Answer:
10.35 miles per hr
Step-by-step explanation:
first convert ft into mi
then calculate the distance traveled in one min
multiply the answer by 60
then you get the answer
Find a formula for the given polynomial.
In this question, we have to identify the zeros of the polynomial, along with a point, and then we get that the formula for the polynomial is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
------------------------
Equation of a polynomial, according to it's zeros:
Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.
------------------------
Identifying the zeros:
Given the graph, the zeros are the points where the graph crosses the x-axis. In this question, they are:
[tex]x_1 = -2, x_2 = 0, x_3 = 3[/tex]
Thus
[tex]p(x) = a(x - x_{1})(x - x_{2})(x-x_3)[/tex]
[tex]p(x) = a(x - (-2))(x - 0)(x-3)[/tex]
[tex]p(x) = ax(x+2)(x-3)[/tex]
[tex]p(x) = ax(x^2 - x + 6)[/tex]
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
------------------------
Leading coefficient:
Passes through point (2,-8), that is, when [tex]x = 2, y = -8[/tex], which is used to find a. So
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
[tex]-8 = a(2^3 - 2^2 + 6*2)[/tex]
[tex]16a = -8[/tex]
[tex]a = -\frac{8}{16} = -0.5[/tex]
------------------------
Considering the zeros and the leading coefficient, the formula is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
A similar problem is found at https://brainly.com/question/16078990
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Based on the Fundamental Theorem of Algebra, we understand that Polynomials with real Coefficient have at least one real Root and at most a number of Roots equal to its Grade. The Grade is the maximum exponent that Polynomial has and root is a point such that [tex]p(x) = 0[/tex]. By Algebra we understand that polynomial can be represented in this manner known as Factorized form:
[tex]p(x) = \Pi\limits_{i=0}^{n} (x-r_i)[/tex] (1)
Where:
[tex]n[/tex] - Grade of the polynomial.
[tex]i[/tex] - Index of the root binomial.
[tex]x[/tex] - Independent variable.
We notice that polynomials has three roots in [tex]x = -2[/tex], [tex]x = 0[/tex] and [tex]x = 3[/tex], having the following construction:
[tex]p(x) =(x+2)\cdot x \cdot (x-3)[/tex]
[tex]p(x) = (x^{2}+2\cdot x)\cdot (x-3)[/tex]
[tex]p(x) = x^{3}+2\cdot x^{2}-3\cdot x^{2}-6\cdot x[/tex]
[tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex]
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Here is a question related to the determination polynomials: https://brainly.com/question/10241002
Subtract.
7x2 - 5x+3
(2x² + 7x-4)
Answer:
7×=14
5×3=15
5+3=8
7×4=28
7-4=3
2×2=4
if add this all will get the answer as 72
if we will subtraction answer will be as -44
Step-by-step explanation:
so we will get the answer asaddition = 72
subtraction= -44
so this is the answerplease give me points
Find the sum of the arithmetic series given ai = 45, an = 85, and n = 5.
Answer:
C. 325.
Step-by-step explanation:
The last term a5 = 85
a1 = 45
Sum of n terms = n/2 (a1 + l)
So here we have n = 5, a1 = 45 and the last term l = 85
= (5/2)(45 + 85)
= 5/2 * 130
= 325.
The required sum of the arithmetic series is 325.
Arithmetic series is defined as a sequence of numbers arranged in a particular pattern.
The sum of the nth term of an arithmetic sequence is expressed as:
[tex]S_n = \frac{n}{2}[a+l]\\[/tex] where:
n is the number of terms
a is the first term
l is the last term
Given the following
a = 45
n = 5
an = l = 85
Substitute the given values in the formula above:
[tex]S_5= \frac{5}{2}(45+85)\\ S_5=\frac{5}{2}(130)\\ S_5=5 \times 65\\S_5=325[/tex]
Hence the sum of the arithmetic series is 325
Learn more here: https://brainly.com/question/21473794
Find the equation of the tangent line at the point (0,1) of the graph of the function f(x) = x^3 - 2x + 1 ?
9514 1404 393
Answer:
y = -2x +1
Step-by-step explanation:
The derivative of the function is ...
f'(x) = 3x^2 -2
so the slope at x=0 is f'(0) = -2. In slope-intercept form, the equation of the tangent line is ...
y = -2x +1
The quadrilaterals JKLM and PQRS are similar. Find the length x of SP
Answer:
4.8
Step-by-step explanation:
The scale factor is (3.6)/3=1.2. Hence x/4=1.2, x=4.8
Solve for X
(Ignore the math I did on top)
Find the measure of the missing angles.
Answer:
e- 77
d- 52
f- 51
Step-by-step explanation:
Step-by-step explanation:
d=52° (,vertically opposite angle)
77+52+f=180 (linear pair)
f=180- 129
f=51°
52+51+e=180
e=180- 103
e=77°
prove that tan² theta + cot² theta = sec² theta cosec² theta- 2
Step-by-step explanation:
Tan² theta = sec² theta - 1
Cot² theta = cosec² theta - 1
Tan²+Cot² = sec²-1+cosec²-1
= sec²+cosec²-2
Please find attached herewith the solution of your question.
If you have any doubt, please comment.
if f(n) = 6-2n, find f(-1)
Answer:
8
Step-by-step explanation:
f(n)= 6-2n
f(-1) = 6- 2(-1)
= 6+2
=8
Write each as a decimal round to the thousands place 44%
Answer:
44 as a decimal is 0.44 and you can multiply 0.44 by a number to get 44 percent of that number.
HELP !
Find the measure it the given angle.
Answer:
it's 90
Step-by-step explanation:
inscribed angle intercepts a semicircle is always 90
Solve the given differential equation by using an appropriate substitution. The DE is of the form dy/dx = f(Ax + By + C), which is given in (5) of Section 2.5. dy/dx = 4 + (y − 4x + 6)^1/2
dy/dx = 4 + √(y - 4x + 6)
Make a substitution of v(x) = y(x) - 4x + 6, so that dv/dx = dy/dx - 4. Then the DE becomes
dv/dx + 4 = 4 + √v
dv/dx = √v
which is separable as
dv/√v = dx
Integrating both sides gives
2√v = x + C
Get the solution back in terms of y :
2√(y - 4x + 6) = x + C
You can go on to solve for y explicitly if you want.
√(y - 4x + 6) = x/2 + C
y - 4x + 6 = (x/2 + C )²
y = 4x - 6 + (x/2 + C )²
Find the slope and the y-intercept of the line with the given equation.
f(x) = 7 -4/5x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is
(Type an integer or a simplified fraction.)
B. The slope is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The y-intercept is
(Simplify your answer. Type an ordered pair, using integers or fractions.)
B. There is no y-intercept.
Answer:
The slope is -4/5
The y intercept is (0,7)
Step-by-step explanation:
f(x) = 7 -4/5x
Rewriting
y = -4/5x +7
This is in slope intercept form
y = mx+b where m is the slope and x is the y intercept
The slope is -4/5
The y intercept is (0,7)
According to the U.S. National Center for Health Statistics, there is a 98% probability that a
20-year-old male will survive to age 30.
(a) Using statistical software, simulate taking 100 random samples of size 30 from this
population.
(b) Using the results of the simulation, compute the probability that exactly 29 of the 30 males
survive to age 30.
(c) Compute the probability that exactly 29 of the 30 males survive to age 30, using the
binomial probability distribution.
(d) Using the results of the simulation, compute the probability that at most 27 of the 30 males
survive to age 30.
(e) Compute the probability that at most 27 of the 30 males survive to age 30 using the
binomial probability distribution.
(f) Compute the mean number of male survivors in the 100 simulations of the probability
experiment. Is it close to the expected value?
(g) Compute the standard deviation of the number of
male survivors in the 100 simulations of the probability experiment. Compare the result to the
theoretical standard deviation of the probability distribution
Answer:
0.03398 or 3.398%
Step-by-step explanation:
-This is a binomial probability problem.
-Given p=0.24, n=100, the probability that exactly 30 people is calculated as:
Hence, the probability that exactly 30 people have hypertension is 0.03398
Please help! There is 2 questions in this pic! Thank you so much to whoever helps me
Answer:
[tex]{ \sf{thats \: it}}[/tex]
Plz help me find side x and y thanks
Answer:
2sqrt3
Step-by-step explanation:
Since this seems to be a 45, 45, 90 triangle, x and y are the same.
The hypoteneuse is always the side lengths *sqrt2
We divide the hypoteneuse by sqrt 2 and get sqrt12
sqrt12 simplified is 2sqrt3
4. Eric has 54 yards of fencing to use for a flowerbed. Some possible measurements are
shown below. For which flowerbeds does Eric have enough fencing? Color in all the
possible answers.
A.
length = 30 yards
area = 300 square yards
B.
length = 20 yards
width = 5 yards
C.
width = 12 yards
perimeter = 48 yards
D.
length = 26 yards
width = 22 yards
E.
length = 16 yards
width = 14 yards
F.
width = 9 yards
area = 162 square yard
Answer:
B,C,F
Step-by-step explanation:
A=L*W
P=2L+2W
P≤54
for A, 2L is already greater than 60
B works as 2W+2L in this case is 50
C states that perimeter is less than 54
D doesn't work, as 2L+2W=96
E doesn't work, see above, P=60
F, area=W*L
162/9=18
L=18
2L+2W=48, so F works
Answer:
trả lời:
B,C,F
Giải thích từng bước:
A = L * W
P = 2L + 2W
Trang ≤54
đối với A, 2L đã lớn hơn 60
B hoạt động như 2W + 2L trong trường hợp này là 50
C nói rằng chu vi nhỏ hơn 54
D không hoạt động, vì 2L + 2W = 96
E không hoạt động, xem ở trên, P = 60
F, diện tích =W*L
162/9=18
L =18
2L + 2W = 48, vì vậy F hoạt động
Please help!!! what is x: |6n+7|=8
Answer:
-5/2, 1/6
Step-by-step explanation:
|6n+7|=8
6n+7=8
n=1/6
6n+7=-8
n=-5/2
Answer:
[tex]n=-\frac{5}{2}[/tex] and [tex]n=\frac{1}{6}[/tex]
Step-by-step explanation:
There is no x variable present in the question, but if you are asking for the value of n, I can help with that.
The absolute value function always results in a positive number, so that means 6n+7 can equal 8 or negative 8, and the absolute value function takes care of the rest. First, we will solve for 6n + 7 equaling 8.
[tex]6n+7=8[/tex]
Subtracting 7 from both sides gets us
[tex]6n=1[/tex]
Dividing by 6 from both sides is equal to
[tex]n=\frac{1}{6}[/tex]
Now we will solve for 6n + 7 equaling negative 8.
[tex]6n+7=-8[/tex]
Subtracting 7 from both sides is equal to
[tex]6n=-15[/tex]
Dividing by 6 from both sides gets us
[tex]n=-\frac{15}{6}[/tex]
Simplifying, we have
[tex]n=-\frac{5}{2}[/tex]
find the h.c.f of 2⁴×3×5²×7,5²×3²×5
Answer:
To find the HCF we multiply the numbers in the overlapping quadrant together:
Step-by-step explanation:
Help please:)) 2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answer:
a. The radius r = 5.42 cm and the height h = 10.84 cm
b. 553.73 cm²
c. i. Beauty ii. Design
Step-by-step explanation:
a. What would be the optimal dimensions (radius and height) to minimize surface area?
The volume of the standard container is a cylinder and its volume is V = πr²h where r = radius of container and h = height of container.
Since V = 1000 cm³,
1000 cm³ = πr²h (1)
Now, the surface area of a cylinder is A = 2πr² + 2πrh where r and h are the radius and height of the cylinder.
From (1), h = 1000/πr².
Substituting h into A, we have
A = 2πr² + 2πrh
A = 2πr² + 2πr(1000/πr²)
A = 2πr² + 2000/r
To maximize A, we differentiate A with respect to r and equate to zero to find the value of r at which A is maximum.
So, dA/dr = d[2πr² + 2000/r]/dr
dA/dr = d[2πr²]/dr + d[2000/r]/dr
dA/dr = 4πr - 2000/r²
Equating the equation to zero, we have
4πr - 2000/r² = 0
4πr = 2000/r²
r³ = 2000/4π
r = ∛(1000/2π)
r = 10(1/∛(2π))
r = 10(1/∛(6.283))
r = 10/1.8453
r = 5.42 cm
To determine if this value of r gives a minimum for A, we differentiate dA/dr with respect to r.
So, d(dA/dr)/dr = d²A/dr²
= d[4πr - 2000/r²]/dr
= d[4πr]/dr - d[2000/r²]/dr
= 4π + 4000/r³
Substituting r³ = 2000/4π into the equation, we have
d²A/dr² = 4π + 4000/r³ = 4π + 4000/(2000/4π) = 4π + 2 × 4π = 4π + 8π = 12π > 0
Since d²A/dr² = 12π > 0, then r = 5.42 cm gives a minimum for A.
Since h = 1000/πr²
h = 1000/π(5.42)²
h = 1000/92.288
h = 10.84 cm
So, the radius r = 5.42 cm and the height h = 10.84 cm
b. What would the surface area be?
Since the surface area, A = 2πr² + 2πrh
Substituting the values of r and h into A, we have
A = 2πr² + 2πrh
A = 2πr(r + h)
A = 2π5.42(5.42 + 10.84)
A = 10.84π(16.26)
A = 176.2584π
A = 553.73 cm²
c. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
i. Beauty
ii. Design
Does the point (0, 0) satisfy the equation y = 9x?
Answer:
yes it does
Step-by-step explanation:
because the equation y=9x does not have a y-intercept (all slopes come in the form y=mx+b -- it can be written differently though) and since there is no 'b' that means the y-intercept is 0. So whenever there is no y-intercept, the slope starts at 0.
please helpppp.
Which of these could be the graph of F(x) = In x + 3?
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answer:
c
Step-by-step explanation:
Try desmos
Let S be a set of linearly dependent vectors in Rn. Select the best statement. A. The set S could, but does not have to, span Rn. B. The set S spans Rn, as long as no vector in S is a scalar multiple of another vector in the set. C. The set S cannot span Rn. D. The set S must span Rn. E. The set S does not span Rn if some vector in S is a scalar multiple of another vector in the set. F. The set S spans Rn, as long as it does not include the zero vector. G. none of the above
Answer:
The set S could, but does not have to, span Rn ( A )
Step-by-step explanation:
Assume S is a set of linearly dependent vectors in Rn
The best statement from the options is ; The set S could, but does not have to, span Rn
This is because S could span Rn ( as stated in option c ) but will not necessary span Rn ( as seen in option D )
Write 55% as a fraction in simplest form
Answer:
11/20
Step-by-step explanation:
find the greatest number than divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
15 is the greatest number that divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
Let write the factors of each number:
45: (1,3,5,9,15,45)
60:(1,2,3,4,5,6,10,12,15,20,30,60)
75:(1,3,5,15,15,75).
The greatest common factor is 15. So the answer is 15.
Fatima purchased a new mattress when it was on sale. The sale price was 27% less than the regular price. If the sale price was $409, what was the original price? (Round your answer to the nearest dollar).
Answer:
560
Step-by-step explanation:
Let x be the original price
27% off
original price minus discount = new price
x - .27x = new price
.73x = new price
.73x = 409
Divide each side by .73
.73x/.73 = 409/.73
x=560.2739726
To the nearest dollar
x = 560
A person's email for one day contained a total of 78 messages. The number of spam
messages was two less than four times the number of other messages. How many of
the email messages were spam?
Answer:
62 of the email messages were spam
Step-by-step explanation:
Let the number of spam and other messages be s and o respectively.
Total number of messages= 78
s +o= 78 -----(1)
s= 4o -2 -----(2)
Substitute (2) into (1):
4o -2 +o= 78
Simplify:
5o -2= 78
+2 on both sides:
5o= 78 +2
5o= 80
Divide both sides by 5:
o= 80 ÷5
o= 16
Since s +o= 78, s= 78 -o.
s= 78 -16
s= 62
Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below.
A= 1 3 8 2 7 1 3 8 2 7
2 7 20 6 20 --- 0 1 4 2 6
-3 -12 -36 -7 -19 0 0 0 1 4
3 13 40 9 25 0 0 0 0 0
Start 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 2 2nd Column 7 3rd Column 20 4st Column 6 5st Column 20 3rd Row 1st Column negative 3 2nd Column negative 12 3rd Column negative 36 4st Column negative 7 5st Column negative 19 4st Row 1st Column 3 2nd Column 13 3rd Column 40 4st Column 9 5st Column 25 EndTable
tilde
Start 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 0 2nd Column 1 3rd Column 4 4st Column 2 5st Column 6 3rd Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 5st Column 4 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 EndTable
A basis for Col A is given by
StartSet nothing EndSet
(Use a comma to separate vectors as needed.)
The dimension of Col A is
3.
A basis for Nul A is given by
StartSet nothing EndSet
(Use a comma to separate vectors as needed.)
The dimension of Nul A .
Answer:
skip counting by 0
Step-by-step explanation:
skipcount by 0 to get to 100 for the third column.
Answer:
its the first graph
Step-by-step explanation:
I got it right bc im cool like that ig
prove:
sin²A-cos²B=sin²B-cos²A
Step-by-step explanation:
thwashm m GB DC GM 3hka it g feeds ygzdkzyzuzjz indin, mi, hn zbe
Answer:
Solution given:
L.H.S
sin²A-cos²B
we havesin²A=1-cos²A and Cos²B=1-sin²B
nowreplacing value
1-cos²A-(1-sin²B)
open bracket1-cos²A-1+sin²B
keep together like terms1-1+sin²B-Cos²A
=sin²B-Cos²A
R.H.S
proved.If x+7 is an even number, is x+11 an even number or odd number?
Answer:
x + 11 is an even number.
Step-by-step explanation:
Even numbers can only be obtained from the sum of two odd numbers or two even numbers. Since we know that x + 7 is even, x + 11 must be even as well.
