Describe and correct the error a student made in factoring 2x^2 + 1 1 x + 15.
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Answers
The student forgot to divide the factors, 5 and 6, by the "a" value. In this case, that is 2. Then, simplify the fractions. Once we have these values, the numerator is the constant value and the denominator is the coefficient.
5/2 = 5/2 ➜ (2x + 5)
6/2 = 3 ➜ (x + 3)
This student should have factored the expression as;
(2x + 5)(x + 3)
Answer:
(2x + 5)(x+3) = 0
Step-by-step explanation:
ac = 5 * 6 = 30
b = 5 + 6 = 11
Factorizing 2x² + 11x + 15,
2x² + 6x + 5x + 15 = 0
2x(x + 3) + 5(x+3) = 0
(2x + 5)(x+3) = 0
∴ x = [tex]\frac{-5}{2}[/tex], -3
(There was a mistake probably because the quadratic equation was considered with 1 as the coefficient as x², so the factorized equation was for x² + 11x + 30. You must take the coefficient of x² as 2 instead, according to the given equation.)
Related Questions
Identify the factor pairs of ac you could use to rewrite b to factor each trinomial by grouping. (27, 29, 31)
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Answers
Answer:
Step-by-step explanation:
(27) [tex]7x^2[/tex] + 9x + 2
= [tex]7x^2[/tex] + 7x + 2x + 2
= 7x(x+1) + 2(x+1)
= (7x+2)(x+1)
(29) [tex]8x^2[/tex] - 2x - 1
= [tex]8x^2[/tex] - 4x +2x - 1
= 4x(2x-1) +1(2x-1)
= (4x+1)(2x-1)
(31) [tex]15x^2[/tex] - 16x - 7
= [tex]15x^2[/tex] + 5x - 21x - 7
= 5x(3x + 1) - 7(3x+1)
= (5x-7)(3x+1)
What is the value of n in the equation n + 7.6 = 13.82?
Group of answer choices
n = 14.58
n = 6.22
n = 21.42
n = 13.08
Thanks!
Answers
Explanation: N is the number that you are trying to find and if N + 7.6 is equal to 13.82, an easy way to find N is by subtracting 7.6 from 13.82 (13.82-7.82=6.22)
The correct answer will get brainliest!
Find the 3 smallest positive x-intercepts of the graph of
y = cos(12x) + cos(16x) and list them in increasing order.
Please give your answers as a list of x-coordinates from least to greatest.
Answers
Recall that [tex]\cos(x)+\cos(y)=2\cos \left(\frac{x+y}{2} \right)\cos \left(\frac{x-y}{2} \right)[/tex].
[tex]\cos(12x)+\cos(16x)=0 \\ \\ 2\cos(2x)\cos(14x)=0 \\ \\ \cos(2x)\cos(14x)=0[/tex]
If [tex]\cos(2x)=0[/tex], then [tex]x=\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \cdots[/tex].
If [tex]\cos(14x)=0[/tex], then [tex]x=\frac{\pi}{28}, \frac{3\pi}{28}, \frac{5\pi}{28}, \cdots[/tex].
So, the three smallest positive [tex]x[/tex] intercepts are [tex]\frac{\pi}{28}, \frac{3\pi}{28}, \frac{5\pi}{28}[/tex].
Evaulate each expression when n = 2.3
N + 8n2 - 17=
Answers
Answer: 27.62
Step-by-step explanation:
plug in 2.3 wherever 'n' is
I'm assuming that the '2' in 8n2 is an exponent
2.3 + 8(2.3)² - 17 =
Using PEMDAS
start out with exponent since there isn't any parenthesis
(2.3)² = 5.29
2.3 + 8(5.29) - 17
move on to multiplication
8(5.29) = 42.32
2.3 + 42.32 - 17
with addition and subtraction, you do whichever comes first and since this equation starts with addition we'll start there
2.3 + 42.32 = 44.62
then the subtraction
44.62 - 17 = 27.62
Answer:
Step-by-step explanation:
The answer is 27.62
help me please!!!
i need an higher grade!
Answers
Answer:
A. Slope= -3
B. Slope= -4/3
C. Slope= 11/2
D. Slope= undefined
Step-by-step explanation:
The way I solved it was by graphing the points and then counting the rise/run.
HELP LIKE ASAP!!!!!!!!!!!!!!!!
Answers
Answer: A C and D
Step-by-step explanation:
What I did was look at point A, we see it starts at (-8, 6) this means that if it were to be shifted right 9 and down 4 we would get (1, 2). so, all the answers claiming that the points were shifted right 9 and down 4, or x+9 y-4 are correct.
your answer would be the first option the 3rd and the last option
Make x the subject of the formula
y = a√x
Answers
Answer:
17
Step-by-step explanation:
Explanation: I just know
Use factoring to arrange the following algebra tiles first into one rectangle and then into two rectangles of equal size.
(image)
Answers
Answer:
hmm
Step-by-step explanation:
Please help me I'm desperate
Answers
Answer:400
Step-by-step explanation:The formula for volume is L×W×H so, you have to multiply 20×10×2. 20×10 is 200 and 200×2 is 400
Help please im soo close to finishing !!!11!
Answers
Answer:
138.2
Step-by-step explanation:
find area of small circle and subtract from area of big circle
A=pi*r^2
A=pi*12^2
A=144pi
A=pi*r^2
A=pi*10^2
A=100pi
144pi-100pi=44pi
44pi=138.2
Answer:
Step-by-step explanation:
Area of shaded region = A of outer circle - A of inner circle
r of outer circle = 12 cm
r of inner circle = 10 cm
Now,
As we know, area of circle = [tex]\pi r^2[/tex]
=> [tex](\frac{22}{7} * 12^2) - (\frac{22}{7} * 10^2)[/tex]
= 452.57 - 314.28
= 138.29 cm sq
Round off to nearest tenth = 140 cm sq
Hope this helped. Pls mark it the BRAINLIEST!
Order the fractions from least to greatest.
five twelfths, one fourth, two thirds
five twelfths, one fourth, two thirds
five twelfths, two thirds, one fourth
one fourth, two thirds, five twelfths
one fourth, five twelfths, two thirds
Answers
Good luck hope this helps
:)))
What is the solution to the equation?
9/10 x+4/5=28.3
choices:
x=133/5
x=275/9
x=97/3
Answers
Answer:
x = 275/9
Step-by-step explanation:
AGAIN PLEASEEEEE HELP AND QUICK!! SEVENTH GRADE MATH !!
Answers
Answer:
A numerical expression contains numbers and operations. An algebraic expression is almost exactly the same except it also contains variables
Answer:
Step-by-step explanation:
Both are similar as they result of both is same. The only difference is their methods of solving them. In numeric expressions, it takes long calculation while in algebraic expressions, we break the expression and then solve it to obtain the result in simpler form.
Hope it helps. Mark my answer the BRAINLIEST!
The correct answer gets brainliest
Let theta be an angle such that cos(theta)=-1/9 and 0<=theta<=2pi
Assume that cos(theta/2)<0. Then if
Terminal point of theta/2 = (a_1, a_2),
enter a_1 and a_2 in that order.
Answers
Using the cosine half angle formula,
[tex]\cos \frac{\theta}{2}=-\sqrt{\frac{1-\frac{1}{9}}{2}}=-\frac{2}{3}[/tex]
Using the sine half angle formula,
[tex]\sin \frac{\theta}{2}=\sqrt{\frac{1+\frac{1}{9}}{2}}=\frac{\sqrt{5}}{3}[/tex]
So, [tex]a_1=-\frac{2}{3}[/tex] and [tex]a_2=\frac{\sqrt{5}}{3}[/tex].
The unit circle is a circle with a radius of 1 that is centeed at the origin (0,0) in the coordinate plane. For any angle theta in the interval [0, 2pi), the terminal point of theta in the unit circle can be found using the coordinates (cos(theta), sin(theta)).
Since cos(theta/2)<0, the terminal point of theta/2 lies in either the 2nd or the 3rd quadrant of the coordinate plane. In the unit circle, the 2nd and 3rd quadrants are defined by the points with negative y-coordinates, so for the terminal point of theta/2, we have:
a_1 = cos(theta/2)
a_2 = sin(theta/2)
Both a_1 and a_2 are negative because the terminal point of theta/2 lies in the 2nd or 3rd quadrant.
What are all possible values of b for which 7x^2 + bx+ 3 is factorable, if the factors have integer coefficients and constants?
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Answers
Answer: 10
Step-by-step explanation:
b can be 10 as,
7*3 = 21
7+3 = 10
∵ [tex]7x^2[/tex] + 10x + 3
Can you solve this for me? Thanks! :>
Answers
Answer:
5.047, 5.105, 5.12, 5.132, 5.406
Step-by-step explanation:
enter Durham right after Raleigh
a - 8 = 42
1/3 - 8 = 42
3 - 8 = 42
\Order a, b, and from least to greatest.
Answers
Answer:
Step-by-step explanation:
a is 50-8 =42
1/3 -17 +59=42
3-8=5-47=42
PLEASE ANSWER ASAP
A study was conducted comparing the speeds of 2 different fish, Fish A and Fish B. The table shows the distance, in meters, Fish A travels in seconds. Scientists
concluded that Fish B travels 3 meters every 2 seconds.
Assuming both fish swim at a constant rate, which fish swims faster and by how many meters per second?
Answers
Answer:
Fish A travels faster and by 0.1 meters per second.
Step-by-step explanation:
According to the table, you can see that the seconds are not being measured constantly. To determine the rate of change of meters per second, we can use subtraction on both the numerator and denominator of the expression. Where we divide it into 1 second.
meters/second → 4.8 – 1.6 / 3 – 1 = 3.2 / 2 =
1.6 meters/second.
Now we can compare the rate from fish B by also diving it into 1 second.
3 meters every 2 seconds → 3/2 =
1.5 meters/second.
Since 1.6 > 1.5, Fish A is faster!
And to compare the simplified rates
1.6 – 1.5 = 0.1 meters.
So Fish A is 0.1 meters faster!
which one is correct 0.061 > 0.510 0.501 < 0.510 0.510 > 0.510 0.500 > 0.510
Answers
Answer: 0.501 < 0.510
Step-by-step explanation:
0.510 is larger than 0.501
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Answers
Answer:
12 and 78 are complementary.
80 and 100 are supplementary.
50 and 50 are neither.
Step-by-step explanation:
Hope it helps! =D
Factor the trinomial represented by the algebra tiles.
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Answers
Answer: [tex]2x^2[/tex] + 7x + 5
Step-by-step explanation:
--> No. of blocks of [tex]x^2[/tex] = 2
So, 2 * [tex]x^2[/tex] = [tex]2x^2[/tex]
--> No. of blocks of x = 7
So, 7 * x = 7x
--> No. of blocks of 1 = 5
So, 1 * 5 = 5
∴ Hence, [tex]2x^2[/tex] + 7x + 5 is the answer.
Please mark my answer BRAINLIEST!In front of a school are several gardens in rectangular raised beds. For each of the areas of a rectangular garden given, use factoring to find possible dimensions. Could the garden be square? If so, explain why.
a. x² + 32x + 256
b. x² — 4y²
c. x²- 20x + 100
Answers
Answer:
Step-by-step explanation:
(a) [tex]x^2[/tex] + 32x + 256
Factorisation by pairing:
([tex]x^2[/tex] + 16x) + (16x + 256)
= x(x+16) + 16(x+16)
= (x+16)(x+16)
∴ Side of the square = (x+16)
(b) [tex]x^2 - 4y^2[/tex]
Identity: [tex]a^2 - b^2[/tex] = (a+b)(a-b)
[tex](x)^2 - (2y)^2\\[/tex]
= (x+2y)(x-2y)
∴ Length of rectangle = (x+2y)
Breadth of rectangle = (x-2y)
(c) [tex]x^2 - 20x + 100[/tex]
[tex]= x^2 - 10x - 10x +100x[/tex]
= x(x-10) -10(x-10)
= (x-10)(x-10)
∴ Side of square = (x-10)
The factorization of the polynomial x²-20x+100 is (x-10)(x-10).
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
a) x²+32x+256
By using splitting middle term method, we get
x²+16x+16x+256
= x(x+16)+16(x+16)
= (x+16)(x+16)
b) x²-4y²
Using the identity a²-b²=(a+b)(a-b)
Now, x²-(2y)²
= (x+2y)(x-2y)
c) x²-20x+100
By using splitting middle term method, we get
x²-10x-10x+100
= x(x-10)-10(x-10)
= (x-10)(x-10)
Therefore, the factorization of the polynomial x²-20x+100 is (x-10)(x-10).
To learn more about the factorization visit:
https://brainly.com/question/26923098.
#SPJ2
Please help me I'm desperate
Answers
Answer:
240
Step-by-step explanation:
I think you just add them all together
Need help again please help
Answers
example: if it says rotate it 90 degrees clockwise, then rotate the paper that way with the (2,-6) mark on there
Answer:
(-2, -6)
Step-by-step explanation:
Please help me I'm desperate
Answers
Now you have 10/42 simplify it and you have 5/22
please help!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1. 16 inches
2. 1256 square feet
help me plsssss!!!!!
Answers
Answer: The correct answer is 34.5
Step-by-step explanation:
1. She did not need to multiply both sides by -7.5
2. A negative * a negative will make a positive number
Hope this helps!
A rectangular patio has an area of 2x² + 13x — 24 ft2. Use factoring to find possible dimensions of the patio. The patio is to be enlarged so that each dimension is 2 ft greater than it was originally. What are the new dimensions of the patio? What is the new area of the patio?
Answers
Answer:
Step-by-step explanation:
[tex]2x^2[/tex] + 13x - 24 to be factorised to find the dimensions:
[tex]2x^2[/tex] + 13x - 24
= [tex]2x^2[/tex] + 16x - 3x - 24
= 2x(x+8) - 3(x+8)
= (2x-3)(x+8)
Length = (2x-3)
Breadth = (x+8)
∴ Increasement in length = 2x - 3 +2 = (2x -1)
Increasement in breadth = x + 8 + 2 = (x+10)
Please mark my answer BRAINLIEST!!Please help me I'm desperate
Answers
Answer:
42% (Sorry if I'm wrong!)
Answer:
40.7%
Step-by-step explanation:
the question was tricky but I am glad I was able to help
What is the product of a number and 15 plus 12, written as an algebraic expression?
Answers
Answer:
15x + 12
Step-by-step explanation:
Answer: hope this helps ♡
15x+12
