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2 years ago

What is true about sides opposite congruent angles within a triangle?

Mathematics

1 answer:

nignag [31]2 years ago

8 0

Answer:

The converse of the base angles theorem is always true. The base angles theorem states that if two sides of a triangle are congruent the angles opposite them are also congruent. The converse of this statement is that if two angles in a triangle are congruent, then the sides opposite them will also be congruent

Step-by-step explanation:

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Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

3 years ago

What is the value of z in the equation 2(4z − 3 − 1) = 166 − 46?

shepuryov [24]

Refine $2(4z-3-1)$

$= 2(4z-4)$

Refine : $166 - 16 = 120$

therefore:

$2(z-4) = 120$

Divide both sides by 2 :

$\frac{2(z-4)}{2} = \frac{120}{2}$

$4z-4 = 60$

add 4 to both sides:

$4z-4+4 = 60+4$

$4z = 64$

Divide both sides by 4 :

$\frac{4z}{4} = \frac{64}{4}$

$z = 16$

hope this helps!

8 0

3 years ago

Read 2 more answers

The formula K=59(F−32)+273.15 converts temperatures from Fahrenheit F to Kelvin K.

Semmy [17]

Answer:

9/5 (K-273.15) + 32=F

Step-by-step explanation:

K=5 /9(F−32)+273.15

Subtract 273.15 from each side

K-273.15=5/9(F−32)+273.15-273.15

K-273.15=5/9(F−32)

Multiply by 9/5 on each side

9/5 (K-273.15)= 9/5 *5/9(F−32)

9/5 (K-273.15)=(F−32)

Add 32 to each side

9/5 (K-273.15) + 32=F−32 +32

9/5 (K-273.15) + 32=F

4 0

3 years ago

Read 2 more answers

If x+y=10 and x-y=4,find the value of x*x-y*y

Irina18 [472]

Hi,
$x^2-y^2=(x+y)*(x-y)=10*4=40$

6 0

3 years ago

Find the lateral area of a cylinder with the given measurements. Use 3.14 for π and round your answer to the nearest tenth. Heig

Zolol [24]

Answer:Lateral surface area is 847.8 centimeters^2

Step-by-step explanation:

The formula for determining the lateral surface area of a cylinder is expressed as

Lateral surface area = 2πrh

Where

r = radius of the cylinder

h = the height of the cylinder

From the information given,

r = 9 centimeters

h = 15 centimeters

π = 3.14

Lateral surface area = 2 × 3.14 × 9 × 15 = 847.8 centimeters^2

6 0

3 years ago

Read 2 more answers