The velocity of the particle, in meters per second is 0.78 m/s
How to determine the velocity of the particle, in meters per second?The position function is given as:
x(t) = e-(t - 3)2
Rewrite properly as
x(t) = e^-(t - 3)^2
Next, we differentiate the above function to determine the velocity function.
Using a graphing calculator, we have:
x'(t) = -2(t - 3) * e^-(t - 3)^2
At t = 2.5 s, we have:
x'(2.5) = -2(2.5 - 3) * e^-(2.5 - 3)^2
Evaluate
x'(2.5) = 0.78
Hence, the velocity of the particle, in meters per second is 0.78 m/s
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Estimate the sum of 12.15,16.85 and1.74 by rounding each number to nearest tenth
The Sum of the given numbers is 30.80.
What do we mean by the sum of numbers?When we add two or more numbers, the result or answer is known as the SUM. Addends are the numbers that are added. In the preceding example, 6 and 4 are addends, and their sum is 10. In other words, the sum of 8 and 5 equals 13, or 8 plus 5 equals 13.SUM:
12.15 + 16.85 + 1.7429 + 1.7430.74Rounding off to nearest tenth = 7 + 1 = 30.80
Therefore, the Sum of the given numbers is 30.80.
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678876590* 34567845678
Answer:
ano yan ang tanong mo
Step-by-step explanation:
ano yan
Quadratic equation whose roots are -6 and -1 with leading coefficient is 1
The quadratic equation whose roots are -6 and -1 with leading coefficient 1 is [tex]x^{2} +7x+6=0[/tex].
Given that a Quadratic equation whose roots are -6 and -1 with leading coefficient is 1 and asked to find the equation of quadratic equation.
Quadratic equation:
The polynomial equations of degree two in one variable of form f(x) = a[tex]x^{2}[/tex] + bx + c = 0 and with a, b, c, ∈ R and a ≠0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x).
For a quadratic equation if (a,b) are roots then,
(x-a)(x-b) is the quadratic equation having roots "a" and "b"
The equation with roots -6 and -1 is
⇒(x+6)(x+1)
⇒[tex]x^{2}[/tex]+7x+6
Threfore,The quadratic equation whose roots are -6 and -1 with leading coefficient 1 is [tex]x^{2} +7x+6=0[/tex].
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Which of the following are equivalent to -5×1/4×3
The equivalent expression of the expression given as: -5 × 1/4 × 3 is -15/4
How to determine the equivalent expression?The expression is given as:
-5 × 1/4 × 3
Multiply -5 and 1/4
So, we have:
-5 × 1/4 × 3 = -5/4 × 3
Multiply -5/4 and 3
So, we have:
-5 × 1/4 × 3 = -15/4
Hence, the equivalent expression of the expression given as: -5 × 1/4 × 3 is -15/4
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ABC, if m CAD = 29°, what is m&CAB?
D
Answer:
Step-by-step explanation:
[tex]m[/tex]∠[tex]CAD[/tex]≅[tex]m[/tex]∠[tex]BAD[/tex]
and
[tex]m[/tex]∠[tex]CAB[/tex]=[tex]m[/tex]∠[tex]CAD[/tex]+[tex]m[/tex]∠[tex]BAD[/tex]
so
[tex]m[/tex]∠[tex]CAB[/tex][tex]= 29[/tex]°+[tex]29[/tex]°
[tex]m[/tex]∠[tex]CAB=58[/tex]°
Hope this helps!
Step-by-step explanation:
the graphic shows that the angle at A is split in half by the line AD (because the angles at both sides of the line are marked as equal, so the whole angle must be 2 times of one of these parts).
so, as CAD = 29°, CAB = 2×CAD = 2×29 = 58°
Please Answer Math 10
Answer:
Hello,
Step-by-step explanation:
[tex]1) \ 4,7,10,13,16,....\\u_n=4+(n-1)*3=1+3n\\\\2)\ -10,-6,-2,2,6....\\u_n=-10+(n-1)*4=-14+4n\\\\3)\ \frac{6}{3} ,\frac{7}{3} ,\frac{8}{3} ,\frac{9}{3} ,\frac{10}{3} ...\\\\u_n=\frac{6}{3} +(n-1)*\frac{1}{3} =\frac{5}{3} +\frac{n}{3} \\[/tex]
Mary’s backyard vegetable garden measures 20 ft by 30 ft, so its area is 20*30=600 ft 2. She decides to make it longer, as shown in the figure, so that the area increases to A=20(30+x). Which property of real numbers tells us that the new area can also be written A=600+20x?
the answer is 60020 I am not sure if it is correct
Answer:
Distributive Property
Step-by-step explanation:
Example of distributive property is: 5 (4 + 7) = 5 × 4 + 5 × 7
ZE and ZF are supplementary. The measure of ZE is 54 more than the
measure of ZF. Find the measures of each angle.
Answer:
43xgfsstib dhibfdhbkfvh
Jaiden earned $84 last week. Peter earned only $12. Jaiden's earnings are how many times greater than Peter's.
Answer:
×7
Step-by-step explanation:
[tex]84 \div 12 = 7[/tex]
Right now, James earns an annual salary of $46,453. He is considering a job offer with an annual salary
of $51,255. What is the difference in the weekly pay for these two jobs, rounded to the nearest cent?
Answer:
$92.35
Step-by-step explanation:
Subtract 46,453 from 51,255 to get 4,802. Now divide that result by 52 to get 92.346. Round that to the nearest cent to get 92.35.
The list below shows the ages (in years) of 10 people riding in a van to a math competition. C
mean age of the people in the van. Round your answer to the nearest tenth of a year.
ages
Mean =
Median =
15
15 14 11 11 14 10 15 39 48
Submit Question
years (Please round your answer to the nearest tenth.)
years (Please enter an exact answer.)
Hint: Textbook Measures of Center
Answer i dont get it
Step-by-step explanation:
Give the rate in miles per hour round to the nearest tenth Rachel jogs 20 feet in three seconds
According to the formula speed = distance / time The rate in miles per hour is 4.54
If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed.
Rachel jogs 20 feet in 3 seconds
then by the formula
speed = distance/time
speed = 20 feet / 3 seconds
speed = 6.666667 feet per hour
but this speed is in feet per seconds to convert the speed from feet per seconds to miles per hour we need to multiply by 0.681818,
speed = 6.66667*0.681818
speed = 4.5454 miles per hour
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Pierre deposits $9,000 in a certificate of deposit that pays 1.4% interest, compounded semi-annually
How much interest does the account earn in the first six months?
What is the balance after six months?
Answer:
Interest = $63
Balance = $2,063
Step-by-step explanation:
Compound Interest Formula
[tex]\boxed{\sf I=P\left(1+\frac{r}{n}\right)^{nt} -P}[/tex]
where:
I = Total interest.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Number of time periods (years) elapsed.Given:
P = $9,000r = 1.4% = 0.014n = 2 (semi-annually)t = 0.5 (half a year)Substitute the given values into the formula and solve for I:
[tex]\implies \sf I=9000\left(1+\dfrac{0.014}{2}\right)^{2 \times 0.5}-9000[/tex]
[tex]\implies \sf I=9000\left(1+0.007\right)^{1}-9000[/tex]
[tex]\implies \sf I=9000\left(1.007\right)-9000[/tex]
[tex]\implies \sf I=9063-9000[/tex]
[tex]\implies \sf I=63[/tex]
Therefore, the account earns $63 interest in the first six months.
The balance after six months is $2,063.
PLEASE HELP GIVING BRAINLIEST
Answer:
y=x+3
Step-by-step explanation:
Find the integers that correspond to the given description. fewer than 28 people Select the correct choice below and fill in the answer box to complete your choice. (Type a whole number.) A. The integers greater than B. The integers less than C. The integers less than or equal to D. The integers greater than or equal to
The Integers which corresponds to the word phrase as given in the task content is; Choice B; The integers less than 28.
Inequality signsIt follows from the task content that the word phrase which is as given in the task content is to be determined.
It is noteworthy to understand the meaning of various signs as follows;
> means more.< means fewer.>= means at least.<= means at most.Hence, since the word phrase; fewer than 28 people represents integers less than 28.
Ultimately, by virtue of the inequality signs and what they represent, fewer than 28 people represents integers less than 28.
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A cylinder with a height of 24 centimeters has a volume of 2, 713 cubic centimeters.
Which is closest to the radius of the cylinder?
A. 3 cm
B. 6 cm
O C. 18 cm
D. 36 cm
Answer:
18 cm Is the Answer To your Question
WILLL MARK BRAINLIEST AND GIVE POINTS Pls solve the check mark problems
Answer: 97. -10<n<8
99. g>=7 or g<0
101. x<5 or x>=6
Step-by-step explanation:
97. -1<9+n<17
-1-9<9-9+n<17-9
-(1+9)<n<17-9
-10<n<8
99. g+5>=12
g+5-5>=12-5
g>=7
g/9 < 0
g<0
g>=7 or g<0
101.
2x<10
x<5
x/2 >=3
x>=6
x<5 or x>=6
Which of the following shows 12 more than a number, written as an algebraic expression?
A: 12 − n
B: 12 + n
C: n − 12
D: 12n
Answer:
the answer is
Step-by-step explanation:
So 12 more than N would be 12 + N.
Answer:
b) 12 + n
Step-by-step explanation:
The statement is,
→ 12 more than a number.
Now equation will be,
→ 12 + n
≈ (or) n + 12
So, option (b) is correct.
If x = −3 and y = −6, what is the value of 3x + 4y + 15?
A: 48
B: 35
C: −18
D: −48
Answer: -18 ==> C
Step-by-step explanation:
x = −3 and y = −6
3x + 4y + 15=
3(-3) + 4(-6) + 15=
-9 + (-24) + 15 =
-9-24+15=
-(9+24)+15=
-33+15=
-(33-15)=-18 ==> C
Answer:
c) -18
Step-by-step explanation:
Given that,
→ x = -3
→ y = -6
Let's solve the problem,
→ 3x + 4y + 15
→ (3 × -3) + (4 × -6) + 15
→ -9 - 24 + 15 = -18
Thus, the solution is -18.
1) Write an absolute value equation that has the given solutions of x= -6 and x=10
2) write an absolute value equation that has the given solutions of x= -10 and x= -5
Answer:
1) [tex]|x-2| = 8[/tex]
2) [tex]|x+7.5|=2.5[/tex]
Step-by-step explanation:
graph the line in the image please
The equation shows that the slope of the line is 3 and the y-intercept is 4 that is the line will pass through the point (0, 4)
Graphing linear equation
The standard linear equation is expressed as y = mx + b where;
m is the slope
b is the y-intercept
Given the linear equation (y-1) = 3(x+3)
Expand
y-1 = 3x + 3
y-3x = 3 + 1
y-3x = 4
y = 3x + 4
The equation shows that the slope of the line is 3 and the y-intercept is 4 that is the line will pass through the point (0, 4)
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Form a polynomial whose zeros and degree are given Zeros: -2, multiplicity 1; 3, multiplicity 2; degrees 3
The polynomial of 3rd degree whose zeros and degree are given as for zero of (-2), multiplicity 1 and for zero of (3), multiplicity 2 is [tex]f(x)=(x^{3}-10x^{2} -15x+18)[/tex]
As per the question statement, a 3rd degree polynomial has a zero of (-2), multiplicity 1 and another zero of (3), multiplicity 2.
We are required to determine the polynomial.
Since, (-2) is a zero of the polynomial, then [tex][x-(-2)]=(x+2)[/tex] will be a factor of the polynomial. And since for zero of (-2), multiplicity is 1, this means that the factor of (x + 2) is only multiplied once.
Similarly, as (3) is another zero of the polynomial, then [tex](x-3)[/tex] will be a factor of the polynomial. And since for zero of (3), multiplicity is 2, this means that the factor of (x - 3) will be multiplied twice, i.e., [tex](x-3)^{2}[/tex].
Therefore, our function, say, f(x) will be [tex](x+2)(x-3)^2[/tex]
[tex]or, f(x) = (x+2)(x-3)^2\\or, f(x) = (x + 2)(x^{2} +9-12x)\\or,f(x) =x^{3}+9x-12x^{2} +2x^{2} +18-24x\\ or, f(x)=x^{3}+(2x^{2}-12x^{2})+(9x-24x)+18\\or, f(x)=(x^{3}-10x^{2} -15x+18)[/tex]
Hence, our required polynomial is [tex]f(x)=(x^{3}-10x^{2} -15x+18)[/tex]
Polynomial: A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)Degree of a Polynomial: The highest value of power of the variable of a polynomial is known as the degree of the polynomial.Zero of a Polynomial: The value of the variable for which, the polynomial or equation equates to zero, is known as Zero of the Polynomial.To learn more about Polynomials, Degrees and Zeroes, click on the link below.
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20. Bernadette is a bus driver for the local transit authority, and she earns a regula
hourly wage of $17.08. She receives overtime pay, at 1.5 times her regular hourly
wage, for any hours more than 40 hours that she works in a week. This week,
Bernadette will work 48 hours. What will be her weekly gross pay?
The weekly gross pay will be $2732.80.
How to calculate the gross pay?Based on the information, the extra hours that was spent will be:
= 48 - 40 = 8 hours
Therefore, the gross pay will be;
= ($17.08 × 40) + (8 × $17.08 × 1.5)
= $683.20 + $2049.6
= $2732.80
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Figure F is a scale image of figure E as shown. Enter the scale factor applied to figure E to produce figure F.
Step-by-step explanation:
that means that there is one scale factor for all sides of the triangles.
so,
2 × f = 14
f = 14/2 = 7
and to control, this has to work also for the other given side :
3 × 7 = 21
correct.
so, the scaling factor to get from E to F is 7.
Help me pls with this! :)
Answer: 48 red beads
Step-by-step explanation:
3 red beads: 1 bracelet
16 bracelets * 3 read beads/1 bracelet=
16*3/1=
16*3=48 red beads
I need to know
m 1=
m 2=
Answer:
angle 1 = 51
angle 2 = 39
Step-by-step explanation:
The sum of two angles is equal to 90° since they are complementary angles
angle 1 + angle 2 = 90° rewrite equation using given values
x + 38 + 3x = 90 add like terms
4x + 38 = 90 subtract 38 from both sides
4x = 52 divide both sides by 4
x = 13 now to find the measure of each angle replace x with 13
angle 1 = 51
angle 2 = 39
What is the y intercept?
Answer:
0=y
Step-by-step explanation:
Answer: -3
Step-by-step explanation:
The y-intercept is the place where the line crosses the y-axis, the vertical line in the middle of the graph.
what is the solution to |2x-8|<6 ?
Answer:
1 < x < 7
Step-by-step explanation:
Hello!
There are two cases for this equation:
2x - 8 < 62x - 8 > -6Solve for x in each case.
Solve for x2x - 8 < 6The solution set is 1 < x < 7.
Can someone help me please
Answer: U'=(8, 5)
V'=(7, 5)
W'=(6, 10)
Step-by-step explanation:
When rotated around the origin by 180 degrees, the triangle will have all its coordinates' x and y values negated.
U=(-8, -5) ==> U'=(8, 5)
V=(-7, -5) ==> V'=(7, 5)
U=(-6, -10) ==> W'=(6, 10)
x/6 - 7 = -4 helpppppppp
Answer:
x = 18
Step-by-step explanation:
x/6 - 7 = -4
x/6 = -4 + 7
x/6 = 3
x = 6*3
x = 18
Check:
18/6 - 7 = -4
3 - 7 = -4