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Liula [17]
3 years ago
13

when (2x - 3)^2 is subtracted from 5x^2, what is the result? And how can I show the answer? Thank you x

Mathematics
2 answers:
Leni [432]3 years ago
3 0
5x^2 - (2x - 3)^2 = 
5x^2 - ((2x - 3)(2x - 3)) =
5x^2 - (4x^2 - 6x - 6x + 9) =
5x^2 - (4x^2 - 12x + 9) =
5x^2 - 4x^2 + 12x - 9 =
x^2 + 12x - 9 <===
sladkih [1.3K]3 years ago
3 0
First expand (2x-3)^2
(2x-3)(2x-3)=(2x-3)(2x)+(2x-3)(-3)=4x²-6x-6x+9=4x²-12x+9

so
5x²-(4x²-12x+9)=5x²-4x²+12x-9=x²+12x-9
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Classify each conic section and write its equations in standard form. Show work.
svp [43]

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

8 0
2 years ago
Find the gradient and the coordinates of the y - intercept for the graph: y= 4 + 2x
LiRa [457]
Well gradient means "slope" I just found out from searching the web.
First let's put y = 4 + 2x into slope intercept form of y = mx + b
y = 2x + 4
"m" is the slope, in this equation it would be 2.
The slope or "gradient" is 2.

The y-intercept of any equation in slope intercept form is the value of "b"
In this equation, the y-intercept is 4.
8 0
3 years ago
Read 2 more answers
Miguel is ordering 6 bags of cat food from Canada. Each bag has a mass of 7.5 kg. To determine the shipping costs, Miguel needs
nadezda [96]

Answer:

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Step-by-step explanation:

7.5×6=45kg

1kg=2.2lb and we have 45kg because this is direct proportion what you do to one side you havbe to do to the other

so 2.2lb×45 gives you 99 pounds

8 0
2 years ago
One toothpick is 0.13 inch long, another is 0.33 inch. Which length is greater?
strojnjashka [21]
Well, 0.33 > 0.13.
So, 0.33 inches is greater than 0.13 inches.
7 0
2 years ago
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Austin is going to invest in an account paying an interest rate of 2.2% compounded daily. How much would Austin need to invest,
Elden [556K]

Answer:

Principal, P = $23675.90

Step-by-step explanation:

Given the following data;

Interest rate = 2.2 %

Future value = $27000

Time = 6 years

Number of times = 365 days

To find the principal amount, we would use the compound interest formula;

A = P(1 + \frac{r}{n})^{nt}

Where;

A is the future value.

P is the principal or starting amount.

r is annual interest rate.

n is the number of times the interest is compounded in a year.

t is the number of years for the compound interest.

Substituting into the equation, we have;

27000 = P*(1 + \frac{0.022}{365})^{365*6}

27000 = P*(1 + 0.000060)^{2190}

27000 = P*(1.000060)^{2190}

27000 = P*(1.1404)

P = \frac {27000}{1.1404}

Principal, P = $23675.90

8 0
3 years ago
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