The velocity of the car is the rate of change of distance over time.
The car comes to a complete stop at 12 seconds
The velocity function is given as:
[tex]\mathbf{V(t) = 0.5t^2 - 8t + 24}[/tex]
When the car comes to a complete stop, V(t) = 0.
So, we have:
[tex]\mathbf{0.5t^2 - 8t + 24 = 0}[/tex]
Expand
[tex]\mathbf{0.5t^2 - 6t - 2t + 24 = 0}[/tex]
Factorize
[tex]\mathbf{0.5t(t - 12) - 2(t - 12) = 0}[/tex]
Factor out t - 12
[tex]\mathbf{(0.5t - 2)(t - 12) = 0}[/tex]
Split
[tex]\mathbf{(0.5t - 2) =0\ or\ (t - 12) = 0}[/tex]
Solve for t
[tex]\mathbf{0.5t =2\ or\ t = 12}[/tex]
This gives
[tex]\mathbf{t =4\ or\ t = 12}[/tex]
12 > 4.
Hence, the car comes to a complete stop at 12 seconds
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Gina Wilson all things algebra unit 4 homework 3 questions 12-15
Step-by-step explanation:
the essential thing to remember here (and please, burn this into your brain for life) : the sum of all angles in a triangle is always (really always) 180 degrees.
therefore, in 12 and 13 we only need to add all 3 angles, and their sum must be 180.
from there we get really all 4 answers.
the next thing to consider is when a triangle had two equal angles, then it is an isoceles triangle (the 2 sides leading away from these 2 angles are equally long). that gives us the answers for 14 and 15.
12.
3x + 18 + 7x - 58 + 2x - 8 = 180
12x - 48 = 180
12x = 228
x = 19
angle A = 3x+18 = 3×19 + 18 = 57+18 = 75 degrees
angle B = 7x-58 = 7×19 - 58 = 133-58 = 75 degrees
angle C = 2x-8 = 2×19 - 8 = 38 - 8 = 30 degrees
13.
8x - 17 + 19x + 4 + 5x + 1 = 180
32x - 12 = 180
32x = 192
x = 6
angle Q = 8x-17 = 8×6 - 17 = 48-17 = 31 degrees
angle R = 19x+4 = 19×6 + 4 = 114+4 = 118 degrees
angle S = 5x+1 = 5×6 + 1 = 30+1 = 31 degrees
14.
KL = 9x - 14
LM = 7x - 37
KM = 3x + 23
angle K = angle L
so, the sides LM and KM must be equally long. that gives us
7x - 37 = 3x + 23
4x = 60
x = 15
KL = 9x-14 = 9×15 - 14 = 135-14 = 121
LM = 7x-37 = 7×15 - 37 = 105-37 = 68
KM = 3x+23 = 3×15 + 23 = 45+23 = 68
15.
XY = 13x - 21
YZ = 8x - 6
XZ = x + 4
angle X = angle Z
so, the sides XY and ZY (or YZ) must be equally long. that gives us
13x - 21 = 8x - 6
5x = 15
x = 3
XY = 13x-21 = 13×3 - 21 = 39-21 = 18
YZ = 8x-6 = 8×3 - 6 = 24-6 = 18
XZ = x + 4 = 3+4 = 7
A coach purchased a soccer ball for each of his 18 players. If each soccer ball cost $12.99, how much did the coach spend before sales tax was added?
Answer:
$233.82
Step-by-step explanation:
$12.99 a ball times 18 players (12.99x18) equals 233.82$
Suppose that there are 500 students in the school about how many of them study between 4.2 and 5.8
{1, 2, 3, 4, 5, ..., 198, 199, 200}
How many members of the set shown above are multiples of 6 but not a multiple of 9?
(I need a faster way of doing this question. Not listing the factors of 6 and 9 one by one.)
Thank you so much. I will give brainliest!!!
Answer:
22
Step-by-step explanation:
The least common multiple of 6 and 9 is 18. Consider a group of 18 numbers, 1–18, for example. The multiples of 6 are 6, 12, and 18, of which two are not multiples of 9.
There are 11 groups of 18 numbers in 1–200, with 2 left over. That means there will be 11×2 = 22 numbers that are multiples of 6 but not 9.
__
200/18 = 11 remainder 2
Khaled is preparing to paint his room. If it would take three workers 8 hours to apply two coats of
paint, how long would it take four workers to apply one coat of paint?
Answer:
20 minutes
Step-by-step explanation:
hope it helps u
plzz plzz plzz mark as brainliest
Answer: 3 hours
Step-by-step explanation:
To solve this problem, utilize something called the unit rate.
Because it takes three workers(x) 8 hours to apply two coats of paint, simply write: x/3 = 8 ÷ 2.
x/3 = 4
x = 4 * 3
x = 12
Thus, it takes one worker 12 hours, or 720 minutes to apply one coat of paint. Thus, because the number of workers is multiplied by 4, divide the time spent by 4, to get 3 hours, or 180 minutes.
Hope it helps :) and let me know if you want me to elaborate.
N.B. This is an inverse relationship, as when the number of workers increases, the amount of time decreases.
Kate bought 5 pounds of hamburger and 2 pounds of hotdogs and paid $28.50. Eric bought half the amount of hamburger and a fourth of the amount of hotdogs that Kate did and paid $12.50. Find the cost per pound of hamburgers and hotdogs.
This is a system of equations
Answer:
hamburgers - $4.30 hotdogs- $3.50
The required cost of a hamburger and a hotdog is $4.3 and $3.5 respectively.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
here,
Let the cost of the hamburger be x and the cost of hotdogs be y.
According to the quesiton,
5x + 2y = 28.50 - - - - (1)
5x /2 + 2y / 4 = 12.50
10x + 2y = 50 - - - -(2)
From equation 1 and 2
5x = 21.5
X = $4.3
Now,
5×4.3 + 2y = 28.50
y = 7 / 2
y = $3.5
Thus, the required cost of hamburgers and hotdogs is $4.3 and $3.5 respectively.
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y = -7x - 21
What is the slope of this equation and what is the Y intercept.
Answer:
Slope is -7
Y intercept = -21
Step-by-step explanation:
The equation is Y=mx+b
M is the slope so -7 would equal the slope
B is where your Y- intercept already is so that would equal -21
WHAT IS THE AREA OF THE FIGURE BELOW? 8 units. 9 units. 10 units. 12 units.
Sorry, I can't upload the picture so If you know the answer you can tell me.
Answer:
8
Step-by-step explanation: 6 (half the perimeter). By truial and error, 2 units by 4 units.
Find the quotient. 1,329 ÷ 4
Answer:
Quotient is basically division.
Step-by-step explanation:
1329/4 is basically
332.25 is the answer
Which statement describes the end behavior of the exponential equation y = 3^x?
A as x -> - ♾ , y -> - ♾
B as x -> - ♾ , y -> 0
C as x - > ♾ , y -> - ♾
Combine Like Terms:
7X + 3M - 2(2X + 8) + 24 + 8M - X
so hard
Answer:
11M + 2X + 8
Step-by-step explanation:
Hope this helps!! :))
Answer:
11M + 2x + 8
I did the math
it rights tho
2x+5+2x+3x in One sloution, and no solution.
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A store has 120 customers in 6 hours. what is the unit rate in cumstomers per hour?
6.
Write an equation you can solve to answer each problem.
Solve each equation.
a) Ruby has 27 pages of stamps in her collection.
Zachary has 8 fewer pages than Ruby.
How many pages of stamps does Zachary have?
b) Nemo has 3 times as many DVDs as Ashley.
Ashley has 16 DVDs.
How many DVDs does Nemo have?
c) Adrian walked 19 km less than Sheba.
Sheba walked 35 km.
How far did Adrian walk?
Answer:
a) 27 - 8= 19 pages of stamps
b) 16 × 3 = 48 DVDs
c) 35km - 19km = 16km
Two trains, Train A and Train B, weigh a total of 557 tons. Train A is heavier than Train B. The difference of their weights is 371 tons. What is the weight of each train?
Answer:
A=464
B=93
Step-by-step explanation:
A+B=557
A-B=371
Solving the two equations simultaneously gives A=464 and B=93
Find the value of 'y' if 27^y = 9/3^y.
Help me please..
Answer:
y = 1/2.
Step-by-step explanation:
Note that 27 = 3^3 and 9 = 3^2:
27^y
= (3^3)^y
= 3^3y.
9/3^y
= 3^2/3^y
= 3^(2-y)
So 3^3y = 3^(2-y)
and therefore:
3y = 2 - y
4y = 2
y = 1/2.
Given that:
27^y = 9/3^y
⇛27^y × 3^y = 9
⇛(3^3)^y × 3^y = 9
⇛3^3y × 3^y = 9 [°.° (a^m)^n = a^mn]
⇛3^(3y+y) = 9 [°.° a^m×a^n = a^m+n]
⇛3^(4y) = 9
⇛3^(4y) = 3^2 [Bases equal ⇛exponents to equal]
.°. 4y = 2
y = 2:4 = 1/2
Hence, the value of y is 1/2.
A rhombus is a special parallelogram. Which are true about a rhombus that is not true about all parallelograms? Pick up to 3 answers. A. Diagonals create a right angle where they interesect B. All sides are congruent C. Diagonals bisect vertex angles D. Diagonals are congruent E. Opposite angles are congruent
The statement that is true about a rhombus that is not true about all parallelograms are as follows;
Diagonals create a right angle where they intersect All sides are congruent Diagonals bisect vertex anglesDiagonals of a rhombus are perpendicular bisector of each other. This means they form a right angle where they intersect.
This is not true for parallelograms. The diagonal only bisects each other.
All sides are congruent for a rhombus .
This is not true for a parallelogram. Only opposite sides are congruent for a parallelogram.
The diagonal bisect the vertex angles of the rhombus.
This is not true for a parallelogram.
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plz answer this 20 points
35,000 is invested at 5% compound interest.What is the interest at the end of three years
Answer:
$40,516.86
Step-by-step explanation:
start by taking 35,000 and multiplying it by 0.05 to get 5% of the number. then add that number (1,750) to the original 35,000 and you should get 36,750. this would be the first year. Then multiply 36,750 by 0.05 again and add that number (1837.5) to the original 36,750 and you should get 38,587.5. Finally multiply that by 0.05 and add that number (1,929.375) to the original 38,587.5 and you should get 40516.875. Round to the hundredths since it is money.
the store marked up the shirt by 20% the original shirt cost $40 how much does the new shirt cost
Answer:
48
Step-by-step explanation:
First find the amount of the markup
40 * 20%
40 *.2
8
Add this to the original price
40+8 = 48
PLS HELP WILL MARK BRANLIEST ! NO FAKE ANSWERS!!!
Combined Area Expression:
(36 + x - 2 + x - 2)(20 + x - 2 + x - 2) = (32 + 2x)(16 + 2x)
= 4(16 + x)(8 + x)
Area:
4(16 + 5)(8 + 5) = 4 * 21 * 13
= 1092 m^2
Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Use the ranges listed in the table:
Range Number of Values
1 – 5
6 – 10
11 – 15
16 – 20
21 – 25
What value should be placed in the second column for the range 11 – 15?
A: 4, B: 3, C: 5, D: 6
3
5
6
Answer:
4
Step-by-step explanation:
Which component is missing from the researcher’s process?
A.
B.
C.
D.
Answer:
It is B I believe, if not it's you're fault for not putting the choices...
Brandie lives on the twelfth floor of her apartment building. She walks down 2 flights to visit a friend, then up 3 flights to
deliver a message to a neighbor. Which integer best represents the number of flights Brandie must walk to get back to
her starting point?
0-12
O-1
05
7
Mark this and return
Save and Exit
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Submit
Last year at a certain high school, there were 60 boys on the honor roll and 100 girls on the honor roll. This year, the number of boys on the honor roll increased by 10% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
19.3%
Step-by-step explanation:
There were 10% * 60 = 6 more boys, and 25% * 100 = 25 more girls, so in total 31 more students got on the honor roll. From 160 to 191, the percentage is 31/160 = 0.19375
0.19375 = 19.3%
plz help look at the pic below
Answer:
You can use the exponential rule where
[tex](n^x)^y=n^{xy}[/tex]
Therefore,
[tex](a^3)^{-2}=a^{3*(-2)}=a^{-6}[/tex]
[tex]\\ \rm\leadsto (a^3)^{-2}[/tex]
(a^m)^n=a^mn[tex]\\ \rm\leadsto a^{-6}[/tex]
[tex]\\ \rm\leadsto \dfrac{1}{a^6}[/tex]
Which equation can be simplified to find the inverse of y = 2x2?
1/y=2x^2
y=1/2x^2
-y=1/2x^2
x=2y^2
Answer:
D. x = 2y²Step-by-step explanation:
The step in working out the inverse is to swap over the variables.
If we apply same to given equation, we'll have:
y = 2x² → x = 2y²It gives us the option D
Answer:
Option D
Step-by-step explanation:
y=2x²Interchange x and y
x=2y²Hence option D is correct
y²=x/2y=√x/22. If triangle ABC is congruent to triangle DEF by SAS, AB=DE,
Answer:
I can't Respond since I have no picture to help you or me
Step-by-step explanation:
Without the Picture I can't determine if the triangle ABC is congruent to triangle DEF by SAS, AB=DE
A truck rental is $25 plus $.30/mi. Find out how many miles Ken traveled if his bill was $50.20.
Lets start by finding the equation.
25 is the constant, .3 is the slope, and 50.2 is the final.
This means that our equation is:
50.2 = .3x + 25
50.2 - 25 = .3x
25.2 = .3x
25.2 / .3 = x
84 = x
This means that Ken travelled 84 miles if his bill was $50.2.
I hope this helps! :)
The Smiths spend 6% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $2,880 on entertainment. What was their total budget last year?
Answer:
Total budget this year = $ 2000 more than last year. Let x = Budget for this year. Money on entertainment = 0.06x = 2760. ⇒ Budget for this ...
Step-by-step explanation: