So, how far is the car from where it was at t = 0 is 40 m
Velocity of the carSince the location x of the car in meters is given by the function x = 30t - 5t² where t is in seconds, we need to find the time at which its velocity is 10 m/s in the negative direction by differentiating x with respect to t to find its velocity, v.
So, v = dx/dt
= d(30t - 5t²)/dt
= d30t/dt - d5t²/dt
= 30 - 10t
When v is 10 m/s in the negative direction, v = -10 m/s.
So, v = 30 - 10t
-10 = 30 - 10t
-10 - 30 = -10t
-40 = -10t
t = -40/-10
t = 4 s
The distance at 4 s when its velocity is -10 m/s
Since at t = 4 s, its velocity is -10 m/s and x = 30t - 5t² is the car's location. The car's distance from t = 0 after its velocity is -10 m/s is
x(4) - x(0) = 30(4) - 5(4)² - [30(0) - 5(0)²]
= 120 - 5(16) - [0 - 0]
= 120 - 80 - 0
= 40 m
So, how far is the car from where it was at t = 0 is 40 m
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At a certain college, there were 700 science majors, 300 engineering majors, and 500 business majors. If one student was selected at random, the probability that the student is an engineering major is
Answer:
300/1500, 1/5, or 20%
Step-by-step explanation:
There are 1500 students total, but only 300 engineering students. We can represent this as a fraction: 300/1500. When reduced it comes out to 20%.
Using PEMDAS
1.) 10 - 8 ÷ 4 + (7 - 2)
2.) 3² + 2 (6) - 3
2.) 18
P - arenthesisE - xponents M - ultiplication D - ivisionA - ddition S - ubtractionSOLUTION1:10 - 8 ÷ 4 + (7 - 2)10 - 8 ÷ 4 + 510 - 2 + 58 + 513SOLUTION2:3² + 2 (6) - 39 + 2 (6) - 39 + 12 - 321 - 318#LearningWithMath
If WX is tangent to circle y, find wx
that statement is very true
Which of the following functions is graphed below?
Answer:
y=x+6+3 it's d or c it's really hard
write a pair of equivalent fractions for 2/5?.
Step-by-step explanation:
4/10
6/15
8/20
10/25
these were some
Find the slope and the y-intercept of the graph of the linear equation.
y = 4x-7
The slope is (Answer here)
and the y-intercept is (Answer here)
Answer:
The slope is 8.000/2.000 = 4.000
The y-intercept is -7/1 = -7.00000
Step-by-step explanation:
^^
Find the area of the figure
Step-by-step explanation:
To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
Find the slope of the line through the pair of points: ( − 3 , 4 ) and ( 0 , 2 ) .
Answer:
[tex]-\frac{2}{3}.[/tex]
Step-by-step explanation:
1) the required slope can be calculated if to use the ratio:
slope=(y(B)-y(A))/(x(B)-x(A)), where x(A)=-3; y(A)=4; x(B)=0 and y(B)=2;
2) according to the formula above:
s=(2-4)/(0+3)=-2/3.
The slope of the line through the given points is: -2/3.
What is the Slope of a Line?Slope of a line= change in y / change in x = rise/run.
Given the points:
(-3, 4) = (x1, y1)
(0, 2) = (x2, y2)
Slope = (4 - 2)/(-3 - 0)
Slope = 2/-3
Slope of the line = -2/3
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8-109. Solve each equation.
.
a. 6x+12=-x-2
Answer:
x = -2
Step-by-step explanation:
6x+12 = -x-2
7x+12 = -2(bring x to the left)
7x = -14(bring constants to the right)
x = -2
Karl is putting a frame around a rectangular photograph. The photograph is 12 inches long and 10 inches wide, and the frame is the same width all the way around. What will be the area of the framed photograph?
guys please help......................................................
Answer:
angles A+ 100 + B are supplementry and add up to 180 degress. Angle A and 20 degree angle are congruent, so angle A is 20 degrees. Angle B and 60 degrees are congruent so B is 60 degrees. Angle C and 100 degrees are congruent so C is 100 degrees.
Step-by-step explanation:
Question 6 of 10
f(x) = 5x + 1) – 3
g(x) = 4
Find (f - g)(x).
Answer:
Answer:
5x + 6
Step-by-step explanation:
(f-g)(x) is nothing but f(x) - g(x)
f(x) is |5x + 1| - 3 and g(x) is 4 so the equation is [|5x+1| - 3] - [4]
Once this is solved, the answer is 5x - 6. Since there's absolute value, remove the negative and change it to a positive to get the answer 5x + 6.
At the market, I can buy 12 avocados for $18.00. What is the unit cost of an avocado?
Answer:
1.5$
Step-by-step explanation:
if you divide 18 by 12 you get 1.5 meaning each avacado is 1.5$ incase of more explanation\simple explanation: 1.5+1.5+1.5+1.5+1.5+1.5+1.5+1.5=12$
Answer:
$18.00./12 avocados gives the right answer
Each marble bag sold by Sam’s marble company contains 4 orange marbles for every 7 green marbles if a bag 20 orange marbles how many green marbles does it contain
Utilize graphing to find the solution to
the following system of equations.
y = 2x + 1 AND y = x - 3
(-4, [?])
What’s the answer that goes in the green box picture below:
How many years it will take to double your money if your
beginning balance is $1,000.00 and earns 10% interest
compounded quarterly?
Answer:
Step-by-step explanation:
The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.
(2x – 4) and ( 5x²-2x+6)
Answer:
2(x-2)(5x^2+4)
maybe i am wrong sorry if i am
I need help with a word problem
Answer:
what is it.Step-by-step explanation:
I NEED A QUESTION THEN , I WILL ANSWER IT.BRAINLIEST PLEASE.What is the scale factor the smaller rectangle to the larger rectangle?
A
6
B
2
C
48
D
1/2
Answer:
scale factor is larger larger length over the smaller length.
[tex]\[\Boxed\]\ \space\ Hello mathematicians[/tex]
Find the perimeter and the area of a circle when radius is 10 cm.
Note:
✯ No spam
✯ No short answers
Answer:
Step-by-step explanation:
Using 3.14 as pi.
Perimeter of a circle = 2*pi*radius
= 2*3.14*10
= 62.8 cm
Area of a circle = pi*radius*radius
= 3.14*10*10
= 314 cm^2
Solution:
Formulas to remember:
Circumference of circle = 2πr (r = radius)Area of circle = πr² (r = radius)Finding the circumference of the circle:
Circumference of circle = 2πr=> Circumference of circle = 2 x 22/7 x 10=> Circumference of circle = 44/7 x 10=> Circumference of circle = 440/7 ≈ 62.86 cmFinding the area of the circle:
πr² = Area of circle=> 22/7 x 10 x 10 = Area of circle=> 22/7 x 100 = Area of circle=> Area of circle = 2200/7 cm² ≈ 314.29 cm²please help fast!!!!!!!!!!!!!
Answer:
a. 6+y b. 5- (10x c)
C. 14 +(6 x c) d. x +y=18 f. x - 12 = 7
Step-by-step explanation:
6) 10 ft is what percent of 135.8 ft?
Answer: 7.364%...............
Answer:
Step-by-step explanation:
small amount = 10
Large amount = 135.8
% = (small amount / large amount ) * 100
% = (10 / 135.8) * 100
% = 0.0736* 100
% = 7.36%
12. Find all x- and y-intercepts, state the multiplicity of each zero and tell if the graph crosses or
bounces, and state the end behavior Then graph each polynomial by hand,
P(x)=x^2(x-3)^2(x+2)
P(x)=x^4-4x^2
Step-by-step explanation:
12a. To
find x intercepts, set each factor equal to zero
[tex] {x}^{2} = 0[/tex]
[tex]x = 0[/tex]
[tex](x - 3) {}^{2} = 0[/tex]
[tex]x = 3[/tex]
[tex]x + 2 = 0[/tex]
[tex]x = - 2[/tex]
So the x intercepts are( 0,-2,3.)
The multiplicity of 0 and 3 is 2,
The multiplicity of -2 is 1.
The y intercepts are
[tex]0 {}^{2} (0 - 3) {}^{2} (0 + 2) = 0[/tex]
The y intercept is 0.
End Behavior: Since this is a positve 5th root function, as x increases, f(x) increases while as x decreases, f(x) decreases.
The First picture shows the graph of the function. Notice ried the zeroes that have a multiplicity of 2 have a parabolic reflection after thre function reaches their zero.
The zero that have a multiplicity of 1 have just passes through the graph.
12b. We have
[tex] {x}^{4} - 4 {x}^{2} [/tex]
We can easily find y intercept, which is 0.
To find x intercept,
Factor
[tex] {x}^{2} ( {x}^{2} - 4)[/tex]
[tex] {x}^{2} (x + 2)(x - 2) = 0[/tex]
[tex]x = 0[/tex]
[tex]x = 2[/tex]
[tex]x = - 2[/tex]
So the x intercepts are (0,2,-2).
The multiplicity of 0 is 2 while 2 and -2 is 1.
End Behavior: Since this is a positve quartic function, as x increases or decreases , f(x) increases
Look at the second graph,
Answer:
[tex]P(x)=x^2(x-3)^2(x+2)[/tex]
y-intercept is when x = 0:
[tex]\implies P(0)=0^2(0-3)^2(0+2)=0[/tex]
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
[tex]\implies x^2(x-3)^2(x+2)=0[/tex]
[tex]\implies x^2=0\implies x=0[/tex]
[tex]\implies (x-3)^2=0\implies x=3[/tex]
[tex]\implies (x+2)=0\implies x=-2[/tex]
Therefore, x-intercepts are:
(0, 0) with multiplicity 2 → bounces(3, 0) with multiplicity 2 → bounces(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is odd,
[tex]P(x) \rightarrow - \infty \textsf{ as }x\rightarrow - \infty[/tex]
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty[/tex]
-------------------------------------------------------------------------------
[tex]P(x)=x^4-4x^2[/tex]
y-intercept is when x = 0:
[tex]\implies P(0)=(0)^4-4(0)^2=0[/tex]
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
[tex]\implies x^4-4x^2=0[/tex]
[tex]\implies x^2(x^2-4)=0[/tex]
[tex]\implies x^2(x-2)(x+2)=0[/tex]
[tex]\implies x^2=0 \implies x=0[/tex]
[tex]\implies (x-2)=0 \implies x=2[/tex]
[tex]\implies (x+2)=0 \implies x=-2[/tex]
Therefore, x-intercepts are:
(0, 0) with multiplicity 1 → crosses x-axis(2, 0) with multiplicity 1 → crosses x-axis(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is even,
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow - \infty[/tex]
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty[/tex]
Find the surface area of this net.
Answer:
B
Step-by-step explanation:
pls mark me as brainest
Matt is carpeting his bedroom. The room measures 12 feet by 14 feet. If carpet costs $2.29 per square foot, then how much will Matt spend to carpet his bedroom?
6. From a 5-pound bag of flour, Maura used 2 3/16 pounds to bake
cakes. Find the weight of the flour left in the bag.
You purchase a car for $36,000. Five years later, the car is worth $28,500. a. By how much is the car decreasing in value per year?
Answer:
1,440
Step-by-step explanation:
that is how much your car decreasing
hope it helps
Blake is saving up to buy a
new pair of headphones. He
has $20 saved already, and
he earns $ 10 for every lawn
he mows. How many lawns will
he have to mow to have at
least $90 saved?
Answer: He will need to mow 7 lawns.
Step-by-step explanation:
He already has $20
90-20=70
70/10=7
How do I find the ordered pair with an x-value of 2, for the equation f(x)=4x-1? What is the ordered pair? urgent please
Step-by-step explanation:
f(2)=4(2)-1 = 7
the ordered pair is (4,7)
7/6 - 1/4 - 1/2 = ? What is the answer
Answer:
0.41666666666 is the correct answer