The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
How to complete the blanks?The equation is given as:
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2
Complete the blanks using alphabets
ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2
Open the brackets
ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2
Factorize the expression
(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2
By comparison, we have:
a + c = de
-ab = df - 1
Rewrite the second equation as:
ab + df = 1
So, we have:
a + c = de
ab + df = 1
Set a = 2 and c = 10.
So, we have:
a + c = de ⇒ de = 2 + 10 ⇒ de = 12
ab + df = 1 ⇒2b + df = 1
Express 12 as 3 * 4 in de = 12
de = 3 * 4
By comparison, we have:
d = 3 and e = 4
So, we have:
2b + df = 1
This gives
2b + 3f = 1
Set b = 11.
So, we have:
2 * 11 + 3f = 1
This gives
22 + 3f = 1
Subtract 22 from both sides
3f = -21
Divide by 3
f = -7
Hence, the complete equation is:
2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
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Given that
y=1/27x^3
express each of the following in the form kx^n where k and n are constants.
(a) y^1/3
(b) 3y^-1
(c) √(27y)
Express the following in the form kx^n where k and n are constants.
(a) y=x^3
(b)y=3x^-1
(c) y=x^3/27
To express each of the following in the form kx^n where k and n are constants.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given that:
y=1/27x^3
express each of the following in the form kx^n where k and n are constants.
(a) y^1/3
Let y^1/3=x
by cubing both sides we get,
y=x^3
The equation in the form of kx^n
where,
k=1
n=3
(b) 3y^-1
Let 3y^-1=x
3/y=x
y=3/x
By simplify
y=3x^-1
The equation in the form of kx^n
where,
k=3
n=-1
(c) √(27y)
Let (27y)^1/3=x
by cubing both sides we get,
27y=x^3
y=x^3/27
The equation in the form of kx^n
where,
k=1/27
n=3
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A measure of the strength of the relationship between two variables is referred to as the.
A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.
What is the correlation coefficient?Correlation coefficients are used to evaluate the strength of the linear relationship between two variables.
When the correlation coefficient value is less than zero, it indicates a bad association, while a number higher than zero indicates a good relationship.
There is no correlation between the two variables being compared, as shown by a correlation coefficient of zero.
The idea of a negative correlation, also referred to as an inverse correlation, is essential to the construction of diversified portfolios that may be better able to withstand portfolio volatility.
It is often done by entering data into a calculator, computer, or statistics application because computing the correlation coefficient requires time.
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Guided Practice
Cans of Soup
Number of Servings
1
4
2
8
3
12
4
16
Write a function rule for the table.
A.
s = 4c
B.
c = 4s
C.
s = c + 4
D.
c = 4 + s
The function rule for the table is A. s = 4c
How to depict the function?From the table, it can be seen that when the cans of soup is 1, the number of serving is 4. Also, when it's 2, the number or servings is 8.
This implies that:
4/1 = 8/2
= 4.
Therefore, the function rule for the table is s = 4c
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if p is a prine number greater than 5 and q is an odd number greater than 5 whihc of the following is true
The first statement p + q is not a prime number is a true option (A) correct.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
First statement:
p + q is not a prime number.
Let p = 7
q = 9
= 7 + 9 = 16 (16 is not a prime)
= 7×9 = 63 (no factor of 63)
p = 7, q = 7
q/p = 7/7 = 1 (1 is integer)
Thus, the first statement p + q is not a prime number is a true option (A) correct.
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What is the y-intercept of the graph that is shown below?
On a coordinate plane, a line goes through points (negative 2, 0) and (4, 0).
(–2, 0)
(–1, 2)
(0, 4)
(4, 0)
Answer:
0,4
Step-by-step explanation:
X is 0 and Y is 4 it'll be touching the vertical line
Answer:
0,4
Step-by-step explanation:
How many times could you expect to roll a number that is not 5 if you rolled a standard die 360 times?
The number of times I would expect to roll a number that is not a 5 is 300 times.
What is the number of times a 5 won't be rolled?A standard die has 6 faces. There are 5 numbers that are not 5 on a standard die. They are 1, 2, 3, 4, 6.
The number of times a 5 won't be rolled = (5/6) x 360
5 x 60 = 300 times
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By rounding each number to 1 significant figure,
estimate the answers to:
a)763 x 42
_______
82
b)39 × 52
_______
3.8 x 4.9
Answer:
see explanation
Step-by-step explanation:
rounding each number to 1 significant figure
(a)
763 × 42
≈ 800 × 40
= 32000
(b)
39 × 52
≈ 40 × 50
= 2000
(c)
3.8 × 4.9
≈ 4 × 5
= 20
Solve The Following
( Solving equations)
Answer:
a) x = 4
b) x = 1
Step-by-step explanation:
a) [tex]\frac{4x-1}{2} = x + 7[/tex] multiply both sides by 2 so we can simplify the fraction by getting rid of 2
4x - 1 = 2x + 7 transfer like terms to the same side of the equation
4x - 2x = 7 + 1
2x = 8 divide both sides by 2
x = 4
b) [tex]3x + 2 = \frac{2x+13}{3}[/tex] again, get rid of the fraction by multiplying both sides by 3
9x + 6 = 2x + 13 transfer like terms to the same side of the equation
9x - 2x = 13 - 6
7x = 7 divide both sides by 7
x = 1
What number is it that, when multiplied by 18,27,36,45,54,63,72,81, or 99, gives a product in which the first and last figures are the same as those in the multiplier, but which when multiplied by 90 gives a product in which the last two figures are the same as those in the multiplier?
The given multipliers are factors of 9, the possible number will have 1 as first and last digit which gives the number as 101
How can the correct number be found?The given numbers are;
18, 27, 36, 45, 54, 63, 72, 81, 99
Given that the first and the last figures are those of the multipliers, we have;
The first and last and last digit of the number can be 1, which gives;
Possible numbers includes; 11 and 101
By trying the possible numbers, the difference found is presented as follows;
99 × 11 = 1089 (The first and the last digit are not the same as the multiplier)
99 × 101 = 9999 (First and last digit are not the same as the multiplier)90 × 11 = 990
90 × 101 = 9090
The correct option is therefore 101
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I need some help guys!
Answer:
0.18
Step-by-step explanation:
What is the area of a square with radius 7.5m
Answer:
48.375
Step-by-step explanation:
Area of square- area of circle
Side^2 - pieR^2
(15)^2 - 3.14*7.5*7.5
225 - 176.625
= 48.375
Hope this helps
The area of the square is 56.25 m².
The area of the square is:
Area = Side²
Area = (7.5 m)²
Area = 56.25 m²
{ Pisces04 }
PLEASE HELP!!!
Determine the measure of the angle formed by the line y=3/2x and the positive x-axis.
Answer:
the angle = ~56.3 degrees
Step-by-step explanation:
1. y=3/2(x) and y=0
2. say x is equal to 4. the length along the x axis is 4. you would plug x=4 into y=3/2x to get the length along the y axis (which would be 6). then you would use these lengths to find the angles value with tan. tan^-1(6/4), so the answer would be ~56.3 degrees
Solve the system of equations:
8x + 3y = 13
3x + 2y = 11
Answer:
1.x=13/8-3y/8
2.x=11/3-2y/3
Step-by-step explanation:
Which of the following gives a single solution of the inequality |x+3|-2<0 and shows a graph that can be used to determine the entire solution set of the inequality?
The solution to the inequality |x + 3| - 2 < 0 is -5 < x < -1 as shown in the graph attached
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is an expression used to show the non equal comparison of two or more numbers and variables.
Given that:
|x + 3| - 2 < 0
Hence:
(x + 3) - 2 < 0 and -(x + 3) - 2 < 0
x < -1 and x > -5
The solution to the inequality |x + 3| - 2 < 0 is -5 < x < -1 as shown in the graph attached
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Answer: The answer to the question is Answer Choice "B"
Step-by-step explanation:
Proof that It's actually correct as you can see it on the screenshot :)
help me find the answer plss
Answer:
about 8.2 cm
Step-by-step explanation:
The key is to realize that the volume never changes.
The formula for the volume of a sphere is (4/3)*pi*radius^3
22/7 is being substituted in place of pi in this problem
The volume of one of the small spheres is
(4/3)*(22/7)*2^3 is about 33.524 cm^3
64 of those spheres would have a volume of 33.524*64, or about 2145 cm^3
Now, the problem is to find a sphere with a volume of 2145 cm^3
Volume = (4/3)*(22/7)*radius^3
plug in and solve
2145 = 4.1905*r^3
r^3=511.87
r is about equal to 8.2 centimeters
in each of the following graphs, the two given polygons are similar. write precisely a single dilation (coordinated of center and coefficient) by which the image (labled with primed letters) was obtained.
The single dilation of the shape is a dilation by a scale factor of 1.5 with center R
How to determine the dilation rule?From the graph, we have the center of dilation to be point R.
This is so because R = R'
Also, we have:
R = (-1, -4)
S = (2, 0)
S' = (3.5, 2)
Calculate the distance RS and RS' using
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
This gives
[tex]RS = \sqrt{(0 + 4)^2 + (2+ 1)^2} = 5[/tex]
[tex]RS' = \sqrt{(2 + 4)^2 + (3.5+ 1)^2} = 7.5[/tex]
Divide RS' by RS to determine the scale factor (k)
k = 7.5/5
k = 1.5
Hence, the single dilation of the shape is a dilation by a scale factor of 1.5 across point R
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Can someone help with these geometry questions? I gotta have answers fast, it’s urgent:(
Can't answer 1-6 cause I have no idea what you need
7) A triangle with two congruent sides is isosceles.
8) [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex]
9) [tex]\angle C[/tex]
10) [tex]\overline{AB}[/tex]
11) [tex]\angle A, \angle B[/tex]
12) isosceles triangle
Select the correct answer.
Which statement is true about function f, which is shown in the graph?
The graph shows a cubic function. The curve is drawn using the points (minus 1, 8), (minus 1, minus 3.5), (0, 0), (1, 3.5), and (1, minus 8) which intercepts (1, 0), and (minus 1, 0)
A.
Function f is neither even nor odd.
B.
Function f is odd.
C.
Function f is both even and odd.
D.
Function f is even.
Convert the degree measurement to radians. Express answer as multiple of π: 126°
Answer:
.7 pi Radians
Step-by-step explanation:
There are pi radians in a 180 degrees :
pi / 180 * 126 = .7 pi Radians
Answer:
[tex]\frac{7}{10} \pi[/tex] or 0.7π radians
Explanation:
For converting degree to radians, multiply by π/180
Here given:
126°Conversion:
126° × π/180 = [tex]\frac{7}{10} \pi[/tex] or 0.7π
Similarly (additional),
1) 100° = 100 × π/180 = [tex]\frac{5}{9} \pi[/tex]
2) 320° = 320 × π/180 = [tex]\frac{16}{9} \pi[/tex]
help me please U_U......
Distance traveled = dependent variable
Gasoline left in tank = independent variable
Robert, Richard and David were working on a project to redesign coke cans. First, Robert measured the original coke can and found the circumference to be 8.6 inches. Richard measured the height to be 15.2 cm.
David calculated the volume to be 131.3 cm3.
Choose the true statement(s) below.
Select one or more:
a.David's calculations are incorrect, he needed to convert centimeters to inches before finding the radius then use the area of the base times the height .
b.David is correct.
c.David's calculations are incorrect, he used the circumference and the height to find the volume.
The true statement is David's calculations are incorrect, he used the circumference and the height to find the volume.
VolumeCorrect calculation:
Height = 15.2 cmCircumference = 8.6 inchesC = 2πr
8.6 = 2 × 3.14 × r
8.6 = 6.28r
r = 8.6/6.28
r = 1.36942675159235 inches
convert 1.36942675159235 inches to cm
= 3.478343949044569 cm
Approximately,
r = 3.5 cm
Volume = πr²h
= 3.14 × 3.5² × 15.2
= 3.14 × 12.25 × 15.2
= 584.668 cm³
Approximately,
volume = 584.7 cm³
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The population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 20% in 10 years. what will be the population in 20 years? (round your answer to the nearest person.)
The population in 20 years is 719 people.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
According to the question
[tex]\frac{dP}{dt} = kP[/tex] where P is population at any time
solving equation,
[tex]\int[/tex][tex]\frac{dP}{dt} =\\[/tex] [tex]\int kP[/tex]
[tex]lnP=kt+C[/tex] -(1)
Applying the conditions,
at t=0, P = 500
[tex]ln500=C[/tex] -(2)
at t=10, P= 600
putting it in equation gives
[tex]ln(600) = k(10)+ln(500)[/tex]
ln(6/5) = k(10)
[tex]k = \frac{ln(6/5)}{10}[/tex]
at t=20 , P= ?
[tex]lnP=(\frac{ln(6/5)}{10})20 + ln500[/tex]
[tex]lnP=({ln(6/5)}{2 + ln500[/tex]
On putting the values of ln(6/5) , ln(500)
[tex]lnP=0.182(2) + 6.214[/tex]
[tex]P = e^{6.578}[/tex]
P = 719.099
On rounding off
P ≈ 719 people
Thus the population in 20 years is 719 people.
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A dilation is a nonrigid transformation that can produce enlarged or reduced images from a given pre-image. How do you know that a dilation will produce similar figures? Explain
The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
What is dilation?It should be noted that dilation simply means a transformation to resize an object
In this case, the dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
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Answer:
The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
Step-by-step explanation:
Geometry question I need help with true of false
Answer:
RS = 12 False
x=4 True
x=3 False
QT=16 True
Step-by-step explanation:
22/11,594 I need a step by step answer
Answer:
1.89753
Step-by-step explanation:
22/11,594
Multiply the numerator and denominator by 1000 to remove decimal[tex]\frac{22}{11.594} * 1000 = \frac{22000}{11594}[/tex]
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At a school book fair, 3/5 of the books are nonfiction books. of the nonfiction books, 1/4 are animal books. what fraction of the book fair books are animal books? move numbers to the boxes to show the fraction.
Answer:
Animal books make up (3/20) of all books
Step-by-step explanation:
Let X be the total number of books, made up of nonfiction, animal, and all others.
(3/5)X are nonfiction books.
Of the nonfiction books, 1/4 are animal books: (3/5)*(1/4)X = (3/20)X are animal books
[This means that Nonfiction, less animal books is: (3/5)X - (3/20)X]
Animal books make up (3/20) of all books.
(LOOK AT IMAGE)
The diagram shows a circle with a tangent.
a) What is the size of angle x?
b) Choose the theorem below which allows you to find x.
a) By the alternate segment theorem, [tex]x=53^{\circ}[/tex]
b) Alternate angles are equal
This coordinate plane shows the journey of a plane between two cities. The journey starts from City A, indicated by a green point, and ends in City B, indicated by a red point. In which quadrant did the journey start and in what quadrant did it end?
A. Started in Quadrant III and ended in Quadrant I.
B. Started in Quadrant I and ended in Quadrant II.
C. Started in Quadrant II and ended in Quadrant IV.
D. Started in Quadrant I and ended in Quadrant III.
Started in Quadrant II and ended in Quadrant IV.
==========================================================
Explanation:
Refer to the diagram below. It shows how the four quadrants are labeled using roman numerals. We start in the upper right corner (aka northeast corner) and work counterclockwise when labeling quadrant I, II, III, and IV in that order.
The green point A is located in quadrant II in the northwest. Meanwhile point B in red is in the southeast quadrant IV.
Therefore, we started in quadrant II and ended in quadrant IV which points us to choice C.
Which of the following lines is parallel to the given line?
Answer:
y=10x
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula
y−y1=m(x−x1) to find the line parallel to y=10x−45
.
HELLP HEELEP SOS EMERGENCY
Answer:
15 in.
Step-by-step explanation:
P = 2(L + W)
36 = 2(L + 3)
18 = L + 3
L = 15
Answer:
Hello! The answer is 15 in.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2l + 2w. We can substitute our w-value since it's provided for us:
2l + 2(3) = 36
Now, we can solve the equation:
2l + 6 = 36
-6. -6
----------------
2l = 30
-- --
2 2
l = 15 in