helpp pleacee??!!!!!

Check the picture below atop.

we know is an equilateral triangle, meaning that all its interior angles are 60°, and thus if we run a line from the top vertex as you see there, we end up with a 30-60-90 triangle, either way there's an equation to get its height, and anyhow the altitude of it is 6√3.

As the rectangle moves up and down the triangle, with the rectangle having a width of "w" and a length of "L", the triangle that it forms above itself is a triangle, always with a base of "L" and a height of 6√3 - w.

BTW we laid the rectangle as you see on the bottom side, but laying it anywhere else it'd have ended up in the same arrangement.

well, with the bottom of the rectangle beign parallel to that of the side of the circumscribing triangle, the small upper triangle is similar to the containing triangle by AAA, and since we have similar triangles, we can say that.

[tex]\cfrac{6\sqrt{3}}{12}=\cfrac{6\sqrt{3}-w}{L}\implies \cfrac{\sqrt{3}}{2}=\cfrac{6\sqrt{3}-w}{L}\implies L\sqrt{3}=12\sqrt{3}-2w \\\\\\ L=\cfrac{12\sqrt{3}-2w}{\sqrt{3}}\implies L=12-\cfrac{2w}{\sqrt{3}}\implies L=2\left(6-\cfrac{w}{\sqrt{3}} \right) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Area of the rectangle}}{A=wL\implies A(w)=w\cdot 2\left(6-\cfrac{w}{\sqrt{3}} \right)}\implies A(w)=2\left(6w-\cfrac{w^2}{\sqrt{3}} \right)[/tex]

[tex]\cfrac{dA}{dw}=2\left(6-\cfrac{2w}{\sqrt{3}} \right)\implies \cfrac{dA}{dw}=4\left(3-\cfrac{w}{\sqrt{3}} \right) \\\\[-0.35em] ~\dotfill\\\\ 0=4\left(3-\cfrac{w}{\sqrt{3}} \right)\implies \boxed{w=3\sqrt{3}}[/tex]

hmmm the way I usually run a 1st derivative test is, by using the critical point and slicing from it just a tiny bit, like say 3√3 - 0.000000001 to check the region on the left and then 3√3 + 0.000000001 to check the region on the right.

Check the picture at the bottom, the 1st derivative test more or less gives us those values, positive on the left-side and negative on the right-side, meaning as you can see in the arrows, is a maximum at that point.

[tex]\stackrel{\textit{we know that}}{L=2\left(6-\cfrac{w}{\sqrt{3}} \right)}\implies L=2\left(6-\cfrac{3\sqrt{3}}{\sqrt{3}} \right)\implies \boxed{L=6}[/tex]

The cost of one Gatorade is $32.95.

The total cost of both gatorade is the sum of the value of the gift card and the total cost.

Total cost of both gatorade = value of the gift card + total cost  

$25 + 40.90 = $65.90

In order to determine the cost of one gatorade, divide $65.90 by 2

The cost of one gatorade = Total cost of both gatorade / 2

$65.90 / 2 = $32.95

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Answer:

x ≈ 229.8

Step-by-step explanation:

using the cosine ratio in the right triangle

cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{LM}{KM}[/tex] = [tex]\frac{71}{x}[/tex] ( multiply both sides by x )

x × cos72° = 71 ( divide both sides by cos72° )

x = [tex]\frac{71}{cos72}[/tex] ≈ 229.8 ( to the nearest tenth )

Answer:

I think -1 cuz 2+1--1 so yh I guess

Answer:

a. 3/10

b. 7/10

Step-by-step explanation:

a. Total number of marbles = 10

Number of red marbles = 3

Probability = Number of outcomes/ Total number of outcomes

= 3/10

b. Total number of marbles = 10

Number of red marbles = 3

Number of marbles excluding the red marbles

= 10 - 3 = 7

Probability = Number of outcomes/ Total number of outcomes

= 7/10

Answer:

06>4

Step-by-step explanation:

yes that. is the answer because 06 is greater than 4

Answer: Graph attached

Answer:

view attached graph.

Step-by-step explanation:

0.04x + 0.02y = 0.08.

0.02y = -0.04x + 0.08

/0.02    /0.02

y = -2x + 4

Hope this helps!

Hope it helps you mate

have a good night

If it is reflected about the line x = 5, the new point is (3, 2), (3, 6), (1, 1) and (1, 8)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Given the figure with vertices at (7, 2), (7, 6), (9, 1) and (9, 8). If it is reflected about the line x = 5, the new point is (3, 2), (3, 6), (1, 1) and (1, 8)

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The amount invested in the account that pays a 5% interest is $2100 and the amount invested in the account that pays a 7.5% interest is $1400.

0.05a + 0.075b = (0.06 x $3500)

0.05a + 0.075b = $210 equation 1

a + b = $3,500 equation 2

Where:

a = amount invested in the account that paid a 5% interest

b = amount invested in the account that paid a 7.5% interest

In order to determine this value, multiply equation 2 by 0,05

0.05a + 0.05b = 175 equation 3

0.025b = 35

b = $1400

a + $1400 = $3500

a = $3500 - 1400

a = $2100

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Answer:

inbox I think maybe I can help

Answer:

The correct answer is letter D: tow the car of a homeowner who has parked in the street overnight five nights in a row.

This rule was not mentioned in the said contract. HOA specifically notified that if a person violates the rule more than three times, fines will be given to this violator.

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

did the test got it wrong but it showed the answer

Answer:

66763

Step-by-step explanation:

47000*(1+0.105+0.17)+338+6500

Answer:

Answer:

V = 288π in³

Step-by-step explanation:

[tex]V = \frac{4}{3}\pi r^3[/tex]

The radius is 6 in

[tex]V = \frac{4}{3} \pi (6)^3[/tex]

[tex]V= \frac{4}{3} \pi (216)[/tex]

[tex]V = \frac{4}{3} (216)\pi[/tex]

[tex]V=\frac{864}{3} \pi[/tex]

[tex]V = 288\pi in^3[/tex]

For safety reasons \theta should not be greater than 70 and with the current scenario\theta= 79.52

the ladder will not be safe at this height

\theta= 79.52

Question Parameters:

Joshua has a ladder that is 18 ft long.

He wants to lean the ladder against a vertical wall so that the top of the ladder is 17.7 ft

Generally the equation for the angle ABC is mathematically given as

Let ∠ABC = \theta

In the right angle triangle ACB,

Hence

sin ∠ABC  = AC / AB

sin \theta = 17.7 / 18

[tex]\theta = sin-1 (17.7 / 18)\\\\\theta = 79.52[/tex]

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AB = AX+XB = 6+18 = 24

The ratio of AB to AX is AB/AX = 24/6 = 4

AC = AY+YC = 10+25 = 35

The ratio of AC to AY is AC/AY = 25/10 = 3.5

The results of each division are 4 and 3.5

We do not get the same result, which means that the proportion [tex]\frac{AB}{AX} = \frac{AC}{AY}[/tex] is not true. This is sufficient to prove that the triangles aren't similar. We need them to be in proportion so that we can use the SAS similarity rule.

Answer:

see below

Step-by-step explanation:

let's convert it into slope intercept form first as it will get rid of the decimals. so we must get it to follow the form of y = mx + b.  

so we must isolate the y variable:

- subtract 0.04x from both sides

- now we have 0.02y = 0.08 - 0.04x, and to follow the form this can also be 0.02y = -0.04x + 0.08

- divide both sides by 0.02

- now we have y = -2x + 4, so we know the slope is -2

now lets find the intercepts:

y intercept => set x=0

y = -2(0) + 4

y = 4

so we have (0,4)

x intercept => set y=0

0 = -2x + 4

-4 = -2x

x= 2

now we have (2,0)

graph it:

with two points (the intercepts) and the slope we can find a graph that looks like this

Answer:

miami

Step-by-step explanation:

Answer:

[tex]0.8\, t^{12}[/tex] (assuming that [tex]a \ge 0[/tex].)

Step-by-step explanation:

The rule [tex]a^{2} - b^{2} = (a + b)\, (a - b)[/tex] describes a way for factoring the difference between two perfect squares [tex]a^{2}[/tex] and [tex]b^{2}[/tex].

Setting [tex]a^{2} = 0.64\, t^{24}[/tex] and [tex]b^{2} = 9[/tex] would ensure that [tex](a^{2} - b^{2})[/tex] match the given expression.

Take the square root of both sides of the equality [tex]a^{2} = 0.64\, t^{24}[/tex]. Make use of the fact that for all [tex]x \ge 0[/tex], [tex]\sqrt{x} = x^{1/2}[/tex].

[tex]\displaystyle \sqrt{a^{2}} = \sqrt{0.64\, t^{24}}[/tex].

[tex]\begin{aligned} a &= \left(\sqrt{0.64}\right)\, \sqrt{t^{24}} \\ &= 0.8\, (t^{24})^{1/2}\\ &= 0.8 \, t^{24 \times (1/2)} \\ &= 0.8\, t^{12}\end{aligned}[/tex].

Answer:

x = 13.773

Step-by-step explanation:

cos(∠ABC) = [tex]\frac{BC}{AB}[/tex]

cos(37°) = [tex]\frac{11}{x}[/tex]

x = 13.773

Answer:

your answer is D

yes, I checked

Answer:

[tex]63a - 42b \\ \\ = 21(3a - 2b)[/tex]

# be care#

Answer:

[tex]y=\frac{3}{5} x-3[/tex]

Step-by-step explanation:

Slope-intercept form: y = mx+ b

m = slope

b = y-intercept

Rearrange the equation:

[tex]-20y=-12x+60[/tex]

Divide each side by -20:

[tex]\frac{-20y}{-20} =\frac{-12x}{-20} +\frac{60}{-20}[/tex]

[tex]y=\frac{3}{5} x-3[/tex]

[tex]y=\frac{3}{5} x-3[/tex] is your simplified, slope-intercept form equation.

Togetherly Paige and Malia can complete the job in 2.4 hours,

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
Let the amount of work be x,
Paige complete x work in 6 hours
So the unit rate of doing work of page = x / 6
Similarly,
The unit rate of doing x work of Malia = x / 4

Sum of the unit rate = x / 6 + x /4 = 5x/12
Now,
Time = work/unit rate
Time = x / [5x/12]
Time = 12/5
Time = 2.4 hours

Here, togetherly Paige and Malia can complete the job in 2.4 hours,

Learn more about the rate of change here:

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