A worker at a snack stand opened a new box of cups. On the first day, the worker used 30 cups from the box. On the second day, the worker used 15% of the remaining cups in the box. A total of 90 cups were used on the second day. What was the original number of cups in the box before any cups were used?

Answer:

Approximately [tex]21.9\; \rm ft[/tex] (assumption: this tree is perpendicular to the ground.)

Step-by-step explanation:

Refer to the diagram attached (not drawn to scale.)

Label the following points:

Segment [tex]\rm SB[/tex] would then denote the wire between the tree and the stake. The question states that the length of this segment would be [tex]24\; \rm ft[/tex]. Segment [tex]\rm AB[/tex] would represent the [tex]1.5\; \rm ft[/tex] between the top of this tree and the point where the wire was connected to the tree.

The question is asking for the height of this tree. That would correspond to the length of segment [tex]\rm AC[/tex].

If this tree is perpendicular to the ground, then [tex]\rm \angle A\hat{C}S =90^\circ[/tex]. Triangle [tex]\rm \triangle BCS[/tex] would be a right triangle with segment [tex]\rm SB[/tex] as the hypotenuse.

The question states that the angle between the wire (segment [tex]\rm SB[/tex]) and the ground (line [tex]\rm SC[/tex]) is [tex]58^\circ[/tex]. Therefore, [tex]\rm \angle A\hat{S}C = 58^\circ[/tex].

Notice, that in right triangle [tex]\rm \triangle BCS[/tex], segment [tex]\rm BC[/tex] is the side opposite to the angle [tex]\rm \angle B\hat{S}C = 58^\circ[/tex]. Therefore, the length of segment [tex]\rm BC\![/tex] could be found from the length of the hypotenuse (segment [tex]\rm SB[/tex]) and the cosine of angle [tex]\rm \angle B\hat{S}C = 58^\circ\![/tex].

[tex]\displaystyle \cos\left(\rm \angle B\hat{S}C\right) = \frac{\text{length of $\mathrm{BC}$}}{\text{length of $\mathrm{SB}$}} \quad \genfrac{}{}{0em}{}{\leftarrow\text{opposite}}{\leftarrow \text{hypotenuse}}[/tex].

Rearrange to obtain:

[tex]\begin{aligned}& \text{length of $\mathrm{BC}$} \\ &= (\text{length of $\mathrm{SB}$}) \cdot \cos\left(\angle \mathrm{B\hat{S}C}\right)\\ &= \left(24\; \rm ft\right) \cdot \cos\left(58^\circ\right) \approx 20.35\; \rm ft\end{aligned}[/tex].

In other words, the wire is connected to the tree at approximately [tex]20.3\; \rm ft[/tex] above the ground.

Combine that with the length of segment [tex]\rm AB[/tex] to find the height of the entire tree:

[tex]\begin{aligned}&\text{height of the tree} \\ &= \text{length of $\mathrm{AC}$} \\ &= \text{length of $\mathrm{AB}$} + \text{length of $\mathrm{BC}$}\\ &\approx 20.35\; \rm ft + 1.5\; \rm ft \\ &\approx 21.9\; \rm ft\end{aligned}[/tex].

Answer:

δy

δx = 2x − 4 + δx;

and the limit as δx → 0 is

dy

dx = lim

δx→0

µδy

δx¶

= 2x − 4.

Step-by-step explanation:

dy/2d=(2-1)(2+3)

dy/2d=4+6-2-3

dy/2d=5

dy=5(2d)=10d

2d=5/dy

dy=5×(5/dy)= 25/dy

2d=5/dy

dy^2=25

dy=√25=5

2d=5/dy=5/5=1

d=1/2

dy=1/2×10=5 y=10

plug all of the values

5/(1/2×2)=5

=

4+6-2-3=5

so finally: 5=5

any questions?

Answer:

it's the last choice, by process of elimination that's the only one that includes the 4. and of course the math adds up

Answer:25 percent

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

3/12 as a present is 25%

Answer:the answer is the first graph

(0,-4) with a slope of 2

Step-by-step explanation:

Answer:

8 cm

Step-by-step explanation:

4+4=8 To get the diameter, double the radius and add them together.

Answer:

24 total arrangements,  

Step-by-step explanation:

thats all i know for this question, the rest are lost within my brain... somewhere

Answer:

7.11 > -7.1

Step-by-step explanation:

Answer:

$11.49

Step-by-step explanation:

Answer:

13 + 6i

Step-by-step explanation:

expand the brackets (basically drop them), then rearrange the numbers (8 + 5 + 7i - i) then you will get your answer.

Answer:

A. 16/20

General Formulas and Concepts:

Trigonometry

Step-by-step explanation:

Step 1: Identify

Angle θ

Opposite Leg = 16

Hypotenuse = 20

Step 2: Find Ratio

Answer:

A. 16/20

Step-by-step explanation:

The sine ratio is the opposite leg over the hypotenuse, opp/hyp.

For angle theta, the opposite leg is 16. The hypotenuse is 20.

sin (theta) = 16/20

Answer: A. 16/20

Answer:

113 inches or 3.13889 yards

Answer:

x = 12 and y = 22

Step-by-step explanation:

It is given that,

3 times the difference of x and y is -30

3(x-y) = -30

3x-3y = -30 ....(1)

2/3 of x plus 1/2 of y is 19.

[tex]\dfrac{2x}{3}+\dfrac{y}{2}=19\\\\\dfrac{4x+3y}{6}=19\\\\4x+3y=114\ ...(2)[/tex]

Add equation (1) and (2).

3x-3y + 4x+3y = -30 +114

7x = 84

x = 12

Put the value of x in equation (1)

3x-3y = -30

3(12)-3y = -30

36+30 = 3y

3y = 66

y = 22

Hence, the value of x and y are 12 and 22.

Answer:

Right

Step-by-step explanation:

Trust me

Answer:

lion

Step-by-step explanation:

you multiply what is outside the parenthesis to everything inside the parenthesis

Answer:

quiz let or brainy helps me just look up the chapter question and you will get the answer

Step-by-step explanation:

hope this helps

f(x) can be considered as a linear function because of the following conclusions -

1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.

2 → The slope of the function is constant.

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 the following statement representing a function - f(x), that models the depth of water in a wading pool that is filling at a rate of 11 gallons per minute.

Assume that we represent the depth of the water rate by [y] and the time in minutes by [m]. We can write the function f(x) as -

y = f(x) = 11m

This is a linear relation and its graph will be a straight line passing through origin.

From this equation, we can make the following conclusions -

1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.

2 → The slope of the function is constant.

Therefore, f(x) can be considered as a linear function because of the following conclusions -

1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.

2 → The slope of the function is constant.

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

brainly.com/question/2954112

#SPJ6

Answer:

y= -4x+4

Step-by-step explanation:

so the slope is -4x

Answer:

5/2 is the slope

Step-by-step explanation:

Rise/Run= 5/2

so, slope=5/2

Answer:

x^2+x-6

Step-by-step explanation:

i did a thing

hope this is correct and helps

Answer:

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

Step-by-step explanation:

Hello!

We can utilize the factored form of a parabola to find a possible equation.

Factored Form: [tex]y = a(x - h)(x - k)[/tex]

Since the roots of the parabola are given, we can plug in the roots for h and k, and plug in 1 for a and multiply to find the equation.

One possible equation is [tex]y = x^2 + x - 6[/tex].

Answer:

1013500000

Step-by-step explanation:

Addition, mate.

it is 1,013,500,000

Step-by-step explanation:

Answer:

%50

Step-by-step explanation:

hope this helped luv!

Answer:

d=-13

Step-by-step explanation:

Let's solve your equation step-by-step.

−7(6+d)=49

Step 1: Simplify both sides of the equation.

−7(6+d)=49

(−7)(6)+(−7)(d)=49(Distribute)

−42+−7d=49

−7d−42=49

Step 2: Add 42 to both sides.

−7d−42+42=49+42

−7d=91

Step 3: Divide both sides by -7.

−7d−7=91−7

d=−13

Hope this helps have an amazing day :))

Answer:

30 inches

Step-by-step explanation:

240/20=12

12x2.5=30

Answer:

30 inches jrjdbdbrbejjr

Answer:

1

Step-by-step explanation:

2x + 1 = -3x + 6

add 3x

5x + 1 = 6

subtract 1

5x=5

Divide by 5

x=1

If this is correct, please mark brainliest!

Answer:

x=7

Step-by-step explanation:

2x + 1 = 15

-3x+6 = - 15

Since they are equal the equation is true