Answer:
......
Step-by-step explanation:
With these types of problems, it's best to label the unknowns and figure out an equation for what we want to find. Here, we're interested in weight in pounds, which I'll call W, as a function of the number of weeks that have gone by, which I'll call n. So if we can get an equation that relates W to n, we can answer the question of "how many weeks to reach 175 pounds?" by plugging in W = 175 to our equation and solving to find out what value of n gives us that.
Suppose Alex weighs P pounds at the start of his diet. We don't know what P is yet, but we'll aim to find its value later with the information the question gives us.
After 1 week, Alex will lose 2 pounds and will weigh P - 2 pounds
After 2 weeks, Alex will lose another 2 pounds and weigh (P - 2) - 2 = P - 4 pounds
After 3 weeks, Alex will weigh (P - 4) - 2 = P - 6 pounds
You can see the pattern here: after every week, knock off 2 pounds. So in general after n weeks, Alex will lose 2n pounds from his start weight, and he will weigh P - 2n
That gives the equation W = P - 2n, or equivalently
W = -2n + P
We can recognize this as a linear equation, which takes the form y = mx + b, where:
- x is the independent variable,
- y is the dependent variable (the thing that changes as a function of x),
- m is the slope (how much y changes for every unit change in x), and
- b is the y-intercept (that is, the value of y when x = 0).
In our equation W = -2n + P, the number of weeks n is the independent variable, weight W is the dependent variable (it varies as a function of the number of weeks), -2 is the slope (because Alex weight 2 pounds less for every week that goes by), and P - whose value we don't know yet - is Alex's starting weight (i.e., the value of W when n = 0).
To find the value of P, we can use the information in the question that after 6 weeks, Alex weighs 205 pounds. In other words, when n = 6, W = 205. Plug that into our equation and get:
205 = P - 2*6
We can solve that for P:
205 = P - 12
Add 12 to both sides:
P = 205 + 12 = 227
So Alex weighs 227 pounds when he starts the diet, and we have
W = -2n + 227
This is the linear equation the question is asking for.
To find how many weeks Alex needs to reach his target weight of 175 pounds, set W = 175 in the equation and solve it for n:
175 = -2n + 227
Move the -2n over to the other side:
2n + 175 = 227
Subtract 175 from both sides:
2n = 227 - 175
2n = 52
Divide both sides by 2:
2n/2 = 52/2
n = 26
So if he keeps losing 2 pounds per week, Alex will reach his target weight of 175 pounds after 26 weeks.
Of course in real life weight loss doesn't necessarily work like in this question (usually, the rate of loss slows down closer to the goal and the body adapts to eating less). But for the purposes of this question and with this simple linear model of weight loss, Alex would reach his goal weight in half a year.
A zoo measured the wingspan, in millimeters of 9 butterflies What is the median length of the wingspan
Help me pleaseeee due a 3 will mark branliest
Answer:
0 | 20
10 | 30
12 | 32
Y | Y+20
40 | 60
R-20 | R
Can you find the square’s perimeter
I’m marking branliest
Answer:
[tex] \large{ \tt{♕ \: EXPLANATION }}: [/tex]
Firstly , What do you mean by square ? - A parallelogram in which all sides are equal & each angle is 90° is called a square.Here , We're provided a figure of square with the length ( L ) of ( 4x - 8 ) & we're asked to find out the perimeter of given square. Let's get started ![tex] \boxed{ \large{ \tt{✺ \: PERIMETER \: OF \: SQUARE \: ( \: P \: )= 4l}}}[/tex]
- Plug the value of length ( L ) of square :
[tex] \large{ \tt{↬P = 4(4x - 8)}}[/tex]
- Distribute 4 through the parantheses :
[tex] \large{ \tt{↬P = 4 \times 4x - 4 \times 8}}[/tex]
[tex] \large{ \boxed{ \tt{↬P = 16x - 32 \: units}}}[/tex]
✺ Hardwork will never disappoint you! ♪
♡ Hope I helped! ツ
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A suspicious monkey offers you and your classmates fruit to eat. As you consider eating the fruit he tells you that 60 out of 1240 of the fruit trees are poisonousness what percent of trees are poisonousness?
Answer
4.84%
Step-by-step explanation:
trust me
Find the next 3 terms of the following sequence 10,17,24
Answer:
31,38,45
Step-by-step explanation:
Answer:
31, 38, & 45
Step-by-step explanation:
The sequence 10, 17, 24 increases by 7 each term.
10 + 7 = 17
17 + 7 = 24
24 + 7 = 31
31 + 7 = 38
38 + 7 = 45
Juan is a teacher and takes home 68 papers to grade over the weekend. He can grade at a rate of 6 papers per hour. How many papers would Juan have remaining to grade after working for 7 hours?
Answer:
26 papers
Step-by-step explanation:
Well this is pretty straight forward
if he can grade 6 papers an hour
we just multiply 6 by 7 to get how many papers he graded in 7 hours
6*7= 42
now we subtract 42 from 68 to get how many papers are left to be graded
68-42=26
26 papers are left
Tim wants to buy a new sound system for $145. He has already saved $65. He gets $20 for each lawn that he mows. Write an equation to show how many lawns Tim must mow in order to have enough money for his new sound system.
Step 1: Define your variable:
Step 2: Place the total or what you are trying to get on the right side of the equals sign 145:
Step 3: Figure out what goes on the left side of the equals sign (the other numbers in the problem with the variable).
Step 4: Solve N =
SOMEONE HELP ME WITH MY HOMEWORK I WILL LOVE U FOREVER
Answer:
4 lawns
Step-by-step explanation:
$145=$65+N*$20
where N= no. of lawns he needs to now
$80=$20N
N=4
If m is a common divisor of x and y, then x/y = (x ÷ k)/______
Answer:
[tex]\frac{x}{y} = \left(\frac{x}{y} \right)\cdot 1 = \left(\frac{x}{y}\right)\cdot \left(\frac{m}{m} \right) = \frac{\frac{x}{m} }{\frac{y}{m} }[/tex]
Step-by-step explanation:
The common divisor is the greatest natural number so that two or more natural numbers have no remainder. If [tex]m[/tex] is a common divisor of [tex]x[/tex] and [tex]y[/tex], then [tex]p = \frac{x}{m}[/tex] and [tex]q = \frac{y}{m}[/tex], where [tex]p[/tex], [tex]q[/tex] [tex]\in \mathbb{Z}[/tex]. Then, we have the following expression:
[tex]\frac{x}{y} = \left(\frac{x}{y} \right)\cdot 1 = \left(\frac{x}{y}\right)\cdot \left(\frac{m}{m} \right) = \frac{\frac{x}{m} }{\frac{y}{m} }[/tex]
21 POINTS HELPPPP
ASAP
Answer:
-3 1/4 + 4 3/4= 1 1/2
Step-by-step explanation:
please help I'll be your best friend
Answer: Check out the diagram below
[tex]1.5 \le x \le 5.5[/tex]
The lengths can be between 4 and 12 units
=======================================================
Explanation:
Let's find an expression that represents the area.
The length is 2x+1 and the width is 3. Multiply those two and we get
3(2x+1) = 6x+3
The area is 6x+3 square units.
In other words, A = 6x+3 represents the area.
------------------
We're then told that [tex]12 \le A \le 36[/tex] saying that the area is between 12 and 36 square units (including both endpoints).
We'll replace the A with 6x+3 and solve for x like so:
[tex]12 \le A \le 36\\\\12 \le 6x+3 \le 36\\\\12-3 \le 6x+3-3 \le 36-3 \ \text{ .... see note1}\\\\9 \le 6x \le 33\\\\\frac{9}{6} \le \frac{6x}{6} \le \frac{33}{6} \ \text{ .... see note2}\\\\\frac{3}{2} \le x \le \frac{11}{2}\\\\1.5 \le x \le 5.5\\\\[/tex]
note1: I subtracted 3 from all sides to undo the "plus 3"
note2: I divided all sides by 6 to undo the multiplication
------------------
We just found that [tex]1.5 \le x \le 5.5\\\\[/tex] so it says that x is between 1.5 and 5.5 including both endpoints.
Plug in the smallest possible x value to find the smallest possible length
length = 2x+1
L = 2(1.5)+1
L = 3+1
L = 4
The smallest possible length is 4 units. Multiply this with the height 3 and we get L*W = 4*3 = 12 which is the smallest possible area.
------------------
Now use x = 5.5 to find the largest value of L possible
L = 2x+1
L = 2(5.5)+1
L = 11+1
L = 12
Then note how L*W = 12*3 = 36 is the max area possible, which matches with that your teacher wrote. So this confirms we have the correct value.
If you're not sure which values go where, check out the diagram below.
FT is tangent to OP at T. If FP = 39 and FT = 36, what is PT?
39
T
36
A 20
B. 12
C. 3
D. 15
Answer:
[tex]D) 15[/tex]
Step-by-step explanation:
[tex]39^{2}=36^{2} +PT^{2}[/tex]
[tex]PT^2=39^2-36^2[/tex]
[tex]PT=\sqrt{39^2-36^2}[/tex]
[tex]PT=15[/tex]
------------------------
hope it helps...
have a great day!!
Plzzzz helpppppppp!!!!!
Answer:
I say electrons
Step-by-step explanation:
It has more electrons than protons so it becomes - charged
The water tank in your school holds 20 liters of water. One day it was 34 full. That day, 14 liters of tank capacity was used up. How many liters of water remained in the tank at the end of the day
Answer:
20
Step-by-step explanation:
The water tank in the school hold 20 liters of water
One day it was 34 liters full
14 liters of water was used up
Therefore the quantity of water left can be calculated as follows
= 34-14
= 20
Hence 20 liters of water remains in the tank
The Sum Of 2 Numbers are -11 and their difference is 41.
Answer:
15 and - 26
Step-by-step explanation:
let x and y be the 2 numbers , x > y
x + y = - 11 → (1)
x - y = 41 → (2)
Add the 2 equations term by term to eliminate y
2x = 30 ( divide both sides by 2 )
x = 15
Substitute x = 15 into either of the 2 equations and solve for y
Substituting into (1)
15 + y = - 11 ( subtract 15 from both sides )
y = - 26
The 2 numbers are 15 and - 26
HELP, 66% because of you beauty's! CAN WE GET TO 80, tho?
Pwease
Answer:
49 square miles
Step-by-step explanation:
Sorry on the last question :(
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Have a good day :)
Answer:
49 square miles
Step-by-step explanation:
7 × 5 = 35
9 - 5=4
4 × 8 = 32
32 ÷ 2 = 16
35 + 16 = 49
NEED HELP ASAP PLEASE ILL GIVE BRAINLIEST!!!
Answer:
the answer is in the picture
Step-by-step explanation:
SOMEONE PLEASE HELP ME
A pyramid has a base that is a right triangle with legs measuring 10 cm and 14 cm. The height of the pyramid is 9 cm.
The volume of the pyramid is ___ cubic cm.
Answer:
420 cm cubed
Step-by-step explanation:
not entirely sure how to do this, but saw a similar post. hope this helps:
https://brainly.com/question/22267794
(or u can copy + paste ur question it'll show up either way)
How to find Co factor of elements of Determinant
Answer:
Step-by-step explanation:
We can easily find the determinant of a matrix of which will be the cofactor of 2. Multiplying the diagonal elements of the matrix, we get. Now subtract the value of the second diagonal from the first, i.e, 48 – 3 = 45. Check the sign that is assigned to the number
HELP PLEASE! I'M STUCK, THANK YOU!
Answer:
Negative.
Step-by-step explanation:
You can see the line is declining. The y value is decreasing.
Always read the line from left to right, you’ll easily see it’s a negative slope.
Answer:
It's negative
Step-by-step explanation:
It's going from top to bottom so it's gotta be negative
I need help
The lateral area of a cylinder is 1872 square cm.The height is 6 cm.What is the radius.
Answer:
9.97 i think
Step-by-step explanation:
Answer:
r = 24.41cm
Step-by-step explanation:
If you're only trying to find the radius, use the equation:
[tex]Area = \pi r^2[/tex]
When rearranged to make r the subject:
[tex]r = \sqrt\frac{Area}{\pi }[/tex]
When the variables are added:
[tex]r = \sqrt\frac{1872}{\pi }[/tex]
[tex]r = 24.41[/tex]
4 If angle A = x + 5, angle B = 2x – 35, and angle C = 3x,
what is the value of x
8, 10, 3, 9, 12, 4, 3
Median Mode
Mean
Range
Answer:
the Midian is 9
mode is 3
mean is 6
it ranges from 3 to 12
Determine whether the relationship is a function or not. Explain why or why not!
Answer:
Yes or No: Yes
Explanation: It is a function because each input is paired with only one output, as shown in the table.
Step-by-step explanation:
The perimeter of a rectangular pool is more then 62 meters, and the width is at least 10 meters less then the length. Witch system of inequalities represents the possible length in meters, /, and the possible width in meters, w, of the pool?
Answer:
Step-by-step explanation:
The perimeter of a rectangular pool is more then 62 meters, and the width is at least 10 meters less then the length. Witch system of inequalities represents the possible length in meters, /, and the possible width in meters,
What are the zeros of the function below? Check all that apply
Answer:
-7. is the answer so tick it mark me brainlist
Answer:
1, -1
Step-by-step explanation:
just took the test
a small chocolate sundae costs $3. each topping you add costs $0.50. how much would it cost to get a small sundae with P toppings added?
Answer:
3=0.5p
Step-by-step explanation:
The cost to get a small sundae with P toppings added represented as 3 + 0.5p.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Let's consider the toppings added to the chocolate sundae represented by p.
We will use the unitary method,
The cost of topping added to one chocolate = $0.50
The cost of topping added to p chocolate = $0.5p
So, the cost to get a small sundae with P toppings added is;
3 + 0.5p
Therefore, the cost to get a small sundae with P toppings added represented as 3 + 0.5p
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ5
Without graphing, determine whether the system of linear equations has one solution, infinitely many solutions, or no solution. Explain your reasoning.
[tex]y=15x+1[/tex]
[tex]y=15x+2[/tex]
[tex]\huge{ \mathcal{ \underline{ Answer} \: \: ✓ }}[/tex]
First equation :
[tex]y = 15x + 1[/tex][tex]y - 15x - 1 = 0[/tex]Second equation :
[tex]y = 15x + 2[/tex][tex]y - 15x - 2 = 0[/tex]Now, the equations are in the form of
[tex]a_1x {}^{2} + b_1x + c_1 = 0[/tex][tex]a_2x {}^{2} + b_2x + c_2 = 0[/tex]where,
[tex] \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2} [/tex]
therefore the equations would have no solution .
_____________________________
[tex]\mathrm{ \#TeeNForeveR}[/tex]
In Toss-N-Turn at the County Fair, contestants flip a fair coin and then spin the pointer of a spinner with seven equal sections, numbered 1–7. Contestants win if the coin lands heads up and the pointer lands on an even number.
If Paulina wants to win a prize, should she play Toss-N-Turn or a different game that has a theoretical probability of winning of 15
1
5
? Explain
Answer:
will for here to win a prize from a toss n turn or another game would be impossible first of all she has to get it a heads if she gets it a head that's good now the next thing she has to land it on a even number if she passes that she gets a prize but it is impossible for here to get a prize in a 1 out of 5 flip chances
Step-by-step explanation:
Answer:
i need points sorry
Step-by-step explanation:
T: 76x + 3) = 7(x + 5) Part B: Luisa knows only one number was torn off, and she knows that the equation has an infinite number of solutions. What must be the missing number? Show and explain your work?
Answer:
yea same
Step-by-step explanation:
if f(x)=-3+10 find f(4)
Answer:
A) -2
Step-by-step explanation:
Plus 4 in place of x
f(x) = -3x+10
f(4) = -3*4+10
f(4) =-12+10
f(4)=-2