Recall the definition of absolute value:
• |x| = x if x ≥ 0
• |x| = -x if x < 0
So you need to consider 4 different cases (2 absolute value expressions with 2 possible cases each).
(i) Suppose 2x + 3 < 0 and x - 2 < 0. The first inequality says x < -3/2 and the second says x < 2, so ultimately x < -3/2. Then
|2x + 3| + |x - 2| = 6x
-(2x + 3) - (x - 2) = 6x
-2x - 3 - x + 2 = 6x
-3x - 1 = 6x
9x = -1
x = -1/9
But -1/9 is not smaller than -3/2, so this case provides no valid solution.
(ii) Suppose 2x + 3 ≥ 0 and x - 2 < 0. Then x ≥ -3/2 and x < 2, or -3/2 ≤ x < 2. Under this condition,
|2x + 3| + |x - 2| = 6x
(2x + 3) - (x - 2) = 6x
2x + 3 - x + 2 = 6x
x + 5 = 6x
5x = 5
x = 1
This solution is valid because it does fall in the interval -3/2 ≤ x < 2.
(iii) Suppose 2x + 3 < 0 and x - 2 ≥ 0. Then x < -3/2 or x ≥ 2. So
|2x + 3| + |x - 2| = 6x
-(2x + 3) + (x - 2) = 6x
-2x - 3 + x - 2 = 6x
-x - 5 = 6x
7x = -5
x = -5/7
This isn't a valid solution, because neither -5/7 < -3/2 nor -5/7 ≥ 2 are true.
(iv) Suppose 2x + 3 ≥ 0 and x - 2 ≥ 0. Then x ≥ -3/2 and x ≥ 2, or simply x ≥ 2.
|2x + 3| + |x - 2| = 6x
(2x + 3) + (x - 2) = 6x
2x + 3 + x - 2 = 6x
3x + 1 = 6x
3x = 1
x = 1/3
This is yet another invalid solution since 1/3 is smaller than 2.
So there is one solution at x = 1.
Determine the decimal equivalent of 5 over 8
Answer:
3.125
Step-by-step explanation:
We know that
258
is the same as
25÷8
Then using
Long Division for 25 divided by 8
and rounding to a Max of 3 Decimal Places gives us
=3.125
pls help everyone this is due tomorrow at 8 am <3
Answer:
e=19.6h
Step-by-step explanation:
If in 21 hours, she earns 411.60 dollars, then we need to find how much she makes in ONE hour.
21 h 1 hour
--------- = ------------------
411.60 dollars xdollars
To get from 21 to 1, I would have to divide by 21, right? So, do the same for the denominators.
411.60 / 21= $19.6
Now, since we know the unit rate, we can make an equation!
e=19.6h
A system of linear equations includes the line that is created by the equation Y = 0.5x-1 and the line through the
points (3, 1) and (-5, -7), shown below.
What is the solution to the system of equations?
A. (-6, -4)
B. (0, -1)
C. (0, -2)
D. (2, 0)
Step-by-step explanation:
the answer I think D should be
Answer:
The answer is (2,0)
Step-by-step explanation:
We know one equation [tex]y =0.5x - 1[/tex] and the other points (3, 1) and (-5, -7).
For the first step, we need to graph the equation we know, since the points already plotted, and therefore have its own line.
As we can tell it crosses over points (2,0) making this equation having exactly one solution.
Making the correct awnser D; (2,0)
Write the following statements in the form of equations.
c. One third of a number plus 7 is 26.
Answer:
Brainless please?
Step-by-step explanation:
1/3x +7=26
Factor out the GCF
4g^3-6g+20g^2
Answer:
[tex]\sf 2g(2g ^2-3+10g)[/tex]Step-by-step explanation:
[tex]\sf 4g^3-6g+20g^2[/tex]
GFC: 2g
We'll Write the GCF first, then, divide each term by the GCF.
[tex]\sf 2g(\frac{4g^3}{2g}-\frac{6g}{2g} +\frac{20^2}{2g} )[/tex]
[tex]\sf 2g(2g ^2-3+10g)[/tex]
In a survey, 3 out of 20 students were left-handed. Based on this information, if 300 students were interviewed, how many of them could be expected to be left-handed?
Based on the information given, from the fraction, it can be noted that the number of left-handed people will be 45.
From the information given, it was stated that in the survey, 3 out of 20 students were left-handed.
Therefore, in a population of 300 people, the number of left handed people will be:
= 3/20 × 300.
= 3 × 15
= 45
There are 45 left handed people.
Learn more about fractions on:
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I need help or the answer no one knows what to do
[tex]61 + (6x - 31) = 90[/tex]
Subtract both sides 61
[tex]61 - 61 + 6x - 31 = 90 - 61[/tex]
[tex]6x - 31 = 29[/tex]
Add both sides 31
[tex]6x - 31 + 31 = 29 + 31[/tex]
[tex]6x = 60[/tex]
Divide both sides by 6
[tex] \frac{6x}{6} = \frac{60}{6} \\ [/tex]
[tex]x = 10[/tex]
____________________________________________
Have a great day ♡
Answer:
x = 10
Step-by-step explanation:
It's a 90˚ angle so subtract 61 from 90, which is 29.
Then add 31 to that 29, which would come out to 60.
60 divided by 6 to isolate the variable would come to 10.
Check your answer by multiplying 10 by 6, subtract the 31, and lastly add the 61 to get back to your 90.
A couple of friends decide to race each other. Liam can run 5 meters per second, and Grace
can run 8 meters per second. Because he is slower, Liam also gets a head start of 12 meters.
Shortly after they start running, Grace will catch up to Liam. How far has Grace run at that
time? How long will that take?
Answer:
32 m
4 sec
Step-by-step explanation:
just trust me i did the math
Answer:
i agree with the other person
Step-by-step explanation:
Calculate the HCF of 8a³-27, 4a²-9 and 4a²-12a+9
[tex] \: \: \: \: \: [/tex]
first add
(3a²-5a+5)+(a³-5a²+8)
=3a²-5a+5+a³-5a²+8
=a³-2a3a²-5a²+5+8
=a³-2a²+13
and now,
substract a³-2a²+13 from a²-4a²-9
=7a²-4a²-9-(a³+13)
=7a²-4a²-9-a³+2a²-13
= a³+7a²-4a²+2a²-9-13
=-a³+5a²-22
hope it helpsLailah earns $9 per week working at the aquarium. Write and solve an inequality that can be used to find how many hours she must work in a week to earn at least $135. Explain the solution.
Answer: 15
Step-by-step explanation:
9 x h = 135
9 x 15 = 135
Solve 12 + 5= 7.
A. x = -2 and x = 12
B. x = -2 and x = -12
C. X = 2 and x = -2
O D. x = 2 and x = = -12
Answer:
if you mean 12-5=12 this answer is x=144
here is the step by step explanation.
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x/12-5-(7)=0
Step by step solution :
STEP
1
:
x
Simplify ——
12
Equation at the end of step
1
:
x
(—— - 5) - 7 = 0
12
STEP
2
:
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 12 as the denominator :
5 5 • 12
5 = — = ——————
1 12
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x - (5 • 12) x - 60
———————————— = ——————
12 12
Equation at the end of step
2
:
(x - 60)
———————— - 7 = 0
12
STEP
3
:
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 12 as the denominator :
7 7 • 12
7 = — = ——————
1 12
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
(x-60) - (7 • 12) x - 144
————————————————— = ———————
12 12
Equation at the end of step
3
:
x - 144
——————— = 0
12
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
x-144
————— • 12 = 0 • 12
12
Now, on the left hand side, the 12 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
x-144 = 0
Solving a Single Variable Equation :
4.2 Solve : x-144 = 0
Add 144 to both sides of the equation :
x = 144
One solution was found :
x = 144
A class of 25 students has 12 females. What is the ratio of males to females?
PLZ ANSSWER QUICK ITS URGENT FOR MY HOME-WORK!!!
geometry - please help
solve for x & y
Hope it helps.
Don't forget to click the Brainliest button if you like my answer and if you have any query, feel free to ask in the comment section.
I need help and I can’t find any sadly. Help!!
Answer:
Step-by-step explanation:
for 1. The addition property of equality esssentially means that if you were to add/subtract the same value to both sides of the equation, the equation would remain equal. this would be associated with 3. since adding 12 to both sides would give x on one side and 16 on the other which is equal to x=16
for 2. "given" just means the problem, so it is the 1st option. it just means "given the problem..."
for 3. collectiing like terms is the addition of -5x +6x. since they are on the same side eof the equation, and are in the same measurements (of x) they can be combined to eqaul positive x, this is represented by option 2
if p =5 q =3 find the value of 9p2²- 5q²
Answer:
Answer is in the attached file.
Bu sorunu nasil olur?
how can i solve this problem?
Answer:
i can't see your handwriting
Can someone please help me I will mark brainliest please.
Answer:
GE = 8 inches
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, then
GE = 2 × GH = 2 × 4 = 8 inches
What is solution for 7y+9+6y=46
Answer:
combine like terms
7y + 6y
13y + 9
Step-by-step explanation:
here is the solution
13y + 9
Please help with this !
Answer:
16 m
Step-by-step explanation:
12² + b² = 20²
I hope this helps!
Answer:
b = 16 m
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
b² + 12² = 20²
b² + 144 = 400 ( subtract 144 from both sides )
b² = 256 ( take square root of both sides )
b = [tex]\sqrt{256}[/tex] = 16 m
please pick the right anwers no bots please
Answer:
1. 2/3
2. 0
3. 7/2
4. -2
5. -2
6. 1
7. -4/3
8. Undefined
9. 8
10. 9/5
answer this question attached please
Answer:
30 degree
Step-by-step explanation:
sum of the interior angles of a hexagon=720degree
one angle of the hexagon=720/6=120degree
one angle of the rhombus=90 degree
therefore, x=120-90=30
What is an equation of a line that passes through (0,3) and (2,4)
Answer:
y=1/2x+3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-3)/(2-0)
m=1/2
y-y1=m(x-x1)
y-3=1/2(x-0)
y=1/2(x)+3
y=1/2x+3
This is a sketch of the curve with equation y = f(x).
The vertex of the curve is at (2, -3)
У
Х
(2, 3)
Write down the coordinates of the vertex of the curve with equation
a) f(x) + 5
b) –f(x)
help me please
Answer:
Below in bold.
Step-by-step explanation:
a) the curve moves up 5 units, so
the vertex is (2, -3 + 5)
= (2, 2).
b) - f(x) is the image of f(x) in the x-axis so
The vertex is at (2, 3).
Among 320 randomly selected airline travelers, the mean number of hours spent travelling per year is 24 hours and the standard deviation is 2. 9. What is the margin of error, assuming a 90% confidence level? Round your answer to the nearest tenth.
The margin of error of the random selection is 0.29
The given parameters are:
[tex]n = 320[/tex] --- the sample size
[tex]\sigma = 2.9[/tex] --- the standard deviation
[tex]\bar x = 24[/tex] --- the mean
[tex]\alpha = 90\%[/tex] --- the confidence level.
The margin of error (E) is calculated as follows:
[tex]E = z \times \sqrt{\frac{\sigma^2}{n}}[/tex]
So, we have:
[tex]E = z \times \sqrt{\frac{3.2^2}{320}}[/tex]
[tex]E = z \times \sqrt{\frac{10.24}{320}}[/tex]
The z-value for 90% confidence level is 1.645.
Substitute 1.645 for z
[tex]E = 1.645 \times \sqrt{\frac{10.24}{320}}[/tex]
[tex]E = 1.645 \times \sqrt{0.032}[/tex]
Take square roots
[tex]E = 1.645 \times 0.1789[/tex]
Multiply
[tex]E = 0.2943[/tex]
Approximate
[tex]E = 0.29[/tex]
Hence, the margin of error is 0.29
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HELP!!!
The difference of x and 15 is 62.
Answer:
x=77
Step-by-step explanation:
x-15 = 62
x = 62 + 15
x = 77
x=77. I hope this helps.
May is going to the grocery store to buy bananas and oranges. The bananas can only be purchased in groups of 65 and the oranges can only be purchased in groups of 5. If May wants to buy the same amount of bananas and oranges, then what is the lowest quantity of bananas that May can buy?
Answer: 1 group 65 bananas
Step-by-step explanation: We want the same number of bananas as oranges so 65 is divisible by 5 which is 13 5s to make 65.
Solve.
−4.8x=−4
What is the solution to the equation?
Enter your answer as a simplified fraction in the box.
x =
-4.8x=-4
The simplified fraction is 5/6
How I solved it:
-4.8 = -24/5 in fraction form.
-24/5 × 5/6 = -120/30
-120/30= -4
Answer:
-4
Step-by-step explanation:
What is the slope of the line that passes through the point (-4,-4)and (6,4)?
Answer:
slope = 0.8
Step-by-step explanation:
HOPE THIS HELPS :)
what set does -15/2 belong to
Answer:
Rational numbers
Step-by-step explanation:
any number that can be written as the ratio of two integers and that is terminating or repeating in decimal form
hoped that helped
Answer:
Rational numbers
Step-by-step explanation:
These numbers are numbers that can be expressed as a ratio of two integers and includes decimals that terminate (they end like 5.1 or 6.349) or repeat (such as 5.33333333333...)
One gallon of gas costs $1.50. Three gallons of gas costs $4.50. How much will 9 gallons of gas cost?
Answer:
9 gallons will cost $13.50
Step-by-step explanation:
1 gallon = $1.50
1.50 x 9 = 13.50
or
3 gallons = $4.50
4.50 x 9 = 13.50
Answer:
13.5 dollars.
Step-by-step explanation:
4.50 times 3 is 13.5 dollars.
Have A Good Day!!! :)
