Answer:
The solutions to the quadratic equation are:
[tex]x=i+2,\:x=-i+2[/tex]
Step-by-step explanation:
Given the equation
[tex]x^2-4x+5=0[/tex]solving the equation
[tex]x^2-4x+5=0[/tex]
subtract 5 from both sides
[tex]x^2-4x+5-5=0-5[/tex]
[tex]x^2-4x=-5[/tex]
[tex]\mathrm{Add\:}\left(-2\right)^2\mathrm{\:to\:both\:sides}[/tex]
[tex]x^2-4x+\left(-2\right)^2=-5+\left(-2\right)^2[/tex]
[tex]\left(x-2\right)^2=-1[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solving
[tex]x-2=\sqrt{-1}[/tex]
As the imaginary rule is given by
[tex]\:\sqrt{-1}=i[/tex]
so
[tex]x-2=i[/tex]
[tex]x=i+2[/tex]
solving
[tex]x-2=-\sqrt{-1}[/tex]
[tex]x-2=-i[/tex] ∵ [tex]\:\sqrt{-1}=i[/tex]
[tex]x=-i+2[/tex]
Therefore, the solutions to the quadratic equation are:
[tex]x=i+2,\:x=-i+2[/tex]
Karen buys apples and bananas for the daycare center she runs. The apples cost $1.50 per pound, and the bananas are $0.50 per pound. The table shows the amounts of apples and bananas she has purchased the previous six weeks. Apples, x (pounds) 5 10 7 3 9 12 Bananas, y (pounds) 5 5 12 14 9 2 This week, Karen will spend $20.50 on apples and bananas. Write an inequality that describes both the amounts of apples and bananas she has purchased in the past six weeks and the amounts she may buy this week. Enter the correct answer in the box. Write your answer in the form ax + by = c, using the appropriate inequality symbol in place of the equal sign.
Answer:
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!
Answer:
x= 53 and y= 143
Step-by-step explanation:
x= 90-37
x= 53
y= 53+90
y= 143
Mr. Richard plans to take 25 students on a school trip. They plan to go to Zoo. The bus fee is $100 for the entire trip. Entrance fee is $2.50 per person. How much should each student pay? Note: Mr. Richard does not need to pay.
Answer:
$162.50
Step-by-step explanation:
+$100
25x2.50= $62.50
+$62.50
100+62.50=162.50
Answer:
Each student should pay $6.50
Step-by-step explanation:
The question is not very clear.
If Mr. Richard has to pay to enter:
Total cost = $100 + ($2.50×26) = $165
Cost per student = [tex]\frac{165}{25}[/tex] = $6.60
Each student should pay $6.60
If Mr. Richard doesn't have to pay to enter:
Total cost = $100 + ($2.50×25) = $162.5
Cost per student = [tex]\frac{162.5}{25}[/tex] = $6.50
Each student should pay $6.50
You triple your account balance by making a deposit. Then you withdraw $125.00 to buy groceries. Your account is overdrawn $5.00 write an equation to find your account balance before you made the deposit
Answer:
3x - 125 = -5
Step-by-step explanation:
the 3 is the triple, x is the deposit and -125 is the withdrawn and -5 is what's left over in the bank account
10t-19=7t-14
what does t=
Answer:
t = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
10t - 19 = 7t - 14
Subtract 7t from both sides;
3t - 19 = -14
Add 19 to both sides;
3t = 5
Divide both sides by 3;
t = [tex]\frac{5}{3}[/tex]
Please please help me i'm begging you!
Answer:
A is 8 ounces/ 12 cupcakes is 12 cupcakes/8 ounces I'm not sure about C and D is 18 cupcakes for 12 ounces of frosting
Step-by-step explanation:
The senior class is planning a trip that will cost $55 per student. If $4180 has been collected  from the seniors for the trip, how many have paid for the trip?
(0, -15), (-12, 18)
Can some one find the slope
Answer:
use this formula the answer is down below.
[tex]\frac{ysub2-ysub1}{xsub2-xsub1}[/tex]
Step-by-step explanation:
this is y. -15-18= -33
this is x. 0--12 (so in this case you would add 12)
the slope is -33/12
Express $3.29 for 24 cans as a unit rate. Round to the nearest cent.
Answer:
0.14 cents per can
Step-by-step explanation:
$3.29 divided by 24 cans gives a unit rate or price per can of $0.14 per unit or per can.
Good luck.
Hope this helps!
Answer: 0.1$
Step-by-step explanation:
$ 3.29 divided by 24 cans would be .137...
If we found to the nearest cent, the answer is .1$
what's y intercept on a graph of y = -5x + 6
The y-intercept on a graph of y = -5x + 6 is 6.
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
We have a linear equation,
y = -5x + 6.
The general slope-intercept form,
y = mx + b.
Where m is the slope and b is the y-intercept.
Comparing,
b = 6.
Therefore, 6 is the y-intercept.
To learn more about the intercepts;
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Hi guys can you please help me with this problem please ill mark brainiest
The answer is y= 23/4
Show your work and write an expression using the following criteria:
Divide 4,200 by a multiple of 10
The quotient is also a multiple of 10
Answer:
420
Step-by-step explanation:
edge
Isaiah is mowing lawns for a summer job for every mountain Charlie charges an initial fee of $10 plus $6 dollars for each additional hour
1. write an equation in slope intercept form
2. how much money does he make after working one job for four hours
Answer:
y = 6x + 10
Isaiah makes $34.00 after working for 4 hours.
Step-by-step explanation:
Slope intercept form is y=mx+b
In this situation the equation would look like so, x = amount of hours:
y = 6x + 10
To solve for how much Isaiah earns after 4 hours plug in 4 instead of x.
y = 6(4) + 10
y = 24 + 10
y = 34
Isaiah makes $34.00 after working for 4 hours.
Hope that helps and have a great day!
which equation represents a line which is perpendicular to the line y=4/3x - 7?
a. 3x + 4y = 8
b.4x + 3y = -6
c. 4x - 3y = 24
d. 4y - 3x = 12
4
Roberta wants to create 32 ounces of new hand lotion, with a minimum 15% concentration of beeswax, from a mixture of
two lotions. One lotion has a 21% concentration of beeswax, and the second lotion has a concentration of 5% beeswax. Based on
the inequality below, how much of the 21% lotion, x, will she need?
0.21x + 0.05(32 - x) > 4.8
A x 20
ОВ.
x > 28
C. x 16
OD. x > 21.33
Reset
Submit
Answer: x _>_ 11.875
Step-by-step explanation:
here is the list of ingredients for making 30 biscuits
225g butter
110g caster sugar
275g plain flour
75g choc chips
Lucas has the following:
900g butter
1000g caster sugar
1000g plain flour
225g choc chips
what is the greatest number of biscuits Lucas can make?
Can someone just tell me how to work it out. I just need the method thanks x
[tex]f(x) = 1 - 2x \\ g(x) = x + 4 \\ h(x) = {x}^{2} + 1[/tex]
[tex]hgf(x) = 4 {x}^{2} + px + q[/tex]
Find the value of p and the value of q
Answer:
(x-3)(x+2) i.e. x2 - x -6 i.e. p = -1 and q = -6
Step-by-step explanation:
Brian and leo are purchasing food at the snack bar. Brian purchases a hot dog for $2.35, chips for $1.65 and a drink for $2. Leo purchased a hamburger for $3, fries for $2.45 and a drink for $2. How much did they spend altogether on food?
Answer:
$13.45
Step-by-step explanation:
add all of the money:
2.35+1.65=4
2+3=5
2.45+2=4.45
add 4, 5, and 4.45 together
13.45
Which is $13.45
What is f(4) for the function f(x) = 6x +3?
f(4)=0
The value of function f(4) is 27.
It is required to find the value of function f(4).
What is function?
A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given that:
The function is
f(x) = 6x +3
Now put the value x=4 in the given function, we get
f(4)=6(4) +3
= 24+3
=27
f(4)=27.
Hence, the value of function f(4) is 27.
Learn more about function here:
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How many eighth notes do you need to total the amount of a half note
Answer:
Four eighth notes
Four eighth notes equal one half note in duration and eight eighth notes equal one whole note.
Step-by-step explanation:
Hope this helps, If it did, then I would really appreciate it if you gave me Brainliest, I only need one more to rank up and it has taken forever to get to where I am currently. Thanks.
At the beginning of the business day a bank vault had $575,900. By the end of the day, $ (3.5 x 10^3) have been added to the vault how much money did the banks fault told at the end of the business day write your answer in standard form.
9514 1404 393
Answer:
$579,400
Step-by-step explanation:
The total will be ...
$575,900 +3.5×10³ = $575,900 +3,500 = $579,400
At the end of the day, the vault held $579,400.
Which of the following is not a function
B is not right
Answer:
The first one
Step-by-step explanation:
They have 2 outputs for the same input
Slope of (-8,2) and (-8,-6)
Answer:
-8
Step-by-step explanation:
9. y + 7 = 2(x + 5)
in standard form
Answer:
y=2x+3
Step-by-step explanation:
1. y+7=2(x+5) (rewrite the problem)
2. y+7=2x+10 (distribute the 2)
3. y=2x+3 (subtract 7 from both sides; 10-7=3)
Which of the following polynomial functions is graphed below?
Answer: B. f(x)=(x+4)(x-2)^2(x+3)
Step-by-step explanation:
in the graph there's two negative x value and one positive x value
so the function should be in a form of f(x)= (x+a) (x-b)^2 (x+c)
the one with negative value has a square, (x-b)^{2}, because that's where the y = 0 (the point is hitting the (x,0))
Answer: B
Step-by-step explanation:
help I want to get sleep
Answer:
I got -45.1 but idek if its right or not
Answer:
-45.1
Step-by-step explanation:
-6*7.1 + 2.5
-42.6 + 2.5
= -45.1
-6 - 5 + 3 =
(worth 10 points)
Answer:
-8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
Mark me as brainliest
Idk how to do this and I need it in an hour
Answer:
a) [tex]2x^2+8-5x+-3x^2-4+7x\\\\= -1x^2+2x+4[/tex]
b) [tex]2x^2+8-5x--3x^2-4+7x\\\\= 5x^2+2x+4[/tex]
1. Which equation represents a line that passes through the point (-2,6) and is parallel to the line whose equation is 8x – 4y = 6?
Answer:
y=2x+10
Step-by-step explanation:
First, let's put the equation into slope-intercept form. We get y=2x-3/2.
Parallel lines have the same slope, so the slope of the line will be 2.
We then substitute the point into the equation to find the y-intercept.
We get y=2x+10
Hope this helps :-)
The gas tank in sampson car has a capacity of 19.1 gallons . on a Tripp to see his cousin , Sampson begins with 12.8 gallons if gas in the tank he stops after driving for 2 hours and fills the tank to capacity with 14.4 gallons. When sampson arrives at his cousins house he has 3.7 gallons of gas left. How much gas , did sampson use on his trip
Answer:
23.5 gallons
Step-by-step explanation:
The gas tank in Daniel's car has a capacity of 19.1 gallons.
On a trip to see his best friend Daniel begins with 12.8 gallons of gas in the tank.
He stops after driving for 2 hours and fills the tank to capacity with 14.4 gallons.
When Daniel arrives at his friend's house, he has 3.7 gallons of gas left.
Total amount of gas filled was (12.8 + 14.4) = 27.2 gallons.
The amount of gas remaining after the trip was 3.7 gallons
The amount of gas, in gallons, used by Daniel on his trip was 27.2 - 3.7 = 23.5 gallons
Answer:
fat nuts
Step-by-step explanation:
i forgor