Answers
Answer:
The solution to this system of equations is (-1, 1).
Step-by-step explanation:
A system of equations is a "a finite set of equations for which common solutions are sought". Or, they are a pair (or more) of equations that either intersect, are parallel, or the same line. For the sake of simplicity, we are going to focus on systems of equations that intersect and only have one solution.
A solution to a system of equations that intersect is represented by a point (x, y). This makes sense because at the intersection of two points, there lies a point.
So how do we find this point? We do this by solving the system of equations. We show that there exists a point in which two lines can be satisfied simultaneously. But how can we do that? Trial and error?! Well, no. There are some ways of approaching this.
The first method is graphing. By either using an external source or doing it yourself, graphing two lines and showing where they intersect is one of the more understandable ways of solving a system of equations. The point where they cross is the solution of the system.
The second method is elimination. This is observing that a system of equations can be combined together to eliminate a variable (x or y) and solving for the other in a one-variable equation. For example, say that I have this system of equations:
x - y = 1
x + y = 1
By simply adding the two together, I get:
2x = 2
x = 1.
Since we already have x = 1, we can substitute it back into one of the original equations to get y.
1 + y = 1
y = 0.
So, the solution to this system of equations would be (1, 0). Speaking of substituting ...
The third method is substitution. This is observing that a variable (x or y) can be written in terms of the other and then using that to substitute in and make one of the equations one-variable.
y = 2x + 3
x - y = -2
We can see that y is already in terms of x in the first equation, so let's substitute y for 2x + 3 in the second equation.
x - (2x + 3) = -2
- x - 3 = -2
- x = 1
x = -1
We can substitute x back into one of the original equations.
y = 2(-1) + 3
y = -2 + 3
y = 1
Therefore, the solution to this system of equations is (-1, 1).
Related Questions
PLEASEEEE HELPPPPPPPPPP
Answers
this will provide you the answer
please help asap !! (images below)
Answers
Answer:
5/4 and then 5/3
Step-by-step explanation:
Felicia has a garden in the shape of a parallelogram as shown.
What is the area of her garden?
72 ft
75 ft
92 ft
96 ft
Answers
Answer:
72 ft
Step-by-step explanation:
i got this question correct
A bike was recently marked down $200. 00 from its initial price. If you have a coupon for an additional 30% off after the markdown, how much will the bike cost if it was originally $950. 00?.
Answers
Percentage is represented by '%' symbol. The final cost of the bike will be equal to $490.
What is Percentage?A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
Given to us
The initial cost of the bike, P = $950
Additional coupon = 30%
Marked down = $200
We know the original cost of the bike which is $950. therefore, when the price of the bike was marked down, its cost will be,
$900 - $200 = $700
Thus, the marked-down cost of the bike will be $700.
As it is given that we have an additional 30% off after the markdown, therefore, cost of the bike will be 70% of the marked price,
[tex]70\%\ of\ \$700\\\\ = 0.70 \times 700\\\\= \$490[/tex]
Hence, the final cost of the bike will be equal to $490.
Learn more about Percentage:
https://brainly.com/question/6972121
What is the original polynomial
Answers
Step-by-step explanation:
We know that divisor = (dividend)(quotient)+remainder.
So we can do (x^2 - x +8)(x+4)-5, which you can just expand out.
Given the above graph of y=-a(x+2)(x-6), where a>0,
(a) write down the equation of the line of symmetry,
(b) find the value of a.
Answers
Answer:
a)line x=2
b)a=3/2
Step-by-step explanation:
a) line of symmetry= x1 + x2/2=(-2)+6/2=2
b) (0,18)---y=-a(x+2)(x-6)
18=-a(0+2)(0-6)
a=18/12
a=3/2
5
When x = 0 and y = 0, which of the following is equivalent to
(5)?
Answers
Answer:
(b) x^15/y^5
Step-by-step explanation:
The exponent outside parentheses multiplies all of the exponents inside parentheses.
(x^3/y)^5 = x^(3·5)/y^(1·5) = x^15/y^5
______
Additional comment
When it comes to exponents, I find it useful to remember that an exponent signifies repeated multiplication: x·x·x = x³. The exponent outside parentheses has the same meaning:
(x³)² = (x·x·x)·(x·x·x) = x⁶
The rule is summarized by ...
(a^b)^c = a^(bc)
12. Suppose n is an integer. Select all statements below that are true:
O n2+ n is always an even integer
O n2+ n is always an even integer when n is even
O n2+ n is always an evet integer when n is odd
O n2+ n is never an even integer when n is odd
O n2+n is is never an even integer
O n2+ n is sometimes an even integer
Answers
Answer:
True statements
n is always an even integer when n is evenn is never an even integer when n is oddn is sometimes an even integerStep-by-step explanation:
Integer: a whole number that can be positive, negative, or zeroe.g. ...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...
True statements
n is always an even integer when n is evenn is never an even integer when n is oddn is sometimes an even integerHELP ASAP!!!
3 2/5 + 5 1/5 + 2 4/5
Answers
Answer:
See below.
Step-by-step explanation:
3 2/5 as a mixed fraction is 17/5.
5 1/5 as a mixed fraction is 26/5.
2 4/5 as a mixed fraction is 14/5.
So, the expression is 17/5 + 26/5 - 14/5, or C.
-hope it helps
easy math problem !,!!,!
Answers
B- 87
C- -2
D -9
hope this helps x!
A- 9B- 87C- -2D -9
Step-by-step explanation:
Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only once.
View Available Hint(s)
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1. The slowly increasing distance between South America and Africa is due to _______.
2. Old Faithful Geyser at Yellowstone National Park in the United States acquires its energy from a ______.
3. Layered ______ exposed by erosion can be seen when looking at the Grand Canyon in the United States.
4. Australia is composed of relatively old and thick _________.
5. The extremely deep ocean Marianas Trench is a result of ______.
6. ______ found in the Atlantic Ocean between North America and Europe is composed of dense and relatively young rock.
7. The earthquakes that occur in Southern California generally occur above a ______.
a. Seafloor Spreading
b. Hot Spot
c. Sedimentary Rock
d. Continental Crust
e. Seafloor Crust
f. Fault
g. Fubduction
Answers
Seafloor spreading can be defined as a process that involves the formation of new oceanic crust as a result of volcanic activities and an upwelling of molten magma at mid-ocean ridges, as well as a slowly increasing distance (outward movement) from the ridge.
The theory of seafloor spreading was established by Harry Hammond Hess and it can be used to explain in details the slowly increasing distance between South America and Africa which grows from the center.
What is a hot spot?A hot spot refers to an area deep within Earth's mantle or under the rocky outermost layer of Earth, from which heat rises through convection and acquired as heat energy by a landform.
In the United States of America, you will see a layered sedimentary rock that is exposed by erosion when you view the Grand Canyon.
Furthermore, Australia is made up of relatively old and thick continental crust. Also, subduction causes the formation of extremely deep ocean Marianas Trench.
Read more on seafloor spreading here: brainly.com/question/12037536
Given m is parallel to n, find the value of x???
Answers
Answer:
x = 62
Step-by-step explanation:
The angle adjacent to 118° is
180° - 118° = 62°
x and 62 are corresponding angles and are congruent , so
x = 62
Suppose 700 students were surveyed. How many more students prefer music over social
studies?
Answers
PLSSS SOMEONE HELP ME FASTt
Answers
Answer:
50%
Step-by-step explanation:
29/58 = 0.5
0.5 = 50%
The difference of a number and 13 is two less than the number doubled,
Three time
wal
quot
Answers
Answer:
The number is 5
Step-by-step explanation:
Let the number be x,
13 - x = 2x - 2
or, 13 + 2 = 2x + x
or, 3x = 15
so, x = 5
Lee recorded the number of push ups he did each each day for six days his data are listed below 68,41,58,75,48,40 what are the mean and the median of lees data set
Hleppppp please
Answers
Answer:
mean : 55; median : 53
Step-by-step explanation:
Given inputs: 68, 41, 58, 75, 48, 40
total numbers of input = 6
total value = 68 + 41 + 58 + 75 + 48 + 40 = 330
Mean → total value / total numbers of input = 330 / 6
= 55
arrange in increasing order: 40, 41, 48, 58, 68, 75
we can see that the median is between, 48 and 58,
so median → (48+58)/2 → 53
Natasha is a regional manager for a chain of supermarkets. She has been tasked with researching the weekly sales records of two branch locations over the past month, which she must present to her board of directors. She was able to assemble the relevant information in the table below, but it is scrambled and hard to read. Sales are listed in thousands of dollars. Week 4 1 1 3 4 2 3 2 Sales 16. 3 17. 8 23. 1 15. 2 20. 2 23. 4 22. 9 17. 6 Branch North South North South South North North South In order to make the data more readable, Natasha has decided to put it into a graph. Which of the following graphs accurately matches the information in the table? I. A bar graph has week on the x-axis and sales (dollars times 1,000) on the y-axis, from 15 to 23. Week 1 North, 23. 1; week 2 north, 23. 4; week 3 north, 22. 9; week 4 north, 16. 3. Week 1 south, 17. 8; week 2 south, 17. 6; week 3 south, 15. 2; week 4 south, 20. 2. II. A line graph has week on the x-axis and sales (dollars times 1,000) on the y-axis, going from 15 to 23. III. A graph has week on the x-axis and sales (dollars times 1,000) on the y-axis, going from 15 to 23. Points are plotted all over the graph. IV. A pie chart titled Sales (dollars times 1,000). North 1, 16. 3; North 2, 17. 8; North 3, 23. 1; North 4, 15. 2; South 1, 20. 2; South 2, 23. 4; South 3, 22. 9; South 4, 17. 6. A. I b. II c. III d. IV.
Answers
The graph which accurately matches Natasha's data for chain of supermarkets is bar graph.
How to read the data from the table?Table is a way to represent the data of the two or more variable.
To read the data from the table look for the value of one variable, and get the resultant value of other variable from the corresponding block.
Natasha was able to assemble the relevant information in the table below,
Sales listed in thousands of dollars.
Week - 4 1 1 3 4 2 3 2
Sales- 16.3 17.8 23.1 15.2 20.2 23.4 22.9 17.6
Branch- North South North South South North North South
To show the sales with respect to the time period, the best data chart is the bar graph. In a bar graph, the height of the bars is proportional to the data value it posses.
Here , for the sales by the Natasha the bar graph should be used as, the bar graph has week on the x-axis and sales (dollars times 1,000) on the y-axis, from 15 to 23.
Week 1 North, 23. 1; week 2 north, 23. 4; week 3 north, 22. 9; week 4 north, 16. 3. Week 1 south, 17. 8; week 2 south, 17. 6; week 3 south, 15. 2; week 4 south, 20. 2.
Hence, the graph which accurately matches Natasha's data for chain of supermarkets is bar graph.
Learn more about the data table here;
https://brainly.com/question/15602982
Answer: A. I
Step-by-step explanation:
its on edge 2022 and the answer they gave made me get it wrong. its A :)
I need help asap this is due the next day
Answers
7. the graphed solution (bold line) shows inequalities x≥-1
this is the same as inequality: x + 1 ≥ 0 (A)
what is
x - 2 5/8 = 6 1/4
Answers
Answer:
x = 8 7/8
Step-by-step explanation:
x + -21/8=25/4
+ 21/8 +21/8
x = 71/8
x = 8 7/8
Multiply
5 ft x 9 ft = __
Answers
because ft times ft is sq ft or ft^2
Explanation: 5•9=45 ft•ft= sq ft
A video game costs $16.40 before tax. What is the total cost after the 5% sales tax?
Answers
Answer:
$17.22
Step-by-step explanation:
→ Find the multiplier
( 100 + 5 ) ÷ 100 = 1.05
→ Multiply answer by cost
16.40 × 1.05 = $17.22
To convert a temperature measured in degrees Fahrenheit to degrees Celsius, there is a formula
C=5/9(F-32)
where C represents the temperature in degrees Celsius and F represents the temperature in degrees Fahrenheit.
If a temperature is 113`F, what is that temperature measured in Celsius?
Answers
Answer:
113`F= 46.11° Celsius
Step-by-step explanation:
(Celsius°C × 9/5) + 32 = Fahrenheit
(Celsius°C × 9/5) + 32 = 113
(Celsius°C × 9/5) = 113 - 32
(Celsius°C × 9/5) = 83
Celsius = 5(83)/9
Celsius = 46.11° Celsius
[tex]\\ \tt\hookrightarrow C=5/9(F-32)[/tex]
[tex]\\ \tt\hookrightarrow C=5/9(113-32)[/tex]
[tex]\\ \tt\hookrightarrow C=5/9(81)[/tex]
[tex]\\ \tt\hookrightarrow C=5(9)[/tex]
[tex]\\ \tt\hookrightarrow C=45°C[/tex]
A number is selected randomly from the integer from 10to30 what is the probability of picking a multiple of 4or5
Answers
Answer:
[tex]\frac{3}{7}[/tex]
Step-by-step explanation:
Start by finding how many integers there are from 10-30...
30-10+1=20+1=21
Note we have to add 1 since it is inclusive.
Now, let's find how many multiples of 4 or 5 there are from 10-30...
4*3=12
4*4=16
4*5=20
4*6=24
4*7=28
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5+5-1=9
Note we have to subtract 1 since 20 is counted twice.
The probability would be...
[tex]\frac{Multiples\ of\ four\ and\ five\ from\ 10-30}{Amount\ of\ integers\ between\ 10-30}=\frac{9}{21}=\frac{3}{7}[/tex]
Can someone help me?
Answers
square: 13² = 169 square units
rectangle: 15 x 8 = 120 square units
What is the equation of the non-proportional relationship given by the table below?
x y
3 76
6 70
9 64
12 58
15 52
y=2x+76
y=-2x+82
y=-2x-76
y=2x-82
Answers
Answer:
i like cheese and GAN rubik's cubes
get one at TheCubicle.com
free 2-3 day shipping unlike amazon
Step-by-step explanation:
Find the area of the triangle
Answers
Step-by-step explanation:
total base length has to be found.
(√(3.6)^2+(3.25)^2+6.2)*3.25*.5=3.97
Coach Brown had to buy baseballs for his team. He bought practice baseballs at $1.75 each, rubber pitching machine balls at $2.80 each, and leather game balls at $6.25 each. He bought 250 balls in total, and 20 fewer game balls than pitching machine balls.
If the total came to $974.65, then how many of each ball were ordered?
A. 130 practice, 113 machine, and 93 game balls
B. 44 practice, 113 machine, and 93 game balls
C. 206 practice, 113 machine, and 93 game balls
D. 114 practice, 113 machine, and 73 game balls
Answers
44 practice, 113 machine, and 93 game balls
===========================================================
Explanation:
x = number of practice baseballsy = number of pitching machine baseballsz = number of game ballsHe bought 20 fewer game balls than pitching machine baseballs, which means,
z = y-20
Since the coach bought 250 baseballs total we can also write
x+y+z = 250
Let's replace z with y-20 and simplify
x+y+z = 250
x+y+y-20 = 250
x+2y = 250+20
x+2y = 270
Now let's calculate the subtotal costs for each type of baseball
1.75x = cost of just the practice baseballs2.80y = cost of just the pitching machine baseballs6.25z = cost of just the leather game balls.Those subtotals add to this
1.75x+2.80y+6.25z = total cost = $974.65
1.75x+2.80y+6.25z = 974.65
Like before, I'll replace z with y-20
1.75x+2.80y+6.25(y-20) = 974.65
1.75x+2.80y+6.25y-125 = 974.65
1.75x+9.05y = 974.65+125
1.75x+9.05y = 1099.65
------------------------------
So far we have this system of equations
[tex]\begin{cases}x+2y = 270\\1.75x+9.05y = 1099.65\end{cases}[/tex]
I'll use substitution to solve the system.
Isolate x in equation (1)
x+2y = 270
x = 270-2y
Then plug this into equation (2) and solve for y.
1.75x+9.05y = 1099.65
1.75(270-2y)+9.05y = 1099.65
472.5-3.5y+9.05y = 1099.65
472.5+5.55y = 1099.65
5.55y = 1099.65-472.5
5.55y = 627.15
y = 627.15/5.55
y = 113
There are 113 pitching machine baseballs.
Use this y value to find x
x = 270-2y
x = 270-2(113)
x = 270-226
x = 44
There are 44 practice baseballs.
Also, we can say,
z = y-20
z = 113-20
z = 93
There are 93 game balls.
------------------------------
Check:
x+y+z = 44+113+93 = 250 baseballs total
A = 1.75*x = 1.75*44 = 77 = cost of just the practice baseballsB = 2.80*y = 2.80*113 = 316.40 = cost of just the pitching machine baseballsC = 6.25*z = 6.25*93 = 581.25 = cost of just the game ballsA+B+C = 77+316.40+581.25 = 974.65 = total cost
Everything checks out. Also note that value of z is 20 fewer than the value of y.
A shirt at the store is being offered at a 5% discount. If the original price of the shirt is x, which answer choice shows an expression that represents the discounted price of the shirt?
1. 0.95x
2. 1.05x
3. 0.05x
4. x + 0.05
Answers
Answer:
1. 0.95x
Step-by-step explanation:
The amount of the discount is 0.05x, so the discounted price is ...
x - 0.05x = x(1 -0.05) = 0.95x
which equation has the solution x=7?
2x+5=19
5x-2=-33
4x-9=13
7x+5=96
Answers
[tex]2x + 5 = 19 \\ 2 \times 7 + 5 = 19 \\ 14 + 5 = 19 \\ 19 = 19 [/tex]
So, The first equation has the solution x = 7
If AS = 20 and BS = 5, what is the measure of AC? Round to the nearest hundredth. Show all your work.
Answers
Answer:
When a radius and a tangent meet it us always 90 degrees therefore as is the hypotenuse and the length of a radius in a circle stays constant finding ac is easy as you use pythagoras theorem
C2-a2=b2
[tex] \sqrt{20 ^{2} } - 5^{2} [/tex]
=19.36
20