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aev [14]
3 years ago
12

The base of a triangle exceeds the height by 9 centimeters. If the area is 56 square centimeters, find the length of the base an

d the height of the triangle.
Mathematics
1 answer:
shepuryov [24]3 years ago
8 0

Answer:

The height of the triangle is 7cm and the base is 16cm

Step-by-step explanation:

First of all we have to know the formula to calculate area of ​​a triangle

a = area = 56

b = base

h = heigth

a = (b * h)/2

we replace the known values and we make 2 equations

56cm² = (b * h)/2

b = h + 9cm

we replace b by (h + 9cm) in the first equation

56cm² = (h + 9cm * h)/2

56cm² * 2 = h² + 9h

0 = h² + 9h - 112cm²

we use bhaskara formula:

(-b (±) √ (b² - 4ac) ) / 2a

we replace with the known values

h = (-9 (±) √ (9² - 4*1*(-112) ) ) / 2*1

h = (-9 (±) √ (81 + 448) ) ) / 2

h = (-9 (±) √529) /2

h = (-9 (±) 23)/2

h1 = (-9 + 23) / 2

h1 = 14 / 2

h1 = 7

h2 = (-9 - 23) / 2

h2 = -32 / 2

h2 = -16

The height of the triangle is 7cm and the base is 16cm

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marysya [2.9K]
First, subtract to get the difference.
2.85 – 2.78 = 0.07

Next, divide 2.78 by 100
2.78 ÷ 100 = 0.0278
So, 0.0278 is 1%. Divide 0.07 by 0.0278 to get the answer.
0.07 ÷ 0.0278 ≈ 2.518
2.518 ≈2.5
Therefore, the percentage increase is approximately 2.5% (that's the answer).

Hope this helps!
8 0
3 years ago
Sandra and Monica are both saving money. The equation y = 82x
Tanya [424]

Answer:

B

Step-by-step explanation:

328= 82 x 4

348/4 = 87

87 - 82 = 5

7 0
2 years ago
A profit of a football club after a takeover is modeled by p(t) = t3 - 14t2 + 20t + 120, which t is the number of years after th
Bogdan [553]
T = 5, so after 5 years
p(t) = t^3 - 14t^2 + 20t + 120

Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10

Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)

0 = 3t - 2
2 = 3t
2/3 = t

Plug 2/3 into original equation, this is a maximum. We want the minimum:

0 = t - 5
5 = t

Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
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6 0
3 years ago
HELP! ASAP!<br> What is the measure of ∠A?<br><br><br> What is the measure of ∠B?
olganol [36]
The opposite angles of a parallelogram are equal.
Therefore
m∠A = m∠C, so that
5y - 3 = 3y + 27
Subtract 3y from each side.
5y - 3y - 3 = 3y - 3y + 27
2y - 3 = 27
Add 3 to each side.
2y - 3 + 3 = 27 + 3
2y = 30
y = 30/2 = 15

Therefore
m∠A = 5*15 - 3 = 72°
m∠C = 72°

Let x = m∠B
Then x = , m∠B = m∠C
Because the sum of the angles in the parallelogram is 360°, therefore
x + x + 72 + 72 = 360
2x = 360-144 = 216
x = 216/2 = 108

Answer:
m∠A = 72°
m∠B = 108°

3 0
3 years ago
Read 2 more answers
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Sergio [31]

Answer: 110

Step-by-step explanation:

11x20=220 220\2=110

6 0
3 years ago
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