We get that value of AC after adding AB and BC as 12 x + 20.
We are given that:
AB = 8 x + 2 and BC = 4 x + 18
We need to find AC.
For this, we will add AB and BC.
Adding AB and BC, we get that:
AB + BC = AC
Substituting the values of AB and BC in the equation which are given to us:
AC = 8 x + 2 + 4 x + 18
Combining the like terms, we get that:
AC = 12 x + 20.
Therefore, we get that value of AC after adding AB and BC as 12 x + 20.
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Calculators were purchased at $100 per dozen and sold at $30 for three calculators. What is the profit on six dozen calculators?
The profit is $
Answer:
30x100= 3000
Step-by-step explanation:
Simplify the quantity 10 minus three fourths times the square root of 16 end quantity squared plus the quantity 2 minus 7 end quantity squared.
a. 1,394
b. 1,344
c. 74
d. 24
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Simplifying the quantity 10 minus three fourths times the square root of 16 end quantity squared plus the quantity 2 minus 7 end quantity squared is: c. 74.
ExpressionThe given expression:
(10 - 3/4 × ✓16)² + (2 - 7)²
Hence,
Now let simplify the expression
(10 - 3/4 × ✓16)² + (2 - 7)²
=(10 - 3)² + (-5)²
= 7² + 5²
= 49+ 25
= 74
Therefore simplifying the quantity 10 minus three fourths times the square root of 16 end quantity squared plus the quantity 2 minus 7 end quantity squared is: option c. 74.
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it takes 50 people 256 days to build a road how long will it take 80 people
The answer is that 80 people will build the same road in 160 days.
Given that 50 people take 256 days to build a road.
And we need to find out how many days will 80 people take to build the same road.
Disclaimer: Assuming that the work done by all the people are same.
If the number of people increases, the time taken to build the road decreases in the same proportion. Clearly, the number of people varies inversely to the number of days.
Let x denote the number of days required to build the road for 80 people.
Then the ratio, 80/50 = 256/x
⇒ x = (256×50)/80 = 160
Therefore, 80 people will build the same road in 160 days.
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Triangle PQR has vertives P(2, -4), Q(4, -5), and R(7, -2). It is translated 6 units left and 3 units up to produce Triangle P'Q'R'. Complete table.
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
What are the locations of the vertices of the triangle after applying rigid transformations?
In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting point T(x, y) - Translation vectorIf we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:
P'(x, y) = (2, - 4) + (- 6, 3)
P'(x, y) = (- 4, - 1)
Q'(x, y) = (4, - 5) + (- 6, 3)
Q'(x, y) = (- 2, - 2)
R'(x, y) = (7, - 2) + (- 6, 3)
R'(x, y) = (1, 1)
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
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A flight averages 460 miles per hour. The return flight averages 500 mph because of a tailwind. The total flying time is 4 hours and 48 minutes. How long is each flight
The first flight is 2 hours and second flight is 2 hours and 48 minutes
The two distances are the same (out and back),
so set them equal.
That distance is cover by having one is (rate)(time) equal to other is (rate)(time).
Let,
One time is “x” and the other is “4.8-x.”
One average rate is 460 per hour
and the other average rate is 500 per hour.
we know , Speed = [tex]\frac{distance}{time}[/tex]
so , distance = speed × time
put in this formula we get the value of X
⇒460 x = 500 (4.8 -x)
⇒460 x = 2400 - 500x
⇒900 x = 2400
⇒x = 2.5 hours for the slower plane.
⇒4.8- x = 2.3 hours for the faster plane.
The formula speed = distance ÷ time can be rearranged, just like any other equation.
Here detail explanation about relation between speed distance and time :
The formula can be rearranged in three ways:
speed = distance ÷ time
distance = speed × time
time = distance ÷ speed
To calculate one of the variables (speed, distance or time) we need the other two.
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On September 22, 2021, the market value of the investments contained in the Martindale Balanced Fund, a mutual fund, was $39,400,000, Liabilities for the
fund were $3,940,000.
If the fund had 1,380,000 shares outstanding, calculate the net asset value per share. Round your answer to the nearest cent.
Answer:
$25.70 (nearest cent)
Step-by-step explanation:
Given:
Market value = $39,400,000Liabilities = $3,940,000Outstanding shares = 1,380,000[tex]\begin{aligned} \textsf{Net Asset Value}_{\textsf{(Per Share)}} & =\dfrac{\textsf{Fund Assets}-\textsf{Fund Liabilities}}{\textsf{Total number of Outstanding Shares}}\\\\\implies \textsf{Net Asset Value}_{\textsf{(Per Share)}} & = \dfrac{\$39,400,000-\$3,940,000}{\$1,380,000}\\\\& = \dfrac{\$35,460,000}{\$1,380,000}\\\\& = \$25.69565217...\\\\\end{aligned}[/tex]
Therefore, the Net Asset Value (NAV) per share is $25.70 (nearest cent).
The given information is,
→ x = $39,400,000
→ y = $3,940,000
→ z = 1,380,000
Formula we use is,
→ (x - y)/z
Now the net asset value per share is,
→ (x - y)/z
→ (39400000 - 3940000)/1380000
→ 35460000/1380000
→ 25.6956521739
→ ≈ $25.70
Hence, the net asset value is $25.70.
the question is in the picture below
Answer: Answer 2, Triangle A is dilated from the origin by a scale of 1/2 to obtain triangle B
Step-by-step explanation:
16. Audrey and Ginnie volunteer each
month to drive meals to elderly
people. The first month they volun-
teered, they delivered a total of 60
meals. The next month they delivered
1
33 percent more than they did the
first month. The third month they de-
livered twice as many meals as the
first two months combined. How
many meals did the two girls deliver
in the third month?
(J) 80
(K) 90
(L) 160
(M) 280
Answer:
280. Answer choice D
Step-by-step explanation:
1st month: 60 meals
2nd month: 33% more than 1st month - 80 meals
(1 + (33/100)) * 60 = (1.33)(60) = 79.8 meals (Round to 80 meals)
3rd month: 2(60+80) = 280 meals
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(M) 280
Step-by-step explanation:
The first month the girls delivered 60 meals. For the second month 133% of 60 is (60 x 1.33) 79.8 which is ~ 80 meals. 80 + 60 = 140, 140 x 2 = 280
The answer is (M) 280
A number is chosen at random from 1 to 10. Find the probability of selecting number 4 or smaller numbers
The probability of selecting number 4 or smaller numbers 2 / 5 .
Probability could be a live of the chance of an occasion to occur. several events can not be expected with total certainty. we are able to predict solely the possibility of an occasion to occur i.e. however doubtless they're to happen, using it. likelihood will direct from zero to one, wherever zero suggests that the event to be Associate in Nursing not possible one and one indicates a definite event.The likelihood formula is outlined because the chance of an occasion to happen is adequate the quantitative relation of variety|the amount|the quantity} of favourable outcomes and also the total number of outcomes.Probability of event to happen P(E) = variety of favourable outcomes/Total variety of outcomes
We have given number from 1 to 10.
The number which are smaller than four and equal to 4 = 4
Total number of outcomes = 10
Probability = 4 /10
= 2 / 5
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Give the equation of the line with a slope of - 5/7 and a y intercept of 5
Answer:
[tex]y=-\frac{5}{7}x+5[/tex]
Step-by-step explanation:
The equation of a line can be written in the form of y= mx +c, where m is the slope and c is the y-intercept. This is also known as the slope-intercept form.
Identify the value of the slope, m:
Given that the slope is [tex]-\frac{5}{7}[/tex], m= [tex]-\frac{5}{7}[/tex].
Substituting the value of m into the equation:
[tex]y=-\frac{5}{7} x+c[/tex]
Identify the value of the y-intercept:
Given that the y-intercept is 5, c= 5.
Substitute c= 5:
[tex]\bf{y=-\frac{5}{7}x+5}[/tex]
Thus, the equation of the line is [tex]\bf{y=-\frac{5}{7} x+5}[/tex].
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The winning times for the 200-meter dash can be approximated by f(x)=-0.05577x+146.2, where x is the year what is the slope of f
The slope of f is m= -0.05577.
Given : The winning times for the 200-meter dash can be approximated by f(x) = - 0.05577x+146.2 , where x is the year.
To find : The slope of f
Solution : Using slope intercept form a linear function is represented as
y = mx+b
where, m is the slope and b is the y-intercept.
We can write the function as f(x) = - 0.05577x+146.2
Comparing with slope intercept form,
m= -0.05577 and y-intercept = 146.2
Therefore, The slope of f is m= -0.05577
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Solve for x
7/8 of x is 14
Answer:
x =16Step-by-step explanation:
Solve for x
7/8 of x is 14
7/8x = 14
x = 14 : 7/8
x = 14 * 8/7
x =16
----------------
check
7/8 * 16 = 14
14 = 14
the answer is good
The sets J and I are given below.
J=(-2, 3, 4, 5, 6, 8)
I=(-2, 0, 4, 8)
Find the union of J and I. Find the intersection of J and I. Write your answers using set notation (in roster form).
The intersection is the set of all elements in both sets, so the answer is {-2, 4, 8}.
The union is the set of all elements in at least one of the sets, so the answer is {-2, 0, 3, 4, 5, 6, 8}.
Which is bigger, 16\frac{1}{6}
6
1
or 0.16? Explain your reasoning.
Answer:
1/6 is greater than 0.16
Step-by-step explanation:
0.16 as a fraction is 4/25
4/25 < 1/6
For the third week of July, Barbara Watson worked 55.50 hours. Barbara earns $10.40 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Suppose the time it takes me to drive from my apartment to campus on any given day is uniformly distributed between 16 and 20 minutes. What is the mean amount of time it takes me to drive to campus?
Question 4 options:
20 minutes
24 minutes
12 minutes
18 minutes
16 minutes
Given that the between 16 and 20 minutes driving times to the campus is uniformly distributed, the mean driving time is 18 minutes
The correct option is therefore;
18 minutes How can the mean of a uniform distribution be found?The time it takes to drive from the apartment to the campus = Between 16 and 20 minutes
The nature of the distribution of the travel time = Uniform distributionThe mean of a continuous uniform distribution between two boundaries, a and b is given by the formula;
[tex] \mu = \frac{a+b}{2} [/tex]
The mean amount of time it takes to drive to campus is therefore;
[tex] \mu = \mathbf{\frac{16+20}{2}} = 18 [/tex]
The correct mean driving time is the option;
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Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
The product of 3 and the difference of 5 and a number.
The sentence "5 is subtracted from the square of a number" represented as an algebraic expression is x² -5.
Algebraic expressions: what are they?
A group of integers or variables combined using the operations +, -, o, or constitute an expression. algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.Given,
Let the number be x and 3 is subtracted from a number.
Represent it in expression.
Step 2
3 is subtracted from a number means 3 is subtracted from x.
Here we have to subtract 3 from x. It can be represented as = x - 3
Let the number be x.
In this exercise, you're required to write an algebraic expression to represent the word problem (sentence). Also, the number would be denoted by the letter x and no need for further simplification of the algebraic expression.
Translating the word problem (sentence) into an algebraic expression, we have;
Square of a number (x) = x²
Subtracting 5 from the the square of x, we have x² -5 .
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is 1/8 equivalent to 2/12
Answer:
No
Step-by-step explanation:
Check by changing to a common denominator
Find the x- and y-intercepts of the graph of the equation. (If an
(a)
X^2-xy+4y=49
Answer:
x=±7; y=12.25.
Step-by-step explanation:
1) x-interception:
(y=0): x²=49, ⇒ x=±7;
2) y-interception:
(x=0): 4y=49; ⇒ y=12.25.
Jane and Jim spend the same amount of money today. If Jim spent 5.25 on food and rode the train three times and Jane spent 12.45 on food and rode the roller coaster twice, then how much does a token cost?
The cost of a Token from the question is; $7.2
How to solve Algebra Word Problems?
We are told that Jane and Jim spend the same amount of money today.
Now, Jim spent 5.25 dollars on food and rode the train 3 times, and Jane spent 12.45 dollars on food and rode the roller coaster twice.
Assuming cost of a token is T, the the algebraic expression formed is;
5.25 + 3T = 12.45 + 2T.
3T - 2T = 12.45 - 5.25
T = $7.2
Thus, we conclude that the cost of a Token is; $7.2
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Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations. If required enter negative values as negative numbers (to 2 decimals).
Z-score of 10 is -1.25; Z-score of 20 is 1.25; Z-score of 12 is -0.75; Z-score of 17 is 0.50; and Z-score of 16 is 0.25.
How do we calculate the Z-scores of each observation?To calculate this, we use the following notations and formulas:
Mean = (sum of the values) / n
Variance = ((Σ(x - mean)^2) / (n - 1)
SD = Standard deviation = Variance^0.5
Z-score = (x - Mean) / SD
Where;
n = number of obsrvations = 5
x = each observation
We now proceed as follows:
Mean = (10 + 20 + 12 + 17 + 16) / 5 = 15
Variance = ((10-15)^2 + (20-15)^2 + (12-15)^2 + (17-15)^2 + (16-15)^2) / (5-1) = 64 / 4 = 16
SD = Variance^0.50 = 16^0.5 = 4
Z-score of 10 = (10 – 15) / 4 = –1.25
Z-score of 20 = (20 - 15) / 4 = 1.25
Z-score of 12 = (12 - 15) / 4 = –0.75
Z-score of 17 = (17 - 15) / 4 = 0.50
Z-score of 16 = (16 - 15) / 4 = 0.25
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Determine if each statement is TRUE or FALSE.
15. LAGF and LBGE are vertical angles..
Answer:
TRUE
Step-by-step explanation:
na sa inyo na answer
Answer:
Add your questions
Step-by-step explanation:
Write the ratio as a fraction in lowest terms.
48 minutes to 3 hours
Answer: 4/15
Step-by-step explanation:
3 hours=
3*60 minutes=180 minutes
48:180=
(24*2):(90*2)=
(12*2*2):(45*2*2)=
(4*3*2*2):(15*3*2*2)=4/15
What are the possible values of x for the following functions? F(x)=2-x / x(x-1)
Answer:
[tex]x \in \mathbb{R}-\{0,1\}[/tex]
Step-by-step explanation:
The denominator cannot be 0 (since division by 0 is undefined), meaning x cannot be 0 or 1.
So, the domain is
[tex]x \in \mathbb{R}-\{0,1\}[/tex]
Marty doesn't have any money saved and he does not want to wait to buy a car . He goes to the dealership and takes out a loan for the $15,000 car . His payments will be $ 500 per month for 3 years (36 months ) . How much will Marty pay for his $ 15,000 car ?
Marty will have to pay $18,000 for his $15,000 car.
While taking out a loan, the amount taken has to be repaid along with an interest. Thus, the amount paid back by the borrower is always greater than the initial amount that the borrower gets from the lender as a loan.
Here, we are given that Marty has to pay $500 per month for 3 years to repay the loan for his $15,000 car.
Thus, for one month he pays = $500
and also we know that 1 year = 12 months
⇒ 3 years = 12(3) = 36 months
Therefore, for 36 months Marty will have to pay,
500 × 36 = 18,000
Thus, Marty will have to pay $18,000 for his $15,000 car.
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Marie is having trouble finding the answer to a math problem, so she asks her older brother for
help. He gives her a hint that the correct answer is a rational number. Assuming the hint is
accurate, which value is most likely the correct answer?
OA 1.4142135623...
OB. 2.7182818284..
OC 3.1415926535.
OD 4.1818181818...
The number 4.1818181818... is a rational number because the number is terminating. Then the correct option is D.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
Let's check all the options, then we have
A 1.4142135623..., the number is an irrational number because the number is non-terminating.
B. 2.7182818284..., the number is an irrational number because the number is non-terminating.
C 3.1415926535..., the number is an irrational number because the number is non-terminating.
D 4.1818181818..., the number is a rational number because the number is terminating.
The number 4.1818181818... is a rational number because the number is terminating. Then the correct option is D.
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Can someone pls help me with this i only have a little bit of time left pls hurry
Given that sin(3x-35)°-cos(x+20)° and x is an acute angle, find it's value
Value of x for the given data sin(3x-35)°-cos(x+20)°=0, where x is an acute angle is equal to 8.75°.
As given in the question,
Given data :
sin(3x-35)°-cos(x+20)° = 0 __(1)
As we know x is an acute angle ,
cos (90 - α)° =sinα°
⇒ sin (3x -35)° =cos (90 -(3x - 35))°
⇒ sin (3x -35)°=cos (55 -3x )° ___(2)
Substitute the value of sin (3x -35)° from (2) to (1),
cos(55 -3x)° -cos(x+20)°=0
⇒cos(55 -3x)° =cos(x+20)°
⇒55 -3x=x+20
⇒x=8.75°
Therefore, value of x for the given data sin(3x-35)°-cos(x+20)°=0, where x is an acute angle is equal to 8.75°.
The complete question is :
Given that sin(3x-35)°-cos(x+20)° =0 and x is an acute angle, find it's value.
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Which expression is equivalent to (a2/3 1/31/22
OA 7/665/6
OB. 44/32/3
Oca1/261/2
C.
OD. a4/361/6
OE.al/361/6
Answer:
E. a^(1/3)b^(1/6)
Step-by-step explanation:
You want an expression equivalent to (a^(2/3)b^(1/3))^(1/2).
Rules of exponentsThe applicable rules of exponents are ...
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
ApplicationThe given expression simplifies to ...
[tex](a^{2/3}b^{1/3})^{1/2}=a^{(2/3)(1/2)}b^{(1/3)(1/2)}=\boxed{a^{1/3}b^{1/6}}[/tex]
If you double a number and then subtract eight the result is 18. Which equation below could be used to represent the situation?
Answer: 2x - 8= 18
2x - 8=18
2x=26
x= 13