Answer:
4 + (or -) 3i
Step-by-step explanation:
Hi!
Alright, so we're going to move all of the variables and constants to one side. Then, using the quadratic formula, we'll find the answer.
1. Move 12x-5 to the left side of the equation by
a. Subtracting 12x from both sides
b. adding 5 to both sides.
1: x^2+4x+20-12x+5
2. Group the common terms
x^2+4x-12x+20+5 --> x^2-8x+25
3. Look at the problem. We can't factor this.
Explanation for why this isn't factorable (you can skip this)
(1) 25 is positive, so its two factors will both be either positive or negative. We're looking for a negative 8, so let's go with negative.
(2) Factors of 25: 1 & 25, 5 &5
Seeing the problem? Ya, none of the factors of 25 sum to eight. So, instead, we're going to use the quadratic formula.
4. So, the quadratic formula: [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Our equation is x^2-8x+25=0
a is the constant in front of the x^2
b is the constant in front of the x
c is the term without any x values
so, a=1, b=-8, and c= 25
Into equation:
[tex]\frac{8+-\sqrt{64-4(1)(25)} }{2a}[/tex]=[tex]\frac{8+-\sqrt{64-100} }{2}[/tex]=[tex]\frac{8+-\sqrt{-36} }{2}[/tex]
8/2 = 4
sqrt(-36) = 6i
6i/2 = 3i (remember, we still have the two in the denominator)
4 + (or -) 3i
Answer:
[tex]x=4+ 3\mathbf{i}[/tex]
[tex]x=4- 3\mathbf{i}[/tex]
Step-by-step explanation:
Solve:
[tex]x^2+4x+20=12x-5[/tex]
Move everything to the left side:
[tex]x^2+4x+20-12x+5=0[/tex]
Simplify:
[tex]x^2-8x+25=0[/tex]
Apply the solver formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Where a=1, b=-8, c=25. Thus:
[tex]\displaystyle x=\frac{8\pm \sqrt{(-8)^2-4(1)(25)}}{2*1}[/tex]
[tex]\displaystyle x=\frac{8\pm \sqrt{64-100}}{2}[/tex]
[tex]\displaystyle x=\frac{8\pm \sqrt{-36}}{2}[/tex]
The solutions are complex numbers:
[tex]\displaystyle x=\frac{8\pm 6\mathbf{i}}{2}[/tex]
Simplifying:
[tex]x=4\pm 3\mathbf{i}[/tex]
Two solutions are found:
[tex]x=4+ 3\mathbf{i}[/tex]
[tex]x=4- 3\mathbf{i}[/tex]
Starting at 11:00 pm a bus makes a stop every 27 minutes. Also starting at 11:00pm a taxi makes a stop every 18 minutes. What is the next time there will be a bus and the taxi at the same place and the same time.
Answer:
11:54pm
Step-by-step explanation:
Key details in the Question:
- Starting at 11:00 pm a bus makes a stop every 27 minutes.
- starting at 11:00pm a taxi makes a stop every 18 minutes.
The task is to find the time in which both the bus and taxi would make a stop.
Since the taxi has the shorter duration for a stop, we would use it as the basis for our calculations.
During the first taxi stop - 11:18pm
The Bus has not yet made its stop.
During the second taxi stop - 11:36pm
The Bus has made it's first stop (11:27pm) but is currently on the road.
During the third taxi stop - 11:54pm
The Bus would also be making it's second stop
Suppose that the original price of a short is 40$ which is better 60% discount of a discount of 30 followed by a discount of 35
Answer:
60% discount is the better buy
Step-by-step explanation
Step one
Original price =$40
Let us compute the various discounts and compare the prices
For 60%
=60/100*40
=0.6*40
=$24
New price = 40-24= $16
For 35%
=35/100*40
=0.35*40
=$14
New price = 40-14= $26
A business trip reimbursed $0.55 per mile. Mr. Jackson has a budget of $70 for the round trip. If he is traveling to a town 61 miles, then will he be under or over budget? Prove your thinking.
Answer:
3355
Step-by-step explanation:
55 x 61 = 3355
HELP!!!! NEED HELP ASAP!!! WILL MARK BRAINLIST!!!!
Answer:
Step-by-step explanation:
Let's consider an exponential function as,
f(x) = 2ˣ
Now we prepare the input-output value table to get the ordered pairs to be plotted.
f(x) 0.25 0.5 1 2 4 8
x -2 -1 0 1 2 3
By plotting these points we get the graph as attached.
Therefore, second option in the last attachment will be the correct option.
please help, i have to solve for X
Answer:
x=2
Step-by-step explanation:
qt =tn
4x+6=5x+4
5x-4x=6-4
x=2
Please Help Will give brainliest, 5 stars and thanks!
rotation 90° clockwise about the origin
Answer:
point s at (0,5) point t at (5,3) point u at (4,1)
Step-by-step explanation:
happy life
What is the slope of the following equation? 8x+3y=9
Answer:
The answer is -8/3.
Step-by-step explanation:
First, you have to make y the subject :
8x + 3y = 9
3y = -8x + 9
y = (-8/3)x + 3
In a linear equation, y = mx + b, m represent gradient (slope). So in this equation the slope is -8/3.
Find the complete factored form of the
polynomial:
-9a666 - 12ab6
Enter the correct answer.
000G
DONE
Clear all
GE
Answer:
(0 - (9 • (a^666))) - (22•3ab^6)
(0 - 32a^666) - (22•3ab^6)
-12ab^6 - 9a^666 = -3a • (4b^6 + 3a^665)
Final result :
-3a • (4b^6 + 3a^665)
Step-by-step explanation:
when using the correct order of operations ,you always add before you subtract.
Answer:
False
Step-by-step explanation:
Additions and subtractions are done in the order they appear from left to right.
Sylvia and Patrick plotted the information they gathered on the weight of cars and the mileage they get. Then they each drew a line on the graph
that they felt best fit the data,
Sylvia's line blank
a line of best fit because her line blank .
Patrick's line blank
a line of best fit blank
as his line blank.
Answer:
The correct options are;
a) Is
b) Passes through the middle of the plotted scatter data points on the graph
b) Is not
e Does not pass through the middle of the plotted scatter data points on the graph
Step-by-step explanation:
Whereby the graph with the line of best fit on the left was drawn by Sylvia and the graph with the line of best fit on the right was drawn by Patrick, we have;
The line of best fit is a line that gives the relationship of the data points within a graph to each other, such that the line of best fit provides an approximation of the data on a graph
The line of best fit is the line that passes through the mid region of all the scatter points within a graph, and closeness of the data points on the scatter plot to the line of best fit, the higher the level of correlation between the line of best fit and the data.
Therefore, we have;
Sylva's line is a line of best fit because her line passes through the middle of the plotted scatter data points on the graph. Patrick's line is not a line of best fit as his line does not pass through the middle of the plotted scatter data points on the graph.
Answer: Sylvia’s line is a line of best fit because her line is close to most of the data points . Patrick’s line is not a line of best fit as his line is not close enough to all the data points .
7
Find the value of the expression. Z + 2y for y = 6 and z = 1
Answer:
13
Step-by-step explanation:
1+2×6=13
boy!!!!!!!!!!!!!!
Solve for c.
a(c + b) = d.
Answer:
c = d/a - b
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesStep-by-step explanation:
Step 1: Define
a(c + b) = d
Step 2: Solve for c
Divide a on both sides: c + b = d/aSubtract b on both sides; c = d/a - bPlease please I need help last question
Answer:
I'm need you to retake to picture for me luv, I cant see the numbers
Q3) Jim is scuba diving. Jim started out 25 feet below the surface. He
descended 13 feet, and rose 7 feet. Then he rested. Find his position
relative to sea level?
Plz help me
Answer:
-31 feet
Step-by-step explanation:
so, -25 is the start point.
he goes anither -13 feet, so hes at -38.
he rises 7 feet, so hes at -31 feet.
PLEASE HELP INWILL GIVE BRAINLIEST
Answer:
$960
Step-by-step explanation:
30^2 is 900
30x2 is 60
900+60 is 960.
Hope this helps plz hit the crown :D
What is the equation in standard form of the line y=1/9 x +5?
Work Shown:
[tex]y = \frac{1}{9}x+5\\\\9y = x+45\\\\9y-45 = x\\\\-45 = x-9y\\\\x-9y = -45\\\\[/tex]
The last equation is in the form Ax+By = C where A = 1, B = -9, C = -45
In the second step, I multiplied each term by 9 to clear out the fraction.
A ruler is used to measure the width of the spine of a book.
1
2
3
4
5
СМ
Using this ruler, what is the greatest level of precision possible for the measurement of the width of the
spine of the book?
1.00 cm
0 0.10 cm
0.02 cm
0.01 cm
Answer:
1.00 cm Is the greatest level of precision possible for the measurement of the width of the spin of the book
Mr. Molier is figuring out the the semester averages for his history students. He can calculate the average of 20 students in an hour. How long does it take him to figure the average for each student? Explain your answer.
Write the equation of a line in
slope intercept form of a line that
has a slope of -1 and contains
(-5, 2).
Answer:
y = -x - 3
Step-by-step explanation:
Sorry it’s late but hope this helps. Pls give brainliest.
A square has sides of length S inches. Suppose the perimeter of the square is P inches, and it's area is A square inches. If P = A, then what's the value of S? (Please show work I need help:(
Step-by-step explanation:
The answer has to be 4.
4×4=16
4+4+4×4=16
Choose the equation that represents a line that passes through points (-1,2) and (3, 1).
Answer:
B) x + 4y = 7
Step-by-step explanation:
Hope this helps. Pls give brainliest.
A $48 aquarium is on sale at a discount of 24%. What is the sale price of the aquarium?
Answer:
36.48$
48x24/100=11.52
48-11.52=36.48
The angle between the incident ray and reflected ray is 90°. Calculate the angle of incidence and the angle of reflection.
Answer:
Step-by-step explanation:
The angle of incidence and reflection is 45°
The angle between them is 90°
they lie on the same plane, and angle of incidence = angle of reflection
the sum of all the angles is 180°
let angle of incidence and reflection be x
therefore,
90 + 2x = 180
x = 45°
Sarah drove 40 miles per hour. In 3 hours, Sarah drove 120 miles. Which is a valid proportion to represent this description?
Answer:
A
Step-by-step explanation:
miles over hours
40 over 1
120 over 3
u = 4i + 9j
8= -8j
Find: u +g
Answer:
4i + j
Step-by-step explanation:
I think you meant g instead of 8.
Given:
u = 4i + 9j
g = -8j
u + g
(4i + 9j) + (-8j)
4i + j
I need help with this question plsss
Find the magnitude of angle A if cos A = 0.5
Step-by-step explanation:
[tex]A = {cos}^{ - 1} 0.5 \\ \: \: A= 60[/tex]
Simplify the following equations
Step-by-step explanation:
Given the expressions
1)
[tex]\sqrt[5]{16} * \sqrt[5]{2} \\= 16^{1/5} * 2^{1/5}\\= 2^{4(1/5)} * 2^{1/5}\\= 2^{4/5} * 2^{1/5}\\= 2^{4/5+1/5}\\= 2 ^{5/5}\\= 2^1\\= 2\\\\[/tex]
2)
[tex]\frac{\sqrt[4]{243}}{\sqrt[4]{3}} \\= \frac{243^{1/4}}{3^{1/4}}\\= \frac{3^{5/4}}{3^{1/4}}\\=3^{5/4-1/4}\\= 3^{4/4}\\= 3[/tex]
3)
[tex](3+\sqrt{2} )(4+\sqrt{7} )\\= 3(4) + 3\sqrt{7} + 4\sqrt{2} + \sqrt{14} \\= 12 + 3\sqrt{7} + 4\sqrt{2} + \sqrt{14} \\[/tex]
If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, determine a quadratic model to represent the tunnel.
State a geometric model that could be used to represent a truck passing through the tunnel.
Answer:
TUNNEL:
f(x) = -2/4.9 [tex]x^{2}[/tex] + 9.8
TRUCK:
Width (m) < 9.8
Height (m) < -2/4.9 ( [tex]Width^{2}[/tex] /4 - [tex]4.9^{2}[/tex] )
Step-by-step explanation:
Please see attachment
If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.
What is a quadratic function?Any function of the form[tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
It is given that, If the maximum height of the tunnel is the same as its maximum width, 9.8 meters.
We have to determine a quadratic model to represent the tunnel.
The quadratic function is formed as,
f(x) =K(x-x₁)(x-x₂)
x₁=width/2
x₁=9.8/2 = 4.9
x₂= -x₁ = -4.9
Substitute the obtained value as,
f(x) = K(x-4.9)(x-(-4.9))
f(x) =K(x²-4.9²)
f(0)=9.8
The value of K is obtained as a result,
K=-2×4.9/(4.9)²
K= -2/4.9
Substitute the value of K as,
f(x) = -2/4.9(x²-4.9²)
f(x) = (-2/4.9)x²+2×4.9
f(x)= (-2/4.9)x²+9.8
Thus, if the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.
Learn more about quadratic function here:
brainly.com/question/17177510
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