Use a graphing utility to graph the equation. Use the graph to approximate the values of x that satisfy each inequality.
y =
1
2
x2 − 2x + 1

The functions are illustrations of trigonometry ratios

[tex]\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}[/tex]

The sine of an angle is calculated as follows

[tex]\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}[/tex]

So, we have:

[tex]\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}[/tex]

[tex]\mathbf{sin\theta = \sqrt{1 - (15/25)}}[/tex]

Take LCM

[tex]\mathbf{sin\theta = \sqrt{\frac{10}{25}}}[/tex]

[tex]\mathbf{sin\theta = \frac{\sqrt{10}}{5}}[/tex]

[tex]\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}[/tex]

The tangent of an angle is:

[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]

Using Pythagoras theorem, we have:

[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]

So, we have:

[tex]\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}[/tex]

[tex]\mathbf{Hypotenuse^2 = 10 + 4}[/tex]

[tex]\mathbf{Hypotenuse^2 = 14}[/tex]

Take square roots

[tex]\mathbf{Hypotenuse = \sqrt{14}}[/tex]

So, the sine of the angle is:

[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]

[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}[/tex]

Rationalize

[tex]\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}[/tex]

[tex]\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}[/tex]

The sine of the angles is:

[tex]\mathbf{sin \theta = \frac{1}{csc\theta}}[/tex]

So, we have:

[tex]\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}[/tex]

[tex]\mathbf{sin \theta = \frac{3}{\sqrt{15}}}[/tex]

Rationalize

[tex]\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}[/tex]

[tex]\mathbf{sin \theta = \frac{\sqrt{15}}{5}}[/tex]

[tex]\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}[/tex]

The sine of an angle is calculated as follows

[tex]\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}[/tex]

So, we have:

[tex]\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}[/tex]

[tex]\mathbf{sin\theta = \sqrt{(1 - 9/6)}}[/tex]

[tex]\mathbf{sin\theta = \sqrt{( - 3/6)}}[/tex]

The sine of the angle does not have a real value

[tex]\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}[/tex]

Start by calculating the tangent of the angle

[tex]\mathbf{tan\theta = \frac{1}{cot\theta}}[/tex]

So, we have:

[tex]\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}[/tex]

[tex]\mathbf{tan\theta = \frac{2}{\sqrt 6}}[/tex]

Rationalize

[tex]\mathbf{tan\theta = \frac{2\sqrt 6}{6}}[/tex]

[tex]\mathbf{tan\theta = \frac{\sqrt 6}{3}}[/tex]

The tangent of an angle is:

[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]

Using Pythagoras theorem, we have:

[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]

So, we have:

[tex]\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}[/tex]

[tex]\mathbf{Hypotenuse^2 = 6 + 9}[/tex]

[tex]\mathbf{Hypotenuse^2 = 15}[/tex]

Take square roots

[tex]\mathbf{Hypotenuse = \sqrt{15}}[/tex]

So, the sine of the angle is:

[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]

[tex]\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}[/tex]

Rationalize

[tex]\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}[/tex]

Rewrite as:

[tex]\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}[/tex]

[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}[/tex]

Read more about trigonometry ratios at:

https://brainly.com/question/24888715

Answer:

$75

Step-by-step explanation:

50% is half of the total, meaning that we can take half of $50, then add it to 50. Half of 50 is 25, so 50 + 25 = 75 dollars.

Answer:

The answer is 61

Answer:

61

Step-by-step explanation:

Answer:

9c

Step-by-step explanation:

if you take 8c and add another c, it equals 9c

Answer:

9C

Step-by-step explanation:

Answer:

-4q+ 40/3

Step-by-step explanation:

Answer:

________

Answer:

should be 40

1.6[3(5(2))-5]

1.6[30-5]

1.6[25]

40

Answer:

(6,0) or (0,-1)

Step-by-step explanation:

X-6y=6

X=6+6y

X/6=1+y

X/6-1=y

y=X/6-1

We'll use substitution to solve the ordered pair. Let's say Y = 0. We'll insert it back into our equation.

0=X/6-1

1=X/6

6=X

(6,0)

We can also start with X being = 0.

y=0/6 -1

y=-1

(0,-1)

I've attached what that would look like as a graph.

Nick's needs to walk 2,085 feet more to get to the library.

Given:

1 mile = 5,280 feet

Distance from Nick's school to his house = 3195 feet

Recall,

Nick’s house is between his school and the library, which is one mile apart

So,

Distance to work to the library from Nick's house = 1 mile - Distance from Nick's school to his house

= 5,280 feet - 3,195 feet

= 2,085 feet

Therefore,

Nick's needs to walk 2,085 feet more to get to the library.

Read more:

https://brainly.com/question/20365394

11

Step-by-step explanation:

first you add seven plus four and then you get your answer that is eleven

Answer:

f(m-5) = 5m-34

Step-by-step explanation:

f(x)=5x-9

Replace x with m-5

f(m-5) = 5(m-5) -9

Distribute

         = 5m-25 -9

         = 5m-34

Answer:

answer is 5m - 34

Step-by-step explanation:

!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

the answer is 3 I think if not than 2

Answer:

175%

hope that helps. :)

Answer:

1 23 then 70 .2 corrected

Answer:

Make all fractions have the same common denominator, and you will find that 3/8 is the smallest value.

Step-by-step explanation:

The movement of the ping pong ball follows a exponential progression.

1. Ping pong ball

The given parameters are:

[tex]\mathbf{a = 235}[/tex] --- the initial height

[tex]\mathbf{r = 75\%}[/tex] --- the common ratio

(a) The expression after bouncing k times

To do this, we make use of

[tex]\mathbf{T_n = a \times r^n}[/tex]

So, we have:

[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]

In this case; k = n.

So, the equation becomes

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

Hence, the expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

(b) The height after bouncing 6 times

This means that k = 6.

So, we have:

[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]

[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]

[tex]\mathbf{T_6 = 41.82}[/tex]

Hence, the height after the 6th bounce is 41.82 ft

(c) The total distance after the 12th bounce

First, we calculate the total height after the 12th bounce using:

[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]

[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]

[tex]\mathbf{S_k = 909.92}[/tex]

So, the total distance is:

[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]

[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]

[tex]\mathbf{Distance = 1584.84}[/tex]

Hence, the total distance after the 12th bounce is 1584.84ft.

(2) Cell division

The given parameters are:

[tex]\mathbf{r = 2/2hr}[/tex] --- rate

[tex]\mathbf{a = 120}[/tex] --- initial number of cells

[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half

So, the number of bacteria is:

[tex]\mathbf{T_t = ar^t}[/tex]

This gives

[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]

[tex]\mathbf{T_t = 31457280}[/tex]

Hence, there will be 31457280 bacteria after a day and a half.

Read more about exponential functions at:

https://brainly.com/question/11487261

Answer:

99

Step-by-step explanation:

Its negation is greater than -100. Hope this helps!

~Just a joyful teen

[tex]SilentNature[/tex]

Answer:

99

Step-by-step explanation:

ANSWER: is there a picture for the question?

Step-by-step explanation:

Answer:

-$500

Step-by-step explanation:

C = 3(1000) + 6500

C = 3000 + 6500

C = 9500

R = 9(1000)

R = 9000

P = 9000 - 9500

P = -500

Answer:

1→10

Step-by-step explanation:

12

27

45

105/4

49/2

2/15

2/9

22/45

7/12

1/3

A = 440

answer...

A

=

a

+

b

2

h

=

25

+

19

2

·

20

=

440

Answer:

The domain should be X

Step-by-step explanation:

I'm a bit unsure but I think it's correct

Expressing the given equation as a power of 10 with the divisor expressed as an whole number can be written as [tex] \frac{42.66 \times 10^{2}}{297}[/tex]

Given the expression :

Expressing the numbers as a power of 10 :

To convert the divisor to a whole number :

Multiply both by 100

Expressing dividend as a power of 10 :

Hence, the equivalent equation would be : [tex] \frac{42.66 \times 10^{2}}{297}[/tex]

Learn more : https://brainly.com/question/18796573

Answer:

18

correct me if I'm wrong❌