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2 years ago

Convert y =(x+1)(x-9) to vertex form

Mathematics

1 answer:

IgorC [24]2 years ago

5 0

Answer:

y = (x - 4)² - 25

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

y = (x + 1)(x - 9) ← expand factors using FOIL, thus

y = x² - 8x - 9

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

y = x² + 2(- 4)x + 16 - 16 - 9

= (x - 4)² - 25 ← in vertex form

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How do you use the metric system?

baherus [9]

Answer:

The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.

8 0

2 years ago

simplify the following expression: (x+7/4x) + (5/x-8) I also attached a photo of the problem if you get confused on how I typed

Gnoma [55]

Answer:

$\frac{x^{2} + 19x - 56}{4 {x}^{2} - 32x}$

Step-by-step explanation:

Start by making the denominators of both fraction the same. This can be done by multiplying one fraction's denominator by the other.

After simplifying and combining the two fractions together, check if the numerator can be factorised such that there is a common factor in the denominator and numerator. In this case, the numerator cannot be factorised.

Lastly, expand the denominator.

$\frac{x + 7}{4x} + \frac{5}{x - 8}$

$= \frac{(x + 7)(x - 8)}{4x(x - 8)} + \frac{5(4x)}{4x(x - 8)}$

$= \frac{x(x) + x( - 8) + 7(x) + 7( - 8) + 20x}{4x(x - 8)}$

$= \frac{ {x}^{2} - 8x + 7x - 56 + 20x }{4x(x - 8)}$

$= \frac{ {x}^{2} + 19x - 56}{4x(x - 8)}$

$= \frac{ {x}^{2} + 19x - 56}{4 {x}^{2} - 32x}$

7 0

1 year ago

Please help me with precal

Doss [256]

Consider the function $f(x)=\sqrt{x}.$ This function has:

the domain $x\in [0,\infty);$
the range $y\in [0,\infty).$

If the domain of unknown function is $[a,\infty),$ then $x\ge a$ or $x-a\ge 0.$ This means that you have $\sqrt{x-a}$ as a part of needed function.

If the range of unknown function is $[b,\infty),$ then $y\ge b.$ This means that you have to translate function b units up and then the expression of the function is

$y=\sqrt{x-a}+b.$

Answer: correct choice is B.

6 0

2 years ago

A gardener makes a new circular flower bed. The bed is teen feet in diameter. Calculate the circumference and the area of the ci

KATRIN_1 [288]

Answer:

I. Circumference of circular flower bed = 31.42 ft.

II. Area of circular flower bed = 78.55 ft²

Step-by-step explanation:

Given the following data;

Diameter = 10 ft

Radius = diameter/2

Radius = 10/2

Radius, r = 5 ft

I. To find the circumference of the circular flower bed;

Circumference of circle = 2πr

Substituting into the formula, we have

Circumference of circular flower bed = 2*3.142*5

Circumference of circular flower bed = 31.42 ft

II. To find the area;

Area of circle = πr²

Substituting into the formula, we have;

Area of circular flower bed = 3.142*5²

Area of circular flower bed = 3.142*25

Area of circular flower bed = 78.55 ft²

8 0

2 years ago

If LMN is equal or congruent to XYZ, which congruences are true by CPCTC? check all that apply.

Kamila [148]

D. Z ~ N
E. ML~ YX
F. X~ L

7 0

3 years ago