trigonometry PIC included

Answer:

9

Step-by-step explanation:

Given that (1, 2) is the vertex of the function represented by the table of values above, the rate of change for the interval from x = 5 to x = 6.

f(5) = 18

f(6) = ?

=>Find f(6) using the vertex form function, f(x) = a(x - h)² + k

Where, h and k are the given vertex of the function = (1, 2).

h = 1, k = 2

Thus,

f(x) = a(x - 1)² + 2

Find the value of a by using any of the points given in the table.

Using (3, 6), we have the following,

6 = a(3 - 1)² + 2

6 = a(2)² + 2

6 = 4a + 2

Subtract 2 from both sides

6 - 2 = 4a

4 = 4a

Divide both sides by 4

1 = a

a = 1

Let's find f(6) using f(x) = a(x - 1)² + 2

Plug the value of a and x

f(6) = 1(6 - 1)² + 2

f(6) = 25 + 2

f(6) = 27

==>Find the rate of change/slope

f(5) = 18

f(6) = 27

Rate of change =

[tex] \frac{f(6) - f(5)}{6-5} [/tex]

[tex] \frac{27- 18}{6-5} [/tex]

[tex] \frac{9}{1} [/tex]

Rate of change = 9

Answer:

Option 1 and Option 2

Step-by-step explanation:

They both come to an intersection at a singular vortex

MARK AS BRAINLIEST

Answer:

Options 1, 2, and 4.

Step-by-step explanation:

Segments PS and OP intersect.

Segments PS and NP intersect.

Segments OR and QS do not intersect.

Segments NO and NP intersect.

Sorry this was a bit late but hope this helps!

Answer:

a) x = 17/8

b) x = 23

c) x = -8/11.

Step-by-step explanation:

a)

-3x + 5 = 5x - 12

Add 3x to both sides:

5 = 8x - 12

Add 12 to both sides:

17 = 8x

Divide both sides by 8:

17/8 = 8x/8

x = 17/8.

---------------------

b)

6(x-3)-4(x+2) = 20

Distribute:

6x - 18 - 4x - 8 = 20

Combine like terms:

2x - 26 = 20

Add 26 to both sides:

2x = 46

Divide both sides by 2:

x = 23.

---------------------

c)

-2/5(x + 3) = 1/3(x - 2)

Distribute:

-2/5x - 6/5 = 1/3x - 2/3

Add 2/5x to both sides by creating a common denominator:

-6/15x - 6/5 = 5/15x - 2/3

-6/5 = 11/15x - 2/3

Add 2/3 to both sides. Create common denominator:

-18/15 = 11/15x - 10/15

-8/15 = 11/15x.

Divide both sides by 11/15:

[tex]\frac{-8}{15}* \frac{15}{11} = \frac{-8}{11} = x[/tex]

x = -8/11.

Answer:

Yes, lines M and N intersect because their slopes are different.

Step-by-step explanation:

First, we can start out by finding the slope of Line M and Line N. The slope formula is (y_2 - y_1)/(x_ 2- x_1)

Slope of Line M:

(3--11) / (3--4)

(3+11) / (3+4)

14/7

2

Now we know that the slope of Line M is 2.

Slope of Line N:

(9--2) / (-6-5)

11/-11

The slope of Line N is -1!

Since the slopes of Line N and M are different, they intersect. The answer is Yes, lines M and N intersect because their slopes are different.

If the slopes were the same, Line N and M would NEVER intersect because they are parallel.

Hope this helps

Answer:

y = x/3 + 10

Step-by-step explanation:

Let y be the number of minutes the flight takes

She can take off 10 minutes later than expected. She will be able to travel at  a speed three times than expected.

Let her expected speed be s, therefore, she can travel at 3s.

x = number of minutes the flight was expected to take.

In terms of distance and speed:

x = d / s ______(1)

where d = total distance traveled

The time for the flight (minus waiting time) is now the division of the distance she traveled and her speed, i.e.:

t = d / 3s

From (1):

=> t = x / 3

The time she spent waiting is 10 minutes.

Therefore, the total time that the flight takes (plus waiting time) is:

y = t + 10

=> y = x/3 + 10

Answer: x>1/6

Step-by-step explanation:

For this problem, you solve it as if it had an equal sign.

-2(8x-4)<2x+5                        [distribute -2]

-16x+8<2x+5                           [combine like terms by adding and subtracting on both sides]

3<18x                                      [divide both sides by 18]

x>1/6

Answer:

[tex]11^{-10}[/tex]

Step-by-step explanation:

When you divide exponents, you subtract their powers:

-5 - 5 = -10

[tex]11^{-10}[/tex]

Answer:

18.027

Step-by-step explanation:

7.264+3.873+6.89

18.027

Answer:

40

Step-by-step explanation:

The angles stay the same but, the position of the triangle changes.

Hope this helps,

kavitha

Answer: A’ = 40ᴼ

Step-by-step explanation:

The angles are congruent and add to equal 180ᴼ

A = 40ᴼ

The measure of A stays the same when the angles are rotated

Answer:

It's the first one.

hope it helps :)

Step-by-step explanation:

Answer:

3,9

Step-by-step explanation:

Factors of 36 = 1,2,3,4,6,9,12,18,36

Those factors which are odd = 1,3,9

Odd Factors which are multiple of 3 = 3,9

So, these are the two numbers Margret might be thinking of.

Answer:

5/12 or 0.416667

Step-by-step explanation:

Plug in the values for x and y.

8(1/3) - 3(3/4)

Evaluate.

8/3 - 9/4

32/12 - 27/12

= 5/12

Answer:

D: 57 units

hope this helps!!

Answer:

C. (4, -3)

Step-by-step explanation:

edge 2020 :D

also different slopes in the y = mx + a, so there are different slopes between 1/2 and 2 and different y-intercepts, -2 and -5. there can be one solution but you gotta figure that out

We can conclude the following answers -

The general equation of a straight line is -

y = mx + c

where -

{m} is the slope of the line.

{c} is the {y} - intercept.

Given is that on a coordinate plane, a line goes through (0, negative 1) and (2, negative 2). This line represents Kaden’s Graph. Also a system of equations is given as -

x + 2y = - 2

y = (x/2) - 5

{ 1 } -

Kaden's graph passes through the points -

(0, - 1)

(2, - 2)

We can write the equation of the Kaden's graph as -

y = {(- 2 + 1)/(2 - 0)}x + {- 1}

y = - x/2 - 1

There is only one equation for Kaden's graph. Hence, it has infinitely many solutions.

{ 2 } -

x + 2y = - 2

y = (x/2) - 5

We can write -

x = - 2 - 2y

So -

y = (- 2 - 2y)/2 - 5

y = - 1 - y - 5

2y = - 6

{y} = -3

x = - 2 - 2 x - 3

{x} = 4

Therefore, we can conclude that -

To solve more questions on straight line equations, visit the link-

https://brainly.com/question/29223887

#SPJ7

Answer:

65°

Step-by-step explanation:

The missing angle is x°

tan x° = [tex]\frac{opposite }{adjacent}[/tex]

tan x° = [tex]\frac{850}{400\\}[/tex]

tan x° = 2.125

Using a calculator insert

tan^(-1)(2.125) ≈ 65°  (after rouding the the nearest unit)

Answer:

3x+4

Step-by-step explanation:

The perimeter is given by

P = 2 ( l+w)

We know the perimeter is  8x+8

8x+8 = 2 ( l+w)

Divide each side by 2

4x+4 = l+w

The width is x

4x+4 = l+x

Subtract x from each side

4x+4-x = l+x-x

3x+4 = l

The length is 3x+4

Answer:

The answer is option B.

Hope this helps you

Answer:

trapezoids

Step-by-step explanation:

i know i can delete rectangles and square, but rhombuses and parallelogram don't really have in common so the answer is trapezoids.

is quite easy 4th grade math

hope this helped :)

Answer:

its c 324cm3

Step-by-step explanation:

i took the test

Based on the calculations, the volume of this pyramid is equal to 324 cm³.

Given the following data:

Mathematically, the volume of a pyramid is calculated by using this formula:

Volume = 1/3 × base area × height

Next, we would determine the height of the pyramid from the right-angled triangle ABC by applying Tan trigonometry:

Tanθ = Opp/Adj = BC/AC

Tan60 = height/6

√3 = height/6

Height = 6√3 cm.

Now, we can calculate the volume:

Volume = 1/3 × base area × height

Volume = 1/3 × 54√3 × 6√3

Volume = 1/3 × 972

Volume = 324 cm³.

Read more on pyramid here: brainly.com/question/16315790

#SPJ2

Answer:

840π

Step-by-step explanation:

To calculate the surface area of a cylender, do S=2(π)*radius*height.

2(π)*12*35 = 840 π

Answer:

(1)55.5 feet

(2)7.5 feet

Step-by-step explanation:

Question 1

The diagram is attached below.

Using Trigonometric ratio

[tex]\tan 48^\circ = \dfrac{h}{50} \\h=50 \times \tan 48^\circ\\h=55.5$ feet (to the nearest tenth)[/tex]

The height of the house is 55.5 feet to the nearest tenth.

Question 2

In the diagram, we are required to find the distance the bird must fly to be directly above the fish. This has been represented by x.

Using Trigonometric ratio

[tex]\tan 15^\circ = \dfrac{2}{x} \\x \tan 15^\circ=2\\x=2 \div \tan 15^\circ\\x=7.5 $ feet (to the nearest tenth)[/tex]

The distance the bird must fly to be directly above the fish is 7.5 feet.

Answer:

2

Step-by-step explanation:

sec∅ is equal to 1/cos∅ or (hypotenuse over adjacent).

With that in mind:

sec∅ = 2/1

sec∅ = 2

Answer:

B. 2

Step-by-step explanation:

We need to find the value of secant for this triangle.

Remember the trigonometric functions: secant = hypotenuse / adjacent, where the hypotenuse is the longest side (2 in this case), and the adjacent is the side right next to the labelled angle but is not the hypotenuse (1 in this case).

Plugging the values into the equation yields:

sec(θ) = hypotenuse / adjacent

sec(θ) = 2 / 1 = 2

The answer is thus B.

~ an aesthetics lover

Answer:

x+5

Step-by-step explanation:

so first you would divide by x (which means you would multiply x+2 by -x)

x^2 + 7x + 10

-x^2 - 2x

5x + 10

then you would divide by 5 (which means you would multiply x+2 by -5)

5x + 10

5x +10

0

So then to check it you would multiply x+5 by x+2

(x+5)(x+2)

x^2 + 2x + 5x + 10

then simplify to get

x^2 + 7x + 10

Answer choices :

less than 0

greater than 0

exactly equal to 0

There is not enough information to answer this question.

Answer: greater than 0

Step-by-step explanation: For a normally distributed data, that is a data which is symmetrical whereby the majority of the values cluster at the center of the distribution. In general, for a normal distribution, the mean is 0 and the standard deviation is 1. Where the mean measures the average and refers to the center of the distribution and the standard deviation measures how spread out the data is.

Z - scores are used to standardize values with values above the average having z-scores greater than 0, those below average having values less than 0 and average value having a z-score of exactly 0.

Answer:

You have to multiply all the sides by 4.

B to C = 2.8*4

2.8 * 4 = 11.2

B to A = 3*4

3*4 = 12

A to C = 2.2*4

2.2*4 = 8.8

Hope this helped!

Answer:

According to the pythagorean theorem, a^2 + b^2 =c^2

c signifies the hypotenuse

a and b are the two legs

the sum of the two legs squared measures will equal the measure of the hypotenuse squared.

Step-by-step explanation:

Answer:

£480

Step-by-step explanation:

we can multiply both terms of ratio with same number without changing the ratio.

Example

a:b = ax: bx (here we have multiplied both terms with x)\

Given

Stevie and Michael share their profit in a ratio 3:5

Let the profit for Stevie and Michael be 3x and 5x

Given Stevie gets £120 more than Michael

Profit for Steve = 120 + profit for Michael

3x = 120 + 5x

3x-5x = 120

=> -2x = 120

=> x= -120/2 = -60

As we see profit is negative , hence it cannot be solution.

It can be solved if Stevie and Michael share their profit in a ratio 5:3

(note: in ratio , bigger number should have bigger term in ratio)

Let the profit for Stevie and Michael be 3x and 5x

Given Stevie gets £120 more than Michael

Profit for Steve = 120 + profit for Michael

5x = 120 + 3x

5x-xx = 120

=> 2x = 120

=> x= x120/2 = 60

Profit for stevei = 5x =5*60 = 300

Profit for Michael = 3x = 3*60 = 180

Total profit for them together = 300 + 180 = 480 Answer.

Answer:

The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly but gets faster each minute after you hear this signal bodeboop. A sing lap should be completed every time you hear this sound. ding Remember to run in a straight line and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark. Get ready!… Start

Answer:  A

Step-by-step explanation:

The standard form of a cosine equation is: y = A cos (Bx - C) + D  where

Plot the points (see graph below).

A = 28

[tex]\dfrac{1}{2}P=6\quad \rightarrow \quad P=12\\\\\\P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 12=\dfrac{2\pi}{B}\qquad \rightarrow \qquad \large\bold{B=\dfrac{\pi}{6}}[/tex]

Phase Shift = 7 = C/B

                      [tex]7=\dfrac{C}{\frac{\pi}{6}}\qquad \rightarrow \qquad \large\bold{C=\dfrac{7\pi}{6}}[/tex]

D = 49

Input the values of A, B, C, and D into the standard form of a cosine equation to get:

[tex]\large\boxed{y=28\cos \bigg(\dfrac{\pi}{6}x-\dfrac{7\pi}{6}\bigg)+49}[/tex]