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4 years ago

How to prove two triangles congruent

2 answers:

7 0

There's a lot of theorems SAS, ASA, SSA, AAS, SSS

S=Side
A=Angle

If the order of the sides and angles in one of the above are congruent, then the triangles are congruent.

Hope this helps :D

yuradex [85]4 years ago

6 0

To prove that two triangles are congruent, all three pairs of corresponding angles need to be congruent and the same. When two angles in one triangle are congruent to at least two angles in another triangle, the third angles are also congruent and therefor the triangles are congruent

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Use completing the square to solve x^2+6x=13

lara [203]

Answer:

x = -3 +/- square root(22)

Step-by-step explanation:

x = -b +/- square root(b^2 - 4ac) / 2a

ax^2 + bx + c = 0

these are both the quadratic formula but one is solved for the x and another for 0

a= 1

b= 6

c = -13

x= -6 +/- square root( 6^2 - 4(1)(13)) / 2(1)

x = -6 +/- sqrt( 36 + 52) / 2

x= -6 +/- sqrt (88) / 2

sqrt of 88 = 2 x sqrt (22)

divide 2 on each

x= -3 +/- sqrt (22)

8 0

3 years ago

The rate of growth of profit (in millions) from an invention is approximated by Upper P prime (x )equals x e Superscript negati

Alecsey [184]

Answer:

The function is $P(x) = \frac{1}{2} e^{-x^2} +0.016$

Step-by-step explanation:

From the question we are told that

The rate of growth is $P'(x) = xe^{x} - x^2$

The total profit is $P(2) =$ $25,000

The time taken to make the profit is $x = 2 \ years$

From the question

$P'(x) = xe^{-x^2}$ is the rate of growth

Now here x represent the time taken

Now the total profit is mathematically represented as

$P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,$

So using substitution method

We have that

$u = - x^2$

$du = 2xdx$

$p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du$

$p(x) = {\frac{1}{2} [ e^{-u}} +c ]$

$p(x) = {\frac{1}{2} e^{-x^2}} + \frac{1}{2} c$ recall $u = - x^2$ and let $\frac{1}{2} c = Z$

At x = 2 years

$P(x) =$ $25,000

Since the profit rate is in million

$P(x) =$ $25,000 = $\frac{25000}{1000000} =$ $0.025 millon dollars

$0.025 = {\frac{1}{2} e^{-2^2}} + Z$

=> $Z = 0.025 - {\frac{1}{2} e^{-2^2}}$

$Z = 0.016$

So the profit function becomes

$P(x) = \frac{1}{2} e^{-x^2} +0.016$

5 0

3 years ago

Approximately 85% of electronic stores marked up the price for a new headset. Suppose a random sample of 12 stores is selected.

Leviafan [203]

Answer:djdjdjxbc. D

Step-by-step explanation:

8 0

3 years ago

3900 workers in 3 buildings. twice as many work in largest building as the smallest of the 3 . there are 500 more workers in the

Svetllana [295]

<h3><u>Question:</u></h3>

There are 3900 workers in the three main buildings downtown. Twice as many people work in the largest building as in the smallest of the three. There are 500 more workers in the second-largest building than in the smallest building. How many workers are in each building?

<h3><u>Answer:</u></h3>

There are 850 workers in smallest building and 1700 workers in largest building and 1350 workers in second largest building

<h3><u>Solution:</u></h3>

Let "b" be the number of workers in smallest building

Given that Twice as many people work in the largest building as in the smallest of the three

number of workers in largest building = 2b

Given that There are 500 more workers in the second-largest building than in the smallest building

Number of workers in second largest building = 500 + b

Given that there are 3900 workers in 3 buildings

b + 2b + 500 + b = 3900

4b + 500 = 3900

4b = 3900 - 500

4b = 3400

b = 850

Thus there are 850 workers in smallest building

workers in largest building = 2b = 2(850) = 1700

workers in second largest building = 500 + b = 500 + 850 = 1350

Thus there are 850 workers in smallest building and 1700 workers in largest building and 1350 workers in second largest building

6 0

3 years ago

Gracie went for a morning walk and met her old friend Suzie and her daughter Jennie after a long time. Gracie asked Suzie how ol

NeTakaya

I believe she is 6 I am not positive about it

7 0

3 years ago