Write the area A of an equilateral triangle as a function of the length s of its sides.

STEP 1: Find the base of the equilateral triangle in terms of s.

STEP 2: The height of an equilateral triangle can be found via the Pythagorean theorem. Use this information to find h in terms of s.

Answer:   3.3 * 10^5

This is approximate. The more accurate value is 3.333 * 10^6 but even that isn't exact because the '3's after the decimal point go on forever

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Work Shown:

(2.5 * 10^8)/(7.5 * 10^2)

(2.5/7.5) * 10^(8-2)

0.3333 * 10^6 .... this is approximate

3.333 * 10^(-1) * 10^6

3.333 * 10^(-1+6)

3.333 * 10^5

3.3 * 10^5

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{3x - 9x + 3y = 1}\\\huge\text{\boxed{\rightarrow} -6x + 3y = 1}\\\huge\text{\boxed{\rightarrow} -6x + 3(3.2) = 1}\\\huge\text{\boxed{\rightarrow} -6x + 9.6 = 1}[/tex]

[tex]\huge\textsf{SUBTRACT \underline{\underline{9.6}} to BOTH SIDES}\\\huge\text{-6x + 9.6 - 9.6 = 1 - 96}\\\\\\\huge\textsf{DIVIDE \underline{\underline{-6}} to BOTH SIDES}\\\\\huge\boxed{\dfrac{-6\mathsf{x}}{-6}= \dfrac{-8.6}{-6}}[/tex]

[tex]\huge\textsf{SIMPLIFY ABOVE \& YOU HAVE YOUR}\\\huge\textsf{RESULT OF THE X-VALUE}\\\\\\\boxed{\huge\boxed{\huge\textsf{x = \bf 1.433333 or } \mathsf{x = \bf \dfrac{8.6}{6}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\boxed{\huge\boxed{\frak{Amphitrite1040:)}}}[/tex]

Answer:

c because 25 members of national club has members which is explained perfectly

Answer:

purchased it for 1600

Step-by-step explanation:

[tex].88x-y\:=\:-16\:\\\:.9x-y\:=\:20[/tex]

Answer:

40

Step-by-step explanation:

Total is 150

Germany=1/3 *150 = 50

Italian= 2/5 * 150 = 60

Total - Germany- Italian= French

150 - 50 -60= 40

it depends upon a persons pace a average pace is 9-10 mins

Answer:

–21.87 ÷ 4.79

≈ -20 ÷ 5

≈ -4

Step-by-step explanation:

front end estimation means to round off to the most left digit.

eg 12 ≈ 10

Answer:

9/16

Step-by-step explanation:

5/8 - 1/4^2

Exponents first

5/8 - 1/16

Get a common denominator

5/8 *2/2 - 1/16

10/16 - 1/16

9/16

Answer:

33/14

Step-by-step explanation:

[tex] - 10 \frac{2}{7} + ( - 4 \frac{4}{11} )[/tex]

[tex] = - \frac{72}{7} \div - ( \frac{48}{11} )[/tex]

[tex] = \frac{72}{7} \times \frac{11}{48} [/tex]

[tex] = \frac{3}{7} \times \frac{11}{2} [/tex]

[tex] = \frac{33}{14} [/tex]

stan dreamcatcher

Answer:

Question number 8 u place the number 1 line before -1 on the left.

Step-by-step explanation:

cuhcuhcuhcuchcuhcuhc

Answer:

4x+11

Step-by-step explanation:

you have to add the like terms,in this case the like terms are 7 and 4.4x isn't a like term cause it has a variable.

so you just have to add 7+4

4x+11

I hope this helps

Step-by-step explanation:

hope this may help you tq

Answer:

288*pi

Step-by-step explanation:

Area=2*pi*(24)^2*(90/360)=288*pi

Answer:

x = 38 is for problem A

x = 180 is for problem C

x = 84 is for problem D

x = 104 is for problem B

Step-by-step explanation:

Explanation for problem A: An angle that has endpoints at the endpoints of an arc is equal to half that arcs angle. (example: in problem A the arc measure is 76 meaning that angle x is equal to half of 76 which is 38. you can also see angle x ends at D and C which are the endpoint of the arc as well) This form of thinking using the rule I mentioned in the first sentence is used to solve each of the problems. Also if the arc measure isn't given and you must solve for it do the opposite; times the angle that has the same endpoints as the arc by 2 (example: In problem B angle ∠S has endpoints of Q and R which are also the endpoints of the arc you're looking for (Arc QR) so since an angle that has the same endpoints as an arc is equal to half that arcs measure, in order to get the arc measure you must times the angle by 2.)

Answer:

(x + 1 , y - 3)

Step-by-step explanation:

Compare x-coordinate of A(-6,1) and A'(-5,-2)

-6 + a = -5

      a = -5 +6 = 1

x- coordinate of A' = x coordinate of A + 1

Compare y-coordinate of A(-6,1) and A'(-5,-2)

1 + a =-2

      a = -2 - 1 = -3

y- coordinate of A' = y coordinate of A - 3

A(-6 , 1) = A'(-6+1 , 1-3) = A'(-5, -2)

D(( -1 , 1) = D'(-1+1, 1 - 3) = D'(0,-2)

C(-2,3) =C'(-2+1, 3-3) = C'(-1,0)

B(-4,3)= B'(-4+1 , 3-3) = B'(-3,0)

Answer:

1, 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

That's an awful lot of points. You don't have to give that many. 10 or 15 points would be more than enough.

The graph touches the x axis at 1 point. That means its basic formula is y = (x - a)^2

Since it  upside down, the formula is y = -(x - a)^2. A couple of other things are true.

a = 1 because that's where the graph touches the x axis. y = - x^2 has shifted 1 unit to the right.

Finally the y intercept is -4 which means that the final equation is y = -4(x-1)^2

That's all preliminary. The actual question is, what does the discriminate look like?

y = -4(x^2 - 2x + 1)

y = -4x^2 + 8x - 4

a = - 4

b = 8

c = - 4

sqrt(b^2 - 4ac)

sqrt(8^2 - 4(-4)(-4) )

sqrt(64 - 64) = 0

The answer is the third one. The answer will always be 0 when the graph touches the x axis and does not go through it.

Answers:

======================================================

How to get those answers:

Let w be the unknown width in centimeters. This variable is some positive real number. This means w > 0 which will be useful later.

The length is "1 cm less than 3 times its width" and it tells us the length is defined by the expression 3w-1. Whatever w is, we triple it to get 3w and then subtract 1 to get the final length.

Multiply the length and width to get the area 102

length*width = area

(3w-1)*w = 102

3w^2-w = 102

3w^2-w-102 = 0

We could guess and check our way to factoring this, but that's not very efficient. The quadratic formula is the better option. It may seem a bit messy, but it's a more direct path that doesn't involve guessing.

[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-102)}}{2(3)}\\\\w = \frac{1\pm\sqrt{1225}}{6}\\\\w = \frac{1\pm35}{6}\\\\w = \frac{1+35}{6}\ \text{ or } \ w = \frac{1-35}{6}\\\\w = \frac{36}{6}\ \text{ or } \ w = \frac{-34}{6}\\\\w = 6\ \text{ or } \ w \approx -5.667\\\\[/tex]

We ignore the second solution (w = -5.667 approximately) because we stated earlier that w > 0. In other words, a negative length does not make sense, so that's why we ignore it.

-----------------

If w = 6 cm is the width, then 3w-1 = 3*6-1 = 18-1 = 17 cm is the length.

Note that length*width = 17*6 = 102 which is the proper area we want. This confirms the answers.

Answer:

72.35%

Step-by-step explanation:

246/340 = .723529

Just multiply it by 100 to get the percentage

.723529 x 100 = 72.3529

Step-by-step explanation:

see the answer in attached picture

pls mark me as brainliest pls

Answer:

If two machine works together it takes 180 minute to complete 6480 shirts

Step-by-step explanation:

2400 ÷ 150 = 6

So here,

1st machine produces 20 shirts per minutes

let, x=minutes for shirt's production

Now,

(16+20)x=6480

36x=6480

x=6480/36

Therefor, x=180 minutes

Answer:

[tex]y=4x-2[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

We're given that the slope is 4. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=4x+b[/tex]

Now, to determine the y-intercept, plug in the given point (1,2) and solve for b:

[tex]2=4(1)+b\\2=4+b\\b=-2[/tex]

Therefore, the y-intercept is -2. Plug this back into [tex]y=4x+b[/tex] as b:

[tex]y=4x+(-2)\\y=4x-2[/tex]

I hope this helps!

[tex]\\ \sf\longmapsto b^2x^2+a^2y^2[/tex]

[tex]\\ \sf\longmapsto b^2(asin\Theta)^2+a^2(bcos\Theta)^2[/tex]

[tex]\\ \sf\longmapsto b^2a^2sin^2\Theta+a^2b^2cos^2\Theta[/tex]

[tex]\\ \sf\longmapsto a^2b^2(sin^2\Theta+cos^2Theta)[/tex]

[tex]\\ \sf\longmapsto a^2+b^2(1)[/tex]

[tex]\\ \sf\longmapsto a^2b^2[/tex]

Answer:

slope is Δy/Δx =

-5/1 = -5

the B intercept is 4

y = -5x + 4

Step-by-step explanation:

Answer: 125 ft.

Step-by-step explanation:

Assuming the perimeter of the park is 400 ft, the equation can be represented as

2l + 2w = 400

Since we know that the width is 50 ft shorter than the length, using algebra, you replace the variable w, with

2l + 2(l-50) = 400

Then, solve for variable l, or length

2l +2l - 100 = 400

4l = 500

l = 125

Now, plug in l and solve for w

2(125) + 2w = 400

250 + 2w = 400

2w = 150

w = 75

2(125) + 2(75) = 400

250+150 = 400

400=400

l = 125, w = 75

So the length is 125 ft

Answer:

125

Step-by-step explanation:

400 is perimeter!

50+w = Length

w = width

Solve:

50+ w + w +w + w + 50 = 400

100 + 4w = 400

4w = 300

w = 75

if w is 75, then length is = 75 +50

Length = 125

Numbers can be estimated by approximating them. So, we need to approximate [tex]\sqrt{71}[/tex] to the nearest integer to get its estimate of the radius in the nearest foot.

The radius to the nearest foot is 8ft

Given that

[tex]r = \sqrt{71}[/tex]

To calculate the radius, we simply determine the square root of 71

[tex]r = 8.42614977318[/tex]

Approximate to the nearest integer

[tex]r = 8[/tex]

Hence, the radius of the circle to the nearest foot is 8ft.

Read more about approximation at:

https://brainly.com/question/9933194

Answer:

x=0  x=4  x=6

Step-by-step explanation:

f(x)=x^3 − 10x^2 + 24x

Factor out the greatest common factor

f(x)=x(x^2 − 10x + 24)

Factor inside the parentheses

f(x)=x(x-4)(x-6)

Setting equal to zero

0 = x(x-4)(x-6)

Using the zero product property

x=0  x-4 = 0   x-6 =0

x=0  x=4  x=6

Answer:

3√3

Step-by-step explanation:

to get x, we divide 6 by 2 and get 3

therefore, we multiply the short leg by √3

the answer finally equals to 3√3

Answer:

[tex]\boxed {\boxed {\sf y=3}}[/tex]

Step-by-step explanation:

We are asked to find y, a missing side in a triangle.

This triangle is special. There is a 30-degree angle and a right angle or 90 degree angle, the unlabeled angle is 60 degrees. This is a 30-60-90 triangle so the sides are always in a specific relationship.

The side across from the 30-degree angle is a, the hypotenuse is 2a, and the side across from the 60-degree angle is √3 a.

y is across from the 30 degree angle, so it is equal to a. However, we have to find a. We are given one side that measures 6. It is the hypotenuse because it is across from the right angle. Therefore, it is equal to 2a.

a is being multiplied by 2. Divide both sides by 2 to solve for a.

y is across from the 30-degree angle, so it is equal to a or 3.

We can also solve using the 3 main trigonometric functions.

y is opposite the 30-degree angle and 6 is the hypotenuse, and we will use sine.

[tex]sin \theta= \frac{opposite}{hypotenuse}[/tex]

[tex]sin (30)= \frac{y}{6}[/tex]

y is being divided by 6. The inverse operation of division is multiplication. Multiply both sides by 6 to solve for y.

[tex]6 * sin(30)= \frac{y}{6} *6[/tex]

[tex]6 * 0.5 = y[/tex]

[tex]3= y[/tex]

The missing side, y , is equal to 3.

Answer:

D. division property of equality

Step-by-step explanation:

The division property of equality tell us basically to divide an equation, we have to divide on both sides.

-5x=4

to isolate x, we would divide -5 on both sides and that would be

-5x/5=4/-5

making x= -4/5, thus make D the correct answer choice

Answer:

A, B, C

Step-by-step explanation:

none of the 4 options changes the shape.

but D changes the size.

C is the only one that also maintains the orientation of the triangle - it only shifts its position.

A and B maintain size and shape, but they do change its orientation.