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3 years ago

4x + 9y = 29 x = 5y - 87

1 answer:

8 0

What I would do here is substitute "5y -87" for x in the first ecquation, since the second equation is already in the form "x=..." so:

4*(5y-87)+9y=29

getting rid of the bracket:

20y-348+9y=29

adding up:

29y=29+348

29y= 377

dividing by 29:

y=13

and now we can calculate x, which is 5*13-87=65-87=-22

so x=-22

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Exercise #4

vlada-n [284]

Answer: im not smart so i cant anwer that

Step-by-step explanation:

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3 years ago

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?

egoroff_w [7]

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:

$-2x^2+4x=-1$ . Now we factor out the -2:

$-2(x^2-2x)=-1$ . Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:

$-2(x^2-2x+1)=-1-2$ . Simplifying gives us this:

$-2(x^2-2x+1)=-3$

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

$-2(x-1)^2+3=y$

From this form,

$y=-a(x-h)^2+k$

you can determine the coordinates of the vertex to be (1, 3)

5 0

3 years ago

Read 2 more answers

What is the equation in point slope form of the line passing through (0,5) and (-2,11)

IRISSAK [1]

The equation of the line passing through $(x_1,y_1)$ and $(x_2,y_2)$ is

$\frac{x-x_1}{y-y_1} =\frac{x_2-x_1}{y_2-y_1}$ . Here

$\frac{y_2-y_1}{x_2-x_1}$ is the slope of the line.

Substituting numerical values, the equation of the line is

$\frac{x-0}{y-5} =\frac{-2-0}{11-5} \\ \frac{x}{y-5} =-\frac{1}{3} \\ 3x=5-y\\ 3x+y=5$

The equation of the line is $3x+y=5$

6 0

3 years ago

1.5.PS-21

dybincka [34]

Answer:

Increase in the length of one side = 3.8 ft

Step-by-step explanation:

Yossi has garage whose area is 280 ft²

After rebuilt their is increment in area by 50%

New Area = 280 × 150% = 420 ft²

Also we know that Area of Square = (Length) × (Length)

⇒ Length of Newly built garage = √420 = 20.5 ft

and Length of Originally garage = √280 = 16.7 ft

⇒ Increase in the length of one side = 20.5 - 16.7 = 3.8 ft

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3 years ago

How do you solve a complex number problem

Rzqust [24]

Find real values of the number a for which a.i is a solution of the polynomial equation. ... u,v and w are the three roots of the equation z3 - 1 = 0 . ... Calculate all solutions of |z-1|.|z-1|=1. ... The equation z3 - (n + i) z + m + 2 i = 0. ... Let z' the conjugate complex number of z.

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3 years ago