Answer:
x=2 and 2.6
Step-by-step explanation:
The required solutions for the given function |3 + 10x| = 23 are x = 2 and x = -2.6.
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
The function is given in the question as:
|3 + 10x| = 23
To solve for x, we can begin by expressing the absolute value as a piecewise function:
|3 + 10x| = 23
(3 + 10x) = 23, if 3 + 10x ≥ 0
-(3 + 10x) = 23, if 3 + 10x < 0
If 3 + 10x ≥ 0, then 3 + 10x = 23, so x = (23 - 3) / 10 = 2.
If 3 + 10x < 0, then -(3 + 10x) = 23, so 3 + 10x = -23. This means that x = (-23 - 3) / 10 = -2.6.
Thus, the solutions for x are x = 2 and x = -2.6.
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This shows two functions.
f(x)=5x-7
g(x)=x+4
which function represents
h(x) = f(x) ⋅ g(x)
Answer:
its c just so u know
Step-by-step explanation:
Alesandra is making paper cranes as decorations for a party. She will have
275 when she is done. After she makes fifteen more, she will be one fifth
of the way to her goal. How many does she currently have?
Answer:
135 is the amount of that she has for now
HELP PLS - ITS DUE TMR
Help!!!!!!!!! An automotive service center would like feedback on its customer service Each customer receives a printed card
after they pay for services with a short survey on which customer service is ranked on a scale from 1 (least
satisfied) to 6 (most satisfied) Customers can then choose to submit the card in a box on their way out of the store.
The store manager finds that 140 cards were filled out in the past week, with an average customer satisfaction
score of 2.47 Which type of bias is most likely to be present in the survey results?
This is undercoverage bias because some types of customers may not have received cards,
This is nonresponse bias because many customers may choose to not fill out the cards
This is question wording bias because the customer service score levels may not be clear to customers.
This is response bias because customers may not be truthful about their experience with customer service.
"This is non response bias because many customers may choose to not fill out the cards"
Not everyone will chose to leave a review when leaving the store, and those that do were probably in some way inconvenienced, and felt inclined to leave one, while the others left and went about their day.
help plssssssssssssssssss
Answer:
35x + 14
Step-by-step explanation:
multiply in the brackets
5x × 7 = 35x
(+)2 × 7 = (+)14
Section 8.1 Introduction to the Laplace Transforms
Problem 1.
Find the Laplace transforms of the following functions by evaluating the integral
[tex]F(s) = {∫}^{ \infty } _{0} {e}^{ - st} f(t)dt[/tex]
[tex](a)t[/tex]
[tex](b) {te}^{ - t} [/tex]
[tex](c) {sinh} \: bt[/tex]
[tex](d) {e}^{2t} - {3e}^{t} [/tex]
[tex](e) {t}^{2} [/tex]
For the integrals in (a), (b), and (e), you'll end up integrating by parts.
(a)
[tex]\displaystyle \int_0^\infty t e^{-st} \, dt[/tex]
Let
[tex]u = t \implies du = dt[/tex]
[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]
Then
[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = uv\bigg|_{t=0}^{t\to\infty} - \int_0^\infty v\, du[/tex]
[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = \left(-\frac1s te^{-st}\right)\bigg|_0^\infty + \frac1s \int_0^\infty e^{-st} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = -\frac1s \left(\lim_{t\to\infty} te^{-st} - 0\right) + \frac1s \int_0^\infty e^{-st} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = \frac1s \int_0^\infty e^{-st} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = -\frac1{s^2} e^{-st} \bigg|_0^\infty e^{-st} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = -\frac1{s^2} \left(\lim_{t\to\infty}e^{-st} - 1\right) = \boxed{\frac1{s^2}}[/tex]
(b)
[tex]\displaystyle \int_0^\infty t e^{-t} e^{-st} \, dt = \int_0^\infty t e^{-(s+1)t} \, dt[/tex]
Let
[tex]u = t \implies du = dt[/tex]
[tex]dv = e^{-(s+1)t} \, dt \implies v = -\dfrac1{s+1} e^{-(s+1)}t[/tex]
Then
[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\dfrac1{s+1} te^{-(s+1)t} \bigg|_0^\infty + \frac1{s+1} \int_0^\infty e^{-(s+1)t} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\dfrac1{s+1} \left(\lim_{t\to\infty}te^{-(s+1)t} - 0\right) + \frac1{s+1} \int_0^\infty e^{-(s+1)t} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = \frac1{s+1} \int_0^\infty e^{-(s+1)t} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\frac1{(s+1)^2} e^{-(s+1)t} \bigg|_0^\infty[/tex]
[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\frac1{(s+1)^2} \left(\lim_{t\to\infty}e^{-(s+1)t} - 1\right) = \boxed{\frac1{(s+1)^2}}[/tex]
(e)
[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt[/tex]
Let
[tex]u = t^2 \implies du = 2t \, dt[/tex]
[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]
Then
[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = -\frac1s t^2 e^{-st} \bigg|_0^\infty + \frac2s \int_0^\infty t e^{-st} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = -\frac1s \left(\lim_{t\to\infty} t^2 e^{-st} - 0\right) + \frac2s \int_0^\infty t e^{-st} \, dt[/tex]
[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = \frac2s \int_0^\infty t e^{-st} \, dt[/tex]
The remaining integral is the transform we found in (a), so
[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = \frac2s \times \frac1{s^2} = \boxed{\frac2{s^3}}[/tex]
Computing the integrals in (c) and (d) is much more immediate.
(c)
[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \int_0^\infty \frac{e^{bt}-e^{-bt}}2 \times e^{-st} \, dt[/tex]
[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \int_0^\infty \left(e^{(b-s)t} - e^{(b+s)t}\right) \, dt[/tex]
[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \left(\frac1{b-s} e^{(b-s)t} - \frac1{b+s} e^{(b+s)t}\right) \bigg|_0^\infty[/tex]
[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \left[\lim_{t\to\infty}\left(\frac1{b-s} e^{(b-s)t} - \frac1{b+s} e^{(b+s)t}\right) - \left(\frac1{b-s} - \frac1{b+s}\right)\right][/tex]
[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \left(\frac1{b+s} - \frac1{b-s}\right) = \boxed{\frac{s}{s^2-b^2}}[/tex]
(d)
[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \int_0^\infty \left(e^{(2-s)t} - 3e^{(1-s)t}\right) \, dt[/tex]
[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \left( \frac1{2-s} e^{(2-s)t} - \frac3{1-s} e^{(1-s)t} \right) \bigg|_0^\infty[/tex]
[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \lim_{t\to\infty} \left( \frac1{2-s} e^{(2-s)t} - \frac3{1-s} e^{(1-s)t} \right) - \left( \frac1{2-s} - \frac3{1-s} \right)[/tex]
[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \frac3{1-s} - \frac1{2-s} = \boxed{-\frac{2s-5}{s^2-3s+2}}[/tex]
The graph shows the cost of bowling at a bowling ally.
How much is the cost of each game?
Answer:
Step-by-step explanation:
( 2 , 26 )
( 0 , 4 )
m = (26 - 4 ) / ( 2 - 0 ) = 11
Cost of each game is $11
Classify this triangle by its sides and angles.
Answer:
[tex]\huge\boxed{\sf acute\ and \ scalene}[/tex]
Step-by-step explanation:
In terms of sides:
Since, all of the sides of the triangles are unequal (As indicated), it is a scalene triangle.
In terms of angles:
All the angles are less than 90 degrees (acute), hence, it is an acute triangle.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Kiran wrote the expression x−10 for this number puzzle: “Pick a number, add -2, and multiply by 5.”
Lin thinks Kiran made a mistake.
How can she convince Kiran he made a mistake?
What would be a correct expression for this number puzzle?
Step-by-step explanation:
the number is represented by x. you need to add -2 first then multiply by 5.
thus, the correct expression will be:
( x + -2) *5 = (x-2) *5 = 5(x-2)
for e.g, let x be 3.
acc to the puzzle,
3+-2 = 3-2=1
1*5= 5
using Kiran's expression:
x-10; 3-10= -7
here you can see the answer is wrong.
using the "correct expression" :
5(x-2) = 5( 3-2)
= 5(1)
= 5.
hope this helped you!
-s.
Using the net below, find the surface area
of the rectangular prism.
7 cm
3 cm
7 cm
5 cm
5 cm
3 cm
3 cm
3 cm
Surface Area
Answer:
the surface area of the rectangular prism is 142cm³
Step-by-step explanation:
35+15+21+21+35+15
Jeff is buying books at a used bookstore he wants to approximate the total cost of his purchase before checking out which amount is the most reasonable approximation of the total price of the five books
Answer:
$35.00
Step-by-step explanation:
I just did it rn
symmentry of pentagon
Answer:
5 is the answer..................
Make this Answer as complex as possible. 5 + 5
Answer:
Tennnnnnnnnnnnn.............
please answer with explanation
Answer:
The length of the other diagonal is 42 cm.
Step-by-step explanation:
Area of Rhombus = 966 cm^2 (squared)
one length of diagonal(d2) =46cm
The are of rhombus= d1 x d2/2
*substitution from equation above* = 966= 46 x d2/2 *plug answer in* : 966=23 x d2 *divide next*
d2=966/23
d2=42cm
I don't know if that makes sense hopefully it helps.
It took 3 apples, 7 orange and 3 bananas to make 4
smoothies. How many fruit would be needed
for 12 smoothies?
Answer:
9 apples, 21 oranges, 9 bananas.
Step-by-step explanation:
i did the math
Answer:
It would be 39 fruits
Step-by-step explanation:
If you add up 3+7+3=13 which makes 4 smothies. So 4×3=12 then you would do 13×3=39
PLEASE HELP ASAP! I am so confused by this for some reason.
=====================================================
Explanation:
You can use your calculator to make short work of this problem. Simply plot the parabola and use the "minimum" feature on the calculator to spot the lowest point (specifically the coordinates of that point).
However, I have a feeling your teacher wants you to use a bit of math here. So I'll focus on another approach instead.
---------
The parabolic equation is of the form y = ax^2+bx+c
In this case, we have
a = 0.3b = -192c = 40357Use the values of 'a' and b to find the x coordinate of the vertex h
h = -b/(2a)
h = -(-192)/(2*0.3)
h = 320
The x coordinate of the vertex is 320.
Plug this into the original equation to find the y coordinate of the vertex.
y = 0.3x^2 - 192x + 40357
y = 0.3(320)^2 - 192(320) + 40357
y = 9637 which is the minimum unit cost, in dollars.
The vertex is (h,k) = (320, 9637). It is the lowest point on this parabola.
Interpretation: If the company made 320 cars, then the unit cost (aka cost per car) is the smallest at $9637 per car.
[tex]f(x) = - 5x - 4[/tex]
which function is the inverse of
Answer:
5 x - 4
Step-by-step explanation:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .
Please help with this fractions problem god bless you and ypur loved ones
Answer:
A=4. B=5. C=24
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Thanks so much!!
Answer:it would be 88 because of the co efficient due to the process of mingus in china which made it a law to not pursue dreams within country borders
Step-by-step explanation:
Please Help me. Thanks!
Multiply.
52 × 4
Enter your answers in the boxes to correctly complete the equations.
Answer:
52 x 4 = (50 + 2) x 4
= 50 x 4 + 2 x 4
=200 + 8
=208
this should be right!
brainliest?
The correct the correct multiple of ( 52 x 4 ) is 208.
What is multiple?The number you obtain when you multiple a certain number by an integer. Multiple as like consisting of, including, or involving more than one.
Assume the multiplication of 52 x 4 is A.
To find the value of A
52 x 4 = ( 50 + 2 ) x 4
52 x 4 = 50 x ( 4 ) + ( 2 ) x 4
52 x 4 = ( 200 ) + 8
52 x 4 = ( 208 ).
A = 208.
Therefore, the correct multiple of ( 52 x 4 ) is 208.
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Q10.
What is the area of the shaded part?
Q 10.
25 m
k
25 m
A. 42.5sq m B.212.5sq m
C.225sqm
D.5312.5sq m
NIA
Answer:
ok so we need to first find the amount of black squares vs white squares
top row: 2 black 3 white
2nd top row: 1 black 4 white
middle row: 3 black 2 white
2nd bottom row: 1 black 4 white
bottom row: 2 black 3 white
so lets add that up
9 black 16 white
so then each one is 5 meters so
9*5=45
45m^2
Hope This Helps!!!
4x^4-2x^3+5x^2+2x÷x^2-x-1
Answer:
The answer is 4x² + 2x + 11
Step-by-step explanation:
4x⁴ – 2x³ + 5x² + 2x ÷ x² – x – 1
Now,
[tex]4 {x}^{2} + 2x + 11\\ x² - x - 1 \sqrt{4 x⁴ - 2x³ + 5x² + 2x} \\ \: \: \: \: \: \: 4 {x}^{4} - 4 {x}^{3} - {4x}^{2} \\ \frac{ \: \: \: - \: \: \: \: \: \: + \: \: \: \: \: \: \: \: + \: \: }{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x {}^{3} + 9x {}^{2} + 2x } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 {x}^{3} - {2x}^{2} - 2x \\ \frac{ \: \: \: \: \: - \: \: \: \: \: \: + \: \: \: \: + }{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 11 {x}^{2} + 4x } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 11 {x}^{2} - 11x - 11 \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: + \: \: \: \: \: \: \: \: + }{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 15x + 11} [/tex]
Thus, The answer is 4x² + 2x + 11
-TheUnknownScientist 72
Answer:
4x² + 2x + 11
Step-by-step explanation:
hope it's helpful
PLEASE HELP ANYONE HELP ME W THIS
Answer:
a. 1
b. 5
Step-by-step explanation:
a.Ordered pairs are (x, f(x)). You want f(2), so you look for an ordered pair that lists 2 as the first number. That one is (2, 1). This means f(2) = 1.
__
b.f(2) is plotted as the point (2, f(2)). That is, the x-coordinate of the point will be 2. The point that has x-coordinate 2 is (2, 5).
As above, this means f(2) = 5.
7. 20 is what percent of 50?
A. 250%
B. 10%
C. 40%
D. 30%
Answer:
I think the answer is B or C
The perimeter of a regular octagon is 96 mm. How long each side?
Answer:
12
Step-by-step explanation:
regular implies that all sides are equal
8 sides
total of 96
96/8
12
Charlotte earns $1675 every month of which she spends $85 on cosmetics. Identify the percent of earnings that Charlotte spends on cosmetics to the nearest tenth of a percent?
O 5.1%
O 2.5%
O 3.9%
O 7.4%
Answer:
5.1%
Step-by-step explanation:
percent = part/whole × 100%
percent = 85/1675 × 100%
percent = 5.1%
The percentage of earnings that Charlotte spends on cosmetics to the nearest tenth of a per cent is 5.1%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Charlotte earns $1675 every month of which she spends $85 on cosmetics.
The percentage will be calculated as,
Percent = part/whole × 100%
Percent = 85/1675 × 100%
Percent = 5.1%
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Find the area of the given figure which have all the squares corners.
Answer:
area of the given figure: 58 m²
Explanation:
area of rectangle: length * width
total area:
( 2 * 5 + 12 * 4 )
58 m²
Answer:
The area of the given figure is 58 m².
Step-by-step explanation:
Dividing the given figure into two parts :
➛ Big rectangle ➛ Small rectangle———————————————————————
Firstly, finding the area of bigger rectangle by substituting the values in the formula :
[tex]\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}[/tex]
➣ l = 12 m➣ b = 4 m[tex]\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 12\times 4}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =48}}}\\\\\qquad{\star{\underline{\boxed{\sf{\pink{A_{(Rectangle)} =48 \: {m}^{2}}}}}}} \end{gathered}[/tex]
Hence, the area of bigger rectangle is 48 m².
———————————————————————
Secondly, finding the area of smaller rectangle by substituting the values in formula :
[tex]\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}[/tex]
➠ l = 5 m➠ b = 2 m[tex]\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 5\times 2}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =10}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{A_{(Rectangle)} =10 \: {m}^{2}}}}}}} \end{gathered}[/tex]
Hence, the area of smaller rectangle is 10 m².
———————————————————————
Now, finding the total area of given figure by substituting the values in the formula :
[tex]\longrightarrow{\pmb{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}}[/tex]
→ [tex]\rm{A_{(Big)}}[/tex] = Area of big rectangle → [tex]\rm{A_{(Small)}}[/tex] = Area of small rectangle[tex] \begin{gathered} \qquad{\longrightarrow{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 48 + 10}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 58}}} \\ \\ \quad{\star{\underline{\boxed{\sf{\red{Total \: Area =58\: {m}^{2}}}}}}} \end{gathered}[/tex]
Hence, the total area of the given figure is 58 m².
[tex]\rule{300}{2.5}[/tex]
Find x. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
14 times 14 then do 15 times 15 then add both answers up and take that answer and square route it
Does anyone know the answer to this question?
Answer:
4
Step-by-step explanation:
You can set up the equation as 5x-3=2x+9. Subtract 2x from both sides, then add three to both sides which gives you 3x=12. Divide both sides by 3, and you get x=4.
How do you solve -8>v-3?
Answer:
v < -5
Step-by-step explanation:
Add 3 to both sides. This gives -8+(-3)>v-3+3, or -5>v. Rewriting the inequality gives v < -5.