solve for x x + 21 = -2x

The constant of variation given that  r varies directly with p and inversely with the product of s and t is one-half

r ∝ p ∝ 1/st

r ∝ p / st

r = Kp / st

Cross multiply

r × st = Kp

Divide both side by p

K = rst / p => constant of variation

K = rst / p

K = (18 × 1/6 × 2) / 12

K = 6 / 12

K = 1 / 2 = one-half

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Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with three sides of a triangle that are as follows ,

And we are asked to :

We know that for finding perimeter of any shape we must have to add all the sides of the shape or ,

[tex] \qquad \: \underline{\boxed{\frak{Perimeter = Sum \: of \: all \: sides}}}[/tex]

Solution : -

( a )

Now adding all the three sides of triangle to find the perimeter .

[tex] \hookrightarrow \quad \: ( x + 5 ) + ( 2 x + 4 ) + ( 2x - 3 ) [/tex]

[tex] \hookrightarrow \quad \: \: x + 5 + 2x + 4 + 2x - 3[/tex]

Combining like terms :

[tex] \hookrightarrow \quad \:x + 2x + 2x + 5 + 4 - 3[/tex]

Now , solving :

[tex] \hookrightarrow \quad \: \red{\underline{ \boxed{ \frak{(5x + 6) \: cm}}}}[/tex]

( b )

Now , we are finding perimeter of triangle when value of x is 10 . So substituting value of x in given sides of triangle ,

First Side :

Second Side :

Third Side :

So , all the sides are 15 cm , 24 cm and 17 cm .

Now , adding all these to find perimeter .

[tex] \hookrightarrow \qquad \: 15 + 24 + 17[/tex]

[tex]\hookrightarrow \qquad \: 39 + 17[/tex]

[tex]\hookrightarrow \qquad \: \red{\underline{\boxed{\frak{56 \: cm}}}}[/tex]

Alternative Solution : -

As above we have find the perimeter of triangle in term of x that is ( 5x + 6 ) cm. So we can put value of x as 10 in this to get perimeter. So ,

Therefore, perimeter of triangle is 56 cm .

To find the perimeter of a shape, we should add all sides , like so :

x+5+2x+4+2x-3

Combine the x's :

x+2x+2x+5+4-3

x+4x+9-3

5x+6

5x+6 cm

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b.

Find the perimeter of the triangle if x = 10

Just write 10 instead of x :

5(10)+6

5(10) simplifies to 50 ↓

50+6

56

hope helpful ~

Answer:

DE=18

Step-by-step explanation:

The reason is because that parallelogram ABCD has most of the sides equal to each other.

The length of DB = 36 and half of 36/2 gets us DE.

DE=36/2=18

DE=18 also equals to BE=18

Diagonals of a parallelogram bisect each other

So

Putting DE=BE

The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees is 0.18.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

In a large company, 45% of the employees wear khaki pants on a daily basis.

40% of employees wearing khaki pants in a random sample of 50 employees

So, 40% of 45% x 50

= [tex]0.40 \times 0.45 \times 50 \\ \\9[/tex]

The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees.

= 9 /50

= 0.18

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Answer:

14x+6+(5x+30+=2190

Step-by-step explanation:

Answer:

about 2195 bacteria

Step-by-step explanation:

After one hour: 800 * 1.4 = 1120

After two hours: 1120 * 1.4 = 1568

After three hours: 1568 * 1.4 = 2195.2

Step-by-step explanation:

y=(8-4x)/2

y=4-2x

I hope it helps

Answer:

y = 4 - 2x

Step-by-step explanation:

4x + 2y = 8

Subtract 4x on both sides,

2y = 8 - 4x

Divide 2 on both sides,

y = ( 8 - 4x ) / 2

y = 4 - 2x

Answer:

 x = -3 , - 15

Step-by-step explanation:

Given:

x² + 18x + 45 = 0

Solve:

[tex]x_{1,\:2}=\frac{-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45}}{2\cdot \:1}[/tex]

Simplify

[tex]-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45=12[/tex]

[tex]x_{1,\:2}=\frac{-18\pm \:12}{2\cdot \:1}[/tex]

Separate the solution

[tex]x_1=\frac{-18+12}{2\cdot \:1},\:x_2=\frac{-18-12}{2\cdot \:1}[/tex]

[tex]x_1=\frac{-18+12}{2\cdot \:1}=-3[/tex]

[tex]x_2=\frac{-18-12}{2\cdot \:1}=-15[/tex]

Thus, the answer are:

[tex]x=-3,\:x=-15[/tex]

Kavinsky

The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.

A rational number is one that has the form p/q, where p and q are integers and q is greater than zero. Some rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The complete question is, Let x = 0.147 and let y = [tex]0.\overline{147}[/tex].  Is x a rational number? Is ya rational number? Which is larger, x or y?

Given the value of x is 0.147. As it can be written in the form of a fraction,

[tex]0.147 = \dfrac{147}{1000}[/tex], we can conclude that x is a rational number.

The value of y = [tex]0.\overline{147}[/tex] can also be written in the form of a fraction,

[tex]0.\overline{147} = \dfrac{147}{999}[/tex], therefore, we can conclude that y is also a rational number.

The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.

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Answer:

$14.55

Step-by-step explanation:

Answer:

27 revolutions

Step-by-step explanation:

Things to remember :

Solving

Answer:

d

Step-by-step explanation:

Answer:

[tex]\sf \boxed{\bold{x=1}}[/tex]

Explanation:

[tex]\rightarrow \sf 7 log_9 (x + 8) = 7[/tex]

divide both sides by 7

[tex]\rightarrow \sf \dfrac{7\log _9\left(x+8\right)}{7}=\dfrac{7}{7}[/tex]

simplify the following

[tex]\sf \rightarrow \log _9\left(x+8\right)=1[/tex]

apply log rules                   [tex]\underline{The \ rule}: \ \bold{log_{b} (a)= c} \ \ \Longrightarrow \sf a = b^c[/tex]

[tex]\sf \rightarrow x+8 = 9^1[/tex]

simplify

[tex]\sf \rightarrow x+8=9[/tex]

subtract both sides by 8

[tex]\sf \rightarrow x=1[/tex]

[tex]\\ \rm\Rrightarrow 7log_9(x+8)=7[/tex]

[tex]\\ \rm\Rrightarrow log_9(x+8)=1[/tex]

[tex]\\ \rm\Rrightarrow x+8=9^1[/tex]

[tex]\\ \rm\Rrightarrow x+8=9[/tex]

[tex]\\ \rm\Rrightarrow x=9-8[/tex]

[tex]\\ \rm\Rrightarrow x=1[/tex]

Answer:

The radius is 7 cm

Step-by-step explanation:

We know the area of a circle is given by

A = pi r^2

49 pi = pi r^2

Divide each side by pi

49 = r^2

Take the square root of each side

sqrt(49) = sqrt(r^2)

7 = r

The radius is 7 cm

Answer:

radius = 7 cm

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

given A = 49π , then

πr² = 49π ( divide both sides by π )

r² = 49 ( take square root of both sides )

r = [tex]\sqrt{49}[/tex] = 7

Answer:

The volume of the cylinder is 141.23 cubic feet

Step by step explanation :

Given-

Now, we know that

where, r is the radius of the cylinder & h is the height of the cylinder.

Now,

Volume of the cylinder = [tex] \frac{22}{7} \times {3}^{2} \times 5[/tex]

[tex] = \frac{22}{7} \times 3 \times 3 \times 5[/tex]

[tex] = 141.428571[/tex] ( approximately )

[tex] = \boxed{ 141.43 \: \mathfrak { {ft}^{3}} }[/tex]

Answer:

1) surface area = 2 · π · r · (r + h)

2) 8x5x6x14x8.94

3) surface area = 2 · π · r · (r + h)

4) 8x14x6

5) 4x4x8

6) 7x8.95x13

7) 3x4x11x3.61 divide by 2

8) 6x6x6 = 36x6 = 216

9) 3x4x10

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph that represents the function

f(x) = (x + 4)(x + 1)(x - 3)

crosses the x-axis three times: at x = -4, x = -1, and x = 3

because we apply the zero product rule and found the roots -4, -1, and 3

x+ 4= 0 → x = -4

x+1 = 0 → x = -1

x-3 = 0 → x = 3

[tex]5x+11x=16x[/tex]

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Distributive Property:

[tex](5x+10x)+(5x+1x)[/tex]

   /    \              /    \

   [tex](16x)[/tex]             [tex](6x)[/tex]

Therfore, by using the distributive property, [tex](5x+10x)+(5x+1x)[/tex], We get [tex]16x[/tex].

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Answer:

see explanation

Step-by-step explanation:

2 chords intersecting inside a circle , then the product of the parts of one chord is equal to the product of the parts of the other chord.

6

BE × ED = AE × CE , that is

10 × 3x = 12(2x + 1) ← distribute parenthesis by 12

30x = 24x + 12 ( subtract 24x from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

then

ED = 3X = 3(2) = 6

7

RJ × JP = SJ × JQ , that is

6 × 3x = 4(4x + 1) ← distribute parenthesis by 4

18x = 16x + 4 ( subtract 16x from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

then

RP = RJ + JP = 6 + 3x = 6 + 3(2) = 6 + 6 = 12

Answer:

Part 1: [ -4 = -8 ]

Part 2: Inconsistent

Step-by-step explanation:

Part 1

1. Move all terms that don't contain x to the right side:

3x - 6y+6y = -12+6y

= 3x = -12 + 6y

2. Isolate x:

[tex]\frac{3x}{3} = \frac{-12+6y}{3}[/tex]

x = -4 + 2y

3. Substitute the new expression into the original:

-4 + 2y - 2y = -8

4. Simplify:

-4 + 0 = -8

[ -4 = -8 ]

Part 2

The two solutions are not equal in value, so, we can conclude that the system of equations has no solution, or is inconsistent.

hope this helps!

Answer:

1. A commercial air carrier determines that the maximum angle of depression of a plane descending to an airport is 11°. Determine horizontal distances

Step-by-step explanation:

Step-by-step explanation:

a) if the population is 3000 and it is being multiplied 1.15 than it is 15%. I found this by multiplying 1.15 by 100 to make it percent than anything over 100 is an increase.

b)im not so sure on this one but I think if t = 0 than it would be p= 3000 x 1.15 x0 which would equal 0

c) p = 3000x 1.15 x 24 p = 82,800

Step-by-step explanation:

pressure = F/A

= 750/ (1.7×9)

= 49 N/m²

Answer:

x=11

Step-by-step explanation:

3x−45=−12

Add 45 to each side

3x−45+45=−12+45

3x = 33

Divide each side by 3

3x/3 = 33/3

x=11

Answer:

10

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

-45 minus 35 is -80 so that's  80 units. and including zero it's 81 units

The shape ABCDE is a regular pentagon with five sides, such that the five sides are congruent

The angle BAE is a vertex angle, and it is calculated using:

BAE = 180 * (n - 2)/n

Where n= 5; i.e. the number of sides.

This gives:

BAE = 180 * (5 - 2)/5

Evaluate

BAE = 108°

Hence, the measure of angle BAE is 108°

When the vertices A and B are joined together, the shape becomes a trapezoid.

Hence, the name of the quadrilateral ABCD is a trapezoid.

See attachment for the new figure.

From the attached figure, we have:

∠EDX + ∠EDC = 180° ---- the sum of angles on a straight line

Where:

∠EDC = ∠BAE = 108°

So, we have:

∠EDX + 108° = 180°

Subtract 108° from both sides

∠EDX = 72°

Hence, the measure of angle EDX is 72 degrees

The quadrilateral BDXE is a parallelogram.

This is so because the opposite sides of BDXE are parallel, but not congruent

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Answer:

77

Step-by-step explanation:

75% of 44 = 33

33 + 44 = 77

Answer:

77.

Step-by-step explanation:

75% of 44

= 3/4 * 44

= 33

33+44

= 77.

Answer:

see below

Step-by-step explanation:

Area = pi r^2     r = radius

  diamter = 94    then radius = 94/2 = 47 cm

area = pi (47)^2 = 2209 pi    or 6939.78  cm^2

Answer:

A ≈ 6,939.8 cm²

Step-by-step explanation:

Given : " the diameter is 94cm "

d = 94

Radius is r = d/2 = 94/2 = 47 cm

Area of a circle is

A= π·r²

A = π·47² ≈ 6,939.8 cm²

Answer:

The value of a side = 5

Step-by-step explanation:

By using PGT theoram

H² = P² + B²

=> 13² = a² + 12²

=> 13² - 12² = a²

=> 169 -144 = a²

=> 25 = a²

=> √25 = a

=> 5 = a

Answer:

a = 5

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

a² + 12² = 13²

a² + 144 = 169 ( subtract 144 from both sides )

a² = 25 ( take square root of both sides )

a = [tex]\sqrt{25}[/tex] = 5