Answers
9514 1404 393
Answer:
a) (x < -3) ∪ (-1 < x)
b) all real numbers
c) x ≤ 1
d) no solution
Step-by-step explanation:
An absolute value inequality of the form |f(x)| ? a resolves to two inequalities:
±f(x) ? a
where ? is some comparison symbol.
__
a) |x +2| > 1
resolves to the inequalities ...
x + 2 > 1 ⇒ x > -1
and the other inequality this resolves to is ...
-(x +2) > 1
-x -2 > 1
-x > 3
x < -3
Then the solution is the union of the disjoint solution spaces:
(x < -3) ∪ (-1 < x)
__
b) |2(x -1)| ≥ 0
2(x -1) ≥ 0 ⇒ x ≥ 1
and the other inequality this resolves to is ...
-2(x -1) ≥ 0
x -1 ≤ 0 . . . . . divide by -2
x ≤ 1
The union of these solutions is ...
x ∈ all real numbers
__
c) 9x -4 ≤ 6 -x
10x ≤ 10 . . . . . . add x+4 to both sides
x ≤ 1 . . . . . . . . . divide by 10
__
d) No solution. (An absolute value cannot be negative.)
__
The attachment shows the solutions plotted against a number line.
_____
Additional comment
When the inequality is of the form ...
|f(x)| < a
it can be written as the compound inequality ...
-a < f(x) < a
If the comparison is > instead of <, using the same "expansion" results in an inconsistency:
-a > f(x) > a . . . . . . never true for a > 0
If you ignore that technicality (which your teacher may not understand), you can do the solution in the same way you would for the other inequality symbol(s). Just remember the result should be the union of the two disjoint solution spaces.
Using (a) as an example:
-1 > x+2 > 1 . . . . . to solve this, we subtract 2 everywhere
-3 > x > -1 ⇒ the solution is (-3>x) ∪ (x>-1)
Related Questions
please include explaination
Answers
Answer: 104 i think is your answer hope this helped
plz make brainly
Step-by-step explanation:
pleassssssssssseeeeeeeee help
Answers
HELP ME I WILL HIVE U 5 stars ON IF ITS RIGHT PLZZZ !!!!!!!
Answers
Answer:
40
Step-by-step explanation:
The two angles form a right angle
A right angle has a measure of 90 degrees meaning that the sum of the two angles is 90
a + 50 = 90
90 - 50 = 40
Thus, a = 40
missing angle is (40⁰) :)
for brainiest:):):):):):):)
Answers
Answer:
8. Yes
9. No
12. No
13. Yes
Step-by-step explanation:
all angles in quadratics must be equal to 360 degrees
Find the constant rate of change for the representation,
24x-28y=14
Answers
Answer:
6/7
Step-by-step explanation:
The constant rate of change is also know as the slope of the expression
Given
24x-28y=14
Write in standard form y = mx+c
m is the slope
24x-28y=14
-28y = -24x + 14
y = -24x/-28 + 14/-28
y = 6/7 x - 1/2
Compare
mx = 6/7 x
m = 6/7
Hence the constant rate of change is 6/7
A company has cups for its water cooler. Each cup has a height of 14 cm and the base has a radius of 3 cm. How much water is needed to fill 125 cups
Answers
Answer:
125 cups can hold 49.5 liters of water.
Step-by-step explanation:
The volume of the cup will tell how much water is needed to fill each cup.
The volume of the cup can be determined by the formula
V= base area* height
V= πr²* h
V= 22/7 (3)² (14)
V= 396cm³
125 cups can hold 125 * 396 cm³= 49500cm³
But 1 cm³= 0.001 Liters
Therefore = 49500*0.001= 49.5 liters
125 cups can hold 49.5 liters of water.
The two lines graphed below are parallel. How many solutions are there to the system of equations?
Answers
Answer:
C. Zero
Step-by-step explanation:
The solution of the system of equations would be the point where they intersect, but since these lines are parallel, they will never intersect, so therefore there are zero solutions.
PLEASE NO LINKS OR SITES!!!! JUST ANSWERS. THANK YOU!
Answers
Answer:2/16
Step-by-step explanation:
Answer:
= 64
do u need the working out?
If the height is 30 yards and the base has an area of 56 what's the volume?
Answers
Answer:
1680.
Step-by-step explanation:
30 * 56
What is the volume of the right rectangular prism with a length of 18 inches, a width of 4 inches, and a height of 10 inches? 32 Inches cubed 64 Inches cubed 720 Inches cubed 1,440 Inches cubed
Answers
Answer:
720in
Step-by-step explanation:
V=LWH
V=(18)(4)(10)
Answer:
720
Step-by-step explanation:
Quick, please!
If 2 answers will vote brainliest!
Answers
Answer:
Hello again! x = 85
Step-by-step explanation:
Because triangles are 180 degrees and
68 + 27 = 95 and 180 - 95 = 85 so our missing angle is 85 hope this helps!
Six times the sum of a number and 4 equals 5
Write as an equation
Answers
Answer:
6 (x+4) = 5
Step-by-step explanation:
Answer:
6(x+4)=5
Step-by-step explanation:
El numero de espectaodres de un concurso de television que comenzo en octubre aumento un 20% en noviembre y disminuyo un 20% en diciembre. Si al terminar diciembre tuvo 1 920 000 espectadores, ¿cuantos tenia en el mes de octubre?
Answers
Answer:
Se me hace que es 1843200
Step-by-step explanation:
Espero que te ayude esto un poco :)
The slope between two points (2,b) and (1, -2) is 4. Find b.
Answers
Answer:
b=2
Step-by-step explanation:
To get slope given two points, take the difference of the y values and divide it by the difference of the x values.
(This is also called change in y over change in x, or rise over run)
b-(-2)/2-1=4
b+2/1=4
b+2=4
b=2
Find Product
-3x(8x^2+2x-4)
Answers
Answer:
−243−62+12
Step-by-step explanation:
..............
A triangle has a base that measures 14 inches.
The area of the triangle is 3.5 square inches.
What is the height of the triangle?
Answers
Please help me with this problem.
Answers
-a-b³+ab if a=-3 and b=2
Answers
Answer:
-11
Step-by-step explanation:
Lets rewrite the equation with the values
-(-3) - 2³ + ab
3 - 8 + (-3*2)
-5 + -6 = -11
-11
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
-11
Step-by-step explanation:
Simply plug in a=-3 and b=2 into the equation provided. Remember the signs (+/-) and be careful with your calculations.
-(-3) - (2)^3 + (-3)(2) = -11
u-5=-8 is tell solution of equation
Answers
Answer:
u = -3
Step-by-step explanation:
Solve for u:
u - 5 = -8
Hint: | Isolate terms with u to the left hand side.
Add 5 to both sides:
u + (5 - 5) = 5 - 8
Hint: | Look for the difference of two identical terms.
5 - 5 = 0:
u = 5 - 8
Hint: | Evaluate 5 - 8.
5 - 8 = -3:
Answer: u = -3
u = -3
step by step
u=-8+5
u =-3
hope that helps
Find the value of x in the figure below.
Answers
Answer:
The sum of alternating angle end up to 180 degress
A recipe requires & cup of oil for every cup of water. How much oil (in cups) is
needed per cup of water?
Answers
Answer:
the answer is one cup of oil for each cup of water. hope this helps!
Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile?
A: 0.68 miles
B: 0.81 miles
C: 1.15 miles
D: 1.44 miles
Answers
Answer: B: 0.81 miles
Step-by-step explanation:
The find the total distance, you must look for firs the missing side. To get use the formula that is derived from the Pythagorean theorem which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The formula for this is: a^2 + b^2 = c^2
So let the first side or a be .19
and the second side be .28
and now we are looking for c which is the missing side
.19^2 + .28^2 = c^20.0361 + 0.784 = .1145
get the square root of .1145
√.1145 = it is approximately 0.34
get the total distance by adding three sides
= .34 + .19 + .28
= 0.81
Answer:
0.68
Step-by-step explanation:
you got to multiply
what is the solution of 2^x = -3x + 5?
Answers
Answer:
1
Step-by-step explanation:
Create my own exponential word problem.
Please show work
Answers
= a(3)^x
162 = (3)^4
a =162/81=2 The equation is =2(3).
9. Ximena made 26 out of 32 penalty kicks with her brother as the goalie.
A In simplest form, what fraction of the penalty kicks did Ximena make?
B. Write a decimal and a percent equivalent to the fraction of the penalty kicks that
Ximena made. Show
your
work
Answers
Answer:
26/32=13/16
Step-by-step explanation:
Plz help I have a geometry exam soon!!!!! :(
Answers
Answer:
a = 93°, b = 120°, c = 150°
Step-by-step explanation:
b + 36 = 78 × 2 => b + 36 = 156 => b = 120°
87 × 2 - b = the minor arc between a and 78
=> 174 - 120 = 54
54 + b + 36 + c = 360
=> 54 + 120 + 36 + c = 360
=> c = 150°
(c + 36) ÷ 2 = a
=> (150 + 36) ÷ 2 = a
=> a = 93°
Marking brainliest...
Answers
Answer:
C. 12
Step-by-step explanation:
Find the percentage of him drawing a blue marble.
4/10 = 0.4
He has a 40% chance of picking blue.
Find 40% of 30.
12
He would draw a blue marble around 12 times.
Answer:
C
Explanation:
So in the bag, there are 10 marbles, and 4 of them are blue, so if he drew from the bag 10 times, we can assume the fraction:
4/10
Next, we see that the denominator, or the number times Cade is drawing from the bag is 30, which makes us multiply most sides of the fraction by 3:
12/30
So I would say 12/30, but again, he wouldn't draw a blue exactly 4 times, and it may be more or less, so either 8/12....
Hope this helps!
Find the perimeter 5 1\2
Answers
Answer:
22
Step-by-step explanation:
If p-1/p=2, find the value of p^3+1/p^3. Help me fast.
Answers
Answer:
[tex]\\\\\frac{P^3 \ + \ 1}{P^3} = 0[/tex]
Step-by-step explanation:
Given;
[tex]\frac{P-1 }{P} = 2\\\\From \ the \ equation \ above \ we \ determine \ the \ value \ of \ p \ as \ follows;\\\\P-1 = 2P\\\\P-2P = 1\\\\-P = 1\\\\P = -1[/tex]
[tex]Now\ solving \ the \ given \ question;\\\\\frac{P^3 \ + \ 1}{P^3} \\\\Substitute \ the \ value \ of \ "P" \ into \ the \ equation;\\\\\frac{P^3 \ + \ 1}{P^3} = \frac{(-1)^3 \ + \ 1}{(-1)^3} = \frac{-1 \ + \ 1}{-1} = \frac{0}{-1} = 0[/tex]
Circumference and Area questions look at the picture
Answers
Note that the formula for the circumference of a circle is πd, while the formula for the area of a circle is πr².
π≈3.14
A. C=πd
Simply plug in the numbers into the formula.
Diameter=Radius*2
17*2=34
C=34(π)
B. (π)(5²)
Plug in the numbers into the formula. Remember that half of the diameter is the radius.
C. (π)(4.5)
There are two possible formulas that could be used to calculate the circumference of a circle: πd and 2πr.
The expression above is simply multiplying the circle's radius times pi. Therefore, it is not a method that could be used to find the circumference of a circle.
D. (π)(6.5²)
Remember that the formula for calculating the area of a circle is πr².
Half of the diameter is 6.5 (13.5/2=6.5). 6.5 cm. is the radius. Now just plug the numbers into the formula.
(π)(6.5²)
Therefore, the last answer choice is the correct answer.