I Need help again! Given the following Venn diagram, choose the correct set for M n N
Answers
Answer:
{2, 3, 5, 6, 8, 9}
Step-by-step explanation:
The universal set is
U = {2, 3, 4, 5, 6, 7, 8, 9}
M = {3, 4, 7, 9}
N = {4, 6, 7}
M n N = {4, 7}
The bar above M n N means the complement of M n N which is all elements of the universal set that are not in M n N.
Answer: {2, 3, 5, 6, 8, 9}
Related Questions
(b) In a group of 140 people, 74 like tea, 104 like milk and each person likes at least one of the two drinks.
How many people like both tea and milk?
(ii) How many people like tea only?
(iii) How many people like milk only?
Answers
Answer:
How many people like both drinks?
To find the overlap, we can do (104 + 74) - 140 = 38.
How many people like tea only?
To find this, we can do 74 - 38 = 36.
How many people like milk only?
To find this, we can do 104 - 38 = 66.
Answer:
Step-by-step explanation:
A = Number of people who likes tea
B = Number of people who likes milk
Total people = n(A U B) = 140
(i) n(AUB) = n(A) + n(B) - n(A ∩B)
n(A∩B) = n(A) + n(B) - n(A ∪B)
n(A∩B) = 74 + 104 - 140
= 178 - 140
n(A∩B) = 38
Number of people who likes both tea and milk = 38
(ii)Number of people who likes tea only = n(A) - n(A∩B)
= 74 - 38
= 36
(iii) Number of people who likes milk only = n(B) -n(A∩B)
= 104 - 38
= 66
Sixty-five percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual? Sixty-five percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?
Answers
Answer:
The outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.
Step-by-step explanation:
The outcomes provided are:
(A) 0, 1, 2, 6, 7, 8
(B) 0, 1, 2, 7, 8
(C) 0, 1, 7, 8
(D) 0, 1, 2, 8
Solution:
The random variable X can be defined as the number of employees who judge their co-workers by cleanliness.
The probability of X is:
P (X) = 0.65
The number of employees selected is:
n = 8
An unusual outcome, in probability theory, has a probability of occurrence less than or equal to 0.05.
Since outcomes 0 and 1 are contained in all the options, we will check for X = 2.
Compute the value of P (X = 2) as follows:
[tex]P(X=2)={8\choose 2}(0.65)^{2}(0.35)^{8-2}[/tex]
[tex]=28\times 0.4225\times 0.001838265625\\=0.02175\\\approx 0.022<0.05[/tex]
So X = 2 is unusual.
Similarly check for X = 6, 7 and 8.
P (X = 6) = 0.2587 > 0.05
X = 6 not unusual
P (X = 7) = 0.1373 > 0.05
X = 7 not unusual
P (X = 8) = 0.0319
X = 8 is unusual.
Thus, the outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.
if the area of the rectangle is 120, what is the area of triangle cpd
Answers
Answer:
Step-by-step explanation:
area of rectangle=120
find area of CPD
area=1/2 (area of the rectangle)
area = 1/2×120=60
The area of triangle CPD IS 30 square units.
If the area of the rectangle is 120, then the area of triangle CPD is 30.
The area of a rectangle is given by the formula:
Area = length × width
In this case, the length of the rectangle is 120/width.
The area of a triangle is given by the formula:
Area = (1/2) × base × height
The base of triangle CPD is the width of the rectangle, and the height of triangle CPD is half the length of the rectangle.
Therefore, the area of triangle CPD is:
(1/2) × width × (120/width) = 30
So the answer is 30.
Learn more about triangle here: brainly.com/question/2773823
#SPJ2
(x+3)(x-5)=(x+3)(x−5)=
Answers
Answer:
(x+3)(x-5)=(x+3)(x-5)
x^2-2 = x^2-2
Step-by-step explanation:
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Let's solve your equation step-by-step.
[tex]( x + 3) ( x - 5) = ( x + 3 ) ( x - 5 ) =[/tex]
Step 1: Simplify both sides of the equation.
[tex]x^2 - 2x - 15 = x^2 - 2x - 15 - x^2\\-2x - 15 = -2x - 15[/tex]
Step 3: Add 2x to both sides.
[tex]-2x - 15 = -2x - 15\\-15 = -15[/tex]
Step 4: Add 15 to both sides.
[tex]-15 + 15 = -15 + 15 \\0 = 0[/tex]
Answer : All real numbers are solutions.
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If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
. In an extra-curricular club with 15 members,7 people played rugby, 6 people played soccer and 4 people neither play rugby nor soccer. How many people played both rugby and soccer?
Answers
Answer:
2
Step-by-step explanation:
In the above question, we are given the following information:
Total member in the club = 15
Rugby = n(R) = 7
Soccer = n(S) = 6
Neither Rugby nor Soccer = 4
Rugby and soccer = n( R ∩ S) = (Unknown)
Total number of club members = n(R) + n(S) - n( R ∩ S) + Neither Rugby nor soccer
15 = 7 + 6 - n( R ∩ S) + 4
15 = 17 - n( R ∩ S)
15 - 17 = - n( R ∩ S)
-2 = - n( R ∩ S)
n( R ∩ S) = 2
Therefore, the number of people that played both rugby and soccer is 2
Please help! Question is given below in form of image!
Answers
Answer:
c
Step-by-step explanation:
Answer:
None of the choices are correct.
Step-by-step explanation:
[tex] 9x^3 + 9x^2 - 4x - 4 = 0 [/tex]
The polynomial has 4 terms and no common factors. We can try factoring by grouping.
[tex] 9x^2(x + 1) - 4(x + 1) = 0 [/tex]
[tex] (x + 1)(9x^2 - 4) = 0 [/tex]
Now we factor the difference of squares.
[tex] (x + 1)(3x + 2)(3x - 2) = 0 [/tex]
[tex] x + 1 = 0~~or~~3x + 2 = 0~~or~~3x - 2 = 0 [/tex]
[tex]x = -1~~or~~x = -\dfrac{2}{3}~~or~~x = \dfrac{2}{3}[/tex]
None of the choices are correct.
answer of a ²-10a+16-6b-b^2
Answers
[tex] \quad a^2-10a+16-6b-b^2[/tex]
$=(a^2-10a)-(b^2+6b) +16$
$=[(a^2-2(5)a+25)-25]-[(b^2+2(3)b+9)-9]+16$
$=(a-5)^2-25-(b+3)^2+9+16$
$=(a-5)^2-(b+3)^2$
The scale for a drawing is 1 centimeter to 5 meters. If the actual object is 35 meters, the drawing is _____ centimeters long.
A. 30
B. 17
C. 7
D. 40
Answers
Answer:
its c.7
Step-by-step explanation:
I took the quiz
Answer:
c. 7
Step-by-step explanation:
i had this quiz also
Pls Answer A and B. You don’t need to explain. Thank you!!
Answers
a). Amount of money in Kareem’s acc:
650 - 40x
Amount of money in Karen’s acc:
850 - 65x
b). 650 - 40(8) = 850 - 65(8)
Find the missing value. Hint: Use the number line to find the missing value. − 7 = −7=minus, 7, equals − ( − 2 ) −(−2)minus, left parenthesis, minus, 2, right parenthesis
Answers
Answer:
The missing value is -9
Step-by-step explanation:
Given
[tex]-7 = _ -(-2)[/tex]
Required
Determine the missing value
Represent _ with a variable
[tex]-7 = x -(-2)[/tex]
Open the bracket
[tex]-7 = x -1*-2[/tex]
[tex]-7 = x + 2[/tex]
Subtract 2 from both sides
[tex]-7 - 2 = x + 2 - 2[/tex]
[tex]-9 = x[/tex]
Reorder
[tex]x = -9[/tex]
Hence, the missing value is -9
Answer:
The answer is 4=−2+6
Step-by-step explanation:
I checked on khan
E campsite shop also sells boxes of Pick-Me-Up teabags. The base of each box is a 120 mm square. The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle. Work out the maximum number of boxes that will fit on the shelf.
Answers
Answer:
The maximum number of boxes that will fit on the shelf = 189 boxes
Step-by-step explanation:
First, to harmonize the units of the dimensions given, let us convert the unit of the Pick-Me-Up teabags to cm.
1 cm = 10mm
1mm = 0.1cm
∴ 120mm = 0.1 × 120 = 12cm
Therefore, the base of each box is 12cm²
Next, let us calculate the area of the shelf.
Dimension of shelf = 65cm × 35cm
∴ Area of shelf = 65 × 35 = 2275cm²
Therefore, to calculate how many boxes will fit into the shelf, we will divide the area of the shelf by the area of the boxes of Pick-Me-Up teabag. This is shown below.
Area of shelf = 2275cm²
Area of boxes = 12cm²
Number of boxes that will fit on the shelf = Area of shelf ÷ Area of boxes
= 2275 ÷ 12 = 189.58 boxes
since there are no fractional boxes, we will round down to the nearest whole number of boxes.
Hence, the maximum number of boxes that will fit on the shelf = 189 boxes
-K2 – (4k - 6n) + 9n; k = - 1 and n= - 4
For k= - 1 and n= -4, -K2 - (4k - 6n) + 9n =
(Simplify your answer.)
Answers
Answer:
The simplified answer of the given equation is -57.
Step-by-step explanation:
For this problem, we are given values for our variables.
k = -1
n = -4
So, let's plug these numbers into our expression so we can easily solve it.
-(-1)² - (4(-1) - 6(-4)) + 9(-4)
Simplify your parentheses.
-(-1)² - (-4 + 24) - 36
-(-1)² - 20 - 36
Now, simplify your exponents.
-1 - 20 - 36
Combine -1 and -20.
-21 - 36
Now, subtract -21 from 36.
-57
Answer:
-18
)())()()()()()()( ;)
A factory costs $280,000. You forecast that it will produce cash inflows of $80,000 in year 1, $140,000 in year 2, and $220,000 in year 3. The discount rate is 12%. What is the value of the factory?
Answers
Answer:
=$339,627.36
Step-by-step explanation:
PV = FV/(1+R)^n
where
PV = Present Value
FV = Future Value
R = Rate
n = number of periods
PV
Year 1=$80,000
Year 2=$140,000
Year 3=$220,000
r=12%=0.12
Year 1:
PV=80,000 / (1+0.12)^1
=80,000 / 1.12
=$71,428.57
Year 2:
PV=140,000 / (1+0.12)^2
=140,000 / (1.12)^2
=140,000 / 1.2544
=$111,607.14
Year 3:
PV=220,000 / (1+0.12)^3
=220,000 / (1.12)^3
=220,000 / 1.404928
=$156,591.65
Value of the factory= 71,428.57 + 111,607.14 + 156,591.65
=$339,627.36
Thirteen people on a sports team show up for a game. a. How many ways are there to choose 10 players to play the game? b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?
Answers
Answer:
a)286 ways
b)1,037,836,800 ways
Step-by-step explanation:
a. How many ways are there to choose 10 players to play the game?
We have to take note of a key word here which is CHOOSE. For question a, order does not matter.
Hence, we use the combination formula. This is given as:
C(n, r) = nCr = n!/r! (n - r)!
n = 13, r = 10
13C10 = 13!/10! (13 - 10)!
= 13!/ 10! × (3!)
= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (3 × 2 × 1)
= 1716/6
= 286 ways.
b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?
For question b as well, we take note of a key word which is ASSIGN. For question b, order is very important.
Therefore, the formula we use is the permutation formula.
P(n, r) = nPr = n!/(n - r)!
n = 13, r = 10
13P10 = 13!/ (13 - 10)!
= 13!/ 3!
= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (3 × 2 × 1)
= 1,037,836,800 ways
PLEASE HELP TO BE MARKED THE BRAINLIEST
Answers
If we have line segment AB, and point C is somewhere on AB, then AC+CB = AB through the segment addition postulate.
This is the idea where basically we can glue together two straight lines to form a longer straight line. Or we can go in reverse to break up a line into smaller parts.
A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps. Design an experiment to test this claim.
Describe a sample procedure.
A) Find the average vertical leap of all the athletes in their regular shoes. Give the control group the new shoes and the experimental group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
C) Find the average vertical leap of a group of athletes in their regular shoes. Then give them each the new shoes and find their average vertical leap. Compare the before and after results.
Answers
Answer:
The correct option is (B).
Step-by-step explanation:
In this case, we need to test whether the claim made by the new brand of gym shoe is correct or not.
Claim: A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps.
So, we need to test whether the average vertical leap of all the athletes increased by 2 inches or not after using the new brand of gym shoe.
The sample procedure would be to compute the average vertical leap of a group of athletes in their regular shoes (or a different pair) and the average vertical leap of a group of athletes in their new shoes.
Compare the two averages to see whether the difference is 2 inches or not.
The experimental group would be the one with the new shoes and the control group would be the one with the different pair of shoes.
Thus, the correct option is (B).
Answer:
B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
Step-by-step explanation:
A hiker starts walking due west from Sasquatch Point and gets to the Chupacabra Trailhead before she realizes that she hasn't reset her pedometer. From the Chupacabra Trailhead she hikes for 8 miles along a bearing of N27°W which brings her to the Muffin Ridge Observatory. From there, she knows a bearing of S38°E will take her straight back to Sasquatch Point. How far will she have to walk to get from the Muffin Ridge Observatory to Sasquach Point, to the nearest tenth of a mile?
Answers
Answer:
9.05 mile
Step-by-step explanation:
From the information given :
Let represent S for Sasquatch Point
Let C represent Chupacabra Trailhead
Let M represent Muffin Ridge Observatory
The diagram for the bearing of the information given can be seen in the attached file below.
At angel C = 90° -27° = 63°
The Alternate angles are shown in the second diagram below.
In order to determine the distance she will have to walk from the Muffin Ridge Observatory to Sasquatch Point, we use the sine formula:
[tex]\mathtt{\dfrac{sin \ C }{c} = \dfrac{sin \ S}{s}}[/tex]
[tex]\mathtt{\dfrac{sin \ 63 }{c} = \dfrac{sin \ 52}{8}}[/tex]
By cross multiply
8 × sIn 63 = c× sin 52
[tex]\mathtt{c = \dfrac{8 \times Sin 63}{Sin \ 52}}[/tex]
[tex]\mathtt{c = \dfrac{7.1281}{0.7880}}[/tex]
c = 9.0458 mile
c [tex]\simeq[/tex] 9.05 mile to the nearest tenth
Beverly made a deposit of 375 into our checking account. Then she
withdraw $65. The next day, she wrote a check for $135. She had 475 before any of these transactions how much money is in her account now?
Answers
Answer:
650
Step-by-step explanation:
475+375-65-135=650
MATT plans to put concrete on a regular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete that needs is $58.07.
Answers
THIS IS THE COMPLETE QUESTION BELOW;
Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?. . [1 foot = 12 inches; 1 yard = 3 feet]. a. 0.5 feet. b. 1.5 feet. c. 3 feet. d. 6 feet
Answer:
OPTION D is correct
d)6feet
Step by step Explanation:
We were given The price of concrete as $98 per cubic yard
Price= $98 /yrd³
But 1 foot = 12 inches
1 yard = 3 feet
Square both side we have,
Then 1yrd³ = 27 ft³.
So we can use this conversion factor to convert $98 /yrd³ to per ft³ as follows
$98 /yd³) ×(1 yrd³ / 27 ft³) = $ 98/27/ft³
If we denote the width of the portion as "y"
then the volume of the rectangular portion of the driveway =
= (8 ft) (1/3 ft) x = 8y/3 ft³
But we're given The total cost of the concrete Matt needs as $58.07,
Total cost = $58.07 = (8y/3)(98/27)
y= 5.99957 ft= 6feet
Therefore, the width of the portion of the driveway is 6feet
Apply the distributive property to create an equivalent expression. ( 1 -2g +4h)\cdot 5 =(1−2g+4h)⋅5=left parenthesis, 1, minus, 2, g, plus, 4, h, right parenthesis, dot, 5, equals
Answers
Answer:
5 - 10g + 20hStep-by-step explanation:
Given three elements A, B and C related together according to the expression A(B+C), according to distributive property, the element A will be distributed to the rest of the element as shown;
A(B+C) = A(B)+A(C)
A(B+C) = AB + AC (Law of distributivity)
Given the expression according to the question (1−2g+4h)⋅5, in order to use the distributive law to find the equivalent expression, we will use the concept above as shown;
= (1−2g+4h)⋅5
= 5.(1−2g+4h)
= 5(1)-5(2g)+5(4h)
= 5 - 10g + 20h
Hence the equivalent expression using the distributive property is 5 - 10g + 20h
Answer:
5 - 10g + 20h
Explain how the tangents of complementary angles are related.
Answers
Answer:
tan(α) = 1/tan(90°-α)
Step-by-step explanation:
The tangent of one is the reciprocal of the tangent of the other.
__
In a right triangle, ...
tan = opposite/adjacent
For the two complementary acute angles in such a triangle, opposite and adjacent are swapped. That is the tangent of one is the inverse of the tangent of the other. (That inverse is also known as the cotangent.)
tan(α) = cot(90°-α) = 1/tan(90°-α)
Deshaun bought 6 bags of sugar for his restaurant. Each bag weighed 6.9 kilograms. How many kilograms of sugar did he buy total?
Answers
Answer:
41.4 kgs
Step-by-step explanation:
Take the number of bags times the weight of each bag
6 * 6.9
41.4 kgs
Answer:
41.4 kilograms of sugar
Step-by-step explanation:
its 41.4 kilograms of sugar because you take the 6 bags and multiply that by the 6.9
Donavan and Jones are randomly choosing chalices to drink from. 4 of the chalices contain purified water, 5 contain spoiled milk, and 6 contain diluted flat soda. Jones gets to choose a chalice from the remaining ones after Donavan drinks from 3 of them. If the chances of Jones choosing a chalice with purified water is then 1/3, how many of the chalices that Donavan drank out of contained purified water?
Answers
Answer:
0
Step-by-step explanation:
Chalice with purified water = 4
With spoiled milk = 5
With flat soda = 6
Probability of Jones drinking from a chalice with purified water after Donovan had drank from 3 = 1/3
Probability = required outcome / Total possible outcomes
Total possible outcomes = (4 + 5 + 6) = 15
After Donovan drinks 3 :
Total possible outcomes = (15 - 3) = 12
If the probability of Jones choosing a chalice with purified water is 1/3 then :
(Required outcome / Total possible outcomes) =1 /3
(Required outcome / 12) = 1 / 3
Required outcome * 3 = 12
Required outcome = 12 / 3
Required outcome = 4
Therefore, since initial number of chalice with purified water is 4,
4 - 4 = 0
Then Donovan did not drink from a chalice containing purified water.
Question 1(Multiple Choice Worth 5 points) (07.02 LC) Celine is playing a game at the school carnival. There is a box of marbles, and each box has a white, a green, a blue, and an orange marble. There is also a fair 12-sided die labeled with the numbers 1 through 12. How many outcomes are in the sample space for pulling a marble out of the box and rolling the die? 48 32 16 8
Answers
Answer: 48
Step-by-step explanation:
Given, A box has a white, a green, a blue, and an orange marble.
Total possible outcomes of pulling marbles = 4
There is also a fair 12-sided die labeled with the numbers 1 through 12.
Total possible outcomes of rolling the die = 12
By Fundamental counting principle , we have
Possible outcomes are in the sample space for pulling a marble out of the box and rolling the die = (Total possible outcomes of pulling marbles ) x (Total possible outcomes of rolling the die)
= 4 x 12
= 48
Hence, the correct answer is "48".
At Horatio's machining company, it takes 2 minutes to manufacture each part and 10 minutes to pack all the parts for an order. Write an expression that shows how many minutes it will take to complete an order, assuming there are x parts in an order.
Answers
Answer:
f(x) = 2x + 10
Step-by-step explanation:
Let's call this function f(x), where f(x) is time to get the order ready and x is the number of parts:
f(x) = 2x + 10 Is the expression of this function.2x is the time to manufacture all parts of the order and 10 min is the time to pack them.
Answer:
2x + 10 is the correct answer :)
What the answer question
Answers
Answer:
P = 44Step-by-step explanation:
JK = JO = 4
MN = NO = 6 ⇒ LM = 18 - 6 = 12
KL = LM = 12
NJ = NO + OJ = 6 + 4 = 10
JL = JK + KL = 4 + 12 = 16
LN = 18
P = NJ + JL + LN = 10 + 16 + 18 = 44
Multiply, if possible.
Answers
Answer:
2
3
-5
0
Step-by-step explanation:
2×0+1×2=2
2×1+1×1=3
2×-3+1×1=-5
2×-2+1×4=0
Answer:
[tex]\large \boxed{\mathrm{Option \ C}}[/tex]
Step-by-step explanation:
[tex]{\mathrm{view \ attachment}}[/tex]
If it takes B hours to walk a certain distance at the rate of 3 miles per hour, the number of hours it takes to return the same distance at 4 miles per hour is...? Will mark brainlist
Answers
Answer:
It will take 0.75B hours for the return leg
Step-by-step explanation:
Here, given that the first leg of the trip was for B hours at 3 miles per hour , we want to calculate the number of hours the return leg will take at 4 miles per hour given that it is the same distance.
Mathematically, we know that ;
Distance = speed * time
So the distance taken on the first leg of the trip would be;
Distance = 3 miles per hour * B hours = 3B miles
Now, this distance was traveled on the return leg also.
This means that the time taken here will be;
Time on return leg = distance/speed = 3B/4 = 0.75B hours
Consider the equation: 12x=13-x^212x=13−x 2 12, x, equals, 13, minus, x, squared 1) Rewrite the equation by completing the square. Your equation should look like (x+c)^2=d(x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation
Answers
Answer:
[tex](x + 6)^2 = 49[/tex]
[tex]x = 1[/tex] or [tex]x = -13[/tex]
Step-by-step explanation:
Given
[tex]12x = 13 - x^2[/tex]
Using Completing the Square
[tex]12x = 13 - x^2[/tex] ---- Add [tex]x^2[/tex] to both sides
[tex]x^2 + 12x = 13 - x^2 + x^2[/tex]
[tex]x^2 + 12x = 13[/tex]
Divide the coefficient of x by 2; then add the square to both sides
[tex]x^2 + 12x + 6^2 = 13 + 6^2[/tex]
[tex]x^2 + 12x + 36 = 13 + 36[/tex]
[tex]x^2 + 12x + 36 = 49[/tex]
Factorize
[tex]x^2 + 6x + 6x + 36 = 49[/tex]
[tex]x(x + 6) + 6(x + 6) = 49[/tex]
[tex](x + 6)(x + 6) = 49[/tex]
[tex](x + 6)^2 = 49[/tex]
Hence, the equation is [tex](x + 6)^2 = 49[/tex]
Solving further
Take square root of both sides
[tex](x + 6) = \sqrt{49}[/tex]
[tex]x + 6 = \±7[/tex]
[tex]x = \±7- 6[/tex]
This implies that
[tex]x = 7 - 6[/tex] or [tex]x = -7 -6[/tex]
[tex]x = 1[/tex] or [tex]x = -13[/tex]
HEnce, the solutions are [tex]x = 1[/tex] or [tex]x = -13[/tex]
Answer:
(x+6)^2=49 and x=−6±7
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for hours, and the second mechanic worked for hours. Together they charged a total of . What was the rate charged per hour by each mechanic if the sum of the two rates was per hour?
Answers
Answer:
The rate charged by first mechanic per hour= x =$85
The rat charged by second mechanic per hour =y = $70
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?
Solution
Let
x= hourly rate of the first mechanic
y= hourly rate of the second mechanic
Derive two equations to solve for the two unknowns
10x + 15y = 1900 (1)
x + y = 155 (2)
From (2)
x + y = 155
x=155-y
Substitute x=155-y into (1)
10x + 15y = 1900
10(155-y) + 15y =1900
1550 -10y + 15y =1900
5y =1900-1550
5y=350
Divide both sides by 5
y= 70
Substitute y=70 into (2)
x + y = 155
x + (70) =155
x=155 - 70
= 85
x= 85
The rate charged by first mechanic per hour= x =$85
The rat charged by second mechanic per hour =y = $70
