Why is it easy to hammer a sharp pin than a blunt pin ? *

1.) 70x/100x^2 = 7/10x

2.) 16x^3/24x = 2x^2/3

3.) 7x(2x+1)/21(2x+1) = x/3

4.) 35x - 35/x^2 - 1 =  35/x + 1

5.) x + 7/x^2 + 4x - 21 = 1/x - 3

6.) x^2 - 6x + 5 = x - 5/5

7.) x^2 - 36/x^2 - 3x - 18 = x + 6/x + 3

8.) x^2 - 3x - 10/x^2 + x - 2 = x - 5/x - 1

Answer:

[tex]\sqrt{15}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{3}[/tex] × [tex]\sqrt{5}[/tex] = [tex]\sqrt{3(5)}[/tex] = [tex]\sqrt{15}[/tex]

Answer:

k = 7

Step-by-step explanation:

Applying,

S = (y₂-y₁)/(x₂-x₁)................ Equation 1

Where S = slope of the line.

From the question,

Given: y₂ = 10, y₁ = 4, x₂ = k, x₁ = 1, S = 1

Substitute these values into equation 1

1 = (10-4)/(k-1)

crossmultiplying,

(k-1) = (10-4)

k-1 = 6

k = 6+1

k = 7

Answer:

[tex] {8x}^{3} + 27 \\ = {8x}^{3} + {3}^{3} \\ let : 8x \: be \: a \\ : 3 \: be \: b \\ = > {a}^{3} + {b}^{3} : \\ {(a + b)}^{3} = (a + b)( {a}^{2} + 2ab + {b}^{2} ) \\ {(a + b)}^{3} = ( {a}^{3} + 3{a}^{2} b + 3a {b}^{2} + {b}^{3} ) \\ ( {a}^{3} + {b}^{3} ) = {(a + b)}^{3} - 3ab(a + b) \\ \therefore( {8x}^{3} + 27) = {(8x + 3)}^{3} - 72(8x + 3)[/tex]

Answer:

y = (x - 3)² - 4      Vertex form

(3, -4)    Vertex

Step-by-step explanation:

f(x) = x² - 6x + 5

Complete the square

y = (x - 3)² + 5 - (-3)²

y = (x - 3)² + 5 - 9

y = (x - 3)² - 4      Vertex form

(3, -4)    Vertex

Answer:

a+k ≤ 35

8a+4k ≤ 190

Some possible combinations are 10 adults and 20 kids

5 adults and 29 kids

Step-by-step explanation:

Let k= number of kids

a = number of adults

a+k ≤ 35  since you can have at most 35

8a + 4k ≤ 190 since the most you can spend is 190

Some possible combinations are 10 adults and 20 kids

(10+30 < 35 and 8*10+4*20 = 80+80 =160< 190)

Another possible combination

5 adults and 29 kids

(5+29 < 35  and 5*10 + 4*29 =50+116=166)

Answer:

625 N

Step-by-step explanation:

First, find the area of the square.

Area = side x side

        = 5 x 5

        = 25 m²

Force = pressure x area

          = 25 x 25

          = 625 N

Hope this helps!

Answer:

answer

maybe monomial ...

Answer:

That would be a monomial.

Step-by-step explanation:

Hope this helped!

Answer:

x<7

therefore {x:x<7}

Step-by-step explanation:

x-4<3

x<3+4

x<7

Answer:

Step-by-step explanation:

r =  3 km

Ф = 90°

Area of a sector = [tex]\frac{theta}{360}*\pi *r^{2}[/tex]

                           [tex]= \frac{90}{360}* 3.14 * 3 * 3\\\\= \frac{3.14*3*3}{4}\\[/tex]

                           = 7.065 sq.km

Answer:

Solution given:

r=3km

area of sector bounded by a 90° arc=90°/360°*πr²

=¼*π*3²

=9/4 π or 7.068km²

is a required answer

Answer:

Step-by-step explanation:

vtrtv

Answer:

[tex]43.7[/tex]

Step-by-step explanation:

Since the triangles are similar, the ratio of their corresponding sides is maintained. Therefore, we can up the following proportion to solve for [tex]OP[/tex]:

[tex]\frac{9}{7}=\frac{OP}{34},\\OP=\frac{34\cdot 9}{7}=43.7142857143\approx \boxed{43.7}[/tex]

43.7

Step-by-step explanation:

Since the two are similar triangles, the ratio of the legs of one triangle is equal to the ratio of the legs of the other triangle.

OP/ON = LM/LK

OP/34 = 9/7

Solving for OP,

OP = 34(9/7)

= 43.7

Answer:

Circumference of circle is 9.42cm.

Step-by-step explanation:

Here we have given that A circle with having radius 3 and 1 / 2 cm. And We need to find circumference of circle.

Formula using

Circumference of circle = π × 2 × radius

substitute the value

Circumference of circle = π × 2 × 3 and 1/2 cm.

cancle the 2

Circumference of circle = π × 3 cm

Using π = 22 / 7

[tex] \small \sf \ Circumference \: of \: \: circle = \frac{ 22}{7 }×3 cm \\ [/tex]

[tex] \small \sf \ Circumference \: of \:circle = 9.42 cm[/tex]

Hence, Circumference of circle is 9.42cm.

Answer:

The region with the highest population density is Binky Lee

The region with the lowest population density is ChesLen

Step-by-step explanation:

The population density is the total number of people per unit of land area.

Population density = Total population / land area

Beer Creek = 12,624/3,412

= 3.6998827667057

Approximately, 3.7

Binky Lee = 462/112

= 4.125

Approximately, 4.1

ChesLen = 3,537/1,263

= 2.8004750593824

Approximately, 2.8

Crow's nest = 2,142/612

= 3.5

The region with the highest population density is Binky Lee

The region with the lowest population density is ChesLen

Answer:

1. Binky lee

2. Cheslen

Step-by-step explanation:

Answer:

my answer is in this picture. sorry about my presentation and English

Answer:

5x-5

This equal : 120

2x+10

the second is 60

Answer:

(-8,5)

Step-by-step explanation:

The standard form of the equation of a circle is expressed as;

(x-a)^2+(y-b)^2 = r^2 where;

(a, b) is the centre

r is the radius

Given the equation (x+8)^2+(y-5)^2=14.

Compare the two expressions

-a = +8

a = -8

Similarly;

-b = -5

b = 5

Hence the centre of the circle is at (-8,5)

Answer:

6 ft

Step-by-step explanation:

Side = √area = √36 = 6 ft (we have to find a positive number that multiply by itself gives 36

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Rule:

if A+B = 90, then cos(A) = sin(B) and sin(A) = cos(B)

This can be rephrased into cos(A) = sin(90-A) and sin(A) = cos(90-A)

We'll focus on the second case sin(A) = cos(90-A)

Simply replace A with x and we have the same idea.

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So,

sin(x) = cos(90-x)

cos(90-x) = sin(x)

cos(90-x) = 4/5

You can prove this by drawing out a right triangle as shown below.

Answer:

6 sides

Step-by-step explanation:

The interior angle and the exterior angle sum to 180° , then

exterior angle = 180° - 120° = 60°

The sum of the exterior angles of a polygon is 360° , so

number of sides = 360° ÷ 60 = 6

Answer:

6 sides

Step-by-step explanation:

180 - 120 =60°

sum of exterior angles is 360°

therefore , 360°/60°

ans = 6 sides

Good luck :-)

Answer:

10√3m

Step-by-step explanation:

Given :-

We need to find the height of the pole . We are given here base. Therefore using ratio of tan ,

=> tan 60° = p/b

=> √3 = h / 10 m

=> h = 10 m× √3

=> h = 10√3 m

Answer:

Step-by-step explanation:

line HI

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Explanation:

You could use synthetic division or polynomial long division to find the answer, but a much quicker way is to apply the remainder theorem.

That theorem says that if we divide p(x) over (x-k), then the remainder is p(k).

We're dividing over x+3, or x-(-3), so we can see that k = -3 in this case.

Plug this into the function

f(x) = x^3+5

f(-3) = (-3)^3 + 5

f(-3) = -27 + 5

f(-3) = -22 is the remainder

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If you want to use polynomial long division or synthetic division, then check out the diagram below.

Answer:

the index of y is -2

Step-by-step explanation:

[tex]y^{-2}[/tex]

=[tex]\frac{1}{y^2}[/tex]

Answer:

Roger

Step-by-step explanation:

Since he is attending more shows, he will benefit. He will save a net amount of $40

Answer:

roger

Step-by-step explanation:

Answer:

1/ 4^2

Step-by-step explanation:

4^4 * 4^-6

We know that a^b * a^c = a^(b+c)

4^(4-6)

4^-2

We also know that a^-b = 1/a^b

1/4^2