State one form of the Law of Cosines and provide a trick for writing the other two forms and explain when Law of Cosines should be used to solve a triangle.

Step-by-step explanation:

let :

the job as lifeguard = A

the job as cashier = B

making 2 equations as follows :

(1) A+B = 14 ==> A = 14-B

(2) 10A + 8B = 124

substitute A (equation (1)) into equation (2) :

10(14-B) + 8B = 124

140 -10B +8B = 124

140- 2B = 124

140-124 = 2B

16 = 2 B

B = 8

A = 14-8 = 6

so, as a lifeguard = 6 working hours

and as a cashier = 8 working hours

Answer:

Step-by-step explanation:

Let the lifeguard hours = x

Let the cashier hours= y

x + y = 14

10*x + 8*y = 124           Multiply the top equation by 8 Put it under here.

8x + 8y =     112           Subtract

2x = 12                          Divide by 2

x = 6

He worked 6 hours as a lifeguard.

x + y = 14

6 + y = 14                      Subtract 6 from each side

y = 14 - 6

y = 8                            

He worked 8 hours as a cashier.

check

6*10 = 60

8 * 8 = 64

total    124

Answer:

1/3n - 3<6

n < 27

Step-by-step explanation:

1/3n - 3<6

Add 3 to each side

1/3n -3+3<6+3

1/3 n <9

Multiply by 3

1/3n *3 < 9*3

n < 27

Answer:

A=13

hope this helped!!!

Answer:

-13

Step-by-step explanation:

-50=6a+28

collect like terms

-50-28=6a

-78=6a

divide both sides by the coefficient of a

-78/6=6a/6

a=-13

Answer:

after 3 seconds, the object hits the ground.

Hope this helps :)

Answer:

[tex]p = 1[/tex]

Step-by-step explanation:

[tex]5p - 8(6p - 5) = p - 4[/tex]

[tex] - 43p - 40 = p - 4[/tex]

[tex] - 43p - p = - 40 - 4[/tex]

[tex] - 44p = - 44[/tex]

[tex]p = 1[/tex]

Answer:

[tex] p =\frac{22}{27} [/tex]

Step-by-step explanation:

5p - 8(6p - 5) = p - 4

-5p - 48p + 40 = p - 4

-53p + 40 = p - 4

-53p - p = -4 - 40

-54p = -44

p = 44 ÷ 54

p = 44/54

simplify with factor 2

p = 22/27

Answer:

x= -6 —> y= 4

x= -11 —> y= 5

Step-by-step explanation:

x= -6 —> y= 4

[tex]f( - 6) = \sqrt{ - ( - 6) - 2} + 2 \\ = \sqrt{6 - 2} + 2 \\ = \sqrt{4} + 2 \\ = 2 + 2 \\ = 4[/tex]

x= -11 —> y= 5

[tex]f( - 11) = \sqrt{ - ( - 11) - 2} + 2 \\ = \sqrt{11 - 2} + 2 \\ = \sqrt{9} + 2 \\ = 3 + 2 \\ = 5[/tex]

I hope I helped you^_^

The value of the function f(x) for the corresponding x = -6 and x =-11 is equal to 4 and 5 respectively.

The function f(x) = √( -x -2) + 2

The value of x and f(x) are ,

x    :   -2   -3    -6    -11

f(x) :   2     3      ?     ?

Now to find the missing value of f(x) substitute the value of x in f(x) we have,

When x = -6

f(x) = √( -x -2) + 2

⇒ f(x) = √( -( -6) -2) + 2

⇒ f(x) = √(6) -2) + 2

⇒ f(x) = √(4) + 2

⇒ f(x) = 2 + 2

⇒ f(x) = 4

And when x = -11

f(x) = √( -x -2) + 2

⇒ f(x) = √( -( -11) -2) + 2

⇒ f(x) = √(11) -2) + 2

⇒ f(x) = √(9) + 2

⇒ f(x) = 3 + 2

⇒ f(x) = 5

Therefore, the missing values of the function are 4 and 5.

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Answer:

8 x 5 x 15 = 600in^3

Answer:

None of the first 4 do. so I guess the answers E.

Step-by-step explanation:

Answer:

x =36

Step-by-step explanation:

The three angles form a straight line which means they add to 180

2x+2x+x = 180

Combine like terms

5x = 180

5x/5 = 180/5

x =36

Answer:

X=36

Step-by-step explanation:

A straight line like the one shown in the image has 180° by one side.

Following that, we should assume that:

2x+2x+x=180°

5x=180°

x=36°

I hope I have helped you.

Answer:

[tex] \sqrt[3]{12} [/tex]

and

[tex] \sqrt[3]{ \frac{1}{18} } [/tex]

because

[tex] \sqrt[3]{12} \times \sqrt[3]{18} = 6 \\ \\ \sqrt[3]{ \frac{1}{18} } \times \sqrt[3]{18 } = 1[/tex]

Answer:

no solution

Step-by-step explanation:

14a – (2a + 9) = (12a - 18)

Distribute the minus sign

14a – 2a - 9 = (12a - 18)

12a -9 = 12a -18

Subtract 12a from each side

12a -9-12a = 12a-18-12a

-9 = -18

This is not a true statement so there is no solution

Answer:

the slope is 5

and the intercept is 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probabilities for each point:

Required probability:

Correct choice is D

Answer:

slope = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

- [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{4}[/tex] y = 24 ( multiply through by 4 to clear the fractions )

- 2x - 3y = 96 ( add 2x to both sides )

- 3y = 2x + 96 ( divide terms by - 3 )

y = - [tex]\frac{2}{3}[/tex] - 32 ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

Answer:

Proven.

Step-by-step explanation:

Answer:

T (6, 5 )

Step-by-step explanation:

Using the section formula

If (x₁, y₁ ) and (x₂, y₂ ) are divided in the ratio m : n , then

( [tex]\frac{nx_{1}+mx_{2} }{m+n}[/tex] , [tex]\frac{ny_{1}+my_{2} }{m+n}[/tex] ) are the coordinates of the internal point

Here (x₁, y₁ ) = A (- 4, 10 ) , (x₂, y₂ ) = B (10, 3) , m : n = 5 : 2

T = ([tex]\frac{2(-4)+5(10)}{5+2}[/tex] , [tex]\frac{2(10)+5(3)}{5+2}[/tex] )

   = [tex]\frac{-8+50}{7}[/tex] , [tex]\frac{20+15}{7}[/tex] )

  = [tex]\frac{42}{7}[/tex] , [tex]\frac{35}{7}[/tex] )

  = (6, 5 )

Answer:

so speed of aircraft carrier is 30. thank you

The speed of an aircraft carrier is 30 km/h.

speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.

Given, An aircraft carrier left Hawaii traveling west seven hours before a container ship. The container ship traveled in the opposite direction going 5 km/h slower than the aircraft carrier.

Since,

Speed = distance/time

time is 13 hours, 7 hours before the container ship left then the 6 hours container traveled.

Let "s" be the speed of the aircraft carrier

=> d = 13s

Container ship:

time is 6 hours

speed is 5 km/h slower, so s-5

=> d = 6(s-5)

Since they are going in opposite directions, add up the distances to find how far apart they are

=> 13s + 6(s-5) = 540

Now solve for s-

=> 13s +6s -30 = 540

=> 19s = 570

=> s = 30

therefore, the Aircraft carrier was traveling at the speed of 30 km/h and the container ship at the speed of 25 km/h.

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Answer:

AC = 22

Step-by-step explanation:

AB + BC = AC , substitute values

4x - 6 + 4 = 2x + 10 , that is

4x - 2 = 2x + 10 ( subtract 2x from both sides )

2x - 2 = 10 ( add 2 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Then

AC = 2x + 10 = 2(6) + 10 = 12 + 10 = 22

Answer:

-53

Step-by-step explanation:

-25-32-14-14+45-13

=53

Answer:

ANS IS -53

AS +45 &-45 WILL GET CANCELLED

AND -14-14-25 WILL GET ADDED

THAT IS -53

Answer:

75

Step-by-step explanation:

Let's say the unknown number is x

x/5 = 15

x = 15*5

x = 75

Answer:

[tex](x+2)^2 + (y-1)^2 = 25[/tex]

Step-by-step explanation:

We want to write the equation of a circle with a diameter of 10 units centered on (-2, 1).

Recall that the equation of a circle has the standard form:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Where (h, k) is the center and r is the radius.

Since our diameter is 10, our radius is 5.

And since the center is at (-2, 1), h = -2 and k = 1.

Substitute:

[tex]\displaystyle (x - (-2))^2 + (y - (1))^2 = (5)^2[/tex]

And simplify. Hence, our equation is:

[tex](x+2)^2 + (y-1)^2 = 25[/tex]

Answer:

x=7

Step-by-step explanation:

HI + IJ = HJ

3x-5 + x-1 = 7x-27

Combine like terms

4x-6 = 7x-27

Subtract 4x from each side

4x-6 -4x= 7x-27-4x

-6 = 3x-27

Add 27 to each side

-6+27 = 3x-27+27

21 = 3x

Divide by 3

21/3 = 3x/3

7 =x

Answer:

x=7

Step-by-step explanation:

Answer:

84.04, 30.14 and 55.95

Step-by-step explanation:

First you add the ratios together then divide by 170 and mutliply each answer by the answer of 170 divided by the sum of 3.5, 1.25 and 2.33

Answer:

84.04, 30.14 and 55.95

Step-by-step explanation:

→ Add the ratios together

3.5 + 1.25 + 2.33 = 7.08

→ Divide the answer by 170

170 ÷ 7.08 = 24.01129944

→ Multiply the answer by 3.5 , 1.25 , 2.33

3.5 × 24.01129944 = 84.04

1.25 × 24.01129944 = 30.14

2.33 × 24.01129944 = 55.95

Answer:

v=20/3

See IMAGE FOR SOLUTION

In the given expression f = uv /(v+t) value of v in terms of t is *4/3t.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given an expression f = uv /(v+t)

Also given

f = 20

u = 5

Hence, From the expression

f =  uv /(v+t)

=> 20 = 5v/(v + t)

Simplifying in the terms of v

20v + 20t = 5v

15v = -20t

v = -4/3t

Therefore, the value of v in the given expression is -4/3t.

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Answer:

It depends in which direction "away" means. If they are five units to the right then the answer should be 1. if they are 5 points away to the left then the answer would be -9.

Step-by-step explanation:

Basically it depends,

if its indicating to the right the equation would be=

-4+5=x

which to do this negative cancells out its positive, so you can just subtract their absolute values. 5-4=1. And to know which symbol it has you just indicate which factor has the greated absolute value. (aka 5 which is positive so the answer should be positive).

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

if its to the left then the equation would be=

-4-5= x

(negative four subtracted by four)

and the easier way to do this would be to turn this equation into addition.

the new equation shall be: -4+(-5)=-9 since they are both negative integers  the sum should be negative.

Answer:

F = (9/5 ×C) + 32

Step-by-step explanation:

Apply Change of subject

Divide both sides by 5/9

9/5 × C = F - 32

》F = (9/5 ×C) + 32