2x - 3y = 3
x + 2y = 5
In the second equation we have an x-term that has a coefficient of 1 (which means the x is all by itself), so we can isolate that x and solve by substitution.
x + 2y = 5
x + 2y - 2y = 5 - 2y
x = 5 - 2y
The expression 5 - 2y will be substituted for x in the first equation.
2x - 3y = 3
2(5 - 2y) - 3y = 3
Solve for y.
2(5 - 2y) - 3y = 3
10 - 4y - 3y = 3 (distribute the 2)
10 - 7y = 3 (collect like terms)
-7y = -7 (subtract 10 from both sides)
y = 1 (divide both sides by -7)
Substitute 1 for y in the second equation to find x.
x + 2y = 5
x + 2(1) = 5
Solve for x.
x + 2(1) = 5
x + 2 = 5 (multiply)
x = 3 (subtract 2 from both sides)
Always check your work. Substitute into the original system.
2x - 3y = 3
2(3) - 3(1) = 3
6 - 3 = 3
3 = 3
x + 2y = 5
3 + 2(1) = 5
3 + 2 = 5
5 = 5
Answer:x = 3 and y = 1; (3,1)
Plz answer all questions!!! 20 points!!!
Questions:
(question A) What two points are a distance of 5 from -2 on a number line?
(question B) What two points are a distance of 4 from 5 on a number line?
(question C) What two points are a distance of 7 from -1 on a number line?
(question D) What two points are a distance from 3 from 7 on a number line?
(question E) What two points are a distance of 10 from 2 on a number line?
(question F) What two points are a distance of 1 from -5 on a number line?
Answer:
A: -7 and 3
B: 1 and 9
C: -8 and 6
D: 4 and 10
Step-by-step explanation:
you just count the distance as your going:
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
......^.........................................^
-7 and 3 are both 5 away from -2
What is 4,226 - 2,958
Answer:
1268
Step-by-step explanation:
4226-2958=1268 mark the brainliest
The difference between 4,226 and 2,958 is 1,268.
Explanation:The question is asking for the difference between 4,226 and 2,958. To solve this, we subtract 2,958 from 4,226. Starting from the rightmost digit, subtract 8 from 6 which gives us 2. Then subtract 5 from 2 and you get a negative number so we need to borrow from the next digit. Borrow 1 from the leftmost digit, which makes it 3, then subtract 5 from 13 and you get 8. Finally, subtract 2 from 3, giving us 1. The answer is 1,268.
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on his fifth birthday ,paul was 42 inches tall. on his seventh birthday he was 48inches tall
Answer:
Paul grew 6 inches in 2 years
Step-by-step explanation: he was 42 inches before now he is 48 inches
The temperature changed from 7°f at 6pm to -5°f at midnight. What was the difference between the high an low temperatures? Whats was the average change in temperature per hour?
Answer:
Difference between high and low temperatures: 12°F
Average change in temperature per hour: 2°F
Step-by-step explanation:
The difference between high and low temperatures was: 7 - (-5) = 12 (°F)
Midnight is 12am, so 6pm to midnight is 6 hours.
The average change in temperature per hour is: 12 / 6 = 2 (°F)
There were some toads in the pond. 3 more jump in. 2 toads jumped out of the pond. There are now 6 toads in the pond. How many toads were in the pond to begin with?
Answer:
5
Step-by-step explanation:
do reverse calculations
we know that we ended with 6
since 2 jumped out we add them back in
6+2 = 8
we remove the toads that jumped in because they are not part of the original group
8-3 = 5
there were 5 toads in the beginning
There were originally 5 toads in the pond. This is determined by reverse calculation of the toads jumping in and out.
Explanation:To solve this math problem you can use a process of reverse calculation. At the end of the toad jumping in and out, there were 6 toads in the pond.
If we take into account the events that happened before we have that 2 toads jumped out so there must have been 8 toads before that(6 + 2).
Further back, 3 toads jumped in which means there must have been 8 - 3 = 5 toads in the pond to begin with.
So, initially, before any of the jumping happened, there were 5 toads in the pond.
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3(b+1)=4b-1 I need help
Answer:
3b + 3 = 4b - 1
3= b - 1
b= 4 is the solution
Andre is helping his father build a toy box for his little brother. The amount of space inside the toy box can be found by multiplying its width, length, and height. Write the amount of space, using an exponent. Then evaluate. The width is 3 ft. The length is 3 ft. The height is 3 ft.
Answer:3^3 (3 to the 3rd power) which is equal to 27 cubic ft.
Step-by-step explanation:
3x3x3=3^3
3^3=27
Simplify each expression. ( 5 v − 4 v 2 − 2 v 4 ) − ( 3 v 3 + 8 v + v 4 )
Answer:
the answer is 0
Step-by-step explanation:
i only have the answer
-32v I did the expression and I got -32v. This is a better answer than the other guy.
Write the expression 10 + 25 in a different way,
using the commutative law of addition, and show
that both expressions result in the same answer.
is 19 2/9 a integer
Answer:No
Step-by-step explanation: Integers are whole numbers that can be positive or negatives no decimals or fractions.
Joe gets paid $20 per hour for his work as a human billboard and this week with the elections so near he plans to work 10 hours overtime by weeks end the government will have taken out $240 in taxes from his check leaving him a total of $760 how many hours does joe normally work per week
Answer:
100 i think im not sure but i think its 100
Step-by-step explanation:
im not dat good at math either
Given l||m and m∠1 = 60°, select all angles that are also equal to 60°.
you can choose more than one
the answer choices are
2
3
4
5
6
7
8
Answer:
m∠2
m∠3
m∠4
Step-by-step explanation:
we know that
m∠2=m∠1 ----> by vertical angles
m∠3=m∠1 ---- by corresponding angles
m∠4=m∠1 ----> by alternate exterior angles
Answer:
m<3
m<2
m<4
Step-by-step explanation:
Please help with this math question graph
Answer:
its the first one
Step-by-step explanation:
2. Write the number in standard form.
4 ten thousands, 1 thousand, 9 hundreds,
8 tens, and 4 ones
21.1984
The number "4 ten thousands, 1 thousand, 9 hundreds, 8 tens, and 4 ones" written in standard form is 41,984.
To write the number 4 ten thousands, 1 thousand, 9 hundreds, 8 tens, and 4 ones in standard form, we can add up the value of each place:
4 ten thousands = 4 × 10,000 = 40,000
1 thousand = 1 × 1,000 = 1,000
9 hundreds = 9 × 100 = 900
8 tens = 8 × 10 = 80
4 ones = 4
Now, add up these values:
40,000 + 1,000 + 900 + 80 + 4
= 41,984
Therefore, the number "4 ten thousands, 1 thousand, 9 hundreds, 8 tens, and 4 ones" written in standard form is 41,984.
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a submarine dives 462 feet beneath the surface. it then climes up 250 feet. what is the depth of the submarine now?
The surface would be 0.
First it dives 462:
0 - 462 = -462 feet,
It then climbs 250:
-462 + 250 = -212
The submarine is at -212 feet. ( 212 feet below the surface.)
Will give brainliest 9 +10
Which expressions represent a perfect square monomial and its square root? Check all that apply.
121: 11
4x2, 2x
9x2 – 1; 3x - 1
25x, 5x
49x4; 7,22
Answer: A,B,E
Step-by-step explanation:
Answer:
Option 1,2 and 5 represent a perfect square monomial and its square root.
Step-by-step explanation:
To find : Which expressions represent a perfect square monomial and its square root? Check all that apply.
Solution :
1) 121, 11
As [tex](11)^2=121[/tex]
This expression represents a perfect square monomial and it’s square root.
2) [tex]4x^2,2x[/tex]
As [tex](2x)^2=4x^2[/tex]
This expression represents a perfect square monomial and it’s square root.
3) [tex]9x^2-1,3x-1[/tex]
As [tex](3x-1)^2=9x^2+1-6x[/tex]
This expression does not represents a perfect square monomial and it’s square root.
4) [tex]25x,5x[/tex]
As [tex](5x)^2=25x^2[/tex]
This expression does not represents a perfect square monomial and it’s square root.
5) [tex]49x^4,7x^2[/tex]
As [tex](7x^2)^2=49x^4[/tex]
This expression represents a perfect square monomial and it’s square root.
Therefore, Option 1,2 and 5 represent a perfect square monomial and its square root.
Desiree and her mother went to the movies two times in the month of April. Each time she was charged the student rate of $7.50 while her mother was charged $9.00. How much money did Desiree and her mother spend on movie tickets in April?
Answer:
They spend $33.
Step-by-step explanation:
multiply 7.50x2=15 and multiply 9.00x2=18. Then add 15+18=33.
Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.
5 - 2x^2 = -15
5-2x2=-15
Two solutions were found :
x = ± √10 = ± 3.1623
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5-2*x^2-(-15)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(5 - 2x2) - -15 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
20 - 2x2 = -2 • (x2 - 10)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2 - 10
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 10 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 3 :
-2 • (x2 - 10) = 0
Step 4 :
Equations which are never true :
4.1 Solve : -2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : x2-10 = 0
Add 10 to both sides of the equation :
x2 = 10
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 10
The equation has two real solutions
These solutions are x = ± √10 = ± 3.1623
Two solutions were found :
x = ± √10 = ± 3.1623
To solve the equation 5 - 2x^2 = -15 using inverse operations, we need to isolate the variable x on one side of the equation.
1. Start by adding 15 to both sides of the equation to eliminate the constant term on the right side:
5 - 2x^2 + 15 = -15 + 15
20 - 2x^2 = 0
2. Next, divide both sides of the equation by -2 to isolate the x^2 term:
(20 - 2x^2) / -2 = 0 / -2
-10 + x^2 = 0
3. Now, move the constant term to the other side by adding 10 to both sides:
-10 + x^2 + 10 = 0 + 10
x^2 = 10
4. To solve for x, we need to take the square root of both sides of the equation:
√(x^2) = √(10)
x = ±√(10)
To check the solutions, substitute them back into the original equation and see if they make it true:
For x = √(10):
5 - 2(√(10))^2 = -15
5 - 2(10) = -15
5 - 20 = -15
-15 = -15 (True)
For x = -√(10):
5 - 2(-√(10))^2 = -15
5 - 2(10) = -15
5 - 20 = -15
-15 = -15 (True)
So, the solutions to the equation 5 - 2x^2 = -15 are x = √(10) and x = -√(10).
How do I do the algebra problem 5(b-1)?
Answer:
5b-5
Step-by-step explanation:
When doing these kinds of problems you want to do dributive property which means you multiply whatever number is outside of the (), which is 5, and multiply that by b and 1.
when numbers are outside the () and right next to them without anything like +,-, or a division sign, it means to multiply.
In order to find the answer to this question you will have to simplify using the distributive property.
[tex]5(b-1)[/tex]
Applying the distributive property:
[tex]5b+5\times-1[/tex]
[tex]5\times-1=-5[/tex]
[tex]5b-5[/tex]
Therefore the answer is "5b-5."
Hope this helps.
One side of a triangle is 3 1/3 cm, another side is 2/3 cm shorter than the first side, and the third side is 1 2/3 cm longer than the first side. What is the perimeter of the triangle?
Thanks so much
Good evening ,
_______
Answer:
perimeter = 22/3 cm
____________________
Step-by-step explanation:
Look at the photo below for the details.
:)
A plumber charges $80 per hour to complete a job. She also charges an
additional fiat fee of $50 for each job. The total charge for one particular job
was $490. This situation is represented by the equation 80x-50 = 490.
How long did the job take?
Answer:
5.5! Now, you need to know why. The total cost was $490, there is a fee of $50, so subtract the fee from the total cost and you should then divide that by $80 because thats how much it is an hour.
The actual equation should be 80x + 50 = 490, not 80x - 50 = 490. By solving it, we find out that the job took 5.5 hours to complete.
Explanation:The given equation in the problem is incorrect. It should be 80x + 50 = 490, where x represents the number of hours the plumber worked. This equation accounts for the hourly charge (80x) and the upfront flat fee ($50). To solve for x, we begin by isolating it on one side of the equation. We subtract 50 from both sides to get 80x = 440. Then we divide both sides by 80, resulting in x = 5.5. Therefore, the plumber worked for 5.5 hours on this particular job.
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Greta added 3/6 of a cup of sugar to her cake mix then sprinkled 1/6 of a cup of sugar over the top of the finished which fraction represents the total amount of sugar that Greta used for the cake? Express the answer in the lowest terms?
a: 1/6 of a cup
b: 1/3 of a cup
c: 3/6 of a cup
d: 2/3 of a cup
Answer:
D
Step-by-step explanation:
4/6 reduced is d
How do you turn 1/8 into a decimal and a percent
Divide 1 by 8 which is 0.125, for a decimal. Then to turn it into a percent move the decimal 2 places to the right, then add the percent to the end; 12.5%
The fraction 1/8 can be converted into a decimal by dividing the numerator by the denominator, yielding 0.125. This decimal can then be converted into a percent by multiplying by 100, yielding 12.5%.
Explanation:To convert the fraction 1/8 into a decimal and a percent, we need to perform two types of conversions: a fraction-to-decimal conversion and a decimal-to-percent conversion.
First, converting the fraction to a decimal. To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). In this case, that gives us 1 ÷ 8 = 0.125.
Then, converting the decimal to a percent. A decimal can be converted to a percent by multiplying it by 100. So 0.125 * 100 = 12.5%. Therefore, the fraction 1/8 is equal to 0.125 as a decimal and 12.5% as a percentage.
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4*3-(24divided6)+8=?
Answer:
16
Step-by-step explanation:
Follow the correct order of operations.
4 * 3 - (24 divided 6) + 8 =
Parentheses first.
= 4 * 3 - 4 + 8
Now, the multiplication.
= 12 - 4 + 8
Now additions and subtractions in the order they appear from left to right.
= 8 + 8
= 16
Chase makes 2 gallons of soup for a dinner party. He serves 10 cups of soup to his guests. How many cups of soup will he have left over?
Answer:
d
Step-by-step explanation:
Answer:
22 cups
Step-by-step explanation:
Answer:
22 Cups of soup Left
Step-by-step explanation:
Given: 2 gallons of soup and 10 cups of soup served to guest.
To find: No. of cups of soup left.
We know that , 1 US Gallon = 16 US cups
⇒ 2 gallon of soup = 2 × 16 = 32 cups of soup
So, Remaining No. of Cups of soup = 32 - 10
= 22
Therefore, 22 Cups of soup Left
What term describes this polygon?
heptagon
dodecagon
17-gon
12-gon
Step-by-step explanation:
heptagon = 7 sides
dodecagon = 12 sides
heptadecagon = 17 sides
Janice caught three trout when she went fishing .one trout weighted 1.38 pounds ,and the second trout weighted 2.01 pounds,and the third trout weighted 1.2 pounds. How much is the total weight of the fish
Answer:
4.59
Explanation:
1.38 + 2.01 = 3.39
1.2 = 1.20
3.39 + 1.20 = 4.59
Make sure the fraction is fully reduced:
3y/13 + 7y/26
Answer:
[tex] \dfrac{y}{2} [/tex]
Step-by-step explanation:
The LCD of 13 and 26 is 26.
[tex] \dfrac{3y}{13} + \dfrac{7y}{26} = [/tex]
[tex] = \dfrac{2 \times 3y}{2 \times 13} + \dfrac{7y}{26} [/tex]
[tex] = \dfrac{6y}{26} + \dfrac{7y}{26} [/tex]
[tex] = \dfrac{13y}{26} [/tex]
[tex] = \dfrac{y}{2} [/tex]
Whats a comparison between the value of the 3 in 17,235 and the value of 3 in 17,352?
Answer: The 3 in 17,235 is in the tens digit and the 3 in 17,352 is in the hundreds digit