Topic: The Quadratic Formula
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your answer
Match each equation on the left with the number and type of its solutions on the right.
x + 3x – 4= 0
two complex (nonreal) solutions
x2 + 3x + 4 = 0
two real solutions
4x² + 1 = 4x
one real solution
Clear
Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your
the target before Feleasing. The target will highlight or the cursor will change. Need help? Watch this vide
Answers
Answer:
Step-by-step explanation:
The quadratic formula for a equation of form
ax²+bx + c = 0 is
[tex]x= \frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]
For the first equation,
x²+3x-4=0,
we can match that up with the form
ax²+bx + c = 0
to get that
ax² = x²
divide both sides by x²
a=1
3x = bx
divide both sides by x
3 = b
-4 = c
. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.
Plugging our values into the equation, we get
[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1[/tex]
as our possible solutions
Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.
Next, we have
x²+3x+4=0
Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus
[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\[/tex]
Because √-7 is not a real number, this has no real solutions. However,
(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions
Finally, for
4x² + 1= 4x,
we can start by subtracting 4x from both sides to maintain the desired form, resulting in
4x²-4x+1=0
Then, a=4, b=-4, and c=1, making our equation
[tex]x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2[/tex]
Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution
Related Questions
Juan starts a bacteria culture and records the number of bacteria in the Petri dish for the first couple of hours.
Hours Bacteria
0
160
1
320
2
640
If the pattern continues, how many bacteria can he expect to find after 17 h?
Enter your answer in the box.
Answers
9514 1404 393
Answer:
20,971,520
Step-by-step explanation:
The population is doubling every hour, so after 17 hours it will be the initial population (160) multiplied by 2^17 = 131,072.
After 17 hours, he can expect to find 160×131072 = 20,971,520 bacteria.
using complex number system Compute the three cube roots of z = −8.
Answers
Write z = -8 in polar form:
[tex]z = -8 = 8e^{i\pi}[/tex]
Then the cube roots of z are
[tex]z^{1/3} = 8^{1/3} e^{i\left(\frac{\pi+2n\pi}3\right)[/tex]
where n ∈ {0, 1, 2}, or
[tex]z^{1/3} \in \left\{8^{1/3} e^{i\pi/3}, 8^{1/3} e^{i\pi}, 8^{1/3} e^{i\,5\pi/3}\right\} \\\\ z^{1/3} \in \left\{2 \left(\dfrac12 + i\dfrac{\sqrt3}2\right), -2, 2 \left(\dfrac12-i\dfrac{\sqrt3}2\right)\right\} \\\\ \boxed{z^{1/3} \in \left\{1+i\sqrt3, -2, 1-i\sqrt3\right\}}[/tex]
Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. If 390 tickets were sold for a total of $2190.00, how many student tickets were sold
Answers
Answer: Therefore 100 student tickets were sold
Step-by-step explanation:
Let the number of student tickets be x
So adult tickets = 390 - x
ATQ
4.5(x) + 6(390-x) = 2190
4.5x + 2340 - 6x = 2190
-1.5x + 2340 = 2190
-1.5x = 2190-2340
-1.5x = -150
x = -150/-1.5
x = 100
Therefore 100 student tickets were sold
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A covered wagon on the Oregon
Trail could travel about 2.5 miles
per hour on flat terrain. About how
many miles could it travel in
9 hours?
Answers
Answer:
3.6miles
Step-by-step explanation:
9/2.5=3.6
(2i+1)/(1+i) is equal to
Answers
Answer:
Step-by-step explanation:
(1 + 2i) / (1 + i) Rationalize the denominator.
(1 + 2i)(1+i) / (1 + i)(1-i) Remove the brarckets
(1 + i + 2i - 2) / (1 - i + i - i^2) Combine
-1 + 3i / (2) i^2 = - 1 in the denominator
find the equation of the line that is perpendicular to y=6x-2) and contains to the point (6-,2)
Answers
Answer:
y = -1/6x - 1.
Step-by-step explanation:
I am assuming that the point id (6, -2).
The slope of the required line = -1/6.
y - y1 = m(x - x1) where m = slope and x1,y1 is a point on the line so we have
y - (-2) = -1/6( x- 6)
y + 2 = -1/6x + 1
y = -1/6x - 1.
-14=3-c+(9+5c) solve for c
Answers
Answer:
c=-26/4 simple addition and multiplation
Step-by-step explanation:
[tex] - 14 = 3 - c + (9 + 5c) \\ - 14 = 3 - c + 9 + 5c \\ c - 5c = 3 + 9 + 14 \\ - 4c = 3 + 9 + 14 \\ - 4c = 26 \\ - 2c = 13 \\ c = - \frac{13}{2} \\ c = - 6.5[/tex]
All 20 children at a party were given one cookie, and then some were given an additional cookie. If a total of
32 cookies were given out, how many children received an additional cookie?
8
O 10
О о о
O 12
o 14
Answers
Answer:
If there were 20 children at a party, and each were given one cookie, then a total of 20 cookies were given out.
However, this is not the case, as 32 cookies were given out. So, we can see that 32 - 20 children, or 12 children, received one additional cookie.
Let me know if this helps!
Due the end of the week pls help.
Answers
This problem seems like a lot when you read through it, but when you start to analyze the problem, the whole first line is extra information that we don't actually need. The part we really need to pay attention to is:
"p = qr - f, write the equation with q solved in terms of p, r, and f."
So, all we are doing here is some manipulating of the equation to get what we want. So, if p = qr - f, we can isolate the variable (q), to get p + f = qr. Now all we have to do is divide both sides by r to isolate the variable (q) even further, and we get [tex]$\frac{p+f}{r}=q$[/tex] or [tex]$r=\frac{p+f}{r}$[tex]
write 20.99988 as a mixed number
Answers
Answer:
Wouldn't it just be
24997
20 ------------
25000
Step-by-step explanation:
Answer:
20 24997/25000
Step-by-step explanation:
1. Convert 0.99988 into a fraction...99988/100000
2.Simplify with greatest common factor.....99988/4=24997 100000/4=25000
24997/25000
3. Add 20 to 24997/25000......20 24997/25000
If (x^2−1)/(x+1) = 3x + 5, then x + 3 =
(A) -3
(B) -2
(C) 0
(D) 2
(E) 4
Answers
Because math
If average of the numbers 3,9,5,7 and Q is 5 times the value of Q, find the value of Q
Answers
Answer:
q=6
Step-by-step explanation:
3+9+5+7+Q=5Q
5Q-Q=24
Q=6
resolve 2x^2+5x-1÷x(x-1)(x+2) into partial fractions.
Answers
——————————
x
What is the slope of the line in the graph?
Answers
Answer:
Hello,
answer slope =-3/4=-0.75
Step-by-step explanation:
Line is passing through (0,1) and (4,-2)
[tex]\Delta y=-2-1=-3\\\\\Delta x=4-0=4\\\\Slope=\dfrac{-3}{4}[/tex]
Which of the following equations have no solutions?
Choose all answers that apply:
-60.2 + 32 = 32x + 60
-60.X + 32 = 322 - 60
-60.2 + 32 = -60.2 + 60
-60x + 32 = -60.2 - 32
Answers
Option 3 is not possible
-60.2 + 32 = -60.2 + 60
And these are not equal
Rest all options have x and are solvable
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........................
use different method of depreciation for each of the assests and explain why u used the method (ex : straight line method, double declining method, unit of production method)
Answers
Step-by-step explanation:
sorry but I don't know this answerA cubical water tank is 80 cm broad. find the volume of tank?
Answers
Answer:
512000
Step-by-step explanation:
l=80cm
v=l^3
=80^3
=512000cm^3
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
Y=-3x+1
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Answers
Answer:
y = 1 m = -3 b = 1
Step-by-step explanation:
y = mx + b y = -3x + 1
y = 1
m = -3
b = 1
[tex]\sqrt{-25[/tex]
Answers
Answer:
±5i
Step-by-step explanation:
sqrt(-25)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(-1) sqrt(25)
±i 5
±5i
8th class maths reader answer
Answers
Answer:
plz complete question
so I can help you.
Write the quadratic function f(x) = x2 - 2x - 8 in factored form.
A) f(x) =(x - 4)(x - 2)
B) f(x) =(x + 4)(x - 2)
C) f(x) =(x - 4)(x + 2)
D) Rx) =(x + 4)(x + 2)
Answers
Answer:
Hello,
answer C
Step-by-step explanation:
[tex]f(x)=x^2+2x-8\\\\=x^2-4x+2x-8\\\\=x(x-4)+2(x-4)\\\\=(x-4)(x+2)\\\\Answer\ C[/tex]
Which equation represents a line with slope į and y-intercept -6?
2x +3y=-6
3x - 2y= 6
2x - 3y= 18
3x - 2y= 12
Answers
Answer:
Answer:y=-2/9+3
Step-by-step explanation:
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. If required enter negative values as negative numbers.
In a regression analysis involving 30 observations
Interpret b1, b2, b3, and b4 in this estimated regression equation (to 1 decimal). Assume that for each coefficient statement, the remaining three variables are held constant. Enter negative values as negative numbers.
b1 = estimated change in y per 1 unit change in x1
b2 = estimated change in y per 1 unit change in x2
b3 = estimated change in y per 1 unit change in x3
b4 = estimated change in y per 1 unit change in x4
Predict y when x1 = 10, x2 = 5, x3 = 1, and x4 = 2 (to 1 decimal).
Answers
In this, question the equation is missing that's why in the solution we define the equation and its complete solution:
Let the given equation:
[tex]\bold{\hat{h}=17.6+3.8x_1-2.3x_2+7.6x_3+2.7x_4}[/tex]
[tex]\bold{b1 = 3.8}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_1}[/tex]
[tex]\bold{b2 = -2.3 }[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_2}[/tex]
[tex]\bold{b3 = 7.6 }[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_3}[/tex]
[tex]\bold{b4 = 2.7}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_4}[/tex]
Calculating the estimated value of the y when:
[tex]\to \bold{x_1 = 10}\\\\ \to \bold{x_2 = 5}\\\\\to \bold{x_3 = 1}\\\\\to \bold{x_4 = 2}\\\\[/tex]
Put the value into the above-given equation:
[tex]\to \bold{17.6 + 3.8(10) - 2.3(5) + 7.6(1) + 2.7(2)} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{68.6-11.5}\\\\\to \bold{57.1}[/tex]
So, the final answer is "57.1".
Learn more:
brainly.com/question/14127435
Need tha answer explained
Answers
Answer:
Bri what do you mean explanation your answer is correct
Please mark me brainliest thanks
Answer:
It is 77.2, so your anwer is correct.
Step-by-step explanation:
Finding decimal divided by decimal too hard? Don't worry, I've got your back! To do division, you can do it the hard way by just dividing it, but there's something more simple.
Move the dividend's decimal point to the right until it's not a decimal. Do the same with the divisor, but it depends on how many decimal places on the dividend was moved by. So in this case, you move it by 2 decimal places for BOTH! Then you just simply divide it. It gives you the same answer.
BTW if I didn't make my explanation clear, please comment.
Write the phrase as an algebraic expression: 3 less than 4 times a number
Answers
Answer:
4x-3 is the expression to your question
Answer:
3[tex]\leq[/tex]4x
Step-by-step explanation:
What's the equation of the graph shown above? ) y = 4x + 2 B) y = 4x – 2 C) y = 5x + 2 D) y = 2x + 4
Answers
Answer:
i need the graph
Step-by-step explanation:
.
Maria is using a meter stick to determine the height of a door. If the smallest unit on the meter stick is centimeters, which measurement could Maria have used to most accurately record the height of the
door?
Answers
Answer:
2.31 m
Step-by-step explanation:
with marking down to centimeter length, one can only estimate accurately to the nearest centimeter or hundredth of a meter.
Answer:2.31 meter
Step-by-step explanation: none
HELP ME PLEASE ANYONE FOR 20 POINTS
Answers
Answer:
The correct answer is no.B
Subtract 4 from both sides, and plug it in the quadratic formula
An integer is eight less than three times another if the product of two integers is 35 then find the integers
Answers
8x < 3x =35
Less means -
So it will be
8x -3x =35
5x = 35
Divide both side by 5
x = 35 divided by 5
x = 7
So that it will be that
8(7) - 3(7) = 35
56 - 21
= 35
So the integers are
a) 56 and
b) 21
Pls thank me byeee
X, 2X + 11 and 4X - 3 are consecutive terms of an arithmetic sequence. Find the constant difference between terms. Give a formula for finding the nth term of the sequence. Use your formula to find the 27th term of this sequence.
Answers
Common difference between the terms is 36
Formula for nth term is [tex]a_n=36n-11[/tex]
27th term is 961
Given :
X, 2X + 11 and 4X - 3 are consecutive terms of an arithmetic sequence
To Find:
We need to find the constant difference between the given terms and also find the nth term . Also find the 27th term .
To find the difference , we need to take the difference of consecutive terms
[tex]2x+11-x=x+11\\\\4x-3=(2x+11)= 4x-3-2x-11=2x-14[/tex]
Both the common differences are equal
[tex]x+11=2x-14\\Solve \; for \; x\\Subtract \; x\\11=x-14\\Add \; 14\\x=25[/tex]
First term is 25
second term is 2(25)+11=61
Difference is 61-25=26
Common difference = 36
Use nth term formula is
[tex]a_n=a+(n-1)d\\a=25 (first term )\\d=36\\a_n=25+(n-1)(36)\\a_n=25+36n-36\\a_n=36n-11[/tex]
To find 27th term , replace n with 27
[tex]a_{27}=36(27)-11=961[/tex]
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