Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of theflagpoleat an angle of elevation 300 . When he moved 10 m towards the flag post the angle of elevation of the top of the flagpole increased to 450. What is the height of the flag pole?

Answer:

The perimeter of the actual playground is 22000 units

Step-by-step explanation:

By measurement, the width of the scale drawing = 16 units

The breadth of the scale drawing = 6 units

Therefore, given that the scale is 1:500, we have that the actual dimensions of the playground are;

Actual width of the playground = 500×16 = 8,000 units

Actual breadth of the playground = 500×6 = 3,000 units

Therefore;

The perimeter of the actual playground = 2 × 8000 + 2 ×3000 =  22000 units.

Answer:

(1,-1)

Step-by-step explanation:

If you try plugging in the numbers for x in the equation y > Ix + 1I - 1, you'll find the answer.

Answer:

I think the answer should be 112

I'm guessing the supports in the water are equally distanced. Therefore, I'd divide 168 by four to get a singular distance between two supports. I got 42 yards.

Answer:

3

Step-by-step explanation:

Adjacent angles have a common side and no common interior points.

2015:

250 members

$95 annual subscription

2016

250 members + 4%

$95 annual subscription + 6%

Work:

250 x 1.04 = 260

95 x 1.06 =  100.7

260 x 100.7 = 26,182

Thus, the club makes $26,182 from 260 members who pay a subscription of $100.7

Answer:

Step-by-step explanation:

[tex] 3{x}^{4} - 48[/tex]

Factor out 3 from the expression:

[tex]3( {x}^{4} - 16)[/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex],factor the expression

[tex]3(( {x}^{2} ) ^{2} - {(4)}^{2} )[/tex]

[tex]3( {x}^{2} - 4)( {x}^{2} + 4)[/tex]

Again, factor using the formula of [tex] {a}^{2} - {b}^{2} [/tex]

[tex]3(x - 2)(x + 2)( {x}^{2} + 4)[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

3(x − 2)(x + 2)(x2 + 4)

Step-by-step explanation:

Took the quiz and got it right hope this helps :) , you can check out the other answer for explanation.

Answer:

The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle

Use rule ; SOHCAHTOA .Where sin x = opp/hyp

cos x = adj/hyp

tan x= opp/adj

Substitute the given values for the three sides

into any of the above rules

[tex]example = Hyp = 2\\opp = 1\\sin- x = 1/2\\x = sin^{-1} 1/2\\x = 30[/tex]

Step-by-step explanation:

I Hope It Helps :)

Answer:

7 formas

Step-by-step explanation:

En la pastelería, se han preparado 30 pasteles.

Cada bandeja contendrá la misma cantidad de pasteles.

Para encontrar de cuántas maneras puedes ponerlos, tenemos que encontrar los factores de 30. Ellos son:

1, 2, 3, 5, 6, 10, 15, 30

Esto significa que podemos tener:

30 bandejas que contienen 1 bandeja cada una

15 bandejas con 2 tortas cada una

10 bandejas con 3 tortas cada una

6 bandejas con 5 tortas cada una

5 pasteles que contienen 6 pasteles cada uno

3 bandejas con 10 pasteles cada una

2 bandejas con 15 tortas cada una

Esto significa que hay 7 formas de colocar los pasteles.

Answer:

Option B.

Step-by-step explanation:

From the given graph it is clear that it is a V-shaped graph. It means, it is the graph of absolute function.

The vertex form of an absolute function is

[tex]y=a|x-h|+k[/tex]

where, a is a constant and (h,k) is the vertex.

From the given graph it is clear that the vertex is at (7,-3). It means h=7 and k=-3.

[tex]y=a|x-(7)|+(-3)[/tex]

[tex]y=a|x-7|-3[/tex]    ...(1)

It passes through (4,0).

[tex]0=a|4-7|-3[/tex]

[tex]3=3a[/tex]

[tex]1=a[/tex]

Put this in (1).

[tex]y=1|x-7|-3[/tex]

[tex]y=|x-7|-3[/tex]

Therefore, the correct option is B.

Answer:

Solution,

Let the length of tunnel be 'l'

Area=25 m^2

Volume of tunnel= cross sectional area* length

[tex] or \: 575 = 25 \times l \\ or \: l = \frac{575}{25} \\ l = 23 \: m[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

$35.2

Step-by-step explanation:

Marked price of hat = $40

Sale discount = 20%

discount in $ = 20% of $40 = 20/100 * 40 = $8

Thus, sale price = marked price - sale discount = $40 - $8 = $32

Now it is given that there is sales tax of 10%

This sales tax will be applied on sale price

thus,

sales tax in dollars = 10% of sale price of hat = 10/100 * $32 = $3.2

Total price paid for hat = Sale price+ sales tax = $32 +$3.2 = $35.2

Thus, Bob ended up paying $35.2 for the hat.

Answer:

49/90 is simplified

Step-by-step explanation:

Answer:

Step-by-step explanation:

49/90

Answer: Distance is 17

Step-by-step explanation:

[tex]d = √((x2-x1)2 + (y2-y1)2)[/tex]

[tex](x2-x1) = (2 -6) = 8[/tex]

[tex](y2-y1) = (17 - 2) = 15[/tex]

Add them all together

[tex](8)2 + (15)2 = 64 + 225 = 289[/tex]

Square 289

[tex]\sqrt{289} =17[/tex]

Step-by-step explanation:

The formula the amusement parc use is  100y-39000=55(x-800)

The slope intercept form of a function is wriiten generally as:

y = mx+c

Let's rewrite our equation in the precedent form

The slope intercept form of this equation is:

y= 0.55x-50

Answer:

y=55x+38992

Explanation:

You have to turn the equation into the form y=mx+b

Step 1: Get y by itself(divide both sides by 100)

100y-39,000=55(x-800)

100/100y-39,000=55(x-800)/100

y-39,000=55(x-800)/100

Step 2: Get y by itself(+ 39000 to both sides)

y-39,000=55(x-800)/100

 +39,000=55x-800/100+39,000

y=55x-800/100=39,000

Step 3: Simplify

y=55x+38992

Answer:

Supongo que tenemos dos ángulos A y B

"la mitad de A mas la tercera parte de B es igual a 15°" (también supongo que son grados)

A/2 + B/3 = 15°

A/2 = 15° - (B/3)

A = 30° - 2*(B/3)

Ahora queremos calcular:

2*sin(3*A)/cos(2*B)

pero podemos reemplazar A por lo que tenemos arriba:

2*sin(3*(30° - 2*(B/3)))/cos(2*B)

2*sin(90° - 2*B)/cos(2*B)

y como sabemos,  

Sin( 90° - x) = Sin(90°)*cos(-x) + cos(90°)*sin(-x) = cos(-x) = cos(x)

entonces:

2*sin(90° - 2*B)/cos(2*B) = 2*cos(2*B)/cos(2*B) = 2*1 = 2.

Answer: A

Step-by-step explanation:

So we know that to find the area of a triangle you have to multiply the base times the height and divide it by two or multiply it by 1/2.Looking the information given it say that theta is equal to 26 degrees  and the length of a or the hypotenuse is 25 and b which in this case is the base is 32. So the information gives us the base but now we need to find the height.

To find  H we need to apply trigonometry solve for h the height.

As we could see theta which is 26 degrees is opposite the height and we know the hypotenuse length. So using soh cah toh we have to know that the length of h is  going to be using the sin formula opposite over hypotenuse.

[tex]sin(26)=\frac{h}{25}[/tex]    solve for h by multiplying both sides by 25.

h= 25 sin(26)

h= 10.96   is being rounded to the nearest hundredth because that is essential

Now we know H is equal to 10.96  which is the Height so now we have all the information we need the height and the base.

Multiply 10.96 by 32 and divide it by 2.

10.96 * 32 =  350.72

350.72 /2 = 176.36  

The best answer is A  because that is the only best approximation to 175.35.

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

B. regular octagon

I hope this will help you

Answer:

2:8 is the ratio to an equal ratio

The width for maximum area will be 40 metres.

Given,Simon has 160 metres of fencing to build a rectangular garden.

The garden's area (in square meters) as a function of the garden's width x(in meters) is modeled by,

[tex]A(x)=-x(x-80)[/tex].

We know that perimeter of rectangle will be,

[tex]P=2(L+B)\\[/tex]

Here p is 160,

So,[tex]160=2(L+B)[/tex]

[tex]\L+B= 80[/tex]

Now we have the sum of length and width off the rectangular garden is 80.

Since,

[tex]A(x)=-x(x-80)\\[/tex]

So, [tex]A(x)=x(80-x)[/tex]

We know that the area of rectangle will be the product of length and , here in question width is [tex]x[/tex] so the length will be[tex](80-x)[/tex].

Now we have to calculate the width for which the area will be maximum.

The area will be maximum when the first derivative of area function will becomes zero.

So,

[tex]\frac{\mathrm{d} }{\mathrm{d} x} A(x)=\frac{\mathrm{d} }{\mathrm{d} x}(-x)(x-80)[/tex]

[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=\frac{\mathrm{d} }{\mathrm{d} x}(-x^{2} +80x)[/tex]

[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=-2x+80\\[/tex]

For maximum area ,

[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=0[/tex]

Hence,

[tex]-2x+80=0\\x=40[/tex]

Hence the width for maximum area will be 40 metres.

For more details follow the link:

https://brainly.com/question/16545343

The maximum area is 1600 sq meters.

The garden's area is modeled by a quadratic function, whose graph is a parabola.

The maximum area is reached at the vertex.

So in order to find the maximum area, we need to find the vertex's y-coordinate.

We will start by finding the vertex's x-coordinate, and then plug that into A(x).

The vertex's x-coordinate is the average of the two zeros, so let's find those first.

A(x)=0    -x(x-80)=0

  ↓                  ↓

-x=0 or x-80=0

x=0 or x=80

Now let's take the zeros' average:

[tex]\frac{(0)+(80)}{2}=\frac{80}{2}=40[/tex]

The vertex's x-coordinate is 40. Now lets find A(40):

A(40)= -(40)(40-80)

        = -(40)(-40)

        = 1600

in conclusion, the maximum area is 1600 square meters.

Hey there! :)

Answer:

x = -6.

Step-by-step explanation:

Given:

[tex]\sqrt[3]{5x-4} = \sqrt[3]{7x + 8}[/tex]

Cube both sides:

5x - 4 = 7x + 8

Subtract 5x from both sides:

-4 = 2x + 8

Subtract 8 from both sides:

-12 = 2x

x = -6.

Answer:

125°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 8 (octagon), thus

sum = 180° × 6 = 1080°

let x represent one of the equal angles, then

3x + 705 = 1080 ( subtract 705 from both sides )

3x = 375 ( divide both sides by 3 )

x = 125

Thus the size of one equal angle = 125°

Answer:

Step-by-step explanation:

Distribute 7 to the first number

7 * -3/4 = -21/4

-21/4 = 5  -1/4

Distribute 7 to the second number

7 * -3

= -21

Put the numbers together

They separated the parenthesis.

So it is still 7 * -3/4

and

7*-3.

Hope this helps,

Kavitha

Answer:

0.0471

Step-by-step explanation:

Here, we want to find the area of the shaded region.

The area of the shade region = 1- area of the unshaded region

The area of the unshaded region is as follows;

P(b) - P(a)

and that is;

P(-1.88<x<2.12) = 0.95294 from z table

So the area of the shaded region = 1-0.95294 =

0.04706 = 0.0471 to 4 d.p

Answer:

A: i

Step-by-step explanation:

i^57=i use the calculator

Answer:

6x to find x on it's own you need to divide by the number infront,

Step-by-step explanation:

Answer:

I guess that we want to create 4 digit numbers that are divisible by 5, only using the odd numbers in the image.

We know that a number is divisible by 5 only if the last digit (the units digit) is a zero or a five, in the image we only have a five, so our 4-digit numbers need to end with a five, so we have a digit fixed in five and the other 3 digits can be other numbers.

We have two different approaches to this:

First, if each odd number can be used only once, we already used the five, so we can use the other 4 numbers.

Then, for the first digit, we have 4 options.

for the second digit, we have 3 options (because we already used one)

for the third digit, we have 2 options (because we already used 2)

then the number of combinations is equal to the product of the number of options for each selection:

C = 4*3*2 = 24 combinations.

The second approach is If the numbers in the image can be repeated (for example, 5555 or 3435 are allowed)

we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third, we also have 5 options, then, with the same reasoning as above, we have:

C = 5*5*5 = 25*5 = 125 combinations.

Answer:

7 red marbles

Step-by-step explanation:

P( red) = red marbles / total marbles = 1/8

We know there are 56 marbles

red marbles/56 = 1/8

Multiply by 56

red marbles = 1/8 *56 = 7

There are 7 red marbles

Answer:

6.04 km

Step-by-step explanation:

From the image attached, both triangles form are similar to each other because their corresponding angles are equal, therefore they are equiangular triangles. equiangular triangles have the same shape but different sizes and the ratio of their corresponding sides are equal.

Therefore since their corresponding sides are equal we can calculate the distance from the main gate to Manatee Springs. It is given by:

[tex]\frac{3500\ yards}{2000\ yards} = \frac{4200\ yards}{x}\\ x= \frac{4200\ yard*2000\ yards}{3500\ yards}=2400\ yards[/tex]

x = 2400 yards.

The distance from the main gate to Manatee Springs = x + 4200 yards = 2400 + 4200 = 6600 yards

The distance from the main gate to Manatee Springs = 6600 yards = (6600 * 0.0009144) km = 6.04 km

The distance from the main gate to Manatee Springs = 6.04 km

Answer:

A ; -4

Step-by-step explanation:

3a = 12b then a = 4b (dividing by 3)

we put 4b in the equation instead of a:

(-4b / b) = -4

.. ..

Answer:

A. -4

Step-by-step explanation:

3a/b = 12

Let b = 2

3a/2 = 12

3a = 24

a = 8

( - a/b)

( - 8/2)

( - 4)