Answer:
4x2+3=
Step-by-step explanation:
Police Chase: A speeder traveling 40 miles per hour (in a 25 mph zone) passes a stopped police car which immediately takes off after the speeder. If the police car speeds up steadily to 55 miles/hour in 10 seconds and then travels at a steady 55 miles/hour, how long and how far before the police car catches the speeder who continued traveling at 40 miles/hour
Answer:
a. 18.34 s b. 327.92 m
Step-by-step explanation:
a. How long before the police car catches the speeder who continued traveling at 40 miles/hour
The acceleration of the car a in 10 s from 0 to 55 mi/h is a = (v - u)/t where u = initial velocity = 0 m/s, v = final velocity = 55 mi/h = 55 × 1609 m/3600 s = 24.58 m/s and t = time = 10 s.
So, a = (v - u)/t = (24.58 m/s - 0 m/s)/10 s = 24.58 m/s ÷ 10 s = 2.458 m/s².
The distance moved by the police car in 10 s is gotten from
s = ut + 1/2at² where u = initial velocity of police car = 0 m/s, a = acceleration = 2.458 m/s² and t = time = 10 s.
s = 0 m/s × 10 s + 1/2 × 2.458 m/s² (10)²
s = 0 m + 1/2 × 2.458 m/s² × 100 s²
s = 122.9 m
The distance moved when the police car is driving at 55 mi/h is s' = 24.58 t where t = driving time after attaining 55 mi/h
The total distance moved by the police car is thus S = s + s' = 122.9 + 24.58t
The total distance moved by the speeder is S' = 40t' mi = (40 × 1609 m/3600 s)t' = 17.88t' m where t' = time taken for police to catch up with speeder.
Since both distances are the same,
S' = S
17.88t' = 122.9 + 24.58t
Also, the time taken for the police car to catch up with the speeder, t' = time taken for car to accelerate to 55 mi/h + rest of time taken for police car to catch up with speed, t
t' = 10 + t
So, substituting t' into the equation, we have
17.88t' = 122.9 + 24.58t
17.88(10 + t) = 122.9 + 24.58t
178.8 + 17.88t = 122.9 + 24.58t
17.88t - 24.58t = 122.9 - 178.8
-6.7t = -55.9
t = -55.9/-6.7
t = 8.34 s
So, t' = 10 + t
t' = 10 + 8.34
t' = 18.34 s
So, it will take 18.34 s before the police car catches the speeder who continued traveling at 40 miles/hour
b. how far before the police car catches the speeder who continued traveling at 40 miles/hour
Since the distance moved by the police car also equals the distance moved by the speeder, how far the police car will move before he catches the speeder is given by S' = 17.88t' = 17.88 × 18.34 s = 327.92 m
I WILL MARK BRAINLIEST:))
Please translate this expression into a verbal expression 4(5j+2+j). (5 points)
PLEASE HELP ME
If f(x) = -3 and g(x) = 4x2 + x = 4, find (f+ g)(x).
ОА
A. 4x2 + x - 1
O B. 6x2 - 7
O 4x
C. 43+ + 2x-1
O D. 4x+3x-7
Answer:
D. 4x² + 3x/2 - 7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x/2 - 3
g(x) = 4x² + x - 4
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in functions: (f + g)(x) = x/2 - 3 + 4x² + x - 4Combine like terms: (f + g)(x) = 4x² + 3x/2 - 7Answer:
The answer is C.
Step-by-step explanation:
(f+g)(x)= f(x)+g(x).
So that would be x/2-3 + 4x^2+x-4.
If you combine like terms that would be:
4x^2+x/2+x-4-3=
4x^2+3/2x-7
How can you use transformations to graph this function?
Answer:
What function?
Step-by-step explanation:
Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the mixture flows out at the rate of 3 gallons per minute, how many pounds of salt will remain in the tank after 16 minutes if 28 pounds of salt are in the mixture initially? (Give your answer correct to at least three decimal places.)
Answer:
Step-by-step explanation:
This is a differential equation problem most easily solved with an exponential decay equation of the form
[tex]y=Ce^{kt}[/tex]. We know that the initial amount of salt in the tank is 28 pounds, so
C = 28. Now we just need to find k.
The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is [tex]\frac{dy}{dt}[/tex]. Thus, the change in the concentration of salt is found in
[tex]\frac{dy}{dt}=[/tex] inflow of salt - outflow of salt
Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:
[tex]3(\frac{y}{400})[/tex]
Therefore,
[tex]\frac{dy}{dt}=0-3(\frac{y}{400})[/tex] or just
[tex]\frac{dy}{dt}=-\frac{3y}{400}[/tex] and in terms of time,
[tex]-\frac{3t}{400}[/tex]
Thus, our equation is
[tex]y=28e^{-\frac{3t}{400}[/tex] and filling in 16 for the number of minutes in t:
y = 24.834 pounds of salt
1=5
2=12
3=39
4=148
5=?
14 Calculate the mode from the following data: 7,8, 6, 5, 10, 11, 4, 5,2 b. 5: а. 3.' 4 6 с. d: 6
MODE IS THE NUMBER THAT IS REPEATED THE HIGHEST TIME..
HERE, IN YOUR QUESTION 5CAME 2 TIMES i.e. it is repeated highest time .so mode=5....
A rectangular garden is 5 ft longer than it is wide. Its area is 1800ft^2. What are its dimensions?
Answer:
The dimensions are 45 feet by 40 feet.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A=w\ell[/tex]
Where w is the width and l is the length.
The length is five feet longer than the width. Thus, we can write that:
[tex]\ell = w+5[/tex]
The total area is 1800 square feet. Substitute:
[tex]1800=w(w+5)[/tex]
Solve for w. Distribute:
[tex]w^2+5w=1800[/tex]
Subtract 1800 from both sides:
[tex]w^2+5w-1800=0[/tex]
Factor. We can use 45 and -40. Hence:
[tex]\displaystyle (w+45)(w-40)=0[/tex]
Zero Product Property:
[tex]w+45=0\text{ or } w-40=0[/tex]
Solve for each case:
[tex]\displaystyle w=-45\text{ or } w=40[/tex]
Since the width cannot be negative, we can ignore the first solution.
So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.
The dimensions are 45 feet by 40 feet.
Help me on this please
Answer:
x = 3.5
Step-by-step explanation:
Triangle to the right:
4^2 + x^2 = 8^2
16 + x^2 = 64
y^2 = 48
Triangle to the left:
x^2 + 6^2 = 48
x^2 + 36 = 48
x^2 = 12
x = sqrt(12)
x = 3.5
Enunciate demerits of classical probability.
Answer:
Some demerits of classical probability are provided throughout the following portion.
Step-by-step explanation:
This could only be utilized if somehow the occurrences are fairly probable as well as predictable. Such supposition is established far in advance of the investigation or testing.This only applies whereas if an overall number of occurrences seems to be limited, one such term has quite a restricted scope, such as coins tossing, picking card numbers, etc.You are planning to buy a house for $800,000. City bank offers a 30 year loan at 4.9 % apr ( Annual percentage interest rate) if you put 20 % down. Calculate your expected monthly payment.
Answer:
3396.65
Step-by-step explanation:
Let's start by cacluating the amount the bank is loaning us
800000*.8=640000
Let's now calculate the effective rate: .049/12= .004083333333
let x= payment
[tex]640000=x\frac{1-(1+.004083333333)^{-30*12}}{.004083333333}\\x=3396.651012[/tex]
A survey found that the median number of calories consumed per day in a certain country was 3,304 and the mean was 3,204.9 calories. If a histogram were constructed for the data, would you expect it to be skewed to the right, to the left, or approximately symmetric
Answer:
Skewed to the left
Step-by-step explanation:
Given
[tex]Median = 3304[/tex]
[tex]Mean = 3204.9[/tex]
Required
The type of distribution
From the given data, we have:
[tex]Median \ne Mean[/tex] --- Mean and Median are not equal
and
[tex]Median > Mean[/tex] --- Median is greater than mean
When the median is greater than the mean; the histogram is expected to be left skewed
1. What is the area of the figure below? (1 point)
5 in.
3 in.
12 in
O 18 in.2
O 30 in.2
O 36 in.2
O 60 in.2
Answer: 36in2
Step-by-step explanation:
A= base *height
=12*3
=36
The Area of the figure is 36 in².
What is Area of parallelogram?The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm2, m2, in2, etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.
two equal, opposite sides,two intersecting and non-equal diagonals, andopposite angles that are equalThe area of a parallelogram can be calculated by multiplying its base with the altitude. The base and altitude of a parallelogram are perpendicular to each other. The formula to calculate the area of a parallelogram can thus be given as,
Area of parallelogram = b × h square units
where,
b is the length of the base
h is the height or altitude
Given:
base= 12 in
height= 3 in
Area of parallelogram,
= base * height
=12* 3
= 36 in²
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what's the answer to this
Answer:
the volume = 1152cm^2
Step-by-step explanation:
> The volume of cylinder =4 spheres
> Volume of sphere = v= 4/3πr³
> radius =6cm
volume of 4 spheres =
[tex]v \: = 4 \times \frac{4}{3} \times \pi \times {6}^{3} \\ \\ v = 1152cm {2} [/tex]
Answer:
the unused volume is 18095,57cm cubed
Find the simple interest on the following. 1 ) Rs 1,760 for 3 years 6 months at the rate of 12% p.a.
Plss help me
Answer:
739.2
Step-by-step explanation:
indicate the following pairs of lines are coinciding, parallel ,perpendicular or neither
i need helpp pleaseee
Which equation could represent each grapes polynomial function?
9514 1404 393
Answer:
top graph: y = x(x +3)(x -2)bottom graph: y = x⁴ -5x² +4Step-by-step explanation:
Each x-intercept at x=a corresponds to a polynomial factor of (x -a).
__
The top graph has x-intercepts of -3, 0, +2, so the factors of this cubic are ...
y = (x +3)(x -0)(x -2)
y = x(x +3)(x -2) . . . . . . . matches upper right tile
__
The bottom graph has x-intercepts of -2, -1, 1, 2, so the factors of this quartic are ...
y = (x +2)(x +1)(x -1)(x -2) = (x² -4)(x² -1)
y = x⁴ -5x² +4 . . . . . . . matches lower left tile
Mackenzie earns 4% commission as a salesperson. She sold a digital camera that cost $767. How much commission did Mackenzie earn?
Answer:
like about $500 and because of the ca!erlsn
Get brainly if right!! Plsss help
A dozen roses in a gift box cost 21 dollars. Twenty roses in a
gift box cost 32.6 dollars. How much does a gift box cost? How
much does one rose cost?
Answer: [tex]\$1.45[/tex]; [tex]\$3.6[/tex]
Step-by-step explanation:
Given
A dozen roses in a gift box costs $21
Similarly, 20 roses in a gift box costs $32.6
Suppose the price of single rose and gift box is [tex]x[/tex] and [tex]y[/tex]
[tex]\therefore 12x+y=21\quad \ldots(i)\\\Rightarrow 20x+y=32.6\quad \ldots(ii)[/tex]
Solving (i) and (ii) , we get
[tex]x=\$1.45;y=\$3.6[/tex]
Thus, the price of the one rose is [tex]\$1.45[/tex] and the price of gift box is [tex]\$3.6[/tex]
Answer:
1.45 and 3.5
Step-by-step explanation:
what is the quotient?
Answer:
the result gaven by dividing one number by another
Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question.
A number line going from negative 9 to positive 1.
–3
0
2
Answer:
-5 it is
Step-by-step explanation:
Given the functions below, find f(x)+g(x)
CHECK MY ANSWERS PLEASE
The answer is (a)..........
nen,
Problem: Two towns, A and B, located along the coast of the Pacific Ocean are 30
km apart on a north-south line. From a ship, the line of sight of town A is W30°N,
while that of town B is S400W.
1. How far is the ship from town A?
2. How far is the ship from town B?
Answer:
Step-by-step explanation:
From the picture attached,
m∠COB = 90° - m∠BOS
= 90° - 40°
= 50°
tan(30°) = [tex]\frac{AC}{OC}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{AC}{OC}[/tex]
AC = [tex]\frac{OC}{\sqrt{3}}[/tex] ------(1)
Similarly, tan(50°) = [tex]\frac{BC}{OC}[/tex]
BC = OC[tan(50°)] -------(2)
Now AC + BC = 30 cm
By substituting the values of AC and BC from equation (1) and (2),
[tex]\frac{OC}{\sqrt{3}}+OC(\text{tan}50)=30[/tex]
(1.769)OC = 30
OC = 16.96
1). cos(30°) = [tex]\frac{OC}{AO}[/tex]
[tex]\frac{\sqrt{3}}{2}= \frac{16.96}{OA}[/tex]
[tex]OA=19.58[/tex] cm
Therefore, distance between the ship and town A is 19.58 cm.
2). cos(50°) = [tex]\frac{OC}{OB}[/tex]
0.6428 = [tex]\frac{16.96}{OB}[/tex]
OB = 26.38 cm
Therefore, distance between the ship and town B is 26.38 cm.
Next anyone help it always helps haha 20 points
Answer:
Distance between Amber and Claire's house = 17.63 blocks
Step-by-step explanation:
In this graph three points are showing the locations of Amber's, Betsey's and Claire's houses.
Each unit on the graph represents 1 block.
Amber walks from her house to Claire's house, then on to Betsey's house.
We have to calculate the distance covered by Amber.
Since Distance from Claire's house to Betsey's house = 7 blocks = 7 units
and distance between Amber and Betsey's house = 8 blocks = 8 units
Now we will calculate the distance between Amber and Claire's house by Pythagoras theorem.
Distance² = 7² + 8² = 49 + 64 = 113
Distance = √113 units = 10.63 units
Therefore, total distance walked by Amber = 10.63 + 7 = 17.63 units = 17.63 blocks
Answer:
the answer might be 17. 63 because there are 7 blocks in between them so try that sorry if its wrong
in the pair of triangle, write the similarity statement and identify the postulate of theorem that justifies the similarity.
Answer:
ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem
ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem
Step-by-step explanation:
First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.
Second set :
[tex]\frac{EG}{RQ}[/tex] = [tex]\frac{10}{12}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{EF}{RF}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{FG}{FQ}[/tex] = [tex]\frac{20}{24}[/tex] = [tex]\frac{5}{6}[/tex]
Help ! ASAP please and thank you !!
that alot of work shhheeshhh
X and Y are independent random variables. X has mean 100 and standard deviation 12. Y has mean 30 and standard deviation 9. What are the mean and standard deviation of (X–Y)?
Answer:
x is down and up and y is up then down
Step-by-step explanation:
I think
The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-1); for example, enter xas x^3. Do
not include "G(x) =" in your answer.
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D.
G(x) = (x - 3)^3
The function of the blue curve in the graph is g(x)=(x+3)²+1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=x².
In the image, we have two functions, the red one is a parent function, which is the most basic version of it. The blue function is a transformation of the red one, that is, it was only moved to the left and upwards.
From the graph, we can see that the blue function was moved to the left and upwards, that means we have to sum units to x and f(x).
So, g(x)=(x+3)²+1
Therefore, the function of the blue curve in the graph is g(x)=(x+3)²+1.
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A test taker gets 70 on 1st exam, 80 on 2nd exam, 2/3 of 4/5 of his 2nd exam on his 3rd test. If the professor gives 5 points extra credit on his 4th exam and his average score is 80, what was his score on the 4th exam
=================================================
Explanation:
The phrasing "2/3 of 4/5 of his 2nd exam on his 3rd test" is a bit clunky in my opinion. It seems more complicated than it has to be.
The student got 80 on the second exam. 4/5 of this is (4/5)*80 = 0.8*80 = 64. Then we take 2/3 of this to get (2/3)*64 = 42.667 approximately. If we assume only whole number scores are given, then this would round to 43.
Let x be the score on the fourth exam. Since 5 points of extra credit are given, the student actually got x+5 points on this exam.
So we have these scores
first exam = 70second exam = 80third exam = 43fourth exam = x+5Adding up these scores and dividing by 4 will get us the average
(sum of scores)/(number of scores) = average
(70+80+43+x+5)/4 = 80
(x+198)/4 = 80
x+198 = 4*80
x+198 = 320
x = 320 - 198
x = 122
So the student got a score of x+5 = 122+5 = 127 on the fourth exam.
