Consider the following number line:

Answer:

cscθ = 5/4, secθ = 5/3

Step-by-step explanation:

First, let's view the drawing that I have attached, with the dot in the bottom left representing the origin. We know that cosecant and secant are the reciprocals of sin and cos respectively, and in order to find sin and cos, we must find the opposite, adjacent, and hypotenuse sides. The hypotenuse is opposite the right angle, equal to √(8²+6²) = 10

Next, we can find sin and cos of θ . sinθ = 8/10=4/5, making cscθ the reciprocal of 4/5, or 5/4

Similarly, cosθ = 6/10=3/5, and secθ = 5/3

1. [tex] \: {7}^{1} [/tex]

➺ [tex]\boxed{\: 7 }[/tex]

2. [tex] \: {4}^{0} [/tex]

➺ [tex]\boxed{ \: 1 }[/tex]

( ∵ any number to the power of 0 is 1. )

3. [tex] \: {6}^{ - 1} [/tex]

➺ [tex] \: \frac{1}{6} [/tex]

[tex]( \: ∵ {a}^{ - 1} = \frac{1}{a} )[/tex]

➺ [tex]\boxed{ \: 0.1667 }[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

y = 0 domain is all real numbers and range is 1 i believe

Step-by-step explanation:

hope this helps

Step-by-step explanation:

There are many ways

-1 - 1 = - 2

-5 + 3 = -2

Answer:

(-3+1) and 1,000,000+(-1,000,002)

9514 1404 393

Answer:

  15

Step-by-step explanation:

(2 loaves)(5/2 cups/loaf)/(1/3 cup/scoop) = (2)(5/2)(3/1) scoops = 15 scoops

The baker will need 15 scoops of flour.

Answer:

42 teaspoons of vinegar should be used

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

4 teaspoons of vegetable oil and 12 teaspoons of vinegar. 14 teaspoons of vegetable oil were used

So

4 teaspoons of vegetable oil - 12 teaspoons of vinegar

14 teaspoons of vegetable oil - x teaspoons of vinegar

So

[tex]4x = 12*14[/tex]

Dividing both sides by 4:

[tex]x = 3*14 = 42[/tex]

42 teaspoons of vinegar should be used

Answer:

ans: 4

Step-by-step explanation:

corresponding sides are proportional since given triangle are similar triangle, I.e

(4/5.5) = { (2x+8)/(6x-2)}

8/11 = ( x+ 4 ) / ( 3x - 1 )

8( 3x - 1 )= 11( x + 4 )

24x - 8 = 11x + 44

13x = 52

x = 4

Answer:

I would identify the proportions of the corresponding sides, because that would allow you to identify whether or not the triangles are similar. You could also identify if two triangles are similar using

-SSS (side-side-side) which would tell you if all three corresponding sides are congruent

-SAS (side-angle-side) which would tell you if two sides and the angle between them are congruent

-ASA (angle-side-angle) which would tell you the two angles and the side between them are congruent

-AAS (angle-angle-side) which would tell you if two angles and a non-included side are congruent. You triangles may have all of these, or just one, but it will help you identify the similarity between triangles

Answer:

B, if you have any questions how I did anything, or questions in general, let me know.  

Step-by-step explanation:

First you want to make sure you understand distributing.  Just using variables I will show how to districute a similar expression.

(a - b)(c + d - e)

There are several ways to think of it.  you could treat (a-b) as one term and distribute it into c + d - e like this.  pretend (a- b) = x

x(c + d - e) = cx + dx - ex = c(a-b) + d(a-b) - e(a-b)

Then just do a bit more distributing, then combine like terms.

You could instead make (c + d - e) a single term and distribute that into (a-b)

I prefer doing it all in one step, similar to FOIL-ing.  Take the first term of one of the expression in parenthesis and distribute it, then move on to the second and so on.

so with (a - b)(c + d - e) I would start with a and distribute that into (c + d - e) and get ac + ad - ae then do the same to -b and get -bc - bd + be then you add the two parts together. ac + ad - ae + -bc - bd + be = ac + ad - ae -bc - bd + be.  Then you would combine like terms.  Let me know if you need help with that.  

Anyway, now for your problem.  Keep in mind you can use any of the methods.

(2x^2 - 3y^2)(4x^4 + 6x^2y^2 + 9y^4)

First distribute 2x^2 into (4x^4 + 6x^2y^2 + 9y^4)

8x^6 + 12x^4y^2 + 18x^2y^4

Next distribute -3y^2 into (4x^4 + 6x^2y^2 + 9y^4)

-12x^4y^2 - 18x^2y^4 - 27y^6

Now add the two together.

8x^6 + 12x^4y^2 + 18x^2y^4 + -12x^4y^2 - 18x^2y^4 - 27y^6 = 8x^6 + 12x^4y^2 + 18x^2y^4 - 12x^4y^2 - 18x^2y^4 - 27y^6

Finally combine like terms.

12x^4y^2 - 12x^4y^2 = 0

18x^2y^4 - 18x^2y^4 = 0

So that leaves us with 8x^6 - 27y^6

B is the only answer that works, none of the other 3 can be simplified or adjusted to make them equal what we need, so B is the only right answer.  

If you have any questions though let me know.

Answer:

it could only accomplish it's goal on Friday

Step-by-step explanation:

all you had to do was multiply 8 with the number of people and 2 with the number of tickets on each day and add them together to see if it was more than 1650. it was only more on Friday

Answer:

121.857

Step-by-step explanation:

6×7r = 5118

42r = 5118

r = 121.857

Answer:

121.8571428571429

Step-by-step explanation:

r=  5118/42

Answer:

The exchange rate for Dollars to Euros is of 1.33.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

Exchange rate for Dollars to Euros.

We want to find the number of dollars in a euro.

In 375 euros, there are 500 dollars, so how many dollars in 1 euro?

375 euros - 500 dollars

1 euro - x dollars

Applying cross multiplication:

[tex]375x = 500[/tex]

[tex]x = \frac{500}{375}[/tex]

[tex]x = 1.33[/tex]

The exchange rate for Dollars to Euros is of 1.33.

Answer:

One leg: 3

So, the hypo: 2*3 = 6

And the third is according to the formula for right angle triangles: a^2 + b^ = c^2

So: √9+36= c

6.7 to get an exact number round it: 7

Answer:

sides are √3 ft,2√3 ft,3 ft

Step-by-step explanation:

let one leg=x

length of hypotenuse=2x

third side=3 ft

(2x)²=x²+3²

4x²-x²=9

3x²=9

x²=9/3=3

x=√3 ft

hypotenuse=2√3 ft

Answer:

All values that satisfy [tex]y[/tex] ≤ [tex]\frac{1}{3} x-3[/tex] are solutions

Step-by-step explanation:

The reason why the other equations solutions aren't solutions are because it doesn't satisfy the second equation, but the second equation satisfy both equations because the solutions of the second equations will be in both equations.

Hope this helps

Answer:

8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

7 is it because it is positive

Answer:

PRT%

Step-by-step explanation:

PRT

[tex] = 320 \times 2.3 \times 20 \div 100 = 1472[/tex]

Answer:

C.

Step-by-step explanation:

ASA stands for angle-side-angle.

one side and the 2 angles at the end points of this side are known. only one triangle can be created with that information.

and that is our situation here.

the sides PQ and respectively ST are known (the fact that they are of equal length qualifies for that).

and the angles at the end points of PQ are known (again, the fact that they have the same size as the angles for ST qualifies for that too).

so, ASA applies to prove that both triangles are congruent.

Answer:

-12 can be written as the ratio of -24 and 2, for example.

Step-by-step explanation:

Ratio of a to b:

The ratio of a to b is given by the division of a by b, that is:

[tex]r = \frac{a}{b}[/tex]

−12 as a ratio of two integers.

Here, we want any division in which the result is -12. One example is:

[tex]-12 = \frac{-24}{2}[/tex]

-12 can be written as the ratio of -24 and 2, for example.

Step-by-step explanation:

[tex] \tan(67) = \frac{x}{7} \\ 2.355852366 = \frac{x}{7} \\ x = 16.49 = 16.5[/tex]

Step-by-step explanation:

the answer is in the above image

Answer:

[tex]\frac{1}{240} = 0.0042[/tex] = 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, since the order in which the students are chosen is important, the permutations formula is used to solve it.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Desired outcomes:

Drake then Todd, so only one outcome, which means that [tex]D = 1[/tex]

Total outcomes:

Two students from a set of 16, so:

[tex]T = P_{16,2} = \frac{16!}{14!} = 16*15 = 240[/tex]

What is the probability that the first 2 presentations will be by Drake and Todd, in that order?

[tex]p = \frac{D}{T} = \frac{1}{240} = 0.0042[/tex]

[tex]\frac{1}{240} = 0.0042[/tex] = 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.

Answer:

30.64 inches

Step-by-step explanation:

use Pythagoras theoryum to find the width:

11²=121

121-9²=40

√40=6.32

perimeter is all sides added together so:

6.32+6.32+9+9=30.64

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

v = -6       v = -4/5

Step-by-step explanation:

(6+v) ( 5v+4) = 0

Using the zero product property

6+v =0  5v+4 =0

v = -6      5v = -4

v = -6       v = -4/5

Answer:

Daniel traveled further by 2.73 miles

Step-by-step explanation:

To find the total distance traveled simply multiply average speed times time

For Wendy

She traveled for 3.9 hours at a speed of 68.3 mph

So total distance traveled = 3.9 * 68.3 = 266.37 miles

For Daniel

He traveled for 4.5 hours at a speed of 59.8 mph

So total distance traveled = 4.5 * 59.8 = 269.1 miles

As you can see Wendy traveled 266.37 miles and Daniel traveled 269.1 miles

Daniel traveled further

To find how much further we simply subtract distance Daniel traveled (269.1) from distance Wendy traveled (266.37)

269.1 - 266.37 = 2.73

So Daniel traveled further by 2.73 miles

Answer:

Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.

Step-by-step explanation:

Area of a rectangle:

The area of a rectangle, of length l and height h, is given by:

[tex]A = lh[/tex]

The length of a rectangular wall is 16.5 feet. The height of the wall is 8.625 feet.

This means that [tex]l = 16.5, h = 8.625[/tex]

Estimate of the area:

To use an "easy" multiplication, lets consider [tex]l = 17, h = 9[/tex]. So

[tex]A = lh = 17(9) = 153[/tex]

Cameron determines the area of the wall to be 1423.125 square feet.

Very far from the area of 153, which means that he made a confusion with the decimal places. Thus, the correct answer is:

Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.

Answer:

30 hour

Step-by-step explanation:

girls time

12 20 hour

8 x(let)

now,

12/8=x/20

12×20=8×x

240=8x

x=240/8

x=30,,