Trigonometric identities assignment 4

Simplify 5 sin ø sec ø

A. 5 cot ø
B. 5
C. 5 cos ø
D. 5 tan ø

Answer:

SAS postulate

Step-by-step explanation:

Answer:

5x

Step-by-step explanation:

Answer:

2,4 ((((((((((((((((((((

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Answer:

  21 ≤ x < 48.3343

  19.4030 < t ≤ 62 1/3

Step-by-step explanation:

This sort of geometry has shown up in a number of different problems. Perhaps the most difficult was one in which the angles were given a specific linear relationship. Here, one of the angles is fixed, making the problem somewhat simpler.

The most straightforward approach is to simply say the unknown angle must lie between 0° and 180°. It turns out that is not the possible range of values. Rather there is a limit on the unknown angle. It will have an extreme value when both triangles are isosceles. The lengths of the equal sides in that case can be determined using the triangle with both angle and base length specified.

__

a) For the triangle to be isosceles (MA = MH = MY), the side lengths must satisfy ...

  AM·sin(62°/2) = 7.1/2

  AM = 3.55/sin(31°) ≈ 6.89269

At that point, angle HMY will satisfy ...

  AM = (6.33/2)/sin((2x -42)°/2)

  3.55/sin(31°) = 3.165/sin(x-21°)

  (x -21)° = arcsin(3.165/3.55·sin(31°)) ≈ 27.3343°

  x = 48.3343

Because angle HMY can be smaller than this value, its minimum is 0:

  2x -42 = 0

  x -21 = 0

  x = 21

That is, x can range between 21 and 48.3343.

__

b) Using similar logic on the other triangles, we find the unknown angle has an extreme value when the triangles are isosceles: CA = CB = CD = CD. As above, this will occur when ...

  (3t -7)° = 2·arcsin(17/16·sin(24°)) ≈ 51.2091°

  t = 19.4030

In this geometry, because AB > DE, the angle can only get larger than 51.2091°. Its upper limit is 180°, meaning that ...

  3t -7 ≤ 180

  3t ≤ 187

  t ≤ 62 1/3

In this geometry, the value of t can range between 19.4030 and 62 1/3.

_____

Additional comment

As we said at the beginning, your computer may be expecting you to come up with an answer that makes the unknown angle lie between 0 and 180°. For that range of angles, you have ...

  0 ≤ 2x-42 ≤ 180  ⇒  0 ≤ x -21 ≤ 90  ⇒  21 ≤ x ≤ 111

  0 ≤ 3t -7 ≤ 180  ⇒  0 ≤ t -7/3 ≤ 60  ⇒  7/3 ≤ t ≤ 187/3

Answer:

[tex]\frac{3}{7}[/tex]

Step-by-step explanation:

[tex]\frac{4-1}{5--2}[/tex] =

[tex]\frac{4-1}{5+2}[/tex] =

[tex]\frac{3}{7}[/tex]

Answer:

Y=40

Step-by-step explanation:

Y/8=5

(Y/8)*(8)=(5)*(8)

Y=40

Answer:

£73.71

Step-by-step explanation:

Let's compute first for the cost of the ticket in 2014. Let x be the increase in the cost of the ticket. If the cost of the ticket is 8% of £65, then the expression should be like this:

Let's add £5.2 to £65 ⇒ £5.2 + £65 = £70.2

The cost of the season ticket in 2014 is £70.2.

Next, we'll have to compute the cost of the ticket in 2015. Let y be the increase in cost of the ticket. If the cost of the ticket is 5% of £70.2, then the expression should be like this:

Let's add £3.51 to £70.2 ⇒ £3.51 + £70.2 = £73.71

The cost of the season ticket in 2015 is £73.71. This is also the cost of the season ticket after two price increases.

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Answer:

  4)  6x

  5)  2x +3

Step-by-step explanation:

We can work both these problems at once by finding an applicable rule.

  [tex]\text{For $f(x)=ax^n$}\\\\\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h\to 0}\dfrac{a(x+h)^n-ax^n}{h}\\\\=\lim\limits_{h\to 0}\dfrac{ax^n+anx^{n-1}h+O(h^2)-ax^n}{h}=\boxed{anx^{n-1}}[/tex]

where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.

This can be referred to as the power rule.

Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:

  lim[h→0](f(x+h)-f(x))/h = 2ax +b

__

4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.

5. The gradient of x^2 +3x +1 is 2x +3.

__

If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.

yea the answer is reflection

The type of transformation that's shown in the figure on the left is; reflection

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs,

A reflection is defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis such as; if we're seeing it in a mirror.

We will find that its symmetric, thus each point is equidistant from the axis of reflection such that of the image of that point.

The answer is; reflection

Learn more about reflection here;

https://brainly.com/question/28186407

#SPJ6

1. 500% Increase

2. 40% Decrease

3. 75% Increase

4. 62.5% Increase

Answer:

70.88

Step-by-step explanation:

x/67.5=5/100 cross multiply 100x=337.5 divide 100 x=3.375 or 3.38 67.50+3.38=70.88

70.88 is your correct answer

THE UNIT IS DOLLAR ($).

Step-by-step explanation:

BECAUSE IT IS GIVEN IN TOTAL COST

Answer:

Look Down

Step-by-step explanation:

85+2.5v=115

2.5v=30

v=12

Answer:

Step-by-step explanation:

At the end of practice, Joseph will need to run another 1.75 miles or 1 3/4 miles.

To determine this we need to subtract the amounts he already has run during practice from the goal of 3 miles.

3 miles - 1/2 miles - 1/4 miles - 1/4 miles - 1/4 miles = 1.75 miles

Step-by-step explanation:

please sorry to barge into your question without any reasonable answer all I want to say is that this is a graph and I think that the domain and range this is increasing to calculate like the unit for example you have - 9 and - 3 you should calculate how many units are between -9 and -2 I'm not sure and I just really need marks now point where I can get on with my procedure so sorry for just barging in like that I'm so sorry

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Answer:

  x < -5

Step-by-step explanation:

The function is increasing where its slope is positive. That is where each point is higher than the one to its left. You see that is the case for all points to the left of the vertex, which is at x=-5.

The domain where the function is increasing is x < -5.

_____

Additional comment

At the vertex, the function is horizontal, neither increasing nor decreasing. So, the vertex itself is not included in the domains of increase or decrease.

Answer:

1). x = 0

2). Option 3

Step-by-step explanation:

1). If the two triangles are similar,

   Their corresponding sides will be proportional.

   [tex]\frac{5x+2}{6}=\frac{x+4}{12}[/tex]

   12(5x + 2) = 6(x + 4)

   60x + 24 = 6x + 24

   60x - 6x = 24 - 24

   54x = 0

   x = 0

2). Option 1

   2(x - 6) + 3 - 5x = -3x - 9

   2x - 12 + 3 - 5x = -3x - 9

   -3x - 9 = -3x - 9

   True.

   Option 2

   4(2x - 5) + 10 - 5x = 3x - 10

   8x - 20 + 10 - 5x = 3x - 10

   3x - 10 = 3x - 10

   True

   Option 3  

   5x + 4 = 3x + 4

    False

    Option 4

    8x + 3 - 2 = 8x + 1

    8x + 1 = 8x + 1

    True.

Therefore, option 3 is False.

Answer:

slope is 2.33

Step-by-step explanation:

Answer: 149.5 quarts

Step-by-step explanation:

From the question, we are informed that Jason has a container holding 11.5 quarts of liquid and that he wants to find enough containers to hold 13 times this amount of liquid.

The number of quarts of liquid that the containers need to hold will be:

= 13 × 11.5

= 149.5 quarts

Your answer

Answer:

3/8 of the box

Step-by-step explanation:

On Friday Merinda uses 1/4 of the box of pancake mix to make pancakes.

On Saturday she uses 1 1/2 times as much pancake mix as Friday.

On Friday = 1/4 of the box

On Saturday = 1 1/2 × pancake mix as Friday

[tex]\dfrac{3}{2}\times \dfrac{1}{4}\\\\=\dfrac{3}{8}[/tex]

Hence, 3/8 of the box of pancake mix does Merinda use on Saturday.

Answer:

a^7/8^2

Step-by-step explanation:

Here, we want to write the expression using only positive exponents

An important rule for indices to use here is that;

a^-b = 1/a^b

thus;

8^-2 = 1/8^2

So we have;

1/8^2 * a^7

= a^7/8^2

Answer:

(2,4)

Step-by-step explanation:

thats the point where both lines meet

Answer:

Step-by-step explanation:

Use calculator

but anyways here

24 x 0 = 0

6 x 1 =6

21x 2 =42

11x 5 = 55

Answer:

58 degrees

Step-by-step explanation:

Complementary angles add together to 90 degrees

(5x + 8) + (3x + 2) = 90

8x + 10 = 90

x = 10

5(10) + 8 = 58

Answer:

Angle 5

Angle 8

Step-by-step explanation:

[tex] \angle 5 \:\&\: \angle 8[/tex] measure less than the measure of Angle 1.

Answer:

x = 4, y = 3

Step-by-step explanation:

Answer:

help with what?

Step-by-step explanation:

Answer:

What

Step-by-step explanation:

Answer:

Use points (0,-7) and (1,-5)

please see below if you would like a graph.

Step-by-step explanation:

The equation is y=2x-7

we need two points.

The equation is in y=mx+b form, where m is the slope and b is the y intercept

In that case we already know a point, since -7 is in the place of b. The y intercept as a point is (0,b). Therefore, our first point is (0,-7)

We also know the slope of the line, which is 2. The formula for slope is rise/run That means that the next point would be to go right one, and up 2, (both indicate a positive direction), or to the left one, and down 2(both indicate a negative direction.) Let's use the positive way.

going to the right 1=+1 on x. (1, y)

Going up 2=+2=-7+2=-5

Point is (1,-5)

use points (0,-7), and (1,-5)

please see below for a graph to compare.

hope this helps!