If a, b and c are positive integers for which (a,b,c) is the only
ordered triple such that 6a +9b + 20c = 61, then what is
a+b+c?
If a, b, and c are all positive integers and 6a + 9b + 20c = 61, then right away you know c < 3, because if c = 3, then 20c = 60, and there are no solutions for a and b.
So consider two cases:
• If c = 2, then we're left with 6a + 9b = 21.
• If c = 1, then 6a + 9b = 41.
We have gcd(6, 9) = 3, but 41 is prime and 3 does not divide 41. So we throw out the second case.
This leaves us with 6a + 9b = 21. Notice that if a = b = 1, then 6a + 9b = 15. Add 6 to both sides to get 21. So a = 2, b = 1, and c = 2, and hence a + b + c = 5.
g A circle is a special case of an ellipse. Explain how a circle is different from other ellipses.
Answer:
Main difference between circle & ellipse
Step-by-step explanation:
Circle is a line forming a close loop, all points on the loop line are at equal distance from the centre, that distance is called Radius. Eg : Wheel
Ellipse is also a close loop line, such that distance of locus of all points on the plane to two fixed points (foci) always sum up to same constant. Eg : Orbits of planets
Cricle is the round shape entity in which it contains only radius and double of radius is diameter Thus below explanation is the answer to the Question
Explanation:
Cricle is the most rounded shape. Its different from ellipse because it has the radius, chord and diameter.cricle can be drawn easily with compass and ellipse is oval shape.cricle contains two types perimeter cricle and normal cricle. Ellipse has also two types partial ellipse and normal ellipse.Cricle does not have major and minor axis length both are different.Thus we conclude that cricle is totally different from ellipse
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Jared bought a cell phone for $42, Juanita spent 1 1/2 times as much how much did she spend
answer:
Juanita spent 1 1/2 times as much as Jared, how much did she spend?
$63
explanation:
one and a half of 42 is: 63
so,
the answer is Juanita spent $63!
Juanita paid $63 for the phone, which is equal to 3/2 of what Jared paid while buying the phone.
What is the definition of a mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.How are mixed fractions written?Follow these procedures to convert an incorrect fraction to a mixed number:
Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.Given: Jared spent $42 on a cell phone.
We need to determine 1 and 1/2 which is 3/2 of total amount spent by Juanita.
So,
42(3/2) = $63
Therefore, Juanita spent $63 which is 3/2 amount spent by Jared in buying the cell phone.
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Which of the following cities does NOT rely on lumber for its economy?
Given a 45-45-90 triangle with the hypotenuse measuring 5√7 feet. Which is the exact measure of each leg?
Eliza walked 1 1/2 miles in 2/3 of a hour. what is her walking rate in miles per hour?
Write the slope-intercept form of the equation for
each graph described.
Line passing through (-2,-8) and (9,-8)
Answer:
y=-8
Step-by-step explanation:
First find the slope which is rise over run which equals (y2-y1)/(x2-x1)
(-8-(-8))/(9-(-2))
(-8+8)/(9+2)
0/11
slope = 0
Now you have the slope of 0. You can plug in one of the given point (x,y) to find b
-8=0(9)+b
-8=b
Combine everything
y=0x-8
y=-8
is 13.48 irrational or rational?
Answer:
It is irrational
Step-by-step explanation:
Rational numbers do not have decimals.
15 men can dig a ditch in 10 days, how many day
Will 10men take working at the same rate
Answer:
If 10 men dig a ditch in 12 days .
Total man-days required to dig the ditch
= 10 men × 12 days
= 120 man-days
how long would 15 men take to dig it?
No of days required to finish the job by 15 men
= 120 men-days / 15 men
= 8 days
Answer: 8 days will be required to finish the job by 15 men
Step-by-step explanation:
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Determine wheather the given lines are parallel or not. Write the reasons .
Answer:
yes it is parallel because the alternate interior angles are equal
emilio worked for 19.5 hours he earned 497.25 how much did he earn per hour?
Answer:
25.5 per hour
Step-by-step explanation:
497.25/19.5
Answer:
497.25 devided by 19.5= $25.5 per hour
Step-by-step explanation:
I only have 30 minutes left
Answer:
what is the question?
Step-by-step explanation:
U only posted a picture of a half paragraph
A scale drawing of a building needs to be made using the scale 1 in = 230 ft. How tall will the building in the scale drawing be if the building is 1380 ft tall?
What similarity rule can be used to prove the triangles are similar . plz help
Answer:
SAS
Step-by-step explanation:
Explain the phrase conservation of energy and provide an example.
Answer:
Conservation of energy, principle of physics according to which the energy of interacting bodies or particles in a closed system remains constant. ... For example, when a pendulum swings upward, kinetic energy is converted to potential energy.
Step-by-step explanation:
2 points 5. What property is used to get from Step 1 to Step 2? * Step 1 : 28x + 10 = 66 Step 2: 28x = 56
Answer: subtraction property of equality
Step-by-step explanation:
How many solutions does this equation have
2x + 1 = 2x – 1
Graph the line that passes through the points (-5,2) and (6,2) and determine the equation of the line.
Answer:
y = 2
Step-by-step explanation:
....................
There are 16 boys and 20 girls in a class. What part of the class is boys? What part girls?
Answer:
girls 4/9 or (Decimal: 0.444444) percent is 44.4%
boys 5/9 or (Decimal: 0.555556) percent is 55.5%
An ordered pair that satisfies all the equations in a linear system of equations is called a(n) __________ of the linear system.
Answer:solution
Step-by-step explanation:
An ordered pair that satisfies all the equations in a linear system of equations is called a: solution of the linear system.
A linear function is a function that has a positive relationship between its variables.
Hence, an increase in one variable (input variable) causes an increase in the other variable (output variable) because the variables are directly proportional.
Mathematically, the graph of a linear function is a straight-line and its slope is always constant.
On a related note, a linear system of equation is an algebraic equation of the first order with two variables and each of its term having an exponent of one.
Generally, a system of linear equations in two variables must have at least two solution.
In conclusion, a solution of the linear system is an ordered pair that satisfies all the equations in a linear system of equations.
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Grace is measured for her annual check up. She is 28 1/5 inches tall. Last year she was 25 3/5 inches tall. How much did she grow in one year?
Answer:
2 3/5 inches in a year
Step-by-step explanation:
28 1/5 - 25 3/5 = 141/5 - 128/5 = 13/5 = 10/5 + 3/5 = 2 + 3/5 = 2 3/5
Where is the vertex of f(x) = -2x - 3| +6.4?
Which of the following statements describes the value of the expression 35 – 2x, when x = 6?
Answer:
35-2(6)
= 23
Prime number
Step-by-step explanation:
Answer:
23 . It is a prime number.
Step-by-step explanation:
[tex]35 - 2x \\ x = 6 \\ \\ 35 - 2(6) \\ = 35 - 12 \\ [/tex]
Simplify
[tex]23[/tex]
where does 17 lie between
Which number line shows 1/3 and its opposite
PLZZ ANSWER THE QUESTION
Answer:
c
Step-by-step explanation:
y = mx + b
”m” is the slope, so the slope is -2
”b” is the y - intercept, so the y - intercept is (0 , 1)
A taxi cab in Myrtle Beach charges $2 per mile and $1 for every person. If a taxi cab ride for two people costs $12 how far will the cab travel?
Answer:
5 miles
Subtract the 1 dollar for each person from 12. You get ten, and divide ten by two, which is 5
Shelley and her friend are working together on a group homework assignment. Shelley has
completed 2/12 of the problems and her friend has completed another 9/12 of them.
Together, what fraction of the problems have they completed so far?
Answer: The answer is 11/12 problems
Step-by-step explanation:
You add 2/12 + 9/12 which gives you a result of 11/12
Find mWYZ as well Find mACB please help with both. Thank you every much! Triangles, Need help, right now I’m does adding more stuff so it can stop saying 20 characters.
Answer:
m<WYZ = 23°
m<ACB = 87°
Step-by-step explanation:
Problem 1: Find WYZ
Given,
m<WVX = (3x - 7)°
m<VYZ = (16x - 3)°
∆WYZ ~ ∆WVX, therefore:
m<WYZ = m<WVX (corresponding angles of similar triangles are congruent)
m<WYZ = (3x - 7)° (substitution)
Create an equation to find the value of x.
m<WYZ + m<VYZ = 180° (linear pair)
(3x -7)° + (16x - 3)° = 180° (substitution)
Solve for x
3x - 7 + 16x - 3 = 180
Add like terms
19x - 10 = 180
Add 10 to both sides
19x - 10 + 10 = 180 + 10
19x = 190
Divide both sides by 19
19x/19 = 190/19
x = 10
m<WYZ = (3x - 7)
Substitute x = 10
m<WYZ = 3(10) - 7 = 30 - 7
m<WYZ = 23°
Problem 2: Find m<ACB
Given,
m<A = 62°
m<AED = (11x - 2)°
m<B = (6x + 13)°
∆ADE ~ ∆ACB, therefore:
m<AED = m<B (corresponding angles of similar ∆s are congruent)
(11x - 2)° = (6x + 13)°
Solve for x
11x - 2 = 6x + 13
Collect like terms
11x - 6x = 2 + 13
5x = 15
Divide both sides by 5
5x/5 = 15/5
x = 3
m<ACB + m<B + m<A = 180° (sum of ∆)
m<ACB + (6x + 13) + 62° = 180° (substitution)
Plug in the value of x and solve
m<ACB + (6(3) + 13) + 62° = 180°
m<ACB + (6(3) + 13) + 62° = 180°
m<ACB + (18 + 13) + 62° = 180°
m<ACB + 31° + 62° = 180°
m<ACB + 93° = 180°
Subtract 93 from both sides
m<ACB = 180° - 93°
m<ACB = 87°
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