x - y = -2
4x - y = 4
[tex] \begin{cases} x - y = - 2 \\ 4x - y = 4 \end{cases}[/tex]
Use the elimination method as it is faster. We have to eliminate the y-term. (You can eliminate the x-term but it takes longer than eliminating y-term.)Simply multiply the negative one in one of the equations.
[tex] \begin{cases} - x + y = 2 \\ 4x - y = 4 \end{cases}[/tex]
We can finally eliminate the y-term by adding both equations.
[tex]( - x + 4x) + (y - y) = 2 + 4 \\ 3x + 0 = 6 \\ 3x = 6 \\ x = \frac{ 6 }{3} \longrightarrow \frac{ \cancel{6}}{ \cancel{3}} = 2 \\ x = 2[/tex]
Substitute the value of x in any given equations. I will substitute in the first equation.[tex]x - y = - 2 \\ 2 - y = - 2 \\ 2 + 2 = y \\ 4 = y[/tex]
Check the answer by substituting the value of x and y in both equations.First Equation
[tex]x - y = - 2 \\ 2 - 4 = - 2 \\ - 2 = - 2 \longrightarrow \sf{true} \: \: \green{ \checkmark}[/tex]
Second Equation
[tex]4x - y = 4 \\ 4(2) - 4 = 4 \\ 8 - 4 = 4 \\ 4 = 4 \longrightarrow \sf{true} \: \: \green{ \checkmark}[/tex]
Hence, the solution is (2,4).
Answer[tex] \begin{cases} x = 2 \\ y = 4 \end{cases}[/tex]
Coordinate Form
[tex](2,4)[/tex]
HELPPPP
Write a function that represents the balance after t years.
$2000 deposit that eams 5% annual interest compounded quarterly
Not sure if this is correct but:
Step-by-step explanation: P = 2000
R = 5% = 0.05
n = 4
y = 2000 ( 1 + [tex]\frac{0.05}{4}[/tex]) [tex]^{4t}[/tex] = 2000 ( 1.0125 )
Substitute values in the compound interest formula:
y = P ( 1 + [tex]\frac{r}{n}[/tex])[tex]^{nt}[/tex] .
Hope this helps..
Which one is it?????
13.) The leading scorer in your high school's hockey league finished the season with an average of 4 goals per game for 15 games. As the leagues
second leading scorer, you have an average of 4 goals per game for 14 games. You still have to play your last game. How many goals must you
score in the final game to overtake the leagues' leading scorer?
Answer:
5 goals
Step-by-step explanation:
4 goals per game for 15 games means a total of 60 goals in that season. You have 4 goals per game for 14 games meaning you have a total of 56 goals. To overtake the leading team you must score a minimum of 5 goals to become the leading scorer. (Double-check to make sure I am correct)
Simplify: f (x) – 4g (x)
I don't know how to do any of this
Answer:
Remember that when a variable is times with a number, you will divide it by that number which is times with variable on both sides.
when a variable is divided by the number, you will multiply it by that number on the both sides.
I hope you understand my explanation. Thank you !!
the first 4 terms and the 10th term for 3n+4
Answer:
first 4 terms =7,10,13,16
10th term = 34
Step-by-step explanation:
3n+4
3(1)+4=7
3(2)+4=10
3(3)+4=13
3(4)+4=16
7,10,13,16
10th term = 3(10)+4= 34
The first four terms of the sequence having nth term 3n+4, are 7, 10, 13, 16 and the 10th term is 34.
What is arithmetic sequence ?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.
Given that,
The nth term of a sequence is given by 3n+4,
To find the first 4 terms, substitute the values of n,
At n=1, the first term = 3(1) + 4 = 3 + 4 = 7
At n=2, the second term = 3(2)+4 = 6 + 4 = 10
At n=3, the third term = 3(3) + 4 = 9 + 4 = 13
At n=4, the fourth term = 3(4) + 4 = 12 + 4 = 16
For 10th term, substitute n=10.
At n=10, the tenth term = 3(10) + 4 = 30 + 4 = 34
The first four terms are 7, 10, 13, 16 and the 10th term is 34.
To learn more about Arithmetic sequence on :
https://brainly.com/question/1452631
#SPJ2
Solve for Y
13= 4y+5
y=?
Please help this is my last question and it’s due by 10 PM
sorry there’s only 11 points •.•
Apply the distributive property to factor out the greatest common factor. 14 k + 35 =
Answer:
7(2k+5)
Step-by-step explanation:
Not sure if I’m correct
And the factor is 7 out of 14k+35
What is the value for A? What is the value for B? What is the value for C? What is the value for D?
Step-by-step explanation:
step 1. we must assume the ratio of flour to sugar is 2:1.
step 2. A = 2(3/4) = 3/2 1-1/2.
step 3. B = 1-3/4(1/2) = 7/4(1/2) = 7/8
step 4. C = 1(2) = 2
step 5. D = 2-1/2(1/2) = 5/2(1/2) = 5/4 = 1-1/4.
Please help, and i will mark you BRAINLIEST
Mary is baking cookies, and the recipe calls for 1 1/2 cups of sugar. If she has 6 1/3 cups of sugar left after she bakes the cookies, how much sugar (s) did she have before she started baking cookies? Which equation would you use to solve for (s)? *
s + 1 1/2 = 6 1/3
6 1/3 - s = 1 1/2
s - 1 1/2 = 6 1/3
1 1/2 + s = 6 1/3
Answer: 4 5/6
Step-by-step explanation: 4 5/6+ 1 3/6(aka 1 1/2)= 6 2/6 (aka 6 1/3)
Match the numbers with the correct label pls helpppp
Answer:
first convert all fractions to decimals so you can put least to most on the line
a. -.25
b. − .428571 ( repeating)
c. -.2
now put them in order
a(blue)=b,-3/7
b(pink)=a,-2/8
c(green)=c-.2
Give the least common denominator: 1/(5n), 1/3 _____
Step-by-step explanation:
step 1. LCD of 1/(5n) and 1/3 is 15n.
Can someone help me out please
Angle E and Angle F are Vertical Angles, If measure of Angle E is 3x + 33 and the measure of Angle F is 4x + 8, what is the value of x?
Answer:
Remember vertical angles are congruent so you can set these expression equal to each other and then solve the equation.
Angle F = angle E
4x + 8 = 3x + 33
Now solve for the x variable.
Step-by-step explanation:
10.
X/2 + X-3/5 = 3
If anyone could help with #10 I would be very grateful
A $350 purchase is discounted 15%. You use a 20% coupon. What is the total paid?
Answer:
238 should be the answer
Step-by-step explanation:
A relation is plotted as a linear function on the coordinate plane starting at point C at (0, −1)and ending at point D at (2, −11) .
What is the rate of change for the linear function and what is its initial value?
20 points Select from the drop-down menus to correctly complete the statements.
The rate of change is
Choose...
and the initial value is
Answer:
The rate of change is -5 and the initial value is -1.
Step-by-step explanation:
Hope this helps
P.S. (from k12)
PLS HELPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Between April and May
Step-by-step explanation:
April and May have a rate of change of 5 (79-74). February and March have a lesser rate of change.
Answer:
Option 2 :- February and March
Step-by-step explanation:
Rate of change between February and March is $ 5 i.e, ($79-$74)
Rate of change between April and May is $ 3 i.e, ($75-$72)
Thus, Rate of change is greater in February and March.
Hope this helps you.
100 POINTS! The midpoint of GH is M(4, -3). One endpoint is G(-2, 2). Find the coordinates of endpoint H.
Answer:
(10, -8)
Step-by-step explanation:
Answer:
solution given:
G(x1,y1)=(-2,2)
H(x2,y2)=(x,y)
Mid point M(a,b)=(4,-3)
we have
(a,b)=((x1+x2)/2,(y1+y2)/2)
(4,-3)=((-2+x)/2,(2+y)/2)
comparing corresponding value
4=(-2+x)/2
8+2=x
x=10
again
(2+y)/2=-3
2+y=-6
y=-6-2
y=-8
So coordinates of H is (10,-8).
Evaluate f(x)=7x+7 when x=-9
Answer:
-56
Step-by-step explanation:
f(x) = 7x + 7
x = -9
We meed to plug in x = -9 into the first equation:
f(-9) = 7(-9) + 7
We can open up the parentheses:
f(-9) = -63 + 7
And then simplify:
f(-9) = -56
if you go out to eat and your meal was $72.50 you decide to tip your waiter 15% How much do you pay in total
Answer:
$83.38
Step-by-step explanation:
multiply 72.5 by 1.15: 72.5 x (100% of meal + 15% of meal)
The Sullivans purchased $195.60 worth of school
clothes during their back to school shopping haul.
The sales tax in their state is 6%. How much sales
tax did they have to pay?
Answer:
$11.74
Step-by-step explanation:
195.60/100 X 6 = 11.736
monetary unit so round to 2dp
11.74
Which of the following have 4 as the GREATEST common factor (GCF).
Select ALL that apply.
4 + 8y
4x + 40y - 400
24x - 16y
x - 4y + 16x
4 - 12x
Answer:
4-12
4+8y
I hope this helped.
Solve the following equations:
x/3+1=7/5
Answer:
8/5..............…is the answer
Answer:
Standard Form: 6/5 Mixed Number: 1 1/5 Decimal: 1.2
Step-by-step explanation:
1. Subtract 1 from both sides of the equation
x/3 + 1 = 7/5
x/3 + 1 - 1 = 7/5 - 1
2. Simplify
2a.
x/3 + 1 - 1 = 7/5 - 1
x/3 = 7/5 - 1
2b.
x/3 = 7/5 - 1
x/3 = 2/5
3. Multiply all terms by the same value to eliminate fraction denominators
x/3 = 2/5
3 x x/3 = 3 x 2/5
4. Simplify
4a. Cancel multiplied terms that are in the denominator
cross out the threes in 3 x x/3 then you should get x = 3 x 2/5
4b. Multiply the numbers
x = 3 x 2/5
x = 6/5
And your answer should be 6/5|
I hope this helps you or anyone
What is the approximate distance between point A (-8, 7) and point B (-2, 3)?
A. 3.6units
B. 7.2units
C. 52 units
D. 104units
Answer:
7.2units
Step-by-step explanation:
Plz help !!!!!!!!!!!!!!!!!!
Answer:
Quadrant 1: 10x^2
Quadrant 2: -4x
Quadrant 3: 5x
Quadrant 4: -2
Step-by-step explanation:
Plz help due tomorrow
Answer:
1/2
Step-by-step explanation:
The problem is asking for the coefficient of the sum of the two expressions, which are 2/3 and -1/6.
2/3 + -1/6 = 1/2, therefore, the answer is 1/2.
There are 376 students in 8th grade at Samuel's school. There are 47 8th graders trying out for football last Thursday. What percent of 8th graders did not try out for football?
Answer:
87.5%
Step-by-step explanation:
There are 376 students in 8th grade at Samuel's school. There are 47 8th graders trying out for football last Thursday.
The number is students not trying out for football last Thursday is calculated as:
376 students - 47 students
= 329 students
The percent of 8th graders that did not try out for football is calculated as:
329 students/376 students × 100
= 329/376 × 100
= 87.5 %
10v+6=-54
What is happening to the variable?
How do you solve for the variable?