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:

B

Step-by-step explanation:

The side you have drawn in is 4√3 (calculate via pythagoras as √(8²-4²) = √48 = √16·3 = √4²·3 = 4√3)

So the area of the small triangle is 4*2√3 and the area of the small rectangle is 2*4√3. Together makes 4*2√3 + 2*4√3 =  16√3

Answer:

3846.5 in.

Step-by-step explanation:

πr² = (3.14)(35)² = 3846.5 in.

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

a² = b² + c²

where a is the hypotenuse

From the question x is the hypotenuse

So we have

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

2 sqrt(41) =c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10^2 = c^2

64+ 100 = c^2

164 = c^2

take the square root of each side

sqrt(164) = sqrt(c^2)

sqrt(4*41) = c

2 sqrt(41) =c

Answer:

Step-by-step explanation:

We know, for square

[tex](side)^2=(Area)\\=>X^2=8\\[/tex]

∴[tex]X=2\sqrt{2}[/tex] unit

[tex]Now, Side=3X[/tex]

[tex]Then,Area=(3X)^2=(3*2\sqrt{2} )^2=(6\sqrt{2} )^2=72 sq. unit[/tex]

hope you have understood this...

pls mark my answer as the brainliest

The area of square of side 3X is 72 square unit.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

Area of square having side X is 8.

Since, formula for area of square having side X is X².

Implies that,

X² = 8

X = 2√2

The area of square having side 3X
side =3 × 2√2

side = 6√2

The area of square = (6√2)²

                                = 36 x 2

                                = 72

The area of square is 72 square unit.

To know more about Square on:

https://brainly.com/question/28776767

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i hope this helppppsss

Answer:

The correct option is;

Formal

Step-by-step explanation:

The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices

Formal diction is used when when communicating in a situation that is formal

Formal diction uses languages that is devoid of slang and grammatically correct

Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.

Step-by-step explanation:

Soln

Given

Cp of 1 glass tumbler=80.1000

=Rs 80000

Number of broken glass tumbler=50

Number of remaining glass tumbler=1000-50

=950

Sp of one glass tumbler=96

Sp of 950 glass tumbler=96.950

=91200

Now

Sp > Cp so it is profit

Profit%=sp-cp/cp.100

=91200-80000/80000.100

=11200/80000.100

=14%

Answer:

14%profit

Step-by-step explanation:

Cost of 1000 tumblers=1000×80=80,000

50 of them were broken: 1000-50=950

: He sells 950 tumblers of rs.96 each= ( 950×96)

S.P=91200

We can clearly see he gains for rs.11200.

P%=gain/C.P×100

11200×80000×100

=14%

Answer:

That is the graph for y = -|x| + 3

Answer:

46

Step-by-step explanation:

First, start off by substituting the values of a, b, and c, into the equation.

We know a = 5, b = 3, and c = -1, so now substitute.

6a + 2b - 6c + 4

6(5) + 2(3) - 6(-1) + 4

Now that we've substituted the values, we can solve the equation.

6(5) + 2(3) - 6(-1) + 4

30 + 6 + 6 + 4

= 46

So, the answer is 46.

I hope this helps! ôヮô

Answer:

46

Step-by-step explanation:

All you need to do is subsitute the variable with what it says the number is.

Let's first start out with 6a from the equation.  We know that a= 5, so that means it wants you to multiply 6 by 5, which is 30.

Now let's do 2b.  It says b= 3, so do 2 times 3.  It equals 6.

So far we have 30+6-6c+4

Let's do -6c.  We know that c= -1, so let's multiply -1 and -6.  Negative and negative equals positive.  And 6 times 1 is 6.  So the outcome is positive 6.

We got 30+6+6+4

Solve.  

30+6= 36

36+6= 42

And 42+4= 46.  :)

Answer:

87.965

Step-by-step explanation:

surface area of a cylinder,

2πr²+2πrh (where r = radius, h = height)

given, h = 5, r = 2

so,

2πr²+2πrh

= 2π×2²+2π×2×5

= 8π+20π

= 28π

= 87.9645943..

= 87.965 (rounded to the nearest thousand)

Answer:

The upper bound is 97.5 cm

Step-by-step explanation:

The upper bound is given as the value that is larger than or equal to all values in a data set, for example, in the data set, {3, 6, 16, 23, 25}, an upper bound  is 25, however, where the accuracy of the data is given, the upper bound can be found by the following relation

Where the number is given to the nearest 100, add and subtract  half of hundred to obtain the upper bound and lower bound respectively

For the question, given that the size of the television is given as 95 cm, correct to the nearest 5 cm, we add add half of 5 cm to get the upper bound as follows;

Upper bound = 95 cm + 5/2 cm = 97.5 cm

The upper bound = 97.5 cm.

Answer:

The height is 12 cm

Step-by-step explanation:

Hi there!

We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).

This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.  

One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.

Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:

a=15

b=20

c=25  

Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle

15²+20²=25²

225+400=625

625=625

So we can safely say that the triangle is a right triangle

This makes the problem way easier, as there are 2 ways to find the area of a right triangle:

The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2

The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2

First, we need to figure out which sides are the legs, and which side is the hypotenuse

By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs

So let's find the area of the triangle using the legs

A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150

So the area of the triangle is 150 cm²

However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2

Which means that the area is also:

A=[tex]\frac{25x}{2}[/tex] cm²

As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)

[tex]\frac{25x}{2}=150[/tex]

Multiply both sides by 2

25x=300

Divide both sides by 25

x=12 cm

So the height of the triangle is 12 cm

Hope this helps!

Answer:

90

Step-by-step explanation:

Hey there!

Well 90.000 to the nearest tenth is just 90 because there is no decimal places to round.

Hope this helps :)

Answer:

90

Step-by-step explanation:

90 has 0 ones so 90 is just 90, but rounded...

Answer:

Question 1.

Option A: 2m

Question 2

Option D: (1, 1) minimum point

Step-by-step explanation:

Question 1.

Let the original length of the garden (before expansion) be = x

The new length of the garden will be x + 10m

Recall that the garden has a square geometry. That means that its area is obtained by squaring any of its sides.

This means that [tex](x +10)^2 = 144[/tex]

We can now solve for x

[tex](x +10)^2 = 144\\x^2 +20x +100 = 144\\x^2 + 20x =44\\x^2 + 20x - 44=0\\x = 2 or -22[/tex]

x cannot be a negative number, so the original length of a side of the garden is 2m. Option A

Question 2:

The coordinates of the vertex of the graph (turning point) are (x, y) [1,1]

To know whether it is a minimum or maximum point, we will have to check the coefficient of [tex]x^2[/tex] in the equation [tex]y = x^2-2x+2[/tex]

The coefficient of  [tex]x^2[/tex] in the equation is 1. (If no number is present, just know that the coefficient is a one).

If the coefficient is positive, then the point is a minimum point. However, if it is negative, then the point is a maximum point.

Our coefficient is positive hence, the graph has a minimum point.

Answer:

Step-by-step explanation:

To find the value of h use the formula for finding the slope of a line

That's

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Where ( x1, y1) and (x2 ,y2) are the points

From the question

slope = - 3

The points are [4,-9] and [-3,h]

Substitute these values into the equation

We have

[tex] - 3 = \frac{h + 9}{ - 3 - 4} [/tex]

[tex] - 3 = \frac{h + 9}{ - 7} [/tex]

Cross multiply

That's

- 3(-7) = h + 9

21 = h + 9

h = 21 - 9

We have the final answer as

Hope this helps you

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:

Hello

Step-by-step explanation:

Axis of symmetry is vertical:

x=-7 (since (-7,-3) is the vertex)

Answer:

x = -7

Step-by-step explanation:

y = (x+7)^2 -3

This is in vertex form

y =a(x-h)^2+k  where (h,k) is the vertex and the line of symmetry for a vertical parabola is x=h

y = (x- -7)^2 -3

x = -7

1.  - 62.34

2. - 1.4997

3. - $76.49

4. - 23.29

5. - 0.27

6. - $28.26

7. - 0.378

8. - 7.08

9. - 0.3

10. - 1.64

Answer:

1. 62.34

2. 1.4997

3. $76.49

4. 23.29

5. 0.27

6. $28.26

7. 0.378

8. 7.08

9. 0.3

10. 1.64

Answer:

8 / sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan A = BC / AC

tan 30 = BC / 8

8 tan 30 = BC

8 * sqrt(3)/3 = BC

8/3 sqrt(3) = BC

Answer:

Does the answer help you?

Answer:

i think the answer is either $68.25 or $110

i hope this helped

Answer:

The critical value of F for this situation is 2.975.

Step-by-step explanation:

A test is being performed to determine if a particular drug, smartozine, affects maze learning in rats.

The groups are divided as follows:

So, there were in total k = 4 groups with n = 30 rats.

The significance level of the test is, α = 0.05.

Compute the critical value of F as follows:

[tex]F_{\alpha, (k-1, n-k)}=F_{0.05, (4-1, 30-4)}=F_{0.05, (3,26)}=2.975[/tex]

*Use the F-table.

Thus, the critical value of F for this situation is 2.975.

The critical value of F for this situation has been 2.975.

The F value has been the statistical factor that has been used for the determination of the significance of the test.

The high F value has been the representation of the rejected null hypothesis, while the low  F value represents the accepted hypothesis. The study that has been performed with the rats has:

Number of groups of rats = k = 4

Total number of rats = n = 30

The 0.05 significance test has been performed, thus the value of α has been 0.05.

The value of F can be given as:

Critical value = [tex]\rm F_\alpha_\;_,(_k_-_1,_n_-_k_)[/tex]

Substituting the values:

Critical value = [tex]\rm F_0._0_5,_(_4_-_1,_3_0_-_4_)[/tex]

Critical value = 2.975

Thus, the critical value of F for this situation has been 2.975.

For more information about the F value, refer to the link:

https://brainly.com/question/11566053

Answer:

O lines and line t Intersect at Point P

Answer: Choice C

i/j = h/k

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

Explanation:

The triangle proportionality theorem basically says that if we draw a parallel line somewhere inside the triangle like this, then we'll split the sides into smaller pieces that are proportional to one another (eg: the longer side is say 3 times longer than the shorter side for each piece of the original triangle).

One statement we can make is j/k = i/h. This then can be rearranged into i/j = h/k after doing a bit of algebra. Other equations are possible, so there are many combos we could try.

Answer:

D: k*x=y

Step-by-step explanation:

a proportional relationship is basically a linear equation (y=mx+b)

Answer:

c   1/2

Step-by-step explanation:

You are incorrect.

We are going from ABCDEFGH to A'B'C'D'E'F'G'H'. We are going from the large octagon to the small octagon. The scale factor of a dilation is the number you multiply the original lengths to get the lengths of the dilation.

[tex]scale~factor = \dfrac{length~of~dimension~in~dilated~image}{length~of~corresponding~dimension~in~original~figure}[/tex]

Look at point (6, 0) which becomes (3, 0) in the dilation.

The distance from the origin to (6, 0) is 6 units.

The distance from the origin to (3, 0) is 3 units.

scale factor = dilated/original = 3/6 = 1/2

The scale factor of the dilation is 1/2.

Also look at segment AB whose length is 4. The length of segment A'B' is 2.

scale factor = dilated/original = 2/4 = 1/2

Answer: 1/2

Answer:

82

Step-by-step explanation:

78 + 4 = 82

Answer:

82 students

Step-by-step explanation:

The chart has a total of 82 students in the 18 to 22 age category, as 78 + 4 = 82.

Answer:

D

Step-by-step explanation:

the first term is 8, the ratio is 1/2 ( 8*1/2 = 4, 4*1/2 = 2, 2*1/2 = 1)

the formula for an explicit geometric formula is :

[tex]a_{n} = a_{1} * r^{(n-1)}[/tex]

plug in your numbers :

[tex]a_{n} = 8 * (\frac{1}{2}) ^{(n-1)}[/tex]

Answer:

C = 16pi or ≈50.24 units

Step-by-step explanation:

(x − 9)^2 + (y − 3)^2 = 64

This equation is in the form

(x-h)^2 + (y-k)^2 = r^2

The radius is 8

The circumference is given by

C = 2*pi*r

C = 2*pi*8

C = 16 pi

Using 3.14 as an approximation for pi

C = 16(3.14)

C ≈50.24

Answer:

Step-by-step explanation:

0.6821 multiplied by 0.0261 is .01754181

putting that into standard from would be 1.754181 x 10^-2