Which power of Congress is the most important?
Select one:
O a. the authority to regulate commerce
O b. the authority to establish the federal courts.
O c. the authority to make laws
O d. the authority to coin money
Find the general solution of the given higher-order differential equation. y''' − 8y'' − 9y' = 0
The general solution of the given higher-order differential equation y''' − 8y'' − 9y' = 0 is , [tex]y = C_{1} + C_{2} e^{8x} + C_{3}e^{-x}[/tex]
Given higher-order differential equation = y''' − 8y'' − 9y' = 0
We have to find the general solution of the above differential equation
The auxiliary equation for the above differential equation will be : [tex]m^{3} - 8m^{2} - 9m = 0[/tex]
Solve the equation :- [tex]m^{3} - 8m^{2} -9m = 0[/tex]
[tex]m ( m^{2} - 8m - 9 ) = 0[/tex]
m ( m - 8 ) ( m + 1 ) = 0
m = 0 , m = 8 , m = -1
Then the general solution will be like :
[tex]y = C_{1} e^{0x} + C_{2} e^{x} +C_{3}e^{-1x}[/tex]
The above solution can be written as:
[tex]y = C_{1} +C_{2} e^{8x} +C_{3} e^{-x}[/tex]
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The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes. What does the slope of the linear equation that models the data indicate?
The volume of helium inside the balloon decreased at a rate of 0.1 cubic feet per minute. The linear equation that represents the given data is y = -0.1x + 6 and its slope m = -0.1.
What is the equation of a line passing through two points?The equation of the line passing through the points (x1, y1) and (x2, y2) is
(y - y1) = m(x - x1).
Where m is the slope of the line and is calculated by
m = (y2 - y1)/(x2 - x1)
Calculation:The given data in the table represents the volume of helium (cu ft), inside a balloon relative to the elapsed time in minutes.
x: 5, 10, 15, 20, 25, 30, 35, 40
y: 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2
From this table, consider two points (5, 5.5) and (10, 5)
So, the equation of the line is
y- y1 = m(x - x1)
Where slope m = (y2 - y1)/(x2 - x1)
⇒ m = (5 - 5.5)/(10 - 5)
⇒ m = -0.5/5
∴ m = -0.1
Thus, the equation is
y - 5.5 = -0.1(x - 5)
⇒ y - 5.5 = -0.1x + 0.5
⇒ y = -0.1x + 0.5 + 5.5
⇒ y = -0.1x + 6.0
∴ y = -0.1x + 6
Since the slope of the line is negative, the volume of the helium inside the balloon decreased at a rate of 0.1 cubic ft per minute.
So, option 2 is correct.
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hich value, when placed in the box, would result in a system of equations with infinitely many solutions?
y = -2x + 4
6x + 3y =
The value placed in the box that makes the system of equation with infinitely many solution is 12.
How to solve an infinitely many solution equation?An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If we simplify the equation we will notice both sides are equal. This means the equation has an infinitely many solution.
Hence,
y = -2x + 4
Therefore,
6x + 3y = 12
divide the equation(ii) by 3
2x + y = 4
y = -2x + 4
Therefore, both equation are equal if the the box is filled with 12. This means for the value placed in the box that makes the system of equation with infinitely many solution is 12.
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Jane has 8 toy cats and 4 baskets. If she wants to arrange 2 toy cats in each basket, how many different ways can she arrange the toy cats?
Step-by-step explanation:
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
The number of combinations of n objects taken r at a time is determined by the following formula:.
nCr = n! / (n-r)! r!
n = total number of objects in the set
r = number of choosing objects from the set
so here , Jane has 8 toys and first she wants to take 2 toys ....
so , 8C2 = 8! / 6! 2! = 28 ways
so , she selected 2 toys ,,, After she wants to take 2 toys among 6 toys ....
so , 6C2 = 6! / 4! 2! = 15
next , picking 2 toys out of 4
So , 4C2 = 4! / 2! 2! = 6
next , 2C2 = 2! / 0! 2! = 1
total ways to pick toys = 28 × 15 × 6 × 1
= 2520 different ways ..
request :- Sorry if there are some mistakes in my English.
Geometry: complete this proof of theorem 18, ASAP!!!
(Theorem 18: if the side of one angle are parallel to the sides of another angle, right side to left side and left side to right side, then the angle are supplementary)
Supplementary angles are angles that can be summed up to give [tex]180^{o}[/tex], which is the value of the sum of angles on a line.
The required statements and reasons are given below:
Two or more lines are said to be parallel if there is no measure of the angle between them or the measure of the angle between them is [tex]180^{o}[/tex]. Thus the lines would never meet at any point even when extended to infinity.
While supplementary angles are angles that can be summed up to give [tex]180^{o}[/tex], which is the value of the sum of angles on a line.
STATEMENTS REASONS
1. < A and <B with AD ║BE, AC ║BF Given.
2. AD, AC, BE, BF Straight line.
3. <A ≅ <1 Congruent property of
vertically opposite angles.
4. AD + AC ≅ DC Addition property of parts
BE + BF ≅ EF of a given line segment.
5. <A + <B ≅ [tex]180^{o}[/tex] Addition property of
supplementary angles.
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Which equation below
represents exponential
growth?
a. y=3x^2-5
b. y = 3(2/5)^x
c. y=3(5)^x
d. y=3x-5
Determine the unknown length or angle measurement. Round each answer to the nearest whole number.
Answer:
a) 52
b)115
Step-by-step explanation:
which relation is a function?
The relation that is a function is:
b. y = 2x² - 3x + 7
When a relation is a function?A relation is a function if each value of the input is mapped to only one value of the output.
Hence, when both x and y are squared, we have that [tex]x = \pm ay[/tex], hence it is not a function. This is the case for items a and c.
For item d, we have that the relation can be simplified as follows:
x = -y² + 3y
x = y(-y + 3)
The solution above, is associated to two values of y, hence it is also not a function. Then the function is given by:
b. y = 2x² - 3x + 7
In the solution, it can be seen that for each input x, only one value of y can be generated.
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Question
In the xy-plane, what is the y-intercept of the graph of the equation y = 6 (x − 1/2) (x+3)?
-9
-1/2
-1/2
3
9
Answer:
-9
Step-by-step explanation:
To find the y intercept, substitute 0 in for x.
So, the equation looks like this:
[tex]y=6(0-\frac{1}{2} )(0+3)[/tex]
Now, just solve for y and you will get y = -9
The y-intercept of the graph of the equation is y = -9 which is the correct answer that would be an option (A).
What is the equation of a line?The general equation of a line is y = mx + c
where m is the slope of the line and c is the intercept.
A linear equation is defined as an equation in which the highest power of the variable is always one.
Given equation as:
y = 6 (x - 1/2)(x+3)
To determine the y-intercept of the graph of the equation
Substitute the value x = 0 in the equation,
y = 6 (0 - 1/2)(0+3)
Apply the arithmetic operation and solve for y
y = -9
Hence, the y-intercept of the graph of the equation is y = -9.
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Santaniago has a rope that measures 205.95 centimeters.write this number in expanded form
This number in expanded form 200 + 5 + 5/10 + 9/100 .
What is expanded form in math example?
It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. For example, the expanded form of the number 1572 is 1000+500+70+2.Given : 205.95 centimeters.
the number in a expanded form.
200 + 5 + 9/10 + 5/100
we have given 205.95 centimeters.
We can see 2 is at hundred place = 200.
0 is at tens place = 00.
5 is at ones place = 5.
9 after decimal is at tenth place = [tex]\frac{9}{10}[/tex].
5 is at hundredth place = [tex]\frac{5}{100}[/tex] .
Therefore , Expanded form : 200 + 5 + 5/10 + 9/100 .
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there are 6 girls and 8 boys in Mr. Stevenson's class the ratio of girls to boys in the class can be expressed as the simplified ratio ?/4 what is the missing number ?
Answer: 3
Step-by-step explanation:
The missing number in the simplified ratio ?/4 is 3.
Here, we have to find the missing number in the simplified ratio ?/4, we need to determine the ratio of girls to boys in Mr. Stevenson's class.
Given that there are 6 girls and 8 boys in the class, the ratio of girls to boys can be expressed as:
Number of girls : Number of boys = 6 : 8
To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD).
In this case, the GCD of 6 and 8 is 2.
Dividing both 6 and 8 by 2, we get:
Number of girls : Number of boys = 6/2 : 8/2 = 3 : 4
So, the simplified ratio of girls to boys is 3/4.
Therefore, the missing number in the simplified ratio ?/4 is 3.
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The purpose of statistical inference is to make estimates or draw conclusions about a.
When we make estimates of or draw conclusions about one or more characteristics of a population based upon the sample, we are using the process of statistical inference.
To estimate this sample to sample variance or uncertainty is the goal of statistical inference.What is the purpose of statistical inferences ?
To be able to make inferences about a population based on data from a sample is the goal of statistical inference. The process of statistical inference involves selecting a sample, gathering data from that sample, calculating a statistic from the data, and drawing conclusions about the population from that statistic.How is statistical inference used to draw conclusions?
Estimation and hypothesis testing are components of statistical inference (evaluating a notion about a population using a sample) (estimating the value or potential range of values of some characteristic of the population based on that of a sample).
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PLEASE HELP The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
A graph with two linear functions; f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
The transformation of f(x) to g(x) would be 6 units upwards
To transform f(x) to g(x), the equation is; g(x) = f(x) + 6
How to solve transformation problems?We are told that f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.
f(x) passes through (1,3) and (3, 13).
Thus;
slope is; m = (13 - 3) / (3 - 1) = 10/2 = 5
y-intercept is; b = y - mx
Thus;
b = 3 - 5*1 = -2
Equation of the line is;
f(x) = 5x - 2
g of x passes through negative 1, 3 and 1, 13. Thus, the slope is;
m = (13 - 3) / (1 + 1) = 10/2 = 5
y-intercept is; b = y - mx
Thus;
b = -1 - (5)(-1)
b = 4
Equation of the line is; g(x) = 5x + 4
part A: The transformation of f(x) to g(x) would be 6 units upwards
part B: k = 6
part C: To transform f(x) to g(x), the equation is;
g(x) = f(x) + k
g(x) = f(x) + 6
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Find tan 0 if csc 0 = -√5/2 is in the third quadrant.
A. 1/2
B.-2
C.-1/2
D. 2
Answer:
D. 2
Step-by-step explanation:
soh cah toa rule
sine equals opposite over hypotenuse,
cosine equals adjacent over hypotenuse, and
tangent equals opposite over adjacent
csc is 1/sin which is hypotenuse over opposite
if csc is -√5/2 then
hypotenuse is -√5
opposite is 2
3rd quadrant on a graph is bottom left
both x and y values are negative
hypotenuse means its a triangle
pythagorean theorem
a^2 + b^2 = c^2
a^2 + 2^2 = (-√5)^2
a^2 + 4 = 5
a = 1 = adjacent
tangent equals opposite over adjacent
tan is 2 / 1 which is 2
third quadrant means it's still positive
because tan is positive in quadrant 3
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A man left rs 1,800,000 as inheritance.his heirs are 6 daughters and 2 sons.find the share of each heir
Answer:$225,000 each
Step-by-step explanation: Assuming that they each get an equal share of the inheritance, there are 8 shares of the inheritance so we divided the $1.8m by 8 which equals $225,000 each.
A school dance committee has 14 volunteers. Each dance requires 3 volunteers at the door, 5 volunteers on the floor, and 6 floaters. If two of the volunteers, Christine and Samuel, cannot work together since they are new, in in how many ways can the volunteers be assigned?
There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.
Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.
We are required to find the number of ways in which the volunteers can be assigned.
Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.
n[tex]C_{r}[/tex]=n!/r!(n-r)!
Number of ways in which the volunteers can be assigned is equal to the following:
Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.
Number of ways =14[tex]C_{12}[/tex]
=14!/12!(14-12)!
=14!/12!*2!
=14*13/2*1
=91 ways
Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.
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determine the rate of change of the function.
decreasing at increasing rate
increasing at a decreasing rate
decreasing at a decreasing rate
increasing at an increasing rate
Solid rock is an unlevered firm with an ebit of $10 million and an unlevered cost of capital of 12 percent. if the tax rate is 40 percent, what is the value of the firm?
The value of the firm is $50 million
How to determine the value of the firm?The given parameters are:
EBIT = $10 million
Tax Rate, Tc = 40%
Unlevered cost of capital, RU = 12%
The value of the firm is calculated as:
Value = EBIT*(1 - Tc)/Ru
This gives
Value = 10 million *(1 - 40%)/12%
Evaluate the expression
Value = 50 million
Hence, the value of the firm is $50 million
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WILL MARK U BRAINLIEST IF RIGHT PLS EXPLAIN
Answer:
166
Step-by-step explanation:
If the four lines are tangent to the circle, know that:
NA = KA
AD = LD
LC = MC
MB = NB
The question stated that:
NA = 18 --> KA is also 18
BN = 11 --> MB is also 11
AD = 34 --> LD is also 34
BC = 31 --> MC is 20 (Because BC is BM + MC and BM is 11)
We can just add these numbers.
(18+18) + (11 + 11) + (20+20) + (34+34)
= 36 + 22 + 40 + 68
= 76 + 90
= 166
The perimeter of ABCD is 166.
Answer:
130
Step-by-step explanation:
if 2 tangent segments are drawn to a circle from the same external point then they are congruent, then
AN = AK and KD = DL and MC = LC
then AN = AK = 18 and
KD = AD - AK = 34 - 18 = 16 , so KD = DL = 16
now BM = BN = 11 , then
AB = AN + BN = 18 + 11 = 29
MC = BC - BM = 31 - 11 = 20 and LC = MC = 20 , so
CD = LC + LD = 20 + 16 = 36
-----------------------------------------
Perimeter = AB + BC + CD + AD
= 29 + 31 + 36 + 34
= 130
Im trying do it on my own just checking my answer
Answer:
Step-by-step explanation:
find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answer:
628.0 mm²
Step-by-step explanation:
The total surface area of the figure is the sum of the inside lateral area, the outside lateral area, and the area of the donut bases.
Lateral areaThe lateral area of a cylinder is ...
A = 2πrh
The total lateral area of the inside and outside cylinders is ...
A = 2π(r1)h +2π(r2)h = 2π(r1 +r2)h
A = 2(3.14)(3 mm +7 mm)(6 mm) = 376.8 mm²
Base areaThe area of one donut base is the product of the centerline length and the width.
A = πdw = (3.14)(7 mm +3 mm)(4 mm) = 125.6 mm²
Total areaThe total surface area of the composite figure is the sum of its lateral area and the area of the two bases.
surface area = 376.8 mm² +2×125.6 mm² = 628.0 mm²
__
Additional comment
The radius of the centerline of the base donut is the average of the inside and outside radii: half their sum. The diameter of the centerline circle is twice that average radius, so is equal to the sum of the inside and outside radii. This is the value we used above.
The width of the donut is the difference in the radii.
The product of the sum and difference is the same as the difference of the squares of the radii. That difference of squares would be what you have if you compute the overall area and subtract the inner area.
Highest Common Factor of 27 and 36.
Answer:
9
Step-by-step explanation:
listing the factors
27 : 1, 3, 9, 27
36 : 1, 2, 3, 4, 9, 12, 18, 36
the common factors are 1, 3, 9
the highest common factor is 9
Hi :)
The highest common factor is also known as the HCF
———————Let's find the HCF of [tex]\boldsymbol{27}[/tex] and [tex]\boldsymbol{36}[/tex].
[tex]\boldsymbol{Factors\:of\:27: 1, 3, 9, 27}[/tex]
[tex]\boldsymbol{Factors\:of\:36:1,2,3,4,6,9,12,18,36}[/tex]
HCF : [tex]\boldsymbol{9}[/tex]
[tex]\tt{Learn\:More;Work\;Harder}[/tex]
:)
The sector area of a region of a circle is 23 mi². The central angle, 0 (theta), is 25°. What is the radius?
The radius of the sector is 10.27 miles
How to find the radius of a sector?The area of a sector can be represented as follows;
area of a sector = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
∅= 25 degrees
area of the sector = 23 miles²
area of a sector = ∅ / 360 × πr²
23 = 25 / 360 × πr²
cross multiply
23 × 360 = 25πr²
8280 = 25πr²
divide both sides by 25
πr² = 8280 / 25
πr² = 331.2
r² = 331.2 / 3.14
r² = 105.477707006
r = √105.477707006
r = 10.2702336877 miles
Therefore, the radius of the sector is 10.27 miles
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Select the graph of the solution. Click until the correct graph appears.
| x | + 1 > 2
Answer: Third Graph
Step-by-step explanation:
Given inequality
|x| + 1 > 2
Subtract 1 on both sides
|x| + 1 - 1 > 2 - 1
|x| > 1
Simplify the absolute value sign
x > 1 or x < -1
Apply the inequality to the graph
Since it is less than or greater than, the circle should be hollow
Since it is less than -1 or greater than 1, one line should point to the left and another should point to the right
Therefore, it should be the Third Graph
How many different 2-digit numbers are there with the following property:the tenth digit is greater than the units digit?
Answer:
45
Step-by-step explanation:
Simply start by listing out the numbers from smallest to largest.
We start out with the smallest number following this information being the number 10. The next are 21 and 20. The next are 32, 31, and 30. We can start to see a pattern. If the ten's digit is n, then there are n numbers within that ten-group that have a greater 10's digit than unit's digit. The largest ten-group (90 to 98) has 9 integers following the rules established. Thus, the number of 2-digit integers that have ten's digits greater than units digit is 1+2+3+...+9=45
PLEASE HELP!!
Part C
What is the difference of the x-coordinate of point A and the x-coordinate of point B?
The difference of the x-coordinate of point A and the x-coordinate of point B is 0
Coordinates of a pointThe coordinate of a point on an xy-plane is written in the form (x, y). The given figures are circles A and B where the circle A is greater than circle B.
The position of the dots in both sides are positioned at the centre and as such the coordinate point at the centre of both circle will be the origin (0, 0)
According to the question, we are to find the difference of the x-coordinate of point A and the x-coordinate of point B
x-coordinate of pint A = 0
x-coordinate of point B = 0
Take the difference
Difference = 0 - 0
Difference = 0
Hence the difference of the x-coordinate of point A and the x-coordinate of point B is 0
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PLEASE HELP ME!! I'M TIMED
All the digits of a number A are different. A number can be formed using digits that are each larger than the digits of A by one. What is the largest such number of A?
Answer: 87,654,321
Step-by-step explanation: All the digits of the number A are different so the max length of the number A is 10 digits. But, then you realise that 9 can't be used because 9+1 = 10. So, A is only 9 digits long. If we arrange them from largest to least it would be 87,654,321.
Identify if the question is
statistical or non statistical.
"How many students at your
school play soccer?"
Answer: Statistical
Step-by-step explanation:
I think its statistical because its quantitative data, meaning you can count it.
The length of a rectangle is 5 mm longer than the width. If the area of the rectangle is 24 mm^2, what is the width of the rectangle?
Answer:
8
Step-by-step explanation:
This question is asking you to solve for the following system of equations, let x be width and y be height of the rectangle.
[tex]\left \{ {{x=y+5} \atop {x*y=24}} \right.[/tex]
Since the former is already equal to x lets set the second equation to x
[tex]x*y=24[/tex]
[tex]x=24/y[/tex]
Now we have the following system of equations:
[tex]\left \{ {{x=y+5} \atop {x=24/y}} \right.[/tex]
Now that the two equations are equal, we can solve for y:
[tex]y+5=24/y[/tex]
Divide both sides by y
[tex]y^2+5y=24[/tex]
Subtract 24 from the right side setting it to 0:
[tex]y^2+5y-24=0[/tex]
Solve for y using quadratic formula:
[tex]y=\frac{-5\pm \sqrt{5^2-4\cdot \:1\cdot \left(-24\right)}}{2\cdot \:1}[/tex]
[tex]y=3,-8[/tex]
Given the y-values lets plug them into our original equations to find the intersections.
[tex]x=3+5\\x=8[/tex]
Giving intersection vector (8,3)
[tex]x=-8+5\\x=-3[/tex]
Giving intersection vector (-3,-8)
Since both the width and length of the rectangle must be positive lets use the first vector (8,3) as our solution.
The x value being 8 means the width must be 8, y value being 3 the height must be 3, these variable correlate to our original definitions of making the x value equal to the width of the carpet and y value the height of the carpet.
Answer:The width is 3mm
Step-by-step explanation:
Length= 5mm + width
Let the width be represented by W
Area=24mm^2
Since area= length x width
24=(5+ W) x W
24=5W +[tex]W^{2}[/tex]
[tex]W^{2}[/tex] +5W-24=0
The factors are 8 and -3
[tex]W^{2}[/tex]+8w-3w-24=0
Factorise
W(w+8)-3(w+8)=0
(w-3)=0 or (w+8)=0
W=3 0r w= -8
The width cannot be negative.
Hence,W=3mm