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Step2247 [10]
3 years ago
13

Which of the following statements describes a correct method for solving the equation below?

Mathematics
2 answers:
Andrei [34K]3 years ago
6 0
30 + 2w = 2 • (w - 15)

Equation at the end of step 1 :
Step 2 :
Equations which are never true :
Solve : 2 = 0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation
Solve : w-15 = 0

Add 15 to both sides of the equation :
w = 15
TiliK225 [7]3 years ago
3 0

You are trying to solve for "w", to do so you:

20 + 2w = 50     Subtract 20 on both sides  

2w = 30  Divide 2 on both sides to get "w" by itself

w = 15


Your answer is B

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Graph (1,-3) on a grid
k0ka [10]

Step-by-step explanation:

To plot (1,-3), start at the origin (0,0) and move right 1 unit and down 3 units.

hope it helps.

6 0
3 years ago
Find the area of the triangle with sides 40, 50, and 60.
Katyanochek1 [597]

Answer:

B. 992.2

Step-by-step explanation:

Area of Triangle Knowing All Sides:

Sides: 50.000, 60.000, 40.000

Area  : 992.1567

Area of Triangle given by its 3 Sides:

I will show two ways to find the area. One way is very short - The 2000 years old Heron's Formula. The other method may be longer but it's more "educational" as it teaches us important analytic geometry lessons.

But before we even start, we have to verify that the Basic Triangle Inequality is satisfied.

The Basic Triangle Inequality:

The Basic Triangle Inequality states that for a triangle with side lengths a,b,c , the following is true:

    a < b + c,    b < a + c,    c < a + c

What this means, in plain English, is that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Let us now check:

     60.000 < 40.000 + 50.000   true

     40.000 < 60.000 + 50.000   true

     50.000 < 60.000 + 40.000   true

Now that the basic inequalities are satisfied, we know that these three side lengths can make a triangle, so we can move on to calculating the area of said triangle

Heron's Formula for the area of a triangle:

The 2000 year old Heron's Formula states that the area of a triangle whose sides have lengths  a, b,  and  c  is

     SQRT (s(s-a)(s-b)(s-c))

where  s  is the semiperimeter of the triangle; that is,

     s = ( a + b + c ) / 2

Let us calculate

Area =  SQRT ( 75.000 • 15.000 • 35.000 • 25.000 ) =

           SQRT ( 984375.000 ) =

           992.1567  

Find area using the Base Height formula:

Let  B  (for base) denote the length of the longest side of the triangle

Let  h  (for height) denote the length of a perpendicular line, from the vertex opposite that side, to the side itself.

Note that  h  splits our triangle into two right-angled triangles, both having  h  as height, the base of the left triangle is denoted by  X  and the base of the right triangle is denoted by  40.000 - X

To find the area of a triangle, multiply the base by the height, and then divide by 2. In algebraic notation, Area  = 0.5 • 40.000 • h   To be able to find the Area, using this formula, we must know the value of  h

Using the Pythagorean theorem to find the Height:

Applying the Pythagorean theorem to the left right-angled triangle we get:

     h2 = (50.000)2- X2  

While the right right-angled triangle is "telling" us that:

     h2 = (60.000)2- (40.000 - X)2  

Two things which are equal to  h2 , are also equal to one another (It is a property of "Equation" that   if z=p and z=q then p=q ):

     (50.000)2- X2 = (60.000)2- (40.000 - X)2  

Expand the above and simplify :

     (40.000)2 + (50.000)2 - (60.000)2 = 80.000 • X

     500.000 = 80.000 • X

     X = 6.250

Plug this for X in:  h2 = (50.000)2- X2  

     h2 = (50.000)2- ( 6.250)2  

     h2 = (2460.938)

h = sqrt (2460.938) = 49.6078  

Put the Triangle Area Formula to use:

Finally put the formula  Area = Base * Height * 0.5   to use:

    Area  = 40.000 • 49.608 • 0.5

    Area  = 992.1567  

Note that this result is identical to the one we got using Heron's Formula !

Area of Triangle Knowing all Sides :

    Sides: 50.000, 60.000, 40.000      Area  : 992.1567

4 0
3 years ago
Read 2 more answers
(4z^5 - 14z^4 + 10z^3 - 16z^2 + 41z - 2) / (z - 2)
r-ruslan [8.4K]

Answer:

4z4−6z3−2z2−20z+1

Step-by-step explanation:

4z5−14z4+10z3−16z2+41z−2

z−2

=

4z5−14z4+10z3−16z2+41z−2

z−2

=

(z−2)(4z4−6z3−2z2−20z+1)

z−2

=4z4−6z3−2z2−20z+1

(theres no more like terms so u cant)

4 0
2 years ago
The algebraic expression for the sum of 5 and g?
ra1l [238]

Answer:

5 + g

Step-by-step explanation:

The sum of 5 and g,

5 + g

6 0
3 years ago
What is the value of h (-2) when h (3) = 32 +1?<br> Enter your answer in the box.<br> h (-2) =
just olya [345]

Answer:(-22)

Step-by-step explanation:

What is the value of h (-2) when h (3) = 32 +1?

hx3=33

33 divided by 3

which means h=11

that makes 11(-2)

=(-22)

8 0
3 years ago
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