4y - 9 - 6y = 2(y + 5) - 3 solve for y
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{y = - 4}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4y - 9 - 6y = 2(y + 5) - 3}[/tex]
Subtract like terms : 6y from 4y
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2(y + 5) - 3}}[/tex]
Distribute 2 through the parentheses
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2 *y + 2 *5 \: - 3}}[/tex]
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2y + 10 - 3}}[/tex]
Subtract 3 from 10
[tex] \longrightarrow{ \sf{ - 2y - 9 = 2y + 7}}[/tex]
Move 2y to left hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2y - 2y - 9 = 7}}[/tex]
Move 9 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2y - 2y = 7 + 9}}[/tex]
Combine like terms
[tex] \longrightarrow{ \sf{ - 4y =7 + 9}}[/tex]
Add the numbers : 7 and 9
[tex] \longrightarrow{ \sf{ - 4y = 16}}[/tex]
Divide both sides by -4
[tex] \longrightarrow{ \sf{ \frac{ - 4y}{ - 4} = \frac{16}{ - 4}}} [/tex]
Remember : Dividing a positive integer by any negative integer gives a negative integer.
[tex] \longrightarrow{ \boxed{ \sf{y = - 4}}}[/tex]
------------------------------------------------------------
Let's check whether the value of y is -4 or not.
VerificationL.H.S : [tex] \sf{4y - 9 - 6y}[/tex]
plug the value of y and simplify
[tex] \dashrightarrow{ \sf{4 * (- 4 )- 9 - 6 * (- 4)}}[/tex]
[tex] \dashrightarrow{ \sf{ - 16 - 9 - ( - 24)}}[/tex]
[tex] \dashrightarrow{ \sf{ - 16 - 9 + 24}}[/tex]
[tex] \dashrightarrow{ \sf{ - 16 + 15}}[/tex]
[tex] \dashrightarrow{ \sf{ - 1}}[/tex]
R.H.S :[tex] \sf{2(y + 5) - 3}[/tex]
plug the value of y and simplify
[tex] \dashrightarrow{ \sf{2( - 4 + 5) - 3}}[/tex]
[tex] \dashrightarrow{ \sf{2 *1 - 3}}[/tex]
[tex] \dashrightarrow{ \sf{2 - 3 }}[/tex]
[tex] \dashrightarrow{ \sf{ - 1}}[/tex]
∴ L.H.S = R.H.S
The value of y is -4
And we're done!
------------------------------------------------------------
Rules for solving an equationIf any equation contains fractions , multiply each term by the LCM of denominators.Remove the brackets , if any.Collect the terms with the variable to left hand side and constant terms to the right side by changing their signs ' + ' into ' - ' and ' - ' into ' + '.Simplify and get the single term on each side.Divide each side by the coefficient of variable and then get the value of variable.Hope I helped!
Best regards! :D
~TheAnimeGirl
In the diagram below, find the value of x to the nearest hundredth
Answer:
x = √324 = 18
Step-by-step explanation:
x shows up only in the second problem, so I'll focus on that problem.
This is a right triangle because one of the three angles is 90 degrees.
Thus, the Pythagorean Theorem applies: x^2 + 24^2 = 30^2, or
x^2 = 900 - 576 = 324
Then x = √324 = 18
For the following pairs of equations explain why the equations are NOT equivalent.
jess makes salad dressing by mixing lemon juice and olive oil in the ratio 2:5 by volumr.me. shes uses 0.5 litres of lemon juice. work out how much olive oil she uses to make the salad dressing.
Answer:
its 2.5 liters of olive oil because .5 times 5 equals 2.5 needed to satisfy ratio.
Amanda made $276 for 12 hours of work, At the same rate, how many hours would she have to work to make $115
Answer:
5 hours
Step-by-step explanation:
276/12= 23
115/23= 5
Your making chocolate chip cookies. The recipe calls for 1/8 teaspoon salt to 1/4 teaspoon baking soda. How much salt is needed for one teaspoon of baking soda
Answer:
1/2 teaspoon salt
Step-by-step explanation:
We can make this into a ratio of salt:baking soda
1/8:1/4
now, how many 1/4 will we need to make 1?
If we multiply 1/4 by 4, we get one. So, we should do the same to 1/8!
1/8*2=4/8, or 1/2 teaspoon
What is the equation of the line parallel to 8x−16y=−14 and passing through (3,0)?
6x−12y=18
6x+12y=18
12x−6y=−18
12x+6y=18
Answer:
2y = x - 3
Step-by-step explanation:
Parallel lines can be defined as lines that do not intersect and as a result of this, parallel lines have the same slope but different intercepts.
Given the following data;
Points (x, y) = (3, 0)
Equation is 8x - 16y = -14
To find the equation of the line?
First of all, we would have to determine the slope of the line;
y = mx + c ......equation 1
8x - 16y = -14
Rearranging the equation, we have
16y = 8x + 14
Dividing through by 16, we have;
y = 8/16(x) + 14/16
y = 1/2(x) + 7/8
Therefore, the slope, m is 1/2
*To find the intercept*
Since the line is parallel we would use, m = 1/2
Substituting the values into equation 1, we have;
y = mx + c for x = 3 and y = 0
0 = 1/2(3) + c
c = -3/2
Re-writing the equation of line;
Slope, m = 1/2
Intercept, c = -3/2
y = 1/2(x) + (-3/2)
Multiplying all through by the lowest common denominator "2"
2y = x - 3
twice the greater of two integers odd integers is 13 less than 3 times the lesser number. find the integers. what are the integers to this riddle?
Answer:
17 and 19
Step-by-step explanation:
n= lesser integer n+2= greater integer
2(n+2) = 3n -13
2n +4 = 3n-13
n= 17
lesser number =17
The other greater number = 19 (they are odd,so skipping 18)
19 x 2 = 38
17x3 - 13 =51-13 = 38
Cuáles son los métodos de integración
Answer:
Spanish:
Los diferentes métodos de integración incluyen:
Integración por sustitución.
Integración por partes.
Integración mediante identidades trigonométricas.
Integración de alguna función particular.
Integración por fracción parcial
Step-by-step explanation:
English:
The different methods of integration include:
Integration by Substitution.
Integration by Parts.
Integration Using Trigonometric Identities.
Integration of Some particular function.
Integration by Partial Fraction.
help
i dunno it
please please
Answer:
it takes 24 days
answer the question under here yo
What is the slope of the line that passes through the points (-6, -10) and (3,-13)? Write your answer in simplest form.
We must use slope formula* to solve this.
[tex]\frac{-13 - (-10)}{3 - (-6)}\\\\\frac{-3}{9} = -\frac{1}{3}[/tex]
m** = [tex]-\frac{1}{3}[/tex]
*Slope Formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
**m is the symbol for slope.
solve each system of equations using substitution. x=y+1 x=3y+2
Answer:
x=1/2
y=-1/2
Step-by-step explanation:
x = y+1
x = 3y+2
Substitution means that you solve one equation for a variable by plugging it into the other equation. In this case, the first part is already done for you, and all you have to do is plugging in.
As you're given the value of the x in both equations, it does not matter which equation you plug into. You can plug either equation into one another.
For this, I will show you by plugging in the bottom equation for the top equation.
x = y+1
x = 3y+2
As we know x=3y+2, you must SUBSTITUTE that for the "x" in the top equation.
3y+2 = y+1
From there, you must solve it for the "y" value. In order to solve for the "y" value, you must get the "y" by itself onto one side.
So, subtract y from both sides.
(3y-y)+2 = (y-y)+1
Rewrite the equation.
2y+2 = 1
Remember, the goal is to get the "y" BY ITSELF.
There's a "+2" on the side of the y, so that has to be cancelled out. You can cancel it out by doing the OPPOSITE of adding, which is subtracting. So subtract both sides by 2.
2y+(2-2)=(1-2)
When subtracting a bigger number from a smaller number. The pattern is: Keep it, flip it, flip it.
Keep the 1.
Flip the - to a +
Flip the 2 into a -2.
So you get 1+(-2) which is -1. Now, rewrite the equation.
2y=-1
You want the y by itself. Right now, the y is being multiplied by 2, so you have to do the OPPOSITE, which is division. Divide both sides by 2.
y=-1/2
Now, use this value to plug into your ORIGINAL equations (you can pick either)
x = y+1 OR x = 3y+2
x= -1/2 + 1
x=1/2
(1/2, -1/2)
I will brainlist HELP
Answer:
x = 7
y = 10
Step-by-step explanation:
<K and <NLK are marked as being equal.
That means that KN and LN are equal.
So LN = 6
y - 4 = 6
y = 4 + 6 = 10
For the same reason LN = LM
That means that x + 3 = 10
x = 10 - 3
x = 7
Jasmin's dog weighs 62 pounds. Her vet told her that a healthy weight for her dog would be less than or equal to 40 pounds.
Jasmin's dog can lose an average of 3 pounds every week. Write the solution to an inequality that describes all possible number of weeks
z for which her dog can be at a healthy weight.
Answer:
62-3z ≤ 40
Step-by-step explanation:
62 is the starting point. jasmin's dog can lose 3 lbs per week and z represents the number of possible weeks. then we know it has to be less than or equal to 40. so put that there.
h(t) = -10+ - 6
h()= -44
Answer:
-44
Step-by-step explanation:
What is the solution to the inequality 75 > x/15?
______________________________________
A) x 1,125
C) x 5
______________________________________
Answer:
75 > x/15
Step-by-step explanation:
Step 1: Mulitply the 15 on both sides in order to get the x by it self.
Step 2: Simplify. 75 x (15) >x/15 x (15)
Step 3: The 15 on the right hand side cancels out leaving the x by itself.
Final Answr: 1125 > x which translates to x < 1125
The solution to the inequality is: A) (x > 1125)
To solve the inequality 75 > x/15, we need to find the range of values for x that satisfy the inequality.
First, we can start by isolating x on one side of the inequality. To do that, we can multiply both sides of the inequality by 15 (since 15 is a positive number, we don't need to reverse the inequality sign):
75 * 15 > x
Now, simplify the left side of the inequality:
1125 > x
So, the solution to the inequality is x < 1125, which means all values of x that are less than 1125 will satisfy the inequality.
Visually, if we plot the graph of y = x/15 and y = 75, we'll see that y = x/15 is a straight line with a positive slope of 1/15 passing through the origin, and y = 75 is a horizontal line parallel to the x-axis at the y-coordinate of 75. The solution to the inequality is the region below the line y = 75, which corresponds to the values of x that are less than 1125.
In real-world terms, this inequality represents a scenario where 75 is greater than some fraction of x divided by 15. To satisfy the inequality, x must be less than 1125. For example, if x represents the number of items sold in a store, this inequality would indicate that the store must sell fewer than 1125 items to meet the condition. The store's sales would need to be less than 1125 * 15 = 16,875 to maintain the inequality's validity. Beyond this point, if the store sells more items, the inequality would no longer hold true.
To know more about inequality:
https://brainly.com/question/20383699
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answer the question for good boy stars
Answer:
its-5.5°C
explanation
combine it
Answer:
the answer is br-br
Step-by-step explanation:
that is answer bro
What is the value of the expression 5y² + 4x when x = 2.5 and y = 3?
Answer:
55
Step-by-step explanation:
the value of the expression 5y² + 4x when x = 2.5 and y = 3 will be 55.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression 5y² + 4x
To calculate the value of expression at x = 2.5 and y = 3
Substitute the value of x and y in the expression:
=> 5y² + 4x
=> 5* 9 + 4 * 2.5
=> 45 + 10
=> 55
therefore, 55 is the value of the expression 5y² + 4x when x = 2.5 and y = 3.
Learn more about expression here:
https://brainly.com/question/23246712
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A satellite travels 12 miles in 15 minutes at a constant speed. What is the satellite’s speed in mile per hour?
Answer: 46 mph
Step-by-step explanation: 15*4=60 so 12*4=46
I hope this helps!
Help pls I'm gonna be screwed if you don't get this pls pls pls anyone who knows math well pls help me I'm gonna cry it's over due please:( :(
Just last two please
Answer:
WRONG ALL
Step-by-step explanation:
3. Should be:
[tex] - 4 \frac{7}{8} \times \frac{2}{3} \\ \\ - \frac{39}{8} \times \frac{2}{3} \\ \\ \frac{ -13}{4} [/tex]
4. Should be:
[tex] - 3 \frac{1}{5} + - \frac{2}{3} \\ \\ - 3 \frac{3}{15} - \frac{10}{15} \\ \\ - 3 \frac{7}{15} [/tex]
I hope this helps you :)
HELP WILL GIVE BRAINLIEST
Answer:
A. 2000 square inches
B. 53.1 square inches
Answer quick please!
Please help me with this :((
Answer:x=5 or F
Step-by-step explanation:(8x+6)/(5x-2)=2, because it is the midsegment, cross multiply, and you get 2x=10, so x=5
Can someone help me on this? Will mark brainleist if they get it right!
Answer:
2.5
Step-by-step explanation:
2500 ÷ 1000
*Sorry if this is wrong*
Find the product. Write your answer as a mixed number in simplest form. 5 2/9 x 2 3/7
Answer:
12, 43/63
Step-by-step explanation:
Answer: 12 43/63
Step-by-step explanation: it was correct on my test
what is the slope of the line ? please
Answer:
1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
There are 20 students. Two-fifths of the students are girls. How many students are girls?
Answer:
There are 8 girls.
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
20 divided by 5 = 4.
4x2=8
Parker the dog is 2 feet 6 inches long. There are 2.54 centimeters in 1 inch. How many centimeters is Parker the dog?
Answer:
Parker the dog is 76.2 centimeters long.
Step-by-step explanation:
Parker the dog is 2 feet 6 inches long. There are 2.54 centimeters in 1 inch. How many centimeters is Parker the dog? 2 feet = 12 inches. 2(12) + 6 = 30
30(2.54) = 76.2.
Please let me know if you have anymore questions.
Good Luck! :)
1 foot = 12 inches
1 inch = 2.54 centimeters
1 foot = 30.48 centimeters
2 x 30.48 = 60.96
6 x 2.54 = 15.24
60.96+15.24=76.20
Parker the Dog is 76.20 centimeters tall.
If you subtract 16 from my number and multiply the difference by -3, the result is -39 what is my number
Answer:
29
Step-by-step explanation:
Start with -39. We need to do inverse operations to figure out the solution. -39 divided by -3 is 13, and 13 plus 16 is 29.
Answer:
29
Step-by-step explanation:
-39=-3(n-16)
13=n-16
29=n