The value(s) for which the rational expression −5u+12−2u+2 is undefined is u = 1.
What is radial expression?The expression or an equation which can be undefined at some point is a celled the radial expression.
f(u) = -5u +12 / -2u +2
For the function to be undefined, denominator must be equal to zero.
-2u +2 =0
-2u =-2
u = 1
Thus, the value for which the given expression is undefined is 1.
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What is the solution of the quadratic equation (4y-3)^2=72
Answer:
To solve this quadratic equation, take the square root of both sides.
Since the left side is a perfect square, it will just be reduced to:
4y - 3
For the constant on the right side, the positive and negative roots must be considered.
√72 = ±6√2
Equating the two:
4y - 3 = ±6√2
4y = 3 ± 6√2
y = (3 ± 6√2)/4
y = (3 + 6√2) / 4 = 2.87
and
y = (3 - 6√2) / 4 = -1.37
the polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity at x=-2.
find a possible formula for P(x)
P(x)=
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
Given the roots of the polynomial, therefore, the following details can be written as,
The polynomial has a root of multiplicity 2 at x=2, (x-2)²The polynomial has a root of multiplicity 2 at x=0, (x-0)²The polynomial has a root of multiplicity 1 at x=-2, (x+2)¹Therefore, the polynomial will become,
P(x) = (x-2)²(x-0)²(x+2)¹
= (x²+4-4x) (x)² (x+2)
= (x²+4-4x) (x³+2x²)
= x⁵ + 2x⁴ + 4x³ + 8x² - 4x⁴ -8x³
= x⁵ - 2x⁴ - 4x³ + 8x²
Hence, the possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².
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A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder
with a height of 7 cm and a radius of 2 cm. The paper label is wrapped around the can and covers only
the side of the can (not the top or bottom). The company uses, on average, 3612.64 cm² of paper
each minute making these labels. How many labels does the company make, on average, each
minute?
For your calculations, do not round any intermediate steps, and use the button on a calculator. Round
your answer to the nearest hundredth.
The company needs 41 labels on average, each minute.
What is the circumference of a circle?The perimeter of a circle (circumference): 2 π radius
Replacing with the values given:
C = 2 (3.14) 2 = 12.56 cm
So, the area of one label is:
Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.
Now, the number of label be n
87.92 x n = 3612.64 cm2
n = 3612.64 / 87.92
n = 41.09
Hence, The company needs 41 labels on average, each minute.
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hello, please help me match these!
Answer:
1)x+1
2)x-1
3)x+1,R-1
Step-by-step explanation:
please mark me as brainlest
What to do when forget the pasword to the account?
Answer:
usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"
In a recent international sport competition the top three countries country A country B and country C won a total of 120 medals. country B won 11 more medals than country C .country A won 38 more medals than the total amount won by the other two . how many medals did each of the top three countries won.
An equation is formed of two equal expressions. The medals won by country A, country B, and country C is 79, 26, and 11, respectively.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of medals won by country A, country B, and country C be represented by A, B, and C, respectively. Now, the given conditions can be written as,
1.) The top three countries country A, country B, and country C won a total of 120 medals.
A + B + C = 120
2.) Country B won 11 more medals than country C
B = C + 11
3.) Country A won 38 more medals than the total amount won by the other two.
A = B + C + 38
A - 38 = B + C
Substitute the value of B+C form the last equation to the first equation,
A + A - 38 = 120
A = 79
Now, Substitue the value of A and B(from second equation) in the first equation,
79 + C + 11 + C = 120
C = 15
Now, substitute the value of C in the second equation,
B = C + 11
B = 15 + 11
B = 26
Hence, the medals won by country A, country B, and country C is 79, 26, and 11, respectively.
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A coin tossed 5 times. What is the probability of getting
i) All heads?
ii) All tails?
iii) Exactly 2 heads
iv) Exactly 3 tails
v) Exactly 1 head
vi) At least two heads
umm....... I think it was exactly 2 head
A basket contains 3 oranges and 3 mangoes. A playful baby picks two fruits at random from this basket. If X denotes the number of oranges thus picked, determine the probability distribution of X
There are [tex]\binom62=15[/tex] ways of selecting any two fruit from the basket, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
If the baby picks out [tex]k[/tex] oranges, where [tex]k\in\{0,1,2\}[/tex], it can do so in
[tex]\dbinom 3k \dbinom3{2-k} = \dfrac{3!}{k!} \dfrac{3!}{(2-k)! (1 + k)!}[/tex]
ways.
Then the PMF (probability mass function) of [tex]X[/tex] is
[tex]P(X=x) = \begin{cases} \dfrac{\binom30 \binom32}{\binom62} = \dfrac3{15} & \text{if }x=0 \\\\ \dfrac{\binom31 \binom31}{\binom62} = \dfrac9{15} & \text{if }x = 1 \\\\ \dfrac{\binom32 \binom30}{\binom62} = \dfrac3{15} & \text{if }x=2 \\\\ 0 &\text{otherwise}\end{cases}[/tex]
(6.03)
What is the constant term in the expression 6x³y + 8x² + 5x + 7? (Input a numeric value only.)
Numerical Answers Expected!
Answer for Blank 1:
The volume of a cone of height 4cm is 48cm². Find the radius (take π=22/7)
Answer:
22
Step-by-step explanation:
Is easy just multiple
Help help needed for composition of function
Answer:
[tex]\circledast \ \ f\circ f\left( x\right) = x[/tex]
[tex]\circledast \ \ g\circ g\left( x\right) =4x - 21[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{5}{2x}[/tex]
g(x) = 2x - 7
==============
[tex]f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }[/tex]
[tex]=\frac{5}{2\left( \frac{5}{2x} \right) }[/tex]
[tex]=\frac{5}{\left( \frac{5}{x} \right) }[/tex]
[tex]=5\times\frac{x}{5}[/tex]
[tex]=x[/tex]
_____________
[tex]g\circ g\left( x\right) =2(g(x)) - 7[/tex]
= 2(2x - 7) - 7
= 4x - 14 - 7
= 4x - 23
pls help how do i solve for x in this equation??
Answer:
x = -2
Step-by-step explanation:
1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2
In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8.
Triangle D F E is shown. Line segment G H is drawn from side D F to side E F to form triangle G F H. The length of D G is 15, the length of G F is 5, the length of E H is 12, and the length of D E is 8.
To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that
To prove that △DFE ~ △GFH by the SSS similarity theorem, the correct answer is; Option C: HF is 4 units and GH is 2 units
How to prove the similarity theorem?The SSS Similarity theorem states that two triangles are similar If all the three sides of one of the triangles are in same proportion to the three sides of the other triangle.
Since triangle DFE is similar to triangle GHF as seen in the attached diagram, then we can say that;
DF/GF = DE/GH
20/5 = 8/GH
GH = 2 units
Also:
EF/HF = DF/GF
(12 + HF)/HF = 20/5
HF = 4 units
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Answer these 10 questions for 30 points. serious answers only or report and low rating
Answer:
11. always
12. always
13. always
14. never
15. never
16. always
17. always
18. sometimes
19. sometimes
20. never
Step-by-step explanation:
11. A line can be defined by at least two points
12. A plane can be defined by at least three points
13. If two planes intersect, then they form a line at the intersection.
14. If two lines intersect, then they form a point at the intersection (not a segment).
15. A line does not have any endpoints (infinite in both ways).
16. If two planes are not parallel they will always intersect.
17. If two lines are not parallel they will always intersect.
18. Two points are sometimes collinear. It depends on where they are.
19. Two points are sometimes coplanar. It depends on where they are.
20. Ray MN and NM are not the same ray because the end points are different.
A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than two percentage points
Answer:
The number of computers that must be surveyed is 1681.
Step-by-step explanation:
The formula to find the sample size is given by:-
[tex]n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}[/tex]
where p = prior population proportion,
[tex]\frac{z_{\alpha }}{2}[/tex]= Two-tailed z-value for ∝
E= Margin of error.
As per the given, we have
Confidence level :
1 - ∝ = 0.90
⇒∝= 1 - 0.90= 0.10
Two -tailed z-value for ∝= 0.10 : [tex]\frac{z_{\alpha }}{2}[/tex] = 1.64
E= 2%=0.02
We assume that nothing is known about the percentage of computers with new operating systems.
Let us take p=0.5 [we take p= 0.5 if the prior estimate of proportion is unknown.]
The required sample size will be:-
[tex]n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}[/tex]
=> [tex]0.25(82)^{2}[/tex]
=> 1681
Hence, the number of the computer must be surveyed = 1681
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A paramedic maintains a time card for hours she works on the rescue squad. How many hours did she work per week ?
39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:
We can write a mixed fraction in a fraction:
6 1/2 = 13/2
8 1/2 = 33/2
7 3/4 = 31/4
8 1/12 = 97/12
8 5/12 = 101/12
Adding all the fractions:
[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{33}{2}[/tex]
[tex]=23+\dfrac{64}{4}[/tex]
= 39 hours
Thus, 39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
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Find all (a, b, c, d) in R4
such that the given set is orthogonal.
{(1, 2, 1, 0), (1, −1, 1, 3), (2, −1, 0, 1), (a, b, c, d)}
Answer:
[tex]\left[\begin{array}{}0&\\1&\\-2&\\1&\end{array}\right][/tex] t in R Correct option (B)
Step-by-step explanation:
Orthogonal vectors : We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.
Dot product : The dot product of two vectors is equal to the sum of the products of the individual components of the two vectors.
for the given vector (a, b, c, d) to be orthogonal its dot product with each vector must be 0
therefore (1, 2, 1, 0).(a, b, c, d) = 0
a + 2b+ c+ 0 = 0 -------- (i)
similarly (1, -1, 1, 3 ).(a, b, c, d) = 0
a - b + c + 3d = 0 -------- (ii)
(2, -1, 0, 1).(a, b, c, d) = 0
2a - b + 0 + d = 0 ---------- (iii)
subtracting equation (i) from (ii)
a - b + c + 3d - a - 2b - c - 0 = 0
-3b + 3d = 0
b = d
substituting b = d in (iii)
2a + b + 0 + b = 0
2a + 2b = 0
a = 0
substituting a = 0 , b = d in (i)
0 + 2d + c + 0 = 0
c = -2d
thus for any t ∈ R, vector(0, t, -2t, t) will make the given set orthogonal
the above vector can also be written as (0, 1, -2, 1)
therefor option B is correct
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Find the slope of the line
Answer:
3/2
Step-by-step explanation:
comparing the straight line with ax + bx + c = 0,
we get a = 3 and b = -2
we know,
slope of line = -a/b
= -3/-2
= 3/2
Hope it helped
If angle 1= 105°, angle 12= (3x + 15)°, and angle 7 = (8y-5)°, determine the values
of x and y?
The value of the variable x is 30° and the value of the variable y is 10°.
The missing diagram is attached below.
What is an angle?The angle is the distance between the intersecting lines or surfaces.
Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.
Vertically opposite angle – When two lines intersect, then their opposite angles are equal.
Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.
If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.
∠1 = ∠5 = ∠9 = 105° (corresponding angles)
∠1 = ∠4 = 105° (Vertical opposite angles)
∠1 + ∠2 = 180° (linear angle)
∠2 = 75°
∠2 = ∠3 = 75° (Vertical opposite angles)
∠3 = ∠8 = ∠12 = 75° (corresponding angles)
Then the value of x and y will be
∠9 = ∠12
∠1 = ∠12
105° = (3x + 15)°
3x = 90°
x = 30°
∠6 = ∠7
75° = (8y – 5)°
8y = 80°
y = 10°
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you loaned a friend $100 and will charge him 5% annual simple interest when he pay it back
The amount of interest after 3 years will be $15.
The complete question is given below.
You loaned a friend $100 and will charge him 5% annual simple interest when he pay it back. What is the amount of interest after 3 years?
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The interest is given as
I = (P × R × T) / 100
Where, P is the initial amount, R is simple interest rate, and T is the time.
We have
P = $100
R = 5%
T = 3 years
Then the interest will be
I = (100 × 5 × 3) / 100
I = $15
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Which is the graph of f(x) = 100(0.7)?
I assume you meant [tex]f(x)=100(0.7)^{x}[/tex]. The graph is shown in the image below.
Answer:
Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
Step-by-step explanation:
Edge
Account earns 8.5% interest. If you invest $6,609 now how much interest will you earn in 5years
Answer:
simple interest is $281(nearest whole number)
Step-by-step explanation:
S. I=PXTXR
100
P=$6609
T=5
R=8.5 or 85/10
S. I=6609X5X85
100X10
=280.8825
=281
Find the slope of the line passing through the points (-5, -3) and (0, -4).
Answer:
To find the slope:
[tex]\frac{(y_{1} - y_{2})}{(x_{1} - x_{2})} =\frac{(-3-(-4))}{(-5-0)} =\frac{1}{-5}[/tex]
Hope it helps!
Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection. Which function f represents the relationship between the number of stamps (s) and the number of weeks (w)?
A.
s = f(w) = 12 + 4w
B.
w = f(s) = 12s + 4
C.
s = f(w) = 12 + 4s
D.
w = f(s) = 12w + s
E.
s = f(w) = s – 12
The function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection.
The number of stamps is s and the number of weeks is w.
s = f(w) = 12 + 4w
Because Every week, he adds 4 more stamps to the collection
Thus, the function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.
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Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard. (the answer is 10 points but can someone please tell me how to do it and pls explain why)
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Help me PLEASEEE!!! ASAP
A retailer purchases postcards for $0.50 and sells them for $0.70. What is the markup?
0.70 -0.50 = 0.20 cent mark up
0.20/0.50 = 0.40 = 40% markup
GUYS PLEASE HELP WITH THIS PLEASE
Examine how sounds of music are related to trigonometric functions.
What does change of amplitude do? How about frequency?
Using graphs and equations, represent multiple transformations explaining their relevancy to the sound wave
The sounds of music are related to trigonometric functions because trigonometry is used in measuring the level of the pitch of a sound wave or musical note.
How is trigonometry used in sound?It should be noted trigonometry is important for measuring pitch level. The notes are measured in Hertz.
A sound wave's amplitude relates to the change in the pressure that's caused by the wave measured at a specific location.
The sound is perceived as louder when the amplitude increases.
Pieces of music often have repetitive choruses or bars, similar to patterns. In mathematics, we look for patterns to interpret and predict the unknown. Music uses the same techniques. If you look at a piece of music, artists look at the notes they see to find the rare (high or low) and uncommon notes.
In this way, the notes are related. Relationships are important in mathematics and create an interesting link between music and mathematics.
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What is a value plus 8, in algebraic expression
In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F. The highest monthly average temperature occurs in July at 78 °F. Write and graph a sinusoidal curve equation to model the average monthly temperature in Michigan. Assume the period is 12 months and that January is at the origin of the graph of this function. (6 points)
ANSWER ATTACHED
sinusoidal curve equation 29 sin ([tex]\pi[/tex]/9 x)-49
What is Equation of a sinusoidal curve ?Given the graph of a sinusoidal function, we can write its equation in the form y = A·sin(B(x - C)) + D using the following steps. D: To find D, take the average of a local maximum and minimum of the sinusoid. y=D is the "midline," or the line around which the sinusoid is centered.
In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F.
The highest monthly average temperature occurs in July at 78 °F
Assume the period is 12 months and January is at the origin of the graph of this function.
sinusoidal curve equation that models the data y
Then, Graph the curve using x = 0 for January, and x = 11 for December, so that x = 12 will be the start of the next year, or end of the period.
So, using the property of sinusoidal curve equation we have
=29 sin ([tex]\pi[/tex]/9 x)-49
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