Answer:
[tex]\huge\boxed{\sf \frac{a^2+b^2}{2(a^2-b^2)}}[/tex]
Step-by-step explanation:
=> [tex]\sf \frac{a}{2(a+b)} + \frac{b}{2(a-b)}[/tex]
LCM = 2(a+b)(a-b)
=> [tex]\sf \frac{a(a-b)+b(a+b)}{2(a+b)(a-b)}[/tex]
Simplifying further
=> [tex]\sf \frac{a^2-ab+ab+b^2}{2(a^2-b^2)}[/tex]
=> [tex]\sf \frac{a^2+b^2}{2(a^2-b^2)}[/tex]
[tex]\dfrac{a}{2(a+b)}+\dfrac{b}{2(a-b)}=\\\\\dfrac{a(a-b)}{2(a+b)(a-b)}+\dfrac{b(a+b)}{2(a+b)(a-b)}=\\\\\dfrac{a^2-ab}{2(a^2-b^2)}+\dfrac{ab+b^2}{2(a^2-b^2)}=\\\\\dfrac{a^2+b^2}{2(a^2-b^2)}[/tex]
Anyone here who can help me with this?
Answer:
D. 16 years old
Step-by-step explanation:
Step 1: Let T be Tien's age and J as Jordan's age (today),
[tex]T=\frac{1}{4}J[/tex]
Step 2: Let T be Tien's age and J as Jordan's age (in 2 years),
[tex]T+2=\frac{1}{3} (J+2)[/tex]
[tex]T=\frac{1}{3}(J+2)-2[/tex]
Step 3: As their age differences will always be similar we can have the two equations above equal to find Jordan's age,
[tex]\frac{1}{4} J=\frac{1}{3}(J+2)-2\\\frac{1}{4}J-\frac{1}{3}J=\frac{2}{3} -2 \\-\frac{1}{12}J= -\frac{4}{3} \\\\J=16[/tex]
Answer ASAP, Will give brainliest
Answer:
Step-by-step explanation:
1) ABCD is a trapezium. AB ║ CD
∠ADC + ∠DAB = 180° { Co interior angles}
110° + ∠DAB = 180
∠DAB = 180 -110
∠DAB = 70°
2) Sum of all angles of trapezium = 360°
∠A + ∠B + ∠DCB + ∠D = 360
70° + 50° + ∠DCB + 110° = 360
230 + ∠DCB = 360
∠DCB = 360 - 230
∠DCB = 130°
3) For finding the height, use Pythagorean theorem
height² + base² = hypotenuse²
height² + 6² = 10²
height² + 36 =100
height² = 100 - 36
height² = 64
height = √64
height = 8 m
4) a = AB = x m
b = 9 m
h = height = 8 m
Area of trapezium = 120 m²
[tex]\frac{(a+b)*h}{2}\\\\[/tex] = 120
[tex]\frac{(x+9)*8}{2} =120\\\\\\(x +9)*4 = 120[/tex]
x + 9 = 120/4
x + 9 = 30
x = 30 - 9
x = 21 m
AB = 21m
Solve the equation for x.
(x - 4) - (x + 7) = 8x
11
a.
c.
11
8
2
AlE NE
b.
1
d.
11
coin
8
4
Answer:
[tex]x=-\frac{11}{8}[/tex]
Step-by-step explanation:
Hi there!
[tex](x - 4) - (x + 7) = 8x[/tex]
Open up the parentheses
[tex]x - 4 - x - 7 = 8x[/tex]
Combine like terms
[tex]x -x - 4 - 7 = 8x\\-4-7=8x\\-11=8x[/tex]
Divide both sides by 8 to isolate [tex]x[/tex]
[tex]-\frac{11}{8}=x[/tex]
I hope this helps!
factorise [tex]x^{2} + 11x[/tex]
Answer:
x(x+11)
Step-by-step explanation:
x^2+11x
Factor out x
x*x+11x
x(x+11)
Hiiii can you help me ?
Answer:
842, 743, 394, 305, 836
Step-by-step explanation:
We arbitrarily chose the ones digit to start with as 2. (It must be 5 or less.) The other two digits are chosen by a random number generator, as shown in the attached.
The 5 three-digit numbers we chose are ...
842, 743, 394, 305, 836
Answer:
The only criteria the question gives are that there must be 5 numbers, and the numbers must have 3 digits. The ones digit in the numbers should go up by 1.
So, we can have 111, 112, 113, 114, and 115.
Hope this helps!
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Data should be analyzed using each of the following except:
A. measures of central tendency
B. shape
C. population size
D. spread
At a certain auto parts manufacturer, the Quality Control division has determined that one of the machines produces defective parts 18% of the time. A random sample of 7 parts produced by this machine is chosen. Find the probability that more than 1 of these parts are defective.
Using the binomial distribution, it is found that:
0.3677 = 36.77% probability that more than 1 of these parts are defective.
-----------------
For each part, there are only two possible outcomes. Either they are defective, or they are not. The probability of a part being defective is independent of any other part, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success.
At a certain auto parts manufacturer, the Quality Control division has determined that one of the machines produces defective parts 18% of the time.
This means that [tex]p = 0.18[/tex]
A random sample of 7 parts produced by this machine is chosen.
This means that [tex]n = 7[/tex]
Find the probability that more than 1 of these parts are defective.
This is:
[tex]P(X \geq 1) = 1 - P(X < 1)[/tex]
In which
[tex]P(X < 1) = P(X = 0) + P(X = 1)[/tex]
Thus
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{7,0}.(0.18)^{0}.(0.82)^{7} = 0.2493[/tex]
[tex]P(X = 1) = C_{7,1}.(0.18)^{1}.(0.82)^{6} = 0.3830[/tex]
Then
[tex]P(X < 1) = P(X = 0) + P(X = 1) = 0.2493 + 0.3830 = 0.6323[/tex]
[tex]P(X \geq 1) = 1 - P(X < 1) = 1 - 0.6323 = 0.3677[/tex]
0.3677 = 36.77% probability that more than 1 of these parts are defective.
For more on the binomial probability distribution, you can check https://brainly.com/question/15557838
Ava's car used 6 gallons of gas to drive 132 miles. At what rate does her car use gas in gallons per mile? Express your answer in simplest form.
Answer:
Rate of gas in gallons per mile
= 0.045454545 gallon/mile
Or
Rate of gas in gallons per mile
= 1/22 gallon/mile
Step-by-step explanation:
Ava's car uses 6 gallons of gas to drive through a distance of 132 miles.
Thanks rate of gallon to distance will be given by the formula below
Rate of gas in gallons per mile
=Number of gallons/ distance covered in miles
Rate of gas in gallons per mile= 6/132
Rate of gas in gallons per mile= 1/22
Rate of gas in gallons per mile
= 0.045454545 gallon/mile
john is 15 years old. john's mom takes him and his younger soster to a football game. tickets are $22 for adults and $16 for children (18 and under). what is the total cost of thr tickets?
Answer:
$38
Step-by-step explanation:
cost of ticket for adult = $22
cost of ticket for youngster = $16
______________________________
cost of ticket for John's mom = $22 as she is adult
cost of ticket for john = $16 as he is young , his age is less than 18 years
Total cost of ticket for John and his mother = $22 + $16 = $38
Mark all the statements that are true please help
Step-by-step explanation:
the correct answer is option c
answer for brainlyyyyyy
PLSSS
[tex]\huge\mathsf\green{ANSWER}:—[/tex]
[tex]option \: \: c \: \: \: \frac{3}{4} \: is \: the \: correct \: option[/tex]
Know more :-Rational numbers are numbers which can be represent in the form of p/q where p and q are integers and q≠0 that's why 3/4 is the correct option
plz mark me as brainliest answerPlease help with 6 and 7
Answer:
6a) i- 2hrs 36mins ii- 3hrs 12mins
b) car A≈ 76.9km/h car B≈ 62.5km/h
c)------
7a) 35km
b) car A=75km car B=60km
c) 30km
d) car A≈36mins car B≈48mins
Step-by-step explanation:
6a) Using the graph follow the lines until they finish then go downwards until you get to the x-axis. The x-axis is going up by 12mins for each square.
b) Using the answer from a, you divide 200km by the time.
For car A 2hrs 36mins becomes 2.6 because 36mins/60mins=0.6
∴ car A: 200/2.6≈ 76.92km/h
For car B 3hrs 12mins becomes 3.2 because 12mins/60mins=0.2
∴ car B: 200/3.2≈ 62.5km/h
7a) Using the graph go down from where the line of car A finished to meet car B. The y-axis is going up by 5km for each square.
b) Starting from the x-axis at 1 hour go upwards to see where you meet the car B line (60km) and car A line(75km). (sorry if that does not really make sense).
c) Difference from car A line to car B:
155km-125km=30km
d) Going across from 50km meet car A line and go down to see it has been travelling for approx. 36mins. Then continue across to car B line, go down to see it reached 50km at approx. 48mins.
Hope this helps.
What is the justification for step 2 in the solution process? 12 − x = 7x + 32 Step 1: -x = 7x + 20 Step 2: -8x = 20
A. the division property of equality
B.the addition property of equality
C. the subtraction property of equality
D. the multiplication property of equality
Answer:
C. the subtraction property of equality
Step-by-step explanation:
given
12 − x = 7x + 32
Subtract 12 from each side using the subtraction property of equality
Step 1: -x = 7x + 20
Subtract -7x from each side using the subtraction property of equality
Step 2: -8x = 20
Please someone tell me the answer of these questions
Answer:
VERTICALLY OPP ANGLES
Step-by-step explanation:
Multi-Step Literal Equations
Solve the following equation for b. Be sure to take into account whether a letter is capitalized or not.
t+1/2b=Y
[tex]\\ \sf\longmapsto t+\dfrac{1}{2}b=Y[/tex]
take t right side[tex]\\ \sf\longmapsto \dfrac{1}{2}b=Y-t[/tex]
[tex]\\ \sf\longmapsto \dfrac{b}{2}=Y-t[/tex]
[tex]\\ \sf\longmapsto b=2(Y-t)[/tex]
[tex]\\ \sf\longmapsto b=2Y-2t[/tex]
Mukat has five times as many book as usha.If mukat gave 16 books to usha,they each would have the same number.how many books did each girl have?
Mukat gets 40, Usha gets 8
Step-by-step explanation:
Mukat = 5 × Usha
After Mukat gives Usha 16 books ,Usha gets (16 + initial number of books) and Mukat gets (5 × Usha - 16)
Then Mukat = final number of books for Usha
5 × Usha - 16 = Usha + 16
(5 × Usha ) - Usha = 16+16
4 × Usha = 32
Usha = 8 i.e her number of books.
Mukat = 5×8=40.
I HOPE IT'S OK
can anyone help me with this?
Answer:
Step-by-step explanation:
a + 45 + 70 = 180 45 becomes an interior angle by being opposite a given vertically opposite angle.
a + 115 = 180 Subtract 115 from both sides
a = 65
b + 68 + 65 = 180 A straight line is 180 degrees.
b + 133 = 180
b = 180 - 133
b = 47
In the triangle b + c + 100 = 180
b = 47
47 + c + 100 = 180
147 + c = 180
c = 33
If C is an exterior angle then C + 33 = 180
C = 147
You have to decide whether c is an interior angle ( in which it is 33) or an exterior angle (in which case it is 147).
Find the equation of the linear function represented by the table below in slope-intercept form.
Helpp plzz
Answer:
Let's first find the slope.
-13 - (-8) / 2-1
-5/1
-5
The slope is -5.
The y intercept, or where the line crosses the y=axis, is equal to -3.
So, the equation is y=-5x-3
Let me know if this helps!
The numbers in the select boxes are 4 7 and 3 I put them with the photos. Can someone help
Answer:
4:7
Step-by-step explanation:
4 grape candies : 7 total candies (grape + cherry)
Answer:
It is simply 4:3
SP=2x+3, and LN=5x−14. Find SP.
Answer:
43
Step-by-step explanation:
Using Thales theorem:
● SP/LN = RP /RN
Notice that RN = 2×RP
● SP/LN = RP/2RP
● SP /LN = 1/2
● SP / (5x-14) = 0.5
● (2x+3)/(5x-14) = 0.5
● 2x+3 = 0.5(5x-14)
● 2x+3 = 2.5x -7
Add 7 to both sides
● 2x+3+7 = 2.5x-7+7
● 2x+10 = 2.5x
Sustract 2x brom both sides
● 2x+10-2x = 2.5x-2x
● 10 = 0.5x
Multiply both sides by 2
● 10×2 = 0.5x×2
● 20 = x
Replace x with 20 in Sp expression:
● SP = 2x+3
● SP = 2×20+3
● SP = 43
PLEASE HELP QUICK, WILL MARK BRAINLIEST!
Solve for x: −6 < x − 1 < 9
5 < x < 10
−5 < x < 10
−5 > x > 10
5 > x > −10
Answer:
−5 < x < 10
Step-by-step explanation:
−6 < x − 1 < 9
Add 1 to all sides
−6+1 < x − 1+1 < 9+1
−5 < x < 10
Answer:
B
Step-by-step explanation:
Add one to everything
-5 < x < 10
Best of Luck!
A net that can be folded into a rectangular prism.
This net could be folded to form a .
This figure will have faces, edges, and vertices.
Answer:
rectangular pyramid, 5, 8,5
Step-by-step explanation:
Answer:
✔ rectangular pyramid
This figure will have
✔ 5
faces,
✔ 8
edges, and
✔ 5
vertices.
the person above is correct
A diesel generator produced 1,800 kilowatt hours of
electrical energy in 4 hours and consumed 36 gallons
of diesel per hour in the process. How many kilowatt
hours of electrical energy are produced by the
combustion of 1 gallon of diesel?
A) 12.5
B) 45
C) 50
D) 80
The sum of two numbers must be 24 or greater. The product of the two numbers must be less than 60. Which system of inequalities represents this situation?
A
{x+y≥24xy<60
B
{x+y>24xy<60
C
{x+y≥24xy<60
D
{x+y>24xy<60
Answer:
A
Step-by-step explanation:
The sum means +, 24 or greater means ≥ 24
The product means multiplying. less than 60 means < 60
I don't really know how else to explain, so if you still don't understand, sorry.
I hope this helps!
pls ❤ and mark brainliest pls!
Before 8 A.M., there were 64 trucks and 24 cars in a parking lot. Between 8 A.M. and 9 A.M., more cars entered the parking lot and no trucks entered or exited the lot. At 9:00 A.M., the number of trucks represented 1/5 of the parking lot's vehicles. How many cars entered between 8 A.M. and 9 A.M? A. 56 B. 112 C. 148 D. 192 PLZ EXPLAIN
Answer:
232 cars
Step-by-step explanation:
Let's say the number of cars that entered is c.
At 9:00 am, there are a total of 24 + c cars and 64 trucks. We know that this value of 64 represents 1/5 of the total number of vehicles. The total number of vehicles is (24 + c) + 64 = 88 + c. So, we have:
64/(88 + c) = 1/5
Cross-multiply:
88 + c = 64 * 5 = 320
c = 320 - 88 = 232
Thus, the answer is 232 cars.
Note: as 232 doesn't show up in the answer choices, it's possible that the problem was copied correctly.
~ an aesthetics lover
Answer:
232 cars entered between 8 and 9
Step-by-step explanation:
at 9 am there are 64 x 5 vehicles total = 320
320 - 64 - 24 = 232
Tickets to a movie cost $5 for adults and $3 for students. A group of friends purchased 18 tickets for $82.00. How many adults ticket did they buy?
Answer:
They purchased 14 adult tickets and 4 kids tickets.
Step-by-step explanation:
14 x 5 = 70
3x4=12
and then add 70 plus 12 to get 82 dollars.
The number of adults tickets that were sold for the movie will be 14 tickets.
The equation to solve the question will be:
a + s = 18 .......... i
5a + 3s = 82 ......... ii
Form equation i, s = 18 - a
5a + 3s = 82
5a + 3(18 - a) = 82
5a + 54 - 3a = 82
Collect like terms
5a - 3a = 82 - 54
2a = 28.
a = 28/2
a = 14
Therefore, s will be:
s = 18 - a = 18 - 14 = 4
The number of adults ticket is 14
Read related link on:
https://brainly.com/question/16652625
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse?
Answer:
8.94~9.0
Step-by-step explanation:
If A squared plus B squared equals C squared. Then you can used this formula and find that 4 squared plus 8 squared equals 80. then square root 80 to find 8.94 or rounded to 9. This would equal C or the hypotenuse. Hope this helps!
The required length of the hypotenuse of the triangle is 16√5.
Given that,
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse is to be determined.
In a right-angled triangle, its side, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.
Here,
Applying the Pythagorean theorem,
Hypotenuse² = perpendicula² + base²
Hypotenuse² = 8² + 4²
Hypotenuse² = 64 + 16
Hypotenuse² = 80
Hypotenuse = √80
Hypotenuse = 16√5
Thus, the required length of the hypotenuse of the triangle is 16√5.
Learn more about Pythagorean triplets here:
https://brainly.com/question/10174253
#SPJ2
A gray crayon is made with 5 mL of black wax for every 6 mL of white wax
Which of the following wax mixtures will create the same shade of gray?
choose 2 answers:
A 10 mL of black wax mixed with 24 mL of white wax
B 15 mL of black wax mixed with 18 mL of white wax
C 35 mL, of black wax mixed with 42 mL of white wax
D 20 mL of black wax mixed with 26 mL of white wax
E 45 mL of black wax mixed with 48 mL of white wax
Answer:
B and C
Step-by-step explanation:
The ratio of black to white is 5:6
The only mixtures that have this ratio is B and C
Please help whenever I do this i always get 306 but that's incorrect.
Answer:
$153
Step-by-step explanation:
Divide by 100-sale%
102/.66666=
$153
Check: 153x.666666=102 YES
Answer:
the original price is 153
Step-by-step explanation:
leather jacket is 102 sale price
the sale is 1/3 of original price
the original price=1/2 its price=sale price
x-1/3x=102
2/3 x=102
2x=306
x=306/2
x=153 dollars
Find the slope of the line through each pair
A.) (8, -7) and (5, -3). B.) (-5, 9) and (5, 11).
C.). (-8, -4) and (-4, -9).
Show your work.
Answer:A) -4/3 B) 1/2 C) -5/4
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
For A) let (x1, y1) = (8, -7), (x2, y2) = (5, -3)
Slope = (-3 -(-7)) / (5 - 8) = 4/-3
For B) let (x1, y1) = (-5, 9), (x2, y2) = (5, 11)
Slope = (11 - 9) / (5 - (-5)) = 2/10 = 1/2
For C) let (x1, y1) = (-8, -4), (x2, y2) = (-4, -9)
Slope = (-9 -(-4)) / (-4 - (-8)) = -5/4