[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits \frac{x^3+1}{x^3-x} dx }} \end{gathered}$}[/tex]
We rewrite the integrand.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{x^3+1}{x^3+x}=1+\frac{1}{x-1}-\frac{1}{x} }} \end{gathered}$}[/tex]
We integrate terms by terms:
The integral of the constants have this constant multiplied by the variable of integration.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits 1 \ dx=x } } \end{gathered}$}[/tex]
That u = x -1. Then that du = dx and we put du.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\frac{1}{u} \ du }} \end{gathered}$}[/tex]
Integral 1/u is log(u). If you now substitute u further into:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{log(x-1) }} \end{gathered}$}[/tex]
The integral of the product of a function by a constant is the constant times the integral of this function:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\left(-\frac{1}{x}\right)dx=-\int\limits\frac{1}{x}dx }} \end{gathered}$}[/tex]
Integral 1/u is log(x). Therefore, the result is: -log(x).
The result is: x - log(x) + log(x - 1)
Michael took his kids to get haircuts. The haircut cost $50 for all of the kids combined. He also gave the stove is a 30% tip. What was the total cost including tip of Michael’s three kids to get haircuts
Michael took his kids to get haircuts. The haircut cost $50 for all of the kids combined. He also gave the stove a 30% tip.
The total cost of the haircut including the tip was $65.
What do you mean by cost price?
Cost price is the total sum of money that it costs a manufacturer to make a particular good or offer a particular service. The total expenditure needed to create something or perform a service is the cost. The following methods for determining profitability involve cost price: Profit in monetary terms is calculated as Selling Price (Excluding Tax) – Cost.
Solution Explained:
Given,
Cost of the haircut is $50
Tip that Micheal gave is 30%
So calculating,
Tip = (50 X 30) / 100 = 15
Therefore, the total cost including tip for the haircuts is
= 50 + 15
= 65
To learn more about cost price, use the link given
https://brainly.com/question/19104371
#SPJ1
On November 2, Sheffield Company discounted at Sunshine Bank a $5,760 (maturity value), 129-day note dated August 15. Sunshine's
discount rate was 7%. (Use Days in a year table.)
What proceeds did Sheffield Company receive?
Note: Use 360 days a year. Do not round intermediate calculations.
Proceeds received
Sheffield would get $5,704 in revenues to signify that there are 50 days left before the note matures and that the maturity amount must thus be deducted from the proceeds.
Given,
Maturity value = $5,760
129 day note dated August 15
Sunshine's discount rate = 7%
We have to find the proceeds received by Sheffield Company;
Here,
Number of days that have passed since Note was issued is;
16 days in August
30 days in September
31 days in October
2 days in November
= 16 + 30 + 31 + 2
= 79 days
79 days have already elapsed out of the 129 so days left is;
= 129 - 79
= 50 days
Assuming a 360 day Calendar, Sheffield Company will receive;
= Maturity level - Discount Amount
= 5760 - (5760 × 7% × 50/360)
= 5760 - 56
= $5704
Sheffield would get $5,704 in revenues to signify that there are 50 days left before the note matures and that the maturity amount must thus be deducted from the proceeds.
Learn more about Proceeds here;
https://brainly.com/question/17030958
#SPJ1
No links help please how are triangles similar
Both the triangles of the given figure are similar to each other by SAS
( Side angle Side ) the property of corresponding sides are in proportion and included angle of both the triangles is right angle.
Slope of the both the triangles is (-3/2) .
As given in the question,
For the given diagram of the two triangles,
To prove : Both the triangles are similar to each other.
Side length of the corresponding sides of both the triangles :
Altitude of :
Small triangle : 6 - 3 = 3 units
Big triangle : 3 - (-3) = 6 units
Base :
Small triangle : -2 + 4 = 2 units
Big triangle : 2 - (-2) = 4 units
Corresponding sides are in proportion:
( 3/6) = 1/2 = ( 2 / 4)
And the included between the two sides is equal to 90° ( right angle ).
By SAS ( Side angle Side ) theorem,
Both the triangles are similar to each other.
Now slope of :
Small triangle is equal to,
Consider two end points ( -4, 6) and ( -2 , 3)
Slope = ( 3 -6)/ (-2 + 4)
= -3/2
Big triangle is equal to,
Consider two end points ( -2, 3) and ( 2 , -3)
Slope = ( -3 -3)/ ( 2 + 2)
= -6 /4
= -3/2
Therefore, both the triangles of the given figure are similar to each other by SAS
( Side angle Side ) the property of corresponding sides are in proportion and included angle of both the triangles is right angle.
Slope of the both the triangles is (-3/2) .
Learn more about triangles here
brainly.com/question/2773823
#SPJ1
Select the graph that would represent the best presentation of the solution set for |z| > (1/2).
(I could not all the pics, so if it's none of these just let me know)
Answer: Graph 4
Step-by-step explanation: Because "[z]" is greater than the absolute value of 1/2, any number that is not in between -1/2 and 1/2 is [z]. This is also known as an "or" statement for z can be greater than 1/2 "or" less than -1/2.
[Z]>1/2 (Given)
Plug-in points for "z":
[.25] =.25 & -.25 (subs prop of inequality)
-1/2 <.25 < 1/2 This is an "and" statement, where the line would overlap. So this solution is incorrect
Next, try another number
[1] = -1,1
-1/2<1>1/2 This is an "or" statement meaning the solution can be either less than -1/2 or greater than 1/2 So this would be a solution to the problem
a jet flies 600 kilometers in 3/4 pf an hour. How far can this jet fly in 1/2
Answer:
If you divide 600/ 45 mins you get the kilometers per minute which is 13.33. Then you multiply 13.33 times 30 mins and you get 399.9 or 400 kilometers
Step-by-step explanation:
Question 7:
Several health insurance companies are bidding for an insurance contract. Of these companies, 3
are local, 3 have state-wide operations, and 6 have national operations. Only one company will
be awarded the contract. If each company is equally likely to win the contract, what is the probability
that the contract will be awarded to one of the companies with state-wide operations?
Note: For any final answer that has up to four decimal places, enter your answer without rounding the
number. For any answers with more than four decimal values, round your final answer to four decimal
places.
I
The probability of contract bring given to a state wide operation is 0.2500
What is probability?
The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that a press release is true. associate degree event's likelihood may be a range between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Main body:
Number of local insurance contract operations = 3
Number of state-wide operations = 3
Number of national wide operations = 6
Therefore total companies = 3+3+6
= 12
Probability of contract being given to state wide company = 3/12
P(state wide) = 0.2500
Hence the probability of the given case is 0.2500.
To learn more about probability click on the link below.
https://brainly.com/question/13604758
#SPJ9
Linda is making curtains . She has 2 1/3 yards of material . She wants to make 3 curtains . She needs 8/9 yard for each curtain . Does she have enough material for 3 curtains?
======================================================
Use this formula
a & b/c = (a*c + b)/c
to convert from a mixed number to an improper fraction.
Let's use that formula to find the following
a & b/c = (a*c + b)/c
2 & 1/3 = (2*3+1)/3
2 & 1/3 = 7/3
She has 7/3 yards of material.
Linda wants to make 3 curtains. Each curtain needs 8/9 of a yard.
3*(8/9) = 24/9 = (8*3)/(3*3) = 8/3
Therefore, she needs 8/3 yards of material.
But this is a problem because she needs more material than what she has on hand. In other words, 8/3 > 7/3 since 8 > 7.
-----------
Another way to look at it:
7/3 = 2.333 yards is the approximate amount of fabric she has
8/3 = 2.667 approximately is the total amount of fabric she needs, which is clearly larger than the 2.333 yards she has.
Unfortunately Linda does not have enough fabric to make 3 curtains.
Write y = 4x in function form
Can you please show the equation or rewrite the equation?
Simply 9/24 fraction
Answer: [tex]\frac{3}{8}[/tex]
Step-by-step explanation: dividing the top and bottom of the fraction [tex]\frac{9}{24}[/tex]by 3 will give you the simplest form. Your welcome
Answer:
3/8
Step-by-step explanation:
The fraction 9/24 simplifies to 38. The way to arrive at this solution is to find the greatest common multiple for both the numerator and the denominator. In this case, the greatest common multiple is 3.
Hope that helps! Have amazing rest of your day! Brainliest welcome! :)
Graph the function. f(x)=-3(x+1)^2+5f(x)=−3(x+1) 2 +5
Answer:
See attachment.
Step-by-step explanation:
1. Use the slope-intercept form to find the slope and y-intercept.
y = mx + b ; m= slope b= y-intercept
2. Find the values.
m = 0
b = 7
slope: 0
y-intercept: ( 0, 7)
3. Find two points on the line, then graph them.
x = 0, 1
y = 7, 7
Which ordered pairs in the form (x, y) are solutions to the equation
4x−5y=24
Select each correct answer.
Responses
(1, −4)
Begin ordered pair 1 comma negative 4 end ordered pair
(−9, −12)
Begin ordered pair negative 9 comma negative 12 end ordered pair
(4, 8)
Begin ordered pair 4 comma 8 end ordered pair
(6, 0)
The solutions to the given linear equation are (1, -4), (-9, -12), and (6, 0)
Determining the solutions to a linear equationFrom the question, we are to determine the ordered pairs that are solutions to the given equation
The given equation is
4x - 5y = 24
To do this, we will check for the ordered pairs that satisfy the equation.
(1, -4)
Substitute x = 1 and y = -4
4x - 5y = 24
4(1) - 5(-4) = 24
4 + 20 = 24
24 = 24
Therefore, (1, -4) is a possible solution to the equation
(-9, -12)
Substitute x = -9 and y = -12
4x - 5y = 24
4(-9) -5(-12) = 24
-36 + 60 = 24
24 = 24
Therefore, (-9, -12) is a possible solution to the equation
(4, 8)
Substitute x = 4 and y = 8
4x - 5y = 24
4(4) - 5(8) = 24
16 - 40 = 24
-24 ≠ 24
Therefore, (4, 8) is not a solution to the equation
(6, 0)
Substitute x = 6 and y = 0
4x - 5y = 24
4(6) -5(0) = 24
24 + 0 = 24
24 = 24
Therefore, (6, 0) is a possible solution to the equation.
Learn more on Determining the solutions to a linear equation here: https://brainly.com/question/1757969
#SPJ1
this is reaally hard sombody pleaase help me thnk you
Answer:
Step-by-step explanation:
Ok:
Flour:
2 1/4 cups/1/4c=
9 cups needed
Sugar:
1 7/4/1/4=
11 cups needed
Cocoa:
1 1/2/1/4=
6 cups needed
Oil:
1/2/ 1/4=
2 cups needed
Heavy Cream:
3 2/3/ 1/3=
11 cups needed
Butter:
1/1/3=
3 cups needed
Powdered Sugar:
5 1/3/1/3=
16 cups needed
Cocoa:
1/3/1/3( Sry if I read the 3 wrong because its blurry tell me and I will fix it!)=
1 cup needed
what is 1 1/8 add 2 4/8 =
Answer:
29/8 or 3 5/8
Step-by-step explanation:
How many work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times (in minutes): 6.1, 6.9, 6.9, 6.7, 6.8, and 6.4?
The number of work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times is 23.
What are Sample Mean?
The average value of the provided sample data is determined using the sample mean formula. Instead of expressing them using actual terms, it is occasionally essential to calculate the sample term average. The ratio of the sum of terms to the total number of terms can be used to describe the sample mean formula. The center of the data is measured by the sample mean. The sample mean is used to estimate the mean of any population. Many times, without surveying the entire population, we must make educated guesses about how the population as a whole is behaving or what variables are affecting the population as a whole. In these situations, the sample mean is helpful. The sample mean is the average value obtained from the sample. The variance and subsequently the standard deviation are determined using the sample mean that was so obtained.
For the given data,
Standard Deviation = 0.3204
Mean =(6.1+6.9+6.9+6.7+6.8+6.4)/6=6.633
The margin of error = 2% of mean
Z score for 95.5 confidence interval = 1.96
Number of cycles, sqrt(n)
= (1.96× 0.3204) / (6.633×0.02)
= 4.7337
n = 22.408
Rounding to the next integer, then work cycles = 23
Hence,
The number of work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times is 23.
To learn more about Sample mean, visit;
https://brainly.com/question/15020296
#SPJ1
Determine whether to use a permutation or combination for the following, then
determine the total number of outcomes.
There are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen?
A. Permutation; 45 ways
B. Permutation; 90 ways
C. Combination; 45 ways
D. Combination; 90 ways
For the given condition of choosing president and treasurer from the 10 board members on the Community Arts Council , the total number of outcomes president and treasurer can be chosen as
Combination ; 45 ways.
As given in the question,
Total number of board members in the Community Arts Council = 10
Number of people to be chosen from Community Arts Council (president and treasurer) = 2
Total number of ways to choose a president and treasurer is calculated using combination of selecting 2 people is equal to
= ¹⁰C₂
= ( 10 )! / ( 2! ) ( 10 - 2 )!
= ( 10 × 9 × 8! ) / ( 2 × 1 ) ( 8! )
= 90 / 2
= 45
Therefore, for the given condition of choosing president and treasurer from the 10 board members on the Community Arts Council , the total number of outcomes president and treasurer can be chosen as
Combination ; 45 ways.
Learn more about combination here
brainly.com/question/28042664
#SPJ1
A new jewelery store opened recently. There are several sales associate positions that pay an hourly rate of
$11.00 plus a three percent commission of the total weekly sales. Based on an expected weekly average of
$2600 of sales, write an equation that gives the gross weekly pay (p) if you work a hours per week.
The equation that gives the gross weekly pay (p) if you work a hours per week is 11h+78.
what is equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.
Here,
2600*3/100=26*3
=78
p=11h+78
The algorithm for calculating gross weekly pay (p) if you work a number of hours per week is 11h+78.
To know more about equation,
https://brainly.com/question/10413253?referrer=searchResults
#SPJ1
) You invested your allowance of $270 which gets 15% compounded annually for 3 years.
How much will you have in 3 years?
Answer:
BELOW
Step-by-step explanation:
The equation ( you need to commit to memory) is:
FV = PV ( 1+i)^n FV = future value PV = present value(270)
i = decimal interest per PERIOD = .15
n = # of periods = 3 (it is an ANNUAL Period)
FV = 270 ( 1 + .15)^3 = 410.63 dollars
Answer:
$410.64
Step-by-step explanation:
start with the compound interest formula
plug in p=270 , r=0.15 (divide 15 by 100 to get 0.15), n=1, and t=3
divide 0.15 by 1 to get 0.15
multiply the exponents 1 and 3 to get 3
add 1 and 0.15 to the 3 th power to get 1.520875
multiply 270 and 1.520875 to get 410.63625
so if you invest $270 at an interest rate 15%, which is compounded 1 times a year for 3 years, the return is about $410.64 (which is rounded to the nearest cent)
Then you'll have $410.64 in 3 years.
Can you solve the system of equation using substitution 5x + 2y = 7 4X +y =8
The solution of the given system of equations using substitution is x = 9/5 and y = -1.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
As per the given equations,
5x + 2y = 7 and 4x +y =8
4x +y =8 → 4x = 8 - y
⇒ x = 2 - y/4
Substitute this x into the above,
5(2 - y/4) + 2y = 7
10 - 5/4 y + 2y = 7
10 + y(2 - 5/4) = 7
3y/4 = -3
y = -1
And, 5x + 2(-1) = 7
5x = 9
x = 9/5
Hence "The solution of the given system of equations using substitution is x = 9/5 and y = -1".
For more about the equation,
brainly.com/question/10413253
#SPJ1
On the first of January, Jed had £48 in his bank account and Esther had £180 in her bank account. From then on, at the end of each month Jed put £40 into his account and Esther put £34 into her account. After how many months did they have the same amount of money in their accounts?
After 22 months, Jed and Esther have the same amount of money in their accounts.
How to balance the equations?Simplify both sides of the equation as much as possible using the order of operations (distribute, combine like terms, etc.)
Given: Jed has £48 in his bank account and from then on, at the end of each month he put £40 into his account and
Esther had £180 in her bank account and from then on, at the end of each month she put £34 into her account.
Now, let us consider after 't' months they have same amount of money in their accounts
⇒ £48 + £40t = £180 + £34t
⇒ £40t - £34t = £180 - £48
⇒ 6t = 132
⇒ t = 22.
Therefore, after 22 months, Jed and Esther have the same amount of money in their accounts.
To learn more about time, visit
https://brainly.com/question/14021405
#SPJ1
The headlights on a car are set so the light beam drops 2 in. for each 21 ft measured horizontally. If the headlights are mounted 36 in. above the ground, how far ahead of the car will they hit the ground?
The headlights of the car will hit the ground 378ft
Unitary Method:The unitary method is a numerical process that is used to calculate any value i.e., cost or speed, or any desired quantity. In this method, we will find the desired value for 1 unit so that we can find the value for multiple units.
Here we have
The headlights on a car are set to the light beam drops 2 in. for each 21 ft measured horizontally.
The headlights are mounted 36 in. above the ground
For 2-in - 21 ft measured horizontally
Then for 1 - in = 21/2 = 10.5 ft
then for 36 in = 36 × 10.5 = 378 ft
Therefore,
The headlights of the car will hit the ground 378ft
Learn more about the Unitary method at
https://brainly.com/question/22056199
#SPJ1
From the chart, estimate (roughly) the number of transistors per IC in 2016. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040?
Please explain
The estimate of the number of transistors per IC in 2016 is of:
16,777,216,000
Using Moore's Law, the prediction for the number of transistors per IC to be in 2040 is of:
6.87 x 10¹³
What is Moore's Law?Moore's Law states that the number of transistors per IC is expected to double every two years.
Hence the amount of transistors in t years after 1972 is given by the following exponential function:
[tex]A(t) = 4000(2)^{\frac{t}{2}}[/tex]
The number of years between 2016 and 1972 is given as follows:
2016 - 1972 = 44.
Hence the estimate for the number of transistors per IC in 2016 is of:
[tex]A(44) = 4000(2)^{\frac{44}{2}}[/tex]
A(44) = 16,777,216,000
The number of years between 2040 and 1972 is given as follows:
2040 - 1972 = 68.
Hence the estimate is obtained as follows:
[tex]A(68) = 4000(2)^{\frac{68}{2}}[/tex]
A(68) = 6.87 x 10¹³.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
1) Kyla buys a designer furniture set at a price of $12,000. She pays 25% deposit and interest in 36 months in addition to the outstanding balance. The interest charged on the balance is 12%. Calculate:
a) the deposit Kyla paid
b) the balance inclusive of interest
(a) The deposit that Kyla paid is $3000
(b) the balance inclusive of the interest is $10080 .
In the question ,
it is given that ,
the price of the furniture set = $12000
Part (a)
percent of deposit that Kyla paid = 25% ,
that means the amount paid by Kyla as deposit = 25% of 12000
= 0.25 × 12000
= 3000
So , Kyla deposited $3000 .
Part (b)
the balance amount = price of furniture - amount deposited ,
the balance amount = 12000 - 3000
= 9000
and the rate of interest = 12% ,
So , the interest paid = 12% of balance amount
= 12% of 9000
= 0.12 × 9000
= 1080
So , the balance amount inclusive of interest = 9000 + 1080
= $10080
Therefore , (a) The deposit that Kyla paid is $3000
(b) the balance inclusive of the interest is $10080 .
Learn more about Interest here
https://brainly.com/question/27456785
#SPJ9
another way to write 6axbcx2d without using multiplication sign
????
Answer:
Step-by-step explanation:
(6a)(b)(c)(2d)
If 56 apples were placed in each bag instead how many bags would be left over
Its 112 bags how much?
Answer:
56
Step-by-step explanation:
one apple = one bag
the 56 apples = 56 bags
112 -56 =56
¿De cuántas formas puede un juez otorgar el
primero, segundo y tercer premio en un
concurso que tiene ocho concursantes?
Hay 336 formas diferentes en las que se pueden entregar los 3 premios.
¿De cuantas formas se pueden otorgar los premios?
Sabemos que hay 8 participantes y de estos se elegiran a 3 para darles 3 premios diferentes.
Para el primer premio, hay 8 posibles concursantes que lo pueden recibir.Para el segundo premio, hay 7 concursantes que lo pueden recibir (hay uno menos por que uno ya recibio el primer premio)Para el tercer premio, hay 6 concursantes que lo pueden recibir.El numero total de combinaciones es lo que obtenemos cuando tomamos el producto entre los números de opciones:
C = 8*7*6 = 336
Aprende más sobre combinaciones:
https://brainly.com/question/11732255
#SPJ1
Alexis biked a distance of 6 miles each day for 3 days. Then, she biked 7 miles each day for the next
5 days. What was the total distance in miles that Alexis biked during these 8 days?
O 35 miles
o 40 miles
o 19 miles
O 54 miles
The Anwser to this question
How do you graph it?
Answer:
See picture below
Step-by-step explanation:
Desmos is a free graphing calculator.
x-y = 1 Subtract x from both sides
-y = -x + 1 Divide all the way through by -1
y = x - 1
These line are parallel because they have the same slope.
On the green line I highlightes tow points (0,4) and (3,7) . (0,4) tells us where the line crosses the y anxis. Thiis will be in the form (0,b) b stands for the y intercept. This graph is crossing the green line at 4. The slope is 1. The patern form the first point (0,4) is to move up one and move right one. This pattern continues throuhg point (3,7) and beyond.
The blue line in the slope intercept from is
y = x +1 . Its slope is the same as the first line. It is up one and one to the right and that pattern continues. This line cross the y axis at -1.
A family is comparing different car seats. One car seat is designed for a child up to and including 25 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a
child between 25 lb and 85 lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a 35-lb child?
According to the concept of inequality, the interval notation is 0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85 based on these range the second and third car seats are suitable.
Inequality:
Inequality refers the non equal relation of the sets.
Given,
A family is comparing different car seats. One car seat is designed for a child up to and including 25 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 25 lb and 85 lb, inclusive. Model those ranges with compound inequalities.
Here we need to find in which car seats are appropriate for a 35-lb child
In this question, they provided that, there are three car seats are designed as follows:
First, on is the car seat made for children upto 30lb.
Second one is the seat for children between 15lbs and 40lbs and
And the third one is the seat designed for a child between 30 lb and 85 lb
Here we know that, the seat designed for a child upto and including 30 lb would not be suitable for 35 lb child. Because 35lb is more than the 30 lb.
So, now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 35lb.
Therefore, the interval notation is written as,
=> 0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;
So, the second and third car seats are suitable.
To know more about Inequality here.
https://brainly.com/question/28823603
#SPJ1
Katie wants to collect over 100 seashells. She already has
34 seashells in her collection. Each day, she finds 12
more seashells on the beach. Katie can use fractions of
days to find seashells.
Write an inequality to determine the number of days,
d, it will take Katie to collect over 100 seashells.
The inequality to determine the number of days, d, it will take Katie to collect over 100 seashells is 34 + 12d > 100.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the number of days be represented by d.
In this case, Katie already has 34 seashells in her collection and each day, she finds 12 more seashells on the beach.
The expression will be:
34 + 12d > 100
Collect like terms
12d > 100 - 34
12d > 66
Divide
d > 66/12
d > 5.5
d > 6
The number of days is 6 days.
Learn more about inequalities on:
brainly.com/question/25275758
#SPJ1
(in
9. Give an equation of a line
slope-intercept form) that
is perpendicular to:
-9x=15-3y
The equation of a line that is perpendicular to -9x = 15 - 3y is y = -1/3(x) + c.
Given:
-9x = 15 - 3y
3y = 15+9x
divide by 3 on both sides
3y/3 = 15/3 + 9x/3
y = 3x + 5
m = 3
Perpendicular slope m1 = -1/m
= -1/3
substitute m value in y = m1x +c
y = -1/3(x) + c.
Therefore the equation of a line that is perpendicular to -9x = 15 - 3y is y = -1/3(x) + c.
Learn more about the equation of a line here:
https://brainly.com/question/21511618
#SPJ1
Answer:
16
Step-by-step explanation:
multiply sides