Answers
Answer:
(a) (a² +3a -1)(a² -3a -1)
Step-by-step explanation:
The constant term of the product of the factors will be equal to the product of their constants. Since you want that product to be +1, the signs of the factor constants must be the same. That eliminates choices (c) and (d).
__
To tell which of choices (a) and (b) is correct, we can compute the squared term in their product. Let's do it in a generic way, with the constant (±1) being represented by "c".
We want the a² term in the product ...
(a² +3a +c)(a² -3a +c)
That term will be the result of multiplying both sets of first and last terms, and adding the product of the middle terms:
(a²·c) +(a²·c) -9a² = a²(2c-9)
So, we want the factor (2c-9) to be -11, which means c=-1, not +1.
The correct factorization of the given expression is ...
(a² +3a -1)(a² -3a -1) . . . . matches choice A
Related Questions
1. If x + 13 = 5, then the value of x is
(a) 18
(b)-18
(c)-8
(d) 8
Answers
Answer:
C
Step-by-step explanation:
The best way to find x is to plug in all the answer choices and see if they equal 5
lets start with A
18+13=5
31=5 which is incorrect
Let do B
-18+13=5
-5=5 which is incorrect
Lets do C
-8+13=5
5=5 which is correct!
Lets do D
8+13=5
21=5 which is incorrect
pls mark me brainliest
Answer:
The answer is (C) -8
Step-by-step explanation
x = -8
-8 + 13 = 5
It is basically like subtraction..
You subtract the 13 from the 8 even though its backwards.
-8 + 13 = 5
Write the explicit formula for the sequence. Then find the fifth term in the sequence.
a1= 3, r=-3
Answers
Answer:
a) Explicit Formula : aₙ = 3. (-3)ⁿ⁻¹
b) Fifth term : a₅ = 243
Step-by-step explanation:
This sequence above is the Geometric sequence. The Geometric sequence is calculated using the formula
aₙ= a1.rⁿ⁻¹
where a1 = first term
r = common ratio
n = number of terms
From the above question, we are given
a1= 3, r=-3 and asked to find the explicit formula.
The explicit formula using the geometric sequence formula =
aₙ = 3. (-3)ⁿ⁻¹
b) The fifth term in the sequence is calculated as
aₙ = 3. (-3)ⁿ⁻¹
Where n = 5
a₅ = 3.(-3)⁵⁻¹
a₅ = 3.(-3)⁴
a₅= 243
You are studying for your final exam of the semester. Up to this point, you received 3 exam scores of 81%, 62%, and 94%. To receive a grade of B in the class, you must have an average exam score between 80% and 89% for all 4 exams including the final. Find the widest range of scores that you can get on the final exam to receive a grade of B in the class. [80,81] [76,100] [83,100]
Answers
To get an average score of 89% (out of four exams), a total of 4*89%=356% is needed, so the maximum required for the 4th test is 356-(75+97+60)=124, which is impossible.
So the next exam grade must range between 88 and 100 to get a grade b in the class.
state of the triangles in each pair are similar. If so State how you know they are similar and complete the similarity statement. Part 2
Answers
Answer:
not similar
Step-by-step explanation:
SAS similarity could be used if corresponding sides were proportional. They're not.
36/26 ≠ 16/12
The triangles are not similar.
Tanmay had some chocolates with him. He gave one-third of them to Akash and one-fifth of them to Sharad. Tanmay could do so without breaking any chocolate. Which of these could be the number of chocolates Tanmay had in the beginning?
Answers
Answer:
The possible value of X are;
15, 30, 45, 60 etc
Step-by-step explanation:
The parameters given are
Number of chocolates Tanmay had = X
Number of chocolates Tanmay gave to Akash = 1/3 × X
Number of chocolates Tanmay gave to Sharad = 1/5 × X
Whereby 3 and 5 are factors of X, therefore;
3 × 5 = 15 is the lowest single factor of X
The possible values of X starting from the lowest factor are given as follows;
15 × 1 = 15
15 × 2 = 30
15 × 3 = 45
15 × 4 = 60
Hence, the possible value of X are the arithmetic progression a + (n - 1)×d
Where:
a = 15
n = 1, 2, 3, 4, ...
d = 15
Which includes;
15, 30, 45, 60
1
. a) Write in standard form:
i) 2 470 000
Answers
two million four hundred seventy thousand
.the difference of thirteen and six, multiplied by a number
Answers
Step-by-step explanation:
If n represents the number, then you get;
n(13-6) or n(7) or n * 7
what is the simpllified form of the expression x+x+10+2x-16
Answers
Answer:
4x-6
Step-by-step explanation:
x+x+10+2x-16
Combine like terms
x+x+2x +10-16
4x -6
4x-6
Answer:
[tex]4x - 6[/tex]
Step-by-step explanation:
[tex]x + x + 10 + 2x - 16[/tex]
combine like terms
[tex]x + x + 2x + 10 - 16 \\ 2x + 2x - 6 \\ = 4x - 6[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What number should be added to both sides of the equation to complete the square? x2 + 3x = 6 (StartFraction 3 Over 2 EndFraction) squared 3 62
Answers
Answer:
b
Step-by-step explanation:
The number that should be added to the equation is n = ( 3/2 )²
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
To complete the square for the quadratic equation x^2 + 3x = 6, we need to add a constant term to both sides that will make the left-hand side a perfect square trinomial
First, we need to find the coefficient of the x-term, which is 3. Then we take half of this coefficient, which is 3/2, and square it, giving us 9/4.
To complete the square, we add this value to both sides of the equation:
x² + 3x + 9/4 = 6 + 9/4
The left-hand side can now be factored as a perfect square trinomial:
(x + 3/2)² = 33/4
To solve for x, we take the square root of both sides:
x + 3/2 = ±√(33/4)
x = -3/2 ± (1/2)√33
Hence , the number we need to add to both sides of the equation to complete the square is 9/4
To learn more about quadratic equations click :
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can i get help please?? Earth has a diameter of approximately 8,000 miles. If the circumference of a circle can be found using the formula C = πd, what is the circumference of Earth? (Use 3.14 for π) A. 2,512,000 miles B. 25,120 miles C. 1,256,000 miles D. 12,560 miles
Answers
Answer:
B
Step-by-step explanation:
Circumference is 3.14*d
Where d is the diameter.
3.14*8000
= 25120
The Earth has a circumference of 25120 miles approximately.
Answer:
B. 25,120 miles.
Step-by-step explanation:
Circumference = π * diameter
= 3.14 * 8000
= 25,120 miles.
can someone please answer this math question
Answers
Answer:
The answer is in the picture
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2 l plus 2 w equals 16, where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle? 7 in. 8 in. 9 in. 10 in.
Answers
Answer:
7 in.
Step-by-step explanation:
When 7 in. is used this is what happens
2(7) + 2(w) = 16 in.
14 + 2w = 16 in.
Because the 7 in. option leaves room for the value of the width unlike the others.
Answer: 7 inches
Step-by-step explanation:
I took the test on this and scored 100%
a manager bought some stamps she gave 1/3 of them to the cashier and 1/5 of them to her secretary.if the secretary received 40 fewer stamps than the cashier how many did the cashier receive?
Answers
Answer:
The cashier received 100 envelopes
Step-by-step explanation:
let the number of stamps bought be x.
Cashier will receive 1/3 *x = x/3
Secretary will receive = 1/5 * x = x/5
Now we are told that the secretary received 40 fewer.
This means that the difference between the amounts they received is 40
Mathematically;
x/3 - x/5 = 40
2x/15 = 40
x = (15 * 40)/2 = 600/2 = 300
The cashier received x/3 = 300/3 = 100
Answer:
Cashier received 100 stamps
Step-by-step explanation:
1/3 to cashier
1/5 to secretary
Total stamps=x
Cashier=(1/3)x
Secretary=(1/5)x
Secretary received 40 fewer stamps than the cashier
Difference between cashier and secretary share=40
1/3x-1/5x=40
(2/15)x=40
40×15=2x
600=2x
x=300
Cashier=(1/3)x
=(1/3)300
=100
AB←→ is perpendicular to CD←→. How many 90° angles are formed by the intersection?
Answers
Answer: 4
Step-by-step explanation:
Since AB and CD are perpendicular lines, you know that they make 90° angles. Perpendicular lines make a t or + shape. Since it is 2 lines, you know there will be 4, 90° angles, to make up a full 360°.
Solve the literal equation -cy + 8 = 4d – 3y for y.
Answers
Answer:
y=(4d-8)/(3-c)
Step-by-step explanation:
-cy + 8 = 4d – 3y3y-cy=4d-8y(3-c)=4d-8y=(4d-8)/(3-c)The manager of a clothing store in the mall wants to collect data to find out customers' opinions of the brands of clothing sold at the store. Which group should he survey to collect the best data?
A.
twenty customers who asked to share their opinions of the clothing brands with the store manager
B.
twenty-five customers who visited the store but did not purchase any clothes
C.
thirty randomly selected customers who shopped at the clothing store
D.
forty randomly selected people in the mall parking lot
Answers
Answer:
c
Step-by-step explanation:
Its wouldn't be A since there are numbers bigger than 20 B is not correct since it said 25 people that did not buy any clothes so you would not get a good opinion its not D because out of the 40 people some could have not bought anything from the store. Its C because its the biggest number of people that actually shopped and got things from that store
Answer:
Answer:
c. Thirty randomly selected customers who shopped at the clothing store.
Step-by-step explanation:
in scientific notation, how can you tell if it is less than or greater than 1? Explain
Answers
Answer: See below
Step-by-step explanation:
In scientific notation, you can tell that it is greater or less than 1 by looking at the exponent. The scientific notation looks like _.__×10⁻. Note: The little lines are blanks for you to fill in. The dot at the bottom is a decimal.
If the exponent on top of 10 is positive, you are moving the decimal to the right side, making the number greater.
If the exponent on top of 10 is negative, you are moving the decimal to the left side, making it smaller and smaller.
By those statements, you can tell if a number is greater or less than 1 by looking at the exponent.
Write the polynomial in standard form.
- 4 + 3x - 522
Answers
Answer:
3x-526
Step-by-step explanation:
the 3x would go in the beginning. then you subtract (-4-522)= -526.
given that
10 - √18
—————
√2
= a + b √2 where a and b are integers.
Find the values of a and b.
Answers
Answer:
a = -3
b = 5
Step-by-step explanation:
[tex]\frac{10-\sqrt{18}}{\sqrt{2}}[/tex]
Simplify the square root of 18.
[tex]\frac{10-3\sqrt{2}}{\sqrt{2}}[/tex]
Rationalize the fraction.
[tex]\frac{\left(10-3\sqrt{2}\right)\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]
[tex]\frac{2\left(5\sqrt{2}-3\right)}{2}[/tex]
[tex]5\sqrt{2}-3[/tex]
Rewrite the answer in the form a+b√2.
[tex]-3 + 5\sqrt{2}[/tex]
The given form of expression a + b √2 where a and b are integers then the values of a and b are -3 and 5.
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
[tex]\frac{10 -\sqrt18} {\sqrt 2}= a + b \sqrt 2[/tex]
Simplify the square root of 18 then Rationalize the fraction,
[tex]\\\frac{10 -3\sqrt2} {\sqrt 2}\\\\\frac{(10 -3\sqrt2) \times \sqrt{2} } {\sqrt 2 \sqrt 2}\\\\\frac{ 2(5\sqrt2 -3) } { 2}\\\\(5\sqrt2 -3)[/tex]
Thus, the values of a and b are -3 and 5.
Learn more about factors;
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Marilyn is playing a game where she draws a slip of paper with the words "Rock, Paper, Scissors" written on each slip from a hat. She then flips a coin. She predicts "Paper" and calls Tails. She wins if she is correct. What is the probability she will win?
Answers
Answer:
1/6
Step-by-step explanation:
In a game of "Rock, Paper, Scissors", there are three possibilities. The probability that Marilyn will get Paper is given as
1/3
In a coin flip, the probability that it will land on tails is
1/2
Therefore, the probability that she will win if she predicts "Paper" and calls Tails is the product of the individual probabilities:
1/3 * 1/2 = 1/6
Solve and graph. Thank you so much!
Answers
Answer:
Step-by-step explanation:
6 + x/2 >= -4
x/2 >= -10
x >= -20
solution is b
What is an expression equivalent to 2(7 x + 3 - x ) ??
Answers
Answer: Simplify the expression.
12x+6
Step-by-step explanation:
your answer is 12x+6
What’s the error mica make?
Answers
Step-by-step explanation:
She should have added 2 to the 3, not 1 because on the right side, she added 1, but that was being multiplied by 2 so to balance the equation she should add 2 to the 3. Hope this helps!
Factor the given quadratic function x2 + 9x = 36.
Answers
Answer:
(x + 12)(x - 3)
Step-by-step explanation:
[tex] {x}^{2} + 9x = 36 \\ {x}^{2} + 9x - 36 = 0 \\ {x}^{2} + 12x - 3x - 36 = 0 \\ x(x + 12) - 3(x + 12) = 0 \\ (x + 12)(x - 3) = 0[/tex]
Need help what’s the solution for b^2-14b=0
Answers
Answer:
b = 0 b = 14
Step-by-step explanation:
b^2-14b=0
Factor out a b
b(b-14) = 0
Using the zero product property
b =0 b-14=0
b = 0 b = 14
Our math team had m students last year, but this year it has already n students! By what percent did the number of students grow?
Answers
Answer:
(n-m)/m * 100%
Step-by-step explanation:
The original amount is m
The new amount is n
Take the new amount and subtract the original amount
(n-m)
Divide by the original amount
(n-m)/m
Multiply by 100 %
(n-m)/m * 100%
Answer:
(n-m)/m*100
Step-by-step explanation
trust me its the answer i checked with rsm math homework and it was correct
Each person in Plimouth was given a plot of land 16.7 m wide by 40.8 m long. The Alden family had four members. What was the square area of the plot of land they were allotted?
Answers
Answer:
They were allotted 2725.44 meters² of land.
Step-by-step explanation:
Well a member of the Alden family gets 16.7 meters×40.8 meters or 681.36 meters². Now since there are 4 of them, we multiply how much land one Alden family gets by 4 members.
681.36 m²×4 people = 2725.44 meters²
Answer:
2,725.44 square meters
Step-by-step explanation:
We can do all of the necessary math at once:
(16.7 m)(40.8 m)(4 persons) = 2,725.44 square meters
You cast a fishing lure from 4 feet above the water. Its travel is given by the function h = -16t^2 + 24t + 4, where t = time in seconds. After how many seconds will it reach a height of 12 feet?
Answers
Answer:
Fishing lure will be at a height of 12 feet after 0.19 and 1.31 seconds
Step-by-step explanation:
Travel of a fishing lure has been given by the expression,
h = -16t + 24t + 4
where h = height of the fishing lure
t = time or duration of travel
Height traveled by the fishing lure = 12 - 4 = 8 feet
For h = 8 feet,
8 = -16t² + 24t + 4
-16t² + 24t + 4 - 8 = 0
16t² - 24t + 4 = 0
4t² - 6t + 1 = 0
t = [tex]\frac{6\pm\sqrt{(-6)^{2}-4(4)(1)}}{2\times 4}[/tex]
= [tex]\frac{6\pm\sqrt{36-16}}{8}[/tex]
= [tex]\frac{6\pm\sqrt{20}}{8}[/tex]
= [tex]\frac{6\pm2\sqrt{5}}{8}[/tex]
= 1.31, 0.19 seconds
Can someone help me with this please and don’t guess I really need help
Answers
Answer:
it should be (5,4)
Step-by-step explanation:
♊♊♊
Answer:
A would be reflected across to (5,-4), so, the bottom answer.
Step-by-step explanation:
For reflections across an axis, all I really do is count how many units a point is from the axis you are reflecting across, and then count the many on the other side of the axis. On this problem, A was 4 units above the x-axis, and 5 from the y-axis. I just counted 8 units down, or, 4 units down from the x-axis, and since I didn't change where my point was on the y-axis, it landed on the point (5,-4).
1. Write the following in decimal form and say what kind of decimal expansione Suppose we want to
N.
non-terminating non-recurring lyi
many such numbers.
An example of such a number is 0.150150015000150000...
the previous section, yo
I number has a decimal
to represent it on the n
EXERCISE 1.3
1
nber line. We know t
13.
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36
(iii) 4
11
8
So, let us look close
2
3
329
(vi)
mber line between 2 a
13
11
400
enam
s into 10 equal parts
2. You know that = = 0.142857. Can you predict what the decimal expansions of
rision as in Fig. 1.11 (
4 5 6
7'; right of 2 will repres
are, without actually doing the long division? If so, how?
ficulty in observing th
clear view of the san
Hint. Stuurth
It will
2
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Answers
Answer: ...
Step-by-step explanation:
