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artcher [175]
2 years ago
11

the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle

. pls help. solve using applications of quadratics
Mathematics
1 answer:
inna [77]2 years ago
7 0

Answer:

2m

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

A = \frac{1}{2}bh

They give us the area as 6m^2, so let's include it in the equation.

6 = \frac{1}{2}bh

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that h = b-4

So replace h in the equation with b-4.

You will now get:

6 = \frac{1}{2}b(b-4)

Now we can work towards solving. Let's get simplifying.

12 = b(b-4)\\12 = b^2 - 4b\\

bring everything to one side so we can make a quadratic and factor:

0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2

We get that b=6.

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that h = b - 4, so to find h, we just sub in our b value into that.

h = (6) - 4 = 2

We find that h=2

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Int he figure below find AC
Ahat [919]

Given :-

  • Two triangles with their two angles equal .

To Find :-

  • Measure of AC .

Answer :-

Here in ∆ABC and ∆EDC ,

  • \angle CAB = \angleCED (given )
  • \angle CBA = \angleCDE (given)

Therefore by AA similarity criterion , we can say that ∆ABC ~ ∆EDC . Also we know that corresponding sides of similar triangles are proportional . So ,

→ AC/EC = BC/DC

→ AC/9 = 8/12

→ AC = 8/12 * 9

→ AC = 6

<u>Hence</u><u> the</u><u> </u><u>measure</u><u> of</u><u> </u><u>side </u><u>AC </u><u>is </u><u>6</u><u> </u><u>.</u>

I hope this helps.

7 0
3 years ago
Carlos wants to practice piano 2 hours each day. He practices piano for 3/4 hour before school and 7/10 hour when he gets home.
CaHeK987 [17]

Answer:

Carlos has practiced piano for \frac{29}{20}=1\frac{9}{20} hours.

Carlos needs to practice \frac{11}{20} hours.

Step-by-step explanation:

We have been given that Carlos wants to practice piano 2 hours each day. He practices piano for 3/4 hour before school and 7/10 hour when he gets home.

First of all, we will find piano practiced before school and after school by adding both amounts as:

\frac{3}{4}+\frac{7}{10}

Make a common denominator:

\frac{3*5}{4*5}+\frac{7*2}{10*2}

\frac{15}{20}+\frac{14}{20}

Add numerators:

\frac{15+14}{20}

\frac{29}{20}  

Therefore, Carlos has practiced piano for \frac{29}{20} hours.

Now, we will subtract \frac{29}{20} from 2 find number of hours Carlos needs to practice to reach his goal.

2-\frac{29}{20}

\frac{2*20}{20}-\frac{29}{20}

\frac{40}{20}-\frac{29}{20}

\frac{40-29}{20}

\frac{11}{20}

Therefore, Carlos needs to practice \frac{11}{20} hours before going to bed in order to meet his goal.

7 0
3 years ago
Choose the function that the graph represents.<br> Click on the correct answer.
Lynna [10]

Answer:

y=log_2 (x)

Step-by-step explanation:

We see that the graph passes though the point (2,1). So we can write:

log_a (2) = 1  => a = 2

So it's a log in base 2.

4 0
3 years ago
If a+b=34 then what is 4a-8ba+9a
Klio2033 [76]

Answer:

12x:12x=1:

1 TRUE

Step-by-step explanation:

4 0
2 years ago
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