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4 years ago

58. Graph the function y=x^2+3x-18. How many real roots does the function have?

Mathematics

1 answer:

Airida [17]4 years ago

8 0

9514 1404 393

Answer:

58. 2 real roots; see attached for a graph

59. -6, 3

Step-by-step explanation:

58. A graphing calculator graphs this easily. The graph is shown in the attachment. There are 2 x-intercepts, hence 2 real roots.

59. The x-intercepts are (-6, 0) and (3, 0), so the x-values x=-6 and x=3 satisfy the equation y = 0.

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Help solve equations by completing the square

Allushta [10]

$x^2+10x+22=13\\x^2+10x+22-13=0\\x^2+10x+9=0\\$

Now completing the square.

$(x^2+10x)+9=0\\(x^2+10x+25)+9-25=0\\(x+5)^2-16=0\\(x+5)^2=16$

(x+5)² = 16 is the rewritten equation... For first question btw.

For the solutions to the equation -

$x+5=\sqrt{16},-\sqrt{16} \\x+5=4,-4\\x=4-5,-4-5\\x=-1,-9$

x = -1,-9 is the solution, for the second question.

5 0

3 years ago

Alex is 12 years older than George. Carl is Three times older than Alex The sum of their ages is 68 Find the ratio of George’s a

earnstyle [38]

Ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4

Solution:

Let "a" be the age of Alex

Let "g" be the age of George

Let "c" be the age of Carl

Alex is 12 years older than George

Therefore,

Age of Alex = 12 + Age of George

a = 12 + g

g = a - 12 ---- eqn 1

Carl is Three times older than Alex

Age of Carl = 3 x Age of Alex

c = 3a -------- eqn 2

The sum of their ages is 68

age of Alex + age of George + age of Carl = 68

a + g + c = 68 ----------- eqn 3

Substitute eqn 1 and eqn 2 in eqn 3

a + a - 12 + 3a = 68

5a - 12 = 68

5a = 12 + 68

5a = 80

a = 16

Substitute a = 16 in eqn 2

c = 3(16) = 48

c = 48

Substitute a = 16 in eqn 1

g = 16 - 12 = 4

g = 4

Find the ratio of George’s age to Carl’s age to Alex’s age

Ratio of George’s age to Carl’s age to Alex’s age = g : c : a

g : c : a = 4 : 48 : 16

Divide the above ratio by 4 to reduce to lowest terms

g : c : a - 1 : 12 : 4

Thus ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4

6 0

3 years ago

Need help, please explain

Sever21 [200]

Answer:

(x - 2)(x + 2)

Step-by-step explanation:

x² - 4 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), that is a product of two binomials

Given

x² - 4

= x² - 2²

= (x - 2)(x + 2)

7 0

3 years ago

A cylinder has a height of 6 millimeters and a radius of 4 millimeters. What is its volume? Use ≈ 3.14 and round your answer t

netineya [11]

Answer:

$V=301.44\ \text{mm}^2$

Step-by-step explanation:

Given that,

Height of the cylinder, h = 6 mm

Radius of the cylinder, r = 4 mm

We need to find the volume of the cylinder. The formula for the radius of the cylinder is given by :

$V=\pi r^2 h$

Putting given values,

$V=3.14\times (4)^2 \times 6\\\\V=301.44\ \text{mm}^2$

So, the volume of the cylinder is $301.44\ \text{mm}^2$ .

4 0

3 years ago

Hello can you help me the question is:write two equivalent fractions?

MakcuM [25]

Answer:

Step-by-step explanation:

1)8/12=12/18

2)12/20=18/30

3)4/16=6/24

6 0

3 years ago