What value of x makes the equation 5(x - 3) + 2x = 41 TRUE?
Answer: x = 8
Step-by-step explanation: PLEASE GIVEBRAINLIEST IT HELPS ALOT
Answer:
x=8
Step-by-step explanation:
Follow the order of operations to simplify the equation:
5(x-3) +2x=41
Start by multiplying into the parenthesis: 5x-15+2x=41
Combine like terms: 5x+2x-15=41 then simplify: 7x-15=41
Add 15 to both sides: 7x=56
Divide both sides by 7 to get x by itself: x=8
Hope this helps! (^-^)
1. Here is a number line. Write the two missing numbers in the boxes.
0
2
Answer:
The box on the left is 0.4 and the box on the right is 1.8
The concentration of dichlorodiphenyltrichloroethane (DDT - an infamous pesticide) in Lake Michigan has been declining exponentially over many years. In 1971, the DDT concentration was 13.00 ppm (parts per million). In 1984, the DDT concentration was 2.22 ppm.
Using these data points, determine the exponential decay function to model the DDT concentration decline in terms of years, tt, where t=0t=0 represents the year 1971.
A) Write your function as y = Ce^{rt}y=Ce^rt. Round your value of rr to four decimal places.
B) Another way to write the function down is known as the half-life formula, written as y = C(0.5)^{t/H}y=C(0.5)^t/H, where HH is the time required for the concentration to get cut in half. Using the initial two data points, find the value of HH, rounded to 2 decimal places. Show all Algebraic work.
C) The goal was to reduce the DDT concentration to 0.98 ppm by 1995. Was this possible according to your model?
Answer: A) [tex]y=13e^{-0.1359t}[/tex]
B) H = 5.10
C) Yes
Step-by-step explanation: Exponential Decay function is a model that describes the reducing of an amount by a constant rate over time. Generally, it is written in the form: [tex]y(t)=Ce^{rt}[/tex]
A) C is initial quantity, in this case, the initial concentration of DDT. To determine r, using the data given:
[tex]y(t)=Ce^{rt}[/tex]
[tex]2.22=13e^{13r}[/tex]
[tex]e^{13r}=0.1708[/tex]
Using a natural logarithm property called power rule:
[tex]13r=ln(0.1708)[/tex]
[tex]r=\frac{ln(0.1708)}{13}[/tex]
[tex]r=-0.1359[/tex]
The decay function for concentration of DDT through the years is [tex]y(t)=13e^{-0.1359t}[/tex]
B) The value of H is calculated by [tex]y=C(0.5)^{\frac{t}{H} }[/tex]
[tex]2.22=13(0.5)^{\frac{13}{H} }[/tex]
[tex](0.5)^{\frac{13}{H} }=0.1708[/tex]
Again, using power rule for logarithm:
[tex]\frac{13}{H} log(0.5)=log(0.1708)[/tex]
[tex]\frac{13}{H} =\frac{log(0.1708)}{log(0.5)}[/tex]
[tex]\frac{13}{H} =2.55[/tex]
H = 5.10
Constant H in the half-life formula is H=5.10
C) Using model [tex]y(t)=13e^{-0.1359t}[/tex] to determine concentration of DDT in 1995:
[tex]y(24)=13e^{-0.1359.24}[/tex]
y(24) = 0.5
By 1995, the concentration of DDT is 0.5 ppm, so using this model is possible to reduce such amount and more of DDT.
A 2.5-meter piece of framing lumber has been used to cut a piece 1.65 meters long. How much of the original piece of lumber remains, in meters?
Answer:
0.85 of the original piece of lumber remains.
Step-by-step explanation:
Well, this lumber piece of lumber started as 2.5 meters long. Then, a 1.65 meter piece was cut off of it. All we need to do is subtract.
2.5 - 1.65 =
2.50 - 1.65 = 0.85.
Therefore, 0.85 of the original piece of lumber remains.
Hope this helps! :)
If Triangle ABC is congruent to Triangle SRT, find the possible value(s) for x
Answer:
x = 2 or x = -3
Step-by-step explanation:
Given that ∆ABC ≅ ∆SRT, it follows that their corresponding side lengths are congruent to each other.
Thus:
[tex] RT = BC [/tex]
[tex] (x^2 + x) = 6 [/tex]
Solve for x
[tex] x^2 + x = 6 [/tex]
Subtract 6 from each side
[tex] x^2 + x - 6 = 6 - 6 [/tex]
[tex] x^2 + x - 6 = 0 [/tex]
Factorise
[tex] x^2 + 3x - 2x - 6 = 0 [/tex]
[tex] x(x + 3) -2(x + 3) [/tex]
[tex] (x - 2)(x + 3) [/tex]
x = 2 or x = -3
Consider the two functions given below. What is the y-intercept of g? A. (0,14) B. (0,4) C. (0,9) D. (0,-5)
Note: You probabily forgot to mention the two function. While after some research, I was able to find two functions based on which I would like to solve your query.
Answer:
The y-intercept of the equation will be (0, 4).
Step-by-step explanation:
Considering the assuming functions f(x) and g(x).
[tex]f(x) = -3x - 5[/tex]
[tex]g(x) = f(x)+9[/tex]
So,
[tex]g(x) = (-3x-5)+9[/tex] ∵ [tex]g(x) = f(x)+9[/tex]
[tex]g(x) = -3x+4[/tex]
Now, finding the y-intercept
so putting x = 0 in function g(x)
[tex]g(x) = -3(0)+4[/tex]
[tex]g(x) = 0+4[/tex]
[tex]g(x) = 4[/tex]
Therefore, the y-intercept of the equation will be (0, 4).
Answer:
B
Step-by-step explanation:
PLEASE HELP IM TIMED
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Because it's common sense
PLS SOLVE!!!!! THANK YOU!!!!!
find the slope please :)
Answer:
3/4
Step-by-step explanation:
up 3 over 4
Read the description of f below, and then use the drop-down menus to complete an
explanation of why f is or is not a function,
f relates each student in Mr. Well's history class to their score on a final exam.
Answer:
because a function always gives a determined answer from what was placed into the domain, this is not a function. what is put into the domain (students) may not get the same result through f.
Answer: 1. the students 2. the final exams 3. is- domain- one- range brainliest plzz??
what is 0.125 in a percent
Pls answer 55-62 I will give brainlist
Benjamin wants to buy a video game that costs $24, but he only wants to spend 40% of his savings. How much must Benjamin save in order to buy the game?
Answer:
14.4 there sorry for the wait
There were 935 offenses in 2000 and 2448 offenses in 2019. What is the percentage increase?
Answer:
Approximately 262%
Step-by-step explanation:
To find the percentage increase divide the new amount of offenses by the old amount of offenses:
2448/935 = 2.618
2.618 rounds to 2.62. Convert 2.62 into a percentage: 262%
The percentage increase between the amount of offenses in 2000 and the amount of offenses in 2019 is approximately 262%.
Is x − 8 a factor of the function f(x) = −2x3 + 17x2 − 64? Explain. (2 points)
Answer:
x-8 is a factor of f(x)
Step-by-step explanation:
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).
We are given the function
[tex]f(x)=-2x^3+17x^2-64[/tex]
And it's required to find if x-8 is a factor of f.
Applying the mentioned theorem, we only have to find f(8):
[tex]f(8)=-2\cdot 8^3+17\cdot 8^2-64[/tex]
Operating:
[tex]f(8)=-2\cdot 512+17\cdot 64-64[/tex]
[tex]f(8)=-1024+1088-64[/tex]
[tex]f(8)=0[/tex]
Thus, x-8 is a factor of f(x)
What is the y-intercept in the equation 2y = x -8
Answer:
(0,-4)
Step-by-step explanation:
A store sees 138 customers in 8 hours. What is the unit rate (in customers per hour)?
Answer:
Step-by-step explanation:
138/8 = 17.25
A T-shirt shop charges a $25 set-up fee for a new T-shirt design and $6 for every shirt ordered. Which equation best represents the linear relationship between x, the number of shirts ordered, and y, the total cost of a T-shirt order?
Group of answer choices
A:He started on page 30 and read 6 pages each day.
B:He started on page 30 and read 8 pages each day.
C:He started on page 20 and read 12 pages each day.
D:He started on page 20 and read 10 pages each day.
Answer:
[tex]y = 25 + 6x[/tex]
Step-by-step explanation:
The given options are not in anyway related to the question. So, I will do away with them.
Given
[tex]Set-up\ Fee = \$25[/tex]
[tex]Per\ Shirt = \$6[/tex]
Required
Determine the linear relationship
Let
y represents the total cost
x represents the number of shirts
The relationship between x and y is:
[tex]y = Setup\ Fee + Amount\ Per\ Shirt * x[/tex]
This gives:
[tex]y = 25 + 6* x[/tex]
[tex]y = 25 + 6x[/tex]
factor 2w+6
Please explain? I'd like to understand how you did it so that I can do it myself the next time, thanks a mil :)
Answer:
2( w + 3 )
Step-by-step explanation:
Well first off, since theres no common term to factor out, I had to split 6 in half
so 2 w + 6 becomes 2w + 2 x 3.
I then factored out 2 because it's a common term,
which then leaves: 2( w + 3 )
basically, you have to find a common term to factor out, if you don't see one, you have to do something to a number so there's common terms.
PLS HELP. URGENT
Serena and Derek have 270 stickers in all. Serena has 25% more stickers than Derek. How many stickers does Derek have? (Type out your work and answer)
Polly walked a total of 20 kilometers by making 4 trips to school. How many trips will Polly have to make in all to walk a total of 50 kilometers? Assume the relationship is directly proportional.
Answer:
ffffffffffffffffffffffffffffffffffff
Step-by-step explanation:
What's the diameter of 76cm circle circumference
Answer:
The circumference of a circle is C = 2πr^2 (2nd power) Radius (r) is the distance from the center of the circle to the outside of it. To find radius divide the diameter (d) by 2. The diameter (d) of a circle is the radius (r) multiplied by 2. To find the diameter (d) you need to do C ÷ π.
For example):
Finding diameter - 76/3.14 = 24.19 (d)
Finding radius - 24.19/2 = 12.095 (r)
please help me I need this for school
Answer:
It would be c!
Step-by-step explanation:
-2/3 x 3/4
Please help!
Answer:
-1/2
Step-by-step explanation:
Answer:
-9/8.
Step-by-step explanation:
-3/2 * 3/4
= -3*3 / 2*4
= -9/8.
Amy and rose both compete in a race. Amy takes 42.8 seconds to finish, and Rose finishes in 49.2 seconds. How many seconds faster was Amy than Rose?
Answer:
6.4 seconds
Step-by-step explanation:
you subtract roses time by Amys time to find the difference.
Roxanna has a collection of silver spoons from all over the world.
If the spoons are arranged in sets of 7, there are 5 left over.
If the spoons are arranged in sets of 8, there is 1 left over.
If the spoons are arranged in sets of 15, there are 14 left over.
If she has at least 50 spoons, what is the smallest possible number of spoons in her collection?
Answer: 89
Step-by-step explanation: 8 x 11 + 1 = 89, 7 x 12 + 5 = 89, 15 x 5 + 14 = 89
Wich calculation will ALWAYS have a result greater than 1
Step-by-step explanation:
number less than 1 B.4/9+ a fraction less than 12 C. 1 3/4 - a fraction less than 3/4 D.7/8 a number less than 1
Amy types at an average speed of 38 words per minute. She has already typed 1,450 words of her final paper, which will be more than 4,000 words. Which inequality can be used to solve for x, the number of minutes it will take Amy to finish typing her paper?
A. 38x- 1,450>76
B. 38(x + 1,450)>4,000
C. 38x> 4,000
D. 38x + 1,450> 4,000
Please help me, thanks!
Answer:
Algebraic expression for 75 less than twice Mabel's score is 2m-75
Step-by-step explanation:
We need to translate the phrase 75 less than twice Mabel's score into algebraic expression.
Translating into algebraic expression
Let m represent Mabel's score
Twice Mabel's score = 2m
75 less than Twice Mabel's score = 2m-75
So, algebraic expression for 75 less than twice Mabel's score is 2m-75
F=1.8C+32 solve for given variable
Answer:
Step-by-step explanation:
The formula F = 1.8C + 32 can be used to find the temperature in degrees Fahrenheit F when the temperature is given in degrees Celsius C. For what value is the temperature in degrees Fahrenheit equal to the temperature in degrees Celsius? Justify your reasoning by writing and solving an equation. (Hint: If Fahrenheit and Celsius are equal, they can be assigned the same variable.)