Mathematics College

If 5b = 6a + 16 and 9a = 7b - 20, then what are the values of a and b?

Answers

Answer 1

9514 1404 393

Answer:

  (a, b) = (4, 8)

Step-by-step explanation:

Writing both equations in general form, we have ...

  6a -5b +16 = 0

  9a -7b +20 = 0

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We can make a little array of the numbers in the equations:

  [tex]\left[\begin{array}{cccc}6&-5&16&6\\9&-7&20&9\end{array}\right][/tex]

Note that the first column is repeated at the end.

Now, we can "cross multiply" and form the differences of products in adjacent columns:

  d1 = (6)(-7) -(9)(-5) = 3 . . . . . . left 2 columns

  d2 = (-5)(20) -(-7)(16) = 12 . . . . . middle 2 columns

  d3 = (16)(9) -(20)(6) = 24 . . . . . right 2 columns

Then the solutions to these equations are the solutions to ...

  1/d1 = a/d2 = b/d3

  a = d2/d1 = 12/3 = 4

  b = d3/d1 = 24/3 = 8

The values of a and b are 4 and 8, respectively.

_____

Additional Comment

There are a number of ways to solve linear equations. This is similar to what you would get by doing "elimination". It is also similar to Cramer's Rule and Vedic math techniques. The number of math operations is about the same*. Once you learn the technique, it is fairly fast and requires no decision-making. My other favorite method is using a graphing calculator.

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* This method uses 6 multiplications, 3 subtractions, 2 divisions. In the general case of "elimination", where the coefficients are not "nice" (as here), you would perform 7 multiplications, 4 subtractions and 2 divisions. This method is less work when the coefficients don't cancel easily.

If 5b = 6a + 16 And 9a = 7b - 20, Then What Are The Values Of A And B?

Related Questions

plzz somone i need help plss help me​

Answers

I think is c if I’m wrong sorry

Answer:

Maybe try the last one because

Step-by-step explanation:

it is explaining about how many students does she have meaning you can easily graph this out

Find the volume of this rectangular pyramid.
Be sure to include the correct unit in your answer.

6yd,3yd,7yd,

Answers

Answer:

the volume is 42 yds

Step-by-step explanation:

multiply 6x3x7=126

divide 126 by 3

126/3=42

Which expressions is equivalent to 50c - 25? (There is more than one answer)

5 (10c-10)

5 (10c - 5)

25 (2c-1)

5 (10-5)

Answers

Answer:

C

Step-by-step explanation:

25 (2c-1)

(25 x 2c) - (25 x 1)

50c - 25

PLS ANSWER A B AND C

Answers

Answer:

B if im wrong pls correct me

Step-by-step explanation:

What is the coordinates of point A

Answers

Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis. The coordinates of a given point represent how far along each axis the point is located.

Step-by-step explanation:

Which of the following statements could be a correct step in solving this equation:

12x−7=13(x−12)


A. 12x−7=13x−12


B. 3x−42=2(x−12)


C. 3x−7=2(x−12)


D. 3x−7=2x−12

Answers

Answer:

A

Step-by-step explanation:

I think the answer is A because you have to use 13 to multiply what's in the bracket in order to collect like terms but 13 *12 won't give you 12. That's the reason why am confused


Joe ran 1 1/4 laps in 2 minutes. How many laps did Joe run on average per minute?

Answers

Answer

2.5/4

Step-by-step explanation:

If you do 1 1/4 divided by 2 that would equal 2.5/4 I hope that helps!

HELP as fast as possible plzz

-3.5u=-14

Answers

Answer:

4

Step-by-step explanation:

Answer:

u=4

Step-by-step explanation:

are we solving for "u" ??

-14/-3.5=4

u=4

Martin needs 3.25 gallons of paint for his small barn and 1.25 gallons of paint for his shed. he spends $81 on paint, how much does the paint cost per gallon?​

Answers

Answer:

$24.92, $65

Step-by-step explanation:

1. $81 divided by 3.25 = 24.9230769231 = $24.92

2. $81 divided by 1.25 = $64.8, rounded could be $65.

sorry if I'm wrong :).

Can someone please give me the answer

Answers

Answer:

it’s 3x+4 your adding the x to the 2x

Answer:

6x+8

Step-by-step explanation:

2x*2+(x+4)*2

=4x+2x+8

=6x+8

Write 3+5/10+6/100+8/1000 as a decimal

Answers

Answer:

3.568

Step-by-step explanation:

3+0.5+0.06+0.008=3.568

What is the area of this figure?

Answers

I believe the area is 66

Answer:

Area = 183

Split the shape into two and calculate the area, or something

3 * n + 2 = ?
2 * n + 7 = ?

Answers

Answer:

1.3n+2

2.2n+7

Step-by-step explanation:

for number 1.you are multiplying 3 and n which gives you 3n but 2 you cant because it dosent have a variable to times with it says plus instead of times.

and for number 2 it the same thing 2 times n equals 2n + 7 is 2n + 7 .

If this doesnt help then im sorry but this is how i know and yeah have a wonderful day.

What is the volume of this cube?

Answers

Answer:

50

Step-by-step explanation:

im not that sure sorry

Answer:

The answer is 0.125.

Step-by-step explanation:

The forumla to find volume of a cube is a3. (Let a repersent 0.5) 0.5x0.5x0.5 is 0.125

Which of the following was the immediate cause of the Sepoy Rebellion?

Answers

The immediate cause for the revolt was the introduction of the new Enfield rifle to the British Indian Army.

Answer:

Indian soldiers were forced to use pig- and cow-based cartridges in their guns.

Step-by-step explanation:

what is 2 3/4 as a improper fraction

Answers

Answer:

11/4

Step-by-step explanation:

2x4=8

3+8=11

11/4

Do 2×4+3 over 4 then simplify to get
11/4

20 points | If you're good at math, please help me with this 9th grade math, thank you <3 kinda running out of time here

Answers

Answer:

y = x^2 + 15x + 56

Step-by-step explanation:

The solutions (where the trinomial = 0) is the factors that will turn the trinomial into 010.

(x + 7)(x + 8) = 0

This means that either -7 will turn the trinomial into 0 or - 8 will.

The trinomial is

x^2 + 8x +  7x + 56 will turn the trinomial to 0.

y = x^2 + 15x + 56 when either - 7 or - 8 is put in for x.

y = (-7)^2 + 15(-7) + 56

y = 49 - 105 + 56

49 + 56 = 105

y = 105 - 105 = 0

y = (-8)^2 - 15(-8) + 56

y = 64 - 120 + 56

y = 120 - 120=  0

No other number will turn the trinomial into 0.

-4x + 21 > -3
What could x be??

Answers

Answer:

x < 6

Step-by-step explanation:

subtract 21 on both sides

-4x > -24

divide both sides by -4 and flip the sign (bc you're dividing by a negative)

x < 6

Plz help with this ok

Answers

Ben is wrong due to the fact that the combined volume of the two shaded cubes is equal to 280 and the volume of the other cube is equal to 1000.


Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts?

Answers

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

That's the answer.

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

Tim used 4 1/2 cups of oranges,3 1/2 cups of apples,and 5 1/2 cups of pears in a fruit salad.How many cups of fruit did Tim use altogether?​

Answers

Answer:

13 1/2 cups of fruit

Step-by-step explanation:

4 1/2+ 3 1/2= 8

8+ 5 1/2= 13 1/2

i hope this helps!!!

A quality-assurance worker wants to systematically sample 120 glass jars each day from a conveyor belt in a factory that puts out 3,600 jars each day. If the worker will select every kth jar, what is the best value of k for the worker to use? Enter a whole number.

Answers

Answer:

The best value of k for the worker to use is 30.

Step-by-step explanation:

Sample of 120 jars from a set of 3,600.

If the worker will select every kth jar, what is the best value of k for the worker to use?

The best case would be starting at 0 and ending at 3600, finding 120 values, which means that k is given by the division of 3600 by 120. So

[tex]k = \frac{3600}{120} = \frac{360}{12} = 30[/tex]

The best value of k for the worker to use is 30.

A flag pole casts a shadow that is 10 feet long. A nearby windmill casts a shadow that is 18 feet long. If the flag pole is 18 feet tall, how tall is the windmill, to the nearest tenth of a foot?​

Answers

Answer:

26

Step-by-step explanation:

i need my points

Answer:

26?

Step-by-step explanation:

calculate the perimeter of a quarter circle 2mm use pi=3.14​

Answers

Answer:

Step-by-step explanation:

If the radius of the circle is 2mm, the circumference is 4π mm.

Arc length of the quarter circle = π mm.

Perimeter of the quarter circle = arc length + 2 radii = 4π + 4 mm = 16.56 mm

What are the 10 perfect cubes ?

Answers

This is ten of them

what is the complementary angle of 90​

Answers

the answer would be 0

It is when two Angles add up to 90 degrees

for example 30 + 60

Logan can carry 22 pounds of jars. Each jar weighs 32 ounces. How many jars can Logan carry?

4 jars
8 jars
11 jars
22 jars

Answers

Answer:

11 Jars

Step-by-step explanation:

32 ounces = 2 pounds = 1 jar

So 22 divided by 2 = 11 jars

hope this helps

[tex]1/5(6+3+1)^{2}[/tex]

Answers

Ur answer is 20

Evaluate
6+3+1
10
1/5*10 2

1/5*100

100/5 multiple the #

20

What is 3/4 divided by 1/4

Answers

Answer:

3

Step-by-step explanation:

a group of friends go to the movies and want to order popcorn. a large bucket of popcorn is $0.50 more than a small bucket. the group of friends ordered 3 large buckets and 2 small buckets of popcorn for a total of $23.95 how much was the cost of a small bucket of popcorn and large bucket of popcorn

Answers

Answer:   $4.56 for the small one and &5.06 for the large

Step-by-step explanation:

$23.95-(3x$0.05)=$22.80

$22.80/5=4.56

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