Given that the function graphed is ƒ(x), what is ƒ(1)?
A) −2
B) −1
C) 1
D) 2

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:

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Price of one unit Sausage =  1.65

Sum ( Price x Quantity) = Total Expenditure  

Price of Bread x Quantity of Bread + Price of Ketchup x Quantity of Ketchup + Price of Sausage x Quantity of Sausage

Total Expenditure Value = 10 - 0.45  = 9.55

Let price of sausage = P

Therefore, 2 (1.40) + 1 (1.80) + 3 P = 9.55

2.80 + 1.80 + 3 Ps = 9.55

4.6 + 3 P = 9.55

3P = 9.55 - 4.60 =  4.95

P = 4.95 / 3 = 1.65

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Answer:

450,000

Step-by-step explanation:

The ten thousand digit is 4 and if we compare it to 9, it is bigger then 5 therefore it is rounded up and you get the answer of 450,000

Answer:

1. Triangle XYZ undergoes a translation.

2. Triangle X'Y'Z' undergoes a reflection across the x-axis

Answer:

sorry I can't understand the word

Step-by-step explanation:

first you need to tranfer 1 to RHS do the addition

n/3 = 8+1

=) n/3 = 9

then you need to transfer 3 to RHS and multiply

=> n = 9 x 3

there for n = 27

Answer:

the answer is 5.50 or the last one

Step-by-step explanation:

hope this helps

Answer:

answer is $7.5

Step-by-step explanation:

1shirt=$5

10 shirt= ?

10*5= $50

$5= 100%

what about 150%

(5*150)÷100= $7.5

Given :   Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’s bill is 7%.

To Find : How much is Isaac’s total bill?  

b) 25% discount off  before tax

Solution:

one pair for $37.00

second pair for $42.00

Total Bill before taxes = 37 + 42 =  79 $

7 % Sale Tax = (7/100)79 = 5.53 $

Isaac’s total bill = 79 +  5.53  = 84.53  $

Total Bill before taxes = 37 + 42 =  79 $

Discount 25 % = (25/100)79 = 19.75$

Total Bill before taxes = 79 - 19.75 = 59.25 $

7 % Sale Tax = (7/100)59.25 =4.1475 $

Isaac’s total bill = 59.25  +  4.1475  = 63.3975  $

Please post Question one by one

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The sales tax on a surfboard is $12. What is the percent of sales tax ...

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An article is avilable for rs1540 inclusive of sales tax at 10% .what ...

i had to do the answer as a pic cuz my iPad is gonna die.

sorry <:)

Answer:

Step-by-step explanation:

x = - 23

y = - 5

z = - 10

(x - 12)/(y+z)=

(-23 - 12)/(-5-10)=

45/15=

7/3

Answer:

niether do i

Step-by-step explanation:

Answer:

6x - 14

Step-by-step explanation:

4(2x - 3) - 2(x + 1)

1. Expand both brackets

(8x - 12) - (2x + 2)

2. Simplify

8x - 2x = 6x

-12 - 2 = -14

Therefore, 4(2x - 3) - 2(x + 1) = 6x - 14

Answer:

What makes a number friendly?

In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same "abundancy" form a friendly pair; n numbers with the same "abundancy" form a friendly n-tuple.

Step-by-step explanation:

Answer:32.5

Step-by-step explanation: i used a calculator

Answer:

$162.50

Step-by-step explanation:

Answer:

y = -3x + 6

Step-by-step explanation:

Two lines that are parallel will have the same slope. All we need to do is find the new y-intercept.

-3 = -3(3) + b

-3 = -9 + b

6 = b

Now we can input the stuff we know and solved for back into the original formula [ y = mx + b ].

y = -3x + 6

Best of Luck!

A parallel line means our new line will have a slope equal to the original line.

The original line is in slope-intercept form, y = mx + b, where m is the slope and b is the value of the y-intercept. This tells us that the slope we want to use is m = -3

By using a slope of -3, with the given point (3,-4), we can now use the point-slope formula to find our new line.

Point-slope formula: y - y1 = m(x - x1) where m is the slope and the line passes through the point (x1,y1)

Combining our point and slope, we get:

y + 4 = -3(x - 3)

If we wish, we can rearrange this by distributing on the right hand side.

y + 4 = -3x + 9

We can then subtract 4 from both sides to get our answer in slope-intercept form

y + 4 - 4 = -3x + 9 - 4

y = -3x + 5

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x2 - 8x -12 = 0

divide through by 4

x2 - 2x - 3 = 0

x2 - 3x + x - 3 = 0

(x2 - 3x) + (x - 3) = 0

x(x - 3) + 1(x - 3) = 0

(x + 1) (x - 3) = 0

x + 1 = 0 and x - 3 = 0

x = -1 and x = 3

Answer:

B IS THE ANSWER

Step-by-step explanat

(22x2 -  8x) -  12  = 0

  4x2 - 8x - 12  =   4 • (x2 - 2x - 3)

The first term is,  x2  its coefficient is  1 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -2 .

     -3    +    1    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  1  

                    x2 - 3x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-3)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-3)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-3)

            Which is the desired factorization

4 • (x + 1) • (x - 3)  = 0

A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately  

Any solution of term = 0 solves product = 0 as well.

  Solve  :    x+1 = 0

Subtract  1  from both sides of the equation :  

                     x = -1

   Solve  :    x-3 = 0  

Add  3  to both sides of the equation :  

                     x = 3

Answer:

0884

Step-by-step explanation:

Answer:

C) Minimum at (3,7)

Step-by-step explanation:

Recall that vertex form is [tex]y=a(x-h)^2+k[/tex]:

[tex]y=x^2-6x+16[/tex]

[tex]y=(x^2-6x+9)+7[/tex]

[tex]y=(x-3)^2+7[/tex]

Therefore, the vertex is [tex](h,k)[/tex] or [tex](3,7)[/tex] in this case. Because the parabola is positive, then the vertex has to be the minimum of the parabola, making choice C correct.

Answer: he is currently 69 years old

Step-by-step explanation:

24x3=72-3=69 lol funni number

Answer:

78 years old

Step-by-step explanation:

In 3 years Joanne will be 27. Xavier is 3 times that age by the time Joanne is 27. 27×3=81. but we're looking for Xaviers age today. so we take 81 and subtract 3 which leaves us with 78

Answer:

7/12

1/6 to 2/12 add 5/12 to get 7/12

Answer: A  F D G

Step-by-step explanation:

Answer:

-3.392

Step-by-step explanation:

Math-way

The constraints in the question are given by the definition of the variables;

The constraints are represented by the following equation and inequalities.

Reasons:

The budget of the principal = $225

Number of people expected = 16 people

Number of sandwich per person = 2

Cost of each sandwich = $3

Required:

To select the inequalities that represent the situation's constraint

Solution:

The variable that represent the number of people attending = n

The number of sandwiches = s

From the question , we have;

The number of sandwich per attendee = 2 sandwiches

The total number of sandwich, s, for n attendees = 2·n

Therefore, we have;

s = 2·n

The number of people attending is at least 16, therefore;

n ≥ 16

The cost of the s sandwich = $3 × s

The total cost should be less than or equal to given budget of $225,

therefore;

3s ≤ 225

The equations and inequalities that could represent the constraints are;

A. n ≥ 16, D. s = 2·n, and F. 3s ≤ 225

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Answer:

The missing value is 56.

Step-by-step explanation:

All side angles must add up to 180. So given the 2 angle measures 30+94 = 124.

Then subtract 180 from 124 to get your answer of 56.

When you add up all the angles, it gets you 180 evenly.

Answer:

okay, well, is there any link u wanna post for us to help u? maybe we can explain it?

Step-by-step explanation:

Answer: 5 to 20 intervals.

Step-by-step explanation: