Answer:
(ab+a-b+1)(ab-a+b+1)
Step-by-step explanation:
(1 - a²) (1 - b²) + 4ab= 1 -a²-b² +a²b² +4ab = (a²b² +2ab +1 )- (a²-2ab+b²)=(ab+1)² - (a-b)²=(ab+1 +a-b)(ab+1 -a+b)=(ab+a-b+1)(ab-a+b+1)What is an equation of the line that passes through the point
(−5,7) and is parallel to the line
x+5y=10?
x + 5y - 10 = 0 there you have it
help i will give brainliest
Answer:
see below
Step-by-step explanation:
Formula: Center Not at Origin:
New point = k( x-a) +a, k( y-b) +b where k is the scale factor and ( a,b) is center of dilation
New point = -2( x-4) +4, k( y-6) +6
The scale factor is k = -2
Taking the top point ( 1,9)
New point = -2( 1-4) +4, -2( 9-6) +6
= -2(-3) +4 , -2(3) +6
6+4, -6+6
10,0
Taking the bottom left point ( 1,7)
New point = -2( 1-4) +4, -2( 7-6) +6
= -2(-3) +4 , -2(1) +6
6+4, -2+6
10,4
Taking the bottom right point ( 2,7)
New point = -2( 2-4) +4, -2( 7-6) +6
= -2(-2) +4 , -2(1) +6
4+4, -2+6
8,4
Simplify 2a^2b^3(4a^2+3ab^2-ab)=?
A. 8a^4b^5+3a^3b^5-2a^3b^4
B. 8a^4b^3+6a^3b^5-2a^3b^4
C. 8a^4b^5+3a^3b^5-2a^3-ab=
Simplify 12-(-8)x4=? A. 44 B. -20 C. 16 D. 80
One day when Terry went to school the temperature outside was -15 degrees Fahrenheit. In Terry's classroom the temperature was 68 degrees Fahrenheit. How many more degrees was it inside the building than outside? A. +53 degrees B. +83 degrees C. -53 degrees D. -83 degrees
If Juan purchased thee 24-ounce cans of motor oil for 410.80, how much did he pay per ounce? A. $3.60 B. $.45 C. $2.59 D. $.15
Simplify (x^2+16)(x^2-16)=? A.x^4-32 B. x^4+256 x^4-256 D. x^4+32
If the value of b is 7, then what is the value of the expression -3b^2+25=?
A. 122
B .17
C. 172
D. -122
Answer:
1.) 8a⁴b³ + 6a²b³ab² - 2a²b³ab
2.) A. 44
3.) B. +83 degrees
4.) D. $0.15
5.) x⁴ - 256
6.) D. -122
7.) -6r²s⁴t³
Step-by-step explanation:
1.) To simplify, we simply multiply/distribute and then combine like terms.
2.) To simplify, we use Order of Operations BPEMDAS to solve.
3.) To find, we simply subtract 68 and -15 to get +83 as our answer.
4.) To find, we simply multiply 3 by 24 to get 72, then divide by $410.80 to get $0.15 as our answer.
5.) To expand/simplify, simply use Difference of Squares to get C. as our answer.
6.) To find the value, simply plug in 7 for b to get -122 as our answer.
7.) To find the result, remember that when you divide exponents, you subtract the powers.
How would the fraction
5/1-√3
be rewritten if its denominator is rationalized
using difference of squares?
Answer:
A. [tex] {-\frac{5+5\sqrt 3 }{2}}[/tex]
Step-by-step explanation:
Please wait for more explanation:
[tex] \frac{5}{1-\sqrt 3}= \frac{5}{1-\sqrt 3}\times \frac{1+\sqrt 3}{1+\sqrt 3}\\\\
= \frac{5(1+\sqrt 3) }{1^2 -(\sqrt 3) ^2}\\\\
= \frac{5+5\sqrt 3 }{1 -3}\\\\
= \frac{5+5\sqrt 3 }{-2}\\\\
=\huge\purple {\boxed {-\frac{5+5\sqrt 3 }{2}}} \\[/tex]
The fraction 5/1-√3 can be rewritten if its denominator is rationalized using difference of squares as -5(1 + √3)/2.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
To rationalize 5÷1-√3, by the conjugate of 1 - √3 = 1 + √3.
So 5 ÷ (1 - √3) = 5/(1 - √3),
we multiply the expression by the conjugate of the denominator, we have,
5/(1 - √3) × (1 + √3)/(1 + √3)
= 5(1 + √3)/[(1 - √3) × (1 + √3)]
= 5(1 + √3)/(1² - (√3)²)
= 5(1 + √3)/(1 - 3)
= 5(1 + √3)/-2
= -5(1 + √3)/2
Learn more about factored form of an expression here:
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Find the value of x in the triangle shown below.
Answer:
20
Step-by-step explanation:
This triangle can be solved using the Pythagorean theorem. 16^2+12^2=x^2. 16^2+12^2=400. If we set 400 equal to x^2, x=20.
Help please I’m not good at rational functions.
Answer:
See below.
Step-by-step explanation:
[tex]\frac{6z^2-12z}{4z^2-16z+16} +\frac{3z}{z^2-z-2} \\\\[/tex]
First, factor the numerators and the denominators:
[tex]=\frac{6z(z-2)}{4(z^2-4x+4)}+\frac{3z}{z^2-z-2}\\=\frac{6z(z-2)}{4(z-2)^2}+\frac{3z}{(z-2)(z+1)}\\=\frac{3z}{2(z-2)}+\frac{3z}{(z-2)(z+1)}[/tex]
Now, make the two denominators equivalent. To do this, we can multiply the first term by (z+1) and multiply the second term by 2. This will give us:
[tex](\frac{z+1}{z+1} )(\frac{3z}{2(z-2)})+(\frac{2}{2})(\frac{3z}{(z-2)(z+1)})\\=\frac{3z(z+1)}{2(z-2)(z+1)}+\frac{6z}{2(z-2)(z+1)} \\[/tex]
Now, combine them since they have a common denominator:
[tex]=\frac{3z^2+3z+6z}{2(z-2)(z+1)}\\ =\frac{3z^2+9z}{2(z-2)(z+1)} \\=\frac{3z(z+3)}{2(z-2)(z+1)}[/tex]
This cannot be simplified further.
linear equations: c+2c+12=75
Answer:
c = 21
Step-by-step explanation:
c + 2c + 12 = 75
Combine like terms.
3c + 12 = 75
Subtract 12 from both sides.
3c = 63
Divide 3 on both sides.
c = 21
OK so I need to know what 96÷6 is and I know it is 16 but I need to know how to do it in long division can anyone help me
Answer:
16
____________
6| 96
-6 |
V
36
- 36
0
6 goes into 9 one time because 9-6=3 so there is 1 six in 9. Write 1 at the top because you have 1 6.
Subtract the 6 and you get 3
Bring the 6 from 96 down
you get 36
6 goes into 36 6 times because 36-6-6-6-6-6-6=0 so write a 6 at the top and you get 16 because of the previous 1.
Subtract 36 by 36 to get 0
Hope this helps
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
You have to take each number in the dividend (number being divided) and divide it by the number in the divisor (number that is dividing). Here you would take 9, the first number in the dividend and divide it by 6, and you would put that in the first space of the quotient (answer). You would then take that number and multiply it by 6 and place it in the space below. Subtract 6 from 9 and get 3. Drop down the 6 to get 36. Take 36 and divide that by the divisor 6 and get 6 next to the number 1 you calculated earlier to get your answer 16. Take 6 and multiply it back to get 36 and subtract it from 36 to get a remainder of 0.
I showed how to do it visually in the attachment just in case this explanation didn't make any sense
The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.1. Find the probability that the next two months will both result in three accidents each occuring in this stretch of road
Answer:
P = 0.00072
Step-by-step explanation:
If the number of traffic accidents that occurs follows a Poisson distribution, the probability that x traffic accidents occurs is:
[tex]P(x)=\frac{e^{-m}(m^x)}{x!}[/tex]
Where m is the mean. So replacing m by 8.1 accidents/monts, we get:
[tex]P(x)=\frac{e^{-8.1}(8.1^x)}{x!}[/tex]
So, the probability that the next two months will both result in three accidents each occurring in this stretch of road is calculated as:
[tex]P(3)*P(3)=\frac{e^{-8.1}(8.1^3)}{3!}*\frac{e^{-8.1}(8.1^3)}{3!}\\P(3)*P(3)=0.00072[/tex]
Which equation correctly rearranges the formula D=rt to find the time it will take her to run around the lake?
A) t=d/r
B) t=r/d
C) t=d+r
D) t=d-r
Answer:
t = D/r
Step-by-step explanation:
D = rt
Divide each side by r to isolate t
D/ r = rt/r
D /r = t
The time required is D/r
Help please !!!!!!!!!!!!!!!!
Answer:
x = 6
Step-by-step explanation:
The opposite sides of a parallelogram are congruent, thus
6x - 15 = x + 15 ( subtract x from both sides )
5x - 15 = 15 ( add 15 to both sides )
5x = 30 ( divide both sides by 5 )
x = 6
Answer:
X=6 Read explination
Step-by-step explanation:
A parallelogram has the perrimeter of both opposite sides equal
So we know that
6x-15=x+15
This is because in a parrellelogram the opposite sides are equal
so breaking it down
6x-15=x+15
(add 15 to both sides)
6x=x+30
(subtract x from both sides)
5x=30
(divide both sides by 5)
x=6
A relay with n laps was run by 4 people. The 1st runner ran half the laps. The 2nd runner ran half the number of laps the 1st runner ran. The 3rd runner ran half the number of laps the 2nd runner ran. The remaining laps were completed by the 4th runner. How many laps did the 4th runner complete?
Answer:
n/16
Step-by-step explanation:
I am pretty sure.
please mark me brainliest!
The 4th runner completed n/16 lap.
We have given that,
A relay with n laps was run by 4 people. The 1st runner ran half the laps. The 2nd runner ran half the number of laps the 1st runner ran. The 3rd runner ran half the number of laps the 2nd runner ran. The remaining laps were completed by the 4th runner.
We have to determine How many laps the 4th runner completed.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Therefore we have given total relay in n laps
There are 4 people and 4th lap was completed by the 4th runner.
Therefore the 4th runner completed the n/16 lap.
To learn more about the probability visit:
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Someone please help please
Answer:
-7x + 2y - 2z.
Step-by-step explanation:
Using the distributive property, you basically have...
-1 * 7x + -1 * -2y + -1 * 2z = -7x + 2y - 2z.
Hope this helps!
A school allots £2500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £45 each and are on offer for 1/5
off.
A train ticket for the day will cost £20 each.
If 3 teachers and the maximum number of students attend, how many students go on the trip?
Answer:
Maximum number of students=41
Step-by-step explanation:
Total allotted=£2500
Regular theatre Tickets=£45
1/5 off= 4/5*45
=£36
Train tickets=£20 each
Total cost per person=£36+£20
=£56
If 3 teachers and maximum number of students attend
Let x=maximum number of students
Therefore
£56(x+3) <or= £2500
56x+168 <or= 2500
56x <or= 2500-168
56x <or= 2332
x <or= 2332/56
x<or=41.643
Maximum number of students that will go on the trip=41 students
Total money left over for the school=
Total allotted - cost per person multiplied by number of teacher+students
=2500 - 56(3+41)
=2500-56(44)
=2500-2,464
=£36
Between July 1, 2000 and July 1, 2007, the estimated population of a city declined from 3487 to 2653. What was the percent decrease to the nearest tenth?
Answer:
23.9% decrease
Step-by-step explanation:
The percentage change is calculated from ...
pct change = ((new value)/(old value) -1) × 100%
= (2653/3487 -1) × 100% = -0.2392 × 100%
pct change = -23.9% . . . . rounded to tenths
The population decreased by 23.9% in the given time period.
Izzy gets a loan of $2,800 with an APR of 3.5%. She will repay the loan in monthly payments for 9 months. To find the total amount of interest she will pay, Izzy uses an online calculator. What are the correct numbers she should enter?
Answer: Hold on
Step-by-step explanation: LEt me see this is tricky
Answer: P= 2,800, r= 0.035, n= 12, t= 0.75
Step-by-step explanation:
I guessed and got it right!
A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 4 feet. The area of the logo must be at most 14 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle. Use b for the base length of the triangular logo.
Please can answer my question . When you flip a biased coin the probability of getting a tail is 0.3. How many times would you expect to get tails if you flip the coin 160 times?
Answer:
[tex]\boxed{Probability = 48}[/tex]
Step-by-step explanation:
Probability of getting a tails = 0.3
If it is flipped 160 times, the probability of getting a tails will be
=> 0.3*160
=> 48
Can anyone help me with this question
Answer:
3x + 7
Step-by-step explanation:
1. Distribute the negative into the parentheses.
6x - (3x - 7)
6x - 3x + 7
2. Simplify.
6x - 3x + 7
= 3x + 7
The sides of a square are three to the power of two sevenths inches long. What is the area of the square? (
Answer:
Step-by-step explanation:
The side of the square = 3^2/7
Use the law of exponents . If the power is a fraction, that means it is
3^2/7 = 3^2 x 1/7 = 7√9
To find the area you multiply this by itself.
This gives you 1.87...
Hope this helps
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second.
Answer:
It makes 360 / 60 = 6 revolutions per second. 6 revolutions is 12π radians.
the focal length F of a lens made by combining two lenses of focal length U and V is given I/F=I/U+I/V
A.make V the subject of the formula.
B.find V when F=6,U=10
Answer:
a). [tex]V=\frac{U.F}{U-F}[/tex]
b). V = 15 units
Step-by-step explanation:
Focal length F of a lens made by combining two lenses of different focal lengths U and V will be,
[tex]\frac{1}{F}=\frac{1}{U}+\frac{1}{V}[/tex]
A). By solving the given formula,
[tex]\frac{1}{V}=\frac{1}{F}-\frac{1}{U}[/tex]
[tex]\frac{1}{V}=\frac{U-F}{U.F}[/tex]
[tex]V=\frac{U.F}{U-F}[/tex]
B). If F = 6 and U = 10 then we have to find the value of V.
By substituting the given values in the formula,
[tex]V=\frac{6\times 10}{10-6}[/tex]
[tex]V=\frac{60}{4}[/tex]
V = 15 units
Therefore, focal length (V) of the lens = 15 units
Hi, I’m really struggling, if anyone knows, please could you help?
Answer: a) 26
Step-by-step explanation:
-a would be because as you can see there is a pattern of sticks, so what i did was count up the sticks and i found that there was 6 in the first one. So i counted the second one and it was 10 so i realized that all i had to do was add 4.
and for b i think when it says n it means the nth term which is 4 so i think it means pattern 4 which would be 18 so try that out
hope this helped x
U=12kx^2 What is x equal to?
Answer:
[tex] \sqrt{u \div 12k \\ } [/tex]
Step-by-step explanation:
u=12kx^2
x^2=u/12k
...x=
[tex] \sqrt{u \div 12k} [/tex]
*****(BRAINLIEST ANSWER****)
Segment RT and Segment GJ are chords that intersect at point H. If RH =6 units, HT = 5 units, and GH = 3 units, what is the length of line segment
HJ? *
20
10
5
40
Answer:
10 units
Step-by-step explanation:
By the property of Intersecting chords inside a circle, we have
RH*HT = GH*HJ
6*5 = 3*HJ
30 = 3HJ
HJ = 30/3
HJ = 10 units
Which type of transformation is shown? The transformation is a
Which number line represents the solutions to |x – 2| = 6? A number line from negative 10 to 10 in increments of 1. Two points, one at negative 8 and one at 4. A number line from negative 10 to 10 in increments of 1. Two points, one at 4 and one at 8. A number line from negative 10 to 10 in increments of 1. Two points, one at negative 2 and one at 6. A number line from negative 10 to 10 in increments of 1. Two points, one at negative 4 and one at 8.
Answer:
x = 8 or x = -4, i.e., the last number line
Step-by-step explanation:
|x – 2| = 6 translates to
x-2 = 6 or x-2 = -6 if you eliminate the absolute operation. So there are two solutions that you can solve independently:
x-2 = 6 => x = 8
x-2 = -6 => x = -4
Answer:
d
Step-by-step explanation:
just got it right :)
Translate into an algebraic expression How much x% sugar syrup can you make if you have 100 grams of sugar ?
Answer:
If we have a x% sugar syrup, this means that the ratio between the amount of sugar and the total amount of syrup (water + sugar), times 100%, is equal to x%
So we if we have 100gr of sugar and m grams of water mixed, we have:
100gr + m = M = grams of syrup, then we have:
then we have:
(100gr/M)*100% = x%
then
100gr*(100/x) = M
where M is the total amount of syrup that you can make.
Answer:
10000/x
Step-by-step explanation:
So, we can try to put this into an algebraic expression doing this!
We know that % means, *out of 100*, therefore
x=100
100=1 Which means, 100 over one equals to x over 100!
Cross multiply.
100*100 is 10,000
x*1 is x
you cannot simplify it further so we just leave it as, 10,000 divided by x, because x=10,000, would be 10,000 divided by x!
Cheers! I hope you can understand this now.
Miss Christina deposits her monthly salary $9000 in a bank which pays 7% interest compounded half yearly.How much will she get after 10 years? A.)18,122 B.)18,014 C.)17,908 D.)17,704
THe closest answer i got was 18122
PLEASE HELP A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8 An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome. What is the probability of drawing one blue marble?
Answer:
15/64
Step-by-step explanation:
3 blue
5 red marbles.
since the marble is put back in, the denominator will not change,
so to draw ONE marble, the chances would be
chances of picking a blue marble 3/8
chances of picking a red marble 5/8
3/8 * 5/8 - 15/64
please mark me brainly.
Answer:
The probability of drawing one blue marble is 3/8 because you have three blue marbles out of a total of eight marbles. The probability of drawing a second blue marble is also 3/8 but since you have to draw both marbles consecutively you have to multiply the probabilities of drawing each marble. So,
3/8•3/8 = 9/64.
Now you need to change it to a percent.
We do this by
9/64 x 100 = 14% approx