Mathematics College

find the solution of
2x - 2y = -20 and -2x + 4y = 14

Answers

Answer 1
We will use the elimination by addition/subtraction method to solve for y:

Given   2x - 2y = -20 and -2x + 4y = 14, add the second equation to the first:

 2x - 2y = -20 
 -2x + 4y = 14
----------------------------------------------
          2y   = -6.  Solving for y:  y = -3.

Find x by subst. y=-3 into either of the given equations.

If we choose the first equation, then it becomes 2x - 2(-3) = -20

Solve this for x:  2x + 6 = -20, or 2x = -26, or x = -13.

The solution is (-13,-3).

Related Questions

please help me solve the problem 3 \sqrt[5] 3\sqrt[100]

Answers

3 X squareroot (10 X 100) = 3X (10) X squareroot (10) = [ where the squareroot of 100 is 10] 30 X squareroot (10) = 30 X squareroot (2 X 5) = [where the squareroot of 2 is 1.414] 30 X (1.414) X squareroot (5) = 94.85

how do you Factor this problem 2x^3+4x^2-4x

Answers

Factor out the gcf
2x(x^2+2x-2)

The inner binomial can no longer be factored.
Final answer: 2x(x^2+2x-2)
hello : 
 2x^3+4x^2-4x =  2x (x²+2x - 2)

I need help. Suppose angle ABC equals 110. What is angle DBC? Would it be 70?

Answers

now, notice the "tickmarks" on the angles, that means those two angles are equal, now if ∡ABC is 110, then the remaining is 70, 180 - 110, and if you subtract the 70 from 110, what's left is ∡DBC.

How can I rename 82 thousands?

Answers

82,000. hope that helped
Final answer:

82 thousands can be renamed as 8 ten thousands and 2 thousands, or as 0.082 hundred thousands in the decimal system.

Explanation:

Renaming 82 thousands means expressing this amount in another unit of place value. In the standard decimal system, the next unit larger than thousands is ten thousands. The digit in the ten thousands place represents the number of ten thousands in that number. If you have 82 thousands, this equals 8 ten thousands and 2 thousands, because 82 divided by 10 equals 8 with a remainder of 2. Therefore, 82 thousands can be renamed as 8 ten thousands and 2 thousands. Similarly, 82 thousands can also be expressed as 0.082 hundred thousands, as 82 divided by 1000 equals 0.082.

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What is 0.68 written as a slimplifed fraction

Answers

0.68 = 68/100

68/100 simplest form is 17/25

hope this helps
.68 into a fraction would be 68/100.
To simplify, for starters, divide both sides by 2.
You get 34/50.
Divide by 2 again, because it can still go further.
You get 18/25
You can look at this different ways, try to factor in different numbers, but this is its lowest form.
Your answer is 18/25

Select the correct numeral form of this number written in scientific notation. 5.0 × 10^10 0.000 000 000 5 5,000,000,000 50,000,000,000 500,000,000,000

Answers

10^10=10,000,000,000
5.0 × 10,000,000,000 in scientific notation is 50000000000

Answer:

50,000,000,000.

Step-by-step explanation:

It wouldn't be 5,000,000,000 or 500,000,000,000 or 0.000 000 000 5.

30000 is blank times as much as 30

Answers

1000 is the answer !
30000 is exactly 1000 as much as 30

Which is a correct classification for the triangle? equiangular triangle obtuse triangle acute triangle right triangle Triangle with two angles labeled 22 degrees and 63 degrees

Answers

None of the classifications.  22 + 22+ 63 = 107 degrees but a triangle mus t have 180 degrees.

Answer:

The triangle is obtuse triangle.

Step-by-step explanation:

Given two angles of triangle labelled as 22° and 63°. we have to classify the triangle.

Let the third angle be x°

By angle sum property of triangle,

22°+63°+x=180°

⇒ 85°+x=180° ⇒ x=95°

An equiangular triangle is a triangle where all interior angles are equal.          

An obtuse triangle is a triangle in which one of the angles is obtuse angle.

An acute triangle is a triangle have all three angles acute.

For right triangle one angle must be of 90°.

Hence, one angle of the triangle is 95° which is obtuse i.e greater than 90°

∴ Given triangle is obtuse.

Productive use of machinery on a farm made it possible to decrease the number of tractors by 12 how many tractors does the farm have now if it used to have 1.5 times more

Answers

So first off, the answer to this is 24 now think of x as the  real or original sum or amount, also y as the new sum or amount.
y * 1.5 is x, and y+12 is x. Now flip that to figure out what is y, also which is what we need, and you have x/1.5 = y as well as x-12 = y. Use the equal values method and make an equation x/1.5=x-12. solve this equation to get x, which is 36. to figure out the new amount, y, you need to minus 12, which can help you get the answer which is 24.

simplify 6/5 plus 10.35

Answers

6/5 = 1 1/5 or 1.20

1.20 + 10.35 = 11.55

hope this helps

if you want fraction

6/5 + 10.35

6/5 + 10 35/100

120/100 + 10 35/100

10 155/100

11 55/100 is your answer

hope this helps
6/5+10.35=12/10+10 35/100=120/100+10 35/100=1 20/100+10 35/100=11 55/100

please
work out -7--9

Answers

-7--9
= -7 + 9
therefore = 2

A popular brand of running shoes costs a local store $68 for each pair. If the store sells the shoes for $119, what is the percent of increase for the price?

Answers

Answer:

51/68 * 100

.75 * 100

75%

.


Step-by-step explanation:

That is, there was a 75% increase in the price


there was a 75% increase in the price.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100.

here, given that,

A popular brand of running shoes costs a local store $68 for each pair.

If the store sells the shoes for $119

i.e. increase = $51

so, the percent of increase for the price

=51/68 * 100

=.75 * 100

=75%

That is, there was a 75% increase in the price

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Solve the formula for the specified variable
V=BMU for B

Answers

The answer is V / MU = B. 

Substitute the values of x and y into the expression -3x 2 + 2y 2 + 5xy - 2y + 5x 2 - 3y 2. Match that value to one of the numbers.

1. x = 2, y = -1 A.-1
2. x = 0, y = 2.5 B.14
3. x = -1, y = -3 C.-11.25
4. x = 0.5, y = -1/10 D.9.17
5. x =3/3 , y =2/5 E.0.44
6. x = √2, y = √2 F. 1.665

Answers

for x = 2 and y = -1

-3x²+2y²+5xy-2y+5x²-3y² ⇒ Simplify by collecting like terms
2x² - y² + 5xy -2y ⇒ then substitute the given value
2(2)² - (-1)² + 5(2)(-1) - 2(-1)
2(4) - (1) + 5(-2) + 2 
8 - 1 - 10 + 2
-1

Option 1 matches with option A
-----------------------------------------------------------------------------------------------------------

Given x = 0 and  y = 2.5
Substitute into 2x² - y² + 5xy -2y to get:

2(0)² - (2.5)² + 5(0)(2.5) - 2(2.5) = 0 - 6.25 + 0 - 4.5 = -11.25

Option 2 matches with option C
------------------------------------------------------------------------------------------------------------

Given x = -1 and y = -3
Substitute into 2x² - y² + 5xy - 2y, we obtain:
2(-1)² - (-3)² + 5(-1)(-3) - 2(-3) = 14

Option 3 matches with option B
-----------------------------------------------------------------------------------------------------------------

Given x = 0.5 and y = -1/10
Subsitute into 2x² - y² + 5xy - 2y, we obtain
2(0.5)² - (-1/10)² + 5(0.5)(-1/10) - 2(-1/10) = 0.44

Option 4 matches with option E
--------------------------------------------------------------------------------------------------------------

Given x = 3/4 and y = 2/5
Substitute into 2x² - y² + 5xy - 2y, we obtain
2(3/4)² - (2/5)² + 5(3/4)(2/5) - 2(2/5) = 1.665

Option 5 matches with option F

----------------------------------------------------------------------------------------------------------------

Given x = √2 and y= √2
Subsitute into 2x² - y² + 5xy - 2y, we obtain:
2(√2)² - (√2)² + 5(√2)(√2) - 2(√2) = 9.17

Option 6 matches with option D


                                           




HELP ASAP, WILL GIVE BRAINLIEST:

Given two angles that measure 50 degrees and 80 degrees and a side that measures 4 feet, how many triangles, if any, can be constructed?

Answers

Can 2 sides be 4 feet because given those angles you'd have to make an isosceles triangle (where 2 sides are the same length). If so, id say 2 triangles because the 4 ft side could be one of the congruent sides or the base side. If you cant use it for 2 sides, just 1 triangle can be made
Angle 1 = 50°

Angle 2 = 80°

Angle 3 = x°

The sum of the interior angles of a triangle is 180°

50 + 80 + x = 180

130 + x = 180

x = 180 - 130

x = 50°

Hence, angle 3 = 50°.

Now, we see that two angles of the triangle are equal, hence, the triangle that will form will be an isosceles triangle.

An isosceles triangle has two equal sides whose opposite angles are equal.

So, there could be a chance that two sides of the triangle are 4 ft in length.

One day, after shopping at a department store, Lenny discovered that he only havd $13 left in his wallet. He had entered the store with $81 in his wallet. Which of the equations below could be used to fined out how much money Lenny spent(x)? A. 81-x=13. B.81+13=x. C.x+81=13. D.x-81=13

Answers

A is the correct answer

using long division to divide 3x^4-2x^3+x-1 by x^2-x-2

Answers

check the picture below.

recall to put the dividend as well as the divisor in descending order, and to include any missing terms before the constant.

A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)

A.452.16 cm3

B.840.54 cm3

C.1,055.04 cm3

D.1,456.96 cm3

Answers

Ok so the end equation here is going to be VCy-VCo=
air space. So we need to find the volume of the cone and the volume of the cylinder.

Lets start with the volume of the cylinder since its easiest. The volume of a cylinder is Pi*r^2*h = Volume.
We already know that the radius is 5 and the height is 16 so lets plug them in and solve. 3.14*5^2*16=1,256

Now lets solve to find the volume of the cone. Now this ones a bit harder, the equation is: Pi*r^2*(h/3)= Volume.
The radius is 4 and the height is 12, so now just solve! 3.14*4^2*(12/3)=201

Now we just need to subtract the Volume of the cylinder from the volume of the cone. 1,256-201=1,055

If you have any questions just ask!

What is the mean and median for the length of 20.3 12.5 7.6 13.9 9.2 21.7 7.6 17.5 15.6 14.1

Answers

first list numbers in order
  7.6
  7.6
  9.2
12.5
13.9
14.1
15.6
17.5
20.3
21.7

find mean (the average number of all numbers listed) by adding everything(140) then dividing how many numbers there are(10):
140 divided by 10=14
mean=14

find median (literally the middle number in the set given):
but since there's two middle numbers (13.9 & 14.1), we find the mean (aka the average) of those numbers
28 divided by 2=14
median=14
Answer:

Mean = 14

and Median = 14

Step-by-step explanation:

We are given a data set as:

  20.3   12.5   7.6   13.9   9.2   21.7   7.6   17.5   15.6   14.1

there are a total of 10 data points.

Now, the mean of these data points is the average of the data set.

i.e.

[tex]\text{Mean}=\dfrac{\text{Sum of data points}}{\text{Number of data points}}[/tex]

i.e.

[tex]\text{Mean}=\dfrac{20.3+12.5+7.6+13.9+9.2+21.7+7.6+17.5+15.6+14.1}{10}\\\\\text{Mean}=\dfrac{140}{10}\\\\\text{Mean}=14[/tex]

We know that median is the central tendency of the data and it always exist in the middle of the data set.

Firstly we arrange the data points in the increasing order as follows:

7.6    7.6    9.2    12.5  13.9    14.1   15.6    17.5    20.3    21.7  

Now, we know that the median of the data exist in between 13.9 and 14.1

i.e.

[tex]\text{Median}=\dfrac{13.9+14.1}{2}\\\\\text{Median}=\dfrac{28}{2}\\\\\text{Median}=14[/tex]

a driveway is 40 yards long. About how many meters long is it

Answers

40 yards is 37 meters(rounding up)

Answer:


Step-by-step explanation:


Equivalent decimal for 67/100

Answers

134/200 is a equivalent fraction
The equivalent decimal would just be 0.67.

So since 100/100 = 1.00, then 67/100 would have to be 0.67.

Which statement explains why the perimeter of the rectangle can be found using l + w + l + w or 2l + 2w?

Answers

BOTH    they both are correct bc they both state the same thing     perimeter is both length+ both width's so l+l+w+w=2l+2w

a rectangle has a perimeter,p, length,l, and width,w. which of the following represents l in terms of p and w?

Answers

P = 2 (l + w)
l = length
w = width

so
l + w = P/2
l = P/2 - w
Final answer:

To find the length (l) of a rectangle in terms of the perimeter (p) and width (w), use the formula l = (p - 2w) / 2.

Explanation:

To find the length (l) of a rectangle in terms of the perimeter (p) and width (w), we can use the formula for the perimeter of a rectangle, which is given by:



p = 2l + 2w



Now, solve the equation for l by subtracting 2w from both sides:



p - 2w = 2l



Finally, divide both sides by 2:



l = (p - 2w) / 2

Audryn left a $12 tip on a $68.73 restaurant bill. What percent tip did she leave? Round to the nearest tenth of a percent.

Answers

so, if we take 68.73 to be the 100%, what is 12 in percentage off of it?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 68.73&100\\ 12&p \end{array}\implies \cfrac{68.73}{12}=\cfrac{100}{p}\implies p=\cfrac{12\cdot 100}{68.73}[/tex]

seems Audryn is being generous, she probably got the silverware and the maple leaves tablecloth.

use the formula P=2l+2w to find the length l of a rectangular lot if the width w is 45 feet and the perimeter P is 240 feet

Answers

240=2l+2(45) solve for l 
240=2l+90   240-90=150/2=75

What is the scale factor of 3,6 and 4.5, 9

Answers

To determine scale factor, we have to see what the common factor we multiply each term by in order to get the other two terms. To do this, we have to divide the corresponding values: 4.5/3 = 1.5. 9/6 = 1.5. Thus, since both pairs of numbers produced the same factor, it is 1.5
Final answer:

The scale factor between the numbers (3, 6) and (4.5, 9) is 2, since the second number in each pair is twice as large as the first number.

Explanation:

The scale factor is a ratio that describes how to enlarge or reduce the dimensions of an object to create a new object that is similar to the original. To figure out the scale factor between two similar figures, we calculate the ratio of any two corresponding lengths in the figures.

As per the student's question:

For the pair of numbers (3, 6), the scale factor can be calculated by dividing 6 by 3, which gives us a scale factor of 2.For the pair of numbers (4.5, 9), dividing 9 by 4.5 gives us a scale factor of 2 as well.

In each case, the corresponding lengths in the second object are twice those in the first, meaning you can multiply the dimensions of the first figure by 2 to get the dimensions of the second figure.

Tasha has 12 minutes. She wants to jump rope for 8 minutes and play tag for 5 minutes will tasha have enough time

Answers

No She will not because 8+5=13 minutes

Tasha does not have enough time to play both the games.

Given that, Tasha has 12 minutes. She wants to jump rope for 8 minutes and play tag for 5 minutes.

What is comparison of numbers?

Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

Now, number of minutes Tasha wants to jump the rope = 8 minutes and play tag = 5 minutes

So, total time = 8+5 =13 minutes

Here, 12 minutes < 13 minutes

Therefore, Tasha does not have enough time to play both the games.

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What are the 3 numbers in Marlene's puzzle if the quotient of a & c is 8, the quotient of a & b is -16, the quotient of b & c is -0.5, the product of a & c is 2, the product of a & b is -1,?

Answers

a = 4, b = -0.25, c = 0.5

or a = -4, b = 0.25, c = -0.5



Write down what you know in the form of equations:

a / c = 8

a / b = -16

b / c = -0.5

a * c = 2

a * b = -1



Now see if you can express one variable in terms of another. The a * c = 2 expression looks like a nice place to begin.

a * c = 2



Divide both sides by c

a = 2/c



Now look for another expression that uses a and c. The expression a/c = 8 looks like a good possibility.



a/c = 8



Substitute the expression defining a in terms of c into the expression

(2/c)/c = 8



Multiply both sides by c

2/c = 8c



Multiply both sides by c again

2 = 8c^2



divide both sides by 8

2/8 = c^2

1/4 = c^2



Take the square root of both sides

1/2 = c

0.5 = c



Now that we know the value for c, Calculate a using the a = 2/c expression we made.

a = 2/c = 2/.5 = 4



So we now know that a = 4, and c = 0.5

Look for an expression using b that we can solve. a / b = -16 looks like a good place to try

a / b = -16



Substitute the known value of a

4 / b = -16



Multiply both sides by b

4 = -16 b



Divide both sides by -16

-4/16 = b



Simplify

-0.25 = b



So a = 4, b = -0.25, c = 0.5

Verify using the equations given

a / c = 8: 4 / 0.5 = 8 Correct.

a / b = -16: 4 / (-0.25) = -16 Correct

b / c = -0.5: -0.25 / 0.5 = -0.5 Correct

a * c = 2: 4 * 0.5 = 2 Correct

a * b = -1: 4 * -0.25 = -1 Correct



All of the quotients and products come out as they should, so the values determined for a,b,c are correct.



Note: Since the square root was taken for the equation

0.25 = c^2

0.5 = c

The value of either 0.5, or -0.5 is correct for c. So this problem actually has 2 solutions.

They are a = 4, b = -0.25, c = 0.5

or a = -4, b = 0.25, c = -0.5

You have 120 pieces of fabric to make a blanket. Each piece is a square with a side length of 6 inches. You can use as many pieces as possible to create a square blanket.
What is the area of the blanket?
How many pieces of fabric are left over?
How many more pieces of Gabriel would you need to increase the size of the blanket?

Answers

3600 inches squared, 20 and 1 

The weight of a small bag of sugar is 2.265 kg. the student is baking cakes for a college scholarship fundraiser. it takes 100 grams of sugar to make one small cake. how many cakes can be made from a single bag of sugar?

Answers

2.265 KG = 2265 grams/100 = 22.65 cakes

The total batches of cupcakes that make with one small bag of sugar would be 22 batches.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

From the question, we are given the following

The t of a small bag of sugar = 2.265 kg = 2265 grams

100g of sugar to make one batch of cupcakes,

100g = 1 batch ---- 1

In order to get the number of batches of cupcakes made with one small bag of sugar,

2265g =  x ---- 2

Divide both expressions;

100/2265 = 1/x

100x = 2265

x = 2265/100

x = 22.65 batches

Hence, the batches of cupcakes that make with one small bag of sugar would be 22 batches.

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