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3 years ago

Solve the equation for x, where x is a real number (5 points): -4x^2 + 3x - 1 = 2

1 answer:

6 0

Subtract 2 to both sides so that the equation becomes -4x^2 + 3x - 3 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                                     x = [ -b ± √(b^2 - 4ac) ] / (2a)
                                     x = [ -3 ± √((3)^2 - 4(-4)(-3)) ] / ( 2(-4) )
                                     x = [-3 ± √(9 - (48) ) ] / ( -8 )
                                     x = [-3 ± √(-39) ] / ( -8)
The answers to this question is that there are no real solutions since the discriminant is -39. √-39 is nonreal.

You might be interested in

A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the n

Helga [31]

In equation, let x be the number of male students
a be the number of adults
y be the number of female students.
x= 7a+1
a= x/7 -1
y= x/2 or (7a + 1)/ 2

a + b = 82, let b be the number of students.
a + (x + y) = 82
a + [7a+1 + (7a+1)/2] = 82
a + [{2(7a+1) + 7a+1} / 2] = 82
a + [(14a +2 + 7a +1) / 2] = 82
a + [(21a + 3) / 2] = 82
(2a+ 21a + 3) / 2 = 82
(23a + 3) / 2 = 82
23a + 3 = 164
23a = 164 -3
23a = 161
a = 7

x = 7(7) +1, 49+1 = 50 male students
y=x/2, 50/2, 25 female students

50(male students) + 25(female students) + 7 (adults) = 82

8 0

2 years ago

The monthly gross receipts for the ABC Copy Creation house amounted to $20,834.34. Unfortunately, the expenses amounted to $18,7

____ [38]

Given :

The monthly gross receipts for the ABC Copy Creation house amounted to $20,834.34.

The expenses amounted to $18,750.91.

To Find :

What was the profit for the month.

Solution :

We know, profit is given by :

Profit, P = Monthly income - Expenses

P = $( 20,834.34 - 18,750.91 )

P = $2083.43

Therefore, the profit for the month is $2083.43 .

6 0

3 years ago

If anyone helps me with this i’ll give you brainlist :) please help i’m struggling rn

fredd [130]

Answer:

y intercept is 140, slope is 2/1

Step-by-step explanation:

sorry, not sure about the function

5 0

2 years ago

Read 2 more answers

Find the coordinates of the midpoint of the segment whose endpoints are R(9, 3) and S(-1, -9).

amm1812

Answer:

$(4, -3 )$

General Formulas and Concepts:

Pre-Algebra I

Order of Operations: BPEMDAS

Algebra I

Midpoint Formula: $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )$

Step-by-step explanation:

Step 1: Define

R (9, 3)

S (-1, -9)

Step 2: Find midpoint

Substitute: $(\frac{9-1}{2}, \frac{3-9}{2} )$
Subtract: $(\frac{8}{2}, \frac{-6}{2} )$
Divide: $(4, -3 )$

4 0

2 years ago

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago