How do I write 27/50 as a decimal

Use the completing the square method to find the roots of 2x^2+3x-15=13 include the steps, it would be greatly appreciated thank

Monica [59]

Answer:

The roots are

$x1= \frac{-3+\sqrt{233}}{4}$

$x2= \frac{-3-\sqrt{233}}{4}$

Step-by-step explanation:

we have

$2x^{2}+3x-15=13$

so

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$2x^{2}+3x=13+15$

$2x^{2}+3x=28$

Factor the leading coefficient

$2(x^{2}+(3/2)x)=28$

Complete the square. Remember to balance the equation by adding the same constants to each side

$2(x^{2}+(3/2)x+(9/16))=28+(9/8)$

$2(x^{2}+(3/2)x+(9/16))=233/8$

$(x^{2}+(3/2)x+(9/16))=233/16$

Rewrite as perfect squares

$(x+(3/4))^{2}=233/16$

square root both sides

$(x+\frac{3}{4})=(+/-)\sqrt{\frac{233}{16}}\\ \\(x+\frac{3}{4})=(+/-)\frac{\sqrt{233}}{4}\\ \\x= -\frac{3}{4}(+/-)\frac{\sqrt{233}}{4}$

$x1= -\frac{3}{4}(+)\frac{\sqrt{233}}{4}=\frac{-3+\sqrt{233}}{4}$

$x2= -\frac{3}{4}(-)\frac{\sqrt{233}}{4}=\frac{-3-\sqrt{233}}{4}$

7 0

3 years ago

there are 4 quarters for every one dollar and 10 dimes for every dollar. Without graphing, would the ratio of quarters to dollar

grin007 [14]

Answer:

no

Step-by-step explanation:

remember lines and line equations.

y = ax + b

a line has a slope indicating its angle relative to the basic coordinate axis and grid of x and y.

the slope is "a" in the generic equation, always the factor of x.

and it stands for the ratio y/x. it means how many units is y changing (and in what direction via its sign), when x changes a certain amount of units.

e.g. 3/4 means, when x changes 4 units to the positive (right) side, then y changes 3 units to the positive (up) side.

and also, when x changes 4 units to the negative (left) side, then y changes 3 units to the negative (down) side, as -/- is again +.

or -3/4 means, when x changes 4 units to the positive (right) side, then y changes 3 units to the negative (down) side, as -/+ is -.

and also, when x changes 4 units to the negative (left) side, then y changes 3 units to the positive (up) side, as +/- is again -.

so, we have here 2 ratios : 4/1 (quarters to dollars) and 10/1 (dimes to dollars).

remember what that means : y/x.

when x changes 1 unit to the right (x increases by 1), y changes 4 units up (y increases by 4).

and when x increases by 1 unit, y increases by 10 units.

what do you think is the steeper line ?

both are steep, as y increases much faster than x. but in the 10/1 ratio y increases much faster than in the 4/1 ratio. so, 10/1 is steeper than 4/1.

therefore, the answer is no. the ratio quarters to dollars does not represent a steeper line.

by the way, ratios like 4/1 or 10/1 are simply written 4 or 10.

so, when you see a line equation like y = 3x + 2,

you know the slope is 3 or actually 3/1.

3 0

3 years ago

Is 74 in. Less than 2 yd 2 in.

likoan [24]

74 inches is actually equal to 2 yd, 2 in.

Hope this helps you :) have a good day

4 0

4 years ago

Sean operates a lawn-cutting business. He charges $15 for a single lawn and $25 for a front and back lawn. Sean made $475 from 2

topjm [15]

The system of equations that models the given situation is given as follows:

x + y = 25.

15x + 25y = 475.

<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.

In this problem, the variables are given as follows:

Variable x: Number of single lawns cut.

Variable y: Number of front and back lawns cut.

He had 25 customers, hence:

x + y = 25.

He charges $15 for a single lawn and $25 for a front and back lawn, and made a total of $475, hence:

15x + 25y = 475

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

#SPJ1

3 0

2 years ago

Solve for n: 1/4 (n-2)=1/4n-1/2

alisha [4.7K]

Answer:

See below:

Step-by-step explanation:

So, we start off with the equation: $\frac{1}{4} (n-2) = \frac{1}{4}n-\frac{1}{2}$

If we simplify, we can use the distrubutive property to simplify the equation:

Here is how it goes:

$\frac{1}{4} (n-2) = (\frac{1}{4} * n )+(\frac{1}{4}*-2)$

So upon simplification of that, we get here: $\frac{1}{4}n + -\frac{1}{2}= \frac{1}{4}n-\frac{1}{2}$

Hm, somethings off, do you see that they are the same thing...

So, that means that there would be infinately many solutions.

You can plugin any number and you would get the same result!

7 0

2 years ago