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3 years ago

Of a triangle

Mathematics

1 answer:

arsen [322]3 years ago

7 0

Complete question is attached.

Answer:

a) ED = 6.5 cm

b) BE = 14.4 cm

Step-by-step explanation:

From the triangle, we are given the following dimensions:

AB = 20 cm

BC = 5 cm

CD = 18 cm

AE = 26 cm

We are asked to find length of sides ED and BE.

a) Find length of ED.

From the triangle Let's use the equation:

$\frac{AB}{BC} = \frac{AE}{ED}$

Cross multiplying, we have:

AB * ED = AE * BC

From this equation, let's make ED subject of the formula.

$ED = \frac{AE * BC}{AB}$

Let's substitute figures,

$ED = \frac{26 * 5}{20}$

$ED = \frac{130}{20} = 6.5$

Therefore, length of ED is 6.5 cm.

b) To find length of BE, let's use the equation:

$\frac{AB}{AC} = \frac{BE}{CD}$

Cross multiplying, we have:

AB * CD = AC * BE

Let's make BE subject of the formula,

$BE = \frac{AB * CD}{AC}$

From the triangle, length AC = AB + BC.

AC = 20 + 5 = 25

Substituting figures, we have:

$BE = \frac{20 * 18}{25}$

$BE = \frac{360}{25} = 14.4$

Therefore, length Of BE is 14.4cm

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This is a homeork problem from my class

rosijanka [135]

This is a quadratic function:

f(x)=ax²+bx+c

We have three points:
(0 , 77.6)
(5 , 78)
(10 , 78.6)

Then, we make the function wiht these points:
(0 , 77.6)

x=0
f(x)=77.6

a(0)²+b(0)+c=77.6
c=77.6

(5 , 78)
a(5)²+b(5)+77.6=78
25a+5b=78-77.6
25a+5b=0.4   (1)

(10 , 78.6)
a(10)²+b(10)+77.6=78.6
100a+10b=78.6-77.6
100a+10b=1 (2)

With the equations (1) and (2) we have a system of equations:
100a+10b=1
25a + 5b=0.4

We solve this system of equations by method of elimination.

   100a+10b=1
-4(25a+5b=0.4)
-----------------------------
   -10b=-0.6 ⇒    b=-0.6/-10=0.06

   100a+10b=1
-2(25a+5b=0.4)
----------------------------
   50a = 0.2 ⇒ a=0.2/50=0.004

We have a, b and c:
a=0.004
b=0.06
c=77.6

Therefore, the quadratic funtion is:
f(x)=0.004x²+0.06x+77.6
x=year of the beginning of the interval - 1980

The life expectancy for females born between 1995 and 2000 is when x=1995-1980=15
Therefore:
f(15)=0.004(15)²+0.06(15)+77.6
f(15)=0.004(225)+0.06(15)+77.6
f(15)=79.4

The life expectancy for females born between 2000 and 2005 is when:
x=2000-1980=20
therefore:
f(20)=0.004(20)²+0.06(20)+77.6
f(20)=1.6+1.2+77.6
f(20)=80.4

Answer:
The funtion is:
f(x)=0.004x²+0.06x+77.6
x=year of the beginning of the interval - 1980

The life expectancy for females born between 1995 and 2000 is 79.4 years.
The life expectancy for females born between 2000 and 2005 is 80.4 years.

8 0

2 years ago

Read 2 more answers

PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inher

lana66690 [7]

Answer:

a) $n=\frac{0.76(1-0.76)}{(\frac{0.01}{1.64})^2}=4905.83$

And rounded up we have that n=4906

b) For this case since we don't have prior info we need to use as estimatro for the proportion $\hat p =0.5$

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{1.64})^2}=6724$

And rounded up we have that n=6724

Step-by-step explanation:

We need to remember that the confidence interval for the true proportion is given by :

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

Part a

The estimated proportion for this case is $\hat p =0.76$

Our interval is at 90% of confidence, and the significance level is given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . The critical values for this case are: