Answer:
a) 2400m on the 20th day for Charlie.
1) 728.41m of 20th day for Daniella.
Didn't find n, sorry.
Charlie ran 2400m on day 20 of his fitness program and Daniella ran 728m on day 20 of her fitness program.
It is given that Charlie and Daniella on day one both ran 500m on each subsequent day.
Charlie ran 100m more than the previous day.
Daniella increased her distance by 2% of the distance run on the previous day.
It is required to calculate how far Charlie and Daniella ran on day 20 and the value of n.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Charlie ran 500m on the first day:
[tex]\rm a_1 = 500[/tex]
[tex]\rm a_2 =600[/tex] ( because charlie ran 100m more than the previous day)
It is an arithmetic progression in which the difference between two consecutive terms:
d = 600 - 500 ⇒ 100
and [tex]\rm a_n = a+d(n-1)[/tex]
[tex]\rm a_2_0 = 500+100(20-1)\\\\\rm a_2_0 = 2400m[/tex]( ∵ n = 20 )
Daniella ran 500m on the first day:
[tex]\rm b_1 = 500[/tex]
[tex]\rm b_2 = 500+ 500\times2 \%[/tex] (because Daniella increased her distance by 2% of the distance run on the previous day)
We can write [tex]\rm n^t^h[/tex] terms:
[tex]\rm b_n= 500(1+2\%)^n^-^1[/tex]
[tex]\rm b_2_0= 500(1+2\%)^2^0^-^1[/tex]
[tex]\rm b_2_0= 500(1+0.02)^1^9\\\\\rm b_2_0 = 500\times 1.02^1^9\\\\\rm b_2_0 = 500\times1.456 \Rightarrow 728.40 \approx 728 m[/tex]
[tex]\rm b_n > a_n[/tex] (given in the question)
[tex]\rm500(1+2\%)^n^-^1 > 500+100(n-1) \ \ or \\\\\rm500(1+2\%)^n^-^1 > 100n+400[/tex]
The above expression is not true for all the values of 'n' ie. 'n' can not be determined.
Thus, Charlie ran 2400m on day 20 of his fitness program and Daniella ran 728m on day 20 of her fitness programme.
Learn more about the sequence here:
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I have more question
Answer:
you would need three wholes because each whole would represent a loaf of pumpkin bread
Write slope intercept form of th equation of each line
Answer:
y = 8/5x + (-4) or y = 8/5x -4
Step-by-step explanation:
Slope-intercept form is written like this:
y = mx + b
The variable m, represents slope and b, represents the y-intercept.
To find slope, you have to find the rise/run or in other words, change of y over change of x.
From the look of the line, the slope has to be positive because the line is going up.
To go from the bottom point to the top, we have to go up 8 points and go to the right 5 points. Thus the slope is 8/5.
Now for the y-intercept. This part is easy. Just ask yourself this...
"Which of the two points is on the y-axis?"
In this case, it is the bottom point which is -4.
So your equation should look like this:
y = 8/5x + (-4)
or y = 8/5x - 4 because when you have a plus sign and a minus sign, the result is negative.
hope this helps :)
write an equation of the line below
Answer:
y=-x-2
Step-by-step explanation:
The slope is negative 1 and the y intercept is -2
Find each function value.
f(6) if f(x) = 4x?
f(8) if f(x) = x + 11
Which graph represents 6x-2y>-11
Answer:
Answer:
C
Step-by-step explanation:
Remember when using the inequality sign < or > the line will be dotted so we can immediately eliminate answer choices b and d
Now let us solve for y
6x-2y>-11
step 1 subtract each side by 6x
now we have
-2y>-11-6x
step 2 divide each side by -2
-11-/2=11/2
-6/-2=3
IMPORTANT -when you divide inequalities by a negative number you flip the inequality sign
So now we have
See image below for reference
When the inequality is facing x the solutions are going to be on top of the line
hope this helps!
Step-by-step explanation:
multiply
( 2 x – y ) ( 3 x + y )
[tex](2x-y)(3x+y)\\\\=2x(3x+y) -y(3x+y)\\\\=6x^2 +2xy - 3xy -y^2\\\\=6x^2 -xy -y^2[/tex]
Amanda's family is taking a road trip. Their car can travel no more than 352 miles without needing to refill the gas tank. They have
traveled 108 miles since they last filled the gas tank.
Amanda knows that the inequality representing this situation is 108 + x < 352.
Select from the drop-down menu to correctly interpret the solution of this inequality.
Amanda family cannot travel more than 244 miles without needing to refill the gas tank.
Inequality is the non equal comparison of numbers or variables.
Let x represent the number of miles that they can travel before filling their gas tank.
Their car can travel no more than 352 miles without filling their tank. Also, they have traveled 108 miles since they last filled the gas tank. Hence:
x + 108 < 352
x < 244
This means that Amanda family cannot travel more than 244 miles without needing to refill the gas tank.
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round of the underlined digit in each day decimal number
Answer:
6) 25.57
7) .9
8) don't see a number underlined
Step-by-step explanation:
Hurry help plz
Solve for an angle in right triangles
[tex]\cos \angle B = \dfrac{2}{7}\\\\\implies \angle B = \cos^{-1} \left( \dfrac{2}{7} \right) = 1.28^{\circ}[/tex]
Mr. Adam drives a school bus 5 days a week. Each day he travels 48.8 miles. How many miles does he drive per week?
Answer:
358 steps
Step-by-step explanation:
Express 8^-4 using a positive exponents
deleteddddddddddddddddd
Answer:
i do not think it is possible to delete a question after you have posted it. if i were you i probably would have just edited it and save myself the emmbarasment
Step-by-step explanation:
PLSSSSS HELP>>>>>>>>>>>>>>>>>>>>>>>
When 4/15 is written as a decimal, how many digits are in the smallest sequence of repeating digits? A. 3 B. 2 C. 1 D. 0
Answer:
C. 1
Step-by-step explanation:
We have to convert 4/15 into decimal.
Divide 4 by 15
When we divide 4 by 15, we get 0.26666666666.....
As we can see that, the number 6 is repeating
Only one digit is repeating
Hence, the correct answer is one 6
X^+17x+72=12 factoring quadratic equation
Answer:
The first term is, x2 its coefficient is 1 .
The middle term is, -17x its coefficient is -17 .
The last term, "the constant", is +60
Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .
-60 + -1 = -61
-30 + -2 = -32
-20 + -3 = -23
-15 + -4 = -19
-12 + -5 = -17 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5
x2 - 12x - 5x - 60
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
5 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x-5) • (x-12)
Which is the desired factorization
Equation at the end of step
1
:
(x - 5) • (x - 12) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x-5 = 0
Add 5 to both sides of the equation :
x = 5
Solving a Single Variable Equation:
2.3 Solve : x-12 = 0
Add 12 to both sides of the equation :
x = 12
Supplement : Solving Quadratic Equation Directly
Solving x2-17x+60 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = x2-17x+60
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000
Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :
y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0
or y = -12.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-17x+60
Axis of Symmetry (dashed) {x}={ 8.50}
Vertex at {x,y} = { 8.50,-12.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 5.00, 0.00}
Root 2 at {x,y} = {12.00, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving x2-17x+60 = 0 by Completing The Square .
Subtract 60 from both side of the equation :
x2-17x = -60
Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4
Add 289/4 to both sides of the equation :
On the right hand side we have :
-60 + 289/4 or, (-60/1)+(289/4)
The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4
So adding to both sides we finally get :
x2-17x+(289/4) = 49/4
Adding 289/4 has completed the left hand side into a perfect square :
x2-17x+(289/4) =
(x-(17/2)) • (x-(17/2)) =
(x-(17/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-17x+(289/4) = 49/4 and
x2-17x+(289/4) = (x-(17/2))2
then, according to the law of transitivity,
(x-(17/2))2 = 49/4
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(17/2))2 is
(x-(17/2))2/2 =
(x-(17/2))1 =
x-(17/2)
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-(17/2) = √ 49/4
Add 17/2 to both sides to obtain:
x = 17/2 + √ 49/4
Since a square root has two values, one positive and the other negative
x2 - 17x + 60 = 0
has two solutions:
x = 17/2 + √ 49/4
or
x = 17/2 - √ 49/4
Note that √ 49/4 can be written as
√ 49 / √ 4 which is 7 / 2
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -17
C = 60
Accordingly, B2 - 4AC =
289 - 240 =
49
Applying the quadratic formula :
17 ± √ 49
x = —————
2
Can √ 49 be simplified ?
Yes! The prime factorization of 49 is
7•7
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 49 = √ 7•7 =
± 7 • √ 1 =
± 7
So now we are looking at:
x = ( 17 ± 7) / 2
Two real solutions:
x =(17+√49)/2=(17+7)/2= 12.000
or:
x =(17-√49)/2=(17-7)/2= 5.000
Two solutions were found :
x = 12
x = 5
Step-by-step explanation:
please mark my answer in brainlist
3x + 2 = 2x + 7
Solve x
3x + 2 = 2x + 7
Subtract 2 from both sides:
3x = 2x +5
Subtract 2x from both sides:
x = 5
Answer: x = 5
Maggie makes a scale drawing of a deck. The scale for the actual deck to the scale drawing is 7 ft
to 1 in. The dimensions of the deck are 28 ft by 17.5 ft. What are the dimensions of the deck in the
drawing? Show your work.
Answer:
The width is 2.5 inches
Step-by-step explanation:
The given ratio is 7 ft to 1 in
Now we will have 17.5 to x in
x * 7 = 17.5 * 1
7x = 17.5
x = 17.5/7
x = 2.5 inches
Whitney and Destiny hung out at the mall on Saturday. They spent 45 minutes shopping for clothes and 1 hour at the food court. Then they spent 30 minutes at the video arcade before heading home. It was 12:45 P.M. when Whitney and Destiny left the mall. What time did they start shopping for clothes?
Answer:
11.15 i think
Step-by-step explanation:
Change 41/7 from an improper fraction to a mixed number.
Answer:
5 6/7
Step-by-step explanation:
how many times does 7 go onto 41?
7 x 5 = 35
remainder is 6 so;
5 6/7
Hey there!
41/7
= (5 * 7 + 6)/7
= (5 * 7)/7 + 6/7
= 5 6/7
= 5 6/7 ≈ 41/7
Therefore, your answer is: 5 6/7
Good luck on your assignment and enjoy your day’
~Amphitrite1040:)
16.
Identify the axis of symmetry of the parabola.
A. x = -2
B. x = 1
C. x = -3
D. x = -1
Answer:
i don't know
Step-by-step explanation:
Consider the expression 8ab + 3b + 16 - 4a. (a) How many terms are there? (b) How many factors are in the first term? Identify them. (c) Which term is a constant? pls do this fast
a. There are 4 terms in the expression
b. There are 3 factors in the first term.
c. The constant is 16.
8ab + 3b + 16 - 4a
A term is any signed number, a variable, or a constant multiplied by a
variable or variables.
Therefore, the terms are 8ab, 3b, 16, and -4a. The terms are 4 in numbers.
The first term is 8ab .The first term has the factors 8 , a and b. This means the first term have 3 factors.
The term that is a constant is 16
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A large grouper can weight 1/4 ton. how much does a large grouper weight to the nearest pound. [ please help ]
Answer:
500 pounds
Step-by-step explanation:
Step-by-step explanation:
To do this divide 2000 by 4.This will give you around 500.
The ratio of boys and girls are 2:5. If the total number of students in school are 350, find the number of girls.
Answer:
250 girls
Step-by-step explanation:
Add the ratio together (2+5=7), then do 350÷7=50
50 is one part of the ratio so to find how many girls, you would do 50x5=250
product of x and 4 is decreased by one-quarter
Answer:
x
Step-by-step explanation:
x times 4 = 4x
4x in 4 quarters: x x x x
One quarter^^ = x
There are 13 pieces of chicken at the dinner table. After dinner, only 3 pieces are left. How many pieces were eaten at dinner?
16
8
7
10
Answer:
10
Step-by-step explanation:
13 pieses - 3 pieces = 10 pieces that are eaten
Answer:
10
Step-by-step explanation:
How do you multiply 47.5 by 28
Answer: uhhhh
Step-by-step explanation:
Answer:
Step-by-step explanation:
1330 is the answer
Is 2:4 and 3:8 proportion or not?
Answer:
No
Step-by-step explanation:
While these values are close, they are not equal, so I know the original fractions cannot be proportional to each other. So my answer is: The fractions are not
77=(?+8.1)+7.4
What is the solution to “?”
Answer:
61.5
Step-by-step explanation:
61.5 + 8.1 + 7.4 = 77
you're welcome
Separate 846 into 3 parts so that the second part is twice the first part and the third part
is triple the second part.
x=1st
2x= and
32x)= 3(2x)
Answer:
it is 1 ok have fun babby and enjoy your Christmas ok baby bye bye
Answer:
1) 94, 2) 188, 3) 564
Step-by-step explanation:
This is pretty simple. The first thing you want to do is come up with an algebraic equation to solve this. It will be x + 2x + 6x=846 . The first x represents the smallest part, or the first part. The second part is represented by 2x because it is twice the first, and 6x is 3 times the second part which is 6 times the first part. Combine like terms to get 9x = 846. Now isolate the variable by dividing 9 from both sides. This will give you x = 94. Now just plug in the x to find the second and third part.
Hope this helped :)
Which expression represents the number of thirds in 1
Answer:
A third is written as ¹/₃
Step-by-step explanation:
The way to understand this is the number on the bottom is the number of pieces being divided into;
So ¹/₃ is 1 whole divided into 3 parts;
So, you need 3 ¹/₃ parts to make a whole
[tex]a \ * \ \frac{b}{c} = \frac{ab}{c} \\\\ 3 \ * \ \frac{1}{3} = \frac{3 \ * \ 1}{3} \\\\ = \frac{3}{3} \\\\ = 1[/tex]
Solve by factoring
Y^2+5y+6=0
•-3
•4,8
•2,3
•-4,3
Step-by-step explanation:
y²+5y+6=0
y²+2y+3y+6=0
y(y+2)+3(y+2)=0
(y+2)(y+3)=0
:. y=2,3
option C.
hope this helps you.
Answer:
Step-by-step explanation:
Y^2+5y+6=0
5^2 - 4*2*6
25-48
23 i
-5 +4.79i => -0.21 => 0.5i
2*2 4
-5 +4.79i => -9.79 => 2.44i
2*2 4