Answer:
C table one hope this helps ya
How would you solve absolute value equations with "or" and "and"? Sometimes even with coefficients.
9514 1404 393
Explanation:
In general, a system of equations has a solution that satisfies all of the equations. That is, the solution set is the intersection (and) of the solution sets of the individual equations in the system. Equations involving the absolute value function are no different.
That being said, you need to consider the meaning of an equation involving the absolute value function.
The function itself is piecewise defined:
[tex]\displaystyle |x|=\left\{ {x, x\ge0} \atop {-x, x<0}} \right.[/tex]
So, any equation involving the absolute value function automatically resolves to two equations, each with its own condition on the function value.
__
Example 1:
|x+1| > 3
is equivalent to the two disjoint conditional equations ...
(x +1) > 3 and (x +1) ≥ 0 . . . . OR
-(x +1) > 3 and (x +1) < 0
the first of these has the solution x > 2; the second of these has the solution x < -4. The solution set of this equation is the OR of the two solution sets:
x < -4 or x > 2
__
Example 2:
|x +1| < 3
is equivalent to the two disjoint conditional equations ...
(x +1) < 3 and (x +1) ≥ 0 . . . . OR
-(x +1) < 3 and (x +1) < 0
The first of these has the solution -1 ≤ x < 2, and the second of these has the solution -4 < x < -1. Again, the solution set of this equation is the OR of the two solution sets. However, we find we can write that union as a single compound inequality:
-4 < x < 2
__
When an absolute value equation involves more than one absolute value function, then the equation will probably resolve into multiple equations, each defined on its own domain. Sometimes keeping those domains straight can be tedious.
Above, we have considered inequalities. If you have an equation, you need to consider that it will likely resolve to two equations. The solution set will be the OR of the solutions to those two equations.
Example 3:
|x +1| = 3
is equivalent to the two conditional equations ...
(x +1) = 3 and (x +1) ≥ 0 . . . . OR
-(x +1) = 3 and (x +1) < 0
The first of these has the solution x = 2; the second has the solution x = -4. The solution set is the OR of these two solutions:
x = -4 or x = 2
__
The "and" condition restricts the domain of each of the individual pieces of the equation. The "or" condition applies to the collection of solutions that may exist in each of those restricted domains.
To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor. a. How much would the painting company charge to paint a house that needs 20 hours of labor?
Answer:
For 20 hours it would be $1,500.
Step-by-step explanation:
The equation for this problem would be Y = 50x + 500.
Y is the total charge and x is the number of hours.
Hope this helps! Sorry if it was not what you were looking for!
Answer: 1500
Step-by-step explanation: 50x20=1,000 plus the addition price of the supplies 1,000+500= $1500
I need help with number 11 and number 12
Answer:
11) 6
12) 3
Step-by-step explanation:
2 log 2 8
so 2(log2 8)
Base 2 so 2^x=8 so 3.
2*3 is 6.
log a a cubed
base a so a^ x = a^3
x=3
so 3.
Hope this helps ;D
Answer:
6 and 3
Step-by-step explanation:
Using the rules of logarithms
log[tex]x^{n}[/tex] ⇔ n log x
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
[tex]log_{a}[/tex] a = 1
(11)
let 2 [tex]log_{2}[/tex]8 = n , then
[tex]log_{2}[/tex] 8² = n
[tex]log_{2}[/tex] 64 = n
[tex]log_{2}[/tex] [tex]2^{6}[/tex] = n
[tex]2^{6}[/tex] = [tex]2^{n}[/tex]
Since bases on both sides are equal, equate the exponents, that is
n = 6
(12)
[tex]log_{a}[/tex] a³
= 3 [tex]log_{a}[/tex] a
= 3 × 1
= 3
the triangle is rotated 90° clockwise around the point (0,0) what will be the coordinates of the image of point L after rotation
Answer:
help please i need helppppp
Solve for r: 7r+ 30 = -65
Answer:
R= - 95/7
Step-by-step explanation:
Write an expression to find how many times Jason will blink in 60 minutes if he continues to blink 19 times a minute.
Solve and state any extraneous solutions
[tex] \frac{3x}{x - 1} + 2 = \frac{3}{x - 1} [/tex]
[tex] \frac{3x}{x - 1} + \frac{2(x - 1) }{ x - 1} = \frac{3}{x - 1} [/tex]
[tex] \frac{3x}{x - 1} + \frac{2x - 2}{ x - 1} = \frac{3}{x - 1} [/tex]
[tex] \frac{3x + 2x - 2}{ x - 1} = \frac{3}{x - 1} [/tex]
[tex]3x + 2x - 2 = 3[/tex]
[tex]5x - 2 = 3[/tex]
[tex]5x = 3 + 2[/tex]
[tex]5x = 5[/tex]
[tex]x = \frac{5}{5} [/tex]
[tex]x = 1[/tex]
Please help ASAP!!!!!!!!!!!
Answer:
5 and 4
Step-by-step explanation:
The GCF, greatest common factor, for 35 and 70 is:
O No answer text provided.
O No answer text provided.
O 5
O 35
O 70
o
None of the above
Answer: 35
Step-by-step explanation:
Given: Triangle WTR with WT = 25 and WR = 40. Identify all possible lengths for TR.
40
17
15
42
52
67
65
14
Answer:
The possible lengths of TR : TR = 17, 40, 42, 52,
Step-by-step explanation:
Given: Triangle WTR with WT = 25 and WR = 40. Identify all possible lengths for TR.
To find the possible lengths of the third side of a triangle:
c - a< b > a + c
a = WT = 25
c = WR= 40
b = TR = ??
40 - 25 < b < 40 + 25
15 < b < 65
The possible lengths of TR has to be greater than 15 and less than 65, Hence: TR = 17, 40, 42, 52,
Two-thirds of a number plus 5 is greater than 12. find the numbers
Answer:
21
Step-by-step explanation:
Please make me brainliest and friend request me!
Allen earns $260.50
doing yard work. He mows 8
lawns for $25
each and weeds gardens for $5.50
each. What equation can be used to find the number of gardens he weeds, w
?
grabriella volunteers at the hospital every 4th day.she volunteers at the food pantry every 6th day.she volunteered at the hospital and the food pantry both on march 31.On what date will she next volunteer at both?
Answer:
April 12th
Step-by-step explanation:
-7[-8-4a]=25+a
A. a= -16
B. a=-5
C. a= -11
D. a=-3
Answer:
-1.48148148
Step-by-step explanation:
-7 x -8 = 56
-7 x -4a = 28a
25-56=-31
27a/-31
a=-1.48148148
the length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle
Answer:
26x47
Step-by-step explanation:
To calculate the length of the rectangle we would do 2(2x - 5) + 2(x) = 146
We simplify and get 6x - 10 = 146,
then divide both side by 6 and plus 10 both sides,
we will get
x = 26
Now we've found one of the length,
to find the other side we do 26 * 2 = 52, and subtract 52 from 146,
which would get 94, then we divide it by 2
94/2 = 47
The dimensions is 26x47
PLEASE HELP! (don't graph, give me the coordinates and i will graph myself)
Answer:X=3
y= -4
Step-by-step explanation:
If we're solving for x or y, then the intercept we're not solving for is equal to zero. Solving for y means x=0, solving for x means y=0.
so solving for x, 4x=12--> x=3, since y=0 in this scenario.
Solving for y, x=0, so -3y=12--> y=(-4)
9514 1404 393
Answer:
see below for a table
Step-by-step explanation:
You can easily identify intercept points by solving for one variable when the other is zero.
x-intercept (y=0)
4x = 12
x = 12/4 = 3
y-intercept (x=0)
-3y = 12
y = 12/-3 = -4
So, the coordinate pairs of these points are ...
(3, 0) and (0, -4)
__
If you solve for y, you get ...
-3y = 12 -4x
y = (4/3)x -4 . . . . . divide by -3
This suggests that x being a multiple of 3 will be useful for finding integer values of y.
We already have points for x=0 and x=3. We can add points for x=6 and x=-3.
y = 4/3(6) -4 = 4
y = 4/3(-3) -4 = -8
So, the additional points are ...
(6, 4) and (-3, -8)
Need help with this question. Thanks
Answer:
C
Step-by-step explanation:
-18x+2y>=-13
2y>= -13+18x
y>= -6.5+9x
Trapezoid QUAD is graphed on the coordinate plane and
then reflected over the x-axis to create trapezoid
Q'U'A'D'.
3
If trapezoid Q'U'A'D'is dilated by a factor of with
4
respect to the origin to create trapezoid Q"U"A"D", what
are the coordinates of A"?
U
A
O (2, 4)
O (-2,4)
3+
2+
1+
Q
D
o , -3)
0 (33)
-5 -3 -2 -1
2
3
/4
sx
-2
-37
UP
-4 -5
A'
Answer:
A''(3/2, -3)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and rotation.
If a point A(x, y) is reflected over the x axis, the new point would be A'(x, -y).
If a point A(x, y) is dilated by a factor k, the new point would be A'(kx, ky).
Given that Trapezoid QUAD has vertices at Q(-4, 0), U(-2, 4), A(2, 4) and D(4, 0). If the trapezoid is reflected over the x-axis to create trapezoid Q'U'A'D', the vertices would be at Q'(-4, 0), U'(-2, -4), A'(2, -4) and D'(4, 0).
If trapezoid Q'U'A'D'is dilated by a factor of 3/4 respect to the origin to create trapezoid Q"U"A"D", the vertices would be at Q''(-3, 0), U''(-3/2, -3), A''(3/2, -3) and D''(3, 0)
Answer:
A''(3/2, -3)
Step-by-step explanation: i just took the test on edge
PLEASE HELP DUE TODAY 20 POINTS!!!
Answer:
13/12
Step-by-step explanation:
compared to last year, the population of Boom Town has increased by 10%. The population is now 6,600. What was the population last year?
Answer:
60
Step-by-step explanation:
6600 x 10% = 60&$;#;,$:#&#>$
Nemos aquarium is filled with 2400 cm³ of water the base of the aquarium is 20 cm long and 12 cm wide what is the height of the water in Nemo’s aquarium
Divide following polynomials 5x2 - 18x-27/x-5
Answer:
[tex]\frac{5x^{3}-18x^{2} -5x-27 }{x}[/tex]
Step-by-step explanation:
rename 4/5 and 5/7 using the least common denominator
Answer:
wh
Step-by-step explanation:
Answer:
4/5 = 28/35 and 5/7 = 25/35
Explanation:
Multiply 5 times 7 to get 35, then multiply 4 times 7 for the numerator of the first fraction and 5 times 5 for the numerator of the second equation.
I'm having trouble with this...
Solve.
{y=x−63x+2y=8
Use any method.
(14, 8)
(3, -3)
(0, -6)
(4, -2)
Answer:
(4, -2) should be the correct answer.
5/6 multiplied by 1/5
Show you work please
Answer:
The answer is 5/30
Step-by-step explanation:
The answer is 5/30 because when multiplying a fraction by a fraction you have to multiply the numerator by the numerator and the denominator by the denominator so if you multiply 5 by 1 you get 5 and when you multiply 6 by 5 you get 30 so the answer is 5/30
ΔZAP has coordinates Z (−1, 5), A (1, 3), and P (−2, 4). A translation maps point Z to Z' (1, 1). Find the coordinates of A' and P' under this translation.
Group of answer choices
A' (−4, 0); P' (−1, −1)
A' (3, −1); P' (0, 0)
A' (−1, −1); P' (−4, 0)
A' (0, 0); P' (3, −1)
Leda makes 73 oatmeal muffins for a bake sale. She accidentally drops five of them and throws them away. She puts as many of the remaining muffins as possible into 13 containers so that each container has the same number of muffins. How many of the remaining muffins does Ieda have left over?
Answer:
She would have 5 muffins left over
Step-by-step explanation:
Do 73-3, because she dropped 3 and threw them awayTake 70 and divide it by 13, there are 70 muffins and 13 containers (I used a calculator)Then you get a decimal (if you use a calculator), look at the whole number which should be 5Next, you multiply 5 by 13, this will allow you to find what you would 'add into' a normal division problem (if you were to do it on paper)Lastly, take 70 and subtract what you got for step for (it should be 65, so the equation would be 70-65)Which is the solution to the inequalit? 1/4 +x less than 5/6
Answer:
x<7/12
Step-by-step explanation:
1/4+x<5/6
1/4+x-1/4 < 5/6-1/4
x<10/12-3/12
x<7/12
Which statement about converting metric units of measurement is true? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
To find the number of meters in 9,382 centimeters, move the decimal point 2 units to the right.
To find the number of kilometers in 6.39 decimeters, move the decimal point 3 units to the left.
To find the number of dekameters in 18 kilometers, move the decimal point 3 units to the right.
Answer:
To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
Mark me brainliest if I am right...PLEASE
Answer:To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
Step-by-step explanation:
A triangle has a base of 15 feet and a height of 9.5 feet. What is the area of the triangle?
O 142.5 ft2
O 71.25 ft2
O 24.5 ft2
O 5.5 ft2
HELP ASAP
Answer:
71.25 ft2
Hope this helps. Pls give brainliest.
Answer:
71.25
Step-by-step explanation:
multiply them together then divide by 2.