The police cruiser travels a total distance of 275.0 meters. It covers 137.5 meters during acceleration and the same distance during deceleration (in the opposite direction), summing up to 275.0 meters in total.
Calculating the distance covered during acceleration:
The equation for distance covered with constant acceleration is given by:
[tex]\[ s = ut + \frac{1}{2}at^2 \][/tex]
Where:
[tex]\( u \)[/tex] = Initial velocity
[tex]\( a \)[/tex] = Acceleration
[tex]\( t \)[/tex] = Time
Given:
Initial velocity [tex](\( u \))[/tex] = 20.0 m/s
Acceleration[tex](\( a \))[/tex] = 3.0 m/s²
Time[tex](\( t \))[/tex]= 5.0 seconds
Let's find the distance covered during acceleration using the above formula:
[tex]\[ s = ut + \frac{1}{2}at^2 \][/tex]
[tex]\[ s = (20.0 \, \text{m/s} \times 5.0 \, \text{s}) + \frac{1}{2} \times 3.0 \, \text{m/s}^2 \times (5.0 \, \text{s})^2 \][/tex]
[tex]\[ s = (100.0 \, \text{m}) + \frac{1}{2} \times 3.0 \, \text{m/s}^2 \times 25.0 \, \text{s}^2 \][/tex]
[tex]\[ s = 100.0 \, \text{m} + 37.5 \, \text{m} \][/tex]
[tex]\[ s = 137.5 \, \text{m} \][/tex]
Therefore, the distance covered during acceleration is 137.5 meters.
Calculating the distance covered during deceleration (slowing to a stop):
The cruiser starts at a speed of 20.0 m/s and decelerates uniformly until it comes to a stop. The distance covered during deceleration will be the same as the distance covered during acceleration but in the opposite direction.
So, the distance covered during deceleration = 137.5 meters (in the opposite direction).
Total distance traveled:
The total distance traveled by the cruiser during acceleration and then deceleration is the sum of these distances (taking the magnitudes):
Total distance = Distance during acceleration + Distance during deceleration
Total distance = 137.5 m + 137.5 m
Total distance = 275.0 meters
Therefore, the entire distance covered by the cruiser in the entire time is 275.0 meters.
A number increased by 3/4 of the number is 14 find the number
Answer:
8
Step-by-step explanation:
Set up an equation:
x+ (3/4)x = 14
Solve for x:
Combine like terms:
(7/4)x = 14
Divide both sides by 7/4
x = 8
Translate the sentence into a mathematical expression: “Twice x is 5”
Answer:
2x = 5
Step-by-step explanation:
when f(x) = 5, x= ?????
Answer:
when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]
Step-by-step explanation:
Considering the expression
[tex]f(x) = 5[/tex]
Rewrite the function as an equation
[tex]y = 5[/tex]
Comparing with slop-intercept form
[tex]y=mx+b[/tex]
So,
[tex]m=0[/tex]
[tex]\mathrm{Axis\:interception\:points\:of}\:5:\quad \mathrm{Y\:Intercepts}:\:\left(0,\:5\right)[/tex]
Therefore, when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]
The graph for [tex]f(x) = 5[/tex] is also attached below.
Keywords: graph, function
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Explain how you would prove the triangles congruent in order to prove the statements true.
Given data:
QP = PT and RP = SP
Let us first prove ΔQPR and ΔSPT are congruent.
In ΔQPR and ΔSPT,
QP ≅ TP (Given side)
∠QPR ≅ ∠ SPT (Vertically opposite angles are congruent)
RP ≅ SP (Given side)
Therefore, ΔQPR ≅ ΔSPT (by SAS congruence rule)
By corresponding parts of congruence triangles are congruence,
⇒ ∠Q ≅ ∠T
Hence ∠Q ≅ ∠T.
(9^(3))^(3) =
9 9
9 0
9 6
81
Step-by-step explanation:
[tex] \because \: ( {a}^{m} )^{n} = {a}^{m \times n} \\ \\ \therefore ( {9}^{3} )^{3} = {9}^{3 \times 3} = {9}^{9} \\ [/tex]
Nat put $550 in an account which pays four percent interest, compounded semiannually. How much will be in the account in three years?
The final answer will be rounding it up to $619.
Step-by-step explanation:
4% = 0.04
1 represents 100%
therefore,
(( 1 + 0.04)^3)x 550
= (1.04^3) x 550
= 1.124864 x 550
= $618.6752
The final answer will be rounding it up to $619.
A number to the 9 power divided by the same number to the 6 power equals 27 what is the number
Answer:
3
Step-by-step explanation:
n^9/ n^6 = 27
n^9 - 6 = 27
n^3 = 27
n = ∛27
n = 3
Joseph drives 125 miles in 2 1/2 hours . at that rate , how far does he travel each hour?
If he drives 125 miles in 2 1/2 hours, he will drive 125 ÷ 2 1/2 miles per hour.
125 ÷ 2 1/2 = 50 miles
answer: 50 miles per hour
If these two figures are similar, what is the measure of the missing angle? 180 90 70 110
Answer:
70
Step-by-step explanation:
Answer:
70
Step-by-step explanation:
please show work read what the question wants in both pictures
Answer:
2) m∠CBD = 60 3) x=15; 95 and 85 4) 12 = x; 98 for both angles
Step-by-step explanation:
2) 2x + 14 + x + 7 = 90 The angles add up to 90 degrees
3x + 21 = 90 Combine like terms
- 21 - 21 Subtract 21 from both sides
3x = 69 Divide both sides by 3
x = 23
Plug 23 in the equation
2(23) + 14
46 + 14
60
3) 2x + 65 + 3x + 40 = 180 The angles add up to 180 degrees
5x + 105 = 180 Combine like terms
- 105 - 105 Subtract 105 from both sides
5x = 75 Divide both sides by 5
x = 15
Plug in 15 into both equations
2(15) + 65 = 95
3(15) + 40 = 85
4) 5x + 38 = 9x - 10
- 5x - 5x Subtract 5x from both sides
38 = 4x - 10
+ 10 + 10 Add 10 to both sides
48 = 4x Divide both sides by 4
12 = x
Plug in 12 into both equations
5(12) + 38 = 98
9(12) - 10 = 98
How many cube-shaped boxes with 12-inch edges can fit into a box thatis 4
feet tall, 4 feet long, and 5 feet wide?
Answer:
80
Step-by-step explanation:
First recall that:
1 inch=12 feet
The volume of cube-shaped boxes with 12-inch edges is 1 cm³
The volume of a box that is 4
feet tall, 4 feet long, and 5 feet wide is
given by:
[tex]Volume = lwh[/tex]
We substitute l=4ft, w=5ft and h=4ft
To obtain:
[tex]Volume = 4 \times 4 \times 5 = 80 {ft}^{3} [/tex]
Therefore 80 cube-shaped boxes with 12-inch edges can fit into a box that is 4
feet tall, 4 feet long, and 5 feet wide.
Problem PageQuestion
A principal of 3700 is invested at 4.75 %interest, compounded annually. How much will the investment be worth after 5 years?
The investment will be worth $4686.62 after 5 years.
Step-by-step explanation:
Principal, P = 3700
Rate, r = 4.75% = 0.0475
Number of years, t = 5 years
Number of times compounded, n = 5 times
Amount = P(1 + r/n)^nt
⇒ 3700 (1 + 0.0475/5)^25
⇒ 3700 (5.0475/5)^25
⇒ 3700 (1.0095)^25
⇒ 4686.62
∴ Amount = $4686.62
A 20,000 deposit earns 3.6% interest for 3 years. If no money is deposited or withdrawn how much interest will ever earned at the end of 3 years?
Answer:2,160
Step-by-step explanation:Multiply 20,000 by the percent then multiply the number you get by 3
U Move It charges $16 per hour plus a fueling fee of $25 to rent a truck. Jamarcus needs to rent a truck and can spend no more than $125. Which inequality represents the situation? A 16h + 25 ≤ 125 B 16h + 25 ≥ 125 C 25h + 16 ≤ 125 D 25h + 16 ≥ 125
Answer:
A. 16h+25≤125
Step-by-step explanation:
From the information, the one-time fee is $25.
The rate per hour is $16
Therefore the total cost involved in renting a car is given by:
16h+25
Jamarcus needs to rent a truck and can spend no more than $125.
This implies that:
16h+25≤125
The correct answer is A.
When the value of t is 60, the value of c is 90 . Explain what this means using the problem context.
Little help!!!!!
Answer:
Step-by-step explanation:
as the temp t increases the number of cricket chirps also increases.
1: The complete table is according to the given function :
t : 40 50 60 70 80 90 100
c : 10 50 90 130 170 210 250
2: It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.
The given function is,
c = 4t - 180
Here t represents the temperature
c represents the cricket chirps per minutes
Now plug in each temperature value and solve for c:
When t = 40:
c = 4(40) - 150
c = 160 - 150
c = 10
When t = 50:
c = 4(50) - 150
c = 200 - 150
c = 50
When t = 60:
c = 4(60) - 150
c = 240 - 150
c = 90
When t = 70:
c = 4(70) - 150
c = 280 - 150
c = 130
When t = 80:
c = 4(80) - 150
c = 320 - 150
c = 170
When t = 90:
c = 4(90) - 150
c = 360 - 150
c = 210
When t = 100:
c = 4(100) - 150
c = 400 - 150
c = 250
Therefore, the complete table is:
t : 40 50 60 70 80 90 100
c : 10 50 90 130 170 210 250
When the value of t is 60, the value of c is 90.
It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.
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How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 30% antifreeze to get a mixture that is 40% antifreeze?
Answer:
70 gallons
Step-by-step explanation:
x gallon of 50%
x * 0.5 + 70 * 0.3 = (x + 70) * 0.4
0.5x + 21 = 0.4x + 28
0.1x = 7
x = 70
To get a mixture that is 40% antifreeze, we need to mix 70 gallons of 30% antifreeze solution with 40 gallons of 50% antifreeze solution. This conclusion is reached by establishing an equation representing the total amount of antifreeze in the mixture before and after and then solving for the unknown.
Explanation:Your question deals with the concept of a weight ratio in a chemical mixture. Specifically, we're going to solve it using algebra. Let's say you need x gallons of the 50% antifreeze solution. We can work this out by forming an equation based on the information given in the problem:
The total amount of antifreeze in the 70 gallons of 30% solution and x gallons of 50% solution must be equal to the total amount of antifreeze in the (70 + x) gallons of 40% solution.
Therefore, we can write: 0.3 * 70 + 0.5 * x = 0.4 * (70 + x)
Solving the equation above, we find that x equals 40 gallons. So, you would need to mix 40 gallons of a 50% antifreeze solution with 70 gallons of 30% solution to obtain a final solution with a 40% antifreeze concentration.
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Find the area of the triangle below. Show as much work as possible. Label your answer appropriately.
Answer:
[tex]Area=\frac{5}{12}x^2[/tex]
Step-by-step explanation:
The area of a triangle is given by:
[tex]Area=\frac{1}{2}*base*height[/tex]
From the diagram [tex]base=\frac{5}{6}x,and,height=x[/tex]
We substitute into the formula to get:
[tex]Area=\frac{1}{2}*\frac{5}{6}x*x[/tex]
This implies that:
[tex]Area=\frac{5}{12}x^2[/tex]
How do you simply 5\8 and 3\10
Answer:
Cannot simplify the fractions further than that
Step-by-step explanation:
The fractions 5/8 and 3/10 have already been simplified so they do not need to be simplified anymore. If you are wanting to put them in decimal form then that is different. All you have to do is plug it in the calculator.
please hurry!!! will mark BRAINLEYST if right!!!!
Answer: 38.47cmsqr
Step-by-step explanation:
In sixth grade, Manuel reads 35 books this year the books he read increase 40% how many books had he read
Answer: 49 books
Step-by-step explanation:
Number of books read by Manuel this year = 35
Increment in reading rate = 40%
Therefore, we now find 40% of 35 and add it to 35 to know the number of books he had read
Number of books read = 40% of 35
= 40/100 x 35
= 14 books
Total number of books read = 35 + 14
= 49 books
Answer:
Step-by-step explanation:
50
If the person in the figure wants his shadow to be 3 feet long, how far should he move and in what direction?
See attached photo
Need answer ASAP please help!!
If the person in the figure wants his shadow to be 3 feet long, Then he should move to right for 11/3 feet distance.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In this problem Triangle ADF is similar to Triangle
by AA Similarity Theorem
15/6=(10+ED)/ED
Apply cross multiplication
15ED=6(10+ED)
15ED=60+6ED
Subtract 6 ED from both sides
9ED=60
ED=60/9
ED=20/3 ft.
ED is the length
He should move to the right x feet
x=20/3-3
x=11/3 feet
Hence, he should move to right for 11/3 feet distance.
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Which one is bigger 64 in or 5 ft
64 inches
Step-by-step explanation:
12 inches equals 1 foot so
12*5=60 inches which means it will be bigger than 5 feet.
television videl watched 6 times as many hours of television over the weekend as dieen. together they watched a total of 14 hours of television. how many hours of television did each person watch over the weekend?
Order -9, 5, 6, and -4 from least to greatest.
a. -9, -4, 5, 6 c. -9, -4, 6, 5
b. 6, 5, -4, -9 d. -4, -9, 5, 6
The answer is a. -9, -4, 5, 6.
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Answer:
Option A: -9, -4, 5, 6
Step-by-step explanation:
Since the lowest number is -9, it should go first
Since the 2nd lowest number is -4, it should go second
Since the 3rd lowest number is 5, it should go third
Since the 4th lowest number is 6, it should go fourth
Answer: Option A, -9, -4, 5, 6
Carle is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that has 100 feet
49 pieces of string can be cut from a ball of string that has 100 feet
Solution:
Given that, Carle is cutting pieces of string that are exactly 24 3/8 inches long
Therefore,
[tex]Length\ of\ each\ string = 24\frac{3}{8}\ inches = \frac{8 \times 24 + 3}{8} = \frac{195}{8}\ inches[/tex]
How many pieces can she cut from a ball of string that has 100 feet
Total length of string = 100 feet
Convert feet to inches
1 feet = 12 inch
100 feet = 1200 inch
Therefore, number of pieces that can be cut is given as:
[tex]\text{Number of pieces } = \frac{\text{total length of string}}{\text{length of each string}}[/tex]
Substituting the values we get,
[tex]\text{Number of pieces } = \frac{1200}{\frac{195}{8}}\\\\\text{Number of pieces } = 1200 \times \frac{8}{195}\\\\\text{Number of pieces } = 49.2307 \approx 49[/tex]
Therefore, 49 pieces of string can be cut from a ball of string that has 100 feet
Rupert is copying some files from his computer to a compact disc, like the one shown above.
If the diameter of the compact disc is 120 millimeters, what is the approximate area ignoring the center hole? (Use 3.14 for pi.)
A.
376.8 mm2
B.
11,304 mm2
C.
753.6 mm2
D.
45,216 mm2
Option B: [tex]11,304 \mathrm{mm} ^2[/tex] is the area of the compact disc.
Explanation:
The diameter of the compact disc is [tex]120mm[/tex].
To determine the area of the compact disc, let us substitute the values in the area of the circle formula,
[tex]A=\pi r^2[/tex] where [tex]r=\frac{d}{2}[/tex]
Substituting the value of d in [tex]r=\frac{d}{2}[/tex], we get,
[tex]r=\frac{120}{2} =60[/tex]
Thus, [tex]r=60[/tex] and [tex]\pi=3.14[/tex]. Let us substitute these values in [tex]A=\pi r^2[/tex], we get,
[tex]A=3.14\times(60)^2[/tex]
Simplifying, we have,
[tex]A=3.14\times3600[/tex]
Multiplying, we get,
[tex]A=11304mm^2[/tex]
Thus, the area of the compact disc is [tex]11,304 \mathrm{mm} ^2[/tex]
Hence, Option B is the correct answer.
(X to the fourth power) squared equals
Answer:
[tex](x^4)^2=x^8[/tex]
Step-by-step explanation:
Because of the power of a power property, which states that [tex](x^n)^m=x^{n\times{m}}[/tex], where m and n are real numbers, the expression you mentioned can be simplified by applying this property like this: [tex](x^4)^2=x^{4\times2}=x^8[/tex]
a paddling canoeist took 2 h to travel 12 km down a river, with the current. It took 4 h to do the return trip up the river, against the current. What was the speed of the current
Answer: The speed of the current is 1.5 km/h .
Step-by-step explanation:
Let x = speed of current and y = speed of canoe.
Since , [tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
As per given , we have
[tex]x+y=\dfrac{12}{2}\\\\ x+y=6......................(1)[/tex]
[tex]y-x=\dfrac{12}{4}\\ y-x=3...............(2)[/tex]
Adding (1) and (2) , we get
[tex]2y=9\\\Rightarrow\ y=\dfrac{9}{2}=4.5[/tex]
Put value of y in (1) , we get
[tex]x+4.5=6\\\Rightarrow\ x=1.5[/tex]
Hence, the speed of the current is 1.5 km/h .
To find the speed of the current, we can use the concept of relative velocity and set up equations for the downstream and upstream journeys.
Explanation:In order to find the speed of the current, we can use the concept of relative velocity. Let's assume the speed of the canoeist in still water is 'v' km/h and the speed of the current is 'c' km/h.
Downstream journey: The effective speed of the canoeist is 'v + c' km/h. Given that the canoeist took 2 hours to travel 12 km downstream, we can set up the equation:
(v + c) * 2 = 12
Upstream journey: The effective speed of the canoeist is 'v - c' km/h. Given that the canoeist took 4 hours to travel 12 km upstream, we can set up the equation:
(v - c) * 4 = 12
Solving these two equations simultaneously will give us the values of 'v' and 'c', and the value of 'c' will represent the speed of the current.
Which table values can be defined by the function y=2x+3
Answer:
beggining poit:3 second point (potentially): 1,5
Step-by-step explanation:
in the y intercept 3 is it so which ever has a 3 as the starting point there could be an option
for the 2x part that is the slope otherwise known as rise over run so what you do is that you turn it to a fraction over or under 1 meaning you rise for 2 and go to the right 1
rise 2
_
run 1
in order to rise 2 you go up 2 from the y intercept(3) and in order to run you go right since its a positive
once you plot those two dots then you draw a line across
Which of the following statements about the relationship between an interior angle of a polygon and its adjacent exterior angle are true? Choose all that apply.
A. They form a linear pair.
B. They are supplementary.
C. They are complementary.
D. They are alternate exterior angles.
9514 1404 393
Answer:
A. They form a linear pair.
B. They are supplementary.
Step-by-step explanation:
An interior angle and its adjacent exterior angle of a polygon are a linear pair. The angles of any linear pair are supplementary.