Answer:
1:12:4
Step-by-step explanation:
Let's say that George's age is x. That means that Alex's age would be x+12
Since Carl is 3 times older, Carl would be 3(x+12)
We put all those in the equation and get this:
x+ x+12 + 3(x+12)=68
2x+12+3x+36=68
5x+48=68
5x=20
x=4
George is 4 years old, Alex is 16, and Carl is 48
Divide every age by 4 to find the ratio
In order of George, Carl, and Alex:
1:12:4
Answer:
1 : 12 : 4.
Step-by-step explanation:
Let's start by assigning some variables to the names! We can use a to represent Alex, g to represent George, and c to represent Carl.
Alex is 12 years older than George, which means that a = g + 12.
Carl is three times older than Alex, which means that c = 3a.
The sum of the ages is 68, meaning that a + g + c = 68.
Since c = 3a, we can say that c = 3(g + 12), and that c = 3g + 36.
That way, we can put it all together...
(g + 12) + g + (3g + 36) = 68
g + g + 3g + 12 + 36 = 68
5g + 48 = 68
5g = 20
g = 4
Now that we have George's age, we can calculate the others!
a = g + 12
a = 4 + 12
a = 16
Now that we have Alex's age, we can calculate Carl's!
c = 3a
c = 3 * 16
c = 48
To check out work, 4 + 16 + 48 = 20 + 48 = 68. 4 + 12 = 16. 16 * 3 = 48. It all matches up!
The question asks for the ratio of George's age to Carl's to Alex's, so we can just find the ratio of g : c : a.
4 : 48 : 16
To simplify, divide all three numbers by 4.
1 : 12 : 4.
You can no longer simplify, so there is your answer!
Hope this helps!
SOMEBODY HELPPP PLEASEEEE. I don’t understand
Answer:
a) 18
b) 10
c) x^2 - 4x + 5
d) 4x^2 + 2
Step-by-step explanation:
f(x) = 4x - 2
g(x) = x^2 + 1
a) f(5) = 4(5) - 2 = 20 - 2 = 18.
b) g(-3) = (-3)^2 + 1 = 9 + 1 = 10.
c) g(x - 2)...
g(x - 2) = (x - 2)^2 + 1 = x^2 - 2x - 2x + 4 + 1 = x^2 - 4x + 5.
d) f(g(x)) = f(x^2 + 1) = 4(x^2 + 1) - 2 = 4x^2 + 4 - 2 = 4x^2 + 2.
Hope this helps!
Find the value of:[(1/4)-1 + (1/3)-2 - (1/2)-3 ] ÷ 52
Answer:
-71/624
Step-by-step explanation:
Easiest and fastest way to do this is to plug it into you calc. If you are doing it by hand, remember BPEMDAS and convert the fractions into same denominators to make adding easier.
ABCD is a rectangle. What is the value of x?
А
63 m
B
165 m
x m
C
A) 2 meters
B) 16 meters
C) 63 meters
D) 65 meters
[tex]AC^{2} = AB^{2} + BC^{2}[/tex] (Pythagorean theorem)
[tex]65^{2} = 63^{2} + x^{2} \\[/tex]
4225 = 3969 + [tex]x^{2}[/tex]
[tex]x^{2} = 4225 - 3969[/tex]
[tex]x^{2} = 256[/tex]
x = [tex]\sqrt{256}[/tex]
x = 16 meters
B) 16 meters
An Indiana corn grower has 1000 bushels of corn that are to be divided between markets in Indianapolis and fort Wayne. These two markets need at least 100 bushels and 300 bushels. Determine the system of inequalities that describes the above situation.
Find five rational numbers between 2/3and4/5
Answer:
61 / 90, 62 /90, 63 /90, 64/90, 65/90
Explanation:
2/3 = 2 x 5 / 3 x 5
= 10 / 15
4/5 = 4 x 3 / 5 x 3
12 / 15
we can find 5 rational numbers betwen 2/3 and 4/5 by multiplying them with 5 + 1 = 6
10 / 15 X 6 /6
= 60 / 90
12/ 15 X 6 /6
= 72 / 90
the rational numbers = 61 / 90 62 /90 63 /90 64/90 65/90
Answer:
31/45, 32/45, 11/15, 34/35, 7/9.
Step-by-step explanation:
The LCM of 3 and 5 is 15 so we can write 2/3 and 4/5 as:
10/15 and 12/15 so one rational number between these is 11/15.
Now 11/15 = 33/45 and 4/5 = 36/45
So 2 rationals between these are 34/45 and 35/45 = 7/9
2/3 = 30 /45 and 11/15 = 33/45
so 2 rationals between these are 31/45 and 32/45.
Which expression is equivalent to
Answer:
Option 2) [tex]x^{\frac{1}{8}}y^8[/tex]
Step-by-step explanation:
=> [tex](x^{\frac{1}{4} } y ^{16} )^\frac{1}{2}[/tex]
=> [tex]x^{\frac{1}{4} * \frac{1}{2} } * y ^{16*\frac{1}{2} }[/tex]
=> [tex]x^{\frac{1}{8}}y^8[/tex]
Triangle Help! Picture Included
Answer:
tan D.
Step-by-step explanation:
tan D = opposite / adjacent side = 5/12.
Answer:
Last Option
Step-by-step explanation:
Since we are trying to find 5/12, we use one way:
tanD = 5/12
*Edit: I don't know why the mod deleted my answer. I had the correct answer and before that I edited my answer to be correct.
Complete the point-slope equation of the line through (-1,-10) (5,2)
Answer:
Step-by-step explanation:
(2+10)/(5+1)= 12/6 =2
y + 10 = 2(x + 1)
y + 10 = 2x + 2
y = 2x - 8
One week, London earned $313.50 at her job when she worked for 15 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $647.90 ?
Answer:
31hr
Step-by-step explanation:
Marika is training for tack race. She starts by sprinting 100 yards. She gradually increases her distance, adding 4 yards a day for 21 days. Which explicit formula models this situation?
Answer:
A(n)= 100 + (n-1)4
Step-by-step explanation:
Follow the steps to finish solving the equation –3x + 18 = 7x. 1. Add 3x to both sides to isolate the variable term. 2. Divide both sides by 10. x =
Answer:
x= 9/5
Step-by-step explanation:
-3x+18= 7x18+= 10x x= 18/10x= 9/5The value of 'x' by using given steps will be 1.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ - 3x + 18 = 7x
Now,
Solve the expression by using the given steps as;
The expression is,
⇒ - 3x + 18 = 7x
Add 3x to both side,
⇒ - 3x + 18 + 3x = 7x + 3x
⇒ 10 = 10x
Divide both sides by 10,
⇒ 10/10 = 10x/10
⇒ 1 = x
⇒ x = 1
Thus, The value of x by using given steps will be 1.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
Suppose that each country currently has 90 workers and each decides to transfer some amount of labor toward its area of comparative advantage. The United States transfers 10 workers away from socks toward producing cell phones. Thailand transfers 18 workers away from cell phones toward producing socks. What will be the new total output of cell phones for both countries combined?
Answer:
I got 41000 cell phones.
Step-by-step explanation:
Step 1: I figured out the amount of each workers from 90
US Sock Production: 18 workers
Thailand Sock Production: 15 workers
US Cell Production: 27 workers
Thailand Cell Production: 30 workers
Step 2: I adjusted the workers amounts to the question's changes
US Sock Production: 18 - 10 = 8 workers
Thailand Sock Productions: 18 + 15 = 33 workers
US Cell Production: 27 + 10 = 37 workers
Thailand Cell Production: 30 - 18 = 12 workers
Step 3: Find the total amount of cell phones produced
4(1000) + 37(1000) = 41000 cell phones
*12/3 = 4 because 3 workers are needed to make 1000 cell phones
What is the parametric form of the line r = (2, -3, 0) + t(1, 0, -1)?
Answer:
d
Step-by-step explanation:
(x,y,z)=(2,-3,0)+t(1,0,-1)
(x,y,z)=(2,-3,0)+(t,0,-t)
(x,y,z)=(2+t,-3,-t)
x=2+t
y=-3
z=-t
If you don't understand, you can ask me :)
Which of the following equations is equivalent to 6.87p + 9.2 = -7.056?
use photo for reference
Answer:
The answer is the second one 687p + 920 = -705.6
Step-by-step explanation:
The decimal place in each number was shifted right 2 spots
Express as a fraction 12 1\2%
Answer:
1/8.
Step-by-step explanation:
12 1/2 %
= 12 1/2 / 100
= (25/2) / 100
= 25/200 Now 200/25 = 8 so the answer is
1/8.
Plz help me I really need it not to beg and be annoying buts its for a test.The 6th term of some arithmetic sequence is 26, and the 7th term is 30. Find its first term and the common difference. Answer: The 1st term is ; The common difference is .
Answer: The first term is 6; the common difference is 4.
Step-by-step explanation:
BRAINLIEST ANSWER
Which trigonometric ratio is correct for triangle DEF? (Hint: Use
Pythagorean Theorem first)
Sin(D)= 24/7
Tan(D)= 24/25
Cos(E)= 24/25
Sin(E)= 7/24
Answer:
/25 is the trigonometric
tan=24
Answer:
cos(e) sin(e) is the he correct ratio
Conjecture about the properties that change and the properties that stay the same when creating quadrilaterals that are not parallelograms. Check all that apply. The sum of the interior angles will still be 360°. Both pairs of opposite sides will not be parallel. Both pairs of opposite sides will not be congruent. The diagonals will not bisect each other.
A quadrilateral is a four sided shape with two diagonals that bisects each other. The sum total of the interior angles is always 360° for any quadrilateral no matter the shape of the quadrilateral.
It must be noted that both pairs of opposite sides of some quadrilaterals are equal e.g Parallelogram while some are not e.g Trapezium, rhombus, trapezoid etc.
When creating quadrilaterals that are not parallelograms, the following property of such quadrilateral will therefore remains the same.
• The sum of the interior angles will still be 360°.
The following properties will change when creating quadrilaterals that are not parallelograms.
• Both pairs of opposite sides will not be parallel. e.g Trapezoids and rhombus
• Both pairs of opposite sides will not be congruent (will not be the same)
Answer:
Options A and C are correct.
- The sum of the interior angles will still be 360°.
- Both pairs of opposite sides will not be congruent.
Step-by-step explanation:
Complete Question
alyssamonae02
04/20/2020
Mathematics
Middle School
+5 pts
Answered
Conjecture about the properties that change and the properties that stay the same when creating quadrilaterals that are not parallelograms. The new quadilateral has angles
Angle LMN = 85°
Angle MNO = 99°
Angle NOL = 81°
Angle OLM = 95°
Check all that apply.
- The sum of the interior angles will still be 360°.
- Both pairs of opposite sides will not be parallel.
- Both pairs of opposite sides will not be congruent.
- The diagonals will not bisect each other.
Solution
A sketch of the new quadilateral is provided in the attached image.
Checking the statements one at a time.
- The sum of the interior angles will still be 360°.
The sum of interior angles for all four sided plane figures is 360°, hence, the new quadilateral too, although, not a parallelogram anymore, will still have interior angles that sum up to 360°. So, this is a statement that doesn't change with change in figure from parallelogram to other quadilaterals.
- Both pairs of opposite sides will not be parallel.
We cannot tell if this is true just from the information on the angles provided.
- Both pairs of opposite sides will not be congruent.
This is evident as one of the condition for opposite sides to be congruent is for opposite angles too to be equal. None of the opposite angles are equal, hence, this statement is true too.
- The diagonals will not bisect each other.
This also isn't evident from the limited information provided. So, we cannot select it as a correct statement.
Hope this Helps!!!
a2 - ab – ac + bc
2 how do you factorize it?
Answer:
[tex]a2 + bc - ac - ab[/tex]
cot(45-A)=tan2A+sec2A
Answer:
cot(45 -A) = cot(90 - (45 + A)) = tan(45 + A) = tan2A + sec2A
Step-by-step explanation:
cot(45 -A) = tan2·(A) + sec2·(A)
We have;
tan2(A) + sec2(A) = sin2(A)/cos2(A) + 1/cos2(A) = (sin2(A) + 1)/cos2(A)
= (sin²(A) + cos²(A) + 2·sin·(A)cos(A))/(cos²A - sin²A)
= (sin(A) + cos(A))²/((cos(A) -sin(A))(cos(A) +sin(A)))
= (sin(A) + cos(A))/((cos(A) -sin(A)))
= (cos(A)(1 + sin(A)/cos(A)))/(cos(A)(1 - sin(A)/cos(A)))
= (1 + tan(A))/(1 - tan(A))
= (tan 45 + tan(A))/(1 - tan(45)·tan(A)) = tan(45 + A)
cot(π/2 - x) = tan(x)
= cot(π/2 - (45 + A)) = tan(45 + A)
π/2 = 90°
= cot(90 - (45 + A)) = tan(45 + A)
cot(45 - A) = tan(45 + A) = tan(2A) + sec(2A).
I need help badly please
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the SUBTRACTION.
so here we are going to use the BODMAS Rule,
Answer is -11
Answer:
Step-by-step explanation:
Can do skmeone help me
You are coordinating the construction of a shelter for homeless people. A large number of college students and members of a religious organization have signed up as volunteers for constructing the shelter. About 30% of these volunteers are skilled, but the rest are not. It is estimated that the total number of man-hours required to complete the construction of the shelter is 1200—if all volunteers are skilled. Three times as many unskilled volunteers are required to complete any job compared to skilled volunteers. The average number of hours a skilled volunteer is available is 10/week while unskilled volunteers are available for 15 hours every week.
Explanation:
The plan outlined here makes nearly best use of available resources and job constraints. It results in job completion in about 12 weeks, or 3 months.
__
For simplicity, we choose to work 5 hours per day, 5 days a week. Each skilled volunteer will complete their weekly 10 hours by working 2 days. Each unskilled volunteer will complete their 15 hours by working 3 days. Some volunteers will work an "interrupted" schedule that consists of non-consecutive work days. The purpose of this is to provide compliance with job site limitations, volunteer hour limitations, and to maximize continuity of communication as the job progresses.
A weekly schedule along these lines is shown in the attachment. It has 2 skilled volunteers and 6 or 7 unskilled volunteers on site each day. The ratio of skilled to unskilled volunteers is 31% : 69%. Each works the maximum number of hours for their skill level.
The net result is that 50 skilled hours and 165 unskilled hours are worked each week.
__
We assume the wording "three times as many unskilled volunteers are required to complete any job compared to skilled volunteers" means that 3 unskilled hours are equivalent to 1 skilled hour. (An alternative interpretation is that 45 hours of unskilled labor is equivalent to 10 hours of skilled labor.)
Using this assumption, job completion occurs at the equivalent rate of ...
50 +165/3 = 105 . . . equivalent skilled hours per week
The total job requirement of 1200 skilled hours can be met in 12 weeks' time, well within the 6-month desired completion period. (Even using the alternate interpretation of labor equivalent, the job can be done in 14 weeks.)
__
In any given week, the 5 skilled volunteers are designated s1–s5, and the 11 unskilled volunteers are u1–u11. The days they're scheduled to work are identified by the weekday labels M, T, W, T, F. Skilled volunteer s1 works only Monday and Friday, and is responsible for week-to-week tie-in. Unskilled volunteers u2, u4, u7, u9 get two (2) days off in the middle of each week.
a square has a perimeter of 36cm2. what is the area of it?
Answer: 81
Step-by-step explanation:
We know that to find the area of a square you have to square the side length.
So since we know that he area is 36 cm square, then we will find the square root of 36.
36/4= 9 Now we know that the side length is 9 and a square has four sides which are all equal. The perimeter is the distance around the shape.
So just multiply 9 by 9 to find the area
9*9 = 81
Which values for e have the same reference angles?
Hey there! :)
Answer:
Choice 4: π/4, 3π4, 7π/4
Step-by-step explanation:
For the values of θ to have the same reference angles, the denominators of the radians must be the same. Therefore:
Choice 1: π/6, π/3, 5π/6 - incorrect. π/3 will have a different reference angle as it has a denominator of 3.
Choice 2: π/3, 5π/6, 4π/3 - incorrect. 5π/6 will have a different reference angle as it has a denominator of 6.
Choice 3: π/2, 5π/4, 7π/4 - incorrect. π/2 will have a different reference angle.
Choice 4: π/4, 3π4, 7π/4 - correct. All of these radians contain the same denominator, and will each have the same reference angles of π/4.
how many miles are in 10,560 yards?
1 mi. = 1,760 yds.
10,560 yds. = ? mi.
Answer:
6 mi
Step-by-step explanation:
10560 yds ÷ 1760 yds = 6 mi.
Answer: 6 miles
Step-by-step explanation:
1 mile = 1,760 yds.
Then 10,560/1,760
= 6
Therefore, 10,560 yards is equal to 6 miles
Which is a better deal? Three movie tickets for 18 dollars or 8 movie tickets for 42 dollars? How do you know? How much money do you save per ticket with the better deal?
Answer:
$42 for 8 tickets
Step-by-step explanation:
To tell which is the better deal you need to find out how much each ticket costs per scenario
$18 for 3 tickets you will need to do 18/3 which will give you $6 a ticket
$42 for 8 tickets you will need to do 42/8 which will give you $5.25 a ticket
$42 option is cheaper per ticket so it is therefore the better option.
pls answer asap i need this answer quick plus the full explanation #8
please help easy time table consumer math <3
Uptown Tickets charges $7 per baseball game tickets plus $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Show your work and explain your thinking in words.
Answer:
No it is not because it is only once when you get the fee
Step-by-step explanation:
So if you look at it, first of all there is not multiplication going on, so there are not ratios, second when there is only once that the fee added no matter to the amount of tickets, it means no propotion
Please find x: x−5=11−3x
Answer:
x−5=11−3x
Group all the constants at one side
That's
x + 3x =11 + 5
4x = 16
Divide both sides by 4
4x/4 = 16/4
x = 4
Hope this helps you
Answer:
x=4
Step-by-step explanation:
x−5=11−3x
take care of all the variables
you want to put the variables on one side and the numbers on the other
x−5=11−3x
+3x +3x
4x-5=11
+5 +5
4x=16
÷4 ÷4
x=4
hope this helps :)