Answer:
-1 ≤ x ≤ 2
Step-by-step explanation:
The given equation can be rewritten as a piecewise function and solved in pieces.
The term |x+1| changes definition at x=-1. For x-values less than that, it is defined as -(x+1). Similarly, the term |x-2| changes definition at x=2. For x-values less than that, its definition is -(x-2). In the following, we consider the three pieces of the function.
__
x < -1In this domain, the absolute value functions both have negative arguments, so the equation is effectively ...
-(x +1) -(x -2) = 3
-2x +1 = 3 . . . . . . . simplify
-2x = 2 . . . . . . subtract 1
x = -1 . . . . divide by -2
This value of x is not in the domain we have defined, so there is no solution in this domain.
__
-1 ≤ x ≤ 2In this domain, the function |x+1| has a non-negative argument, but the function |x-2| has a non-positive argument. The equation is effectively ...
(x +1) -(x -2) = 3
x -x +1 +2 = 3 . . . . . eliminate parentheses, group like terms
3 = 3 . . . . . . . . . true for the entire domain
The solution here is -1 ≤ x ≤ 2.
__
2 < xBoth absolute value terms have positive arguments in this domain, so the equation is effectlvely ...
(x +1) +(x -2) = 3
2x -1 = 3 . . . . . simplify
2x = 4 . . . . add 1
x = 2 . . . . divide by 2
This value of x is not in the domain we have defined, so there is no solution in this domain.
__
The solution to the given equation is -1 ≤ x ≤ 2.
True or false, in a ratio the units are not written
Answer:
True
Step-by-step explanation:
A ratio is normally written using whole numbers only, with no units, in its simplest form. The numbers in a ratio must be written using the same units.
e.g. ratio of 1:2
False, ratio's do no have units.
Estimate how many times larger 5x10^8 is than 24x10^6?
A) 10 times larger
B) 20 times larger
C) 50 times larger
D) 100 times larger
Answer:
20times bc u times 5 by 10 then divide 8 u get 6.2
1 Camille has 26 pieces of ribbon for making cards.
She needs 4 pieces of ribbon for each card.
How many cards can Camille make? How many
pieces of ribbon will be left over?
Answer:
Camille can make 6 cards and will have 2 ribbons left
Step-by-step explanation:
in a certain urban area, the relationship between number of students, x in thousands, and the umber of schools, y , has an x-intercept of -4 and a y-intercept of 3. Write an equation for this relationship in standard form
Answer:
[tex]\sf -3x+4y=12[/tex]
Step-by-step explanation:
x-intercept is when y = 0 → (-4, 0)
y-intercept is when x = 0 → (0, 3)
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{3-0}{0-(-4)}=\dfrac34[/tex]
Substitute one of the points and the found slope into the point-slope form of a linear equation:
[tex]\implies \sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=\dfrac34(x-(-4))[/tex]
[tex]\implies \sf y=\dfrac34(x+4)[/tex]
[tex]\implies \sf 4y=3(x+4)[/tex]
[tex]\implies \sf 4y=3x+12[/tex]
[tex]\implies \sf -3x+4y=12[/tex]
6. Which is the BEST estimate of 2.4679+7.4939? A)O5.5
B)4 x 5
C)6x6
D)5x 6
Answer:
A
Step-by-step explanation:
It because I think it is the correct
PLEASE HELP!! TRYING TO PREPARE FOR A TEST!! TOTAL 50 POINTS WHEN GIVEN BRAINLIEST ANSWER!!
Change the Cartesian integral to an equivalent polar integral, and then evaluate.
∫₋₁₁¹¹ ∫₀√⁽¹²¹⁻ˣ²⁾ dy dx
\int\limits^{11}_{-11} \int\limits^{\sqrt{121-x^{2}} } _{0} dy dx
It looks like the starting integral is
[tex]\displaystyle \int_{-11}^{11} \int_0^{\sqrt{121-x^2}} dy\,dx[/tex]
The key is recognizing the domain of integration as the semicircle centered at the origin with radius 11. In polar coordinates, this integral transforms to
[tex]\displaystyle \boxed{\int_0^\pi \int_0^{11} r \, dr \, d\theta}[/tex]
............................
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Answer:
......................
Step-by-step explanation:
Solve the following expression when
p = 15
P + 4
_
3
Answer:
49/3 or 16.33...
Step-by-step explanation:
15 + 4/3.
15/1 + 4/3
45/3 + 4/3.
ANSWER: 49/3
How do I find the area of the blue shape? Don't worry about the other colored one.
Answer:
80 cm²
Step-by-step explanation:
Let's break down the composite shape into two parts. (Image attached)
Let "a" represent the area of the smaller square.Let "b" represent the area of the bigger square⇒ The side length of "a" is 4 cm.
⇒ The side length of "b" is 8 cm.
First, let's find the area of square "a". Keep in mind that the area of a square is the side multiplied by itself.
⇒ (Side)² = A
⇒ (4)² = Area of "a"
⇒ (4)(4) = Area of "a"
⇒ 16 cm² = Area of "a"
Next, find the area of square "b". Keep in mind that the area of a square is the side multiplied by itself.
⇒ (Side)² = A
⇒ (8)² = Area of "b"
⇒ (8)(8) = Area of "b"
⇒ 64 cm² = Area of "b"
Finally, let's sum up the area of square "a" and "b" to find the area of the composite shape.
⇒ Area of composite shape = Area of "a" + Area of "b"
⇒ Area of composite shape = 16 + 64
⇒ Area of composite shape = 80 cm²
HELP!Use elimination method to solve the system of equations please fast
Answer:
x=1/4 Y=-1/2 z=1/3
Step-by-step explanation:
due to large fractions the answer is explained in the image above
35\40 in simplest form
Answer:
7/3
Step-by-step explanation:
pls mark me brainliest :)
Answer:
7/8
Step-by-step explanation:
Divide both the numerator and denominator by the GCD
35 ÷ 5
40 ÷ 5
Add. Write your answer as a mixed number in simplest from.
7 3/4 + 4 2/7
Answer: 12 1/28
Step-by-step explanation:
Add whole numbers. Solve fractions by finding the LCD.
[tex]\begin{equation}\text { Question: The value of } \lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=0}^{2 n-1} \frac{n^{2}}{n^{2}+4 r^{2}} \text { is }\end{equation}[/tex]
You have something resembling a Riemann sum. Multiply through the summand by 1/n², then you can write
[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{r=0}^{2n-1} \frac{1}{1+4\left(\frac rn\right)^2} = \int_0^2 \frac{dx}{1+4x^2} = \boxed{\frac12 \tan^{-1}(4)}[/tex]
Apr 09,5:30:49 PM
Please help I am lost I’m not smart…
the piece-wise function is, -x - 5 when x ≠ -2
and when x = -2, the function's value is -2
what that means is when x = -4, the subfunction of -x - 5 is the one to use, because x = -4 is in that range
so f(-4) = -(-4) - 5 => f(-4) = -1.
so the function's graph look more or less like the one below, with a solid line going but with a gap at x = -2.
. Complete this calculation
1/2 ×1/4
Answer:
1/8
Step-by-step explanation:
1) Calculating the numerator value
1 x 1 12) Calculating the denominator value
2 x 48The solution will be in the form :
Numerator / Denominator ⇒ 1/8Easy math 2 questions
I only know question 1: 8 inches.
Also, don't delete this.
It's helpful to certain people with the same problem.
Answer:
For problem 11, Q is 16 degrees
For problem 12 I think it is 8 inches
Step-by-step explanation:
Mr. Loy fixes bikes for a living. This month, he plans to fix 747474 bikes. So far, he has fixed 141414 kids' bikes and 252525 adults' bikes.
How many bikes does Mr. Loy still have to fix?
helpppppp pls operations
Help picture below problem 19
Answer:
it's rectangle...
Step-by-step explanation:
mark me brainliest
Answer:
that's C. Its' a rectangle
It has 2 pairs of parallel sides. and they are the same size.
At Silver Gym, membership is $30 per month, and personal training sessions are $35 each. At Fit Factor, membership is $60 per month, and personal training sessions are $25 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Answer: 5 personal training sessions
Step-by-step explanation:
Given only 1 month, then set the 2 equations equal to each other, given that x=# of personal training sessions:
25+45x = 75 + 35x
-25-35x -25-35x
So, 10x=50; divide both sides by 10, to get:
5, so, 5 personal training sessions per month to make the 2 costs equal to one another.
(3*8-3)/3
How do you solve this?
Answer:
7
Step-by-step explanation:
Equation: (3*8-3)/3
Step 1: (24-3)/3
Step 2: 21/3
Step 3: 7
Order of operations is used in this equation. You simplify the terms in the parentheses before the other terms in the equation. According to the order of operations (parentheses, exponents, multiplication, division, addition, and subtraction, you do the multiplication before the subtraction in the parentheses. Then you subtract your three from your multiplication result (twenty-four). This leaves you with 21. Finally, you divide twenty-one by three. This gets you seven.
Easy math will give brainlest
Answer:
1. 3 hours 2. 150 ft
Step-by-step explanation:
1. a) 50 + 60 + 60 + 60 = $230 = 3 hours
b) 80 + 50 + 50 + 50 = $230 = 3 hours
Answer: 3 hours
2. 10 * 5 * 3 = 150 ft
Answer:1 3 hours 2 150
Step-by-step explanation:
A gelatin mold is in the shape of a hemisphere (half-sphere). If its diameter is 4 inches, find the exact volume of gelatin that 10 molds will hold.
Two hemispheres will be equal to a spheres, hence the volume of 10 hemispheres is 266.581 cubic inches
Volume of hemispheresGiven Data
Shape is that of hemisphereNo of hemisphere = 102 hemispheres = 1 sphere10 hemispheres = 5 spheresradius = 4inchesLet us find the volume of sphere
Volume = 4/3 *πr^3
Volume = 4/3*3.124* 4^3
Volume = 4/3*3.124*64
Volume =266.581 cubic inches
Learn more about hemispheres here:
https://brainly.com/question/25641436
the temperature on wednesday was "-17" degrees. From Tuesday to Wednesday it got 24 degrees colder. What was the temperature on Tuesday?
Answer:
-41 degrees
Step-by-step explanation:
Since we're getting colder you would subtract 24 from the current -17 degrees.
-17-24 = -41
Following is the probability distribution for age of a student at a certain public high school.
X
13
14
15
16
17
18
P(x) 0.09 0.22 0.24 0.28 0.15 0.02
(a) Find the variance of the ages. Round the answer to at least four decimal places.
The variance of the ages is
Considering the given discrete distribution, the variance of the ages is of 1.5844.
What is the mean and the variance of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.The variance is given the sum of the difference squared between each outcome and the mean, multiplied by it's respective probability.In this problem, considering the distribution given in the table, the mean is given by:
[tex]E(x) = 13(0.09) + 14(0.22) + 15(0.25) + 16(0.28) + 17(0.15) + 18(0.02) = 15.39[/tex]
Hence, the variance is given as follows:
[tex]Var(x) = 0.09(13-15.39)^2 + 0.22(14-15.39)^2 + 0.25(15-15.39)^2 + 0.28(16-15.39)^2 + 0.15(17-15.39)^2 + 0.02(13-15.39)^2 = 1.5844[/tex]
More can be learned about discrete distributions at https://brainly.com/question/24855677
Select the correct answer.
This is a regular pentagon. The apothem is shown. What is perimeter of the pentagon?
5 cm
OA
18.2 cm
B.
30.7 cm
C.
36.3 cm
D.
43.8 cm
The perimeter of the pentagon with apothem of 5cm is 28.87cm
How to calculate the perimeter of a pentagonThe sum of all the external sides of the pentagon is its perimeter.
First we need to calculate the half of one of its sides using the SOH CAH TOA
tan 30 = x/5
x = 5 tan 30
x = 2.89
One of the sides = 2(2.89) = 5.77 cm
Perimeter of th pentagon = 5(5.77) = 28.87
Hence the perimeter of the pentagon with apothem of 5cm is 28.87cm
Learn more on perimeter of pentagon here: https://brainly.com/question/11484726
f(x)= (x+1)/(x-1)
find the derivative using the definition
[tex]\text{Given that,}\\\\f(x)= \dfrac{x+1}{x-1}\\\\\\f'(x)=\lim\limits_{h \to 0} \dfrac{f(x+h) - f(x) }{h}\\\\\\ ~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\left( \tfrac{x+h+1}{x+h-1}\right) - \tfrac{x+1}{x-1}}{h}\\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{(x+h+1)(x-1) - (x+1)(x+h-1)}{(x+h-1)(x-1)}}{h} \\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{x^2-x+hx-h+x-1 - x^2-xh+x-x-h+1}{(x+h-1)(x-1)}}{h}\\\\\\~~~~~~~~[/tex]
[tex]~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{-2h}{(x+h-1)(x-1)}}{h}\\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{-2}{(x+h-1)(x-1)}\\\\\\~~~~~~~~=\dfrac{-2}{(x+0-1)(x-1)}\\[/tex]
[tex]\\\\~~~~~~~~=\dfrac{-2}{(x-1)(x-1)}\\\\\\~~~~~~~~=\dfrac{-2}{(x-1)^2}[/tex]
5 x 7/20 and i really need help
Answer:
THE ANSWER IS 7/4
Step-by-step explanation:
Step-by-step explanation:
[tex]5 \times \frac{7}{20} \\ = \frac{35}{20} \\ = \frac{7}{4} [/tex]
answerr......
you choose a block from a bag containing one red block, and one green block.
Answer:
50% or 1/2
Step-by-step explanation:
The probability of grabbing either colored block from the bag is 50% or 1/2.
Which expression is equivalent to
Answer:
The second expression
Step-by-step explanation:
[tex]\sum_{n=3}^{20}{n(n+1)}=\sum_{n=3}^{20}{(n^2+n)}=\sum_{n=3}^{20}n^2+\sum_{n=3}^{20}n[/tex]
You can split up sums.