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denis-greek [22]
3 years ago
8

Prove the converse of the Pythagorean theorem using similar triangles. The converse of the Pythagorean theorem states that when

the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures. HELPPP

Mathematics
2 answers:
liraira [26]3 years ago
8 0

Answer:

Step-by-step explanation:By AA similarity postulate

△ADB∼△ABC∼△BDC

therefore the sides of the triangles are proportional, in particular

ADAB=ABAC ACBC=BCDC

By algebra we have the following equations

AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC

this is the same as

AD⋅AC=AB2AC⋅DC=BC2

"Equals added to equals are equal" allows us to add the equations

AD⋅AC+AC⋅DC=AB2+BC2

By distributive property

AC(AD+DC)=AB2+BC2

but by construction AD+DC=AC.

Substituting we have

AC⋅AC=AB2+BC2

this is equivalent to

AB2+BC2=AC2

which is what we wanted to prove

Whitepunk [10]3 years ago
5 0

Answer:

I don't how to exactly put the explanation in words I hope this helps you

Step-by-step explanation:

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I need help with this question
beks73 [17]

Answer:

  1024

Step-by-step explanation:

1 division: 2

2 divisions: 2×2 = 4

3 divisions: 2×(2×2) = 8

The number of viruses is 2^n, where n is the number of divisions.

After 10 divisions, there are 2^10 = 1024 viruses.

4 0
2 years ago
Which graph represents y=1/2x+2 <br><br> please help!!
wel

Answer:

B

Step-by-step explanation:

Let’s first look at the y-intercept. Since the equation is in y = mx + b form, we know that m is the slope and b is the y-intercept, so the slope is 1/2 and the y-intercept is 2, or (0,2). We can narrow down our search by noticing that C and D don’t intersect (0,2). That leaves A and B.

The slope is calculated by (y_1 - y_2)/(x_1 - x_2) given points (x_1, y_1) and (x_2, y_2). The slope for A is (4-0)/(2-(-2)) = 4/4 = 1 and the slope for B is (2-0)/(0-(-4)) = 2/4 = 1/2. The slope of B matches the slope that we are looking for. So, the answer is B.

8 0
3 years ago
Urgent, I need help quickly
Alexeev081 [22]

Answeit is blurry for me take a picture again

Step-by-step explanation:

6 0
3 years ago
Find the Exponential Regression using the table. Write the initial amount, common ratio, and equation for the table.
Triss [41]

Answer:

Initial temperature;

432.76

Common ratio;

-0.067

Equation;

y=432.76e^{-0.067x}

Step-by-step explanation:

In this scenario, the time in minutes represents the independent variable x while the temperature of the pizza represents the dependent variable y.

The analysis is performed in Ms. Excel. The first step is to obtain a scatter plot of the data then finally inserting an exponential trend line to obtain the required equation.

The Ms. Excel output is shown in the attachment below. To obtain the initial temperature we substitute x = 0 in the equation. On the other hand, the common ratio is the exponent in the equation.

6 0
3 years ago
What is the axis of symmetry for f(x) = -3x2 + 18 - 7
solong [7]

The vertex form:

y=a(x-h)^2+k\\\\(h,\ k)-vertex

The axis of symetry is x = h.

y=ax^2+bx+c\to h=\dfrac{-b}{2a}

We have

f(x)=-3x^2+18x-7\to a=-3,\ b=18,\ c=-7

Substitute:

h=\dfrac{-18}{(2)(-3)}=\dfrac{-18}{-6}=3

<h3>Answer: x = 3</h3>
6 0
3 years ago
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