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vazorg [7]
2 years ago
9

The steps to derive the quadratic formula are shown below: Step 1 ax2 + bx + c = 0 Step 2 ax2 + bx = − c Step 3 x2 + b over a ti

mes x equals negative c over a Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared Step 6 Provide the next step to derive the quadratic formula. x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a
Mathematics
1 answer:
Nostrana [21]2 years ago
3 0

Answer:

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

Step-by-step explanation:

<u><em>Step 1:</em></u>

ax^2+bx+c = 0

<u><em>Step 2:</em></u>

ax^2+bx = -c

<u><em>Step 3:</em></u>

\frac{ax^2+bx}{a} = \frac{-c}{a}

<u><em>Step 4:</em></u>

Adding \frac{b^2}{4a^2} to both sides to complete the square

x^2 + \frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}

<u><em>Step 5:</em></u>

x^2 + \frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-4ac+b^2}{4a^2}

<u><em>Step 6:</em></u>

Taking square root on both sides

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

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Lisa says that 43 is a 2-digit odd number that is composite us she correct
kogti [31]
Yes Lisa is correct  43 is a 2 digit number 4 is one digit and 3 is a digit so it makes two digits 43 is a prime number because 43 has no positive divisors rather than 1 and itself.


SO answer is YES
7 0
3 years ago
Read 2 more answers
2) -84 = 6(4a – 2)<br> A) {2}<br> C) No solution.<br> B) {1}<br> D) -3)
LenaWriter [7]

In this question, you're solving for a.

Solve for a:

-84 = 6(4a - 2)

<em>Distribute the 6 to the variables inside the parenthesis</em>

-84 = 24a - 12

<em>Add 12 to both sides</em>

-72 = 24a

<em>Divide both sides by 24</em>

-3 = a

This means that answer choice D would be the correct answer.

Answer:

D). -3

5 0
3 years ago
3. In a certain school, there are 456 girls. Calculate the total number of students
marin [14]

Answer:

3) girls = 24% = 456

let the total number of students be = x

\frac{24}{100}  \times x = 456

x = 456 \times  \frac{100}{4}

x = 1900

the total number of students is 1900

4) increase = 20%

new salary = 24000 rupees

let his original salary be = y

\frac{20}{100}  \times y = 24000 - y

0.2y = 24000 - y

0.2y + y = 24000

1.2y = 24000

y =  \frac{24000}{1.2}

y = 20000

his original salary is 20,000 rupees

7 0
3 years ago
Please Help! Algebra 2!
eduard

Answer:

The interest rate of the account is 3\%

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=14\ years\\ P=\$1,863\\ A=\$2,830.97\\n=4  

substitute in the formula above  and solve for r

\$2,830.97=\$1,863(1+\frac{r}{4})^{4*14}  

(2,830.97/1,863)=(1+\frac{r}{4})^{56}  

(2,830.97/1,863)^{1/56}=(1+\frac{r}{4})

[(2,830.97/1,863)^{1/56}-1]=\frac{r}{4}    

r=4*[(2,830.97/1,863)^{1/56}-1]\\ \\r= 0.03

Convert to percent

r= 0.03*100=3\%

8 0
3 years ago
The sum of two polynomials is 10a^2b^2-8a^2b+6ab^2-4ab+2 if one addend is -5a^2b^2+12a^2b-5 what is the other addend
spayn [35]

Answer:

The other addend is 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7.

Step-by-step explanation:

The other addend is determined by subtracting -5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5 from 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2:

x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)

x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5

x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7

x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7

The other addend is 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7.

6 0
2 years ago
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