Find areas of the triangles.

Answer:

#2 option: [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]slope=\frac{rise}{run} =\frac{y^2-y^1}{x^2-x^1}[/tex]

[tex]\frac{3-(-1)}{4-(-2)}=\frac{-4}{-6} =\frac{-2}{-3} =\frac{2}{3}[/tex]

=  [tex]\frac{2}{3}[/tex]

Jason's monthly pension is the product of the final three-year average salary is $32,625. Then the correct option is C.

Jason is planning on retiring after 25 years of employment.

For the last three years he has made $60,000; $56,000; and $58,000.

His employer offers a defined benefit plan in which the annual pension is calculated as the product of the final three-year average salary, the number of years of service, and a 2.25% multiplier.

Then Jason's monthly pension will be

[tex]\rm Monthly \ pension = \dfrac{(60,000+56,000+58,000)}{12} \times 2.25\\\\Monthly \ pension = 14500 \times 2.25\\\\Monthly \ pension = \$ \ 32,625[/tex]

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Problem 6

It's not clear what the instructions are, but I'm assuming your teacher wants you to rationalize the denominator.

If so, then we could have these steps

[tex]\sqrt{\frac{3\text{x}}{7}}\\\\\frac{\sqrt{3\text{x}}}{\sqrt{7}}\\\\\frac{\sqrt{3\text{x}}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\frac{\sqrt{3\text{x}*7}}{(\sqrt{7})^2}\\\\\frac{\sqrt{21\text{x}}}{7}\\\\[/tex]

In the third step, I multiplied top and bottom by [tex]\sqrt{7}[/tex] so that the denominator can get rid of the square root.

======================================================

Problem 7

We'll follow the same idea for this problem.

[tex]\sqrt{\frac{5m^2}{2}}\\\\\frac{\sqrt{5m^2}}{\sqrt{2}}\\\\\frac{\sqrt{5m^2}*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{5m^2*2}}{(\sqrt{2})^2}\\\\\frac{\sqrt{10m^2}}{2}\\\\\frac{\sqrt{10}*\sqrt{m^2}}{2}\\\\\frac{m\sqrt{10}}{2}\\\\[/tex]

Where m is nonnegative.

In the second to last step, I split up the root so I could use the rule [tex]\sqrt{x^2} = x \text{ when } x \ge 0[/tex]

======================================================

Problem 8

[tex]\sqrt{\frac{12\text{x}^3}{5}}\\\\\frac{\sqrt{12\text{x}^3}}{\sqrt{5}}\\\\\frac{\sqrt{12\text{x}^3}*\sqrt{5}}{\sqrt{5}*\sqrt{5}}\\\\\frac{\sqrt{12\text{x}^3*5}}{(\sqrt{5})^2}\\\\\frac{\sqrt{60\text{x}^3}}{5}\\\\\frac{\sqrt{4\text{x}^2*15\text{x}}}{5}\\\\\frac{\sqrt{4\text{x}^2}*\sqrt{15\text{x}}}{5}\\\\\frac{\sqrt{(2\text{x})^2}*\sqrt{15\text{x}}}{5}\\\\\frac{2x\sqrt{15\text{x}}}{5}\\\\[/tex]

where x is nonnegative.

Answer:

Step-by-step explanation:

Y= 4x+3 make x the subject

4x = y - 3

x = (y-3)/4

Answer:

Radius of cone = 5cm

Step-by-step explanation:

You can figure out a radius of the base of the cone by using Pythagoras as you know the hypotenuse (slant height) and the height of the triangle so:
[tex]13^2-12^2 =radius^2[/tex]

[tex]169-144 =25 = radius^2\\[/tex]

[tex]radius = 5[/tex]cm

Answer:

5cm

Step-by-step explanation:

Answer:

14 is 269000-2500=266500

Step-by-step explanation:

Step-by-step explanation:

here you go hope it helps you

Answer:

2. Polynomial

3. Not a polynomial

4. Polynomial

5. Polynomial

Step-by-step explanation:

Since that is a right triangle, we can use pythagorean theorem.

[tex]c^2=a^2+b^2[/tex]

solve.

[tex]c^2=40^2+9^2\\\\c^2=1681\\\\\sqrt{c^2}=\sqrt{1681} \\\\c=41[/tex]

the value of x is 41

Answer:

  10,071 years

Step-by-step explanation:

If 'a' is the fraction remaining, it satisfies the equation ...

  a = (1/2)^(t/5750)

Solving for t, we get ...

  log(a) = log(1/2)×t/5750

  t = 5750×log(a)/log(1/2) ≈ -19,101.09×log(a) . . . years

__

If 70.3% is lost, then 1 -0.703 = 0.297 is the fraction remaining. The age is estimated to be ...

  -19,101.09×log(0.297) ≈ 10,071 . . . years

The bones were about 10,071 years old.

Answer:

980.18 cm^3

Step-by-step explanation:

Volume of cylinder w/out spheres = pi r^2 h

  = pi 8^2 *6

 now subtract the volume of the TWO spheres

      2   * 4/3 pi * 3^3

for result = 980.18 cm^3

The answer is that skiers are faster by 20%, with the top speed ever recorded on a ski coming in at 250kph, while the top speed recorded on a snowboard is 200kph. If we want to discuss which sport is cooler, then we can have a lively conversation! The Basics Of Biomechanics

Answer:

x=72.4

Step-by-step explanation:

Since we have an angle that is facing a known side, we are able to use sine

Step 1- Prepare your equation: sin(∅°)=opposite/hypotenuse

Step 2- Substitute: sin(28°)=34/x

Step 3- Calculate: use a graphing calculator to solve the equation, make sure to have the answer to degrees not radians

Step 4- Answer: 72.4 by calculator

ur wlcm :)

brainliest?

Answer:

3 gallons

Step-by-step explanation:

Answer:

Step-by-step explanation:

P(Walk or Bike)=[tex]\frac{72}{466} +\frac{90}{466}[/tex]

                        =[tex]\frac{81}{233}[/tex]  = 0.347

Answer:

2 pi

Step-by-step explanation:

Period of the function graphed = 2π

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

Given,

Graph of a function.

Period of the function = Distance between two peaks or two troughs in the graph

Period of the function = 2π - 0 = 3π - π = 2π

Hence, 2π  is the period of the function graphed.

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The sequence of operations is multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x. The correct option is - b)

From the question, we are to determine the sequence of operations that would produce the correct x- or y-value of the solution to the given system of equations

The given systems of equations are

2x+y=9

x+3y=-13

That is

-3 × (2x+y=9)

-6x-3y=-27

-6x-3y=-27

+(x+3y=-13)

-----------------

-5x = -40  

Thus, we can solve for x

These sequence of operations will enable us to eliminate y and solve for x

Hence, the sequence of operations that would produce the correct x- or y-value of the solution to the system of equations is multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x. The correct option is - b)multiply the first equation by –3 and add the result to the second equation to eliminate y and solve for x

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Answer:

2/5

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

2 green / 8 total colors

2/8

Simplify to 1/4 of a chance

Answer:

Step-by-step explanation:

20+24

⇨2(10+12)

Therefore ⬇︎

2(10+12) is our expression with 2 as a factor for each term ツ

Answer:

35x - 7

Step-by-step explanation:

7(5x - 1)

--> 7 x 5×

= 35x

--> 7 x -1

= -7

==> 35x - 1

Hope it helps :))

Answer:

35x - 7

Step-by-step explanation:

Q) 7(5x - 1) = ?

→ 7(5x - 1)

→ 35x - 7

So, the answer is 35x - 7.

Answer:

B

Step-by-step explanation:

Answer choice A,C, and D are all linear based on their context. Answer choice B "doubles" resulting in an exponential function.

Answer:

1 radians

Step-by-step explanation:

Here,

Arc length ( l ) = 8π cm

Radius ( r ) = 8 cm

To find : Angle θ ( in radians )

Formula : -

θ = l / r

θ = 8π / 8

θ = 1π

Note : -

Radians is denoted by " π ".

Answer:

the difference is the slope

Step-by-step explanation:

y = mx+b

m is the slope

b is the y-intercept

2x+4

3x+4

4x+4

the m constant changes meaning the slope is the difference

Answer:

D) 3x + 7y = 49

E) x / 3 = 9

F) 2x + 4

Answer:

(5 × 4) - 13 = 7

Step-by-step explanation:

Given that,

→ n = 5

Let's solve the problem,

→ x = n × 4

→ x = 5 × 4

→ [ x = 20 ]

Then 13 less than the product will be,

→ x - 13

→ 20 - 13 = 7

Therefore, the solution is 7.

Answer:

1/12 for red marbles

1/12 for black marbles

Step-by-step explanation:

reason why both 1/12 it because you picked a marble first and you brought it back, then you pick again

Answer:

£15.10

x + 20

64 counters in the bag

Total money = £21.30

Step-by-step explanation:

20p = £0.20

50p = £0.50

100p = £1.00

Total value:

⇒ 8 × 20p + 5 × 50p + 11 × £1 = 8 × 20p + 5 × 50p + 11 × 100p

                                                = 160p + 250p + 1100p

                                                = 1510p

                                                = £15.10

-----------------------------------------------------------------------------------------------------

20 more than x:   x + 20

-----------------------------------------------------------------------------------------------------

If one quarter of the counters in a bag are yellow, and there are 16 yellow counters in the bag:

⇒ total number of counters in the bag = 16 × 4 = 64

-----------------------------------------------------------------------------------------------------

Let x = number of 20p coins

Let y = number of 50p coins

Let z = number pf £1.00 coins

Given:

⇒ 0.20x = 2.80

⇒ x = 2.80 0.20

⇒ x = 14

Therefore, there are 14 twenty pence coins.

Given:

We have calculated that there are 14 twenty pence coins, therefore:

⇒ total number of coins = number of 20p × 3            

                                        = 14 × 3

                                        = 42

As the total number of coins is 42:

⇒ x + y + z = 42

⇒ 14 + y + z = 42

⇒ y + z = 42 - 14

⇒ y + z = 28

Therefore, the total number of 50p and £1 coins is 28.

Given:

⇒ y = z + 10

Substitute  y = z + 10  into y + z = 28 and solve for z:

⇒ (z + 10) + z = 28

⇒ 2z + 10 = 28

⇒ 2z = 18

⇒ z = 9

Therefore, there are 9 one pound coins

total number of coins:

⇒  x + y + z = 42

substituting the found values of x and z:

⇒  14 + y + 9 = 42

⇒  23 + y = 42

⇒  y = 19

Therefore, there are 19 fifty pence coins

20p coins = 14

50p coins = 19

£1 coins = 9

Therefore, total money:

= 14 × 20p + 19 × 50p + 9 × 100p

= 280p + 950p + 900p

= 2130p

= £21.30

The linear equations are 6x + y = 5, x + 2 = −8, y = 1, and y = −2/3x + 3. Then the correct options are A, B, E, and G.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

If the power of the variable is one then the equation will be a linear equation.

The equations are given below.

A.  6x + y = 5, this is the linear equation.

B.  x + 2 = −8, this is the linear equation.

C.  2x² + 3x − 8 = 19, this is not a linear equation.

D.  3 + 8 = 11, this is not a linear equation.

E.  y = 1, this is the linear equation.

F.  4x³ = 32, this is not a linear equation.

G.  y = −2/3x + 3, this is the linear equation.

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