A webmaster makes $24 an hour for the first 38 hours she works during a
week and $31 an hour for each hour worked over 38 hours. Which piecewise
equation models her total weekly pay y in dollars as it relates to the number
of hours x that she has worked during the week?
24x
O A. e=1
OSXS38
x > 38
(31x+912
0
[24x
O B. y = {31(x – 38) +912 x > 38
S24x
(31x
C. y =
OSXS 38
X> 38
(24x
OSX 38
D. y = {31(x-38)
x > 38
Answers
A piecewise function is consists of different relationships between the variables over different intervals
The correct piecewise equation that models her total weekly pay is option B.
[tex]\mathbf{B.} \ y = \begin{cases} 24 \cdot x& \ 0 \leq x \leq 38 \\ 31\cdot (x - 38) + 912 & \ x > 38 \end{cases}[/tex]
The given parameters are;
The amount made by the webmaster for the first 38 hours she works = $24
The amount she makes for each hour worked after the first 38 hours = $31 an hour
Required:
To find the piecewise equation that models the total weekly pay, y, in dollars in relation to the number of hours x that she has worked during the week
Solution:
If she works for x ≤ 38 hours
The amount she makes working x less than or equal to 38 hours, y = $24/hour × x hours = $24 × x hours
The total amount the webmaster wakes by working all through the normal 38 hours is $24/hour × 38 hours = $912
If she works over 38 hours, (x > 38) we have;
The number of hours she works over 38 hours = x - 38
The amount she makes each hour after working 38 hours, y = $31/hour × (x - 38) hours
The total amount she makes y working for more than 38 hours is given as follows;
y = 31·(x - 38) + 912
The piecewise equation that models her weekly pay is therefore, presented as follow;
[tex]y = \begin{cases} 24 \cdot x& \ 0 \leq x \leq 38 \\ 31\cdot (x - 38) + 912 & \ x > 38 \end{cases}[/tex]
The above piecewise function is the same as option B
Learn more about piecewise function here:
https://brainly.com/question/11514494
Related Questions
(2x³)⁴= ? What is the right answer, with full explanation please:
A. 16x⁷
B. 16x¹²
C. 8x⁷
D. 8x¹²
Answers
2 times 4 is 8
4 times 3 is 12
Then you plug it In 8x^12
So your answer is D
Hope this helps *smiles*
The required simplified value of the given expression is 16x¹². Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
=(2x³)⁴
As we know that,
[xᵃ]ᵇ = xᵃˣᵇ
So,
(2x³)⁴ = 2⁴x³ˣ⁴
= 16x¹²
Thus, the required simplified value of the given expression is 16x¹².
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
Simplify. √ −18
A -3i√2
B 3i√2
C 9i√2
D -3√2
Answers
Is 8,916,699 divisible by 4?
yes
no
Answers
Answer: no
Step-by-step explanation:
Can anyone help me to solve this question ??
find the zeroes for P(x)=6x³-13x²+x+2 given 0.5 is one of the zeroes
The answers :
-1/3 , 0.5 , 2
Answers
Step-by-step explanation:
that means the expression is the result of a multiplication with (x-0.5) being one factor.
so, we divide the whole expression by this and then deal with the remaining quadratic equation.
6x³ - 13x² + x + 2 / x - 0.5 = 6x² - 10x - 4
- 6x³ - 3x²
----------------------------
- 10x² + x + 2
- - 10x² + 5x
----------------------------
- 4x + 2
- - 4x + 2
----------------------------
finished. 0
so, the whole expression is also
P(x) = (x-0.5)×(6x² - 10x - 4)
now we need to find the 2 zero points of the quadratic part.
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 6
b = -10
c = -4
x = (10 ± sqrt(100 - 4×6×-4))/12 =
= (10 ± sqrt(100 + 96))/12 = (10 ± sqrt(196))/12 =
= (10 ± 14)/12
x1 = (10+14)/12 = 24/12 = 2
x2 = (10-14)/12 = -4/12 = -1/3
The volume of a sphere is a function of its radius,
V=43πr3.
Evaluate the function for the volume of a volleyball with radius
11.6
cm.
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]6525\text{cm.}^3[/tex]
Keep in mind that this is APPROXIMATE.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Volume of a Sphere Is:}}\\\\V = \frac{4}{3} \pi r^3\\----------------\\\rightarrow \text{We are given the radius of } 11.6\text{ cm.}\\----------------\\V = \frac{4}{3}(3.14) (11.6)^3\\\\V = \frac{4}{3}(3.14) 1560.896\\\\V \approx 6534.95125\text{cm.}^3\\\\\boxed{V \approx 6535\text{cm.}^3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
An alphabetic character representing a number
Answers
Answer:
a variable
Step-by-step explanation:
The answer is a variable because it's a letter that stands in place of a number
Answer:
simply refers to the type of Latin and Arabic characters representing the numbers 0 - 9, the letters A - Z
I forgot how to do this for my brother
Answers
Answer:
11
Step-by-step explanation:
Add:
26 + 19 + 43
^ ^
45 + 43
88
Divide:
88 / 8 = 11
So, each tank has 11 fish.
Hope this helped.
B) Lim[2f(x)-3g(x)]
Please do all if possible:) thank you!
Answers
Recall some limit properties…
• limits distribute over sums:
[tex]\displaystyle \lim_{x\to c}(f(x)+g(x)) = \lim_{x\to c}f(x)+\lim_{x\to c}g(x)[/tex]
• limits distribute over products:
[tex]\displaystyle \lim_{x\to c}(f(x)\times g(x)) = \lim_{x\to c}f(x)\times\lim_{x\to c}g(x)[/tex]
• limits distribute over quotients, provided that the denominator doesn't approach 0 :
[tex]\displaystyle\lim_{x\to c}\frac{f(x)}{g(x)} = \frac{\displaystyle\lim_{x\to c}f(x)}{\displaystyle\lim_{x\to c}g(x)}[/tex]
• if f(x) is continuous at x = c, then the limit "passes through" a composition:
[tex]\displaystyle \lim_{x\to c}f(g(x)) = f\left(\lim_{x\to c}g(x)\right)[/tex]
# # #
(a) This limit is 2. At x = 2, we have f (2) = 1, but from either side of x = 2, we see f(x) approaching the point (2, 2). So
[tex]\displaystyle \lim_{x\to 2}(f(x)+g(x)) = \lim_{x\to2}f(x)+\lim_{x\to2}g(x) = 2+0 = 2[/tex]
(b) This limit does not exist. We would have
[tex]\displaystyle \lim_{x\to1}(2f(x)-3g(x)) = 2\lim_{x\to1}f(x)-3\lim_{x\to1}g(x)[/tex]
but g(x) approaches 2 from the left of x = 1, and g(x) approaches 1 from the right of x = 1. The one-sided limits don't match, so the two-sided limit doesn't exist.
(c) This limit is 0. It looks like f(x) passes through the origin, while g(x) ≈ 3/2 at x = 0. So
[tex]\displaystyle\lim_{x\to0}f(x)g(x) = \lim_{x\to0}f(x)\times\lim_{x\to0}g(x)=0\times\frac32 = 0[/tex]
(d) This limit does not exist since
[tex]\displaystyle \lim_{x\to-1}g(x)=0[/tex]
(e) This limit is 16. Nothing tricky here, just use the same property as in (c).
[tex]\displaystyle\lim_{x\to2}x^3f(x) = \lim_{x\to2}x^3\times\lim_{x\to2}f(x) = 8\times2=16[/tex]
(f) This limit is 1. f(x) is continuous at x = 1, while g(x) approaches 2 from the left.
[tex]\displaystyle\lim_{x\to1^-}f(g(x)) = f\left(\lim_{x\to1^-}g(x)\right) = f(2) = 1[/tex]
√5•√10
please show a step by step explanation
Answers
=5 √2. (Final answer)
Show two ways fivepeople cans hare a 3-segmant chewy fruit worm
Answers
Answer:
ethethe
Step-by-step explanation:
thethetht
Anyone who knows this mathematic question.to help please. Am giving the brainliest.
Answers
Use the identities!
Log 2x square = log 16x
2x square = 16 x
2x sqr - 16x = 0
2x(x-8) = 0
X = 0 or 8
According to logarithms x can’t be 0 so it’s 8
what is other way to write 3x(4+7)
Answers
Answer:
[tex]3 \times (4 + 7) =( 3 \times 4) + (3 \times 7) \\ thank \: you[/tex]
(1-\sqrt{x})/1+\sqrt{x}
Answers
Answer:
[tex] \frac{1 - 2 \sqrt{x} + x }{1 - x} [/tex]
Step-by-step explanation:
[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } [/tex]
Rationalize the denominator by multiplying by it conjugate.
[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } \times \frac{1 - \sqrt{x} }{1 - \sqrt{x} } = \frac{1 - 2 \sqrt{x} + x}{1 - x} [/tex]
Ken Ken 5x5 please help
Answers
Answer:
5x5= 25
Step-by-step explanation:
5+5+5+5+5= 25
14. The cost of 10 dozen of caps is Rs.800. How many caps can bebought for Rs.200.
Answers
Answer:
30 caps can be bought
Step-by-step explanation:
[tex]{ \sf{Rs.800 = (10 \times 12) \: caps}} \\ { \sf{Rs.200 = ( \frac{200 \times 10 \times 12}{800}) \: caps}} \\ \\ { \sf{ = 30 \: caps}}[/tex]
A 3-foot piece of brass wire costs $18.00. What is the price per inch?
Answers
Answer:
50¢
Step-by-step explanation:
$18.00=1800.
3*12=36
1800/36=50
Answer:
Step-by-step explanation:
the price of per inch is $2
Find the length of the third side. If necessary, round to the nearest tenth.
Answers
Answer:
a = 6
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + 8^2 = 10 ^2
a^2 +64 = 100
a^2 = 100 -64
a^2 = 36
Take the square root of each side
sqrt(a^2) = sqrt(36)
a = 6
The sum of twice a number and three
Answers
doneeee
Is this a function? Input: students first name, Output: students favorite color
Answers
If f(x)=2x-1and g(x)=x^2-3x-2,find( f+g)(x)
Answers
Answer:
[tex](f+g)(x)=x^2-x-3[/tex]
Step-by-step explanation:
We have [tex]f(x)=2x-1[/tex] and [tex]g(x)=x^2-3x-2[/tex]
Recall that [tex]f+g[/tex] is defined by [tex](f+g)(x)=f(x)+g(x)[/tex], therefore
[tex](f+g)(x)=f(x)+g(x)=2x-1+x^2-3x-2=x^2-x-3[/tex]
In a GP the second and fourth terms are 0.04 and I respectively find the common ratio and the first term
Answers
Answer:
common ratio=0.5, a1= 0.08
Step-by-step explanation:
r=a3/a2
r=a4/a3
compare both we get:
a3/a2=a4/a3
subtitute a2=0.04 and a4=1
a3/0.04=1/a3
(a3)^2=0.04*1
(a3)^2=0.04
taking square root in both sides
a3=0.02
For r, r=a3/a2
subtitute a3 and a2 above
r=0.02/0.04
r=0.5 common ratio
For a1
r=a2/a1
0.5=0.04/a1
a1=0.04/0.5
a1=0.08
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
The first term of the geometric sequence is 0.08.
The common ratio of the geometric sequence is 1/0.02.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
Geometric sequence:
The second term = 0.04
The fourth term = 1
In a geometric sequence the nth term is given as:
[tex]a_{n}[/tex] = [tex]a_1 r^{n-1}[/tex]
Second term = 0.04
[tex]a_2[/tex] = 0.04
[tex]a_1 r^1 = 0.04[/tex]
[tex]a_1r[/tex] = 0.04 _____(1)
Fourth term = 1
[tex]a_4 = 1[/tex]
[tex]a_1 r^3[/tex] = 1 _____(2)
From (1) and (2) we get,
0.04/r = 1/r³
r³ = r / 0.04
r² = 1/0.04
r = 1/0.02 ____(3)
Putting (3) in (1) we get
[tex]a_1[/tex] = 0.04 x 0.02 = 0.08
Thus,
The first term of the geometric sequence is 0.08.
The common ratio of the geometric sequence is 1/0.02.
Learn more about geometric sequence here:
https://brainly.com/question/2321576
#SPJ2
The logarithmic function f(x) = ln(x) is the ___ logarithmic function and has a base ___
Answers
Answers:
naturaleThe logarithmic function f(x) = ln(x) is the natural logarithmic function and has base e
=======================================
Explanation:
The ln(x) or Ln(x) is the natural log function. The order of L and n is backwards compared to "natural log", but you can think of it "log that is natural" or something along those lines.
The Ln(x) function is of the form [tex]\log_b(x)[/tex] where the base b is the special constant e = 2.718... (this constant is similar to pi = 3.14...)
help pls ! (i mark brainliest).
Answers
Answer: The answer is
25 Units
Answer:
36 units
please mark me brainleast
Write in standard form 4.025x10 2
Answers
Answer:
402. 5
Step-by-step explanation:
This is your answer hope this helps
And also pls mark me brainliest
Write 4 2/5 as an improper faction
Answers
Answer:
22/5
Step-by-step explanation:
4 [tex]\frac{2}{5}[/tex]
new numerator for improper fraction = (4 x 5) + 2 = 20 + 2 = 22
=> 22/5
Both Raquel and Felipe attempt to make a scale drawing of the original parallelogram shown
Answers
Answer:
Both of them drew the parallelogram right.
Step-by-step explanation:
In Raquel's drawing we can see that the parallelogram is shorter and smaller but both the opposite lines are congruent to each other and match the scale size to the original drawing. And it Felipe's drawing the parallelogram is longer and bigger than the original drawing but the opposite line are also congruent to each other and match the scale size to the original drawing!!
I hope you get it right! :)
How many right triangles have a hypotenuse that measures 4x + 2 meters and legs that measure 4x-2 meters and x + 6 meters? What are the dimensions of the triangle(s)?
Answers
9514 1404 393
Answer:
2 triangles; x={2, 18}10 m, 6 m, 8m74 m, 70 m, 24 mStep-by-step explanation:
The given sides will form a right triangle when ...
(4x +2)² = (4x -2)² +(x +6)² . . . . . the Pythagorean theorem is satisfied
16x² +16x +4 = 16x² -16x +4 +x² +12x +36 . . . . eliminate parentheses
x² -20x +36 = 0 . . . . . simplify to standard form
(x -2)(x -18) = 0 . . . . . . factor
x = 2 or 18 . . . . . . . . values of x that make the factors zero
There are two triangles.
For x = 2
hypotenuse = 4(2) +2 = 10
leg1 = 4(2) -2 = 6
leg2 = 2 +6 = 8
dimensions are 6 m by 8 m with hypotenuse 10 m.
For x = 18
hypotenuse = 4(18) +2 = 74
leg1 = 4(18) -2 = 70
leg2 = 18 +6 = 24
dimensions are 24 m by 70 m with hypotenuse 74 m.
v=n/4(c+H) what is the answer for H?
Answers
Answer:
H = (n/4v) - c
Step-by-step explanation:
I ASSUME the equation is
v = n/(4(c + H))
multiply by (c + H)
v(c + H) = n/4
divide by v
c + H = n/4v
subtract c
H = (n/4v) - c
If the equation is v = (n/4)(c + H)
Then
H = (4v/n) - c
the ratio of two number is 4:7 and their hcf is 6 .find their lcm
Answers
168
this is the full process
Are the following sets of points coplanar? 8. E, B, and F 9. DB and FC 10. AC and ED 11. AE and Dc 12. F, A, B, and C 13. F, A, B, and D 15. FB and BD 14. plane Q and EC
Answers
Answer: 8.EB and F: yes
9.DB and FC:no
10.AC and ED:yes
11.AE and DC:yes
12.F,A,B and C:yes
13.F,A,B and D:no
14.plane Q and EC:yes
15.FB and BD:yes
Step-by-step explanation:
hope this helps have a good day!