Answers
EQUATION 2: 3x+y=4
STEP 1:
solve for one variable in equation 1
x - y= 12
add y to both sides
x= 12 + y
STEP 2:
use x value from step 1 and substitute in equation 2
3x + y= 4
3(12 + y) + y= 4
multiply 3 by parentheses
(3*12) + (3*y) + y= 4
multiply inside parentheses
36 + 3y + y= 4
combine like terms
36 + 4y= 4
subtract 36 from both sides
4y= -32
divide both sides by 4
y= -8
STEP 3:
substitute y value from step 2 into either equation
x - y= 12
x - (-8)= 12
x + 8= 12
subtract 8 from both sides
x= 4
CHECK:
x= 4, y= -8
3x + y= 4
3(4) + (-8)= 4
12 - 8= 4
4= 4
ANSWER: The x value is 4 and the y value is -8.
Hope this helps! :)
Related Questions
Each side of ΔABC is 75 units in length. Point D is the foot of the altitude drawn from side A to side BC. Point E is the midpoint of segment AD. What is the length of BE
Answers
Area = √(s(s-a)(s-b)(s-c))
Where s is half the perimeter and a, b, and c are the lengths of the triangle.
s = 0.5(3×75) = 112.5
Since our triangle is equilateral, a=b=c
Area = √(112.5(112.5-75)³)
= √5,932,617.188
= 2,435.696448 square units.
The same area can be found using the formula, 0.5(bh). Where b is the base length and h is the altitude from the base length.
In this triangle, b=75.
∴ 2,435.696448 = 0.5(75×h)
h = 4,871.392896÷75
=64.95190528 units
Since E is the midpoint of AD, then DE=h÷2=32.47595264 units
Now we have a right triangle BDE, where BE is the hypotenuse and BD=75/2.
∴ BE = √((BD)²+(DE)²)
=√(37.5²+ 32.47595264²)
= √2,460.935815
= 49.6078 units.
SOlution:
Area = √(s(s-a)(s-b)(s-c)).s = 0.5(3×75) = 112.5So,Area = √(112.5(112.5-75)³) = √5,932,617.188 = 2,435.696448 square units.
2. 2,435.696448 = 0.5(75×h)
h = 4,871.392896÷75 =64.95190528 unitsDE=h÷2
=32.47595264 units
3. BE = √((BD)²+(DE)²) =√(37.5²+ 32.47595264²) = √2,460.935815 = 49.6078 units.
please help the temperature in degrees fahrenheit can be estimated by counting the number of times a cricket chirps in one minute write an algebraic expression for the following written expression
the number of chirps divided by 4 added to 37
Answers
We have been given that the temperature in degrees Fahrenheit can be estimated by counting the number of times a cricket chirps in one minute.
Let us start with assuming the number of chirps as x.
We are supposed to write an algebraic expression for the number of chirps divided by 4 added to 37.
Let us first write an algebraic expression for number of chirps divided by 4. The algebraic expression for this will be [tex]\frac{x}{4}[/tex].
Let us now write an algebraic expression for number of chirps divided by 4 added to 37. The algebraic expression for this will be [tex]\frac{x}{4}+37[/tex].
Therefore, the required algebraic expression is [tex]\frac{x}{4}+37[/tex].
how would I set up and solve this problem?
Answers
You don't need trig.
You have a right triangle with two known sides, so just use the Pythagorean theorem to find the third side.
The sides measuring 325 m and 500 m form the right angle, so they are the legs.
The side you are looking for, x, is the hypotenuse.
leg1^2 + leg2^2 = hyp^2
325^2 + 500^2 = x^2
105,625 + 250,000 = x^2
x^2 = 355,625
x = sqrt(355,625)
x = 596.343
Answer: 596 ft
Write about a real-world situation that can be represented by the equation y=4x.
Answers
[tex]y=4x[/tex]
If x tickets are bought at $4, the total cost will be y.
need an answer as soon as possible.
asking for a friend.
Use the sequence: 1, –2, 4, –8, . . .
a. Find the common ratio in the sequence.
b. Write a rule for the sequence.
c. Find the next three terms
Answers
Answer: The common ratio is -2
-----------------------------------
Explanation:
To get the common ratio r, we divide any term by the previous one
One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2
Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time
Side Note: each term is multiplied by -2 to get the next term
============================================================
Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
-----------------------------------
Explanation:
Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio
The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)
============================================================
Part C
Answer: The next three terms are 16, -32, 64
-----------------------------------
Explanation:
We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms
-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64
showing that the next three terms are 16, -32, and 64
An alternative is to use the formula found in part B
Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier
Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier
Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier
while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
Emanuel was charged $32\$32$32dollar sign, 32 for a 1429 km14\dfrac29 \text{ km}1492 km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride. What was the cost per kilometer?
Answers
We are required to find the cost per kilometer of Emmanuel.
The cost per kilometre is $2.25 OR $2 and 25cents.According to the question, the total cost of the journey = $32
The total distance covered during the journey =
14 2/9 km
Therefore, the cost per kilometre can be evaluated mathematically as follows;
Cost per kilometer = cost of the journey ÷ Distance of the journey
= 32 ÷ 14 2/9
By converting 14 2/9 to an improper fraction; we have;
= 32 ÷ 128 / 9= 32 × 9/128= (32×9) / 128= 288 / 128= 2 32/128= 2.25 dollar per kilometerTherefore, the cost per kilometer is $2.25
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3/4 + 5/7 reduce to lowest term
Answers
_
5 is they answer
Write a word problem that can be described by the division expression 9 1/3÷2 3/4 . Use complete sentences in your answer. im very bad with word problems
Answers
The word problem involves dividing 9 1/3 loaves of bread into servings of 2 3/4 each to find out the total number of servings.
Explanation:Lisa baked 9 1/3 large loaves of bread for a community event. She wants to split each loaf into servings that are 2 3/4 each. How many total servings can Lisa make? This problem can be solved by dividing 9 1/3 by 2 3/4, with the result representing the total number of servings.
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Solve. 5x+10+7x=-3+13+7x+12
Answers
7x comes over and become -7x
10 goes over and becomes -10.
5x+7x-7x=-3-10+13+12.
-3-10=-13, which cancels out the positive 13.
-7x+7x=0 which cancels each other out.
Now, 5x=12
Divide each side by 5.
x=2.4 <--- final answer.
5x + 10 + 7x = -3 + 13 + 7x + 12
Add like terms.
(5x + 7x) + 10 = (-3 + 13 + 12) + 7x
Simplify.
12x + 10 = 22 + 7x
Now, we have to isolate x. To do that, we must start out by subtracting 10 from both sides.
12x = 22 + 7x - 10
Then, subtract 7x from both sides.
12x - 7x = 22 - 10
Simplify.
5x = 12
Divide both sides by 5.
x = 12/5 OR as a decimal, x = 2.4
~Hope I helped!~
please help50 points and brainliest to first one to answer
Answers
Which of these is an example of a random sample?
A.
The manager of a baseball team asks his team members about their views on the previous game they played.
B.
For a survey on air travel, 100 people are chosen randomly from five different airports.
C.
Five players from a basketball team are chosen for a game.
D.
Three members of a band are chosen for a concert.
Answers
Answer:
b
Step-by-step explanation:
the others are incorrect because they talk about group so its not random.
I'm deeply sorry for my inconvenience. Hopefully this is my last question. Will someone help?
(I forgot how to do taxes and discounts)
Answers
For taxes do the same thing but instead of subtracting add your product to the amount.
You just have to multiply by the percentage when it's a discount and subtract it from the original amount, 50% becomes .50. 99.50*.5=49.75 99.4-49.75=$47.75
2) D 103.48
You multiply by the percentage (0.04) and then add it to the original price when it's a tax
3) D 4.74
The same process as tax multiply by percentage (.2) and add to the original price
The difference between a markup and tax is the store controls the markups while taxes are usually state-controlled on a certain product (soda 5c or 10c tax is by state)
Please help (puppy eyes)
Answers
5 / 8 = 0.625
It can't be an Integer because decimals can't be intergers, so that's ruled out
It can't be repeating as it does end, so that's also ruled out
Since the decimal does end it can't be non-terminating, non-repeating
So the answer is Terminating Decimal by process of elimination
a jar contains blue, red, yellow, and green marbles. p(blue) = 1/4. what type of probability isillustrated and why
Answers
Hope I'm right!!
Give me 5 stars and brainliest if so.
What does the phrase “took to It like a duck takes to water” mean in this sentence?
When the young woman started learning how to play the saxophone she “took to It like a duck takes to water”
A) she practiced often
B) she found It natural
C) she played for others
D) she improved gradually
Answers
The phrase means the young woman found it natural and quickly developed a liking for learning how to play the saxophone.
Explanation:The phrase "took to it like a duck takes to water" means that the young woman found it natural and took a liking to learning how to play the saxophone effortlessly and quickly. It implies that she had a natural talent and aptitude for playing the instrument. This expression is often used to describe someone who picks up a new skill or activity easily and enthusiastically.
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Figure a’b’c’d’f is a dilation or figure abcdf by a scale factor of 1/2. The dilation is centered at (-4,-1)
Which statement is true?
Answers
In the box, complete the first 4 steps for graphing the quadratic function given. (Use ^ on the keyboard to indicate an exponent.) Then print a sheet of graph paper and graph the quadratic function to turn in to your teacher. Be sure to label the axes and vertex.
y = -x2 - 4x - 3
hellllllllllllllp
Answers
Answer:
This was my answer, hopefully it helps!
To graph the quadratic function y = -x^2 - 4x - 3, find the vertex, plot additional points, and connect them with a curve.
Explanation:To graph the quadratic function y = -x2 - 4x - 3, follow these steps:
Identify the coefficients and constant term: a = -1, b = -4, c = -3.Find the x-coordinate of the vertex using the formula x = -b/(2a):x = -(-4)/(2*(-1)) = -4/(-2) = 2Substitute the x-coordinate of the vertex into the equation to find the y-coordinate:y = -(2)2 - 4(2) - 3 = -4 - 8 - 3 = -15Plot the vertex at (2, -15) on the graph paper.Use the symmetry of the parabola to plot two additional points, equidistant from the vertex:If we move 1 unit to the right of the vertex (x = 3), we find y = -(3)2 - 4(3) - 3 = -9 - 12 - 3 = -24.If we move 1 unit to the left of the vertex (x = 1), we find y = -(1)2 - 4(1) - 3 = -1 - 4 - 3 = -8.Connect the three points with a smooth curve to complete the graph.Label x-axis, y-axis, the vertex, and any other relevant points or lines.How much interest is earned in four years on a deposit of 10,000 if it is allowed to accumulate in an account paying 7% interest compounded annually
Answers
0.07(10000) + 10000
But for 4 years:
4(0.07(10000)) + 10000
0.28(10000)) + 10000
We can make it simpler:
1.28(10000)
Multiply:
12800
YOU WILL HAVE $12800
john surveyed a random sample of 10 students in 7th grade seven of them they would vote for tammy as class president if there are 230 students in 7th grade what is the best estimate of the students who would vote for tammy
Answers
x= # of people who vote Tammy
7 out of 10= x out of 230
7/10= x/230
cross multiply
(7*230)= (10*x)
1610= 10x
divide both sides by 10
161= x
ANSWER: 161 people in 7th grade would vote for Tammy.
Hope this helps! :)
Two lines, C and D, are represented by the equations given below: Line C: y = x + 14 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why?
Answers
Answer:
(6, 20), because both lines pass through this point
Step-by-step explanation:
We see that both equations are equal to y. This means we can set the two equations equal to each other:
x+14 = 3x+2
Subtract x from each side:
x+14-x = 3x+2-x
14 = 2x+2
Subtract 2 from each side:
14-2 = 2x+2-2
12 = 2x
Divide both sides by 2:
12/2 = 2x/2
6 = x
Substitute this into the first equation:
y = x+14
y = 6+14
y = 20
This makes the solution (6, 20).
The solution for the given system of equations are (6, 20).
What is a linear system of equations?A system of linear equations is a set of two or more equations involving two or more variables. All of the equations must be considered at once in order to find the solution, which is any pair of values that makes each equation true independently.
The given system of linear equations are y=x+14 -----(i) and y=3x+2 -----(ii).
From equation (i) and (ii), we get
x+14=3x+2
3x-x=14-2
2x=12
x=6
Substitute x=6 equation (i), we get
y=20
Therefore, the solution for the given system of equations are (6, 20).
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Please help me!
How many possible outcomes are there when you roll four dice?
A. 1416
B. 1296
C. 24
D. 36
Answers
When rolling four six-sided dice, there are 1296 possible outcomes. This is calculated by raising the number of outcomes for one die (6) to the power of the number of dice (4).
Explanation:The subject of this question pertains to the probability in Mathematics, specifically focusing on the number of possible outcomes when rolling a die multiple times. In this case, we're looking at rolling four six-sided dice.
When you roll one die, there are indeed 6 possible outcomes, as a standard die has 6 faces. But if you roll two dice, the number of possible outcomes increases to 36 (6 outcomes for the first die times 6 outcomes for the second die).
Now in our case we are rolling four dice. Hence, the number of outcomes will be 6 to the power of 4, which means 6 * 6 * 6 * 6 = 1296. Therefore, the correct answer is B. 1296.
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Find the percent of decrease from 280 to 210. Round to the nearest tenth of a percent, if necessary.
a 0.3% b 25% C 33.3% D 133.3%
Answers
Isolate n:
n = 0.75
1.0 - 0.75
25% decrease, option b
Plsssssssss help i willmark brainliest
Answers
C : Add all the lengths = 84
A board game that normally costs $30 is on sale for 25 percent off. What is the sale price for the game?
Answers
Plz mark brainliest, glad to help.
find the value of x.
Answers
Make all the angles equal 360 degrees.
x + 92 + 82 + 47 = 360
x + 221 = 360
x = 139°
jerry built a coffee table for his living room. His table, that also serves as storage bin, is in the shape of a trapezoid. He wants to build a shelf in the middle of the coffee table to separate his photo album storage from his magazines. the top opening of the box is 22 inches and the base of the box is 12 inches. How long should he make the shelf to fit in the middle?
Answers
Answer: The correct answer is 17 inches.
Answer:
17 inches
Step-by-step explanation:
Given that jerry built a coffee table for his living room. His table, that also serves as storage bin, is in the shape of a trapezoid. He wants to build a shelf in the middle of the coffee table to separate his photo album storage from his magazines. the top opening of the box is 22 inches and the base of the box is 12 inches.
To make the trapezium into two halves he can draw a middle line from the mid points of the two non parallel sides.
Since base I =22 inches and base II = 12 inches we get
the middle line would be the average of the two bases
(Recall mid point theorem on triangles extended to trapeziums)
Hence we have the length required
=[tex]\frac{1}{2} (22+12)\\\\=\frac{1}{2} (34)\\=17 inches[/tex]
Find a irrational number between 7.7 and 7.9 explain why it’s irrational
Answers
Irrational numbers are:
Numbers that repeat
7.7777777 repeats the number 7 after the decimal
Numbers that CANNOT be written as a simple fraction.
7.7777777 cannot be written as a fraction in simplest form.
Answer = 7.777777777 repeating
~Aamira~
Hope this helped :)
5/8 0.67 1.2 3/5 Greatest to least
Answers
0.67
5/8
3.5
I think this is what it would be.
The local volleyball team hosts a concession stand to raise money. They spend $120 to purchase popcorn, candy, and drinks. They buy 95 bags of popcorn at $0.75 each and 35 bags of candy at $1.20 each. How much money does the volleyball team have left to spend on drinks?
a. $7.25 b. $15.50 c. $6.75 d. $20.25
Answers
This is found by multiplying 95 by $0.75 and adding the product ($71.25) to the product of 35 times $1.20 ($42). Then subract $113.25 (sum of $42 and $71.25) from 120 to get your final answer.
I hope this helps!
The money left to spend on drinks is $6.75.
Correct option is (C).
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations. The term "arithmetic" (which comes from the Greek word "arithmos," "number") often refers to the fundamental concepts in number theory, measurement, and computation (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).
As per the given data:
Total money spend = $120
95 bags of popcorn at $0.75 each
35 bags of candy at $1.20 each
Money spend on popcorn = 0.75 × 95 = $71.25
Money spend on candy = 1.20 × 35 = $42
Money spend on popcorn and candy = $71.25 + $42 = $113.25
Money left to spend on drinks:
= Total money - Money spend on popcorn and candy
= $120 - $113.25
= $6.75
Hence, the money left to spend on drinks is $6.75.
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How to Factor out the coefficient of the variable 3n-24
Answers
Now divide each term by 3 inside the equation.
3n / 3 = n
- 24 / 3 = - 8
So your new equation is 3(n - 8).