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vivado [14]
3 years ago
8

Consider the quadratic equation x squared = 4x - 5. how many solutions does the equation have?

Mathematics
1 answer:
snow_lady [41]3 years ago
5 0

Answer:

The quadratic equation has two complex solutions

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^{2}=4x-5  

Equate to cero

x^{2}-4x+5=0  

so

a=1\\b=-4\\c=5

substitute in the formula

x=\frac{4(+/-)\sqrt{-4^{2}-4(1)(5)}} {2(1)}

x=\frac{4(+/-)\sqrt{16-20}} {2}

x=\frac{4(+/-)\sqrt{-4}} {2}

Remember that

i^{2}=-1

so

x=\frac{4(+/-)2i} {2}

x=2(+/-)i

therefore

The quadratic equation has two complex solutions

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ASAP!! WILL MARK BRAINLIEST!!!!!!!!
Artyom0805 [142]

Answer:

x = -0.35

Step-by-step explanation:

tep 1 - Multiply 64 and 0.5x. The answer ends up being 32x

Step 2 - You need to get all of the variables on one side and the regular numbers on the other side. To do that, you need to subtract 2.5x from each side so you are left with the equation -10.5 = 29.5x

Step 3 - The final step is to isolate the variable. To do this, you divide each side by 29.5 meaning that x = -0.35

8 0
3 years ago
I need help with letters (D) and (E). My model equation from letter (C) is: P = -55/4 t+ 340.
IceJOKER [234]

Answer:

(a) The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope is m = -55/4

The slope means the rate of decreases of the owl population was 55/4

per year (P decreased by 55/4 each year)

(c) The model equation is P = -55/4 t + 340

(d) The owl population in 2022 will be 216

(e)  At year 2038 will be no more owl in the park

Step-by-step explanation:

* Lets explain how to solve the problem

- The owl population in 2013 was measured to be 340

- In 2017 the owl population was measured again to be 285

- The owl population is P and the time is t where t measure the numbers

 of years since 2013

(a) Let t represented by the x-coordinates of the order pairs and P

   represented by the y-coordinates of the order pairs

∵ t is measured since 2013

∴ At 2013 ⇒ t = 0

∵ The population P in 2013 was 340

∴ The first order pair is (0 , 340)

∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years

∴ At 2017 ⇒ t = 4

∵ The population at 2017 is 285

∴ The second order pair is (4 , 285)

* The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)

     is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)

∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285

∴ m = \frac{285-340}{4-0}=\frac{-55}{4}

* The slope is m = -55/4

∵ The slope is negative value

∴ The relation is decreasing

* The slope means the rate of decreases of the owl population was

  55/4 per year (<em>P decreased by 55/4 each year</em>)

(c) The linear equation form is y = mx + c, where m is the slope and c is

    the value of y when x = 0

∵ The population is P and represented by y

∵ The time is t and represented by t

∴ P = mt + c , c is the initial amount of population

∵ m = -55/4

∵ The initial amount of the population is 340

∴ P = -55/4 t + 340

* The model equation is P = -55/4 t + 340

(d) Lets calculate the time from 2013 to 2022

∵ t = 2022 - 2013 = 9 years

∵ P = -55/4 t + 340

∴ P = -55/4 (9) + 340 = 216.25 ≅ 216

* The owl population in 2022 will be 216

(e) If the model is accurate , then the owl population be be zero after

    t years

∵ P = -55/4 t + 340

∵ P = 0

∴ 0 = -55/4 t + 340

- Add 55/4 t to both sides

∴ 55/4 t = 340

- Multiply both sides by 4

∴ 55 t = 1360

- Divide both sides by 55

∴ t = 24.7 ≅ 25 years

- To find the year add 25 years to 2013

∵ 2013 + 25 = 2038

* At year 2038 will be no more owl in the park

8 0
3 years ago
Write the standard form of 1x1/10 + 8x1/100
alisha [4.7K]
We are given the expanded form and we need to write the standard form:
10 + 8x(1/10) + 3 x(1/100) + 9 x (1/1000)
So, that is:
10 + 0.8 + 0.03 + 0.009
= 10.839
6 0
3 years ago
Read 2 more answers
!!25 POINTS AND BRAINLIEST!! A recipe calls for 2 cups of pizza sauce. I only want 3/4 OF the full 2 cups. How will I figure out
Nutka1998 [239]

Mathematical Answer: 2cups*3/4 = 1 and 1/2 cups or 1.5 cups.

How to do it while cooking:

  1. Get out a container large enough to hold at least 4 cups sauce
  2. Get out a "1 cup" and "1/2 cup" measuring cup.
  3. Measure out 1 cup of sauce with the "1 cup" measuring cup.
  4. Measure out  1/2 of a cup of sauce with the '1/2 cup' measuring cup.
  5. pour both cups into the larger container.

And there you go you have 3/4 of 2 cups of sauce.

<em>Hoped this helped!</em>

5 0
3 years ago
Read 2 more answers
What are the coordinates of the point (-4,-10) after a 180 rotation about the orgin and then a translation 1 unit right
goblinko [34]

1. Rotation by 180° (clockwise or anti-clockwise) about the origin has a rule:

(x,y)→(-x,-y).

Then

(-4,-10)→(4,10).

2. Translation 1 unit to the right has a rule:

(x,y)→(x+1,y).

Then

(4,10)→(5,10).

3. After rotation and translation the image of point (-4,-10) is point (5,10).

Answer: (5,10).

5 0
3 years ago
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