All categories

3 years ago

X^2 = 6x + 27; COMPLETING THE SQUARE

Mathematics

2 answers:

serg [7]3 years ago

5 0

Answer:

Step-by-step explanation:

x^2 = 6x + 27

x^2 - 6x = 27

x^2 - 6x + 9 = 27 + 9

(x - 3)^2 = 36

x - 3 = ± √ 36

x = 3 ± 6

x = 3 + 6 = 9

x = 3 - 6 = -3

solutions are : x = -3 or x = 9

DedPeter [7]3 years ago

3 0

x^2 = 6x + 27

x^2−6x−27=0

(x−9)(x+3)=0

x=9,−3

You might be interested in

I’m stuck on this question. any help would be greatly appreciated

Mademuasel [1]

Using the Pythagorean theorem we get:

$y^2+8^2=12^2.$

Simplifying the above result we get:

$y^2+64=144.$

Subtracting 64 from the above equation we get:

$\begin{gathered} y^2+64-64=144-64, \\ y^2=80. \end{gathered}$

Therefore:

$y=\sqrt{80}\approx8.9.$

Answer:

$y=8.9.$

4 0

2 years ago

If a line has a slope of 2 and contains the point (-2, 1) what is the equation in point slope form

Elden [556K]

Answer:

y - 1 = 2(x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 2 and (a, b) = (- 2, 1), thus

y - 1 = 2(x - (- 2)), that is

y - 1 = 2(x + 2) ← in point- slope form

4 0

3 years ago

Mr. Jones bought a piece of land for 60 000. The land increased in value by 20% in a year. The new value of the land is

borishaifa [10]

Answer:

$72,000

Step-by-step explanation:

If we take 60,000 and then take 20 percent of it, we get 12,000. Then we add 12,000 to 60,000 and it gives us 72,000.

4 0

3 years ago

U-substitutions only work for specific kinds of expressions. Below, you are asked to choose a value of n for which u-substitutio

Dahasolnce [82]

Answer:

Step-by-step explanation:

(a) $\int x^n e^{5x^4+1} \ dx$

Suppose $5x^4 + 1 = f$

by differentiation;

$\implies \ 20 x^3 dx = df --- (1)$

Suppose n = 3

Then, the integral

$I = \int x^ 3 e^{5x^4 + 1} \ dx$

$= \int e^f \ \dfrac{df}{20}$

$= \dfrac{1}{20} \int e^f \ dt$

$= \dfrac{1}{20} e^f + C$

recall that $f = 5x^4 + 1$

Then;

$\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}$

(b) $\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx$

suppose; $\dfrac{1}{x^3} = f$

$x^3 = f$

$\implies -3x^{-4} \ dx = df$

$\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df$

If n = u, then the integration is:

$I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx$

$= \int -\dfrac{1}{3} \ cos \ f \ df$

$= -\dfrac{1}{3} \int \ cos \ f \ df$

$= -\dfrac{1}{3} \ sin \ f + C$

Since; $x^3 = f$

Then;

$\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}$

Suppose $x^2 + 8x - 4 = f$

Then, by differentiation of both sides

$(2x + 8) \ dx = df$

$(x + 4) \ dx = \dfrac{1}{2} \ df$

Suppose n = 4 in integration, then:

$I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx$

By substitution;

$I = \int \dfrac{1}{2}\dfrac{1}{f} \ df$

$= \dfrac{1}{2} \ \ { In |f|} + C$

$\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}$

7 0

3 years ago

Find the surface area of the pyramid shown to the nearest whole number.

Snezhnost [94]

Answer:

<h3>The answer is option A</h3>

Step-by-step explanation:

Surface area of a pyramid =

area of base + area of triangular faces

Since it's a square based pyramid

It's surface area is

area of base + 4( area of one triangular face)

Since the square has equal sides

<u>For square base </u>

Area of a square = l²

where l is the length

From the question l = 5

So we have

Area of square base = 5² = 25ft²

<u>For one of the triangular face</u>

Area of a triangle = ½ × base × height

base = 5

height = 6

Area = ½ × 5 × 6 = 15ft²

So the surface area of the pyramid is

25 + 4(15)

= 25 + 60

We have the final answer as

<h3>Surface area = 85 ft²</h3>

Hope this helps you

7 0

3 years ago