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PIT_PIT [208]
3 years ago
5

The base of a triangle is seven more than twice the height. The area of the triangle is 135 square meters. Find the measures of

the base and height of the triangle.
Mathematics
1 answer:
Lemur [1.5K]3 years ago
3 0

Answer:

Height = 10 m

Base = 27 m

Step-by-step explanation:

The base of a triangle is seven more than twice the height

The area of the triangle is 135 m²

Height = x

Base = 2x + 7

Area of a triangle = \frac{1}{2} × base × height

∴

\frac{1}{2} × (x) × (2x + 7) = 135

2x² + 7x - 270 = 0

Applying the quadratic formula we get;

x = 10 or -13.5

Since we can't have a length being negative, the height of this triangle is 10 m

The base = 2(10) + 7 = 27

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SashulF [63]

Answer:

  -2 °C

Step-by-step explanation:

Add 3 °C to get a temperature 3 °C higher.

  -5 °C + 3 °C = -2 °C

8 0
3 years ago
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A rectangular swimming pool is 4 ft deep. One side of the pool is 3.5 times longer than the other. The amount of water needed to
sukhopar [10]

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Step-by-step explanation:

5 0
3 years ago
The volume of this rectangular solid is?
Maru [420]

Well, volume is: length x width x height


so, 5 x 14 x 8= 560 inches

8 0
3 years ago
A line is tangent to the circle x^2+y^2=41, at the point (-4,-5)
VashaNatasha [74]
If the equation of the circle is x^2+ y^2 = 41, we must first understand the parts of the equation.
 A general circle's equation is (x-h)^2+(y-k)^2= r^2  
(h.k) is the radius of the circle
r is the radius of the circle
Another useful fact to know is that tangent lines touch the circle at one point (4,5)

Since in our original equation there are no h or k values, we can assume that the center of the circle is (0,0). 

The formula for slope is <u>Y1-Y2</u>
                                   X1-X2
We can break this down with our two points (center and tangent)
  (0,0)    and   (-4,-5)
(X1,Y1) and (X2,Y2)

therefore, we will put the equation as such
<u>0-(-5)= 5</u>  = <em> </em><u><em>5</em></u>
0-(-4)= 4     <em> 4</em>

<em>this is our slope from the center to the point of tangency.</em>

We know that tangent lines are perpendicular to the radius, which we've already found the slope of. Perpendicular lines are opposite reciprocals of the line they are perpendicular to. 

Therefore, we take our slope from center to the tangent, and make it opposite and then take the reciprocal of that slope, which will give us the slope of the tangent line itself. (note: reciprocal means flip the numerator and denominator)
<u>5</u> =  <u>-5</u>  =  <u>-4</u><u>
</u>4     4        5   

Now, we have a point on the line, and the line's slope. We can use slope-intercept equation to find the equation of the line.

Slope-int      y=mx+b
(x,y) is a point,
m is the slope
b is the y intercept  ( the point where x=0, or where its on the y axis)

now we plug things in
(-4,-5) is our point,
<u>-4</u>  is our slope
5

-5=<u>-4</u>(-4)+b       After we plug things in, solve for b
     5

-5= 3.2+b

-1.8= b  or  b=  <u />1 <u>4</u>
                         5

Now we just need to rewrite our equation with all our components.
(-4.-5) = point
<u>-4</u>  = slope<u>
</u>5
1 <u>4</u> = y-intercept<u>
</u>   5

<em>y=</em><u><em>-4</em></u><em> x+ 1 </em><u><em>4</em></u><em>     This is the equation of the tangent line</em><u>
</u><em>    5         5</em>


Hope that helped
7 0
3 years ago
A 12 foot ladder is leaning up against a wall. If the angel made between the ladder and the ground is 80 degrees. How far up can
lorasvet [3.4K]

Answer:

<h3>11.8 feet</h3>

Step-by-step explanation:

Given

Length of the ladder = 12foot

angle of elevation = 80 degrees

Required

Height of the wall (opposite side)

The set up will form a right angled triangle where

length of the ladder is the hypotenuse

height of the wall is opposite;

Using SOH, CAH, TOA trig identity

According to SOH

sin 80 = opp/hyp

sin80 = opp/12

opp = 12sin80

opp = 11.82 feet

Hence the height of the wall is 11.8feet (to the nearest tenth)

5 0
3 years ago
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