First, what is an equation?
➳ A mathematical statement which shows that two algebraic expressions are equal is called and equation.
Or, LHS = RHS
Example:- 3x - 5 = x + 8
An equation is said to be a linear equation if it contains only one variable (literal) with highest power 1.
_______________________
Solving an equation:-
To solve the equation x + 5 = 7 means to find the value of an unknown algebraic quantity used in the equation.
Example:-
To solve the equation x + 5 = 7 means to find the value of x.To solve the equation 3y + 2 = 9 means to find the value of y.To solve the equation [tex]\sf \dfrac{2a}{3} + 4 = 10[/tex] means to find the value of a ⠀⠀⠀⠀⠀⠀and so on!⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
★ Rules for solving an equation by the substitution method:-
Rule ❶
If x = 2, the value of the expression 3x + 2 = 3 × 2 + 2 = 6 + 2 = 8
Rule ❷
If x = 0, the value of the expression 3x + 2 = 3 × 0 + 2 = 0 + 2 = 2
Rule ❸
If x = -2, the value of the expression 3x + 2 = 3 × -2 + 2 = -6 + 2 = -4
Now consider the algebraic expression 5x - 2y
This expression consists of variables x and y.
Now if :-
x = 3 and y = 2, 5x - 2y = 5 × 3 2 × 2 = 15 - 4 = 11x = 8 and y = 5, 5x - 2y = 5 × 8 - 2 × 5 = 40 - 10 = 30⠀⠀⠀⠀⠀⠀⠀⠀
The process of finding the value of an algebraic expression by substituting the given value of its variable is called substitution.⠀⠀
The ratio of male to female students in a junior high
school is 13:17. Find the total population of the
school if there are 715 male students.
plsss.......answer
the total no of population=1650
13:17 first add the two numbers 13+17=30
then 13/30×y =715 , i make 13 at the numerator because it's males ratio
after that 30/13×13/30y =715 ×30/13
y =715×30/13
y =1650
after u find the total no it's simple to find the no of females
17/30×1650=935
Please help! What mistake did I make?
Answer:
Step-by-step explanation:
to make a negative, in addition, you can’t add a negative with a positive or the number would go from -3 + 2 = -1.
A baseball team had 70 players show up for tryouts last year and this year had 85 players show up for tryouts. Find the percent increase in players from last year to this year.
Answer:percent increase in players from last year to this year= 7.14%
Step-by-step explanation:
percent increase = (Increase in number of players /Initial value of players Last year) x 100
value of players for tryouts last year = 70
value of players for tryouts this year = 85
Increase in tryouts = 85-70 =5
percent increase = 5/70 x 100
= 7.14%
2+2=?
What does it equal
Answer:
4
Step-by-step explanation:
2 + 2 = 4
LE{LLEASE HELP THIS IS duE IN AN HOUR
Tony and tiffany collect semi-precious stones at the rockhound ht tiffany paid $38 for 9 pounds of snowflake obsidian. at the solid rock shop, tony paid 19 for 3 poi\unds of the same crystal. what id each person pay per pound and who made the better buy
Solve the equations 25 - 3x = 40. Write the problem on the sketch pad then solve the problem algebraically. I need the answer and how you work it out :)
Answer:
Step-by-step explanation:
25-3x=40
25-25-3x=40-25
-3x=15
-3x/-3=15/-3
x=-5
Just finding the area!
Answer:
160yds²
Step-by-step explanation:
A = ((a + b) ÷ 2) × h
A = ((19 + 13) ÷ 2) × 10 = 160
good luck, i hope this helps :)
What is the measure of angle 1?
60
125
45
120
Answer:
120 degrees
Step-by-step explanation:
What’s the answer ???
Answer:
Option 2 [tex]\frac{4\sqrt{6} }{3}[/tex]
Step-by-step explanation:
[tex]\frac{4\sqrt{2} }{\sqrt{3} } = \frac{4\sqrt{2} \sqrt{3} }{\sqrt{3}\sqrt{3} } = \frac{4\sqrt{6} }{3}[/tex]
Find the value of X round to the nearest 10th law of cosines.
Image of triangle is missing, so i have attached it.
Answer:
x = 18
Step-by-step explanation:
From the diagram attached, we can see that the 3 given sides have dimensions of x, 16 and 30.
Also, we see the angle opposite the dimension of x is 30°
Thus,we can use law of cosine to fjnd the value of x. Thus:
x² = 16² + 30² - 2(16 × 30)cos 30
x² = 256 + 900 - (960 × 0.866)
x² = 324.64
x = √324.64
x = 18.02
Approximating to the nearest tenth gives; x = 18
I need help pweaseeee
Answer:
C=1.80g
Step-by-step explanation:
Could someone answer all 5 questions please
Answer:
3=111
Step-by-step explanation:
In addition to his base salary, Ron earns a commission. Last week he sold $14000 worth of clothing and brought home an extra $840 in commission. What is his rate of commission? If his base salary is $500, how much money did he earn last week?
Answer:
His rate is
[tex].0243[/tex]
The money he earned last week is 340
What’s the answer for this one??
Answer:
It is the second one.
Step-by-step explanation:
a and e are equal because they are mirrored. d and b are equal because they are on the same line and at the same point where the parallel lines go through. b and f are also mirrored. That leaves c and e which don't match.
Which value of x is in the domain of (photo)
A. X = 2
B. X = 0
C. X = 1
D. X = -2
Answer:
X=1
Step-by-step explanation:
The two objects are the same height, and the cylinder is just wide enough for the the box to fit inside with all 4 vertical edges of the box touching the inside of the cylinder. if the box of pasta fits 8 cups of rice, estimate how many cups of rice will fit inside the cylinder. Expalin or show your reasoing
Answer:
The answer is below
Step-by-step explanation:
The volume of a box with a length of l, width of w and a height of h is given by the formula:
volume of the box = length * width * height = lwh
The volume of a cylinder with a height of h, and radius r is given by the formula:
volume of the cylinder = π * radius² * height = πr²h
Since the box and the cylinder have the same height and the cylinder is wide enough for the box to be placed inside, this means that the box has a volume greater than that of the cylinder. Hence:
If the box can take 8 cups, the cylinder would be able to take 10 cups.
i need help on my math i wasn't there that day my class did it
Answer:
(a-4)x-b+9
Step-by-step explanation:
hope this helps
Consider the line x-2y=-1 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
Answer:
slope of line that is parallel is 1/2
slope of line that is perpendicular is -2
Step-by-step explanation:
parallel lines have the same slope
perpendicular lines have slopes that are opposite and reciprocal
x - 2y = -1
-2y = -x -1
y = 1/2x + 1/2
the coefficient of the 'x' term represents the slope
Solve the following system of equations
1/× + 3/y = 3/4
3/× - 2/y = 5/12
Put the solution as an ordered pair (x,y)
Show your work
Answer:
(4,6)
Step-by-step explanation:
i used a ca lC uLator
Are the triangles below obtuse, acute, or right?
Answer: A is right. B is acute, C is obtuse, and D is right.
Step-by-step explanation:
The right triangles have the square in the corner.
Triangle C is a little bit bigger than a right triangle.
Triangle B is acute because its smaller than a right triangle.
solve for x...................................................................................
Answer:
x = 36°
Step-by-step explanation:
x + 20° + 4x = 200° { exterior angle of a triangle is equal to the sum of two opposite interior angles }
5x = 200° - 20°
5x = 180°
x = 180° / 5
x = 36°
Hope it will help :)
Need help on this please help
Answer:
204
Step-by-step explanation:
The area of the top triangle = 5*12/2 = 30
The area of the bottom triangle = 30
The hypotenuse of the top triangle is
5^2 + 12^2 = hypotenuse^2
25 + 144 = hypotenuse^2
169 = hypotenuse squared.
hypotenuse = sqrt(169)
hypotenuse = 13
Now the back face = 13 * 8 = 104
The area of the left side rectangular face = 5*8 = 40
The total area = 30 + 30 + 104 + 40 = 204
$325 is borrowed from a bank that charges 4% interest compounded annually. How much is owed after 1 year, 3
years, 7 years, and 20 years?
Answer:
338
365.58
427.68
712.12
Step-by-step explanation:
for annually compounding interest
PV(1+i)^n
for one year
325(1.04)
338
for 3 years
325(1.04)^3
365.58
For 7 years
325(1.04)^7
427.68
for 20 years
325(1.04)^20
712.12
Krutika was thinking of a number. Krutika halves the number and gets an answer of 86. Form an equation with x from the information.
PLEASE SOMEONE HELP!!!!
A 2-column table with 9 rows. The first column is labeled year with entries 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010. The second column is labeled pounds of trash with entries 3.25, 3.25, 3.66, 3.83, 4.57, 4.52, 4.74, 4.69, 4.44.
The table shows the average number of pounds of trash generated per person per day in the United States from 1970 to 2010. Use the statistics calculator to calculate the mean and median. Round the answers to the nearest hundredth.
Answer:
The median of a list of numbers is the center number when you order the numbers from least to greatest.
Since there are 9 numbers; the center number is the fifth number. Four numbers below and four numbers above. Median is 4.44 and the mean or average is 4.09.
Step-by-step explanation:
List in order from least to greatest
(3.25, 3.25, 3.66, 3.83) 4.44 ( 4.52, 4.57, 4.69, 4.74) Notice 4 numbers below 4.44 are lower and 4 numbers above 4.44 are higher. So the median number is 4.44
For the mean you add all the number and divide the sum by the number of numbers you have. We know you have 9 numbers from the first part. So, add the numbers from the list (3.25 +3.25+ 3.66 + 3.83 + 4.44 + 4.52 + 4.47 + 4.69 + 4.74) = 36.85 Then divide by 9 = 4.09
-4 (2y + 4)= 48 help plz
Answer:
y=-8
Step-by-step explanation:
-8y-16=48
+16+16
-8y=64
y=-8
Answer:
y=-8
Step-by-step explanation:
-4(2y+4)=48
2y+4=-12
y+2=-6
y=-8
-4(2(-8)+4)=48
48=48
Anna has a recipe for pumpkin bars. She uses 2 ½ cups of sugar for every 3 pans of pumpkin bars. AJ wants to follow the same recipe. He will make h pans of pumpkin bars using g cups of sugar. Which of these equations best represents the relationship between h and g?
Answer:
[tex]2.5h = 3g[/tex]
Step-by-step explanation:
Given
[tex]Sugar = 2\frac{1}{2}\ cups[/tex]
[tex]Bars = 3\ pans[/tex]
Required
Determine the equation for h pans and g cups
We have that:
[tex]Sugar = g[/tex]
[tex]Bars = h[/tex]
To do this, we make use of the following equivalent ratios.
[tex]Bars : Sugar = Bars : Sugar[/tex]
So, we have:
[tex]3 : 2\frac{1}{2} = h : g[/tex]
Express fraction as decimal
[tex]3 : 2.5 = h : g[/tex]
Express as fraction
[tex]\frac{3}{2.5} = \frac{h}{g}[/tex]
Cross multiply
[tex]2.5h = 3g[/tex]
No options were given. So, I will stop here
Solve please I don’t know how to do this.
Answer:
its 63 lol
Step-by-step explanation:
Answer:
63
Step-by-step explanation:
x/3-10=11
x/3=21
crisscross then
x=21×3
c=63
-30÷5=
bunun cevabı 6 mı??
Answer:
-6
Step-by-step explanation:
-30÷5=-6
this is the ans
plz help and show me the steps so I know how to do this!! thank you!!
Answer
6th of the power of 1 would be 5th power
Step-by-step explanation: