Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled by the equation a(t) =
Answers
Answer:
a. Alice
b. Briana
c. 0.51 minutes
Step-by-step explanation:
a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for
2t - 1 > 0
2t > 1
t > 1/2 minutes
b. They finish when their covered distance is equal to 5 kilometers. For Alice:
t/4 = 5
t = 5*4 = 20 minutes
For Briana:
√(2t - 1) = 5
2t - 1 = 5²
2t = 25 + 1
t = 26/2
t = 13 minutes
c. They are side by side when they have covered the same distance, that is:
t/4 = √(2t - 1)
(t/4)² = 2t - 1
t²/16 = 2t - 1
t² = 16*(2t - 1)
t² = 32t - 16
t² - 32t + 16 = 0
Using quadratic formula:
[tex]t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]
[tex]t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)} [/tex]
[tex]t = \frac{32 \pm 30.98}{2} [/tex]
[tex]t_1 = \frac{32 + 30.98}{2} [/tex]
[tex]t_1 = 31.49 [/tex]
[tex]t_2 = \frac{32 - 30.98}{2} [/tex]
[tex]t_2 = 0.51 [/tex]
Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.
Answer:
a) Alice starts first, b) Briana gets the finish line first, c) [tex]t \approx 0.509\,min[/tex]
Step-by-step explanation:
a) Alice starts first, since binomial inside the squared root is equal to zero when [tex]t = \frac{1}{2}\,min[/tex], whereas Alice begins at [tex]t = 0\,min[/tex].
b) The instant when each competitor reach finish line is:
Alice
[tex]5\,km = \frac{t}{4}[/tex]
[tex]t = 20\,min[/tex]
Briana
[tex]5\,km = \sqrt{2\cdot t - 1}[/tex]
[tex]25\,km^{2} = 2\cdot t - 1[/tex]
[tex]t = 13\,min[/tex]
Briana gets the finish line first.
c) Alice and Briana are side by side when [tex]a(t) = b(t)[/tex]. Then:
[tex]\frac{t}{4} = \sqrt{2\cdot t - 1}[/tex]
[tex]\frac{t^{2}}{16} = 2\cdot t - 1[/tex]
[tex]t^{2} - 32\cdot t + 16 = 0[/tex]
The roots of the second order polynomial are:
[tex]t_{1} \approx 31.492\,min[/tex] and [tex]t_{2} \approx 0.509\,min[/tex]
Just the second roots makes sense, as they must be side by side at one instant before getting the finish line.
Related Questions
76.98 divided by 45.2
Answers
Answer:
1.7030973451327434
Step-by-step explanation:
Answer:1.7039735
Step-by-step explanation:
Please help free Brainliest to correct answer!!!!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
[tex]\frac{5}{6}[/tex]÷[tex]\frac{1}{5}[/tex]
Keep, change, flip.
So, [tex]\frac{5}{6}[/tex] stays the same.
The division sign changes to multiplication.
[tex]\frac{1}{5}[/tex] changes to 5.
So now you have
[tex]\frac{5}{6}[/tex]×[tex]\frac{5}{1}[/tex]= [tex]\frac{25}{6}[/tex]
6·4=24
25-24=1
D= [tex]4\frac{1}{6}[/tex]
Answer:
The correct answer is D. Brainliest plz. I am trying to level up and only have 2 out of the 5 needed. Thanks! Have a good day
A scatter plot is shown below:
Which statement is most likely correct about the line ?
A. It can be a line of best fit because it is close to most data points.
B. It can be a line of best fit because it passes through all data points
C. It cannot be a line of best fit because it’s not close to most of the data points
D. You cannot be the line of best fit because it does not show a positive association
Answers
It’s far off from most of the points
−3x−4y=4
−5x+y=2
Is (2,10)left parenthesis, 2, comma, 10, right parenthesis a solution of the system?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
Answers
Substituting the solution (2,10) into both equations of the system shows that it does not satisfy either equation, hence it is not a valid solution.(Choice B.No)
Explanation:To verify the solution of the system of equations, we can substitute the ordered pair (2,10) into both equations. Let's do this:
In the first equation, -3x - 4y = 4, we substitute x = 2 and y = 10. This gives us -3*2 - 4*10 = -6 - 40 = -46, which is not equal to 4.In the second equation, -5x + y = 2, we substitute x = 2 and y = 10. This gives us -5*2 + 10 = -10 + 10 = 0, which is not equal to 2.Since the ordered pair (2,10) does not satisfy either of the two given equations, we can say that (2,10) is not a solution of the system of the equations.
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The point (2,10) is not a solution to the system of equations -3x - 4y = 4 and -5x + y = 2, as it does not satisfy either equation when substituted.
To determine if the point (2,10) is a solution of the given system of equations:
-3x - 4y = 4
-5x + y = 2
we need to substitute x=2 and y=10 into each equation to see if the left-hand side equals the right-hand side.
For the first equation:
-3(2) - 4(10) = -6 - 40 = -46
which does not equal 4, therefore the point (2,10) is not a solution to this equation.
For the second equation:
-5(2) + (10) = -10 + 10 = 0
which does not equal 2, so (2,10) is also not a solution to the second equation.
Since (2,10) does not satisfy either equation, we can conclude that:
(Choice B)
No, (2,10) is not a solution to the system of equations.
Some of the students at Kahlo Middle School like to ride their bikes to and from school. They always ride unless it rains. Let d be the distance in miles from a student's home to the school. Write two different expressions that represent how far a student travels by bike in a four week period if there is one rainy day each week.
Answers
Answer:
32d
Step-by-step explanation:
-The students ride their bikes to and from school every day. The distance is thus;
[tex]d_t=2d[/tex]
-Taking that there are 5 school days per week and that it rains in one per week. the total number of days is:
[tex]Days=Days \ per \ week \times \ number \ of \ weeks\\\\=(5-1)\times 4\\\\=16\ days[/tex]
Now, we multiply the distance per day by the total number of days:
[tex]Distance, D=2d\times 16\\\\=32d[/tex]
Hence, the total distance in a 4-week period is expressed as 32d ( where d is the distance from home to school).
will give brainiest to the first person who answers correctly!!!!
Answers
Answer:
Option B
Step-by-step explanation:
Its the same because its basically just like stacking the same shape over and over to make a prism
Answer:
answer is B your welcome:)
Step-by-step explanation:
What is -9-x when x= 4.3
Answers
Answer:
-9-x=13.3
Step-by-step explanation:
x=4.3
-9-x=
-9-4.3=-13.3
Solve the equation
[tex] {x}^{2} = 196[/tex]
Show your work and explain your steps.
Answers
because you have to a square 196
NEED HELP ASAP A survey was conducted with high school students in
each grade to see how many prefer math or science.
Some of the data are shown below.
Which statement is true about the joint frequencies in
this table?
40
11 | 12 |
Total
O Twenty-three 9th graders and fifteen 11th graders
prefer math.
O Fourteen 11th graders prefer math and eight 10th
graders prefer science.
O Thirty-five 12th graders prefer math and nine 10th
graders prefer science.
Twenty-three 9th graders and thirty-two 12th
graders prefer math.
Math
18
90
Science 40
15
95
Total
63
26
29
67
185
Answers
Question:
a. Twenty-three ninth graders and fifteen eleventh graders prefer math.
b. Fourteen eleventh graders prefer math and eight tenth graders prefer English.
c. Thirty-five twelfth graders prefer math and nine tenth graders prefer English.
d. Twenty-three ninth graders and thirty-five twelfth graders prefer math.
e. Eighteen tenth graders prefer English and fourteen eleventh graders prefer math.
Answer:
Therefore, the correct options are;
b. and d.
Step-by-step explanation:
Here we have a table with blank boxes and totals from which we can fill the boxes;
For the 12th graders, we have a total of 67 pupils with 32 preferring English, therefore the number of the 12th graders that prefer math is 67 - 32 = 35 pupils
Similarly for the 11th graders we have total pupils = 29 with 15 preferring English, therefore the number of the 11th graders that prefer math is 29 - 15 = 14 pupils
Also for the 10th graders we have total pupils = 26 with 18 preferring math, therefore the number of the 11th graders that prefer English is 26 - 18 = 8 pupils
Finally for the 9th graders, we have a total of 63 pupils with 40 preferring English, therefore the number of the 9th graders that prefer math is 63 - 40 = 23 pupils
From the above, the correct option is
Answer:
b only
Step-by-step explanation:
An large pizza has a diameter of 14 inches and is cut into 6 equal pieces . Find the area of 2 pieces , rounded to the nearest hundredth
Answers
Answer
51.312in^2
hope this helps...
y varies directly with x. If x=6 when y=30, determine y when x=8.
Answers
Answer:
Y=40
Explanation:
Due to the nature of both X and Y varying directly, you can view the problem as a proportion. If x=6 and y=30, that must mean that when x=8 y must equal 40.
6:30 = 8:40
or
30/6= 5
Y/8= 5
Because they vary directly they are equivalent, and so multiply 8 by 5 and get 40.
Answer:40
Step-by-step explanation:
6 times 5 is 30
so 8 times 5 = 40
PLEASE ANSWER QUICK! A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.8. The police officer's estimate is 14. Find the absolute error and the percent error of the police officer's estimate. If necessary, round your answers to the nearest tenth
Answers
Answer:
The absolute error is 0.2
The percent error is 1.45
Step-by-step explanation:
Please kindly check the attached for explanation
The absolute error of the police officer's estimate is 0.2, and the percent error is approximately 1.5%
Explanation:In Mathematics, absolute error is determined by the absolute value of the difference between the estimated value and the actual value. Therefore, the absolute error in this case is |14 - 13.8| = 0.2.
Percent error, on the other hand, is calculated by first finding the absolute error, then dividing the absolute error by the actual measurement, and finally multiplying the result by 100% to turn it into a percentage. So in this case, the percent error is given by (0.2 / 13.8) * 100 = 1.45%. Since we should round it off to the nearest tenths, the percent error will be roughly 1.5%.
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Find the slope of the line through (-9,-10) and (-2,-5).
A. -5/7
B. 7/5
C. 5/7
D.-7/5
Just need help with this thank you.
Answers
Hope this will help u...:)
Look at the attached picture...!!
Find the area of a regular hexagon with an apothem of 15cm
Answers
Final answer:
The area of a regular hexagon with an apothem of 15 cm is approximately 1166.55 cm².
Explanation:
The area of a regular hexagon can be found by using the formula:
Area = (3 x apothem x side length) / 2
In this case, the apothem is given as 15 cm. We need to find the side length to calculate the area. The side length can be found using the formula:
side length = 2 x apothem / tan(180° / 6)
Using a calculator, we can find that the side length is approximately 25.98 cm. Plugging in the values into the area formula, we get:
Area = (3 x 15 cm x 25.98 cm) / 2 = 1166.55 cm²
Given that there are four Cups in a quart and 4 quarts in a gallon which quantity below is equal to 16 quarts?
16 gallons
16 cups
64 cups
126 cups
Answers
Answer:
64 cups
Step-by-step explanation:
16 quarts ; 1 quart = 4 cups ; 16*4=64
Answer:
1 quart = 4 cups
Therefore 16 quarts = 16 * 4 cups or
64 cups.
Step-by-step explanation:
Use Appropriate Tools
1) A group of students were
on a school bus. At the last
stop, the bus picked up 16
more students. The bus
arrived at school with a
total of 25 students. How
many students were on the
bus before the last stop?
Solve this problem any way
you choose.
Answers
Answer:
9
Step-by-step explanation:
just subtract 16 from 25
a child should no longer play in the kid zone area when they reach 4'4" tall joe is 54" tall is he allowed to play in the kid zone area
Answers
Answer: No.
Step-by-step explanation: Joe is 4'6" tall. Convert 54" to feet by dividing by 12. 54/12=4.5. Half of a foot is 6 inches.
Joe is 54 inches tall, which is taller than the kid zone's maximum allowed height of 52 inches (4 feet 4 inches). Therefore, he is not allowed to play in the kid zone area.
To determine if Joe is allowed to play in the kid zone area, we must compare his height to the maximum height allowed for the kid zone. The maximum height for the kid zone is 4 feet 4 inches, which needs to be converted to inches to compare easily with Joe's height.
First, we know that 1 foot equals 12 inches. So, 4 feet is equal to 4 x 12 inches, which is 48 inches. Adding the extra 4 inches from the height limit gives us 48 + 4 inches, which is 52 inches. This is the maximum height allowed for the kid zone.
Since Joe is 54 inches tall, which is greater than the maximum 52 inches, it means he is too tall to play in the kid zone. Therefore, he is not allowed to play there according to the height restriction.
Researchers surveyed one hundred students on
which superpower they would most like to have.
The two-way table below displays data for the
sample of students who responded to the survey.
Superpower Male
Female
TOTAL
Fly
40
Invisibility
-
30
12
10
10
32
6
44
16.
Other
TOTAL
52
48
100
Given that the student chosen was a female, find
the probability that the student chose invisibility
as their superpower.
P (invisibility| female) =
Answers
Answer:
⅔
Step-by-step explanation:
Total females: 48
Female and invisibility: 32
P(invisibility/female) = 32/48
2/3
The probability that a female student chose invisibility as their superpower is 2/3
Probability determines the chance that an event would occur. The chance that an event would occur is between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
In this question, two groups of students were surveyed : male and female. Also, there were three groups of superpowers: fly, indivisibility and others.
The probability of a female student chose indivisibility as superpower = number of female students that chose indivisibility as superpower / number of female students
= 32/48
To simplify, divide both numerator and the denominator by 18
= 2/3
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An aeroplane is flying horizontally, directly towards the city of Melbourne at an altitude of 400 metres. At a given time the pilot views the city lights of Melbourne at an angle of depression of 1.5°. Two minutes later the angle of depression of the city lights is 5°. Find the speed of the aeroplane in km/h, correct to one decimal place.
Please include a diagram
Answers
A diagram and review of the basic trig functions will show that the distance d flown by the plane between observations is
d = 400 cot 1.5° - 400 cot 5° = 10700m = 10.7km
10.7km/2min * 60min/hr = 321 km/hr
Hope this helps
What is the positive solution of x2 – 36 = 5x?
Answers
Answer:
x² - 5x - 36 = 0
(x - 9)(x + 4) = 0
x = 9 is the positive solution.
From the equation, find the axis of symmetry of the parabola.
y = 3x2 - 12x+11
a. x = -2
b. x = 2
c. x = 1
d. x = -1
Answers
Answer:
B. x=2
Step-by-step explanation:
The formula to find the axis of symmetry is -b/2a.
So, in this case, we find our b and a, which are 3 and -12.
Plug them into the formula.
-(-12)/2(3)
The negative sign times another negative makes it into a positive, now we have a positive 12 and then 2 multiplied by 3 equals 6.
Our new equation is 12/6.
Then, simply solve it, 12 divided by 6 equals 2.
Therefore, B would be your answer, x=2.
The axis of symmetry of the parabola defined by the equation y = 3x^2 - 12x + 11 is x = 2.
Explanation:To find the axis of symmetry of the parabola defined by the equation y = 3x2 - 12x + 11,
we can use the formula for the axis of symmetry for a parabola in standard form which is x = -b/2a.
In this equation, a is the coefficient of x2, which is 3, and b is the coefficient of x, which is -12.
Plugging the values into the formula, we get x = -(-12)/(2*3) = 12/6 = 2.
Therefore, the axis of symmetry of the given parabola is x = 2.
Apply the distributive property to factor out the greatest common factor. 24+32p =
Answers
Answer: 8(4p + 3)
Step-by-step explanation: Let's first rewrite this as 32p + 24.
If you're asked to factor a polynomial, the first thing you want to look for is the greatest common factor between the terms that are involved.
So what is the greatest common factor between 32p and 24?
Well if you use a factor tree, you'll figure out that the greatest common factor between 32p and 24 is 8.
What that means is that 2 factors out of this polynomial and what you're left with is each of these terms divided by the number that factors out.
In other words 32p divided by 8 or 4p and 24 divided by 8 which is 3.
So your answer is 8(4p + 3) and that is a factored version of 24 + 32p.
Answer:
8(4p + 3)
Step-by-step explanation:
Sofia makes and sells stuffed toys. She uses special fabric to cover a foam
cube to make a letter block. How much fabric did Sofia use to make
this block?
Answers
Answer:
384 square cm
Step-by-step explanation:
Fabric used will be equal to the total surface of the cubical block.
[tex]fabric \: used \\ = 6 {side}^{2} \\ = 6 \times {8}^{2} \\ = 6 \times 64 \\ = 384 \: {cm}^{2} \\ [/tex]
Simplify the expression Square root of 63
Answers
Answer:
[tex]3\sqrt{7}[/tex]
Step-by-step explanation:
Step 1: Simplify
[tex]\sqrt{63}[/tex]
[tex]\sqrt{3^2 * 7}[/tex]
[tex]3\sqrt{7}[/tex]
Answer: [tex]3\sqrt{7}[/tex]
Answer:
7.94 0r 3 square root of 7
Step-by-step explanation:
The square root of 63 is 7.9372539331937717715048472609178. If you round it to two places it is 7.94. In radical form it is 3 square root of 7.
what is 25x10^9 in standard form
Answers
[tex]25*10^9=25*100000000=2500000000[/tex]
The stem-and-lear plot lists the scores earned
by students on a science test.
Stem | Leaf
40
How many students earned a core of 85 or
greater?
5 57
610
7 00 78
Enter your answer in the box.
8 2 2 2 556
9111455
40
Key: 410 means 40.
Answers
Answer: I'm sure it is 33
Find a number that is not a solution to 3x-1>8 or 7-x>3
Answers
Answer:
All of the numbers are solutions.
Step-by-step explanation:
Step 1: Solve for x in the first equation
[tex]3x - 1 + 1 > 8 + 1[/tex]
[tex]3x / 3 > 9 / 3[/tex]
[tex]x > 3[/tex]
Step 2: Solve for x in the second equation
[tex]7 - x - 7 > 3 - 7[/tex]
[tex]-x / -1 > -4 / -1[/tex]
Since you divided by a negative, you must flip the sign.
[tex]x < 4[/tex]
Step 3: Find the number
x > 3 and x < 4
Answer: All of the numbers are solutions.
Joan has a cafe. Each day, she bakes 24 muffins. She gives away 3 and sells the rest. Each day, she also bakes 36 bagels. she gives away 4 and sells the rest. Write an expression to represent the total number of muffins and bagels Joan sells in 5 days. Then evaluate the expression to find the total amount of muffins and bagels Joan sells in 5 days.
Answers
Answer:
(24+36)×5 First you do whatever is in the parentheses first which would be 60. Next you would multiply it by 5 which is 5 days. It is 500. Joan sells 500 muffins and bagels in a day.
The function f(x) = 2* is translated left 3 units and down 2 units. Which is the equation of the translated function?
g(x) = 2x-3-2
g(x) = 2x -2-3
g(x) = 2x - 2 + 3
g(x) = 2x + 3-2
Answers
Answer:
g(x) = 2^(x+3) -2
Step-by-step explanation:
To translate a function f(x) right h units and up k units, it becomes ...
g(x) = f(x -h) +k
Here, your translation is (h, k) = (-3, -2), so the function becomes ...
g(x) = f(x +3) -2
g(x) = 2^(x+3) -2 . . . . matches the last choice
Answer:
D.
Step-by-step explanation:
Mr abbot mowed1/4 of his lawn .his son mowed 3/7 of it who mowed most of the lawn how much of the lawn still needs to be mowed
Answers
His son mowed 3/7 of the lawn.
The first thing to do is get a common denominator, in this case a good one to use is 28. it has to be a number divisible by 4 and 7.
1/4=7/28
3/7=12/28
so now we can see that the son mowed more. now add these two numbers together to get how much they mowed in total
(7+12)/28=19/28 of the lawn is mowed.
that means 9/28 of the lawn still has to be mowed.
Mr Abbot's son mowed more of the lawn. In total, they mowed 19/28 or approximately 68% of the lawn. Hence, approximately 32% or 9/28 of the lawn still has to be mowed.
Explanation:To find out who mowed more lawn and how much of the lawn is still left to be mowed, we need to compare the fractions and then add them together.
Mr. Abbot mowed 1/4 of his lawn and his son mowed 3/7 of it. To compare these fractions, you can turn them into decimals or percent by dividing the numerator (the top number) by the denominator (the bottom number). Doing that, we find Mr. Abbot mowed 0.25 (or 25%) of the lawn and his son mowed approximately 0.43 (or 43%) of the lawn. Therefore, the son has mowed more lawn.
To figure out how much lawn is still left to be mowed, we add up the fractions of the lawn that Mr. Abbot and his son mowed: [tex]1/4 + 3/7 = 7/28 + 12/28 = 19/28[/tex]. Thus, 19/28 of the lawn have been mowed, and to figure out what fraction is left, we subtract this number from 1 since 1 represents the whole or 100% of the lawn: [tex]1 - 19/28 = 9/28[/tex]. So, 9/28 of the lawn still needs to be mowed.
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