Answers
Answer:
[tex](x-6)^2=-1[/tex]
Step-by-step explanation:
Given equation:
[tex]-6x^2+64x-222=-8x[/tex]
When completing the square, first move the terms in x to the left and the constant to the right of the equation:
[tex]\implies -6x^2+64x-222=-8x[/tex]
[tex]\implies -6x^2+64x-222+222=-8x+222[/tex]
[tex]\implies -6x^2+64x=-8x+222[/tex]
[tex]\implies -6x^2+64x+8x=-8x+222+8x[/tex]
[tex]\implies -6x^2+72x=222[/tex]
Factor out the leading coefficient -6 from the left side, then divide both sides by -6:
[tex]\implies -6(x^2-12x)=222[/tex]
[tex]\implies \dfrac{-6(x^2-12x)}{-6}=\dfrac{222}{-6}[/tex]
[tex]\implies x^2-12x=-37[/tex]
Add the square of half the coefficient of the term in x to both sides, forming a perfect square trinomial on the left side:
[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2=-37+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]\implies x^2-12x+\left(-6\right)^2=-37+\left(-6\right)^2[/tex]
[tex]\implies x^2-12x+36=-37+36[/tex]
[tex]\implies x^2-12x+36=-1[/tex]
Factor the perfect square trinomial on the left side:
[tex]\implies (x-6)^2=-1[/tex]
To solve:
[tex]\implies \sqrt{(x-6)^2}=\sqrt{-1}[/tex]
[tex]\implies x-6=\pm i[/tex]
[tex]\implies x-6+6=\pm i+6[/tex]
[tex]\implies x=6 \pm i[/tex]
Therefore, the solutions are:
[tex]x=6+i, \quad x=6-i[/tex]
Related Questions
a. A group of 30 students were surveyed and it was found that 18 of them took
Calculus and 12 took Physics. If all students took at least one course, how
many took both Calculus and Physics? Illustrate using a Venn diagram.
Answers
No student took both calculus and physics out of the 30 students.
Given that, total number of students are 30. Out of which 18 took calculus and 12 took physics. Then, we have to calculate how many took both calculus and physics. So, by using venn diagram we have,
Total number of students = 30
Students who took calculus = P(A) = 18
Students who took physics = P(B) = 12
Students who took both calculus and physics = P(A∩B) = x
Students who took only physics = P(B)-x = (12-x)
Students who took only calculus = P(A)-x = (18-x)
From venn diagram, we get
(18-x)+x+(12-x) = 30
18-x+x+12-x = 30
⇒ x = 0
∴ P(A∩B) = 0
Therefore, No student took both physics and calculus.
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During a marathon, Amy was in second place and was told that the leader was 100 meters ahead of her and that the closest runner behind her was 75 meters back. On a number line, let's say Amy's position is at 0, and the leader's position is on the positive side of 0. Which number sentence correctly compares the distance between Amy and the runner behind her to the distance between Amy and the leader?
A) |-75|< |-100|
B.|-75|<|100|
C.|75|=|-100|
D.|-75|>|100|
Answers
Answer:c
Step-by-step explanation:
c
jon started driving west 2 hours ago and has gone 80 mph. What is his veolcity?
Answers
Answer:
Either 40 or 80, depending on whether you worded the question correctly or not.
Step-by-step explanation:
If you mean he has gone 80 miles:
velocity is distance per time, so 80miles/2hours = 40 miles/hour
If you mean he is going 80mph, then the answer is in the question, 80 miles/hour and the distance he has traveled is in miles, therefore you need to multiply by hours, i.e., 80*2=160 miles.
Help Needed with this
Answers
Answer:
Step-by-step explanation:
Find the average rate of change of
Answers
The approximate rate of change of the function is 224.95
Rate of change of functionThe rate of change of the given function is expressed according to the equation below;
f'(x) = f(b)- f(a)/b-a
Given the interval [-4, 3]
a = -4
b = 3
f(a) = 9(-4)⁴ + 7/(-4)²
f(-4) = 2304+ 7/16
f(-4) = 2304.4375
f(b) = 9(3)⁴ + 7/(3)²
f(3) = 729 + 7/9
f(3) = 729.7778
Substitute to have:
f'(x) = 729.7778-2304.4375/3+4
f'(x) = 1574.65/7
f'(x) = 224.95
Hence the approximate rate of change of the function is 224.95
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Jenna bought a new car for $37,000
$
37,000
. She paid a 10%
10
%
down payment and financed the remaining balance for 72
72
months with an APR of 6.5%
6.5
%
. Assuming she makes monthly payments, determine the total interest Jenna pays over the life of the loan. Round your answer to the nearest cent, if necessary.
Formulas
Answers
Jenna paid a total interest of $4810 (13% of the cost of the car) for the car.
What is APR?Suppose there is initial amount as P.
The interest, or say charge on it is applied annually as 'C' amount.
Taking how much percent of P is C, we get:
[tex]APR = \dfrac{C}{P} \times 100[/tex]
WE have been given that Jenna bought a new car for $37,000 and paid a 10% down payment and financed the remaining balance for 72 months with an APR of 6.5%
Assuming that she makes monthly payments, to determine the total interest Jenna pays over the life of the loan.
The cost = $37,000
Time = 72 months
APR = 6.5%
Then;
Interest = (37,000 x 6.5 x 2) /100
= $4810
Percentage of interest paid = (4810/37,000 ) x 100
= 13%
Therefore, Jenna paid a total interest of $4810 (13% of the cost of the car) for the car.
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Graph the following system of inequalities on the coordinate plane. You will need to explain your work. Each correct line graphed WITH the correct explanation and shading is worth TWO points.
Please tell me how you graphed each line and how you determined where to shade
Answers
Answer:
See attached graphs Graph1, Graph2 and Graph3 and detailed explanation below
Step-by-step explanation:
The process for plotting and shading are essentially the same but with different inequalities
To plot any line
We need two pointsPlug in a value for x and find the corresponding y valueRepeat for another x value and find the corresponding y valueDraw a straight line through the two pointsTo determine area to shade
Choose a point on either side of the line from the graph. See if the corresponding (x,y) values satisfy the inequality. If they do, then that's the area to shade. If not, shade the other area
1. Inequality y > -3x - 2
The line equation is y = -3x -2
Let's choose x = 0. Then y = -3(0) -2 = -2. So one point is (0, -2)
Choose another value for x, say x = 1
y = -3(1) - 2 = -3-2 = -5. So another point is (1,-5).
Draw a straight line through both points (see attached Graph1)
Determining area to shade
Choose a point on the graph on one side of the line. Let's choose (1,2). So x = 1 and y = 2. Does this satisfy the inequality y = -3x -2? Let's see
Is 2 > -3(1) - 2 ?
2 > -3-2 ?
2 > -5 ? YES since a positive number is greater than a negative number. So the area containing (1,2) should be shaded as shown in Graph 1
2. Inequality 4x + 5y ≤ 20
Line equation is 4x + 5y =20
Convert to a function of x as follows
Subtract 4x from both sides ==> 5y = 20 -4xDivide by 5 both sides ==> y = 20/5 - (4/5)x ==> y = 4- 4x/5Choose two values of x and find corresponding y values to get the coordinates of two points
Plug x = 0 into line equation ==> y = 4- 4x/5
==> y = 4 - 4(0)/5 = 4
==> (0, 4) is one point
Choose another value of x, say 5(this is a convenient value since we are dividing by 5)
==> y = 4- 4(5)/5 = 4-4 = 0
==> (5, 0) is another point
Draw straight line through (0,4) and (5,0)
To determine area to shade let's choose a point on the graph. (0,0) is a convenient point. Do the values of x=0 and y=0 satisfy the inequality
4x + 5y ≤ 20?
Plugging in x = 0 and y = 0 gives us
4(0) + 5(0) = 0 and 0 is indeed ≤ 20
So the inequality is satisfied at (0,0)
Shade the region on the side of the line where (0,0) is (see Graph2)
3. Inequality y > -4
The line equation is y = -4
Since this equation does not involve x, the line plot will be a horizontal line at y = -4 for all x values
Simply draw a horizontal line which crosses the y axis at y = -4
To determine which area to shade, choose a point. Use (0,0)
Does y = 0 satisfy the inequality y > -4?
0 > -4 so indeed the point (0,0) satisfies the inequality. Just shade the area on the side of the line which contains (0,0). This will be the region above the line y = -4 See Graph3
Hope that helps :)
A teacher has 15 weeks in which to teach six chapters. Write and then solve
an equation that represents the number of lessons the teacher must teach per week if
there is an average of 8.5 lessons per chapter.
Answers
What is the irrational number 49 squared 34 squared 9/2 squared 13/16 squared
Answers
The required irrational number is 13 / 16 among the options given. Option D is correct.
Given that,
To determine the irrational number among the number given.
Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3, etc.
here,
49² = is rational number
34 ² = rational number
9 / 2 = rational number
13 / 16 = irrational number
Thus, the required irrational number is 13 / 16 among the options given. Option D is correct.
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I’ll give braniest
Find the coordinates of the point
7/10 of the way from A to B.
Answers
[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad B(\stackrel{x_2}{10}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{7}{10}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{10}-\stackrel{x_1}{(-3)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{(-8)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 13 ~~,~~ 13 \right)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left( \stackrel{x_1}{-3}~~+~~\frac{7}{10}(13)~~,~~\stackrel{y_1}{-8}~~+~~\frac{7}{10}(13) \right)\implies \left(-3+\cfrac{91}{10}~~,~~-8+\cfrac{91}{10} \right) \\\\\\ \left( \cfrac{-30+91}{10}~~,~~\cfrac{-80+91}{10} \right)\implies \left(\cfrac{61}{10}~~,~~\cfrac{11}{10} \right)\implies \left(6\frac{1}{10} ~~,~~1\frac{1}{10} \right)[/tex]
A grocery store sells four different jars of peanut butter. Determine which is the best buy, based on the cost per unit.
16 ounces for $1.70 20 ounces for $1.90
26 ounces for $3.33 40 ounces for $
Answers
The least cost per unit of peanut butter is $0.095 for 20 ounces for $1.90 therefore option (B) will be correct.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variable called division.
Given the four options of jars;
1) 16 ounces for $1.70
Cost per ounces = 1.70/16 = $0.10625
2) 20 ounces for $1.90
Cost per ounces = 1.90/20 = $0.095
3) 26 ounces for $3.33
Cost per ounce = 3.33/26 = $0.128
The least cost per ounce is $0.095 for 20 ounces for $1.90.
Hence "The least cost per unit of peanut butter is $0.095 for 20 ounces for $1.90".
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LOOK AT THE EXPRESSION 4.8X107 +6,500,000 WHAT IS THE VALUE OF THE EXPRESSION
Answers
64.00336 × 10⁵ is the solution of the Expression .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.=(48*7) +65 ×10⁵
=((40+8) *7) +65 × 10⁵
=(280+56)+65 ×10⁵
=336+65 × 10⁵
=.336*10^3+65 × 10⁵
=.00336*10^5+65 × 10⁵
=(.00336+65) × 10⁵
= 64.00336 × 10⁵
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Write the next three terms of the following sequences.
5⁄8, 13⁄8, 21⁄8, 29⁄8, 37⁄8, ...
Answers
Answer:
45/8
Step-by-step explanation:
3x - 2y = 15
x = 3
the two lines given by the equations above interest in the xy-plane. What is the value of the y-coordinate of the point of intersection?
Answers
Step-by-step explanation:
y-intersec is (0,y)
sub x=0 in 3x-2y=15
3*0-2y=15
0-2y=15
y=-15/2
What integer describes a loss of 45 yards
Answers
-45 represents a loss of 45 yards (integers include negative numbers)
Which of the following is a unit rate?
A. 56 cubic inches
B. 39 miles to 2.6 hours
C. 90 people per day
D. 5.6 square feet
Answers
Answer:
B & C
Step-by-step explanation:
a rate has to have an incline or decline. A&D are set amounts.
What is 9 x 5.63 show how you got your answer.
Answers
Answer:50.63
Step-by-step explanation: line them up on top of each other and multiply 9 by all them and if its over 10 put the 2nd digit the the next number.
what is the value of x??
please help!!
Answers
A farmer has 220 bushels of wheat to sell at her roadside stand. She sells an average of 15 1/4 bushels each day. Represent the total change in the number of bushels she has for sale after 7 days.
Answers
She has 114 left after the 7 days and has sold 106.
a godown had a stock of cloth of Rs.160000. Due to a fire a part of the merchandise, wroth Rs. 20000, was completely destroyed. find the loss percent?
Answers
The loss percentage of cloth is 12.5%.
Stock of cloth = Rs. 1,60,000
worth of destroyed cloth = Rs. 20,000
A percentage is a number or ratio that can be expressed as a fraction of 100. It is denoted by the symbol %.
Percentage = Value/ Total value × 100%
Loss percentage = Loss/Total value × 100%
So, the loss percentage of cloth = 20,000/1,60,000 ×100%
= 0.125 × 100%
= 12.5%.
3x+4 < 4 pls some one help me pls it’s my last problem for my homework
Answers
Answer:
x < 0
Step-by-step explanation:
We are given this inequality:
3x + 4 < 4
And we want to solve it.
Solving inequalities is very similar to solving equations. We want to isolate the variable (in this case, x) on one side, while leaving the numbers on the other side.
To start, we can subtract 4 from both sides.
3x + 4 < 4
-4 -4
__________________
3x < 0
Now, we have the numbers on one side and the variable on the other, but we aren't done yet, as we want to solve for the value of x, or 1x, not the value of 3x.
So, we'll need to divide both sides by 3.
3x < 0
÷3 ÷3
___________
x < 0
The answer is x < 0.
Write an algebraic expression that represents the verbal expression shown:
"The difference of 40 and the quotient of 60 and 3."
Answers
Answer:
60/3 - 40
Step-by-step explanation:
Answer: 60/3 -40
Step-by-step explanation:
Write 7,855.1 as an Ordinary Notation
Answers
express x^pi in base e
Answers
The representation of x^pi in base e is e^xln3.
What is defined as the exponential functions?An exponential function is a the kind of mathematical function that involves exponents.
A mathematical function of the very next form is an exponential function:f (x) = aˣ
where x is a variable and an is a constant known as the function's base.
The transcendental number e, which is approximately 2.71828, is the most frequently detected exponential-function base. As a result, the preceding expression becomes:f (x) = eˣ
When the exponent in this component increases by one, the function's value increases by a factor of e.
When the exponent is reduced by one, the value of the function is reduced by the same factor (it is divided by e ).
Base-10 exponential functions have been encountered in computers and experimental science. The common form is:f ( x ) = 10ˣ
Now, for the given function.
3x=e^ln3^x
= e^xln3
Therefore, the base e representation of the expression is e^xln3.
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the difference of 15y and 16y is -6
Answers
Answer:
y=6
Step-by-step explanation:
15y-16y=-6 subtract (15y-16y=-1y or -y)
-y=-6 Divide each side by -1 in order to make the -y a positive number.
y=6
You didn't really clarify what you were looking for in your question, but I answered according to what I thought you were talking about. I hope this helps you. If not, reply to me with what you were looking for and I will edit my answer to meet your requirements.
-R+ 6 + 8r - 14
I don’t know how to set this up or solve it
Answers
The solution to the expression is 7r - 8
How to set up and solve the expression?The expression is given as
-r + 6 + 8r - 14
Collect the like terms in the above expression
So, we have
-r + 8r + 6 - 14
Evaluate the like terms in the above expression
7r - 8
Hence, the solution to the expression is 7r - 8
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P(n), given below, is the price in dollars for n grams of vitamins.
P(n) = 0.2n + 5.3
Complete the following statements.
(a) which statement best describes (p^-1) (x)?
(See picture)
(b) p^-1 (x) =
(c) p^-1 (6.6) =
Answers
The statement that best describes the expression p-1(x) is (c) the amount for x grams
How to complete the statements?The equation of the function is given as
P(n) = 0.2n + 5.3
(a) which statement best describes (p^-1) (x)?
The function is given as
P(n) = 0.2n + 5.3
This means that the inverse of the function is represented as p-1(n)
Hence, the statement that best describes the expression p-1(x) is (c) the amount for x grams
(b) The function p^-1 (x)
We have
P(n) = 0.2n + 5.3
Rewrite as
y= 0.2x + 5.3
Swap x and y
x = 0.2y + 5.3
Make y the subject
y = 5x - 26.5
Express as inverse function
p^-1(x) = 5x - 26.5
(c) The value of p^-1 (6.6)
We have
p^-1(x) = 5x - 26.5
This gives
p^-1(6.6) = 5 x 6.6 - 26.5
Evaluate
p^-1(6.6) = 6.5
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state whether each function is a linerar function, write yes or no. explain y = 3/4x
Answers
write an equation in slope- intercept form for the line described.
perpendicular to y = 1/4x + 2 passes through (0,0)
Answers
Answer:
y=-4x+0
Step-by-step explanation:
Slope form is y=mx+b
m is the slope, and b is the y intercept. If the line must pass through (0,0) then the y intercept would be zero.
This give you y=mx+0
Now to find the slope you need a perpendicular line to the previous line. This would mean you have to swap 1/4 which is the previous lines slope.
1/4 is a positive so make it a negative, -1/4
Now flip -1/4 to make is -4/1 which also equals -4
Now with the slope -4 and y-intercept 0, you know you equation
y=-4x+0
A men’s traditional haircut at the Barbara spot cost $20 and a shave cost $25 there is an 8.25% state sales tax what is the total price that Cheyenne must pay if she gets his haircut and beard shaved and he tips the barber 25%
Answers
The total price that Cheyenne must pay if he gets his haircut and beard shaved $60.89
A sales tax is one that applies to the purchase of goods and services for consumers and to the sale of goods and services for businesses. It's a type of consumption tax, meaning it taxes people for spending money.
The formula for calculating the sales tax on a good or service is: selling price x sales tax rate, and when calculating the total cost of a purchase, the formula is:
total sale amount = selling price + sales tax.
Given that
spot cost = $20
shave cost = $25
state sales tax = 8.25%
tips = 25%.
find out the total price that Cheyenne pay.
total selling price = spot + shave cost
total selling price = $20 + $25
total selling price = $45
we know that
sales tax = selling price x sales tax rate
sales tax = $45 x 8.25%
sales tax = $45 x 8.25 / 100
sales tax = $3.7125.
Cost with sales tax = $45 + $3.7125
Cost with sales tax = $48.7125
Tip is calculated on total bill
Tip Total: $ 12.18
Total (Bill + Tip): $ 60.89
hence , total amount of $ 60.89 is that Cheyenne must pay if he gets his haircut and beard shaved with the bill and tip.
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