Please someone explain how to solve this piecewise function!!!! Im super confused
Answers
Answer:
From top to bottom:
[tex]0, 1, 2, -8, -8[/tex]
Step-by-step explanation:
We are given the piecewise function:
[tex]g(x) = \left\{ \begin{array}{ll} 0.5x+1 & \text{if } x \leq 2 \\ -8 & \text{if } x > 2 \end{array} \right.[/tex]
Row 1:
We want to find g(-2).
Since -2 is less than (or equal to) 2, we will use the first equation. Thus:
[tex]g(-2)=0.5(-2)+1=-1+1=0[/tex]
Row 2:
Likewise, 0 is less than or equal to 2. We will continue to use the first equation:
[tex]g(0)=0.5(0)+1=1[/tex]
Row 3:
2 is not less than 2 but it is equal to 2. So we will continue to use the first equation:
[tex]g(2)=0.5(2)+1=1+1=2[/tex]
Row 4 and 5:
Both 4 and 6 are greater than 2. Thus, we will use the second equation. Therefore:
[tex]g(4)=-8\text{ and } g(6)=-8[/tex]
Related Questions
Write down the name of the solid.
Answers
Answer:
Cube
Step-by-step explanation:
There were 45 runners to start a race. In the first half of the race, 2/3
of them dropped out. In the second half of the race, 4/5
of the remaining runners dropped out. How many runners finished the race?
runners?
Answers
Answer:43 8/15
Step-by-step explanation:45-2/3 is 44 1/5 then subtract 44 8/15 by 4/5 and you get 43 8/15
Share £747 in the ratio 2:7 between Tom and ben
Tom will get
Dan will get
Answers
2+7x=747 X83 83(2)=83 83(7)= 581
Step-by-step explanation:
27. The length and breadth of a rectangle are in the ratio 7:5 and the perimeter is 240m, find the area of
the rectangle
Answers
Answer:
[tex]Area = 3500[/tex]
Step-by-step explanation:
Given
[tex]Length : Breadth = 7 : 5[/tex]
[tex]Perimeter = 240m\\[/tex]
Required
Determine the area
The perimeter is:
[tex]Perimeter = 2(Length + Breadth)[/tex]
This is then represented as:
[tex]240 = 2(7x + 5x)[/tex]
[tex]240 = 2 * 12x[/tex]
[tex]240 = 24x[/tex]
[tex]10 = x[/tex]
[tex]x = 10[/tex]
So, the area is:
[tex]Area = Length * Width[/tex]
[tex]Area = 7x * 5x[/tex]
[tex]Area = 7*10 * 5*10[/tex]
[tex]Area = 3500[/tex]
1/2 of 2/2 = ???????????
Answers
Answer:
0.5
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
54
Step-by-step explanation:
you can use a proportion to solve:
6/3=x/27
3x=27x6
3x=162
x=54
Answer:
I Know you already have an answer but its 5
Step-by-step explanation:
I dont mean to steal points and you still have no answer I just figured you already have an answer so I see no wrong in doing this
In a sale the price of a bike is reduced by 40% the sale price of the bike is £192 how much did the bike cost before the sale?
Answers
Suppose 7x-5 M=- 3 x-8 and NE 2 2 x - 5 x - 50 X - 14 x +40 and you want to add the fractions M and N, in other words you want to compute 7x-5 3 x - 8 2 x - 5 x - 50 x - 14 x + 40 and simplify the result. We know that, before you can add the fractions, you must find a common denominator and rewrite each fraction so it has that common denominator. Once the rewritten fractions have the same denominator, you can add them and simplify the result.
There are four text boxes below. In the first text box, enter a common denominator for the two fractions. In the second text box, rewrite M so that it possesses the common denominator you found. Note that your entry in this text box should equal M, however it should have the common denominator you found. In the third text box, rewrite N so that it possesses the common denominator you found. In the last text box, compute your simplified answer for M N . Make sure that your answer is simplified; the numerator and denominator of your answer for M N should not have common factors. Note that your entry for the common denominator should be a polynomial with integer coefficients. Your other three entries should be fractions that contain polynomials. All of your answers should contain no letters other than the variables that appear in M and N. Do not include an equals sign with any of your answers. All of your expressions should be mathematically correct and not contain non-mathematical symbols. After entering your answers, click the Save Answer button. Your computer will display how your answers were interpreted, and you will have the opportunity to accept these answers or modify them.
Enter a common denominator for M and N here:
Enter M rewritten here:
Enter N rewritten here:
Enter your simplified result here:
Answers
Answer:
[tex](a)[/tex] [tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
[tex](b)[/tex] [tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
[tex](c)[/tex] [tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
[tex](d)[/tex] [tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
Step-by-step explanation:
Given
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Solving (a): A common denominator of M and N.
To do this, we simply get the LCM of both denominators
[tex]M = x^2 - 5x - 50[/tex]
[tex]N = x^2 - 14x + 40[/tex]
Factorize both:
[tex]M = (x - 10)(x + 5)[/tex]
[tex]N = (x- 10)(x - 4)[/tex]
The LCM is
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
Hence, the common denominator is:
[tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
Solving (b): Rewrite M
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
Factor the denominator:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of M by (x - 4)
The expression becomes:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)} * \frac{x - 4}{x-4}[/tex]
[tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
Solving (c): Rewrite N
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Factor the denominator:
[tex]N = \frac{3x - 8}{(x-4)(x-10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of N by (x + 5)
The expression becomes:
[tex]N = \frac{3x - 8}{(x-4)(x-10)} * \frac{x + 5}{x + 5}[/tex]
[tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
(d) Solve M + N
[tex]M + N = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)} + \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
Take LCM
[tex]M + N = \frac{(7x - 5)(x-4) + (3x - 8)(x + 5)}{(x+5)(x - 10)(x-4)}[/tex]
Open brackets
[tex]M + N = \frac{7x^2 - 28x - 5x + 20 + 3x^2 + 15x - 8x - 40}{(x+5)(x - 10)(x-4)}[/tex]
Collect Like Terms
[tex]M + N = \frac{7x^2 + 3x^2- 28x - 5x + 15x - 8x + 20 - 40}{(x+5)(x - 10)(x-4)}[/tex]
[tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
A shirt costs 20$ if it was on sale for 75 percent off what is the discount
Answers
Then you would have 100x=75*20 and if you simplify all the way you would get x=15
So the discount would be $15
Hope this helps :)
convert 75% to decimal- so divide by 100; you will get 0.75
then you multiply 20 and 0.75
20 x 0.75 = 15
answer: the discount is $15
(however, remember that the new shirt price would be $5)
if the shirt cost $20 after discount:
we know that 100% is the whole, and 75% is the discount, so this means that the leftover 25% = $20
so using proportions,
25/100=20/x, cross multiply & simplify you would get x = 80
to find the discount, subtract the cost from the original price and get 60
answer: the discount was $60
(however remember the original price of the shirt was $80)
Formula
=6s2
gives the surface area A of a cube with a side length s.
The surface area of a cube that has a side length of 5 inches is _______________inches squared.
*No need to label this answer.*. Please help me
Answers
Answer:
the surface area of the cube is 150 inches squared
Step-by-step explanation:
The computation of the surface area of the cube is shown below:
As we know that
The surface area of the cube is
= 6s^2
= 6(5)^2
= 150 inches squared
hence, the surface area of the cube is 150 inches squared
I need help with this question please
Answers
Answer:
C.
Step-by-step explanation:
Given
[tex]A =(x_1,y_1)[/tex]
[tex]B =(x_2,y_2)[/tex]
[tex]C =(x_3,y_3)[/tex]
[tex]D =(x_4,y_4)[/tex]
Required:
Which condition proves that AB is perpendicular to CD
First, calculate the slopes of both.
For AB
[tex]m_1 = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
For CD
[tex]m_2 = \frac{y_4 -y_3}{x_4 - x_2}[/tex]
The condition of perpendicularity is:
[tex]m_1 * m_2 = -1[/tex]
Substitute values for m1 and m2
[tex]\frac{y_2 -y_1}{x_2 - x_1} * \frac{y_4 -y_3}{x_4 - x_2} = -1[/tex]
Option (c) is correct
what is 4 and half hours in minutes
Answers
Solve the simultaneous equations y=x-2 and y=3x+5
Answers
Answer:
x = -7/2........y = -11/2
Step-by-step explanation:
..….................
Forgive me if wrong
1. Line A ang Line B are parallel lines cut by Transversals x and y. 2 = 57° and 3 = 85°, Find the measure of 5.
Answers
Answer:
Step-by-step explanation:
∠1 = 180° - ∠2 - ∠3 = 38°
∠5 = ∠1 = 38°
PLEASE HELP!! Eliminate the parameter in the equations y = t + 2 and x =t^1/2.How can the rectangular equation be described?
Answers
Answer:
Quadratic (I took the test)
Step-by-step explanation:
y=t+2 equals y-2=t
put t in for x=t^1/2. this is x=(y-2)^1/2, which equals x^2=y-2.
add 2 to both sides, which is y=x^2+2 . This is an example of a quadratic equation (you kinda just need to know the format of different types of equations for the last part. It isn't cubic because it has a number added to it, isn't linear because the x is squared, and tbh I have no clue what quartic is.)
This is an example of a quadratic equation.
We have given that the equation
y=t+2 equals y-2=t
What is the quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax^2 + bx + c = 0, where a,b are and c represents the constant.
put t in for x=t^1/2. this is x=(y-2)^1/2,
Squaring both sides we get,
x^2=y-2.
add 2 to both sides, which is y=x^2+2.
This is an example of a quadratic equation.
To learn more about the quadratic equation visit:
https://brainly.com/question/1214333
#SPJ2
11 and 3/8 pounds of cat food were donated to the shelter
Answers
P = 30x + 50y Corner that maximizes profit: (0, 6) What is the profit?
Answers
Answer:
The profit is 300.
Step-by-step explanation:
x = 0
y = 6
P = 30(0) + 50(6)
P = 0 + 300
P = 300
Hope I helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
The required profit is 300.
What is profit?Profit in Math is considered as the gain amount from any business activity.
Now the given function of profit is,
P = 30x + 50y
The Corner that maximizes profit is (0, 6)
Thus, At (0, 6) the given function is given as,
Put x = 0 and y = 6 in the given function.
P(0, 6) = 30*0 + 50*6
⇒ P(0, 6) = 0 + 300
P(0, 6) = 300
this is the required profit.
Thus, the required profit is 300.
To learn more about the profit visit:
brainly.com/question/26215194
#SPJ2
write the letters of the words VERY WELL on 8 cards and put them in a bag. Shuffle them well.
Do the following:
What is the probability for a v to be drawn?
What is the probability for an E to be drawn?
What is the probability for an R to be drawn?
What is the probability for a Y to be drawn?
What is the probability for a W to be drawn?
What is the probability for an L to be drawn?
Answers
Answer:
1/8
1/4
1/8
1/8
1/8
1/4
Step-by-step explanation:
Probability a letter would be picked = total number of the letter in the bag /sum of letters in the bag
1. v,r,y,w appear once. the numerator would be 1 and the denominator would be 8 = 1/8
e and l would appear twice in the bag, so the numerator would be 2 and the denominator would be 8 = 2/8 convert to its simplest form = 1/4
hehe pls help i nneed it
Answers
Answer:
x = 32
Step-by-step explanation:
180 - 42 - 106 = x
x = 32
in a class the ratio of boys to girls is 3/2. if there are 12 boys in the class, how many girls are there?
Answers
Answer:
8
Step-by-step explanation:
3 times 4 is 12 and 2 times 4 is 8
12/3=4 so that mean you have to multiply 2x4 you get 8
Please help test due in 1 hour and it’s a grade! Will give good review and brainliest!
Answers
Find the area of the shape shown below.
Answers
Answer: 256
Step-by-step explanation:
Answer:
256cm² is the correct answer
n
What is the y-intercept of the equation 4x + 5y = 20?
0 (0.4)
0 (0.5)
0 (4.0)
(5.0)
M
Answers
Answer: (0,4)
Step-by-step explanation:
What is the value of y in the following equation? -10y + 4(3y – 8) = -64
Answers
Answer:
y=-16
Step-by-step explanation:
Answer:
y = -16
Step-by-step explanation:
−10y+4(3y−8)=−64
Step 1: Simplify both sides of the equation.
−10y+4(3y−8)=−64
−10y+(4)(3y)+(4)(−8)=−64(Distribute)
−10y+12y+−32=−64
(−10y+12y)+(−32)=−64(Combine Like Terms)
2y+−32=−64
2y−32=−64
Step 2: Add 32 to both sides.
2y−32+32=−64+32
2y=−32
Step 3: Divide both sides by 2.
2y
2
=
−32
2
y=−16
Answer:
y=−16
Write the difference in factored form. (24x4 - 15x2 + 6x) - (10x4 + 5x2 - 4x)
Answers
Answer:
The factored difference is: [tex]2x(7x^3 - 10x + 5)[/tex]
Step-by-step explanation:
Difference in non factored form:
To find the difference in non-factored form, we subtract the common terms. So
[tex]24x^4 - 15x^2 + 6x - (10x^4 + 5x^2 - 4x) = 24x^4 - 10x^4 - 15x^2 - 5x^2 + 6x + 4x = 14x^4 - 20x^2 + 10x[/tex]
Greatest common factor:
Of the exponents: Between [tex]x^4, x^2[/tex] and [tex]x[/tex], it is the one with the lowest exponent, so x.
Between 14, 20 and 10:
14 - 20 - 10|2
7 - 10 - 5
So 2
The gcf is 2x, which means that the factored expression is:
[tex]2x(\frac{14x^4}{2x} - \frac{20x^2}{2x} + \frac{10x}{2x}) = 2x(7x^3 - 10x + 5)[/tex]
The factored difference is: [tex]2x(7x^3 - 10x + 5)[/tex]
I don’t know the answer
Answers
For the polynomial function, describe the end behavior of its graph.
f(x) = 2x3 + 5x
Answers
Plss this is timed will mark brain least if shown work!
Answers
Answer:
do 62.31/3 which is 20.77 so 1 shirt cost 20.77
now do 20.77+3.66 which is 24.43
so the answer is C. $24.43
Many studies have investigated the question of whether people tend to think of an odd or an even number when they are asked to think of a single-digit number (0 through 9). Combining results from several studies, Kubovy and Psotka (1976) used a sample of 1,770 people, of whom 741 thought of an even number and 1,029 thought of an odd number. Would a one-sided or a two-sided alternative hypothesis be more appropriate in this case
Answers
Answer:
A two-sided alternative hypothesis would be more appropriate in this case
Step-by-step explanation:
A one-sided hypothesis is one that asserts that a given parameter is either smaller than the null hypothesis value or larger than the value presented by the null hypothesis.
However in a two sided hypothesis, the claim is made that a given parameter is not equal to the parameter given in the null hypothesis, such that the parameter can be either larger than than or lesser than the value of the null hypothesis and still satisfy the condition of the hypothesis
Therefore, given for that for there to be a conclusion, the test should be weather the number of people that think of an odd number are equal to the number of people that think of an even number, or weather the number of people that think of an odd number are not equal to the number of people that think of an even number
Therefore, a two-sided hypothesis should be used since the claim (that the numbers are not equal) is not equal to the value of the parameter in the null hypothesis (that the numbers are equal)
If y=x+4 and y=3x+2, what must be true about x + 4 and 3x+2?
Answers
Answer:
x=1 must satisfy both equations.
Step-by-step explanation:
1)Y=X+4
2)Y=3X+2
IT Means x+4=3x+2
3x-x=4-2;
2x=2 ; x=1 must satisfy both equations