QUESTION:- SOLVE EQUATION BY FACTORISATION
EQUATION:-
[tex] {x}^{2} + x - 72 = 0[/tex]
ANSWER:-
[tex] {x}^{2} + x - 72 = 0\\{x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x +9) = 0 \\ (x - 8)(x + 9) = 0 \\ [/tex]
NOW FOR VALUE OF X ->
[tex]x - 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 9 = 0\\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 9[/tex]
Is -1 rational or irrational
and is √3 + -1 Rational or irrational
explain if u can pls
Answer:
-1: rational
√3 + -1: irration
Step-by-step explanation:
A rational number is negative, if its numerator and denominator are of the opposite signs.
Hope this helps <3
Write the quadratic function f(x) = x2 - 2x - 8 in factored form.
A) f(x) =(x - 4)(x - 2)
B) f(x) =(x + 4)(x - 2)
C) f(x) =(x - 4)(x + 2)
D) Rx) =(x + 4)(x + 2)
Answer:
Hello,
answer C
Step-by-step explanation:
[tex]f(x)=x^2+2x-8\\\\=x^2-4x+2x-8\\\\=x(x-4)+2(x-4)\\\\=(x-4)(x+2)\\\\Answer\ C[/tex]
given the recursive formula below, what are the first four terms of the sequence
Answer:
c
Step-by-step explanation:
The first four terms are 17, 15, 13, and 11.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(n):
f(1) = 17
f(n) = f(n - 1) - 2 if n > 1
Now,
The first term is 17.
The second term.
f(2) = f(2 - 1) - 2
= f(1) - 2
= 17 - 2
= 15
The third term.
= f(3 - 1) - 2
= f(2) - 2
= 15 - 2
= 13
The fourth term.
f(4) = f(4 - 1) - 2
= f(3) - 2
= 13 - 2
= 11
Thus,
The terms are 17, 15, 13, 11
Learn more about functions here:
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It can be shown that the line with intercepts (a, 0) and (0, b) has the following equation:
x/a + y/b= 1, a ≠ 0, b ≠ 0.
Use this result to write an equation of the line.
Point on line:
(−2, 4)
x-intercept: (a, 0)
y-intercept: (0, a)
(a ≠ 0)
The equation of the straight line is [tex]x+y=2[/tex].
Given:
The line with intercepts (a,0) and (0,b) has the equation [tex]\frac{x}{a} +\frac{y}{b} =1, a\neq 0, b\neq 0[/tex] Point on the line: (-2, 4)x-intercept: (a, 0)y-intercept: (0, a)[tex]a\neq 0[/tex]To find: The equation of this line
It is given that a line with intercepts (a,0) and (0,b) has the equation [tex]\frac{x}{a} +\frac{y}{b} =1, a\neq 0, b\neq 0[/tex]
Now, it is given that the referred line has intercepts (a, 0) and (0, a). Then, using the above statement, the equation of this line can be written as,
[tex]\frac{x}{a} +\frac{y}{a}=1[/tex]. It is already given that [tex]a\neq 0[/tex]. So, we need not mention it again.
It is also given that the point (-2, 4) lies on this line. Then, the coordinates of this point must satisfy the equation of the line.
This implies that,
[tex]\frac{-2}{a} +\frac{4}{a} =1[/tex]
[tex]\frac{2}{a} =1[/tex]
[tex]a=2[/tex]
Now, put [tex]a=2[/tex] in the equation of the line, [tex]\frac{x}{a} +\frac{y}{a}=1[/tex] to get,
[tex]\frac{x}{2} +\frac{y}{2} =1[/tex]
[tex]x+y=2[/tex]
So, the equation of the line is [tex]x+y=2[/tex].
Learn more about equations of straight lines here:
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Complete the function table.
Input (n) Output (n-2)
Answer: Choice C
This is because the input n = 2 leads to the output n-2 = 2-2 = 0
As another example: the input n = 4 leads to the output n-2 = 4-2 = 2
Whatever the input is, subtract 2 from it to get the output.
What is the median to 17,19, 20, 21, 22, 25, 29, 30, 32, 35
Answer:
23.5
Step-by-step explanation:
The median is the middle value when the numbers are put in order from smallest to largest
17,19, 20, 21, 22, 25, 29, 30, 32, 35
There are 10 numbers
17,19, 20, 21, 22, 25, 29, 30, 32, 35
The middle is between 22 and 25
(22+25)/2 = 47/2 =23.5
A certain positive integer has exactly 20 positive divisors.
What is the largest number of primes that could divide the integer?
thx for the help in advance
9514 1404 393
Answer:
3
Step-by-step explanation:
20 has at most 3 proper factors greater than 1: 2×2×5. Each of these can represent a prime factor of the number of interest, and is 1 more than that prime's power. That is, the number of interest (n) will have at most 3 prime factors p, q, r, and will be ...
n = p·q·r^4
_____
For some prime factorization ...
[tex]\displaystyle n=\prod_{k=1}^m{p_k^{q_k}}[/tex]
The total number of divisors of n is ...
[tex]\displaystyle\prod_{k=1}^m{(q_k+1)}[/tex]
Help please! it’s due soon
Answer:
33. That means (A) can be any number and b times any number wilo get 0 so any numbr will do
34.It is wrong because if x equals 40 anything multiply that will be more than that and so isnt a good reasoning
write your answer in simplest radical form
9514 1404 393
Answer:
4√2
Step-by-step explanation:
In a 30°-60°-90° triangle, the ratio of side lengths is ...
1 : √3 : 2
That is, the hypotenuse (c) is double the short side (2√2).
c = 4√2
Maximum and minimum value
Answer:
Maximum: 1
Minimum: -1
Step-by-step explanation:
To solve this, we can find the derivative of the function and then solve for when the derivative is equal to 0, finding the local maximum and minimum values in this function. Then, we can compare those points to the endpoints of the interval to find the maximum and minimum.
Using the Quotient Rule, we can say that
(f/g) ' = (f'g - fg')/(g²)
[tex]\frac{2x}{x^2+1}dx = \frac{\frac{d}{dx}(2x) * (x^2+1) - \frac{d}{dx} (x^2+1) * (2x) }{(x^2+1)^2} \\= \frac{2 *(x^2+1) - (2x)*(2x)}{(x^2+1)^2} \\[/tex]
Since we just need to solve for 0, we can disregard for the bottom part, resulting in
2(x²+1)-(2x)(2x) = 0
2x²+2-4x² = 0
2-2x² = 0
add 2x² to both sides to isolate the x² and its coefficient
2x² = 2
divide both sides by 2
x²=1
x = ±1
Therefore, we have 4 possible values for the maximum and minimum over this interval:
-2, -1, 0, 1
Trying each of these numbers into f(x),
f(-2) = -4/5
f(-1) = -2/2 = -1
f(0) = 0/1 = 0
f(1) = 2/2 = 1
Therefore, the maximum and minimum values of the function over the given interval are 1 and -1 respectively
Find the greatest number of students to whom 45 soccer balls and 60 tennis balls can be equally divided.
Answer:
15 studentsStep-by-step explanation:
Find GCF of 45 and 60:
45 = 3*3*560 = 2*2*3*5GCF(45,60) = 3*5 = 15
Find Greatest common multiple or GCF
[tex]\\ \sf\longmapsto 45=3\times 3\times 5[/tex]
[tex]\\ \sf\longmapsto 60=2\times 2\times 3\times 5[/tex]
Now
[tex]\\ \sf\longmapsto GCF=3\times 5=15[/tex]
An automobile manufacturer has given its car a 46.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 46.5. Assume the population standard deviation is known to be 1.1. A level of significance of 0.05 will be used. State the null and alternative hypotheses.
Answer: See explanation
Step-by-step explanation:
The null hypothesis H0: The null hypothesis states that there is no relationship between the two things that are being considered.
The alternative hypothesis is contradictory to H0 and it explains that there is a relationship between the two selected variables.
Based on the question, the null hypothesis H0 is that the rating of car is equal to 46.7 miles per gallon. μ = 46.7 MPG
The alternative hypothesis Ha is that the rating of the car is not equal to 46.7 Miles per gallon. μ ≠ 46.7 MPG
SOVE, REDUCE TO LOWEST TEERMS SIMPLIFY IMPROPER FRACTIONSAS MIXED FRACTIONS
88%
19. What is the solution X in this equation? 2(3x - 7) + 4(3x + 2) = 6(5x+9) + 3
[tex]\\ \sf\longmapsto 2(3x-7)+4(3x+2)=6(5x+9)+3[/tex]
[tex]\\ \sf\longmapsto 6x-14+12x+8=30x+54+3[/tex]
[tex]\\ \sf\longmapsto 6x+12x-14+8=30x+57[/tex]
[tex]\\ \sf\longmapsto 18x+6=30x+57[/tex]
[tex]\\ \sf\longmapsto 30x-18x=6-57[/tex]
[tex]\\ \sf\longmapsto 12x=51[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{51}{12}[/tex]
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.75
Step-by-step explanation:
Please help me, by completing this proof!
Answer:
Step-by-step explanation:
Statement Reasons
1). Line PQ is an angle bisector of ∠MPN D). Given
2). ∠MPQ ≅ ∠NPQ A). Definition of angle bisector
3). m∠MPQ = m∠NPQ F). Definition of congruent
angles.
4). m∠MPQ + m∠NPQ = m∠MPN C). Angle addition postulate
5). m∠MPQ + m∠MPQ = m∠MPN G). Substitution property of
equality
6). 2(m∠MPQ) = m∠MPN B). Distributive property
7). m∠MPQ = [tex]\frac{1}{2}(m\angle MPN)[/tex] E). Division property of equality
please help brainliest to correct answer
Answer:
Question for number 3 is -3
Question for number 4 is 6
Step-by-step explanation:
Brainless please
3/4 + 20 (2/5 x 4/7)
Answer:
i believe the answer is 5.3
Find y when x = 4 (30 points)
Answer:
y = 54/25
Step-by-step explanation:
y = p×q^(x-1)
when x = 1 then y = 10
so,
10 = p×q^(1-1)
or, 10 = p×1
or, p = 10
when x = 6 then y = 0.7776
0.7776=p×q^(6-1)
or, 0.7776=p×q^5
or, 0.7776=10×q⁵
[0.7776 = 7776/10000 = 486/625]
or, 486/625 = 10×q⁵
or, 486/6250=q⁵
or, [tex] \frac{ \sqrt[5]{486} }{ \sqrt[5]{6250} } = q[/tex]
or, [tex]q = \frac{3 \sqrt[5]{2} }{5 \sqrt[5]{2} } [/tex]
or, q = 3/5
so, when x = 4
y = p×q^(x-1)
y = 10×(3/5)^(4-1)
y = 10×(3/5)^3
y = 10×27/125
y = 54/25
1+9+40-40+40+10x2 equals what?
Answer:
70
Step-by-step explanation:
1+9+40-40+40+10*2
----------------------- 20
10+40-40+40+20
50 (-40+40 cancels out to 0) +20
50+20= 70
(Following PEMDAS)
Multiply, add, subtract.
if you were to instead go through it left to right, you would get 120, which is incorrect.
a company has decreased the weight of its boxes of macaroni by 8 %. if the new weight of the box is 13.1ounces, what was the original weight of the box?
Answer:
실례합니다 ?
Step-by-step explanation:
이것이 무엇을 의미하는 질문입니까?
회사는 마카로니 상자의 무게를 8% 줄였습니다. 상자의 새 무게가 13.1온스인 경우 상자의 원래 무게는 얼마였습니까? 오른쪽 ?
Answer:
x*0.92 = 13.1
x = 14.24
Step-by-step explanation:
Please help!!
A) In a movie, a mad scientist enlarges a cow to 100 times its normal size. How much stronger would its legs be than a normal cow?
B) How many times more would it weigh than a normal cow?
C) Can you see how results A and B would yield a cow that would collapse under its own weight?
Answer:
100 times everything.
Step-by-step explanation:
If the cow is 100 times larger than its normal size, obviously everything else should be 100 times stronger and heavier.
I WILL GIVE BRAINLEST FAST PLEASE ANSWER THE QUESTION IN THE IMAGE
Answer:
Cannot be determined
Step-by-step explanation:
We only know one angle and we could only compare one set of sides.
We do not have enough information to determine if the triangles are similar
A research report claims that 20% of all individuals use Firefox to browse the web. A software company is trying to determine if the proportion of their users who use Firefox is significantly different from 0.2. In a sample of 200 of their users, 26 users stated that they used Firefox.
Required:
Using this data, conduct the appropriate hypothesis test using a 0.01 level of significance.
Answer:
Reject H0
Step-by-step explanation:
Z = -2.474873734
survey (positive) 26
n (total) 200
p 0.2
p /point est. 0.13
POPULATION(min) 4000
np >= 5 ? YES 40
n(1-p) >= 5 ? YES 160
Sample is valid
Confidence Level - "P" values
99% 2.58
Confidence Interval - "P" values
(0.0686 , 0.1914 )
Reference=0.2 Reject H0
Which Expression is equivalent to -2(x + 6) 2x + (-12) 2x + 12 2x + 6
Answer:
-2x -8
Step-by-step explanation:
Please help me please! I really need it! Thank you so much!!!!!!!!!!! Sorry Quality is really bad
Answer:
7[tex]\frac{5}{6}[/tex]
Step-by-step explanation:
- 2[tex]\frac{1}{3}[/tex] - ( - 10[tex]\frac{1}{6}[/tex] ) = - 2[tex]\frac{1}{3}[/tex] + 10[tex]\frac{1}{6}[/tex] = - 2[tex]\frac{2}{6}[/tex] + 10[tex]\frac{1}{6}[/tex] = ( 10 - 2 ) + ( [tex]\frac{1}{6}[/tex] - [tex]\frac{2}{6}[/tex] ) = 8 - [tex]\frac{1}{6}[/tex] = 7 + ( [tex]\frac{6}{6}[/tex] - [tex]\frac{1}{6}[/tex] ) = 7[tex]\frac{5}{6}[/tex]
Which shows the image of rectangle ABCD after the rotation () (W)?
13
VA
1
V
Answer:
Graph (1)
Step-by-step explanation:
Given rule for the rotation of a figure is,
A(x, y) → A'(-y, x)
This rule defines the rotation of point A by 90° counterclockwise about the origin.
Coordinates of point A → (-2, 0)
Coordinates of point C → (-1, 0)
Following the rule of rotation,
A(x, y) → A'(-y, x)
A(-2, 0) → A'(0, -2)
C(-1, 4) → C'(-4, -1)
Now search the image points from the graphs attached,
Graph (1) will be the answer.
✓ 1 N 3 4 5 6 Conv A rectangular field is 300 meters long and 250 meters wide. What is the area of the field in square kilometers? Do not round your answer. 1000 millimet 100 centimet 10 decimet 1 decame 2 km Х X 5. ? 1 hectomei 1
Answer:
75 km
Step-by-step explanation:
Area = Length × Width
= 300m and 250m
= 75000m
M to Km => ÷1000
= 75000m ÷ 1000
= 75 km #
Find the minimum turning point of y = x^2 + x - 12
Answer:
(x+4)(x-3)
Step-by-step explanation:
x^2+x-12
=x^2+(4-3)x-12
=x^2+4x-3x-12
=x (x+4)-3 (x+4)
=(x+4)(x-3)
Answer:x=6
Step-by-step explanation:
what is the length of GN, given that figure LMNO is a square PLZ HELP!!!!!
Answer:
A. 4
Step-by-step explanation:
The diagonals are also congruent to each other. Diagonals of a square bisect each other. This implies that:
MO bisects LN, thereby dividing LN into two equal segments, LG and GN.
Thus, LG = GN.
Since the length of LG = 4, therefore:
GN = 4
