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3 years ago

9

What is the domain and range of the equation y = 6/(x+2) + 4?

1 answer:

tiny-mole [99]3 years ago

8 0

Answer:

.2 sdfgghh 45

Step-by-step explanation:

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Solve the following quadratic equation.

Nonamiya [84]

Given:

Consider the given equation is

$(x-18)^2=1$

To find:

The values of x.

Solution:

We have,

$(x-18)^2=1$

Taking square root on both sides, we get

$x-18=\pm\sqrt{1}$

$x-18=\pm 1$

Adding 18 on both sides, we get

$x-18+18=\pm 1+18$

$x=\pm 1+18$

Now,

$x=1+18$ and $x=-1+18$

$x=19$ and $x=17$

Therefore, the correct option is A.

5 0

3 years ago

Area of Square = 45 cm?<br> What is the perimeter?

9966 [12]

It’s 9 centimeters long

4 0

3 years ago

Find all pairs of real numbers (a,b) such that (x-a)^2+(2x-b)^2=(x-3)^2+(2x)^2

Mrrafil [7]

Answer:

$(3,0)$

$(\frac{-9}{5},\frac{12}{5})$

Step-by-step explanation:

Let's expand both sides.

I'm going to use the following identity to expand the binomial squared expressions: $(u+v)^2=u^2+2uv+v^2$ or $(u-v)^2=u^2-2uv+v^2$ .

Left-hand side:

$(x-a)^2+(2x-b)^2$

$(x^2-2ax+a^2)+((2x)^2-2b(2x)+b^2)$

$x^2-2ax+a^2+4x^2-4bx+b^2$

Reorder so $x^2$ 's are together and that $x[tex]'s are together.[tex](x^2+4x^2)+(-2ax-4bx)+(a^2+b^2)$

$5x^2+(-2a-4b)x+(a^2+b^2)$

Right-hand side:

$(x-3)^2+(2x)^2$

$x^2-2(3)x+9+4x^2$

$x^2-6x+9+4x^2$

Reorder so $x^2$ 's are together and that $x[tex]'s are together.[tex](x^2+4x^2)+(-6x)+9$

$5x^2-6x+9$

Now let's compare both sides.

If we want both sides to appear exactly the same we need to choose values $a$ and $b$ such the following are true equations:

$-2a-4b=-6$

$a^2+b^2=9$

So if we solve the system we can find the values $a$ and $b$ such that the left=right.

Let's solve the first equation for $a$ in terms of $b$ .

Add $2a$ on both sides:

$-4b=-6+2a$

Divide both sides by -4:

$b=\frac{-6+2a}{-4}$

Reduce (divide top and bottom by -2):

$b=\frac{3-a}{2}$

Now let's plug this into second equation:

$a^2+b^2=9$

$a^2+(\frac{3-a}{2})^2=9$

$a^2+\frac{9-6a+a^2}{4}=9$ (I used the identity $(u-v)^2=u^2-2uv+v^2$ )

Multiply both sides by 4 to clear the fractions from the problem:

$4a^2+(9-6a+a^2)=36$

Combine like terms on left hand side:

$4a^2+a^2-6a+9=36$

$5a^2-6a+9=36$

Subtract 36 on both sides:

$5a^2-6a-27=0$

Now let's try to factor.

We are going to try to find two numbers that multiply to be 5(-27) and add to be -6.

5(-27)=(5*3)(-9)=15(-9)=-15(9) while -15+9=-6.

So let's replace $-6a$ with $-15a+9a$ and factor by grouping.

$5a^2-15a+9a-27=0$

$5a(a-3)+9(a-3)=0$

$(a-3)(5a+9)=0$

This implies $a-3=0$ or $5a+9=0$ .

Solving the first is easy. Just ad 3 on both sides to get: $a=3$ .

The second requires two steps. Subtract 9 and then divide by 5 on both sides.

$5a=-9$

$a=\frac{-9}{5}$ .

So let's go back to finding $b$ now that we know the $a$ values.

If $a=3$ and $b=\frac{3-a}{2}$ ,

then $b=\frac{3-3}{2}=0$ .

So one ordered pair $(a,b)$ that satisfies the equation is:

$(3,0)$ .

If $a=\frac{-9}{5}$ and $b=\frac{3-a}{2}$ ,

then $b=\frac{3-\frac{-9}{5}}{2}$ .

Let's multiply top and bottom by 5 to clear the mini-fraction.

$b=\frac{15-(-9)}{10}$

$b=\frac{24}{10}$

$b=\frac{12}{5}$

So one ordered pair $(a,b)$ that satisfies the equation is:

$(\frac{-9}{5},\frac{12}{5})$ .

5 0

4 years ago

Write an equation of The line that passes through the given point and is parallel to the given line (4;5);y=-3/2x+3

mojhsa [17]

9514 1404 393

Answer:

y = -3/2x +11

Step-by-step explanation:

The slope of the parallel line is the same as the slope of the given line, so ...

m = -3/2

The y-intercept of the parallel line can be found from ...

b = y -mx

b = 5 -(-3/2)(4) = 11

So, the desired equation is ...

y = mx +b

y = -3/2x + 11

_____

<em>Additional comment</em>

Since you know the slope and a point on the desired line, you can write down the equation directly using the point-slope form. No additional math is required.

y -5 = -3/2(x -4)

6 0

3 years ago

Pls PLSSS help I don’t understand this please help pls

MrRa [10]

Answer:

I'm not that good of math but I think the answer is 3 3 inches

6 0

3 years ago