Answers
Using kinematic equations, we determine that the accelerating police car will catch up to the speeding car moving at a constant velocity in 20 seconds.
Explanation:To solve the problem of when a police car accelerating at 4 m/s² will catch up to a speeding car moving at a constant velocity of 40 m/s, we can use kinematic equations for motion. The speeding car's position over time is given by the equation x = vavgt, where vavg = 40 m/s is the average velocity. Since the police car starts from rest (vo = 0) and has an acceleration of 4 m/s², its position over time is given by the equation x = 0.5at².
We set the displacement of both cars equal to each other to find the time (t) when they are at the same position:
40t = 0.5(4)t².
This simplifies to: 40t = 2t², and by further simplification, we find that t = 20 seconds. Thus, it will take the police car 20 seconds to catch up to the speeding car.
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Related Questions
If volume is 325m to the power of 3,
Find x
Answers
Answer:
13/6
Step-by-step explanation:
volume=length*width*height
so
325m^3=10*15*x
325=150x
x=2.16666666 or 325/150
Write an equation of the lines that passes through (-1,6) and (4,1)
Answers
[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-6}{4-(-1)}\implies \cfrac{1-6}{4+1}\implies \cfrac{-5}{5}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=-1[x-(-1)]\implies y-6=-1(x+1) \\\\\\ y-6=-x-1\implies y=-x+5[/tex]
I don’t understand this question someone plz help!
Express the area of a rectangle with length 5 m4 and width 6m2 as a monomial.
Answers
[tex]A=5m^4\times6m^2=\boxed{30m^6}[/tex]
Landon is saving up to buy a new jacket. He already has $70 and can save an additional $7 per week using money from his after school job. How much total money would Landon have after 5 weeks of saving? Also, write an expression that represents the amount of money Landon would have saved in ww weeks.
Savings after 5 weeks:
Savings after ww weeks:
Answers
For this case we have to:
Let "w" be the variable that represents the number of savings weeks.
We have that Landon's initial amount is $ 70.
We want to know how much money you have after 5 weeks, knowing that you save $ 7 each week, so be "y" the amount of money after "W" weeks:
[tex]y = 70 + 7w[/tex]
After 5 weeks:
[tex]y = 70 + 7 (5)\\y = 70 + 35\\y = 105\[/tex]
Answer[tex]y = 70 + 7w\\y = 105[/tex]
Will mark BRAINLIEST! Help me!
Answers
Answer:
The answer is 5 people.
Step-by-step explanation:
.25 * 20 people surveyed = 5.
The function c(f) = 5/9 (f-32) allows you to convert degrees to Fahrenheit to degrees Celsius. Find the inverse of the function so that you can convert degrees Celsius back to degrees Fahrenheit
Answers
For this case we have the following function:
[tex]c (f) = \frac {5} {9} (f-32)[/tex]
We must find the inverse function. For this we follow the steps below:
Replace c (f) with y:
[tex]y = \frac {5} {9} (f-32)[/tex]
We exchange variables:
[tex]\frac {5} {9} (y-32) = f[/tex]f = \frac {5} {9} (y-32)
We solve for "y":
[tex]\frac {5} {9} (y-32) = f[/tex]
We multiply by[tex]\frac {9} {5}[/tex]on both sides of the equation:
[tex]y-32 = \frac {9} {5} f[/tex]
We add 32 to both sides of the equation:
[tex]y = \frac {9} {5} f + 32[/tex]
We change y by[tex]c^{ -1} (f):[/tex]
[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]
Answer:
[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]
Answer:
[tex]f(c)=\frac{9}{5}c+32[/tex]
Step-by-step explanation:
Given function that is used to convert degrees to Fahrenheit to degrees Celsius,
[tex]c(f)=\frac{5}{9}(f-32)[/tex]
Let y represents the output value of the function and x represents the input value,
[tex]y=\frac{5}{9}(x-32)[/tex]
Switch x and y,
[tex]x=\frac{5}{9}(y-32)[/tex]
Isolate y,
[tex]9x=5(y-32)[/tex]
[tex]\frac{9}{5}x=y-32[/tex]
[tex]\implies y = \frac{9}{5}x+32[/tex]
[tex]\implies f(c)=\frac{9}{5}c+32[/tex]
Which is the required function.
i need help pleaseeeeeeeeee
Answers
Answer:
4 4/2
Step-by-step explanation:
What you do is you have to do 8-4=4 5-1=4 6-4=2 so there for the answer is 4 4/2
Hello There!
We are given the problem 8 5/6 - 4 1/4
Your answer would be 4 7/12
First, we subtract 4 from 8 and get a difference of 4.
Then we have to subtract 1/4 from 5/6.
We have to find a common denominator.
We can get 10/12-3/12=7/12
Then, we add 4+7/12 and we get 4 7/12.
Write the quadratic function
Answers
General vertex formula is
(X-h)^2 +k=y
where (h,k) is the vertex
X^2 +6X+14=y
X^2 +6x +9 +14-9=y
Answer is :
(X+3)^2 +5=y
How much of a radioactive kind of ruthenium will be left after 6 days if the half-life is 3 days and you start with 80 grams?
Answers
After 6 days, 20 grams will be left from the original 80 grams.
The half-life is the time it takes for half of the radioactive substance to decay. In this case, the half-life of ruthenium is given as 3 days. Starting with an initial quantity of 80 grams, we can calculate the remaining quantity after each half-life period.
After the first 3 days, one half-life will have passed, and half of the 80 grams will have decayed:
80 g / 2 = 40 g remaining.
After the second 3 days, another half-life will have passed, so another half of the remaining 40 grams will have decayed:
40 g / 2 = 20 g remaining.
Therefore, after 6 days, which corresponds to two half-life periods, 20 grams of the radioactive isotope of ruthenium will be left.
Is the following number rational or irrational?
\sqrt{99}
(Choice A)
Rational
(Choice B)
Irrational
Answers
Answer:
B. Irrational.
Step-by-step explanation:
√99 is irrational.
Its value just below 10 as √100 = 10.
Order the numbers from least to greatest 2 -5 and 1
Answers
Hello!
LEAST TO GREATEST-5 1 2
Simplify the following algebraic expression 3/4(1/2x-12)+4/5
Answers
ANSWER
[tex] \frac{15x - 328}{40} [/tex]
EXPLANATION
The given expression is
[tex] \frac{3}{4} ( \frac{1}{2} x - 12) + \frac{4}{5} [/tex]
We expand to obtain;
[tex] \frac{3}{8} x - 9+ \frac{4}{5}[/tex]
The least common denominator is 40
[tex] \frac{15x - 360 + 32}{40} [/tex]
This simplifies to:
[tex] \frac{15x - 328}{40} [/tex]
Answer:
That’s wrong
Step-by-step explanation:
thirty-five maths majors, 33 music majors, and 45 history majors are randomly selected from 251 math majors, 518 music majors 332 history majors at the state university
identify the type of sampling (simple random sample, cluster, stratified, convenience, systematic
Answers
It would not be random sample because it is talking about majors in at a state university. The purpose of a random sample to get random people from the whole population, not a specific set of people.
It would not be cluster because a cluster would be selecting a whole group and in this case, they are selecting people within groups
It would be stratified because stratified sampling is selecting randomly from all of the groups
It would not be convenience sampling because that is selecting random from 1 population
It would not be systematic sampling because that is not random.
The scenarios provided represent different types of sampling methods, such as stratified, cluster, simple random, and systematic, based on how the samples are selected from the population.
Explanation:The type of sampling can be determined based on how the samples are chosen from the population. Here, we discuss different sampling methods using the provided scenarios.
Stratified sampling is used when the soccer coach selects players from different age groups to form a team. Each age group is a stratum.Cluster sampling takes place when a pollster interviews all human resource personnel in a few high tech companies. Each company is a cluster.When a high school educational researcher interviews an equal number of female and male teachers, this is an example of stratified sampling as well.The high school principal who polls an equal number of students from each grade level utilizes stratified sampling.A sample of high school students chosen by first organizing by class and then selecting an equal number from each also exemplifies stratified sampling.If a completely random method is used to select students giving each one the same chance of being chosen, this represents simple random sampling.When selecting a sample proportionate to class standings in a college, and drawing from each class based on their representation in the total population, stratified sampling is again used.Using a random number generator to select every 50th student from an alphabetical list represents systematic sampling.35 POINTS PLEASE HELP
Answers
Find the Least Common Multiple (LCM) of the denominator in order to find the Least Common Denominator (LCD).
LCM = 6/5 * (x^2y^2)
Answer = B. 10x^2y^2
Answer:
Your answer is option B. 10x^2y^2
Step-by-step explanation:
Firstly, Find the Least Common Multiple of the denominator.
Then you'll get your Least Common Denominator.
You'll get LCM as :
LCM = 6/5 * ( x^ 2y ^2 )
Your answer you'll get is 10x^2y^2
Please help fast I'll let you know if u got it right:)
Answers
Answer:
the answer is 15 to the nearest tenth
Answer:
add all the points together like
1+3+4+6+6+7+7+7+8+8+8+8+9+9+9+15= 115
the divide by the total number of elements we have. as so
115÷16= 7.18
rounding that to the nearest tenth is going to 7.2
Step-by-step explanation:
hope this helps
correct me if I'm wrong
What is the value of x in the equation 2(x+3)=4(x-1)
Answers
Step 1: Distribute the 2 to numbers and variables inside parentheses
(2 × x) + (2 × 3) = 4 (x - 1)
2x + 6 = 4 (x - 1)
Step 2: Distribute the 4 to numbers and variables inside parentheses
2x + 6 = (4 × x) + ( 4 × - 1)
2x + 6 = 4x+ (-4)
2x + 6 = 4x- 4
Step 3: Combine like terms (x's go with x's) by subtracting 2x to both sides
(2x - 2x) + 6 = (4x - 2x) - 4
6 = 2x - 4
Step 4: Combine like terms by adding 4 to both sides
6 + 4 = 2x - 4 + 4
10 = 2x
Step 5: Isolate x by dividing 2 to both sides
10 ÷ 2 = 2x ÷2
5 = x
x = 5
To check: plug 5 into all the x's of the equation
2(x+3)=4(x-1)
2(5+3)=4(5-1)
2(8) = 4(4)
16 = 16
Hope this helped!
Answer:5
Step-by-step explanation:
These prisms are similar. Find the volume of the larger prism in decimal form. Need help please.
Answers
Answer:
518.4 in³
Step-by-step explanation:
The ratio of the sides of the prisms = 5 : 6, hence
the ratio of their volumes = 5³ : 6³ = 125 : 216
let x be the volume of the larger prism then by proportion
[tex]\frac{125}{300}[/tex] = [tex]\frac{216}{x}[/tex] ( cross- multiply )
125x = 216 × 300 ( divide both sides by 125 )
x = [tex]\frac{216(300)}{125}[/tex] = 518.4
The volume of the larger prism is 518.4 in³
6 consecutive integers starting with 3
Answers
the set of 6 consecutive integers starting with -3:
{ -3,-2,-1,0,1,2 }
Answer:
Step-by-step explanation:
let :
x , x+1 , x +2 , x + 3 , x+4 , x+5 ....... ( 6 consecutive integers )
x +( x+1 ) + (x +2) + (x + 3)+ (x+4) + ( x+5) = - 3
6x+16 = - 3
6x = - 3 - 16
6x = - 18
x v= -18/6
x = - 3
6 consecutive integers are : -3 ; - 2 ; - 1 ; 0 ; 1 ; 2
The sum of a and b is equal to 24. Let b = 11. Which equation can be used to find the value of a?
Answers
Answer: 24-11=a
Step-by-step explanation:
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
Answers
Answer:
The coordinates of the vertex are (-5, 41)
Step-by-step explanation:
For a quadratic function of the form
[tex]f(x) = ax ^ 2 + bx + c[/tex]
Where a, b and c are constants and represent the coefficients of the function, then the symmetry of the parabola always passes through its vertex.
In this case we have the following parabola
[tex]f (x) = -x2 - 10x + 16[/tex]
And we know that its axis of symmetry is the line [tex]x = -5[/tex]
Then we know that this axis of symmetry passes through the vertex of the parabola.
Therefore, the x coordinate of the vertex is -5.
To find the coordinate in y of the vertex, we substitute x = -5 in the function.
[tex]f (-5) = -(- 5) ^ 2 -10 (-5) +16\\\\f (-5) = 41[/tex]
Finally, the vertices are in the point (-5, 41).
Function f is represented by the equation shown.
f(x)=x^2-4x+3
Function g has a vertex at (1,3) and the parabola opens downwards.
Which statement is true?
A.
The y-intercept of function f is greater than the y-intercept of function g.
B.
The y-intercept of function f is less than the y-intercept of function g.
C.
The minimum of function f is at (-4,3).
D.
The minimum of function g is at (1,3).
Answers
Answer:
[tex]\boxed{\text{A. The y-intercept of function f is greater than the y-intercept of function g}}[/tex]
Step-by-step explanation:
A. y-Intercept of ƒ(x)
ƒ(x) = x² - 4x + 3
f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3
The y-intercept of ƒ(x) is (0, 3).
If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).
Statement A is TRUE.
B. y-Intercept of g(x)
Statement B is FALSE.
C. Minimum of ƒ(x)
ƒ(x) = x² - 4x + 3
a = 1; b = -4; c = 3
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
h = -b/2a = -(-4)/(2×1 = 2
k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1
The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).
Statement C is FALSE.
D. Minimum of g(x)
g(x) is a downward-opening parabola. It has no minimum.
Statement D is FALSE
if y=-3x, find x's and y's value in 4x-2y=-20
Answers
Answer:
x=-2
Step-by-step explanation:
Answer:
x = - 2
y = 7
Step-by-step explanation:
4x - 2y = - 20
Now substitute - 3x for y.
4x - 2(-3x) = -20 combine the xs in the brackets
4x + 6x = - 20 Make the addition
10x = - 20 Divide by 10
x = - 20/10 Do the division
x = - 2
===============
3x - 2y = - 20 Put - 2 in for x
3(-2) - 2y = - 20 remove the brackets
- 6 - 2y = - 20 Add 6 to both sides
-2y = - 20 + 6 Combine
-2y = - 14 Divide by - 2
y = - 14/-2
y = 7
math algebra Please help pick the best answer please
Answers
[tex]\bf \cfrac{4}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{(1)1-(2)5}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1-10}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{-9}{4}~~} \\\\\\ \cfrac{4}{1}\cdot \cfrac{4}{-9}\implies \cfrac{-16}{9}[/tex]
can you find x for the following equation?
7x+12=3(5x-12)
Answers
7x + 12 = 3(5x - 12)
Step 1: Distribute the 3 to the numbers in the parentheses (5x and -12)
7x + 12 = (3 × 5x) + (3 × (-12))
7x + 12 = 15x + (-36)
Step 2: Combine like terms
x's go with x's (7x and 15x)
Subtract 7x to both sides
(7x - 7x) + 12 = (15x - 7x) + (-36)
(0) + 12 = 8x - 36
12 = 8x - 36
Normal numbers go with normal numbers
Add 36 to both sides
12 + 36 = 8x + (-36 + 36)
48 = 8x
Step 3: Isolate x by dividing 8 to both sides
48/8 = 8x/8
6 = x
Hope this helped!
Answer:
x = 6
Step-by-step explanation:
Eliminate parentheses using the distributive property.
7x +12 = 15x -36
You have x-terms and constants on both sides of the equal sign. One way to approach this is to find the x-term with the least coefficient (it is 7x) and subtract everything on that side of the equation.
(7x +12) -(7x +12) = (15x -36) -(7x +12)
Simplify, also known as "collect terms."
0 = 8x -48
Now, divide by the coefficient of x: 8.
0 = x -6
Add the opposite of the constant: 6.
6 = x
__
Alternate solution
By looking for the x-term with the smallest coefficient, we get a positive result when we subtract that term. If we were to subtract 15x from both sides of the equation, it would be ...
-8x +12 = -36 . . . . . . . with a negative x-coefficient
You can still work the problem this way, but it can introduce errors if you're not careful with signs. To finish this, we would subtract 12 to get the x-term by itself:
-8x = -48
Then we would divide by the x-coefficient, -8.
x = -48/-8 = 6 . . . . . same solution; same number of steps
_____
Whenever you add, subtract, multiply, divide, you do the same thing to both sides of the equation.
Ms. Williams wants to analyze the scores for the first unit test of her NC Math 1 class
The scores for the class are below.
Scores:
82, 100, 94, 68, 34, 72, 70, 96, 99,92,
90, 85, 70, 46, 71, 71, 77, 78, 95, 82,
80, 100, 99,72,69,74,84,87
Calculate the the following for the class. Round answers to the nearest whole number.
mean =
median =
standard deviation =
interquartile range =
Answers
Answer:
Mean:79
Median:81
Standard deviation:15
Interquartile range:22
Mean (aka average)-79.8928
add all the numbers together and divide by how many numbers there are
sum of terms-2237
number of terms-28
Median- 81
I do it this way-
order the numbers from least to greatest
cross off the front number and back number until you are left with a middle
in this case there were 2
80 and 82
the average of those two is 81
Standard Deviation-15.37237
Interquartile Range-22.5
25th percentile-71
50th percentile-81
75th percentile-93
The following box plot shows the number of years during which 24 schools have participated in an interschool swimming meet:
A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years.
At least how many schools have participated for 1 year or less?
6 schools
8 schools
12 schools
14 schools
Please explain, best answer and explanation gets brainliest
Answers
Answer:
The answer is 6 schools.
In a box and whisker plot, every piece of whisker or box represents 25% of the whole number of schools.
The schools participated 1 year or less are represented by the left part of the whisker. Which stands for 25%.
BOOM
Step-by-step explanation:
On analyzing the boxplot, we find that 6 schools have participated for 1 year or less.
What is a boxplot?A boxplot is a standardized way of displaying the distribution of data based on a five number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum).
The box extends from 1 to 6 on the number line. This implies first quartile (Q1) = 1 and third quartile (Q3) = 6.
There is a vertical line at 3.5, median = 3.5.
The whiskers end at 0 and 8, i.e., minimum = 0 and maximum = 8.
Since, Q1 = 1, this implies 25% of the schools participated for 1 year or less.
(First quartile (Q1) is the value under which 25% of data points are found when they are arranged in increasing order.)
Number of schools that have participated for 1 year or less = 25% of 24 = [tex]\frac{25}{100} * 24 = 6[/tex]
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b) Work out (6 * 10^2) /(3 x 10^-5)
Give your answer in standard form.
Answers
The result of the calculation (6 * 10^2) / (3 x 10^-5) is 2 x 10^7, when written in standard form.
Explanation:To solve the equation (6 * 10^2) / (3 * 10^-5), we first simplify both sides. 6 * 10^2 equates to 600, and 3 x 10^-5 equates to 0.00003. Therefore, we are left with the simple division: 600 / 0.00003.
To divide these two numbers, you would get a result of 20000000. However, the problem asks for the answer in standard form. Standard form is a way of writing numbers that are too large or too small to be conveniently written in decimal form. In standard form, 20000000 is represented as 2 x 10^7.
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What is on a graphY<7
Answers
in short, we simply graph her countertpart of y = 7, and then we test a point for "true" or "false" for that region.
say for example the point ( 3, 5 ), meaning x = 3, y = 5
y < 7
5 < 7
is that really true? 5 smaller than 7? yeap, so that region is the "true" region, and is the region we shade.
the line in the graph is a dashed one, because it does NOT include the points at the border, y < 7, "y" is less, not equals to, but less than 7.
Check the picture below.
I'm sorry but there is no graph, If you could put up the graph I can answer. Thank You!
What is the domain and range of f(x)= x^2 + 4x - 21
Answers
Answer:
The domain is all real numbers.
The range is y ≥ −25
Step-by-step explanation:
The equation has no domain restrictions.
Select the correct answer.
Which operation should be performed first for calculations involving more than one arithmetic operation?
A. parentheses
В. exponents
C.multiplication
D.division
Answers
Answer:
parenthesis
Step-by-step explanation:
A common technique that is being used in solving with several arithmetic operations is the PEMDAS. It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". It is the order to be followed when calculating involving more than one arithmetic operation.
The correct first operation to perform in a calculation involving multiple arithmetic operations is parentheses, as per the order of operations, known as PEMDAS or BEDMAS.
The correct operation that should be performed first for calculations involving more than one arithmetic operation is parentheses. According to order of operations, the sequence you would follow is: Parentheses (or grouping symbols), Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). This is also commonly remembered by the acronym PEMDAS in the American system or BEDMAS in the Canadian system, indicating the sequence: Parentheses/Brackets, Exponents, Multiplication/Division, and Addition/Subtraction.