Explicación paso a paso:
La distancia recorrida el primer día = 500 m
Si aumenta la distancia en 200 m diariamente, entonces el total corrido diariamente formará una progresión aritmética con el último término de 10 km (10,000) como se muestra;
500, (500 + 200), (500 + 200 + 200) ... 10,000
500, 700, 900 ... 10,000
para que sepamos el número total de días usados para la carrera, usaremos la fórmula para calcular el enésimo término de una secuencia aritmética como se muestra;
[tex]T_n = a+(n-1)d[/tex] where;
n es el número de términos
a es el primer término de la secuencia
d es la diferencia común
Dado a partir de la secuencia:
a = 500
Tn = 10,000
d = 700-500 = 900-700 = 200
Sustituir en la fórmula y calcular el valor de n
[tex]10,000 = 500+(n-1)*200\\10,000 = 500+(200n-200)\\10,000 = 500-200+200n\\200n = 10,000-300\\200n = 9,700\\n = 9,700/200\\n = 48.5[/tex]
Andrea habría alcanzado los 10.000km tras 48,5 días de carrera
The function g(x) represents f(x) = 9 cosine (x minus StartFraction pi Over 2 EndFraction) + 3 after translating StartFraction pi Over 6 EndFraction units left and 4 units up.
Which equation represents g(x)?
Answer:
B
Step-by-step explanation:
Im almost sure it B but if not then its for sure D.
The equation that represents the function g(x) is [tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex].
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
What is translation?Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
The function is given as
[tex]f(x)=9cos(x-\frac{\pi }{2} )+3[/tex]
The function f(x) is first translated [tex]\frac{\pi }{6}[/tex] units left.
The rule of translation is:
[tex](x,y)=(x+\frac{\pi }{6},y)[/tex]
So, we have:
[tex]f'(x)=9cos(x+\frac{\pi }{6} -\frac{\pi }{2} )+3[/tex]
Take LCM
[tex]f'(x)=9cos(x+\frac{\pi-3\pi }{6} )+3[/tex]
[tex]f'(x)=9cos(x-\frac{2\pi }{6} )+3[/tex]
[tex]f'(x)=9cos(x-\frac{\pi }{3} )+3[/tex]
Next, translate f'(x) 4 units up.
The rule of this translation is:
[tex](x,y)=(x,y+4)[/tex]
So, we have:
[tex]g(x)=9cos(x-\frac{\pi }{3} )+3+4[/tex]
[tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex]
Hence, the equation that represents the function g(x) is [tex]g(x)=9cos(x-\frac{\pi }{3} )+7[/tex].
Find out more information about function and translation here
https://brainly.com/question/21145944
https://brainly.com/question/23961993
#SPJ3
log 8-log 4/log 4-log 2
Answer:
-0.39794000867
Step-by-step explanation:
This is the table in which we can see the values of two squared, two cubed, and so on. This is an operation in mathematics, known as exponentiation. If we look at the numbers at the bottom line, we can try to find the power value to which 2 must be raised to get this number. For example, to get 16, it is necessary to raise two to the fourth power. And to get a 64, you need to raise two to the sixth power. Also this is totally the answer
Answer:
1
Step-by-step explanation:
[tex]\frac{log_{10}(2) }{log_{10}(4)-log_{10}(2) }[/tex]
[tex]\frac{log_{10}(2)}{2log_{10}(2)-log_{10}(2) }[/tex]
Add similar elements [tex]\frac{log_{10}(2) }{log_{10}(2) }[/tex]
Apply rule [tex]\frac{a}{a}=1[/tex]
=1
:)Hope you enjoy this:)A hardback book cost $7.00 more than a paperback book. Write an expression for the total cost of 1 paperback book and 3 hardback books
Answer:
Tc=3x+(x-7)
Step-by-step explanation: So, the Tc stands for total cost. The x stands for the variable for the hardback books and the x-7 is the price of the paperback book. You could introduce another variable, but that might be more confusing
Martene got a small aquarium for her birthday. The aquarium is a right rectangular prism 18.5\,\text{cm}18.5cm18, point, 5, start text, c, m, end text long by 15\,\text{cm}15cm15, start text, c, m, end text wide. Martene put 3885\text{ cm}^33885 cm 3 3885, start text, space, c, m, end text, cubed of water in the aquarium. How deep is the water in the aquarium? \text{ cm} cm
Answer:
[tex]Depth = 14[/tex]
Step-by-step explanation:
Given
[tex]Length = 18.5cm[/tex]
[tex]Width = 15cm[/tex]
[tex]Volume = 3885cm^3[/tex]
Required
Determine the deep of the aquarium
Volume is calculated as thus:
[tex]Volume = Length * Width * Depth[/tex]
Substitute values for Volume, Length and Width
[tex]3885 = 18.5 * 15 * Depth[/tex]
[tex]3885 = 277.5 * Depth[/tex]
Solve for Depth
[tex]Depth = 3885/277.5[/tex]
[tex]Depth = 14[/tex]
Hence;
the depth is 14cm
Answer:
14
Step-by-step explanation:
Got it right in Khan
a line is perpendicular to y - 5 = -1/4(x + 8) and goes through the point (-1,2). What is the lines y-intercept?
Answer:
y = 4x + 6
Step-by-step explanation:
Turn the equation we are given into slope-intercept form.
y - 5 = -1/4(x + 8)
y - 5 = -1/4x - 2
y = -1/4x + 3
The slope of a perpendicular line is the opposite reciprocal of the original line.
-1/4 -> 4/1 -> 4
Find the new y-intercept using the point given.
y = 4x + b
2 = 4(-1) + b
2 = -4 + b
6 = b
Fill in everything we solved for.
y = 4x + 6
Best of Luck!
Vaness’s team won their softball game and scored sixty-three points total. If Vanessa scored fifteen of the points and everyone else scored six points each, how many players were on her team?
√50
A. 5√2
B. 3√5
Which one?
Answer: A. 5√2
Apply the radical rule: √xy = √x·√y
√50 = √25·2 = √25·√2 = 5√2
∴ √50 = 5√2.
The graph of y = x² is the solid black graph below. Which function
represents the dotted graph?
Answer:
y= -(x-4)^2
Step-by-step explanation:
y=X^2 is the parent function
The new graph is reflected and shifted to the right 4 units
y= -(x-4)² function represents the dotted graph
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph
y=X² is the parent function
Reflections of graphs involve reflecting a graph over a specific line. Reflecting functions are functions whose graphs are reflections of each other.
The new graph is reflected and shifted to the right 4 units
y= -(x-4)²
Hence, y= -(x-4)² function represents the dotted graph
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ5
What is the common difference or common ratio for the sequence: 27, 9, 3, 1, 1/3, ...
Answer:
It's dividing by 3 everytime, so 1/3
Step-by-step explanation:
14 out of 22 students surveyed enjoyed playing baseball. If 308 students are surveyed, how many would you expect to say they enjoy playing baseball?
Answer:
124
Step-by-step explanation:
14 -22=8
8= the number of students that didn't like playing baseball
Somehow 8 = 800%
if you subtract 800%-308 it gives you -124
124 students don't like playing baseball
Help me plz!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-2
Step-by-step explanation:
-2+5=3
What is the value of x?
A.9.4
B)7
C)-9.4
D)-7
Answer:
the answer is B
Step-by-step explanation:
You can automatically eliminate C and D because it is not a negative and the parallel is a positive number. Then you can eliminate A because it is not a decimal. To check your work you but 7 in for X and you will get 74°
A toy company manufactures sealed cubes that contain a colored liquid that glows in the dark. The liquid completely fills the cubes. If 8 cubic blocks with a side length of m are needed to find the volume of each cube, how much of the liquid can each cube hold?
Answer:
[tex]Volume = 8m^3[/tex]
Step-by-step explanation:
Given
[tex]Cubes = 8[/tex]
[tex]Length = m[/tex] for each
Required
Determine how much all cubes can hold
First, we need to determine the volume of each.
[tex]Volume = m * m * m[/tex]
[tex]Volume = m^3[/tex]
For the 8 cubes, we have:
[tex]Volume = 8 * Volume\ of\ 1[/tex]
[tex]Volume = 8 * m^3[/tex]
[tex]Volume = 8m^3[/tex]
PLEASE HELP !!!!
Determine whether each equation is correct
Answer:
yes
Step-by-step explanation:
Heeeeeeeeelp plsssssssss
A music video website received 5,000 comments on a new song they released. The next day, the artist performed the song on television and an additional 1,500 comments were made on the website. What was the percent of increase? Round the percent to the nearest tenth if necessary.
Answer:
30%
Step-by-step explanation:
To be able to calculate the percent of increase between two numbers, you have to divide the increase by the initial number and multiply by 100:
Increase= 1,500
Initial number=5,000
Percent of increase=(1,500/5,000)*100
Percent of increase=0.3*100
Percent of increase=30%
According to this, the answer is that the percent of increase was 30%.
Answer:
30%
Step-by-step explanation:
A secret recipe requires you mix chocolate and cream cheese in the ratio 3:2, based on weight. If you use 21 oz of chocolate, how much cream cheese do you need?
Answer:
14
Step-by-step explanation:
21/3
7*2
Would you rather discover alien life or an animal that was thought to be extinct?
[tex]\boxed{I\; would\; say\; an\; animal\; that\; was\; thought\; to\; be\; extinct.}[/tex]
≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈
The reason i say this is because i don't really want to run into something that i don't know much about. I do know quite a bit about extinct animals more than i do aliens. So, that's my reasoning.
≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈
[tex]\boxed{Hope\;i\;helped!}\\\\\boxed{Thanks,\;AnimeBrainly}[/tex]
Here is a data set: 5 10 10 10 15 100 after studying the data, the research realized that the value 100 was meant to be recorded as 15. What would happens to the mean and standard deviation of the data set when the 100 is changed to a 15 for the original data set, with the 100, would the median or the mean be a better choice of measure for the center? Explain your reasoning
Answer:
The mean and SD will change
The median is a better measure of the center since it will not change in this case
Step-by-step explanation:
Given that the value 100 was changed to 15, what will happen is that the value of the mean will decrease since there is a lower total value now. This will consequently decrease the value of the standard deviation too.
Yes, the median will be a better choice
This is because, by changing the value of 100 to 15, the value of the median stays the same and thus the previous information would not be changed if the median we used .
PLEASE HELP I WILL GIVE YOU 13 POINTS
Answer:
I think it would be C.
Step-by-step explanation:
For y [tex]\geq[/tex] the line should be solid and it should be shaded above the line because ≥ means greater than.
For y > the line should be dashed and it should be shaded above the line because it means greater than.
For y [tex]\leq[/tex] the line should be solid and it should be shaded below the line because it means less than.
For y < the line should be solid and it should be shaded below the line because it means less than.
Hope this helps!
Which method represents a correct way to solve the equation?
-x+(-3+x)2 = 6
Multiply -3 by 2.
Multiply x by 2.
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
OA.
Square -3.
Square x.
Subtract -7x from both sides.
OB. Subtract 9 from both sides.
Take the square root of both sides.
Square -3.
Square x.
Combine like terms
OC. Subtract 6 from both sides.
Use the quadratic formula to solve for x.
OD
Square the quantity (-3 + x).
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
Answer:
Multiply -3 by 2.
Multiply x by 2.
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
Step-by-step explanation:
Given:
-x (-3 + x )2 = 6
-x (-3 + x )2 = 6
-x (-6 + 2x) = 6
-6x + 2x^2 = 6
2x^2 - 6x - 6 = 6 - 6
2x^2 - 6x - 6 = 0
Multiply -3 by 2.
Multiply x by 2.
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
Is it correct? Please tell me I’m not sure lol I’ll give brainliest
HELP HAVING BAD DAY
Stanley practices his running, swimming and biking every day. During these practices he runs at 9 mph, bikes at 16 mph and swims at 2.5 mph. Yesterday he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?
If Stanley swam for t hours yesterday, what was his running time?
Answer:
9
Step-by-step explanation:
9 (t3+0.5)
his running time is 9
Answer:
1.5 Hrs
Step-by-step explanation:
SWIM: Time: T Rate: 2.5mph Distance: 2.5T
RUN: Time: T+0.5 Rate: 9mph Distance: 9T+4.5
BIKE: Time: 2T+1 Rate: 16mph Distance: 32T+16
2.5T+9T+4.5+32T+16 = 64
43.5T+20.5=64
43.5T=43.5
T=1
RUN: T+0.5= 1+0.5=1.5
It costs $2.37 to paint one square foot of wall. You need to paint a wall that measures 864.5 square feet. It will cost to paint that wall. (Round your answer to the nearest hundredth)
a $204.88
b $2,048.87
c $2,048.86
d. $2,848.87
Answer:
B- hope this helps:)
Step-by-step explanation:
The total cost to paint 864.5 square feet of wall is $2,048.87.
It is given that the cost to paint one square foot of wall is $2.37.
We are asked to find the total cost to paint 864.5 square feet of wall.
What are the different place values in a given number with a decimal point?If we have a number that has a decimal point then we have two parts.
The whole number part and the fractional part.
After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.
You can also see the given figure below.
We know that,
One square foot = $2.37.
Remember that Feet is the plural form of the foot.
We can write,
864.5 square feet = 864.5 x one square foot
Because in 864.5 square feet we have 864.5 one square foot.
And since one square foot cost $2.37.
864.5 square feet will cost 864.5 x 2.37 dollars.
Now,
864.5 x 2.37 = $2048.865.
Rounding to the nearest hundredth.
6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.
Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.
Learn more about rounding decimal numbers here:
https://brainly.com/question/15482780
#SPJ2
Hanna will spend $150 on music festival tickets. Reserved seat tickets cost $25 and general admission tickets cost $10. She wrote the following to represent the situation with a linear equation. What kind of equation did she use?
Answer: Standard Form
Step-by-step explanation:
In the slope intercept form, you can only solve for one equation at a time.
Ex: y = -2.5x + 15
but when using standard you can easly get the answer for both ticket prices
Ex: 25x + 10y = 150
5r + 2g = 30 is the linear equation that best describes the scenario.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given this, Hanna will spend $150 on music festival tickets. Reserved seat tickets cost $25 and general admission tickets cost $10.
Let "r" be the Number of reserved tickets she bought
and "g" be the number of general admission tickets she bought
Money spent od reserved ticket = 25 * r
Money spent in general tickets = 10 *g
Since she totals spent 150$
Thus, the equation will be
25r + 10g = 150
Divide by 5 into both the sides
5r + 2g = 30
therefore, The linear equation that represents the given situation is 5r + 2g = 30.
Learn more about Linear equations here:
https://brainly.com/question/11897796
#SPJ2
8oz./1 cup = ?/12 cups. How many ounces are in 12 cups?
Answer:
12cups=96oz.
Step-by-step explanation:
multiply the volume value by 8
12 oz equals 1.50 cups. 1 ounce is equivalent to 0.125 cups, and there are 1.50 cups in 12 ounces.
Find the measure of the labeled angles
Answer:
x would equal 23, so (x+92) would equal 115°, & (5x) would equal 115°.
3x-100 what does x equal?
Someone help me w 8 and 9 please please
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Combine like terms to simplify the expression. 5 x + 4 + 2 x + 5
Answer:
[tex] \huge{ \boxed{ \bold{ \text{7x + 9}}}}[/tex]
Step-by-step explanation:
[tex] \text{5x + 4 + 2x + 5}[/tex]
[tex] \text{Combine \: like \: terms} : [/tex]
[tex] \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}[/tex]
[tex] ➝ \: \text{5x + 2x + 4 + 5}[/tex]
➝ [tex] \text{ 7x + 4 + 5}[/tex]
[tex] \text{Add \: the \: numbers : 4 \: and \: 5}[/tex]
[tex] ➝ \: \text{7x + 9}[/tex]
[tex] \text{Hope \: I \: helped}[/tex]!
[tex] \text{Best \: regards}[/tex]!
~[tex] \mathfrak{TheAnimeGirl}[/tex]
Answer:
7x + 9
Step-by-step explanation:
Combine like terms, means put the ones that have something in common together; in this case they are the terms with an 'x' value, and a regular numeric value.
5x+2x = 7x
5+4 = 9
therefore:
7x+9