The correct roots of the equation are (a) 9 and 1
From the complete question, their mistakes are:
Anu
Roots: 8 and 2Wrong constant termAji
Roots: -9 and -1Wrong coefficientA quadratic equation is represented as:
[tex]ax^2 + bx + c = 0[/tex]
Where:
[tex]\alpha\beta = \frac ca[/tex] --- product of roots
[tex]\alpha + \beta = -\frac ba[/tex] --- sum of roots
Anu made a mistake in the constant term, so we consider the sum of roots
[tex]Sum = 8 + 2[/tex]
[tex]Sum = 10[/tex]
Aji made a mistake in the coefficient, so we consider the product of roots
[tex]Product = -9 \times -1[/tex]
[tex]Product = 9[/tex]
The possible equations from the above sum and products are:
[tex]x^2 + 10x + 9 =0[/tex].[tex]x^2 - 10x + 9 =0[/tex].[tex]x^2 + 10x - 9 =0[/tex].[tex]x^2 - 10x - 9 =0[/tex]Of all the above equations, the most likely equation is [tex]x^2 - 10x + 9 =0[/tex], and it has a root of 9 and 1
Hence, the correct roots are (a) 9 and 1
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John solves the equation 5(x-3)+4=18. which 2 choices could be his next step in solving the equation?
5x-15+4=18
5(x-3)=22
5(x-3)=14
5x-13+4=18
Answer:
5x-15+4=18
technically there's only one answer because you do parentheses first but if you did do parentheses first then the other answer could be
5(x-3)=14
In the figure given below CP=x+3, PA=3x+19, CQ=x and QB=3x+4 then, what value of x will make PQ || AB?
Topic:CBSE board Class 10
Correct answer will be mark as brainliest.
Given that
PQ || AB
CP = x+3
PA = 3x+19
DC = x+3
CA = x
QB = 3x+4
We know that
By Basic Proportionality Theorem,
CP / PA = CQ / QB
On substituting these values in the above formula
⇛ (3x+19) / (x+3) = (3x+4) / x
On applying cross multiplication then
⇛ x(3x+19) = (3x+4)(x+3)
⇛ 3x²+19x = 3x(x+3)+4(x+3)
⇛ 3x²+19x = 3x²+9x+4x+12
⇛ 3x²+19x = 3x²+13x+12
⇛ 3x²+19x-3x²-13x = 12
⇛ (3x²-3x²)+(19x-13x) = 12
⇛ 0+6x = 12
⇛ 6x = 12
⇛ x = 12/6
⇛ x = 2
∴ , x = 2
Answer: The value of x for the given problem is 2
Additional comment:
Basic Proportionality Theorem
" A line drawn parallel to the one side of a triangle intersecting other two sides at two different points, then the line divides the other two sides in the same ratio".
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Solve each system of linear equations by elimination.
X-6y=7
-x+6y= -7 -
Answer:
Infinitely many solutions.
Step-by-step explanation:
x-6y=7
-x+6y=-7
--------------
0=0
infinitely many solutions.
Use a Quadratic formula to solve for X
3x^2+9x=-4
Round to the nearest hundreth.
Which function is represented by the graph?
O f(x) = (x – 11 + 3
O f(x) = 5x + 11 – 3
O f(x) = |x – 11 – 3
Of(x) = x + 1] + 3
Answer:
b
Step-by-step explanation:i took the quiz
The ratio of cats to dogs seen at CyFair Animal Hospital is 2 to 5. If Dr. Blue, Dr. Ross, and Dr. Lavigne see 40 dogs altogether, how many cats AND dogs did they see in all? Explain your answer.
Please
The number of cats and dogs the doctor saw is 56.
Ratio expresses the relationship between two values. It shows the frequency that one value is contained another value. The sign of ratio is :.
The equation that can be used to determine the total number of dogs that the doctor saw is:
(ratio of dog / total number of dogs and cats) x total number of animals = number of dogs
5/7 x a = 40
Where a is the total number of dogs and cats
In order to determine the value of a, divide both sides of the equation by 7/5.
40 x 7/5 = 56
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Solve this system of equations using the Substitution method. Don't forget to write your final answer as a coordinate point.
3x + y = -2
y = 2x + 3
Answer:
(x, y) = (-1, 1)
Step-by-step explanation:
help me plsssssssssssssssssssssssss
when -3 - 2m < 0 => -2m < 3 => m > -3/2
ANSWER: C
Ok done. Thank to me :>
C.
Find the 4th term in the expansion of (y + 2)
8,17,26 find the 31st term
Answer:
T31= 278
Step-by-step explanation:
formula is Tn=a +(n-1)d
T31= 8+(31-1)9
T31=8+(30)9
T31=8+270
T31=278
Solve V = twh for w.
Answer:
w = V/lhStep-by-step explanation:
Given equation:
V = lwhSolve for w:
V/lh = lwh/lh Divide both sides by the lh to isolate the wV/lh = w Cancel same variablesw = V/lh Swap left and right sidesAnswer:
V/lh
Step-by-step explanation:
Given,
V = lwh
Here we know
V = volume
l = length
w = width
h = height
Now,
On solving for w
V = lwh
V = l × w × h
V/l = w × h
V/l × h = w
V/lh = w
Find the solution(s) for x in the equation below.
x2 – 25 = 0
Answer:
x=5,-5
Step-by-step explanation:
Robert and Tony love to read. Robert reads 30 pages the first day and 20 pages each day after that. Tony reads 40 pages the first day and 15 pages each day after that. Will the boys ever read the same amount of pages? If so, how many days will it take them to read the same number of pages? A. Yes. They will read the same amount of pages in 3 days. B. Yes. They will read the same amount of pages in 5 days. C. Yes. They will read the same amount of pages in 6 days. D. No. They will never read the same amount of pages.
Answer:
Yes they will read the same amount of pages in 3 days
Step-by-step explanation:
Because when you do the math they add up to the same amount of pages.
The correct statement is;
''Yes. They will read the same amount of pages in 2 days.''
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Robert reads 30 pages the first day and 20 pages each day after that.
And, Tony reads 40 pages the first day and 15 pages each day after that.
Now,
Let the number of days for same pages read = x
So, We can formulate;
For Robert;
Number of pages = 30 + 20x
For Tony;
Number of pages = 40 + 15x
For equal days, we get;
⇒ 30 + 20x = 40 + 15x
Solve for x as;
⇒ 20x - 15x = 40 - 30
⇒ 5x = 10
⇒ x = 2
Thus, The correct statement is;
''Yes. They will read the same amount of pages in 2 days.''
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Marvin has read 8% of the novel he started reading last Saturday. Which decimal is equivalent to the percentage of the novel Marvin has read?
Answer:
0.8 or 0.08 i believe
Step-by-step explanation:
hope this helps!
3. Luigi lives 10 miles from work and rides his fancy Segway there each day. He rides past one
block every 45 seconds. Each block is 360 feet long. What is the rate, in feet per second at
which Luigi rides his Segway?
А
36 feet per second
B
80 feet per second
с
4.5 feet per second
D
8 feet per second
Harry spends $7.83 on 3 bags of walnuts. The bags all cost the same amount. What is the cost of each bag?
Answer:
i think the cost of each bag is $2.61
Step-by-step explanation:
suppose the cost of each bag is $x
7.83 = 3x
7.83/3 = x
2.61 = x
so the cost of each bag is $2.61
Rich borrowed $5000 at a 7% interest rate for 6 years. What was the total interest? Enter your answer in the box. Hint: Use the formula I= P*R*T where I= Interest Earned/Owed P= Principal R= Rate T= Time
Answer:
$700.000 is the interest
Step-by-step explanation:
hope the answer helps
Simple interest is the interest calculated on the principal at a given rate for a time period.
The simple interest is given as,
SI = (Px R x T) / 100
The total interest is $2100.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
The simple interest is given as,
SI = (Px R x T) / 100
We have,
P = $5000
R = 7%
T = 6 years
SI = P x R x T / 100
SI = 5000 x 7 x 6 / 100
SI = 50 x 7 x 6
SI = 50 x 42
SI = $2100
Thus,
The total interest is $2100.
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Please help. Picture uploaded below.
Answer: The answer is the number of each type of topping ordered.
I need helppp pleaseee
Answer:
One solution
Step-by-step explanation:
Start by simplifying the equation.
Distribute 3 to 4 and 2 to get 12x + 6Combine 8x and -2x to get 6xThen you have 12x + 6 = 6x + 24,
Continue to solve
Subtract 6 from the left and right to get 12x = 6x + 18Subtract 6x from both sides to get 6x = 18Divide both sides by 6 to get x = 18Because x is equal to one digit and not x = x or 3 = 5, you have one solution
(Infinite) or (none)
Hope this helps!
when x varies directly as 2y and x=6 when y=20 find y when x=9
Answer:
x=k×2y
substitute x for 6 and y for 20
6=2(20)×k
6=40k
Divide both sides by the coefficient of k
6/40=40k/40
3/20=k
To find y, when x=9
9=3/20×2y
9=6y/20
cross multiply
9×20=6y×1
180=6y
Divide both sides by the coefficient
y=30
24 kg of tomatoes cost $216 how much would one kg cost
Answer:
$9
Step-by-step explanation:
Cost of 24 kg of tomatoes = $216
Cost of 1 kg of tomatoes = 216/24
= $9
Hope it helped you!
Can a right angle be formed by acute angles?
Answer:
Yes, 2 or more acute angles can be in a right angle based on the degree.
Step-by-step explanation:
A right angle is 90 degrees so any acute angle would be less than 90 degrees which means that there can be multiple acute angles based on the degrees. There can be 2 or more acute angles based on degrees that lead up to 90 degrees in total.
30. Ben purchases a fish tank that is shaped like a
cube and will hold 216 cubic inches of water. What
are the dimensions (length, width, and height) of the
fish tank?
Answer:
the answer should have equal sides
Step-by-step explanation:
the answer 36 for the length, width, and height because if a cube has 6 sides each sould have the same amount of cubic inches.
Hedi Earns 3% commission on the jewelry she sells each week last week she sold $730 worth of jewelry how much commission did she make
730*0.03=21.9
She makes $21.90
A worker at a clothing store earns a 20% commission on a sale of $85.00. How much is the commission
Answer:
16$
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the graph of gx)?
A. g(x) = (x+4)2
B. g(x) = x2 - 4
C. g(x) = x2 + 4
D. g(x) = (x - 4)
NO LINKS YOU BOTS
Answer:
the answer should be A Hope this helps!
Question 2 of 5
-64
O A. - 16
O B. -4
O C. 4 or -4
OD. -8
Answer:
B.-4
Step-by-step explanation:
Hope it help!!!!!!
In the diagram below B is the midpoint of AC if AB equals 2X and BC equals X squared -24 find the value of X and the length of AC
Answer:
x = 6
AC = 24
Step-by-step explanation:
The midpoint divides the segment into two congruent parts.
AB = BC
BC -AB = 0
x^2 -24 -2x = 0
(x -1)^2 = 25 . . . . . . add 25, write as a square
x = 1 +√25 = 6 . . . . only the positive solution is of interest.
AC = 2(AB) = 2(2x) = 4(6) = 24
The value of X is 6, and the length of AC is 24 units.
If B is the midpoint
AB=BCx²-24=2xx²-2x-24=0x²-6x+4x-24=0(x-6)(x+4)=0x=6,-4Distance is positive
x=6AC
2(2x)4x4(6)24How many complex roots does the polynomial equation below have? x7 - 3x5 + 4x2 - 1 = 0
Answer:
4 complex rootsStep-by-step explanation:
The easiest way is to use a graphing tool and solve it graphically.
We did it with Desmos and it shows 3 real roots, see below.
The polynomial is of degree 7, hence it should have 7 roots.
Since there are 3 real roots, the remaining ones are complex, so there are 4 complex roots
Answer:
4 complex roots
Step-by-step explanation:
y-2=-7/5(x--2). Please include explanation when giving your answer. I'm really struggling with this. 20 points for whoever can answer this.
Answer:
[tex]x=\frac{10y-27}{5\left(-2+y\right)};\quad \:y\ne \:2[/tex]
Step-by-step explanation:
First, you have to simplify [tex]\frac{-7}{5(x-2)}[/tex] to become [tex]-\frac{-7}{5(x-2)}[/tex]
Next, you multiply both sides by [tex]5(x-2)[/tex] to make [tex]y\cdot \:5\left(x-2\right)-2\cdot \:5\left(x-2\right)=-\frac{7}{5\left(x-2\right)}\cdot \:5\left(x-2\right)[/tex]
After that, you need to simplify again to become [tex]y\cdot \:5\left(x-2\right)-10\left(x-2\right)=-7[/tex]
Now, expand [tex]5(x-2)-10(x-2)[/tex] to become [tex]5xy-10y-10x+20=-7[/tex]
Then, add 10y to both sides [tex]5xy-10y-10x+20+10y=-7+10y[/tex]
Next, you simplify to create [tex]5xy-10x+20=-7+10y[/tex]
After that, subtract 20 from both sides to make [tex]5xy-10x+20-20=-7+10y-20[/tex]
Now, simplify again to get [tex]5xy-10x=10y-27[/tex]
Next, factor [tex]5xy-10x[/tex] to get [tex]5x(y-2)[/tex]
Finally, divide both sides by [tex]5(y-2)[/tex] to get [tex]\frac{5x\left(y-2\right)}{5\left(y-2\right)}=\frac{10y}{5\left(y-2\right)}-\frac{27}{5\left(y-2\right)};\quad \:y\ne \:2[/tex]
If you did it right your final answer should be [tex]x=\frac{10y-27}{5\left(-2+y\right)};\quad \:y\ne \:2[/tex]
Hope this helps explain it!