Answer:
x = 2 + i sqrt(66) or x = 2 - i sqrt(66)
Step-by-step explanation:
Solve for x:
x^2 - 4 x + 70 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 70 from both sides:
x^2 - 4 x = -70
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 4 to both sides:
x^2 - 4 x + 4 = -66
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 2)^2 = -66
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 2 = i sqrt(66) or x - 2 = -i sqrt(66)
Hint: | Look at the first equation: Solve for x.
Add 2 to both sides:
x = 2 + i sqrt(66) or x - 2 = -i sqrt(66)
Hint: | Look at the second equation: Solve for x.
Add 2 to both sides:
Answer: x = 2 + i sqrt(66) or x = 2 - i sqrt(66)
A clothing store is having a sale. A shirt normally sells for $30. The store is
offering a 15% discount. What is the discounted price?
A. $4.50
B. $25.50
C. $26.50
D. $24.50
Answer:
B. $25.50
Step-by-step explanation:
This is a bit of a trick question.
To find how much money is taken off the price, you would do 15% (0.15) • 30 and you get $4.50. This is the discount that is taken off of the price, not the discounted price. To find the new discounted price, subtract the $4.50 from $30.00.
$30.00 - $4.50 = $25.50
Find the equation of the line that goes through the points (12, 11) and (7,1)
Answer:
8,4
Step-by-step explanation:
Step 1: Find the slope of the line.
Step 2: Use the slope to find the y-intercept.
Step 3: Use steps 1 and 2 to write the answer.
I will explain these steps by looking a several examples. Please understand that there are often several
different ways to complete each math problem, but I have found through the years that students are most
successful when the do problems the same way each and every time they attempt the problem. If you
know a different way to find the answer that is great, but I am going to show how to do the problem one
way and use the same technique everytime I see this problem.
Example 1: Find the equation of the line passing through the points (–1, –2) and (2, 7).
Step 1: Find the slope of the line.
To find the slope of the line passing through these two points we need to use the slope
formula:
( )
( )
So the slope of the slope of the line passing through these two points is 3.
Step 2: Use the slope to find the y-intercept.
Now that we know the slope of the line is 3 we can plug the slope into the equation and
we get:
y = 3x + b
Next choose one of the two point to plug in for the values of x and y. It does not matter
which one of the two points you choose because you should get the same answer in either
case. I generally just choose the first point listed so I don’t have to worry about which
one I should choose.
(–1, –2) → –2 = 3(–1) + b Multiply to simplify the problem.
–2 = –3 + b Solve for b and you will have the y-intercept.
b = 1
Functions A,B and C are linear functions. Some values of function A are shown in the table. Function B has y-intercept of (3,0) and a x-intercept of (5,0). Function C is defined by the equation y=3x+1.
HERES THE TABLE
X. 3,5,6
Y. 3,7,9.
Create equations for each of the 3 functions given above?
Order the linear functions based on rate of change from least to greatest?
Answer:
In order of increasing slope:
B: y = 0
A: y = 2x-3
C: y = 3x+1
Step-by-step explanation:
(3,3), (5,7), and (6,9) are points on line A.
Use the coordinates of two of the points to find the slope of A.
Δy =7-9 = -2
Δx =5-6 = -1
Slope = Δy/Δx = 2
Equation for line of slope 2 that passes through (3,3):
y-3 = 2(x-3)
y = 2x-3
(3,0) and (5,0) are points on line B. They are horizontally aligned, so the equation for line B is y=0. Slope = 0.
You were given the equation for C: y = 3x+1. Slope = 3
In order of increasing slope:
B: y = 0
A: y = 2x-3
C: y = 3x+1
Function c is defined by the equation c(n)=50+4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n. What is the inverse function.
Answer:
(x - 50 / 4) = y
Step-by-step explanation:
On photo
To find the inverse function, you will have to write n in terms of c (which means number of visits as function of monthly cost).
The inverse function would be:
[tex]n = \dfrac{c-50}{4}[/tex]
Given that:c(n) = 50 + 4nc is monthly cost in dollars, of visiting a gym.n is the number of visits.To find:Inverse function of given function.
What is inverse function and when is it possible to find such function?The inverse function of f is a function of f which can remove the effect of f on its input.
Inverse is only possible if the function f is bijective (one to one correspondence, which means one input to one output uniquely and one output is connected to only one input by mapping f)
Since the given function is a linear function and not a vertical line, thus, one input n uniquely maps to one output cost and one cost uniquely is obtained by one and only one value of n.
Finding the inverse function of c(n) = 50 + 4n:[tex]cost = 50 + 4n\\ 4n = cost - 50\\\\ n = \dfrac{\text{c - 50}}{4} \text{\: (assuming cost to be denoted by c)}[/tex]
Thus, we have the inverse function of given function as:
[tex]n = \dfrac{c-50}{4}[/tex]
Learn more about inverse functions here:
https://brainly.com/question/1422702
Write the missing term in the pair of equivalent ratios.
63:90 = 14: ___
Please help I will reward brainliest
Answer:
20
Step-by-step explanation:
14/63=2/9=20/90
9. Con 12 libros de diferentes autores, cuántas selecciones de 7 libros se pueden
hacer si:
a. Un libro determinado se incluye siempre.
b. Un libro determinado nunca se incluye.
please answer all 3 questions
Answer:
x = 30°DB = 26AD = BC = AB = DC = 7Step-by-step explanation:
Diagonals of a square are congruent and perpendicular and bisect each otherQ4m∠AEB = 3x
m∠AEB = 90°
3x = 90° ⇒ x = 30°Q5AE = 3x - 2
EC = 2x + 3
AE = EC3x - 2 = 2x + 33x - 2x = 3 + 2x = 5DB = EC = 2(AE) = 2(3*5 - 2) = 2(13) = 26
Q6AD and BC are the sides, which are equal
2x - 1 = 5x - 135x - 2x = 13 - 13x = 12x = 4AD = BC = AB = DC = 2*4 - 1 = 7
Answer:
mhanifa is right
Step-by-step explanation:
A baker has three canisters of flour in her supply room Canister A can hold 30 pounds, canister B can hold 45 pounds, and
canister C can hold 60 pounds.
· Canister A contains 71% of its capacity
. Canister B is 16 full
Canister C has 8.8 pounds more than half its capacity
The baker estimates that she does not have the 70 pounds of flour needed for this weekend's planned baking
Use estimation strategies to determine which statements are true.
The total amount of flour in the three canisters is approximately 55 pounds.
The total amount of flour in the three canisters is approximately 70 pounds.
The baker does not have enough flour for the weekend's planned baking
The baker's estimate is not reasonable
The total amount of flour in the three canisters is approximately 90 pounds.
The baker has enough flour for the weekend's planned baking
The baker's estimate is reasonable
Answer:
its
2
6
5
Step-by-step explanation:
INTRO TO RATIOS
pls help its due tomorrow
Answer:
3:5, 5:4 for the first two oon the top. i dont have time to do the rest bc my teachers calling on me sorry :(((
Step-by-step explanation:
What is the equation of the line shown on the graph?
(1)y=2x+2
(2)y=2x-1
(3)y=x+2
(4)y=x-1
(5)y=1/2x+2
Is it possible for y to be an independent variable?????????
Answer:
Well uh that's a good question I actually don't know but ill see
Step-by-step explanation:
snog can you answer this question what is (3x4)-4(3-6)+14(7x8)
Answer: 808
Step-by-step explanation:
Need this grade please help!!!
Answer:
6 = 36450
Step-by-step explanation:
1. A car dealership marks up their cars 7% in order to make a profit. Find the selling price
2. Josie is fundraising for her soccer team; she buys candy bars for $0.75 each and marks
them up 80%. What is the selling price of each candy bar?
Answer:
1) selling price is 1.07 multiplied by whatever they paid for the car
2) selling price is $1.35
Step-by-step explanation:
2) to get 80% markup on 0.75 you can multiply 0.75 x 1.8
At the moment my brain is dead. I would appreciate it if you could answer this for me, thank you.
Answer:
yes,no,yes,yes,no
Step-by-step explanation:
if it is wrong im sorry
i tryed
Roberta bought 9/10 pound of raisins. She put 2/5 pound in bags for her lunch. How many 2/5 pound bags can Roberta fill? Does she have any left over?
Answer:
2 pound bags and have a remeinder of 1/10
Step-by-step explanation:
Answer:
She can fill 2 bags for her lunch and will have 1/10 pound left.
Step-by-step explanation:
It is easier if there is a common denominator, so I made the 2/5 into 4/10, so it is the same as 9/10 pound she bought.
4/10 is one bag, and if you double that, it is 8/10 pounds used. This is two bags of raisins for her lunch.
9/10 - 8/10 leaves 1/10 pound remaining, and not in a bag.
1. Find the distance of a line segment with endpoints G (4,9) and H (7,1).
about 8.5 units
about 10.4 units
about 3.6 units
about 7.8 units
Answer:
a) d = 8.5 units
The distance of a line segment with end points
d = 8.5 units
Step-by-step explanation:
Step(i):-
Given points are G(4,9) and H( 7,1)
By using distance formula
G H = [tex]\sqrt{x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Step(ii):-
[tex]d = \sqrt{7-4 )^{2} +(1-9 )^{2} }[/tex]
d = [tex]\sqrt{3)^{2} +(-8 )^{2} } = \sqrt{9+64} = \sqrt{73}[/tex]
d = 8.5 units
Hi, I have a question. So, A car travels 104 miles in 3.2 hours.
Find the car's rate of speed in miles per hour. Use division and the formula for rate of speed to solve. Can you help me? Thank you. :)
Answer:
32.5MPH
Step-by-step explanation:
Drew is buying a $325,000 house. He will put a 4.5% down payment and finance the
rest of the price with a mortgage loan. What is the mortgage loan amount? Round your
answer to the nearest thousand
$310,000
$300.000
0 $311.000
$275,000
Answer:
$311,000
Step-by-step explanation:
Original cost of house = $325,000
Mark down percent = 4.5%
Markdown price = 4.5% * 325000
Markdown price = 0.045*325000
Markdown price = $14,625
Mortgage loan amount now = $325,000 - $14,625
Mortgage loan amount now = $310,375
Mortgage loan amount now tom the nearest thousand is $311,000
- y - 5 > -7 solve the inequality
Answer:
y=2
Step-by-step explanation:
which sequence of transformations will carry triangle ABC onto triangle A'B'C'?
Answer:
B
Step-by-step explanation:
start at A and got to A'
In order to get to to A' you need to count how many blocks down and how many blocks left or right. Repeat
A squar has an area of 64cm2 find the perimeter of the square
Answer: 32 cm
Step-by-step explanation:
Answer:
All of the sides of the square are 8 cm. So the prementer would be 32 cms
Step-by-step explanation:
To find the sides of the square, you got to think what x what = 64. This shows you that 8 x 8 is 64. and since it is a square, all of the sides are the same. So 8+8+8+8 = 32 or you can do 8 x 4 = 32
Sorry for any spelling mistakes.
What is the range of the following set of numbers:
50, 61, 85, 104, 69, 84, 101
Answer:
Step-by-step explanation:
104-50 = 54
range = 54
Rectangle GHIJ is dilated to be a smaller shape. What is the name of the image after the dilation? GHIJ G prime H prime I prime J prime IGJH J prime I prime H prime G prime
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Lines C and D are represented by the equations given below: Line C: y = x + 6 Line D: y = 3x + 2 Which of these shows the solution to the system of equations and explains why? (10 points)
A. (2, 8), because both lines pass through this point
B. (2, 8), because the point does not lie on any axis
C. (4, 14), because one of the lines passes through this point
D. (4, 14), because the point lies between the two axes
Answer:
C) y = x + 6
D) y = 3x + 2 We multiply C) by -1
C) -y = -x -6
D) y = 3x + 2
0 = 2x -4
x = 2
y = 8
Step-by-step explanation:
Answer:
It's A
Step-by-step explanation:
4
Select the equation below that has solutions of 1-3i and 1+3i *
(1 Point)
O A. O = x2 – 2x - 10
O B. 0 = x2 -- 2x + 10
O C. O = x2 – 2x + 8
O D. 0 = x2 - 2x - 8
PLS HELP!!!
Answer:
[tex]x^2 - 2x + 10[/tex], option B
Step-by-step explanation:
Complex numbers:
The most important relation that involves complex numbers is given by:
[tex]i^2 = -1[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
The solutions are:
[tex]x_1 = 1 - 3i, x_2 = 1 + 3i[/tex]
We have to find the polynomial. All option have [tex]a = 1[/tex]. So
[tex](x - (1 - 3i))(x - (1 + 3i)) = x^2 - x(1 + 3i) - x(1 - 3i) + (1 - 3i)(1 + 3i) = x^2 - x -3ix - x + 3ix + 1^2 - (3i^2) = x^2 - 2x + 1 - 9i^2 = x^2 - 2x + 1 - 9(-1) = x^2 - 2x + 10[/tex]
The correct answer is given by option b.
Find the slope and y-intercept of the equation y= -4x-8
Answer:
-8
Step-by-step explanation:
.
Answer: the slope is -4 and the y-intercept is -8.
Step-by-step explanation: please mark me brainliest
A watermelon weighs 6.45 kilograms. How many grams does the watermelon weigh?
Answer:
A watermelon weighs about 3 (grams /(kilograms) 3.
Step-by-step explanation:
Answer:
6,450 g
Step-by-step explanation:
Since there are 1000 grams in 1 kilogram, you multiply 6.45 kg x 1000 g.
6.45 x 1000 g equals 6,450 grams. Move the decimal 3 times to the right because there are 3 zeroes in 1000.
You always move your decimal to the right when multiplying decimals.
Jack and Jill each go out shopping.
Jack spends 1/3 of his money.
Jill spends 40% of her money.
Frank says Jack spent more because 1 /3 is greater than 40%.
Alice says you cannot tell who spent more.
Who do you agree with, Frank or Alice? Explain why.
I agree with Alice because you do not know how much money Jill and Jack had before they went shopping. If they had the same amount of money Jill would have spent more because 40 percent is greater than 1/3.
Step-by-step explanation:
Thank me later
A parallelogram is
a regular polygon.
A. always
B. sometimes
C. never