Answers
[tex]|x|^2 -2|x|-3=0\\\\\implies |x|^2 - 3|x| + |x| - 3 =0\\\\\implies |x|(|x| -3) + (|x| -3) = 0\\\\\implies (|x| - 3)(|x| +1) =0\\\\\implies |x| -3 = 0~~ \text{Or} ~~ |x| +1 =0\\\\\implies |x| = 3 ~~ \text{Or}~~ |x| = -1;\\\\\text{For}~ |x|= -1 ,~\text{ there are no solution for } x \in \mathbb{R}\\\\\text{So,}\\\\|x| = 3 \implies x = \pm 3[/tex]
Related Questions
A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m^3/min. How fast is the height of the water increasing
Answers
Answer:
[tex]\frac{3}{25\pi}[/tex] meters per minute
Step-by-step explanation:
Given:
[tex]V=\pi r^2h[/tex]
[tex]r=5[/tex]
[tex]\frac{dV}{dt}=3[/tex]
[tex]\frac{dh}{dt}=?[/tex]
Substitute r=5:
[tex]V=\pi r^2h[/tex]
[tex]V=\pi(5)^2h[/tex]
[tex]V=25\pi h[/tex]
Differentiate both sides:
[tex]\frac{d}{dt}V=\frac{d}{dt}(25\pi h)[/tex]
[tex]\frac{dV}{dt}=25\pi\frac{dh}{dt}[/tex]
Solve for dh/dt:
[tex]3=25\pi\frac{dh}{dt}[/tex]
[tex]\frac{3}{25\pi}=\frac{dh}{dt}[/tex]
Therefore, the height of the water is increasing at a rate of [tex]\frac{3}{25\pi}[/tex] meters per minute.
The school purchased 35 tickets for the ballet. Adult tickets were $10, and student tickets were $7. The total cost was $266.
If x represents the number of adult tickets purchased, and y represents the number of student tickets purchased, which system of equations represents this situation?
Answers
Answer:
Not too sure, but maybe this is what you need.
(Students = S, Adults = A) So, Ax + Sy = 266?
Or
x10 + y7 = $266
Step-by-step explanation:
I think the second one is the most accurate one, ignore the first equation. T^T
A TV has a listed price of $900.99 before tax. If the sales tax rate is 6.75%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.
Answers
$900.99 + $60.82 = $961.81 total cost.
I need help please? ????????
Answers
Answer:
ummmmm i really don't get it but I think its 17/66
Step-by-step explanation:
multiply in to each fraction
A local pizza shop has a membership program for frequent buyers. The membership costs $25 per month and members get a discounted price of $1.25 per slice of pizza. Tristan purchased a membership to this pizza shop. How much would Tristan have to pay the pizza shop if he bought 9 slices of pizza this month? What would be the monthly cost for xx slices of pizza?
Answers
Answer:
Step-by-step explanationcvm
Answer:
25
25+1.25x
Step-by-step explanation:
At least you got an actual answer this time hope this helps
Segment AB and CD intersect at point E, measure of angle ABC =6x+20 and measure of angle DEB=10x. What is the value of x?
Answers
Answer:
x = 5
Step-by-step explanation:
6x + 20 = 10x
I hope this helps!
please help me it's important
Answers
Answer:
circumference=2×3.142×radius
radius=16.8÷2=8.4
so,
circumference=52.7856cm
How many groups of are there in 30?
Answers
Answer:
6
Step-by-step explanation:
divide or multiply by 5 to get 30
Answer:
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A medication with an initial concentration of 1. 5 milligrams per liter is administered to a
patient, and the decay rate of the drug is 10% per hour. Which equation can be used to model
the concentration, C, of the drug in the patient’s body as a function of time, t, in hours since the
drug was administered?
Answers
Answer: Exponential decay model:
y
=
x
(
1
−
r
)
t
, half life of tablet is about
2
hours and after
t
=
3
hours , remaining drug on patient's system is
42.875
mg.
Step-by-step explanation: Initial drug
x
=
125
mg ; rate of decay
r
=
30
100
=
0.3
gm/hour
Exponential model:
y
=
x
(
1
−
r
)
t
=
125
(
1
−
0.3
)
t
=
125
⋅
0.7
t
Half life:
y
=
125
2
=
62.5
mg
∴
62.5
=
125
⋅
0.7
t
or
0.7
t
=
1
2
. Taking logarithm on both sides we get ,
t
log
(
0.7
)
=
log
(
0.5
)
∴
t
=
log
(
0.5
)
log
(
0.7
)
≈
1.94
(
2
d
p
)
hour
The half life of tablet is about
2
hours.
After
t
=
3
hours , remaining drug on patient's system is
y
=
125
⋅
0.7
t
=
125
⋅
0.7
3
=
42.875
mg [Ans]
At the beginning of the month you have $1500 in your bank account. Each time you visit the ATM you take $60 out. What is the rate at which your balance is changing each time you visit the ATM?
Group of answer choices
$3
-$60
$60
-$63
-$1500
-$3
Answers
6 divided by 20 write your answer in a decimal form
Answers
Answer:
0.3
Step-by-step explanation:
I just need 20 characters so yeah
Answer:
0.3
Step-by-step explanation:
What’s the an and the a10
Answers
Answer:
an = -6 + n
a10 = -6+ 10 =4
Step-by-step explanation:
an should start at one behind the first number so it should be -6. Then we add whatever the sequence is increasing by, which is 1 in this case, multiplied by n.
an = -6 + n
a10 = -6+ 10 =4
Alright I need help.. I will mark brainliest .
;-;
Answers
Answer:
x - y = 9
Step-by-step explanation:
When x goes up by 1, y goes up by 1. That means there is a constant difference between the values. That difference is x1 -y1 = 1 -(-8) = 9.
An equation relating the values is ...
x - y = 9
_____
Some folks like to see the relation in "y =" form. You can add y-9 to both sides to get that form:
y = x -9
Please and thank youuuuuu! :)
Answers
We know the slope intercept formula. Using the formula, we can find the slope.
Formula: y = mx + bGiven equation: y = 4x - 6m = Slopeb = y-interceptNow, let's compare both equations to find out what is the slope.
=> y = mx + by = 4x - 6
Conclusion:We can clearly see that m is replacing with 4. That basically means the slope is 4.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
find the circumference of a cd that has an diamater of 5 round your andwer to the nereast tenth
Answers
Answer:
15.7
Step-by-step explanation:
C = 2πr
C = 2(3.14)(2.5)
C = 15.7
can anyone please help?
Answers
Answer:
-1 or 1.
Step-by-step explanation:i hope thats what your looking for.
if 10 seeds are planted, what is the probability that exactly 3 don't grow?
Answers
Answer:
10:7
Step-by-step explanation:
take 10 as it is and it becomes 10
then,10-3 it is because when 3 don't grow it subtracts and becomes 7
Heather works 40 hours a week and she earns $11. 50 per hour. When Heather works over 40 hours, her pay is 1. 5 times her hourly pay. How much does Heather earn if she works 46 hours in one week?.
Answers
11.5 x 1.5 is 17.25
17.25 x 6 is 103.5
103.5 + 460 is 563.5
the answer is $563.50
The amount that Heather earns if she works 46 hours in one week is; $563.5
Amount she earns per hour if she works for 40 hours a week = $11.5 per hour
If she works over 40 hours, her hourly pay is 1.5 times the previous rate.
Thus;
Amount she earned for 40 hours is;
11.5 × 40 = $460
Amount she earned for the 6 extra hours to make it 46 hours is;
1.5 × 11.5 × 6 = $103.5
Total amount she earned for the 46 hours = $460 + $103.5 = $563.5
Read more on proportion word problems at; https://brainly.com/question/160640
What is the y-intercept of a line that passes through the points (1,-7) and (5,-15)?
Answers
Answer: (0,-5) or just -5
Step-by-step explanation:
gradient = change in y/change in x = (-7+15)/(1-5) = -2
y = -2x + c
-7 = -2 x 1 + c
c = -7 + 2 = -5
y intercept is (0, -5)
The recipe for Nestle Tollhouse Chocolate Chip Cookies calls for 2
2
cups of chocolate chips to make 5
5
dozen cookies. If you want to bake 9
9
dozen cookies, how many cups of chocolate do you need?
Answers
Answer:
6 cups of chocolate chips
Step-by-step explanation:
2:5 5+4=9 so add 4 to each side of the ratio
6:4
Write a function for the line with a slope of 5 that passes through the point (2, 1). Enter the correct equation in the box.
Answers
Answer:
brainly
Step-by-step explanation:
wich of the following functions maps 3 to -5?
Answers
Answer:
A
Step-by-step explanation:
Consider all options and find f(3):
A.
Then
Not -5, so this option is false.
B.
Then
This option is true.
C.
Then
Not -5, so this option is false.
D.
Then
Not -5, so this option is false.
Write the word sentence as an equation. Then solve the equation.
The quotient of a number and -1.5 is 21.
a
Equation:
Solution: x=
Answers
Answer:
Step-by-step explanation:
"The quotient of a number and -1.5 is 21."
Let X be the "number."
X/-1.5 = 21
X = -1.5*(21)
X = - 31.5
PLS HURRY!!! NO LINKS, NO STEALING POINTS, AND NO USELESS ANSWERS OR YOU WILL BE REPORTED!!!!!!
What type of triangle is this?
Answers
Answer:
It's an obtuse Scalene Triangle
Step-by-step explanation:
Look up triangle angle calculator and enter in the sides
What is the equation of the line in slope-intercept form?
Line on a coordinate plane. The line runs through points begin ordered pair negative 5 comma 0 end ordered pair and begin ordered pair 0 comma 3 end ordered pair.
Enter your answer in the boxes.
y =
x +
Answers
Step-by-step explanation:
Use the slope formula
Taking two points on the line:
(0,3) and (-5,0)
3-0/0+5
You will get: 3/5 as your slope
The y-intercept is (0,3)
Therefore:
y = 3/5x + 3
find x and y for this triangle
Answers
Answer:
x = 1.25
x = 1.75
Step-by-step explanation:
I marked the points of this triangle in the attached image so it's easier to explain.
ΔABC is similar to ΔADE, and all pairs of corresponding sides are proportional as a result.
[tex]\frac{DE}{BC}=\frac{AD}{AB}=\frac{AE}{AC}[/tex]
The length of the sides BC and DE is given, so I'll start with that and set it equal to the proportion between AB and AD.
[tex]\frac{DE}{BC}=\frac{AD}{AB}\\\\\frac{10}{8}=\frac{x+5}{5}\\\\10\times5=(x+5)\times8\\50=8x+40\\10=8x\\x=1.25[/tex]
Now, you can do the exact same thing for y:
[tex]\frac{DE}{BC}=\frac{AE}{AC}\\\\\frac{10}{8}=\frac{y+7}{7}\\\\10\times7=(y+7)\times8\\70=8y+56\\14=8y\\y=1.75[/tex]
Which equation could have been used to create this table? need answer fast
y = x + 6
y = x + 5
y = 6x
y = 7x
Answers
Answer:
y=6x
Step-by-step explanation:
Each value for y is can be divided by 6 for the value of x
Answer:
y=6x
Step-by-step explanation:
Find the product:
[tex] \frac{1}{8} \times \sqrt{8} [/tex]
Answers
Answer:
≈ 0.35
Step-by-step explanation:
First simplify [tex]\sqrt{8}[/tex] and [tex]\frac{1}{8}[/tex] :
[tex]\sqrt{8}[/tex] ≈ 2.83
[tex]\frac{1}{8}[/tex] = 0.125
Now multiply them as shown in the original equation:
0.125 x 2.83 = 0.35375 ≈ 0.35
there are 63 counters in total. the total number of counters in box A and box B is 36. the difference between box A and C is 10. work out the number of counters in each box
Answers
Answer:
A 17, B 19, C 27
Step-by-step explanation:
A + B = 36
A + B + C = 63
63 - 36 = 27, which is C
C - A = 10
27 - A = 10
A = 17
A + B + C = 63
17 + B + 27 = 63
63 - 44 = 19
A copy machine makes 32 copies per minute. How long does it take to make 144 copies?
?????