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3 years ago

GEOMETRY HELP! SIMILAR TRIANGLE!

Mathematics

1 answer:

mylen [45]3 years ago

7 0

1) Yes
2)B. AA
3) The angles are congruent and both are right triangles.
4) 90
5) 60
6) 60
7) 90
9) 4

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Solve the system of equations

rewona [7]

Answer:

x = 1/4

y = -1/2

z = 9/4

Step-by-step explanation:

Here we have a system of 3 equations with 3 variables:

4*x + 2*y + 1 = 1

2*x - y = 1

x + 3*y + z = 1

The first step to solve this, is to isolate one of the variables in one of the equations, let's isolate "y" in the second equation:

2*x - y = 1

2*x - 1 = y

Now that we have an expression equivalent to "y", we can replace this in the other two equations:

4*x + 2*(2*x - 1) + 1 = 1

x + 3*(2*x - 1) + z = 1

Now let's simplify these two equations:

8*x - 1 = 1

7*x - 3 + z = 1

Now, in the first equation we have only the variable x, so we can solve that equation to find the value of x:

8*x - 1 = 1

8*x = 1 + 1 = 2

x = 2/8 = 1/4

Now that we know the value of x, we can replace this in the other equation to find the value of z.

7*(1/4) -3 + z = 1

7/4 - 3 + z = 1

z = 1 + 3 - 7/4

z = 4 - 7/4

z = 16/4 - 7/4 = 9/4

z = 9/4

Now we can use the equation y = 2*x - 1 and the value of x to find the value of y:

y = 2*(1/4) - 1

y = 2/4 - 1

y = 1/2 - 1

y = -1/2

Then the solution is:

x = 1/4

y = -1/2

z = 9/4

7 0

2 years ago

What is the best approximation for the input value when f(x)=g(x)?

Lostsunrise [7]

Answer:

$x=0$ and $x=1$ .

Step-by-step explanation:

If we have to different functions like the ones attached, one is a parabolic function and the other is a radical function. To know where $f(x)=g(x)$ , we just have to equalize them and find the solution for that equation:

$x^{2}=\sqrt{x} \\(x^{2} )^{2}=(\sqrt{x} )^{2}\\x^{4}=x\\x^{4}-x=0\\x(x^{3}-1)=0\\$

So, applying the zero product property, we have:

$x=0\\x^{3}-1=0\\x^{3}=1\\x=\sqrt[3]{1}=1$

Therefore, these two solutions mean that there are two points where both functions are equal, that is, when $x=0$ and $x=1$ .

So, the input values are $x=0$ and $x=1$ .

8 0

2 years ago

Read 2 more answers

Which statement best explains a negative impact that zebra mussels can have on an ecosystem?

Oduvanchick [21]

The correct answer is D

8 0

2 years ago

There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the outp

Mariana [72]

Answer:

<em> 15</em>
<em> 42,250</em>

Step-by-step explanation:

The given function is,

$P=40000+300x-10x^2$

where,

P = the total production of apples,

x = the number of trees added.

As the quadratic function has a negative leading coefficient, so it will open downward and at the vertex the value of function is maximum.

The vertex will be at $\left(-\dfrac{b}{2a},-f\left(\dfrac{b}{2a}\right )\right)$

The value of the function will be maximum at,

$x=-\dfrac{b}{2a}$

Putting the values,

$x=-\dfrac{300}{2\times (-10)}=\dfrac{300}{2\times 10}=\dfrac{300}{20}=15$

So at x=15 or for 15 number of trees the production will be ,maximum.

Putting x=15 in f(x) will yield the maximum production of apples.

$P=40000+300(15)-10(15)^2=42,250$

4 0

2 years ago

Solve for this equation. x-2/5=1/5

Studentka2010 [4]

Answer:

3/5 or

0.6

Step-by-step explanation:

You could change these fractions to decimals, but you may not be convinced that the answer you get is the same as just using fractions. I'll start by using fractions.

x - 2/5 = 1/5 Add 2/5 to both sides

x - 2/5 + 2/5 = 1/5 + 2/5 The left side cancels to 0.

x = 1/5 + 2/5 The denominators (bottom the fraction) are the same. Just add the tops.

x = (1 + 2)/5

x = 3/5

=======================

If you use your calculator to find 2/5 and 1/5, you can get the same answer as 3/5

0.4

By the same method, 1/5 = 0.2

Substitute into the original equation

x - 0.4 = 0.2 Add 0.4 to both sides

x - 0.4 +0.4 = 0.2 + 0.4 The left side reduces just to x

x = 0.2 +0.4

x = 0.6

If you let your calculator do the work, like this

0.6

The answers are the same.

7 0

2 years ago

Read 2 more answers