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2 years ago

Which choices are solutions to the following equatior Check all that apply. X^2 -5x=-9/4

Mathematics

1 answer:

svlad2 [7]2 years ago

7 0

The solution of the equation 4x² - 20x + 9 = 0 will be 0.5 and 4.5.

<h3>What is a quadratic equation?</h3>

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The equation is given below.

x² - 5x = -9/4

Then the equation can be written as

4x² - 20x + 9 = 0

Then the factor of the equation will be

4x² - 20x + 9 = 0

4x² - 18x - 2x + 9 = 0

2x(2x - 9) -1 (2x - 9) = 0

(2x - 1)(2x - 9) = 0

Then the solution of the equation 4x² - 20x + 9 = 0 will be

x = 0.5, 4.5

More about the quadratic equation link is given below.

brainly.com/question/2263981

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For g(x)=x^2-2, determine g(x+2)

Svetlanka [38]

Answer:g(x)=-4^2+4x-5

Step-by-step explanation:

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3 years ago

Problem ID: PRABK2AZ

Vaselesa [24]

Answer: f(n+1) = 3 f(n)

Step-by-step explanation:

A recursive formula is used to determine each term of a sequence using preceding term or terms.

Given sequence : 2.5, 7.5, 22.5, 67.5, 202.5,...

Here,

$2.5\times 3=7.5\\7.5\times3= 22.5\\22.5\times 3= 67.5\\67.5\times3=202.5$

Common ratio = 3

Let f(n) be a term in this sequence then the next term will be f(n+1) = 3 f(n), where n is a natural number .

Required recursive formula : f(n+1) = 3 f(n)

8 0

3 years ago

What are three different ways to write 5 to the 11 power

Olin [163]

(5)(5)(5)(5)(5)(5)(5)(5)(5)(5)(5)
5^11
That is two of the three but I'm not quite sure if there is a third.

3 0

3 years ago

Read 2 more answers

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

3 years ago

B Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a

skelet666 [1.2K]

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

Given that;

Amount of water needed to fill the dam A = 30000 litres
Pump rate r = 75 litres per minute
Time needed to fill the dam T = ?

To determine how long it take to fill the dam, we say;

Time need = Amount of water needed ÷ Pump rate

T = A ÷ r

T = 30000 litres ÷ 75 litres/minute

T = 400 minutes

Note that; 60min = 1hrs

Hence,

T = 6hours 40minutes

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

Learn more word problems here: brainly.com/question/2610134

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8 0

2 years ago