -(-20)/2(2) so the value of x is 5.  Determine the value of y by evaluating f(5) = 2(5)^2 - 20(5) +7.

[tex]5^2 - \left(\dfrac 14 \right)^2= 25 - \dfrac{1}{16} = \dfrac{400-1}{16} = \dfrac{399}{16}=24\dfrac{15}{16}[/tex]

Answer:

this table is linear

Step-by-step explanation:

there is a difference of 4 each time

Answer:

linear

Step-by-step explanation:

the difference in x and y values is constant

Answer: A (-7,-4)

Step-by-step explanation:

Took the same test

Cost is 6 USD

Selling price is 6 + markup

Markup = 6 * 120 /100 put this expression and check again selling price

Selling price =  6 + (6 * 120) / 100

= 13,2 usd

The expected value of the game is the mean value of the game

The expected value of the game is $1

There are 13 spades in a deck of card of 52

So, the probability of selecting a spade is:

P(Spade) = 13/52

Simplify

P(Spade) = 1/4

Winning = $7

The probability of not selecting a spade is:

P(Not spade) = 1 - 1/4

Simplify

P(Not spade) = 3/4

Lose = $1

The expected value of the game is:

[tex]E(x) = \sum x * P(x)[/tex]

This gives

[tex]E(x) = \frac 14 * 7 - 1 * \frac34[/tex]

Simplify

[tex]E(x) = \frac 74 - \frac34[/tex]

Evaluate

[tex]E(x) = 1[/tex]

Hence, the expected value of the game is $1

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Answer:

[tex] \frac{19}{3 } \: or \: 3 \frac{4}{5} [/tex]

Step-by-step explanation:

Change the mixed number into a regular fraction.

[tex] \frac{23}{5} - \frac{4}{5} [/tex]

Subtract the numerator.

[tex] \frac{19}{5} [/tex]

As a mixed number:

[tex]3 \frac{4}{5} [/tex]

Answer:

66+20+x=180(sum of angle in a triangle)

x=180-(66+20)

x=180-86

x=94