CH 7 Forces: pages 294 & 296
Calculate net forces. Draw an arrow to show direction. SC.6.P.13.3
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combined Forces
Net Force
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30 N
70 N
30 N
40 N
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60 N
60 N
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18 N 12 N
30N

Answer:

35.1 and 276.48

Step-by-step explanation:

Answer:

The correct answer is: 1.0266 ×104

Step-by-step explanation:

Answer:

It's 7

Step-by-step explanation:

Complete Question

The Hollywood cats are a group of cats that have settled in along the Hollywood Beach in Florida. A group of volunteers feed them and care for them while trying to humanely reduce their numbers (as they are considered a nuisance). If there were 100 cats in the year 2012 and the rate of population change is given

by     [tex]-\frac{1}{4} t-2[/tex]

where t is measured in years, how many cats are projected to be in the group in 2020.

Answer:

The number of total cats left after 8 years T

[tex]T=76[/tex]

Step-by-step explanation:

From the question we are told that

Number of cats 2012 n=100

Number of years t=2012-2020=>8 years

Generally the equation of change in population is mathematically Given as

   [tex]\frac{dp}{dt}= -\frac{1}{4} t-2[/tex]

  [tex]\int dp=\int_0^8 (-\frac{1}{4} t-2)[/tex]

  [tex]p=\frac{-64}{8} -16[/tex]

   [tex]p=-24cats[/tex]

Therefore the number of total cats left after 8 years T is given as

[tex]T=100-24[/tex]

[tex]T=76[/tex]

Answer:

Leena walked 5/7 miles with her friend

Step-by-step explanation:

7/7 = 1

7 +4 =11

Answer:

5/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=2

a=1.25

m=3.75

tell me if u need any steps

Answer:

[tex] x = 6\sqrt{2}[/tex]

Step-by-step explanation:

Reference angle = 45°

Adjacent side = 6

Hypotenuse = x

Applying trigonometric ratio, we have:

[tex] cos(45) = \frac{6}{x} [/tex]

Multiply both sides by x

[tex] x*cos(45) = 6 [/tex]

Divide both sides by cos(45)

[tex] x = \frac{6}{cos(45)} [/tex]

[tex] x = \frac{6}{\frac{\sqrt{2}}{2} [/tex] (cos 45 = √2/2)

[tex] x = \frac{6}*{\frac{2}{\sqrt{2}} [/tex]

[tex] x = \frac{12}{\sqrt{2}} [/tex]

Rationalize

[tex] x = \frac{12*\sqrt{2}}{\sqrt{2}*\sqrt{2} [/tex]

[tex] x = \frac{12*\sqrt{2}}{2} [/tex]

[tex] x = \frac{6*\sqrt{2}}{1} [/tex]

[tex] x = 6\sqrt{2}[/tex]

Answer:

x=1.7320508075688772 or x=−1.7320508075688772

Step-by-step explanation:

(x2−3)(x2+12)=0

x4+9x2−36=0

(x2−3)(x2+12)=0

x2−3=0 or x2+12=0

x=1.7320508075688772 or x=−1.7320508075688772

Answer:

a.)Point C will be either (4.82, 7.41) or ( -4.82, 2.59)

b.) -x² + 2x + 6y - y² - 5= 0  , 8y - 4x = 11

Step-by-step explanation:

As given A(2,1,3) and B(0,5,0)

a.)

We have to find C  in the xy-plane

⇒ C is of the form (x, y, 0)    ( Because in xy plane , z coordinate is zero)

Now, given AB and BC are the legs of the right triangle .

AB = (0, 5, 0) - (2, 1, 3) = ( -2, 4, -3)

BC = (x, y, 0) - (0, 5, 0) = ( x, y-5, 0)

As AB and BC are legs of triangle

⇒AB is perpendicular to BC

⇒(AB).(BC) = 0

⇒( -2, 4, -3).( x, y-5, 0) = 0

⇒ -2x + 4(y-5) -0 = 0

⇒ -2x + 4y- 20 = 0

⇒ -x + 2y- 10 = 0

⇒ 2y = 10 + x

⇒ y = 5 + [tex]\frac{x}{2}[/tex]         ......(1)

As ABC is making an isosceles right triangle

It means two sides of the triangle are equal

Now,

|AB| = √(-2)² + (4)² + (-3)² = √4+16+9 = √29

|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²

Now,

AS AB = BC

⇒|AB| = |BC|

⇒|AB|² = |BC|²

⇒29 = (x)² + (y-5)²

⇒29 = (x)² + (5 + [tex]\frac{x}{2}[/tex] -5)²

⇒29 = (x)² + ( [tex]\frac{x}{2}[/tex] )²

⇒29 = x²( 1 + [tex]\frac{1}{4}[/tex] ) = x²(  [tex]\frac{5}{4}[/tex] )

⇒ x² = [tex]\frac{116}{5}[/tex] = 23.2

⇒ x = 4.82 , -4.82

⇒y = 7.41 , 2.59

so, Point C will be either (4.82, 7.41) or ( -4.82, 2.59)

b.)

As given AB is the hypotenuse of the right triangle

S, AC and CB will perpendicular to each other

Now,

AC = (x, y, 0) - ( 2, 1, 3) = ( x-2, y-1, -3)

CB = (0, 5, 0) - (x, y, 0) = (-x, 5-y, 0)

As, AC and CB is perpendicular

⇒(AC).(CB) = 0

⇒( x-2, y-1, -3).(-x, 5-y, 0) = 0

⇒(x-2)(-x) + (y-1)(5-y) - 0 = 0

⇒-x² + 2x + 5y - y² - 5 + y = 0

⇒-x² + 2x + 6y - y² - 5= 0    ..........(2)

As ABC is making an isosceles right triangle

It means two sides of the triangle are equal

Now,

|AC| = √(x-2)² + (y-1)² + (0-3)² = √(x-2)² + (y-1)² + 9

|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²

Now,

AS AC = BC

⇒|AC| = |BC|

⇒|AC|² = |BC|²

⇒(x-2)² + (y-1)² + 9  = (x)² + (y-5)²

⇒x² + 4 - 4x + y² + 1 - 2y + 9 = x² + y² + 25 - 10y

⇒ 4 - 4x + 1 - 2y + 9 = 25 - 10y

⇒14 - 4x - 2y  = 25 - 10y

⇒10y - 2y - 4x = 25 - 14

⇒8y - 4x = 11            ........(3)

Now, we have 2 equations

-x² + 2x + 6y - y² - 5= 0  , 8y - 4x = 11

Solve these equations to find x, y

Answer:

[tex]P(A \cup B) =0.45[/tex]

Step-by-step explanation:

From the question we are told that

Consumers seen the soap [tex]P_A=40\% =0.40[/tex]

Consumers used the soap [tex]P_B=20\% =0.2[/tex]

Consumers seen/tried the soap [tex]P_x=15\% =0.15[/tex]

Generally the probability that consumers have seen and tried the soap is

[tex]P(A \cup B=P(A)+P(B)-P(A \cap B[/tex]

[tex]P(A \cup B=0.4+0.2-0.15[/tex]

[tex]P(A \cup B) =0.45[/tex]

Answer:true

Step-by-step explanation:

Answer:

The faster computer will complete the job in 20 minutes alone.

Step-by-step explanation:

Given that:

Time taken by both computers = 12 minutes

Time taken by slower computer = 30 minutes

Let,

x be the time taken by faster computer.

[tex]\frac{1}{x}+\frac{1}{30} = \frac{1}{12}[/tex]

[tex]\frac{1}{x} = \frac{1}{12}-\frac{1}{30}\\\\\frac{1}{x} = \frac{5-2}{60}\\\\\frac{1}{x} = \frac{3}{60}\\\\\frac{1}{x} = \frac{1}{20}\\\\x= 20[/tex]

Hence,

The faster computer will complete the job in 20 minutes alone.

Answer:

4,400

Step-by-step explanation:

Answer:

[tex]x = \frac{5}{3}[/tex]

Step-by-step explanation:

The expression under the square root is [tex]\sqrt{4x^2 - 20x + 25}[/tex]

This is equivalent of [tex](2x-5)^2[/tex]

We can check this by using the formula
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]

where [tex]\\a = 2x so a^2 = (2x)^2 = 4x^2\\\\b = -5 so b^2 = (-5)^2 = 25\\\\2ab = (2)(2x)(-5) = -20x\\[/tex]

So

[tex]\sqrt{4x^2 - 20x + 25} = \sqrt{(2x-5)^2}[/tex] which is [tex](2x-5)[/tex]

(The square root of the square of an expression is the expression itself)

So that gives us

[tex]2x - 5 = 5-2x\\[/tex]

Collecting like terms on each side gives us

[tex]2x + 2x = 5 -(-5)\\\\4x = 10\\\\x = 10/4 = 5/3[/tex]

Answer: They have 775 miles left to be traveled

Step-by-step explanation:

Miles required to travel for vacation = 1,325 miles

Miles already traveled = Miles driven this week + miles driven today

= 420 miles + 130 miles

-=550 miles

Miles remaining to be covered =Miles required to travel for vacation --- Miles already traveled

= 1,325 miles - 550 miles

= 775 miles

Answer:

1762 is the answer

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

25 x 12

Answer:300

Step-by-step explanation: its just 25 x 12

Answer:

True.

Step-by-step explanation:

The range of the 10  values is 10 - 3 = 7  so that is true.

The median will be the mean of the 2 middle values so that is possible also. The distribution could be, for example:

3 3 3 4 4 4 7 8 8 10  when the median = (4 + 4) / 2 = 4.

Answer:

True.

Step-by-step explanation:

the range of 10 values is 10-3 = 7 so that is true

Answer:

x = (3, 4)

(I'm assuming the missing sign in the picture is a negative (-))

Answer:

x={3, 4}

Step-by-step explanation:

that may answer po

Answer:

Step-by-step explanation:

6.7 – (-2.5)

2.5+6.7

6.7 + (-2.5)

-2.5+6.7

6.7-2.5

neither

-2.5-6.7

2.5-6.7

-6.7+2.5

Answer:

I believe communist just because or there influences in world war I and world war II they were on the communist side and part of the USSR at the time

Answer:

7

Step-by-step explanation:

hhfndbdbdbueheheheheheheh

Answer:

18.33

Step-by-step explanation:

600 -50 ÷ 30

550 ÷30 = 18.333