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2 years ago

PLEASE HELP QUICK!!!

Mathematics

1 answer:

DaniilM [7]2 years ago

7 0

Answer:

$y = 2x + 3$

Step-by-step explanation:

Given :-

Two points are given to us .
The points are (3,9) and (0,3) .

And we need to find the equation in slope intercept form. So here we can find the equation of the line using two point form , as ,

$\implies y - y_1 = \dfrac{ y_2-y_1}{x_2-x_1}( x - x_1)$

Now plug in the respective values ,

$\implies y - 9 = \dfrac{ 3-9}{0-3}( x - 3) \\\\\implies y - 9 =\dfrac{-6}{-3}( x - 3 ) \\\\\implies y - 9 = 2( x - 3 ) \\\\\implies y - 9 = 2x - 6 \\\\\implies y = 2x - 6 +9 \\\\\implies \boxed{ y = 2x + 3 }$

Hence the equation in slope intercept form is y = 2x + 3. 

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Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)

zubka84 [21]

$\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } 
$

This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

$\frac{ \sqrt{-49}}{7-2i-4-9i}$

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result:

$\frac{ \sqrt{-49} }{3-11i}$

Now, the $\sqrt{-49}$ must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to $\sqrt{49} \sqrt{-1}$
This means that we get the result 7i for the numerator.

$\frac{7i}{3-11i}$

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: $x^2 - y^2 =(x+y)(x-y)$
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

$\frac{7i (3+11i)}{(3-11i)(3+11i)}$

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how $(3-11i)(3+11i)= 3^2 -(11i)^2$ therefore, we can finally write:

$\frac{7i(3+11i)}{3^2 - (11i)^2 }$

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product $7i(3+11i) = 21i+77i^2$ .
You should know from your classes that i^2 = -1, thefore the numerator simplifies to $-77+21i$
You can do it as a curious thing, but simplifying yields the result:
$\frac{-77+21i}{130}$

7 0

3 years ago

22. A rectangular container, whose base is a square

Pie

Answer:

the will be volume is 6cm

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3 years ago

Sketch a quadratic function with the given characteristics.

xeze [42]

Answer:

See photo below

Add arrows to the two ends of the parabola.

Step-by-step explanation:

To sketch this quadratic function, we to connect three dots: the two roots and a vertex.

The given roots are -1 and 1.

Draw two dots at the x-intercepts, which are (-1, 0) and (1, 0).

Vertex dot: V (x, y)

The vertex x-coordinate always in the middle of the two roots. The middle of -1 and 1 is 0. That's the same as the y-axis.

V (0, y)

Since the function increases when x < 0, the parabola will open up.

We read from left to right. The greater numbers are towards the top of the page.

You can put the vertex anywhere on the y-axis that is below the x-axis.

7 0

2 years ago

18 times the quantity g plus 5

balu736 [363]

Comparing it to a system of equations, the expression is represented as follows:

18g + 5.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, we consider g as the variable. Then:

18 times the quantity g is 18g.

Adding 5 to the expression, we have that 18g + 5.

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

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1 year ago

Please help! What is the formula for simplest interest?

natima [27]

Answer:

A= P(1+rt)

Step-by-step explanation:

8 0

2 years ago

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