A store sells small notebooks for ​$8 and large notebooks for ​$16. If a student buys 6 notebooks and spends ​$80​, how many of each size did he​ buy?

Answer:

a. Sin B = 15/17

b. Cos B = 8/17

c. Tan B = 15/8

Step-by-step explanation:

Recall: SOHCAHTOA

Reference angle = B

Opp = 15

Adjacent = 8

Hypotenuse = 17

a. Sin B = Opp/Hyp (applying SOH)

Substitute

Sin B = 15/17

b. Cos B = Adj/Hyp

Substitute

Cos B = 8/17

c. Tan B = Opp/Adj

Substitute

Tan B = 15/8

Answer:

48 m³

4,186.67 km³

Step-by-step explanation:

volume of pyramid =

⅓×6×6×4 = 48 m³

volume of ball =

4/3 × 3.14 × 10³ = 4,186.67 km³

Answer: 16

Step-by-step explanation:

Answer:

[tex]distance = \sqrt{ {(8 - ( - 8))}^{2} + {( - 6 - ( - 6))}^{2} } \\ = \sqrt{256} \\ = 16 \: units[/tex]

Answer: 4.2

Step-by-step explanation:

Here's the formula for how to find the hypotenuse: (a and b are the two legs for the triangle-- it doesn't matter which leg is a and which leg is b, but c MUST be the hypotenuse)

[tex]a^2+b^2=c^2[/tex]

[tex]1.9^2+3.8^2=c^2[/tex]

[tex]3.61+14.44=c^2[/tex]

[tex]18.05=c^2[/tex]

[tex]\sqrt{18.05} =c[/tex]

[tex]c=4.2[/tex]

Answer:

y = (x² + 1) / (1 – x²)

Step-by-step explanation:

x = √[(y – 1)/(y + 1)]

We can make y the subject of the expression as shown below:

x = √[(y – 1)/(y + 1)]

Take the square of both side

x² = (y – 1) /(y + 1)

Cross multiply

x²(y + 1) = (y – 1)

Clear bracket

x²y + x² = y – 1

Rearrange

x² + 1 = y – x²y

Factorise

x² + 1 = y(1 – x²)

Divide both side by (1 – x²)

y = (x² + 1) / (1 – x²)

Answer:

9

Step-by-step explanation:

To solve this just take b (in this case 6x) divide it by 2 and then square it

which means that c=9

this will factor to (x+3)²

Answer:

no, it wont

Step-by-step explanation:

2g.h = v²

2(33)(40) = v²

2640=v²

v=√2640 = 51.38 ft/s

36 < 51.38

so, the rope will not get to the window

Answer:

The answer is 6 and 12

Step-by-step explanation:

1x3= 3

6×3= 18

2×3=6

4×3=12

Answer:

x=6

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

6x=36

÷6 ÷6

x=6

hope this helps,have a great day!!

~Pinky~

Answer:

x=-0.5 or x=-1/2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

7.5/0.75=10

Answer:

10

Step-by-step explanation:

Answer:

69 miles per hour

Step-by-step explanation:

Given

Trip to:

[tex]t_1 = 6[/tex] --- time

[tex]s_1 = 23 + s_2[/tex]

Trip back

[tex]t_2 = 9[/tex]

Required

Determine the average speed to Johannesburg

Average speed is calculated as:

[tex]speed = \frac{distance}{time}[/tex]

Make distance the subject

[tex]distance = speed * time[/tex]

Since distance is constant, then:

[tex]s_1 * t_1 = s_2 * t_2[/tex]

This gives:

[tex](23 + s_2) * 6 = s_2 * 9[/tex]

Open bracket

[tex]138 + 6s_2 = 9s_2[/tex]

Collect like terms

[tex]9s_2 - 6s_2 = 138[/tex]

[tex]3s_2 = 138[/tex]

Solve for s2

[tex]s_2 = 138/3[/tex]

[tex]s_2 = 46[/tex]

Recall that:

[tex]s_1 = 23 + s_2[/tex]

[tex]s_1 = 23 + 46[/tex]

[tex]s_1 = 69[/tex]

Answer:

perimeter: 36

area: i dont know sorry

Step-by-step explanation:

Answer:

[tex]\angle 1 = 99^\circ[/tex]

[tex]\angle 3 = 99^\circ[/tex]

[tex]\angle 4 = 81^\circ[/tex]

Step-by-step explanation:

Given

[tex]\angle 2 = 81^\circ[/tex]

Required

Determine: [tex]\angle 1 . \angle 3 , \angle 4[/tex]

Solving for [tex]\angle 1[/tex], we have:

[tex]\angle 2 + \angle 1 = 180^\circ[/tex] --- angle on a straight line

So, we have:

[tex]\angle 1 = 180^\circ-\angle 2[/tex]

[tex]\angle 1 = 180^\circ-81^\circ[/tex]

[tex]\angle 1 = 99^\circ[/tex]

To solve for [tex]\angle 3, \angle 4[/tex], we have:

[tex]\angle 3 = \angle 1[/tex]

[tex]\angle 4 = \angle 2[/tex] --- Vertically opposite angles

So:

[tex]\angle 4 = 81^\circ[/tex]

[tex]\angle 3 = 99^\circ[/tex]

Answer:

what question is thiswho would count the balls as many which can fit in it

Answer:

Hypothesis: Whitney thought that 5,000 tennis balls would fit into the room, whereas I ... We then figured out that the ceiling juts, the windows, and the corner windows are ... We had to find the height of the room, too, which was about 9 feet.

Answer:

37.9 degrees

Step-by-step explanation:

Using the law of sines, [tex]\frac{\sin(m\angle C)}{21}=\frac{\sin(47^\text{o})}{25}[/tex]. It follows that [tex]\sin (m\angle C) = \frac{21\sin(47^\text{o})}{25} \approx 0.6143371[/tex]. Therefore, [tex]m\angle C = \sin^{-1}(0.6143371)=37.9^\text{o}[/tex].

[tex]a(n) = 3 + 2n[/tex] for [tex]n \ge 0[/tex] functions generate the arithmetic sequence.

It is a "sequence where the differences between every two successive terms are the same" (or) In an arithmetic sequence, "every term is obtained by adding a fixed number (positive or negative or zero) to its previous term".

The first term of an arithmetic sequence is a, its common difference is d, n is the number of terms.

Arithmetic sequence formula is given as, [tex]a_{n} =a+(n-1)d[/tex].

Given arithmetic sequence

[tex]3, 5, 7, 9,.....[/tex]

n is an integer

[tex]a = 3[/tex]

By considering the above arithmetic sequence, we can say that each term in the sequence is in the form of 3 + 2n, where , n ≥ 0.

So, the correct option is A

[tex]a(n) = 3 + 2n[/tex] for [tex]n \ge 0[/tex]

Thus, [tex]a(n) = 3 + 2n[/tex] for  [tex]n \ge 0[/tex]  functions generate the arithmetic sequence.

Find out more information about arithmetic sequence here

https://brainly.com/question/15412619

#SPJ3

Answer:

y = 25 + 5x

Step-by-step explanation:

Since the cost of Twitch is $25 no matter what, that will be our y-intercept (essentially when no other subscriptions are bought). Since with every purchase x we make, we spend an additional $5, the slope of the line (x coefficient) will be 5.

Answer:

13

Step-by-step explanation:

Given :

3x + 1/4 y^2

For x = 3 ; y = 4

3(3) + 1/4(4^2)

9 + 1/4(16)

9 + 4

= 13

Answer:

14

Step-by-step explanation:

[tex] 5 + (2 \times (14 - 9) - 1) \\ = 5 + (2 \times 5) - 1 \\ = 5 + (10 - 1) \\ = 5 + 9 \\ = 14[/tex]

Answer:

your answer is 41.6667

Answer:

41 2/3 yards

Step-by-step explanation:

Divide by 3 because 3ft in one yard

125 / 3 = 41 2/3 yards

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

sqrt 4^2+3^2=5

Answer:

452.4 cm^2

Step-by-step explanation:

[tex]a = 4\pi {r}^{2} \\ a = 4 \pi \times (6)^{2} \\ a = 452.4 \: cm^{2} [/tex]

I hope that is useful for you :)

Answer:

(AUB)UC=2,3,4,5,6,7,8,9

put all these numbers inside curly bracket

Step-by-step explanation:

Answer:

c. 25°

Step-by-step explanation:

Sum of angles in a triangle:

The sum of the measures of the angles of a triangle is 180º.

In this question:

Angles of 3x, 2x-13 and 5x + 3.

The sum is 180º. So

[tex]3x + 2x - 13 + 5x + 3 = 180[/tex]

[tex]10x - 10 = 180[/tex]

[tex]10x = 190[/tex]

[tex]x = \frac{190}{10}[/tex]

[tex]x = 19[/tex]

Measure of each angle:

3x = 3(19) = 57º

2x - 13 = 2(19) - 13 = 38 - 13 = 25º

5x + 13 = 5(19) + 3 = 95 + 3 = 98º

The smallest angle is 25º, and the correct answer is given by option c.

Answer:

find all numbers, stick together o make an uqaion and solve . simplifi if needed

Step-by-step explanation:

Answer:

D as likely as not.

Step-by-step explanation:

......

Answer:

Explanation:

P (even number) = 3/6 = 1/2

⇒ as likely as not

Answer:

[tex]\angle OPS = 142^\circ[/tex]

Step-by-step explanation:

Given

The attached rectangle

[tex]\angle QOR = 142^\circ[/tex]

Required

Determine [tex]\angle OPS[/tex]

[tex]\angle OPS = \angle QOR[/tex] --- vertically opposite angles

Hence:

[tex]\angle OPS = 142^\circ[/tex]