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mars1129 [50]
1 year ago
6

Solve: x² + x + 1 = 0.​

Mathematics
1 answer:
Hatshy [7]1 year ago
3 0

Answer:

\sf  x = \dfrac{-1 +  i\sqrt{3} }{2}  \quad or \quad \dfrac{-1 -  i\sqrt{3} }{2}

Explanation:

\sf Given : x^2 + x + 1 = 0

Solve it using quadratic formula

\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad \:when\: \:  ax^2 + bx + c = 0

So, here constants are: a = 1, b = 1, c = 1

When the value's are substituted inside the formula

\sf \rightarrow x = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(1)} }{2(1)}

\sf \rightarrow x = \dfrac{-1 \pm \sqrt{-3} }{2}

\sf \rightarrow x = \dfrac{-1 \pm i\sqrt{3} }{2}

\sf \rightarrow x = \dfrac{-1 +  i\sqrt{3} }{2}  \quad or \quad \dfrac{-1 -  i\sqrt{3} }{2}

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If the equation of a line containing the midsegment of a triangle is y = -1/4x -11, what is the slope of the triangle side that
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Answer:2.75


Step-by-step explanation:

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Sir John Franklin was an explorer who traveled in Canada and the United States he was 33 years old when he began exploring North
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Margaret deposits $1,000 in a savings account that pays 1.4% interest compounded
ozzi

Answer:

The balance after 1 year is;

$1,014.05

Step-by-step explanation:

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That will be ;

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

A is the amount generated which we want to calculate

r is the rate = 1.4% = 0.014

P is the amount deposited = $1,000

n is the number of times it is compounded annually which is 2 (semi-annually means 2 times in a year)

this the number of years which is 1

we have this as:

A = 1,000( 1 + 0.014/2)^(2*1)

A = 1,000(1 + 0.007)^2

A = 1,000(1.007)^2

A = $1,014.05

8 0
3 years ago
The sum of 3 integers is 194. the sum of the first and second integers exceeds the third by 80. The third integer is 45 less tha
kirill115 [55]
Let
x = first integer
y = second integer
z = third integer
First equation: x + y + z = 194
Second equation: x + y = z + 80
Third equation: z = x - 45

Let's find the values of x, y and z.
Substitute 3rd eq to 1st eq:
x + y + x - 45 = 194
2x + y = 45 + 194
y = -2x + 239

Plug in both we have solved for y and the 3rd eq to the 2nd eq to find x
x + (-2x + 239) = (x - 45) + 80
x - 2x - x = -45 + 80 - 239
-2x = -204
x = -204/-2
x = 102

Solving for y,
y = -2(102) + 239
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Solving for z,
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5 0
3 years ago
Using V =iwh what is an expression for the volume of the following prism​
vampirchik [111]

Answer:

we know that

The volume of the prism is equal to

V=L*W*H

where

L is the length side of the base of the prism

W is the width side of the base of the prism

H is the height of the prism

In this problem we have

L=\frac{d-2}{3d-9}=\frac{d-2}{3(d-3)}

W=\frac{4}{d-4}

H=\frac{2d-6}{2d-4}=\frac{2(d-3)}{2(d-2)}=\frac{(d-3)}{(d-2)}

Substitute the values in the formula

V=\frac{d-2}{3(d-3)}*\frac{4}{d-4}*\frac{(d-3)}{(d-2)}=\frac{4}{3(d-4)}=\frac{4}{3d-12}

therefore

the answer is the option

4/3d-12

Step-by-step explanation:

7 0
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