Answer:
36
Step-by-step explanation:
Hello,
If [tex]X=x^2[/tex] it becomes
[tex]X^3-289X^2-X+289=(X^2-1)(X-289)[/tex]
and [tex]289=17^2[/tex]
[tex]X^2-1=(X-1)(X+1)=(x^2-1)(x^2+1)=(x+1)(x-1)(x^2+1) \\\\x^2-289=x^2-17^2=(x-17)(x+17)[/tex]
So,
[tex]x^6-289x^4-x^2+289=(x^2-1)(x^2+1)(x^2-289)=(x-1)(x+1)(x+17)(x-17)(x^2+1)[/tex]
a = 1
b = 1
c = 17
d = 17
e = 0
Then a + b + c + d + e = 36
Thanks
A bacteria population increases exponentially at a rate of r% each day. After
32 days, the population has increased by 309%. Find the value of r.
Answer:
r=4.5% daily
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.
Substitute the given values into the model function:
[tex]409\%P_o=100\%P_o(1+r)^{32}[/tex]
Simplifying:
[tex]4.09=(1+r)^{32}[/tex]
We need to solve for r. Taking the 32nd root:
[tex]\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}[/tex]
Simplifying:
[tex]1+r=\sqrt[32]{4.09}=1.045[/tex]
Solving:
[tex]r=1.045-1\Rightarrow r=0.045[/tex]
r=4.5% daily
Find the solution of y=x-3
Answer:
x=3
Step-by-step explanation:
0 = x -3
-x = -3
change the sign to positive so x= 3
How many grams in one dose of medicine?
Answer:
65
Step-by-step explanation:
The equation y =0.7x represents the distance Henry hikes in miles over time in hours. The graph
represents the rate that Cark hikes. Determine which hiker is faster. Complete the explanation
Henry’s unit rate is ___ miles per hour. Clark’s unit rate is 1.5 miles per hour . So, ____ is faster.
Answer:
Henry’s unit rate is 0.7 miles per hour. Clark’s unit rate is 1.5 miles per hour . So, Ckark is faster.
Step-by-step explanation:
Distance covered by Henry is represented by y = 0.7x, where x = time (hrs), and y = distance (miles).
Distance covered in 1 hour by Henry would be:
y = 0.7(1) = 0.7 miles per hour
Distance covered by Clark in 1 hour = 1.5 miles per hour
Ckark covers more miles per hour than Henry covers in one hour, therefore, Ckark is faster.
1.
Solve -x + 9x = -4
Solution x= and x =
Answer:
x = - 1/2Step-by-step explanation:
-x + 9x = -4
8x = -4
x = -4/8
x = -1/2
Write an equation for the description.
Tanmayi wants to raise $150 for a school fundraiser. She has raised $100 so far. How much more (bes she
need to reach her goal? Let m be how much more is needed.
Answer:
answer
Step-by-step explanation:
step by step explanation
What is the perimeter of the rectangle?
5 feet
6 feet
12 feet
X 36 feet
Answer: I think the answer is b
Step-by-step explanation:
I WILL GIVE EXTRA POINTS AND BRAINLIEST HELPPP PLEASE!!!! SHOW ALL WORK!!!
Solve All 4
Answer:
#23 is x+27°=27
2x-17°=-17
#24 is x+23°=23
x+54°=54
#25 is x+79°=79
2x-37°=-37
#26 is 3x+71°=71
5x+37°=37
Step-by-step explanation:
how you ask because when it is like x+55° and 6x+88° that means its going to be a positive number.
but when it is like 5x-78° that means its going to be a negative number.
remember this +=positive and -=negative
hope this helped you out!
5. Find the value of x. (x+16) (4x-5)
Answer:
x = 7
Step-by-step explanation:
Set the equations equal to each other, since the two angles are congruent.
x + 16 = 4x - 5 now solve
21 = 3x
x = 7
Answer:
Step-by-step explanation:
In five towns in the state of Idaho, a new recycling policy started. A sample of 5,000 homes found that 0.56 put out a
recycling bin each week. Using a 95% confidence level, what is the estimate of the population proportion that recycles?
between 55.65% and 56,69%
between 54.97% and 57.03%
between 54.65% and 56.35%
between 55.31% and 56.35%
Which of the following is the value or PQ
Answer:
B. 61
Step-by-step explanation:
Given:
∆PQR ≅ ∆PQS
PQ = 2x + 41
QS = 7x - 24
QR = 3x + 16
Required:
Numerical value of PQ
SOLUTION:
First, create an equation to find the value of x as follows:
Since both triangles are congruent, therefore:
QS = QR
7x - 24 = 3x + 16 (Substitution)
Collect like terms
7x - 3x = 24 + 16
4x = 40
Divide both sides by 4
4x/4 = 40/4
x = 10
Find PQ by plugging x = 10 into PQ = 2x + 41
PQ = 2(10) + 41
PQ = 20 + 41
PQ = 61
David car would cover one lap of the Indy 500 in about 90 seconds. Chris’s car could cover one lap in about 54 seconds. If both cars left the same starting point at the same time, after how many seconds would they meet again at the starting Point ?
Answer:
36
Step-by-step explanation:
it took David's car 90 seconds and chris's car 54 seconds so that means
90-54=36
The number of seconds would they meet again at the starting point will be 270 seconds.
What is the least common factor (LCM)?The corresponding value integer that can be divided by both is known as the lowest relevant multiple, commonly referred to as the lowest common multiple of pair (or more) numerals a and b.
David's car would cover one lap of the Indy 500 in about 90 seconds. Chris’s car could cover one lap in about 54 seconds.
If both cars left the same starting point at the same time. Then the number of seconds would they meet again at the starting point will be given as,
L.C.M. = 90, 54
L.C.M. = 2 x 3 x 3 x 5, 2 x 3 x 3 x 3
L.C.M. = 2 x 3 x 3 x 3 x 5
L.C.M. = 270 seconds
The number of seconds would they meet again at the starting point will be 270 seconds.
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Find the value of x.
Answer:
20
Step-by-step explanation:
angles on a straight line
(x+20)+7x
open bracket
8x +20 = 180
collect like terms
8x= 180-20
8x=160x
x=160/8
x =20
The graph models the heights, in feet, of two objects dropped from different heights after x seconds.
On a coordinate plane, y = f (x) curves down through (0, 35) and (1, 20). G (x) curves down through (0, 30) and (0.5, 25).
Which equation represents g(x) as a transformation of f(x)?
g(x) = f(x) – 5
g(x) = f(x – 5)
g(x) = f(x) + 5
g(x) = f(x + 5)
Answer:
g(x) = f(x) + 5
Step-by-step explanation:
C
Answer: g(x) = f(x) - 5
Step-by-step explanation:
y = mx + b
The Graph of g(x) is 5 units down from the graph of f(x)
using the definition of multiplication to explain why a box that is 5 inches high 4 inches wide and 3 inches long has a volume of 5• (3•4) cubic inches explain the parentheses in the expression 5•(3•4)
Given:
Height of box = 5 inches
Breadth (width) of box = 4 inches
Length of box = 3 inches
Volume of box = 5 • (3 • 4) cubic inches
To find:
The explanation for the parentheses in the expression 5•(3•4)
Solution:
We know that,
Volume of a box is
[tex]Volume = length \times breadth \times height[/tex]
Area of a rectangle is
[tex]Area = length \times width[/tex]
Now,
Volume of box = 5 • (3 • 4) cubic inches
In this expression, (3 • 4) represents the product of length and with of the box. So, it means represents area of the base of box and after multiplying the base area with height we get the volume of the box.
Therefore, the parentheses in the expression 5•(3•4) represents the base area of the box.
The perimeter of a rectangular solar panel is 540 cm. The ratio of the length to the width is 3 : 2. What are the length and width?
Total number of parts = 3 + 2 = 5 parts
[tex]each \: part \: = \frac{(540 \div 5)}{2} \: m[/tex]
[tex] \\ each \: part \: = \frac{108}{2} m \: \\ \\ each \: part \: = 54 \: m[/tex]
Then , the length of this triangle :
[tex]54 \times 3 \: m[/tex]
[tex] = 162 \: m[/tex]
Then , the width of this triangle will be :
[tex]54 \times 2 \: m[/tex]
[tex]108 \: m[/tex]
∴ The length of this rectangle is 162 m and the width of this rectangle is 108 m .
Lesson 3 Practice Problems Ratios
Answer:
1. 6 to 2 and 9 to 3
2. Any ratio that is not equivalent to 3 to 1. For example, 4 to 11.
Step-by-step explanation:
Help!!
...................................................................................
Which equation represents a line that passes through (2,-1/2) and has a slope of 3?
y - 2 = 3(x + 1/2)
y - 3 = 2(x + 1/2)
y + 1/2 = 3(x - 2)
y + 1/2 = 2(x - 3)
Which two ratios show a proportional relationship?
A. 2/8 and 6/20
B. 4/6 and 15/20
C. 10/15 and 12/18
D. 15/18 and 20/25
Which expression is equivalent to Negative 6 (negative two-thirds + 2 x)?
Answer:
hi answers b or a
Step-by-step explanation:
Fill in the missing term on each line. Simplify any fractions.
8(d + 1) = 8
d + 1 =
Divide both sides by 8
d =
Subtract 1 from both sides
Answer:
8 subtract 1 sides fraction
Answer:
8 subtract 1 sides fraction
Step-by-step explanation:
11) The owner of The Nut House wants to mix 100 pounds of cashews and almonds for a holiday special.
Cashews sell for $8 per pound and almonds sell for $3 per pound. How many pounds of each type of nut must
he mix to obtain a mixture that will sell for $6.25 per pound?
Answer:
65 pounds of cashews 35 pounds of almonds
Step-by-step explanation:
do you do vla in ohio? I have the same questions you do
HELP WILL MARK BRAINLIEST
Answer:
a) A = (5, 1), b) A = (1,11)
Step-by-step explanation:
given A is (2,3), question a is represented by a shift of this point 3 units to the right, and 2 units down which means (x,y) → (x +3, y - 2) or T(3,-2)(x,y). (2,3) → (x + 3, y - 2) = (2 + 3, 3 - 2) = (5, 1).
Question b represents a shift of this point one unit to left, and 8 units up which is represented by (x,y) → (x -1 , y + 8) or T(-1,8)(x,y).
(2,3) → (x - 1, y + 8) = (2 - 1 , 3 + 8) = (1, 11).
Find the slope of the line that passes through the pair of points (-1,-9) and (-3,10)
Answer:
-9.5
Step-by-step explanation:
The slope (m) is the ratio of the change in y to the change in x:
m = (y2 -y1)/(x2 -x1)
m = (10-(-9))/(-3-(-1)) = 19/-2
m = -9.5
The slope of that line is -9.5.
__
The graph shows the line through those points, written in point-slope form.
Three hundred yards of fencing is being used to fence in a rectangular garden. The area of the garden is modeled by a
quadratic function of the rectangle's width, A(w). What does the second coordinate of the vertex of the quadratic function.
A(w), represent?
the minimum width that can be used for the fencing
the maximum area that can be enclosed by the fencing
the width that gives the maximum area
the length that gives the maximum area
Answer:
Opction b)
The maximum area that can be enclosed by the fencing
Step-by-step explanation:
I took the test
The solution is, A(w), represents the maximum area that can be enclosed by the fencing.
Here, we have,
If the width of the garden is w (in yards), then the length of the garden is (150-w) and the area is ...
A(w) = w(150 -w) = -(w² -150w)
A(w) = -(w² -150w +75²) +75²
A(w) = -(w -75)² +5625
In this vertex form, the vertex is (75, 5625).
The graph of area versus width is a parabola that opens downward, so the vertex second coordinate is the maximum area that can be enclosed.
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A rectangular garden is fenced on all sides with 278 feet of fencing. The garden is 9 feet longer than it is
wide. Find the length and width of the garden.
Answer:
Length = 74 feet,
Width = 65 feet
Step-by-step explanation:
If length = l, width = w;
l = 9 + w (Given)
2l + 2w = 278 (Definition of perimeter)
Substitute "9 + w" for l in the second equation;
2(9 + w) + 2w = 278 -> Distribute the "2"
18 + 2w + 2w = 278 -> Combine like terms
18 + 4w = 278 -> Subtract 18 on either side
4w = 260 -> Divide either side by 4
w = 260/4 = 65 feet
l = 9 + 64 = 74 feet
solve the polynomial equation:
x^3-7x^2-x+7=0
show your steps please
Answer:
x = {-1, 1, 7}Step-by-step explanation:
Solving for x
x^3 - 7x^2 - x + 7 = 0(x^3 - x) - (7x^2 - 7) = 0x(x^2 - 1) - 7(x^2 - 1) = 0(x - 7)(x^2 - 1) = 0(x - 7) (x + 1) (x - 1) = 0x - 7 = 0 ⇒ x = 7x + 1 = 0 ⇒ x = -1x - 1 = 0 ⇒ x = 1The solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]
The given polynomial is [tex]x^3 - 7x^2 - x + 7 = 0[/tex]
We can observe that the polynomial has a common factor of (x - 1).
By dividing the polynomial by (x - 1), we can simplify the equation:
[tex](x - 1)(x^2 - 6x - 7) = 0[/tex]
Now we have factored the polynomial equation as a product of two factors, [tex](x - 1)[/tex] and [tex](x^2 - 6x - 7).[/tex]
To find the solutions, we set each factor equal to zero and solve for x.
Setting [tex](x - 1) = 0[/tex], we get [tex]x = 1.[/tex]
Now, let's solve the quadratic factor [tex](x^2 - 6x - 7) = 0[/tex]
Using factoring or the quadratic formula, we find the roots of the quadratic equation:
[tex]x^2 - 6x - 7 = 0[/tex]
[tex](x - 7)(x + 1) = 0[/tex]
Setting each factor equal to zero:
[tex]x=7[/tex] and [tex]x=-1[/tex]
Therefore, the solutions to the polynomial equation [tex]x^3 - 7x^2 - x + 7 = 0[/tex]are[tex]x = 1, x = 7,[/tex] and [tex]x = -1.[/tex]
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How do you do this question?
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
PLEASE HELP 50 PTS
For a function j(x), the difference quotient is 3x2 + 3xh + h2. What is the average rate of change of j(x) over the interval [–1, 6]?
15
21
25
31
Answer:
31 is correct guys
Step-by-step explanation:
Since the data is incomplete, for the given question the required average rate of change is given by 15 + 3h.
Given that,
For a function j(x), the difference quotient is 3x2 + 3xh + h2.
The average rate of change of j(x) over the interval [–1, 6] is to be determined.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is independent while Y is the dependent variable.
Here, the average rate of change = f(6) - f(-1) / (6 + 1)
So,
f(6) = 108 + 18h + h²
f(-1) = 3 - 3h + h²
Now,
average rate of change = [(108 + 18h + h²) - (3 - 3h + h²)]/(7)
= [105 + 21 h ] / 7
= 15 + 3h
Thus, the required average rate of change is given by 15 + 3h.
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