Answer:
The roots are;
x = (2 + i)/5 or (2-i)/5
where the term i is the complex number representing the square root of -1
Step-by-step explanation:
Here, we want to use the completing the square method to solve the quadratic equation;
f(x) = -5x^2 + 4x -1
Set the function to zero
0 = -5x^2 + 4x - 1
So;
-5x^2 + 4x = 1
divide through by the coefficient of x which is -5
x^2 - 4/5x = -1/5
We now take half of the coefficient of x and square it
= -2/5^2 = 4/25
add it to both sides
x^2 - 4x/5 + 4/25= -1/5 + 4/25
(x- 2/5)^2 = -1/5 + 4/25
(x - 2/5)^2 = -1/25
Take the square root of both sides
x - 2/5 = √( -1/25
x - 2/5 = +i/5 or -i/5
x = 2/5 + i/5 or 2/5 - i/5
the sum of 4 consecutive integers is -62 write an equation to determine the smallest of the integers
Answer:
x + (x+1) + (x+2) + (x+3) = -62
x = -17
Step-by-step explanation:
x = smallest
x + (x+1) + (x+2) + (x+3) = -62
4x +6 = -62
4x = -68
x = -17
Describe the graph of the inequality x > -1.
Answer:
See below
Step-by-step explanation:
Given
Inequality x > -1This inequality covers the interval greater than - 1
( - 1, + oo)Its graph covers the space to the right from the point -1
The vertical line - 1 is a dotted line as - 1 is nor included
d)) The ratio of the monthly income and expenditure of Sunayana is 5 : 3. If she
increases her income by Rs 5,000 and decreases the expenditure by Rs 3,000, the
new ratio becomes 5:2. Find her income and expenditure.
Answer:
Sunayana's income is ₹25000 and expenditures are ₹15000.
Step-by-step explanation:
Let i denote the monthly income and e denote the expenditures.
We know that the ratio of the monthly income to expenditure is 5:3. So, we can write the following proportion:
[tex]\displaystyle \frac{i}{e}=\frac{5}{3}[/tex]
Let's multiply both sides by e. This yields:
[tex]\displaystyle i=\frac{5}{3}e[/tex]
We know that when the income is increased by 5000 and the expenditures are decreased by 3000, the new ratio is 5:2. So, we can write the following proportion:
[tex]\displaystyle \frac{i+5000}{e-3000}=\frac{5}{2}[/tex]
Let's multiply both sides by [tex](e-3000)[/tex]:
[tex]\displaystyle i+5000=\frac{5}{2}(e-3000)[/tex]
Since we know that [tex]i=\frac{5}{3}e[/tex], substitute:
[tex]\displaystyle \frac{5}{3}e+5000=\frac{5}{2}(e-3000)[/tex]
So, let's solve for the expenditures. Distribute the right:
[tex]\displaystyle \frac{5}{3}e+5000=\frac{5}{2}e-7500[/tex]
Subtract [tex]\frac{5}{2}e[/tex] from both sides:
[tex]\displaystyle -\frac{5}{6}e+5000=-7500[/tex]
Subtract 5000 from both sides:
[tex]\displaystyle -\frac{5}{6}e=-12500[/tex]
Multiply both sides by -6/5. So, the expenditures are:
[tex]e=\text{Rs }15000[/tex]
We can use the original ratio to find Sunayana's income:
[tex]\displaystyle i=\frac{5}{3}e[/tex]
Substitute 15000 for e. Evaluate:
[tex]\displaystyle i=\frac{5}{3}(15000)=\text{Rs }25000[/tex]
So, Sunayana's income is ₹25000 and expenditures are ₹15000.
And we're done!
Answer: Income = 25000, Expenditures = 15000
Step-by-step explanation:
A ratio of 5:3 can also be written in fraction form as [tex]\dfrac{5}{3}[/tex] (which is in simplified format from [tex]\dfrac{5x}{3x}[/tex]).
Adding 5000 to 5x results in 5x + 5000
Subtracting 3000 from 3x results in 3x - 3000
--> [tex]\dfrac{5x+5000}{3x-3000}[/tex]
The new ratio of 5:2 can be written in simplified fraction form of [tex]\dfrac{5}{2}[/tex].
Set the fractions equal to each. Then cross multiply and solve for x.
[tex]\dfrac{5x+5000}{3x-3000}=\dfrac{5}{2}[/tex]
5(3x - 3000) = 2(5x + 5000) Cross multiplied
15x - 15000 = 10x + 10000 Distributed
5x - 15000 = 10000 Subtracted 0x from both sides
5x = 25000 Added 15000 to both sides
x = 5000 Divided 5 from both sides
The original ratio of 5 : 3 --> 5x:3x
where 5x is the income and 3x is the expenditures results in:
income = 5x expenditures = 3x
= 5(5000) = 3(5000)
= 25000 = 15000
Steven has £1100.
He pays £530 for a new TV.
His mortgage payment is £480.
How much money does he have left after paying for the TV and
paying his mortgage?
Answer:
£90
Step-by-step explanation:
Total money=£1100
Cost of new tv=£530
Mortage payment=£480
Therefore total money left =1100-(530+480)
=1100-1010=£90
estimate 1/4 times 21
Answer:
63/4 or 15.75 or 153/4.
You and your friend each purchase an equal number n of magazines. Your magazines cost $1.50 each and your friend's magazines cost $2 each. The total cost for you and your friend is $10.50. Write and solve an equation to find the number of magazines you purchased.
Given:
You and your friend each purchase an equal number n of magazines.
Your magazines cost = $1.50 each
Your friend's magazines cost = $2 each
Total cost = $10.50
To find:
The equation to find number of magazines you purchased.
Solution:
Your magazines cost = $1.50 each
Your friend's magazines cost = $2 each
Number of magazines purchased by you and your friend = n
Total cost = [tex]1.50n+2n[/tex]
It is given that total cost is $10.50.
[tex]1.50n+2n=10.50[/tex]
[tex]3.50n=10.50[/tex]
Divide both sides by 3.50.
[tex]n=\dfrac{10.50}{3.50}[/tex]
[tex]n=3[/tex]
Therefore, required equation is [tex]1.50n+2n=10.50[/tex] and the number of magazines purchased by you is 3.
Gabby says that 8 is a common multiple of 16 and 24. Mark says that 8 is a common factor of 16 and 24. Who is correct?
Answer:
gabby is correct
Step-by-step explanation:
What is the rate of change of this table?
Answer:
- 6
Step-by-step explanation:
The rate of change of the values is the slope m
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 32) and (x₂, y₂ ) = (0, 20) ← 2 ordered pairs from the table
m = [tex]\frac{20-32}{0+2}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6 ← rate of change
please help !!!!! PLEASE !!!
Answer:
answer would be 120 degrees.
Step-by-step explanation:
because 4y+4+60=180
angle Q =4y+4
so 180-60=120
( -6)^0 solve this problem
Answer:
1
Step-by-step explanation:
Answer:
Anything raise to 0 is 1
so (-6)^0=1
Simplify the expression (6^4)^2.What is the simplified form of this expression?
Answer:
6^8Step-by-step explanation:
Use of formula (a^b)^c = a^(bc)Simplify
(6^4)^2 = 6^(4*2) = 6^8Answer:
brainliest plsssssss
Step-by-step explanation:
(6^4)^2
=(6^4)^2
=(6^4) x (6^4)
=(6 x 6 x 6 x 6) x (6 x 6 x 6 x 6)
=6 x 6 x 6 x 6 x 6 x 6 x 6 x 6
=68
=1679616
Help pls
-28 = 5y - 8
Answer:
y=-4
Step-by-step explanation:
Hope this helps :)
Answer:
y = -4
Step-by-step explanation:
Assuming we are solving for y, start by isolating the variable:
-28 = 5y - 8
-20 = 5y (Added 8 on both sides.)
-4 = y (Divided 5 on both sides.)
Antoine made $33,284 last year. He received a 4.5% annual raise.What will his new salary before the coming year
Answer:
$34781
Step-by-step explanation:
i need help with this geometry
What is the slope of the line that passes through points (-6,-7) and (-24,-7) . Write your answer in the simplest form
Answer:
The slope of the line passing through both points is 0
Step-by-step explanation:
Mathematically, we can calculate the slope as follows;
m = (y2-y1)/(x2-x1)
where (x1,y1) = (-6,-7)
(x2,y2) = (-24,-7)
Thus m = (-7 -(-7))/(-24 + 6) = 0/18 = 0
The slope of both is 0
What is the slope of the line that passes through the points (-4,-2) and (-4,-22)
Answer:
It's a line parallel to the y-axis
Step-by-step explanation:
Note that the similar x value in both coordinates.
Then it's a line drawn parallel to the y-axis
Therefore, the slope is infinite as it makes a right angle with the x-axis.
How to build up am international business empire by yourself?
Answer:
Honestly first get rid of all the negative people around you there will always be that person or persons who don't belive in you. But trust me if you belive in yourself give it your 100% and don't stop grinding. ask people for promotions and don't br afraid to experiment try not to stay on the same idea try, trying something new.
Solve for x and y please
Answer:
y=41 73=x
Step-by-step explanation:
180=x+9+98
minus 98 from both sides
82=x+9
minus 9 from both sides
73=x
2y=x+9 because they are corresponding angles
2y=73+9
2y=82
divide by 2 on both sides
y=41
Solve the equation for a
5n + 34 = -2(1 - 7n)
a equals
Answer:
n = 4
Step-by-step explanation:
Where's a or did you mean n?
Answer:
n=4
Step-by-step explanation:
5n+34=-2(1-7n)
1. So first expand.
5n+34=−2+14n
2 Regroup terms.
5n+34=14n−2
3 Subtract 5n from both sides.
34=14n−2−5n
4 Simplify 14n-2-5n to 9n-2.
34=9n−2
5 Add 22 to both sides.
34+2=9n
6 Simplify 34+2 to 36.
36=9n
7 Divide both sides by 9.
36/9=9
8 Simplify 36/9 to 4
4=n
9 Switch sides.
n=4
5. What is the total cost of 4.3 pounds of flour at $1.10 per pound and 0.5 pounds of baking soda at $0.82 per pound?
Answer:
$4.73 for the flour and $0.41 for the baking soda $5.14 together
Step-by-step explanation:
Answer: .....
Step-by-step explanation:
Please help, will give brainiest to whomever gets this right.
Answer: everything except option 2 I think
Step-by-step explanation:
Rational numbers are numbers that can be written as quotients
What conclusion can be made?
Answer: B) The value of k must be between 1 and 2
The function f(x) has a restricted domain [1, 2] which means [tex]1 \le x \le 2[/tex]
So we can only pick inputs in that interval. If x = k, then [tex]1 \le k \le 2[/tex]
A store sells a 33-pound bag of oranges for \$ 3.60$3.60 and a 55-pound bag of oranges for \$ 5.25$5.25. What is the difference between the price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges?
Answer:
0.01364
Step-by-step explanation:
It is given that,
A store sells a 33-pound bag of oranges for $3.60 and a 55-pound bag of oranges for $5.25.
Price per pound of 33 pound bag is 3.60/33 = 0.10909 price per pound
Price per pound of 55 pound bag of oranges is 5.25/55 = 0.09545 price per pound
Difference between price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges is :
D = 0.10909 - 0.09545
D = 0.01364
Therefore, this is the required solution.
Mr. Jones teaches 154 students in 7 classes. How many
students does he have per class? (per single class – unit
rate)
Please help mee
Which set of graphs can be used to find the solution set to 3 log2(x + 4) < 6?
It's D
Answer:
Graph D
Step-by-step explanation:
EDG 2021
Use the distributive property to write an equivalent expression -3(-5x+7)
Answer:
15x - 21
Step-by-step explanation:
-3(-5x+7)
you sidtribute the 3 to both numbers by multiplying both the -5 and the 7 by -3
-3 x -5x = 15x (remember, a negative times a negative equals a positive)
-3 x 7 = -21 (A negative times a positive equals a negative)
15x - 21
A teacher has gallon of water. He pours the water into 5 glasses for children. Each child receives the same amount of water. There is no water left over. How much water, in gallons, does each child receive?
Answer:
ok ok i dont get it
the teacher has 1 gallon of water
the kids get the same amount from that one gallon
now how many GALLONS do EACH child recieve?
thats messed up
find the mistakes
What is the value of the 9 in 194.6
Answer:
90
Step-by-step explanation:
1 is in the hundreds place
9 is in the tens place
4 is in the ones place
6 is in the tenths
The hu family goes out for lunch, and the price of the meal is $57. The sales tax on the meal is 7%, and the family also leaves a 15% tip on the pre-tax amount. What is the total cost of the meal?
The total cost of the meal is $
Answer:
$69.54
Step-by-step explanation:
57 * .07 = 3.99
57* .15 =8.55
8.55+3.99+57 =69.54
PLS HURRY!!!!!!!!
The members of set A are the integer solutions of the inequality 2x−5≤11 and the members of set B are the integer solutions of the inequality −2x+7≤−9. What is one member of the intersection of A and B?
HOPE IT HELPS YOU!!!
