Answer:
x = 10 + √389, y = -10 + √389 // x = 29.7231, y = 9.72308
or
x = 10 - √389, y = -10 - √389 // x = -9.72308, y = -29.7231
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStandard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define Systems
xy = 289
x - y = 20
Step 2: Rewrite Systems
x - y = 20
Subtract x on both sides: -y = 20 - xDivide -1 on both sides: y = x - 20Step 3: Redefine Systems
xy = 289
y = x - 20
Step 4: Solve for x
Substitution
Substitute in y: x(x - 20) = 289Distribute x: x² - 20x = 289Rewrite [SF]: x² - 20x - 289 = 0Define variables: a = 1, b = -20, c = -289Substitute [QF]: [tex]x=\frac{20\pm\sqrt{(-20)^2-4(1)(-289)} }{2(1)}[/tex]Exponents: [tex]x=\frac{20\pm\sqrt{400-4(1)(-289)} }{2(1)}[/tex]Multiply: [tex]x=\frac{20\pm\sqrt{400+1156} }{2}[/tex]Add: [tex]x=\frac{20\pm\sqrt{1556} }{2}[/tex]Simplify: [tex]x=\frac{20\pm 2\sqrt{389} }{2}[/tex]Factor GCF: [tex]x=\frac{2(10\pm \sqrt{389} )}{2}[/tex]Divide: [tex]x=10\pm \sqrt{389}[/tex]Step 5: Solve for y
Possibility 1: x = 10 + √389
Define equation: x - y = 20Substitute in x: (10 + √389) - y = 20Isolate y term: -y = 20 - (10 + √389)Isolate y: y = (10 + √389) - 20Combine like terms: y = -10 + √389Evaluate: y = 9.72308Possibility 2: x = 10 - √389
Define equation: x - y = 20Substitute in x: (10 - √389) - y = 20Isolate y term: -y = 20 - (10 - √389)Isolate y: y = (10 - √389) - 20Combine like terms: y = -10 - √389Evaluate: y = -29.7231Step 6: Identify Solutions
Possibility 1:
x = 10 + √389, y = -10 + √389
x = 29.7231, y = 9.72308
Possibility 2:
x = 10 - √389, y = -10 - √389
x = -9.72308, y = -29.7231
Bruce needs to practice the piano for 1 2/3 hours. He has been practicing for ¾ of an hour. How much longer must he practice?(first person gets brain plz help i need it for test its a alot of my grade
Answer:
55 minutes.
Step-by-step explanation:
1 2/3 - 3/4 = 11/12 hours
11/12 hours = 55 minutes.
Write -7 2/3 as an improper fraction.
Answer:
-19/3
Step-by-step explanation:
-7x3+2=-19. thats the numerator. the denomator is still 3
A designer is decorating a square frame with ribbon. The designer has 50 3 /8 inches of ribbon. The square frame is 8 1/ 4 inches long on each side. How much ribbon will the designer have left after placing ribbon on all four sides of the square frame, written as an improper fraction (fraction greater than one)?
Answer:
Step-by-step explanation:vnmiy
(1) [6pts] Let R be the relation {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} defined on the set {0, 1, 2, 3}. Find the following: 1. [3pts] Reflexive closure of R 2. [3pts] Symmetric closure of R
Answer:
Following are the solution to the given points:
Step-by-step explanation:
In point 1:
The Reflexive closure:
Relationship R reflexive closure becomes achieved with both the addition(a,a) to R Therefore, (a,a) is [tex](0,0),(1,1),(2,2) \ and \ (3,3)[/tex]
Thus, the reflexive closure: [tex]R={(0,0),(0,1),(1,1),(1,2),(2,0),(2,2),(3,0), (3,3)}[/tex]
In point 2:
The Symmetric closure:
R relation symmetrically closes by adding(b,a) to R for each (a,b) of R Therefore, here (b,a) is: [tex](0,1),(0,2)\ and \ (0,3)[/tex]
Thus, the Symmetrical closure:
[tex]R={(0,1),(0,2),(0,3)(1,0),(1,1)(1,2),(2,0),(2,2),(3,0), (3,3)}[/tex]
3. Which of the following equations represents a line that does not intersect the x-axis?
Explain your answer.
a. x = 4
b. y =-5
C. y = 2x - 4
d. 3x - 8y = 17
Please solve need help badly
What is 870 divided by 111 as a decimal
Answer:
7.83783783784
Step-by-step explanation:
So, C is the correct option
Answer:
c
Step-by-step explanation:
what is -7-2n=-27
Solve for n
Pls and ty
Answer:
-10
Step-by-step explanation:
-7-2n=-27
add 7 to both sides
then you have -2n=-20
-2n/-2=-20/-2
n=-10
Answer:
n= -10
Step-by-step explanation:
-7 - 2n = -27
-2n=-27+7
-2n= -20/2
n= - 10
How is 0.1212 wrote in bar notation
Answer:
0.1212...
Step-by-step explanation:
as you see there is another 12 repeating itself, so if on computer you show by:
ellipsis (…) or the repeat bar, when had writing.
does anyone know this?
Answer:
x = 4
Step-by-step explanation:
By BPT
[tex] \frac{10 - x}{x} = \frac{3}{2} \\ \\ 2(10 - x) = 3x \\ \\ 20 - 2x = 3x \\ \\ 20 = 2x + 3x \\ \\ 20 = 5x \\ \\ x = \frac{20}{5} \\ \\ x = 4[/tex]
Andre received and spent money in various ways last month. What would the number 0 represent in this situation?
Answer:
the number 0 might represent the starting amount or what he ended up with.
Step-by-step explanation:
800 hm = _____ cm
8
0.08
80,000
8,000,000
Can someone check my answers an see if correct. TYSM!!
ΔEFG ≅ ΔHJK
Answer:
Is here a pic that goes with it?
Step-by-step explanation:
What is the answer to 60+9
Answer:
60 + 9 is 69 :)))))))))))
Which bottle of shampoo is at the right price 12oz 2.59 16 oz 3.19
Answer:
16 oz is cheaper...
Step-by-step explanation:
Answer:
I would say the second one
Step-by-step explanation:
3 What is the y-intercept of the line with the equation Y = 1/2 - x - 3?
a. -3
b. 6
c. -6
d. 1/2
Answer:
a. -3Step-by-step explanation:
Given Equation :
[tex]y = \frac{1}{2} x - 3[/tex]
Which is in slope intercept form :
[tex]y = mx + b[/tex]
Where :
m = slope
b = y-intercept.
Thus , in the given Equation , the y-intercept is -3
What is the volume of this rectangular prism?
Answer:
295.2 cm³Step-by-step explanation:
volume = length x width x height
= 15 cm x 4.1 cm x 4.8 cm
= 295.2 cm³
What is the ratio of yellow sections to total sections, in the lowest terms?
Determine the quotient of 3/7 divided by 2/3
Answer:
Hello! Your answer is 9/14.
Charles River Bridge in Massachusetts is about 486 yards long. About how many feet is this?
How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain.
Answer:
Sample response: Use the two points of a linear function to write an equation in slope-intercept form by first finding the slope of the function, and then using a point and the slope to determine the y-intercept. Write the equations in slope-intercept form.
Step-by-step explanation:
EDGE2020
Answer:
Use the two points of a linear function to write an equation in slope-intercept form by first finding the slope of the function, and then using a point and the slope to determine the y-intercept. Write the equations in slope-intercept form.
Step-by-step explanation:
Use the points to find the slope.Use slope and a point to find the y-intercept.Write the equations in slope-intercept form.
The cost of 5 scarves is $43.75. What is the unit price?
The unit price is $ per scarf.
Answer:
$8.75 per scarf
Step-by-step explanation:
5 scarves costs $43.75 so to get the price of one scarf, we just need to divide by 5.
43.75 / 5 = 8.75
One scarf costs $8.75
the ordered pair below is a solution to which equation? (40,5)
Answer:
C. y = 1/8x
Step-by-step explanation:
All we have to do here is to express numbers 40 and 5 in each of equations. Note that first number in brackets is always x coordinate and second number is y coordinate
First equation:
5 = 40*8 false
Second
5 = 5*40 false again
Third:
5 = 40/8 = 5 True
checking for just in case last one:
5 = 40/5 = 8 False
Correct one is C)
PLEASE HELP ME WITH THIS SOMEONE
Answer:
try d
Step-by-step explanation:
because if you look at what point a is it you get 9 and if you look at where point b is at you get 9,3 but pint b says 2 so im thinking it was publish error on that one so the answer will be 9,3 have a good day and stay safe
PLS HELP ME IT WOULDN MEAN A LOT ANSWER CHOICES ARE ON THE PICTURE
Answer:
i kinda wanna say it is the first one or second
Step-by-step explanation:
Use the graph to answer questions q- 11.
9. Reflect figure OPOR over the x-axis.
Record the coordinates for P'.
IP
IS
10. Translate figure STUV 7 units down and 5
units left. Record the coordinates for T'.
TRO
2
11. In which Quadrant would figure STUV lie
ofter a rotation 270º counterclockwise?
Answer:
15
Step-by-step explanation:
What does 15÷14 equals to
Answer:
1.07142857143
Step-by-step explanation:
Q no 13 and 14 answer
Answer:
Question 13 : x = 62°Question 14 : x = 2Step-by-step explanation:
Question 13
The diagram in question 13 is a triangle.
The sum of interior angles of a triangle is equal to 180°
To solve for x ;
[tex]x + 69 + 49 = 180 \\ x + 118 = 180 \\ x = 180 - 118 \\ x = 62[/tex]
Question 14
(: represents ratio or /)
x/9 = 18/81
Cross Multiply
81x = 18×9
81x = 162
Divide both sides of the equation by 81
81x/81 = 162/81
x = 2
Which of the following lines represents the equation y = x - 3?
A
B
C
D
Answer:
Line D
Step-by-step explanation:
Line D is the only one that starts at -3
The Equation of Line D in the graph represents the equation y = x - 3. Option D is correct.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
Here,
We have given the equation y = x - 3, and have to determine which line in the graph is represented by the given equation,
So, Just calculate the y-intercept of each line on the graph and match it with the equation (c = -3).
So
Line A has an intercept of C = -2
Line B has an intercept of C = 3
Line C has an intercept of C = 0
Line D has an intercept of C = -3
Thus, the Equation of Line D in the graph represents the equation y = x - 3. Option D is correct.
Learn more about intercept here:
https://brainly.com/question/3605446
#SPJ2
Calvin has been trusted to manage the school candy store, but he is taking advantage of the situation. For every seven pieces of candy that a student buys, Calvin helps himself to three pieces of candy. If Marty buys 42 pieces of candy, how many will Calvin take for himself? Show your work or explain your reasoning.
Answer:
18 piecesStep-by-step explanation:
Calvin takes 3 pieces of candy for each 7 pieces sold.
If 42 pieces sold, Calvin takes x pieces.
Use ratios to find the value of x:
3/7 = x/42x = 3*42/7x = 18