Please help me understand how to solve equations like these, I don’t understand them:
Answers
Answer:
subtract the unwanted b termdivide by the coefficient of bb = 60Step-by-step explanation:
The numbers 4/5 and 9/10 are fractions. They multiply the variable 'b' in each case.
How to solve an equation like this
An example of an equation like this without fractions is ...
6 + 3b = 8b
You solve this sort of equation by rearranging the equation so the terms having 'b' in them are all on one side of the equal sign. You want all of the terms not containing 'b' to be on the other side of the equal sign.
Here, the terms are mixed on the left, but the right has only a 'b' term. So, if we can remove the 'b' term from the left side, we will have reached the goal
In the example equation, we do that by adding -3b to both sides of the equation.
6 +3b -3b = 8b -3b
Simplifying, we have ...
6 = 5b
Now, we divide by the coefficient of 'b', which is 5. We divide both sides of the equation by that:
6/5 = (5b)/5
6/5 = b . . . . after simplifying
_____
How to solve this equation
The given equation is solved exactly the same way. We add the opposite of the 'b' term that we don't want (which is 4/5b):
6 + 4/5b -4/5b = 9/10b -4/5b
Simplifying, this is ...
6 = (9/10 -4/5)b = (9/10 -8/10)b
6 = 1/10b
We can make the coefficient of 'b' be 1 by multiplying it by 10. We have to do that to both sides of the equation:
(10)(6) = (10)(1/10)b
60 = b . . . . . the solution
_____
Comment on equations in general
The one absolute rule in Algebra is that the equal sign must remain valid. You keep that commandment by observing the properties of equality. Essentially, you can do anything you like to one side of an equation, as long as you do exactly the same thing to the other side.
Here, when we say "subtract 4/5b", the way we keep this commandment is that we do it to both sides of the equation. The same is true for "multiply by 10". This is emphasized by the bold highlighting in the solution shown above.
Comment on arithmetic
In solving this equation, we did the arithmetic using the given fractions. Often, for an equation like this, you will be told the first step is to "eliminate fractions". You can do that here by multiplying the equation by 10:
10(6 +4/5b) = 10(9/10b)
60 +8b = 9b
Now, the unwanted term is 8b, so subtracting that (from both sides) gives ...
60 = b
This is essentially a "2-step" equation, either way you do it.
It is helpful if you are comfortable doing arithmetic with fractions, mixed numbers, decimals, percentages, and numbers in scientific notation, as well as integers.
Related Questions
A segment of a line that has an endpoint and extends infinitely in one direction is a
Answers
that would be a ray because it has a single endpoint and extends infinetly in one direction.
For what values of the variable does each of the following expressions make sense? We call the set of this values the domain of the expression. \sqrt{4-6a}
Answers
Given:
The expression is [tex]\sqrt{4-6a}[/tex].
To find:
The domain of the expression.
Solution:
We have,
[tex]\sqrt{4-6a}[/tex]
We know that, the square root is defined for only non-negative values. So,
[tex]4-6a\geq 0[/tex]
[tex]4\geq 6a[/tex]
Divide both sides by 6.
[tex]\dfrac{4}{6}\geq a[/tex]
[tex]\dfrac{2}{3}\geq a[/tex]
Thus, the value of variable less than [tex]\dfrac{2}{3}[/tex] make any sense.
Therefore, the domain of the given expression is [tex](-\infty,\dfrac{2}{3}][/tex].
The domain of a function is the set of input values the function can take
The domain of the expression is: [tex]\mathbf{(-\infty, \frac 23]}[/tex]
The expression is given as:
[tex]\mathbf{\sqrt{4 - 6a}}[/tex]
Set the radicand to 0
[tex]\mathbf{4 - 6a = 0}[/tex]
Add 6a to both sides
[tex]\mathbf{6a = 4}[/tex]
Divide both sides by 6
[tex]\mathbf{a = \frac 23}[/tex]
This means that, the value of a must not be greater than 2/3.
Hence, the domain of the expression is: [tex]\mathbf{(-\infty, \frac 23]}[/tex]
Read more about domain at:
https://brainly.com/question/1632425
Suppose that when a fabric production process is in control, the number of flaws in a piece of fabric of length l yards has a Poisson distribution with mean (.02)l. Suppose that periodically a length of fabric of 10 yards is inspected and the flaws are counted. If there are too many flaws, say more than k, the process will be presumed to be out of control, and stopped, and fixed. What should k be such that the probability of stopping the process when it is really in control is at most 5%
Answers
Answer:
Answer is attached below
Step-by-step explanation:
A length of fabric sampled = 10 yards
number of flaws in a piece of fabric having length = l yards
Poisson distribution mean = 0.02l
If the flaws are > k = process out of control hence would be stopped and fixed
Calculate The value of K such that the probability of stopping the process when it is really in control is at most 5%
using Poisson distribution
attached below is the detailed solution
During a thunderstorm yesterday, 600 millimeters of rain fell in 30 minutes. What is the unit rate for millimeters per minute?
Answers
9514 1404 393
Answer:
20 mm/min
Step-by-step explanation:
To find the rate in mm per minute, divide mm by minutes:
(600 mm)/(30 min) = 20 mm/min . . . unit rate
Which point on the graph represents the y-intercept?
у
5
V
4
N 03
W
>
1
1
N
-5 4 -3 -2 -14
1 2 3 4
12
4
25
Answers
Take a picture of the assignment and post it in your question.
Answer:
a
Step-by-step explanation:
did it on edge 2020
construction company builds an average of 48 houses per year. How many houses per month does the company build?
Answers
Answer:
48 per year would be 4 houses a month
Step-by-step explanation:
4 * 12 = 48
Give the next three terms of each Sequence.
1. 2,9,16,23,30,...
2. 49,44,39,34,29,...
3. 81,27,9,3,1,...
4. 1,4,9,16,25,...
5. 18,14,10,6,2,.....
Answers
2.)24
3.)1/3
4.)36
5.)-2
Hope it helps !!
Josie deposited $450 in a bank account
Answers
Answer:
What is the question?
Step-by-step explanation:
Deposit means add so he added $450 to his bank account
Please answer I need help thank you
Answers
Answer:
what is the question
Step-by-step explanation:
How much less than -2 is -6?
Answers
Answer is :
-4
Step-by-step explanation:
because -2-4=-6
Juliet wants to read more this year. So far, she has read two books for a total of 730 pages. Juliet's goal is to read 25 pages each day for the rest of the school year. Let x represent the number of days that she has followed her plan, and let y represent the total number of pages read.
Which of the following linear equations can Juliet use to model her plan and calculate the total number of pages read?
y=25−730xy is equal to 25 minus 730 x
y=730−25xy is equal to 730 minus 25 x
y=25+730xy is equal to 25 plus 730 x
y=730+25x
Answers
Answer: y= 730+25x
Step-by-step explanation:
Given: Total pages she already read = 730
Pages read by her in 1 week = 25
Let x = number of days that she has followed her plan, and let y = the total number of pages read.
Then total pages she will read in x days = 25x
therefore , Total pages she read till now(y) =730 + 25x
Hence, the linear equations can Juliet use to model her plan and calculate the total number of pages read:
y= 730+25x
What is the slope of the line that passes through the points
(4, -3) and (8, -2)?
Answers
Step-by-step explanation:
Hey there!
The points are;(4,-3) and (8,-2).
Use slope formula.
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
Put all values.
[tex]m = \frac{ - 2 + 3}{8 - 4} [/tex]
[tex]m = \frac{1}{4} [/tex]
Therefore, the slope is 1/2.
Hope it helps...
which statement is true about the transformation
Answers
Answer:
Where are the statements
Answer:
The answer is A
Step-by-step explanation:
Got this from edge
WHAT IS THE AVERAGE OF -2.5, 5.2, 1.7, -0.8?
Answers
-2.5 + 5.2 + 1.7 + (-0.8) = 3.6
3.6 / 4 = 0.9
Answer:
0.9
Step-by-step explanation:
-2.5 + 5.2 + 1.7 + -0.8 = 3.6
3.6 / 4 = 0.9
how could you change the expression -8 * -5 * -3 so that product is positive?
Answers
Answer:
yes just multiply it once more by -1
Step-by-step explanation:
“CAN”
PLACE VALUE
How does the 5 in the tens place
compare to the 5 in the ones place?
3,055
Answers
The 5 in the ones place is 5 in value
pleas help me y'all please
Answers
Answer:
D
Step-by-step explanation:
in order to compare all the numbers, we have to express them all in the same form to compare them easily, we will choose to convert all of them to decimal form:
20% = 20/100 = 0.2
1/3 = 0.33333
3.4 x 10⁻¹ = 0.34
-5/2 = -2.5
comparing all these numbers, it is now clear that in decending order:
0.34 > 0.33333 > 0.2 > -2.5
or
3.4 x 10⁻¹ > 1/3 > 20% > -5/2
(Answer D)
Help please.... I have got this wrong 2xs only once chance left
Answers
Answer:
a: 5x-1 = -6
b: 5x-1 = -6
+1 +1
5x = -5
divide
x = -1
wwe.iw What is the square root of -1? Oi O1 O1
Answers
Answer:
i (imaginary number)
Step-by-step explanation:
[tex] \sqrt{ - 1} = i(imaginary \: number)[/tex]
You hire 2 students to deliver takeout menus around town. One student (Darla), delivers 350 menus in 2 hours, and another student (Drew, delivers 510 in 3 hours. Who works the faster?
Answers
Darla is faster she gets more done in less time yes drew has a higher total but he worked a extra hour
help and explain if you can please
Answers
A scientist measured the water pressure at different depths. She made a table showing her findings. The x-values represent the depth, in meters. The y-values represent the pressure in atmospheres (atm).
x
y
0
0
15
3
30
6
Assuming there is a proportional relationship, which additional set of values could be included in the table?
(10, 2)
(40, 9)
(50, 38)
(100, 76)
Answers
Answer:
(10, 2)
Step-by-step explanation:
I just did the quiz.
The additional set of values that could be included in the table will be ( 10, 2). the correct option is A.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given table is as follows:-
x y
0 0
15 3
30 6
Here the x-values represent the depth, in meters. The y-values represent the pressure in atmospheres (atm).
The ratio between the values x and y is 15:3 or 30:6 or 5 :1. From the given options the additional set of values that could be included in the table having the same ratio of 5:1 is ( 10, 2 ).
Therefore, the additional set of values that could be included in the table will be (10, 2). the correct option is A.
To know more about ratios and proportions follow
https://brainly.com/question/12024093
#SPJ2
[tex]\frac{x}{5}[/tex] + 7 = -3
Answers
Answer:
[tex]\huge{\fbox{\sf{ x = -50}}}[/tex]
Step-by-step explanation:
[tex]\frac{x}{5} + 7 = -3[/tex]
Take the L.C.M of 5 and 1 ( i.e 5 )
⇒[tex]\frac{x+7 * 5}{5} = -3[/tex]
⇒[tex]\frac{x+35}{5} = -3[/tex]
Do cross multiplication
⇒[tex]x + 35 = -3 * 5[/tex]
⇒[tex]x + 35 = -15[/tex]
Move 35 to right hand side and change its sign
⇒[tex]x = -15 - 35[/tex]
Remember : The negative integers are always added but posses the negative ( - ) sign.
⇒[tex]x = -50[/tex]
The value of x is [tex]\boxed{\sf{ -50}}[/tex]
Hope I helped!
Best regards!
~[tex]\text{ TheAnimeGirl}[/tex]
Here's a linear equation in variable x and we have to compute the value of x for the above equation.
Given equation:
[tex] \large{ \rm{ \dfrac{x}{5} + 7 = - 3}}[/tex]So, Let's start solving the above equation:
Move 7 to the Right hand side,
Remember: Inverse of addition is subtraction
[tex] \sf{ \dfrac{x}{5} = - 3 - 7}[/tex]
[tex] \sf{ \dfrac{x}{5} = - 10}[/tex]
Now multiplying 5 in other side because again the inverse of division is multiplication,
[tex] \sf{ x = - 10 \times 5}[/tex]
[tex] \sf{x = \boxed{ \red{ - 50}}}[/tex]
And the required value for x is -50. So, we are done....
Carry On Learning !
Consider the line y=-1/2x+8
What is the slope of a line parallel to this line?
What is the slope of a ine perpendicular to this line?
Answers
Given parameters:
Equation of the line is y = -[tex]\frac{1}{2} x[/tex] + 8
Unknown:
Slope of line parallel to this line = ?
Slope of line perpendicular = ?
Solution:
A line parallel to this line will have the same slope with it.
A line perpendicular will have the negative inverse of this slope;
Slope of line = - [tex]\frac{1}{2}[/tex]
Slope of line parallel to this line = [tex]-\frac{1}{2}[/tex]
Slope of line perpendicular = negative inverse = -( -([tex]\frac{1}{\frac{1}{2} }[/tex])) = 2
So, the slope of line parallel to this line is - 1/2 and that perpendicular is 2
Marcus hiked 4 3/2 miles. John hiked 3 1/3 miles. How much further did Marcus hike?
Answers
Answer:
2.16666666667
plz give me brainliest
PLEASE PLEASE HELP WILL MARK BRAINLIEST
Find the equation of the line in slope-intercept form through (−5, 6) with slope = 3
Answers
Answer:
The answer is
[tex] \huge y = 3x + 21[/tex]
Step-by-step explanation:
To find an equation of a line given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
where
m is the slope
( x1 , y1) is the point
From the question the point is (−5, 6) and slope = 3
The equation of the line is
[tex]y - 6 = 3(x + 5) \\ y - 6 = 3x + 15 \\ y = 3x + 15 + 6[/tex]
We have the final answer as
[tex]y = 3x + 21[/tex]
Hope this helps you
Answer:
The answer is y=3x+21
Step-by-step explanation:
Solve the formula −4x+y=−6 for y.
Answers
Answer:
y=4x-6
Step-by-step explanation:
The formula for y is -6+4x from the equation −4x+y=−6.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is −4x+y=−6
Minus four times of x plus y equal to minus six.
We need to solve the formula for y.
In the given equation x and y are the variables.
Isolate the variable y by add 4x on both sides of the equation
y=-6+4x
Hence, the formula for y is -6+4x from the equation −4x+y=−6.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
the function f(x)=-4x+9 has a range given by {1, -3, -7, -15, -19, -23} select the domain values of the function from the list. complete the explanation for how you arrived at your answer. btw this isn’t actually a test it’s assigned as hw but please help
Answers
Let's see what to do buddy....
_________________________________
Remember from now on ,
rang = output
and also Remember ,
output = y = f(x)
So : range = f(x)
So we must put the range number instead of f(x) and solve for x.
Let's do it...
=======================================
[tex]f(x) = 1[/tex]
[tex] - 4x + 9 = 1[/tex]
Both sides minus 9
[tex] - 4x = 1 - 9[/tex]
[tex] - 4x = - 8[/tex]
Negatives simplified
[tex]4x = 8[/tex]
Divided both sides by 4
[tex]x = \frac{8}{4} \\ [/tex]
[tex]x = 2[/tex]
_________________________________
[tex]f(x) = - 3[/tex]
[tex] - 4x + 9 = - 3[/tex]
[tex] - 4x = - 3 - 9[/tex]
[tex] - 4x = - 12[/tex]
[tex]4x = 12[/tex]
[tex]x = \frac{12}{4} \\ [/tex]
[tex]x = 3[/tex]
_________________________________
[tex]f(x) = - 7[/tex]
[tex] - 4x + 9 = - 7[/tex]
[tex] - 4x = - 7 - 9[/tex]
[tex] - 4x = - 16[/tex]
[tex]4x = 16[/tex]
[tex]x = \frac{16}{4} \\ [/tex]
[tex]x = 4[/tex]
_________________________________
[tex]f(x) = - 15[/tex]
[tex] - 4x + 9 = - 15[/tex]
[tex] - 4x = - 15 - 9[/tex]
[tex] - 4x = - 24[/tex]
[tex]4x = 24[/tex]
[tex]x = \frac{24}{4} \\ [/tex]
[tex]x = 6[/tex]
_________________________________
[tex]f(x) = - 19[/tex]
[tex] - 4x + 9 = - 19[/tex]
[tex] - 4x = - 19 - 9[/tex]
[tex] - 4x = - 28[/tex]
[tex]4x = 28[/tex]
[tex]x = \frac{28}{4} \\ [/tex]
[tex]x = 7[/tex]
_________________________________
[tex]f(x) = - 23[/tex]
[tex] - 4x + 9 = - 23[/tex]
[tex] - 4x = - 23 - 9[/tex]
[tex] - 4x = - 32[/tex]
[tex]4x = 32[/tex]
[tex]x = \frac{32}{4} \\ [/tex]
[tex]x = 8[/tex]
=======================================
So the domain values are :
x = { 2 , 3 , 4 , 6 , 7 , 8 }
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
0.12k = 10.08
A.)48
B.)84
C.)0.48
D.) 0.048
Answers
Answer:
[tex] k = 10.08 \times 100 \div 0.12 \times 100 = 1008 \div 12 = 84[/tex]
Step-by-step explanation:
option B 84
.
Which of the following quantities are inversely proportional? WILL GIVE BRAINLIEST AND 25 POINTS
a
The number of hours worked and the amount of money earned, assuming the worker is paid by the hour
b
The height of a rectangular fish tank and the area of its base, if the volume is constant
c
The amount of candy purchased for $25.50 and the price per pound
d
The time it takes to use a 5 lb bag of dry cat food and the number of cats, if each cat eats the same amount of food per same time interval.
Answers
Answer:
I believe the answer is D
Step-by-step explanation:
Inverse proportion occurs when one value increases and the other decreases
D is the answer because as each cat eats the same amount of dry cat food, there is less dry cat food in the bag; so this is why D best answers the question.
Hope this helps!
Answer:
a is false, B is true,
Step-by-step explanation:A is false because the more hours you work, the more money you get.
B is true because if the volume is constant, the bigger the length, the smaller the width, or vice versa.