20x4=10
30x13=12
10x12=3
40x11=

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².

a = 51 m, b = 37 m, c = 20 m

semiperimeter:  p = (51+37+20):2 = 54 m

Area of triangle:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2[/tex]

Rate:  ₹ 3 per m².

Cost:  ₹ 3•306 = ₹ 918

2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.

a = 5 cm

a+2b = 11 cm  ⇒  2b = 6 cm   ⇒  b = 3 cm

p = 11:2 = 5.5

[tex]A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2[/tex]

3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

[tex]A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2[/tex]

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

2x + 2•3x = 32 cm  ⇒ 8x = 32 cm   ⇒  x = 4 cm  ⇒ a = 8 cm, b = 12 cm

p = 32:2 = 16 cm

[tex]A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2[/tex]

Answer:

The square root of a prime number is always an irrational number, then the product of the square root of a prime number and a nonzero rational number is equivalent to:

"the product of an irrational number and a rational number different than zero...."

We know that the product of an irrational number and a rational number (different than zero) is ALWAYS an irrational number.

Then "When is the product of the square root of a prime number and a nonzero rational number a rational number?"

Never, the product will always be irrational.

Answer:

x=23, y=14

Step-by-step explanation:

The triangles are indeed simular

Answer:

10

Step-by-step explanation:

Given that:

There are a total of 5 members on a student council.

2 of these members will serve in Spring Formal Committee.

To find:

How many possible spring formal committees can be there ?

Solution:

If the observe this problem closely, we are actually asked nothing but the number of ways to select 2 members out of 5.

This is a simple selection problem in which we have to find the number of ways to select [tex]r[/tex] objects out of [tex]n[/tex].

The number of ways = [tex]_nC_r =\frac {n!}{r!(n-r)!}[/tex]

Here,

[tex]n = 5\\r=2[/tex]

Hence, the required number of ways are:

[tex]_5C_2 =\frac {5!}{2!(5-2)!}\\\Rightarrow \dfrac {5!}{2!3!} = \dfrac {5\times 4\times 3!}{2!3!}\\\Rightarrow \dfrac {5\times 4}{2} = \dfrac{20}{2}\\\Rightarrow \bold{10}[/tex]

So, the number of possible spring formal committees are 10.

Answer:

domain (-inf, +inf)

range [-30, +inf)

y-int = -30

x-int = -10, 3

Step-by-step explanation:

Answer:

  y = 3x -7

Step-by-step explanation:

The 2-point form of the equation of a line is useful for this.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (-1 -(-4))/(2 -1)(x -1) -4

  y = 3(x -1) -4

  y = 3x -7

Answer:

$288

Step-by-step explanation:

Answer:

  x ≠ 5

Step-by-step explanation:

For the two points to represent a function, the value of x cannot be repeated. The only restriction on the values of x and y is that x is not 5. (x can be anything but 5.)

Answer:

The value of x can be

✔ any real number except 5

.

The value of y can be

✔ any real number

Step-by-step explanation:

i got it correct on edguinty

Answer:

11.4

Step-by-step explanation:

You find the square root

Answer: 3 toppings

Step-by-step explanation:

Let x=the number of toppings

12+2.5x=19.5

     2.5x=7.5

           x=3

Hope this helps!! :)

Please let me know if you have any question

Answer:

[tex]=\left(\frac{15}{2},\:\frac{5}{2}\right)[/tex]

Step-by-step explanation:

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(6,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:1\right)\\\\=\left(\frac{9+6}{2},\:\frac{1+4}{2}\right)\\\\=(\frac{15}{2} , \frac{5}{2} )\\\\[/tex]

Answer: 24%

Step-by-step explanation:

There are a total of  2610 graduates and if that is the divided by the total which is  10730   you will get 0.2432   which is about 24%

Answer:

24%

Step-by-step explanation:

I checked it on the test to make sure, I have acellus too.

Answer:

[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]

Step-by-step explanation:

Let be [tex]f(x,y) = \log_{4}(2\cdot x^{2}-20\cdot x +12\cdot y)[/tex], this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:

[tex]r_{1,2} = \frac{20\pm \sqrt{(-20)^{2}-4\cdot (2)\cdot (12\cdot y)}}{2\cdot (2)}[/tex]

[tex]r_{1,2} = 5\pm \sqrt{25-6\cdot y}[/tex]

The polynomial in factorized form is:

[tex](x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})[/tex]

The function can be rewritten and simplified as follows:

[tex]f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})][/tex]

[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]

Answer:

53°, 127°, 127°

Step-by-step explanation:

Two intersecting lines form two pairs of angles:

So if one of the angles is measured 53°, then the other angles are:

Answer:

[tex]x<1[/tex]

Step-by-step explanation:

So we have the inequality:

[tex]1+7x+5x<13[/tex]

First, combine like terms:

[tex]1+12x<13[/tex]

Subtract 1 from both sides:

[tex]12x<12[/tex]

Divide both sides by 12:

[tex]x<1[/tex]

And that's our answer :)

Answer:

Step-by-step explanation:

12x + 1 < 13

12x < 12

x < 1

Answer:

Step-by-step explanation:

Using the formula for calculating the standard error of the mean to get the standard deviation. The standard error of the mean is expressed as;

SE = S/√n where;

S is the standard deviation

n is the sample size

Given SE = 25 months and n = 1, on substituting this parameters into the formula, we will have;

25 = S/√1

25 = S/1

cross multiply

S = 25*1

S = 25 months

Hence the standard deviation based on the sample is 25 months

Answer:

z = -5

y = 1

x = 4

Step-by-step explanation:

2z = -10 ➡ z = -5

4y -(-5) = 9 ➡ 4y = 4 and y = 1

2x + 3 + (-5) = 6 ➡ 2x = 8 and x = 4

Answer:

Lulu's money = £81

Ruby's money= £108

Emma's money= £72

Step-by-step explanation:

Let

Lulu's money = x

Ruby's money= y

Emma's money= z

x+y+z= 261

Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.

2/3x = 1/2y= 3/4z

2/3x= 1/2y

4/3x= y

2/3x= 3/4z

8/9x= z

x+y+z= 261

x+4/3x+8/9x= 261

9x+12x+8x= 2349

29x= 2349

X= 81

4/3x= y

4/3(81) =y

108= y

8/9x= z

8/9(81)= z

72= z

Answer:

Step-by-step explanation:

Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.

1 answer

·

Top answer:

Answer:Lulu= £81Ruby=£108Emma=£ 72

Answer:

($3.75)n ≤ $20

Step-by-step explanation:

Represent this number by n.  Then the total purchase price can be represented by ($3.75)n ≤ $20, which is appropriate because Cooper can't spend more than $20.

The desired inequality is ($3.75)n ≤ $20.  If a solution is desired, divide both sides by $3/75):

        $20

n ≤ ______ = 5 1/3.

      $3.75

Cooper can purchase up to 5 whole packs of paper and have a bit of money left over.

Answer:

B) 14

Step-by-step explanation:

We can plug in the values of m and p into the equation:

1/2 m + 3p = 1/2 (16) + 3 (2) = 8 + 6 = 14.

Answer:

The eight in the first number is ten times larger than the eight in the second number.

Answer:

The answer is 615 inches

Step-by-step explanation:

The formula for solving the area of a circle is :

A= 1/4 π d^2

So since we only know the diameter the formula would be:

A= 1/4 of 3.14 x 28^2

Hope this helped :)

Answer:

a. (0,0), (2,0), (4,0)

b. (0,0)

Step-by-step explanation:

To find the x-intercept points, you set the equation equal to 0.

0=x³-6x²+8x                                [factor out an x]

0=x(x²-6x+8)                                [factor (x²-6x+8)]

0=x(x-2)(x-4)                               [set each factor equal to 0]

x=0

x-2=0                                           [add both sides by 2]

x=2

x-4=0                                            [add both sides by 4]

x=4

Now, we know our x-intercept points: (0,0), (2,0), (4,0).

To find the y-intercept points, we know that it is located on the y-axis, meaning x=0. We plug in 0 for x, and we will know our y-intercept point.

y=(0)³-6(0)²+8(0)                         [multiply]

y=0

The y-intercept point is (0,0).

Answer:

GE = 11 cm.

Step-by-step explanation:

The figure provided is attached below.

The information given is:

CD = 11.5

DE = 5.3

BC = 8

AH = 11

Perimeter = 73.8

BC = FG = EF

HA = GH

AB = GE

The perimeter of any figure is the sum of all its sides.

The perimeter of the figure provided is:

Perimeter = AB + BC + CD + DE + EF + FG + GH + HA

Perimeter = AB + BC + CD + DE + BC + BC + HA + HA

         [tex]73.8=AB+8+11.5+5.3+8+8+11+11[/tex]

         [tex]73.8=AB+62.8[/tex]

         [tex]AB=11[/tex]

The value of side AB is 11 cm.

Then the value of GE is also 11 cm.

Prime factorization of 100 is 2 * 2 * 5 * 5

100 as a product of prime factors will be 2 ×2×5×5 .

Given,

Number = 100

Now,

To write 100 as prime factor product ,

Take LCM of 100

LCM 100 = 2 ×2×5×5

Thus the factors obtained in the LCM is prime factors only .

So we can write 100 as the product of prime factors:

100 = 2 ×2×5×5

Know more about prime factors,

https://brainly.com/question/29763746

#SPJ6

Answer:

75%

Step-by-step explanation:

Answer:

6/8

Step-by-step explanation:

An easy way to do this is to draw a giant rectangle. when you do you simply want to stay a line going straight across in the middle. draw 3/4 ontop and 6/8 on the bottom. or another fraction that's close to it. then shade in 3/4 and the same with 6/8. if the shading is the same length, that's how you know it's equivalent

Answer:

A) 22812 hotdogs per run

B) 75 runs/yr

C) 4 days in a run

Step-by-step explanation:

We are given;

Production rate;p = 5750 per day

Steady Usage rate;u = 270 per day

Setup cost of hotdog;S = $67

Annual carrying cost (H) = 47 cents = $0.47 per hot dog

No. of Production days; d = 297 days

A) Let's first find the annual demand given by the formula;

Annual demand;D = pd

D = 5750 × 297

D = 1707750 hot dogs/yr

Now, formula for optimal run size is given by;

Q_o = √[(2DS/H) × (p/(p - u))]

Plugging in the relevant values gives;

Q_o = √[(2 × 1707750 × 67/0.47) × (5750/(5650 - 270))]

Q_o =√520375454.7971209

Q_o = 22812 hotdogs per run

B) formula for Number of runs per year is given as;

No. of Runs = D/Q₀

Thus;

no. of runs = 1707750/22812

no. of runs ≈ 75 runs/yr

C) Length of a run is given by the formula;

Length = Q₀/p

Length = 22812/5750

Length ≈ 4 days in a run

Answer:

X = 6

Step-by-step explanation:

Subtract 1 x from both sides so the equation will be 3x = 18.  Then divide 3x by 3 and 18 by 3 to get 6

Answer: [tex]x=6[/tex]

Subtract x from both sides

[tex]4x-x=x+18-x\\3x=18[/tex]

Divide both sides by 3

[tex]3x=3=18/3\\x=6[/tex]