The car will catch up the cyclist 3 hours after it starts moving.
In how many hours the car will catch up the cyclist?The cyclist travels at 9 miles per hour, and travels for 4 hours before the car starts moving, so the equation for the position of the cyclist as a function of time, t, is:
C(t) = 9*4 + 9*t = 36 + 9*t
And the car moves at 21 miles per hour, then the position is:
P(t) = 21*t
The car will catch the cyclist when:
C(t) = P(t), this gives:
36 + 9*t = 21*t
36 = 21*t - 9*t = 12*t
36/12 = t
3 = t
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El valor de x que se cumple con 6x-10=2 es
Answer:
the answer is 2
need answer asap please
The graph of the defined piece-wise function is sketched at the end of the answer.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In the context of this problem, the function has three definitions, as follows:
To the left of x = -3. (x <= -3).Between x = -3 and x = 4. (-3 < x < 4).To the right of x = 4. (x >= 4)For the first definition, to the left of x = -3, the function assumes a constant value of 3, hence it is an horizontal line at y = 3.
For the second definition, between x = -3 and x = 4, the function is a increasing linear function, with intercept 1 and slope 2, due to the rule y = 2x + 1.
For the third definition, to the right of x = 4, the function assumes a constant value of -2, hence it is an horizontal line at y = -2.
With each of these definitions, the graph of the function is given at the end of the answer.
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A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 12 granola bars. The camp bought a total of 9 boxes that have 100 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
The system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased is b + s = 9 and 10s + 12s = 100
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the small box be represented as s.
Let the big box be represented as b.
Each small box has 10 granola bars and each large box has 12 granola bars. The The camp bought a total of 9 boxes that have 100 granola bars altogether.
The equation will be:
b + s = 9
10s + 12s = 100
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Answer:
10x + 12y = 100
x + y = 9
Step-by-step explanation:
Define Variables:
Let x = the number of small boxes purchased
Let y = the number of large boxes purchased
Each small box has 10 granola bars, so small boxes have 10x granola bars.
Each large box has 12 granola bars, so large boxes have 12y granola bars. Therefore, the total number of granola bars 10x + 12y equals 100:
10x + 12y = 100
Since a total of 9 boxes were purchased, we know x + y must equal 9.
x + y = 9
find the area of the circle. Use 3.14 for pie. Do not round your answer.
Answer: A = 452.16 ft²
Step-by-step explanation:
This gives us the formula to solve for the area.
A = πr²
The radius (r) is the same as the diameter divided by 2.
24 ft / 2 = 12 ft
We will input these given values and solve.
A = πr²
A = (3.14)(12)²
A = 452.16 ft²
Answer:
452.16 ft²
Step-by-step explanation:
To find the radius, you divide the diameter (24) by 2, which equals 12. The area of a circle formula is πr². To find area, you do 12² * 3.14. That equals 144 * 3.14, which equals 452.16.
Draw a polygon with vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2). What is the perimeter, in units, of polygon RSTU? Draw a polygon with vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2). What is the perimeter, in units, of polygon RSTU?
Answer:
The perimeter of rectangle RSTU is 20 unitsStep-by-step explanation:
Given Vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2).To find The perimeter of the RSTUSolutionPlot the points, we see it is a rectangle.
Side lengths are:
RS = TU = 2 - (-4) = 6, the difference of x-coordinates,ST = RT = 2 - (-2) = 4, the difference of y-coordinates.The perimeter is:
P = 2(l + w)P = 2(6 + 4) = 2(10) = 20 unitsThe perimeter of polygon RSTU is
How to find distance between straight line?A straight line connects any two places with the smallest distance possible. The distance formula can be used to get this distance. It is possible to define the distance between two positions (x 1, y 1) and (x 2, y 2) as d=√(x2-x1)² + (y2 - y1)².
Distance between R and S is;
√(2+4)² + (2 - 2)²= 6 units
Distance between S and T is;
√(2-2)² + (-2 - 2)²= 4 units
Distance between T and U is;
√(-4+-2)² + (2 - 2)²= 6 units
Distance between T and U is;
√(-4+4)² + (2 + 2)²= 4 units
The total perimeter is of polygon is:
6+4+6+4 = 20 units
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Choose two statements that are true for this expression
Maria runs of a mile every 8 minutes. Althea runs 2 miles every of an hour. Who runs ata faster 2 3 1 3 speed – Maria or Althea? Explain your reasoning.
The fact that Maria runs of a mile every 8 minutes means that we runs faster.
How to calculate the speed?The speed is measured as the distance with respect to the time. This will be illustrated thus:
Maria runs of a mile every 8 minutes. Althea runs 2 miles every of an hour. It should be noted that an hour is 60 minutes. That means the she runs 1 mile in (60 / 2) = 30 minutes.
In this case, Maria runs faster. This is because of her speed.
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Reflect the given triangle over the y - axis [[3,6,3],[-3,3,3]]
By using a reflection over the y-axis, the coordinates of the image of the triangle are (- 3, - 3), (- 6, 3) and C'(x, y) = (- 3, 3).
How to determine the coordinates of the vertices of a triangle by rigid transformations
Rigid transformations are transformations applied on geometric loci such that the form of the construction is not altered. Reflections over the y-axis are examples of rigid transformations. In this problem we need to apply this kind of transformation on the three vertices of the triangle: A(x, y) = (3, - 3), B(x, y) = (6, 3), C(x, y) = (3, 3).
The reflection over the y-axis is described by the following formula:
P'(x, y) = P(x, y) + (- 2 · p, 0)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointp - x-Component of P(x, y).If we know that A(x, y) = (3, - 3), B(x, y) = (6, 3) and C(x, y) = (3, 3), then the image of the vertices of the triangle:
A'(x, y) = (3, - 3) + (- 6, 0)
A'(x, y) = (- 3, - 3)
B'(x, y) = (6, 3) + (- 12, 0)
B'(x, y) = (- 6, 3)
C'(x, y) = (3, 3) + (- 6, 0)
C'(x, y) = (- 3, 3)
Now we present the picture of the two triangles.
The coordinates of the image of the triangle are A'(x, y) = (- 3, - 3), B'(x, y) = (- 6, 3) and C'(x, y) = (- 3, 3).
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Find the equation of the tangent at f(x) at x=0
Given:
The function
[tex]f(x)=\frac{2x}{x^2+1}[/tex]Required:
Find the equation of the tangent at f(x) at x=0.
Explanation:
The slope of f(x),
[tex]f^{\prime}(x)=\frac{2(-x^2+1)}{(x^2+1)^2}[/tex]Now, the slope of function at x = 0 is f'(x) = 2.
The line with slope m = 2 and passing through (0, 0).
[tex]f(x)=2x[/tex]Answer:
Equation of tangent of the function at x = 0, f(x) = 2x.
Garth is baking cookies for his class! Once he
removes the cookies from the oven, the
temperature of the cookies (in °F) can be
modeled as a function of time (in minutes):
f(x) = 278(0.58)* + 72.
After 5 minutes, the cookies will be
°F (round to one decimal place).
Answer:
7358.84
Step-by-step explanation:
a researcher separated the people in a population into three political categories: democrat, republican, or independent. she then selected a random sample from each of these three groups. what kind of sample did she select?
The researcher makes use of stratified sampling method to select a random sample from each of the three groups mentioned.
It is given to us that -
A researcher separated the people in a population into three political categories:
Democrat
Republican
or, Independent.
It is also mentioned that she then selected a random sample from each of these three groups.
We have to determine the kind of sample she selected.
In this case, stratified sampling is used by the researcher to select a random sample.
Stratified sampling is a type of probability sampling method where the total population is segmented into homogenous groups to successfully complete the sampling technique.
Here we see that the researcher has separated the total population into homogenous groups of democrat, republican, or independent.
From these homogenous groups, she selected random samples.
Thus, the kind of sample selected by the researcher is stratified sampling.
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What is the operation rule from number of ounces of flour to number of cupcakes?
Please use the graph above.
(A.) Multiply by 3
(B.) Multiple by 2
(C.) Add 8
(D.) 2
Answer: (B) Multiply by 2
Step-by-step explanation:
For every ounce of flour, 2 cupcakes can be made.
Question 4 options:
Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism
What is the Law of Syllogism?The law of syllogism is defined as a type of logical argument using deductive reasoning.
Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:
(1) If a , then b .
(2) If b , then c .
Then we can derive a third true statement:
(3) If a , then c .
Now, applying that law to our question, we see that;
1) If I'm a student, then I go to school.
2) If I go to school, then I learn.
Then we can derive a third true statement:
3) If I'm a student, then I learn.
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Part 1
Tell whether the sequence is arithmetic. If it is, identify the common difference.
-1,4,9,14
PLEASE HURRY
Answer:
It is arithmetic, the common difference is 5
Step-by-step explanation:
What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic
A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 16 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive
for a total of 18 minutes.
a What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
In linear equation, 864 is distance the flowerbed from the hive .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that includes just one variable. It has the formula Ax + B = 0, with A and B being any two actual values and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.a) The equation is so called "time equation"
D%2F12 + 16*60 + D%2F8 = 19*60 seconds
(b) To determine the distance D, solve the equation
D%2F12 + D%2F8 = 19*60 - 16*60 = 3*60,
multiply both sides by 24
2D + 3D = 3*60*24
5D = 4320
D = 4320/5 = 864
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Math
Show your solution please the question is in the picture
Answer: A) x^2+y^2 B) x^3+y^3 C) a^2b^2c^2 D) c^2/d^2
Step-by-step explanation:
For A, you add all the powers. This is because the bases are the same. Any number or letter without a visible power on top most likely means that is has a power of 1. Because this is a multiplication question, you have to add the powers. (Example n*n = n^2 or n^3*n^7 = n^10)
This is same for B.
For C, you multiply abc by abc so it's a*a, b*b, c*c. This is because they are inside a bracket. Anything inside the bracket that has a power outside the bracket is multiplied by itself.
For D, you multiply c and d so it's c*c, d*d. This is the same as C.
0.8 divided by 0.6 then round to nearst hundredth
Answer: 1.33
Step-by-step explanation:
0.8 divided by 0.6= 1.33333333333
3 is in the hundredths place and 3 is in the thousandths place.
Since the digit in the thousandths place (3) is less than 5, the digit in the hundredths place (3) does not change.
The digits to the right of the hundredths place are dropped.
1.33333333 rounded to the nearest hundredth (two decimal places) = 1.33.
Can someone help me with this please?
The output of the linear function is -n+3 when the input is n.
What is a slope?The slope of a line can be used to calculate its steepness. The slope or gradient of a line is a number that indicates its direction and steepness.The slope is calculated by dividing the vertical change by the horizontal change between any two distinct points on a line. The ratio is sometimes written as a quotient, which produces the same number for every two distinct points on the same line.How to find the output of the linear function?A linear equation is given by ,
f(x) = mx+ c ---(1)
From the table,
x value increases by 1
y value decreases by 1
The function's slope, or the coefficient that converts an increase in x to an increase in y, is represented by the letter m.So, the coefficient slope(m) magnifies the decrease by 1Substituting slope m = - 1 in (1)
f(x) = -x+ c ---(2)
Substitute (1, 2) in (2)
2 = -1 +c
c = 2 + 1
c = 3
Substitute slope m and c in (2)
f( x ) = - x + 3
When input is n output is given by,
f(n) = - n + 3
The output of the linear function is -n+3 when the input is n.
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can someone tell me if im right?
Travis rents an apartment in a historic, all-brick building downtown. The value of the belongings in the apartment is about $11,000. If Travis wishes to insure his belongings while renting, how much will he have to pay for insurance per year? Use the table above to solve.
I did:
it fell under 0.39 for building and 0.43 for contents so I did
0.39 x 12=4.68 then added the 100 dollar bonus and got $104.68
The amount of insurance that Travis will have to pay for the year is of:
$47.3.
What is the amount of insurance that Travis has to pay?He is renting the apartment, in which the belongings are worth $11,000, hence the insurance will be paid over that amount.
The number of hundredths in $11,000 is given by:
11000/100 = 110.
He pays an insurance of $0.43 for each $100 in belongings, hence the total insurance is of:
0.43 x 110 = $47.3.
There is no information regarding the value of the building, hence we are going to consider that he does not pay insurance for the building.
This insurance was taken from the table, as the apartment is in the city (downtown), and all brick, hence the coefficient is of 0.43.
Missing informationThe table with the rates is given by the image at the end of the answer.
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is 13 over 12 a proper or an improper fraction?
Step 1
An improper fraction is a fraction in which the numerator(top number) is greater than or equal to the denominator ( the bottom number)
Step 2
Conclude based on step 1
Hence
[tex]in\text{ }\frac{13}{12}\text{ the numerator 13 is bigger than the denominator 12, th}erefore\text{ it is an improper fraction}[/tex]Therefore the right answer is an improper fraction
If a fraction has a numerator of 2, then the fraction can be reduced. A counter example is ____ option below.
a) 10/15
b) 11/22
c) 1/10
d) 2/11
Answer:
The answer is d
Step-by-step explanation:
2/11 has a numerator of 2 but cant be reduced
Answer:
Step-by-step explanation:
I misunderstood the question. So, please disregard this answer. Thank you.
A shirt that normally costs $30 is on sale for
$21.75. What percent of the regular price is
the sale price?
Answer:
72.5%
Step-by-step explanation:
Hello!
We can find the percentage by dividing the sale price by the original price, then multiplying that by 100.
Find the Percentage[tex]\frac{21.75}{30} * 100[/tex]0.725 * 10072.5The percentage is 72.5%.
ANSWER ASAP For a ride on a rental scooter, Kevin paid an eight dollar fee to start the scooter +6 cents per minute of the ride. The total bill for Kevin’s ride was $14.36 for how many minutes did Kevin ride the scooter.
Answer:
106 seconds
Step-by-step explanation:
14.36-8=$6.36 $6.36=636 cents so 636/6=106 so 106 seconds
Use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values. One of the expressions should have a value of 37.
The use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values will be:
1. 5 × 6 + 7 = 37
2. 5 + 6 - 7 = 4
3. 5 + 6 + 7 = 18
What is addition?Addition simply means the sum of the numbers that are given. It should be noted that addition is represented by the sign +.
In this case, we are told to use 5, 6 and 7 to create different values. These are represented above. The addition of 5, 6, and 7 gives 18.
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How to search question up on this?
Answer:
find search bar
Step-by-step explanation:
see answer
Just 5 and 6! Please!!✨
The three statement true about the the distance of a dog from a post are-
f(0) = 1.5f(60) = 4f(t) < 5What is termed as the function notations?Function notation is a method of representing a function utilizing symbols and signs.The most common function notation is f(x), which is read as "f" of "x." In this case, the letter x enclosed in parentheses, as well as the entire symbol f(x), represent the domain set as well as range set, respectively.For the given graph in the question,
Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.
The time is denotes on the x axis and the distance covered by the dog on the y axis.
This can be described using the function as.
f(t) = d
Consider values from graph.
When, t = 0, d = 1.5 feet
Function notation ; f(0) = 1.5 ......statement 1
When t = 60, d = 4 feet
Function notation ; f(60) = 4 ......statement 2
Now, the maximum value is 5.
Thus, f(t) < 5 .....statement 3
Therefore, the three statement are formed.
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The correct question is -
Write three statement that are true about this situation. Use function notations.
Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.
Use the = sign in at least one statement and < sign in another statement.
Find all of the numbers less than100 that have at least 2 and at least one 5 in their prime factorization
Answer: [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex]
Step-by-step explanation:
If the numbers have at least one 2 and at least one 5, then they are multiples of 10 (since [tex]10=2 \times 5[/tex]).
So, these numbers are [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex].
What is the absolute value of −1/4 ?
Plot your answer on the number line.
Answer:
1/4
Step-by-step explanation:
Hope this helps!
please quickkkk :((((
According to given function the final value is [tex]$f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$[/tex]
[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k}(x+i y)$$[/tex]
[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}$$[/tex]
Divide both sides by [tex]$x+i y ; \quad x \neq-i y$[/tex]
[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y} ; \quad x \neq-i y$$[/tex]
Simplify
[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}$$[/tex]
Simplify[tex]$\frac{f(x+i y)}{x+i y}: f$[/tex]
Simplify [tex]$\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}: \frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2}$[/tex]
[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]
[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
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What is the slope shown below?
Answer:
5/8
Step-by-step explanation:
Slope = rise/run
In this problem:
rise = 5
run = 8
Therefore, Slope = 5/8