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3 years ago

Really need this todayyyyyy

Mathematics

2 answers:

Bond [772]3 years ago

7 0

Answer:

Q3: x1=2+i, x2=2-i Q4: x1=-3/2+i, x2=-3/2-i

Step-by-step explanation:

$x^{2} - 4x + 5 =0$

( $4$ ± $\sqrt{16 - 4*1*5}$ ) / $2$ = (

x1= 2+i

x2= 2-i

$2x^{2} +6x + 5 =0$

( $-6$ ± $\sqrt{36 - 4*2*5}$ ) / $4$ = (-6 ± $\sqrt{-4}$ )/4= (-3 ± i)/2

x1 = -3/2 +i

x2 = -3/2 -i

Papessa [141]3 years ago

3 0

Answer:

3x^2+12=0

3x^2=0-12

3x^2=-12

X^2=12/3

x^2=4

X= root under4

x=2

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3 years ago

15. Fatima bought a video game that has a

OleMash [197]

Answer:

Step-by-step explanation:

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3 years ago

Use the discriminant to determine what type of roots the equations will have, and categorize the equations according to their ro

topjm [15]

Step-by-step explanation:

The discriminant of the quadratic equation $ax^2+bx+c=0$ :

$\Delta=b^2-4ac$

If Δ < 0, then the equation has two complex roots $x=\dfrac{-b\pm\sqrt\Delta}{2a}$

If Δ = 0, then the equation has one repeated root $x=\dfrac{-b}{2a}[/tex If Δ > 0, then the equation has two discint roots [tex]x=\dfrac{-b\pm\sqrt\Delta}{2a}$

$1.\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\Delta=(-4)^2-4(1)(2)=16-8=8>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=2\sqrt2\\\\x=\dfrac{-(-4)\pm2\sqrt2}{2(1)}=\dfrac{4\pm2\sqrt2}{2}=2\pm\sqrt2\\\\==============================\\\\2.\ 5x^2-2x+3=0\\\\a=5,\ b=-2,\ c=3\\\\\Delta=(-2)^2-4(5)(3)=4-60=-56$

$3.\ 2x^2+x-6=0\\\\a=2,\ b=1,\ c=-6\\\\\Delta=1^2-4(2)(-6)=1+48=49>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt{49}=7\\\\x=\dfrac{-1\pm7}{(2)(2)}\\\\x_1=\dfrac{-8}{4}=-2,\ x_2=\dfrac{6}{4}=\dfrac{3}{2}\\\\==============================\\\\4.\ 13x^2-4=0\qquad\text{add 4 to both sides}\\\\13x^2=4\qquad\text{divide both sides by 13}\\\\x^2=\dfrac{4}{13}\to x=\pm\sqrt{\dfrac{4}{13}},\ \bold{two\ distinct\ roots}\\\\==============================$

$5.\ x^2-6x+16=0\\\\a=1,\ b=-6,\ c=16\\\\\Delta=(-6)^2-4(1)(16)=36-64=-28$

$7.\ 4x^2+11=0\qquad\text{subtract 11 from both sides}\\\\4x^2=-11\qquad\text{divide both sides by 4}\\\\x^2=-\dfrac{11}{4}\to x=\pm\sqrt{-\dfrac{11}{4}}\\\\x=\pm\dfrac{\sqrt{11}}{2}\ i,\ \bold{two\ complex\ roots}$

6 0

3 years ago

Read 2 more answers

3. Suppose your credit card has a balance of $7800 and an annual interest rate of 16%. You decide

Blizzard [7]

Answer:

$274.22 per month
$2071.92 in total interest
$433.48 more per month
$1379.52 less in interest

Step-by-step explanation:

a) The amortization formula is used to find the monthly payment (A):

A = P(r/n)/(1 -(1 +r/n)^(-nt))

for a loan of a principal amount P at annual rate r compounded n times per year for t years.

For a borrowed amount of $7800 at 16% compounded monthly for 3 years, the payment will be ...

A = $7800(.16/12)/(1 -(1 +.16/12)^(-12·3)) ≈ $274.22

You must pay $274.22 each month to pay off the credit card in 3 years.

b) The total amount repaid is 36 times this monthly payment, so is ...

$274.22 × 36 = $9871.92

The amount by which this exceeds the principal borrowed is ...

$9871.92 -7800 = $2071.92

You will pay $2071.92 in interest.

c) Changing the time period to 1 year gives the payment value ...

A = $7800(.16/12)/(1 -(1 +.16/12)^(-12·1)) ≈ $707.70

The additional amount you must pay is ...

$707.70 -274.22 = $433.48

You must pay $433.48 more each month.

d) Your total interest with the higher payments will be ...

$707.70×12 -7800 = $692.40

The difference in interest amounts is ...

$2071.92 -692.40 = $1379.52

You will pay $1379.52 less in total interest.

_____

<em>Caveat</em>

Here, the monthly amounts are rounded and the total repayment amount is based on that rounded value. In an actual payment situation, the final payment will be adjusted by a small amount to account for the fact that the monthly payment shown is not exact. That will affect the total interest and the difference in interest.

8 0

3 years ago

Work out the area of this quarter circle of radius 8 cm.<br> Give your answer in terms of pie

Bess [88]

16pi

Step-by-step explanation:

pi x r² = ans ÷ 4 = Answer for area

Pi×8²=64pi ÷ 4 = 16pi

3 0

3 years ago