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.
Find the measure of the arc.
A
146°
E
ĀC = [ ? ]
Answer:
90°
Step-by-step explanation:
m arc AC = 90°
_____________
The measure of the arc length AC is 90 degrees.
What is an arc length of a circle?The arc length of a circle is the distance between two points on the curve of the circle.
We have,
The arc length and the angles with the center on a circle are equal.
So,
Arc length AC makes a 90-degree angle with the center of the circle.
Now,
Arc AC = 90 degrees.
Thus,
The measure of the arc length AC is 90 degrees.
Learn more about arc lengths here:
https://brainly.com/question/16403495
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Ken recorded the weights (in pounds) of 78 boxes. He created a box plot of his data. What is the interquartile range of Ken’s data?
A) 8
B) 10
C) 17
D) 48
The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.
What is the interquartile range of a data?The interquartile range(IQR) = third quartile(Q3) - first quartile(Q1)
The third quartile of in the box plot given is : 56 pounds
The third quartile of the data as represented in the box plot given :
39 pounds
The interquartile range(IQR) of ken's data = 56 - 39
= 17 pounds
Hence, The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.
Find more information about the interquartile range here
https://brainly.com/question/4102829
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find the volume of the cone
Answer:
A≈249.02cm
Step-by-step explanation:
A new 54 inch flatscreen TV cost $1245 at Best Buy. If Harry has a 15% off coupon what will he pay for the TV
Answer: 1,058
Step-by-step explanation:
You have 2 green marbles, 2 red marbles, 3 purple marbles, and 5 gold marbles in a bag. What is
the probably of the following event if no marble is replaced after pulling it?
Answer:
Green(before) : [tex]\frac{2}{12}[/tex]
Red(before) : [tex]\frac{2}{12}[/tex]
Purple(before) : [tex]\frac{3}{12}[/tex]
Gold(before) : [tex]\frac{5}{12}[/tex]
That is before. Now there are only 11 marbles, so that is the new total. Depends on which color you got to tell the new probability.
If a circle has a radius of 16, and an arc length of 12, what is the angle measure of the central angle that matches that arc?
Answer:
135°
Step-by-step explanation:
The arc length is calculated as
EF = circumference of circle × fraction of circle
= 2πr × [tex]\frac{?}{360}[/tex]
Given EF = 12π , then
2π × 16 × [tex]\frac{?}{360}[/tex] = 12π ( divide both sides by 2π )
16 × [tex]\frac{?}{360}[/tex] = 6 ( multiply both sides by 360 to clear the fraction )
16 ? = 2160 ( divide both sides by 16 )
? = 135°
Simplify:
2
(
5
+
3
x
)
+
(
x
+
10
)
2(5+3x)+(x+10)
Answer:
7x + 20
Step-by-step explanation:
I dont have a explanation, but this could be right. :)
A farmer had 4,999 chickens.Each chicken laid one egg.Later in the day he recieved 664 more chickens. They each laid an egg too
Answer:
4'999 + 664 = 5663
Step-by-step explanation:
all chickens laid one egg so that is 4'999 then the next day 664 of them laid one egg that is how I know what it is.
your welcome for the help.
10V
c
8
A'
B
6
D
с
4
2
А
В B.
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2.
4
6
8
10
Fine the scale factor of the dilation.
Answer:
either 2 or 1/2, depending on what the original shape was
Step-by-step explanation:
going from small to large it is clearly visible that 3 units of side length turn into 6 units. so, the scaling factor is 2.
going from large to small it is clear that 6 units of side length turn into 3 units. so, the scaling factor is 1/2.
Find the area of the triangle. b 22 in h 4 1/2 in.
Answer:
22 times 4 1/2 divided by 2
Which of the following functions is graphed below?
the diameter of a circle is 24 meters what is the circumference
Answer:
The circumfrence is 75.36
Step-by-step explanation:
I hope this helps
Hi guys I need help this is exterior angles of a triangle so plz do me a favor 3x+20x+120
Answer:3x+140
Step-by-step explanation:
Answer:
23x+120
Step-by-step explanation:
3x+20x+120
Combine Like Terms:
=3x+20x+120
=(3x+20x)+(120)
=23x+120
solve the equation for
x 3/4(x+21) = 10.5
x =
✽✽✽✽
[tex]\frac{x\cdot \:3}{4\left(x+21\right)}=10.5[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}4\left(x+21\right)[/tex]
[tex]\frac{x\cdot \:3}{4\left(x+21\right)}\cdot \:4\left(x+21\right)=10.5\cdot \:4\left(x+21\right)[/tex]
[tex]3x=42\left(x+21\right)[/tex]
[tex]3x=42x+882[/tex]
[tex]\mathrm{Subtract\:}42x\mathrm{\:from\:both\:sides}[/tex]
[tex]3x-42x=42x+882-42x[/tex]
[tex]-39x=882[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-39[/tex]
[tex]\frac{-39x}{-39}=\frac{882}{-39}[/tex]
[tex]x=-\frac{294}{13}[/tex]
❅❅❅❅❅❅❅❅❅❅
hope it helps...have a great day!!A comic costs $3 and a mystery series costs $5 each.If Ken spend all his money on the comics, he has $6 left. If he wants to buy the mystery series, he needs another $8. How many comics or mystery books is Ken buying? How much money does he have?
Whoever posts this on jiskha gets 50 points
Answer:
7 books
$27
Step-by-step explanation:
3x + 6= 5x - 8
3x - 5x = -14
-2x= -14
x= 7 books
he has (3×7)+6= $27
Let comics be c and mystery be m
Cost be y
c=m
The equations are
y=3m+6y=5m-8Solve for m
3m+6=5m-82m=18m=7booksHe has
7(3)+621+6$27What is the scale factor?
NEED HELP ASAP!
Answer:
scale factor = 2
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original
C'D' = 6 and CD = 3 then
scale factor = [tex]\frac{6}{3}[/tex] = 2
Omar compra una bicicleta, que tiene un descuento del 75%. Si el precio que pago es de Q 70.00. ¿Cuál fue el precio original?
Answer: Por ejemplo, un televisor podría costarle originalmente $ 5000. Determine el porcentaje de descuento: en nuestra tienda de ejemplo, todo tiene un 75% de descuento. La suma que queda en su bolsillo, sus ahorros, es simplemente estos dos valores multiplicados entre sí: 75% * $ 5000 = 0,75 * $ 5000 = $ 3750.
Describe the relationship between GF and CD when the two lines are perpendicular to AB. Also describe the relationship between GF and CD when CD is not perpendicular to AB . Zoom in or out on the coordinate plane, if needed.
Answer:
See Explanation
Step-by-step explanation:
Given
Lines GF, CD and AB
Required
Relationship between GF and CD
The question is incomplete, as there is no attachment to support the given parameters.
The general solution goes thus:
(a) CD and GF perpendicular to AB
If two lines are perpendicular to another line; then the two lines are parallel to each other.
This means that CD and GF are parallel, and they have the same slope
(b) CD is not perpendicular to AB
Here, we know that GF is perpendicular to AB, CD is not;
This means that GF and AB are not parallel.
More information is needed to determine the actual relationship between GF and AB; but for sure, they are not parallel.
find the simple interest of Rs 4000 for 2 years at the rate of 8%
Answer:
Rs 4640
Step-by-step explanation:
8/100 x 4000 = 320
320 x 2 = 640
4000+ 640 = Rs4640
Feel free to mark it as branliest
Somebody plz help me solve!!
Answer:
C) x = 3
Step-by-step explanation:
factor out a 2 to get:
2(x² - 6x + 9) = 0
(x-3)² = 0
x = 3
Answer and Step-by-step explanation:
First, to find the zeros of the function, we can take out a common factor from the equation, and then factor.
The equation has a common factor of 2 (so distribute of the 2 from all of the numbers).
2([tex]x^2 - 6x + 9[/tex])
Now, we factor. Find two numbers that multiplies to [tex]9x^2[/tex] and adds up to -6x.
-3x and -3x.
Now, we substitute these two for -6x.
[tex]2(x^2 - 3x-3x+9)[/tex]
Factor.
[tex]2(x - 3)(x-3)[/tex]
Finally, we set all of the values to 0 and solve for x.
2 ≠ 0
x - 3 = 0 x = 3
x - 3 = 0 x = 3
That means the answer is C. x = 3
(Not shown, but the multiplicity of this x value is 2, because there are two
x = 3)
#teamtrees #PAW (Plant And Water)
Multiply and divide the following fractions. Remember to invert the divisor and then multiply the fractions.
1/2 x 2/3
1 1/2 x3/4
4/4 x 7/6
3 divided by 1/2
2/3 divided by 1/2
Answer:
1/2 x 2/3 = 0 . 3
1 1/2 x3/4 = 1. 125
4/4 x 7/6 = 1 . 27
3 divided by 1/2 = 6
2/3 divided by 1/2 = 1. 3
Step-by-step explanation:
1/2 x 2/3
= 0.33333333333
= 0 .3
1 1/2 x3/4
= 1.125
4/4 x 7/6
= 1.16666666667
= 1.27
3 divided by 1/2
= 6
2/3 divided by 1 / 2
= 1.33333333333
= 1. 3
Hope this answer helps you :)
Have a great day
Mark brainliest
Answer:
1. 5/6
2. 5/8
3. 29/44
4. 3/8
5. 2/15
6. 0.3
7. 1.125
8. 1.27
9. 6
10. 1.3
11. 345,000
12. 128,000
13. 42
14. 40
15. $365.47 and $365
16. $125.66 and $126.
Step-by-step explanation:
The number of hours that each of 6 students spent reading last week is shown in the bar graph below. For the data in the bar graph, which measure is the LEAST? *
1 point
Captionless Image
what do u add to 5 5/8 to make 9 ?
Answer:
5+5=9and mark me as brainlestttt
Answer:
27/8
Step-by-step explanation:
9 - 5 5/8 = 27/8
Thomas bought shoes for $45.50. The tax rate on the shoes was 8%. What is the total amount that Thomas paid for his shoe purchase?
Answer:
$49.14 is the total amount
$3.64 is the sales tax
Step-by-step explanation:
45.5 x 0.08 = 3.64
45.5 + 3.64 = 49.14
Math screen shot photo
Answer:
30625
Step-by-step explanation:
Answer:
175²
Step-by-step explanation:
7 × 7 × 5 × 5 × 5 × 5
= (7 × 7) × (5 × 5 × 5 × 5)
= 7² × 5⁴
= 49 × 625
= 30.625
[tex] \sf = \sqrt{30.625} [/tex]
[tex] \sf = \sqrt{175 \times 175} [/tex]
[tex] \sf = 175[/tex]
[tex] \sf = {175}^{2} [/tex]
Conclusion:
Exponential Form of 7 × 7 × 5 × 5 × 5 × 5 adalah 175².
no one has answered this one
Answer:
[tex]\displaystyle x = \frac{25\sqrt{2}}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] cosθ = adjacent over hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 45°
Adjacent Leg = 25
Hypotenuse = x
Step 2: Solve for x
Substitute in variables [cosine]: [tex]\displaystyle cos(45^\circ) = \frac{x}{25}[/tex][Multiplication Property of Equality] Multiply 25 on both sides: [tex]\displaystyle 25cos(45^\circ) = x[/tex]Rewrite: [tex]\displaystyle x = 25cos(45^\circ)[/tex]Evaluate: [tex]\displaystyle x = \frac{25\sqrt{2}}{2}[/tex]I actually have two questions that are similar.
A card is drawn from a standard deck of cards. What is the probability
that a spade is drawn, then replaced, and a red card is drawn second?
A card is drawn from a standard deck of cards. What is the probability that a spade is drawn, NOT replaced, and another spade is drawn?
Answer:
how much would you have paid for 2000 units in August 2019
Based on the pattern in the picture, how many squares do you think will be used to create the 5th figure? make a table.
Answer:
I think it is 7 squares.
Step-by-step explanation:
As you can see they added 3 more squares to the first block which gave you 4. Then they added 5 squares to the second one. If you take the third block, you will count 7 squares on the outside of the third block.
helpppp!!!
Make a conjecture about the number of units produce in 50 hours
Please helppppppppppppppppppp :) .
Answer and Step-by-step explanation:
I think this is the correct answer (in picture):
This is because you can either get Heads or Tails, so once you flip it once, you just flip it again and you will get either heads or tails.
#teamtrees #PAW (Plant And Water)