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Nezavi [6.7K]
1 year ago
14

Please help me I dont understand any of this. Ps it might take me a while for me to understand. :/

Mathematics
1 answer:
Tems11 [23]1 year ago
8 0

How to clear an equation/solve for any given variable?

Lets say you have two identical cups of coffee, a and b.

You can say they're both equal. If you want to add a tablespoon of sugar to cup a, and you also want both cups to remain equal, you'll have to add the same tablespoon of sugar to cup b.

We use this fact, called conservation of an equality, to clear an equation (A.K.A solving for a variable)

Mathematically speaking,

<em>Cups </em>a <em>and </em>b<em> are equal</em>

a=b

<em>If you modify </em>a<em>, you'll have to modify </em>b <em>the same way</em>

\begin{gathered} a+3=b+3 \\ a-1=b-1 \\ a\times4=b\times4 \\ \frac{a}{5}=\frac{b}{5} \end{gathered}

Now, let's apply that logic to the equation we have.

We know cup of coffee a is

6y-1.5x

And cup b is

8

We also know both cups of coffee are equal, so

6y-1.5x=8

We're being asked to solve for y. In other words, we have to clear y from this expression.

Let's add our first tablespoon of sugar: adding 1.5x to both sides:

\begin{gathered} 6y-1.5x=8\rightarrow6y-1.5x+1.5x=8+1.5x \\ \rightarrow6y=8+1.5x \end{gathered}

See how the -1.5x canceled out? That's what we're looking for! We want y to be left alone in its side.

Now, let's divide both sides by 6 to cancel out the 6 from 6y:

\begin{gathered} 6y=8+1.5x\rightarrow\frac{6y}{6}=\frac{8+1.5x}{6} \\ \rightarrow y=\frac{8+1.5x}{6} \\ \rightarrow y=\frac{8}{6}+\frac{1.5}{6}x \\ \rightarrow y=1.33+0.25x \end{gathered}

He have cleared y / solved the equation for y

<em>Let's try with another example</em>

<em />

e.g:

<em>Solve the following equation for </em>b

3b+9a+12=6

Solution: Let's substract 12 from both sides:

\begin{gathered} 3b+9a+12=6\rightarrow3b+9a+12-12=6-12 \\ \rightarrow3b+9a=-6 \end{gathered}

Then, let's substract 9a from both sides

\begin{gathered} 3b+9a=-6\rightarrow3b+9a-9a=-6-9a \\ \rightarrow3b=-6-9a \end{gathered}

Let's divide both sides by 3

\begin{gathered} 3b=-6-9a\rightarrow\frac{3b}{3}=-\frac{6}{3}-\frac{9a}{3} \\ \rightarrow b=-2-3a \end{gathered}

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A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 8 feet. Find the radius.
siniylev [52]

9514 1404 393

Answer:

  6 feet

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr^2·h

For a sphere, the volume is ...

  V = 4/3πr^3

You want the volumes to be the same when h=8, so we have ...

  πr^2·8 = 4/3πr^3

Dividing by πr^2, we have ...

  8 = 4/3r

  r = 3/4·8 = 6

The radius is 6 feet.

8 0
2 years ago
Five widgets and three gadgets cost $109. 90.
erma4kov [3.2K]

Answer:

one gadget costs $15.80

Step-by-step explanation:

Let w = cost of one widget

Let g = cost of one gadget

Given:

  • Five widgets and three gadgets cost $109. 90

⇒ 5w + 3g = 109.9

Given:

  • One widget and four gadgets cost $75. 70

⇒ w + 4g = 75.7

Rewrite  w + 4g = 75.7  to make w the subject:

⇒ w = 75.7 - 4g

Substitute into  5w + 3g = 109.9  and solve for g:

⇒ 5(75.7 - 4g) + 3g = 109.9

⇒ 378.5 - 20g + 3g = 109.9

⇒ 378.5 - 109.9 = 20g - 3g

⇒ 268.6 = 17g

⇒ g = 15.8

Therefore, one gadget costs $15.80

To find the cost of one widget, substitute the found value for g into
w = 75.7 - 4g and solve for w:

⇒ w = 75.7 - 4(15.8)

⇒ w = 75.7 - 63.2

⇒ w = 12.5

Therefore, one widget costs $12.50

5 0
2 years ago
If the measure of angle 1 is 110 degrees and the measure of angle 3 is (2 x + 10) degrees, what is the value of x?
user100 [1]

Answer:

Correct option is

B

90

∘

,90

∘

,90

∘

Let AB and CD be two lines Intersecting at O, such that, ∠AOD=90

∘

Now, ∠AOD=∠COB=90

∘

(Vertically opposite angles)

⟹∠AOD+∠DOB=180

o

(Angles on a straight line)

⟹90+∠DOB=180

o

∠DOB=90

∘

∠DOB=∠AOC=90

∘

(Vertically opposite angles)

Thus, all angles are 90

∘

.

7 0
2 years ago
2. The cost of a bicycle is * 2895. Find the cost of 1486 bicycles,
forsale [732]

Answer:

4,301,970

5,149,815

Step-by-step explanation:

The cost of a bicycle is 2895

Therefore the cost of 1486 bicycles is

= 2895×1486

= 4,301,970

A truck can carry 6785 kg of food

Therefore the amount in which 759 truckj can carry can be calculated as follows

= 6785×759

= 5,149,815

7 0
2 years ago
If h(x) = │5x - 17│, find h(3).
arsen [322]

Answer:

2

Step-by-step explanation:

5x - 17

5(3) - 17 = 15 - 17 = -2

However, there is an absolute value sign over the expression. Abs value makes negatives turn positive. So -2 becomes 2.

7 0
3 years ago
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