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Luden [163]
3 years ago
5

Consider the quadratic function f(x)= 9x^2+30x+25=0

Mathematics
1 answer:
Alchen [17]3 years ago
4 0

Answer:

D) 0

There is 1 real solution.

Step-by-step explanation:

Hi there!

f(x)= 9x^2+30x+25=0

This is written in standard form:

f(x)=ax^2+bx+c

This means:

a=9

b=30

c=25

The discriminant states:

D=b^2-4ac

If D>0, there are 2 real solutions.

If D=0, there is 1 real solution.

If D<0, there are 2 complex solutions.

Plug in the values:

D=30^2-4(9)(25)\\D=0

Therefore, there is 1 real solution.

I hope this helps!

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Which binomial is a factor of x^2+2x-24
Effectus [21]

Answer:

C (x+12)

Step-by-step explanation:

XxX=x^2 12x2=24

8 0
3 years ago
Every year, a town surveys the size of its wetland ecosystems. This equation estimates the total wetland area, in acres, over ti
nignag [31]

Answer:

When t=10, the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

Step-by-step explanation:

Given

f(t) = 740 * (0.95)^t

Required

The true statements

(a)\ f(10) = 443

We have:

f(t) = 740 * (0.95)^t

Substitute 10 for t

f(10) = 740 * (0.95)^{10

f(10) = 443

<em>Hence, (a) is true</em>

(b)\ f(t) = 740

We have:

f(t) = 740 * (0.95)^t

Substitute 740 for f(t)

740 = 740 * (0.95)^t

Divide through by 740

1 = 0.95^t

Express 1 as 0.95^0

0.95^0 = 0.95^t

Cancel out the bases

0 = t

t = 0

Hence, the area had 740 acres initially;

(b) is true

(c)\ r = 5\%

We have:

f(t) = 740 * (0.95)^t

Using the general formula

f(t) = a * b^t

By comparison:

b = 0.95

0.95 < 1 means that:

b = 1 - r --- where r = rates

0.95 = 1 - r

Collect like terms

r = 1 - 0.95

r = 0.05

Express as percentage

r = 5\%

Hence, (c) is true

(d)\ f(10) = 492

In (a)

f(10) = 443

Hence, (d) is false

(e)\ r = 95\%

In (c)

r = 5\% ---- decrement

Hence, (e) is incorrect

5 0
3 years ago
James is 6 times older than his friend Zach, if Zach added 8 to his age and multiplied this sum by 3. Write an equation that can
Neko [114]

Answer:

The equation is 3x + 24 = 6x

Step-by-step explanation:

Let

Zach's age = x

If Zach added 8 to his age and multiplied this sum by 3.

Zach = 3(x + 8)

= 3x + 24

James = 6x

Zach's age = James's age

3x + 24 = 6x

Collect like terms

24 = 6x - 3x

24 = 3x

Divide both sides by 3

x = 24/3

= 8

x = 8

Check

Zach = 3(x + 8)

= 3(8+8)

= 3(16)

= 48 years

James = 6x

= 6(8)

= 48 years

The equation is 3x + 24 = 6x

3 0
3 years ago
Two angles of a triangle are 5x+20 and 2x+30 find the third angles​
n200080 [17]

Answer:

Third angle is 130-7x

Step-by-step explanation:

We have sum of angles is 180^{0}

Let the third angle be y

Hence

5x+20+2x+30+y=180\\\\y=130-7x

Third angle is 130-7x

3 0
3 years ago
Which of these is the area of a sector of a circle with r = 18”, given that its arc length is 6π?
Igoryamba
22/7*18^2*6π/2π*18 = 169.65
4 0
3 years ago
Read 2 more answers
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