37.50
Step-by-step explanation:
What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 i? f(x) = x2 – 2x 2 f(x) = x3 – x2 4x – 2 f(x) = x3 – 3x2 4x – 2 f(x) = x2 – x 2
The polynomial with the lowest degrees and a leading coefficent of 1 will be f(x) = x^2 – x
Polynomial functionThese are function with leading degree of 3 and above
Given the standard polynomial function of degree 3
ax³+bx²+cx+d
The leading coefficient is "a"
The polynomial with the lowest degrees and a leading coefficent of 1 will be f(x) = x^2 – x
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Elias was given a lock for his school locker. The lock contains numbers between
O and 59 (60 different numbers). If 3 numbers are used to unlock the lock, and
the numbers can't repeat, how many codes can his lock have?
Answer:
34,220
Step-by-step explanation:
Because order doesn't matter, but the numbers can't be repeated, we need to find the number of combinations where 3 individual numbers can be chosen out of 60 possible numbers using the binomial coefficient:
[tex]\binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{60}{3}=\frac{60!}{3!(60-3)!}\\\\\binom{60}{3}=\frac{60!}{3!(57)!}\\\\\binom{60}{3}=\frac{60*59*58}{3*2*1}\\ \\\binom{60}{3}=34220[/tex]
Thus, Elias can make 34,220 unique 3-number codes given 60 different numbers.
Would somebody be willing to help me please! I really need to pass this lesson!!
Answer:
x= -2 y= 36 (-2. 36)
x = -1 y = 6 (-1, 6)
x = 1 y = [tex]\frac{1}{6}[/tex] (1, [tex]\frac{1}{6}[/tex])
Step-by-step explanation:
Our function is [tex]y = (\frac{1}{6})^x[/tex]
all we need to do is fill in our x (given in the table) to solve for y
[tex]y = (\frac{1}{6})^{-2}[/tex]
[tex]y = 36[/tex]
[tex]y = (\frac{1}{6})^{-1}[/tex]
[tex]y = 6[/tex]
[tex]y = (\frac{1}{6})^1 = \frac{1}{6}[/tex]
How many different trains can you make of length three?
Using the combination formula, and supposing that you have n parts, it is found that the number of trains you can make is of:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
The order in which the parts are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 3 parts are taken from a set of n, hence the total number of trains is given by:
[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]
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◄) There were 60 dogs at the dog park last Saturday, and 30 of them were purebreds.
Considering this data, how many of the next 18 dogs to arrive at the park next Saturday
should you expect to be purebreds?
purebreds
Submit
30!outcof 60 were purebreds 30/60 = 1/2
1/2 of the dogs were purebreds.
18 x 1/2 = 9
Answer: 9 dogs
Answer:9 points
Step-by-step explanation:in the hyperproberbillity of things it’s this answer.
Simplify the expression.
-81 ÷ (-9)
Please help
Answer:
-81/-9
both minus will be cut so
81/9
9
Step-by-step explanation:
the answer is 9
a shoe company needs to create a shoe box...
Answer:
Step-by-step explanation:
21/7=3
5*3=15 width
3*3=9 height
Alice’s backyard is a rectangular piece of property that is twice as long as it is wide. the total area of her yard is 1,000 m2. what is the approximate width of her backyard? a = lw 11.2 m 15.8 m 22.4 m 44.8 m
Which factor do 64x2 + 48x + 9 and 64x2 – 9 have in common?
Answer:
They have the factor (8x +3) in common.
Explanation:
Factorize 1
64x² + 48x + 9
64x² + 24x +24x + 9
8x(8x +3) +3(8x +3)
(8x +3)(8x+3)
Factorize 2
64x² – 9
(8x)² – 3²
[tex]\sf {Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
(8x-3)(8x+3)
Please simplify this!
Answer:
May be the answer is 5 . I don't think it's the answer .
Solve for y y/8 = 4
Answer:
32
Step-by-step explanation:
Multiply both sides by 8.
y/8 = 4
y/8 × 8 = 4 × 8
y = 32
There are 6 marbles in a bag: 1 blue, 1 red, 1 white, 1 yellow, 1 green, and 1 black. Mary picks one marble at random and then her sister chooses another from those left in the bag.
What is the probability that Mary picks the red marble and her sister picks the blue marble?
Answer:
1 in 30
Step-by-step explanation:
1 in 6 chance Mary picks the red marble in the first place. After this there is a 1 in 5 chance her sister picks the blue one. 5 multiplied by 6 is 30.
The probability that Mary picks the red marble and her sister picks the blue marble is [tex]\frac{1}{30}[/tex] .
Concept:Firstly, we need to find the probability of Mary picking a red marble from the 6 marbles.Secondly. we need to find the probability of Mary's sister picking a blue marble from the 5 left marbles.As both are mutually exclusive events , the required probability is the multiplication of both above.How to solve the given question?P(A) = Mary picking a red marble out of 6 marbles = [tex]\frac{1}{6}[/tex]P(B) = Mary's sister picking a blue marble out 5 left marbles = [tex]\frac{1}{5}[/tex]P(E) = Required probability = P(A) × P(B) = [tex]\frac{1}{6}[/tex] × [tex]\frac{1}{5}[/tex] =Thus, the probability that Mary picks the red marble and her sister picks the blue marble is [tex]\frac{1}{30}[/tex] .
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what is the surface area of a rectangular prism that has a length of 5 cm, a height of 14 cm, and a width of 12 cm? a. 298 cm2 b. 378 cm2 c. 616 cm2 d. 596 cm2
Answer:
sorry for being late but the answer is c 616 cm
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Can someone please answer this, ill give you brainliest Would be very appreciated.
Explanation:
f(x) = (x-4)(x+2)
1) For x-intercept, y will be 0
(x-4)(x+2) = 0(x-4) =0, (x+2) = 0x = 4, x = -2x-intercept: (4, 0), (-2, 0)
2) For vertex: x = -b/2a where ax² + bx + c
Quadratic function:
(x-4)(x+2)x² +2x-4x -8x² -2x -8vertex:
x = -(-2)/2(1)x = 1y: (x-4)(x+2) = (1-4)(1+2) = -9
ordered pair of vertex: (1, -9)
3) For y-intercept, x will be 0
(x-4)(x+2)(0-4)(0+2)-8y-intercept: (0, -8)
Answer:
(4, 0) and (-2, 0)(1, -9)(0, -8)Step-by-step explanation:
Q1 : Finding x-intercepts
Take f(x) to be 0, because the intercepts lie on the x-axis0 = (x - 4)(x + 2)x = 4 and x = -2The x-intercepts are : (4, 0) and (-2, 0)Q2
Coordinates of vertex are : (h, k)Expand the polynomialx² - 2x - 8h = -b/2a = 2/2 = 1k = -D/4aD = b² - 4ac = 4 - 4(1)(-8) = 4 + 32 = 36k = -36/4 = -9The vertex is : (1, -9)Q3
Take x = 0y = 0² - 2(0) - 8y = -8y-intercept is : (0, -8)On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. it crosses the y-axis at (0, 4). what is the initial value of the exponential function shown on the graph? 0 1 2 4
Answer:
its 4
Step-by-step explanation:
trust me bro im a geinus
The initial value of the exponential function shown on the graph should be 4.
What is an exponential function?The exponential function represents a dependency relationship. In this type of mathematical operation there is a variable in the exponent and the real number in the base.
In this case, the exponential function is:
F(X)=Y
Knowing that the given points correspond to X=0 and Y= 4, when placing in the formula of the function, one finds:
F(0)=4
F(4)=0
So, the initial value of the exponential function shown on the graph should be 4.
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Problem 4.2
A textbook has 428 numbered pages, starting with 1.
A textbook has 428 numbered pages, starting with 1.
You are equally likely to stop on any of the pages if you flip through the book randomly.
What is the probability that you turn to an even-numbered page?
Answer:
50%
half of the numbers are even
Step-by-step explanation:
Please, please help. Unit test is due. (K12 User)
△ACB is bisected by CP←→. m∠PCB=65° and PB=11 ft.
What is the approximate area of each half of △ACB ?
28 ft²
56 ft²
67 ft²
143 ft²
The approximate area of each half of △ACB is 28 square feet
Area of a triangleThe formula for calculating the area of a triangle is expressed as:
A = 0.5absintheta
Given the following
PB =11ft
<PCB = 65degrees
Using the SOH CAH TOA identity
tan<PCB = 11/CP
CP = 11/tan65
CP = 5.13 ft
Determine the required area
Area = 0.5(11)(5.13)sin90
Area = 5.5 * 5.13
Area . = 28 square ft
Hence the approximate area of each half of △ACB is 28 square feet
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Find the equation of a line parallel to -x + y = -5 that passes through the point
(-6,-8).
Oy=x-5
O-x+y=-2
Submit Answer
Oy=-x-2
O-z-y=14
Answer:
O -x+y=-2
Step-by-step explanation:
-x + y = -5
⇔ y = x - 5
a line parallel to y = x - 5 must have the same slope as the line y = x - 5
Then
The equation of the parallel line is of the form : y = x + p
Finding p :
the point (-6,-8) lies on the parallel line means :
-8 = -6 + p
Then
p = -8 + 6 = -2
Finally :
y = x - 2 ⇔ -x + y = -2
Nabhitha has a collection of vintage action figures that is worth $420. If the collection appreciates at a rate of 13% per year, what equation would represent the value of the collection after 6 years?
Answer:
498
Step-by-step explanation:
dI'd the math
The equation that represents the value of collection after 6 years is $420 + 54.6(6).
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given data provided by the question,
The worth of the vintage collection = is $420
The price of the collection appreciates per year = by 13%
The price appreciates per year = 420 × 13/100 = $54.6.
So, the equation for n years is,
$420 + $54.6(n)
Where n is the number of years.
$420 + $54.6(6) = $747.6
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Janet and Bill leave their home at the same time, Janet has 60 miles to travel and drives at 40 mph. Bill has 80 miles to travel and also drives at 40 mph.
a) How long does Janet's journey take?
b) How much longer does Bill spend driving than Janet?
Answer:
Question 1 = 1 hour 30 minutes
Question 2 = he spent 30 more minutes driving
Step-by-step explanation:
time = distance ÷ speed
Answer:
Below in bold.
Step-by-step explanation:
Speed = distance / time.
a) Janet's journey:
40 = 60 / t
4ot = 60
t = 60/40 = 1 1/2 hours.
Janet's journey takes 1 1/2 hours.
b) Bills journey:
40 = 80/t
t = 80/40 = 2 hours.
Bill travels for 1/2 hour more than Janet.
Segment side a e is 7 inches and side a h is 7 startroot 3 endroot inches. what is the length of side e h? round to the nearest tenth. a cube. the top face has points a, b, d, c. the bottom face has points e, f, h, g. 7.0 inches 9.9 inches 12.1 inches 14.0 inches
The length of the side eh can be found using Pythagoras theorem. Therefore, EH = 9.9 inches
How to use Pythagoras theorem?Pythagoras theorem can be used to find eh.
Therefore,
c²= a² + b²
where
c = hypotenuse sidea and b are the other two legs.Therefore,
AE = 7 inches
AH = 7√3 inches
Therefore,
EH² = ( 7√3 )² - 7²
EH² = 147 - 49
EH = √98
EH = 9.89949493661
EH = 9.9 inches
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Answer: ITS BBBBBBBBBBBBBBBBBBBBB
Step-by-step explanation:
Prove the following tan^2 A/(tan A -1 )+ cot A/(1 - tan A)=1 +sec A cosec A
In Image, Question is No.4 (vi)
See below for the proof of the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
How to prove the trigonometry identity?The trigonometry equation is given as:
[tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite the equation as:
[tex]\frac{\tan^2(A) }{\tan(A) - 1} - \frac{\cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^2(A) - \cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Express cot(A) as 1/tan(A)
[tex]\frac{\tan^2(A) - \frac{1}{\tan(A)}}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^3(A) - 1}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Apply the difference of two cubes on the numerator
[tex]\frac{(\tan(A) - 1)(\tan^2(A) + \tan(A) + 1)}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Cancel out the common factors
[tex]\frac{\tan^2(A) + \tan(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite as:
[tex]\frac{\tan(A) + \tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Split the fraction
[tex]1 + \frac{\tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Express [tex]\tan^2(A) + 1[/tex] as [tex]\sec^2(A)[/tex]
[tex]1 + \frac{sec^2(A)}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Divide [tex]\sec^2(A)[/tex] by [tex]\tan(A)[/tex]
[tex]1 + \frac{1}{\sin(A)\cos(A)} = 1 + \sec(A)\csc(A)[/tex]
Take the inverse of sin and cosine
[tex]1 + \sec(A)\csc(A) = 1 + \sec(A)\csc(A)[/tex]
Both sides of the equation are the same.
Hence, the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex] has been proved
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For what values of x is x2-36=5x true? -9 and -4 -4 and 9 4 and -9 9 and 4.
Answer: -4 and 9
Step-by-step explanation:
#57 will give brainliest to the best answer. please explain
Answer:
(x+y)(z+1)
Step-by-step explanation:
trust me .......
Answer:
(x+y) (z+1)
Step-by-step explanation:
xz + x + yz + y
- group the first two terms and the last two terms.
(xz + x ) + yz + y
- factor out the greatest common factor (GCF) from each group.
x (z + 1) + y (z + 1)
- factor the polynomial by factoring out the greatest common factor, z + 1.
(x+y) (z+1)
Evaluate
6x+4y-z. X:4,y:-2,z:3
Step-by-step explanation:
x = 4
y = -2
z = 3
= 6x + 4y - z
= 6.4 + 4.-2 - 3
= 24 - 8 - 3
= 13
Solve the following literal equation for y 16=2y-4x
Answer:
y=2x+8
Step-by-step explanation:
Move 4x to other side and divide everything by 2
Combine the like terms to create an equivalent expression.
2q+2+92
Answer:
2q + 94
Step-by-step explanation:
2q + 2 + 92 ← collect like terms
= 2q + (2 + 92)
= 2q + 94
Answer:
2q + 94Step-by-step explanation:
2q + 2 + 92
Reorder and group
2q + (2 + 92)
Caculate
2q + 94
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Classify the shapes shown below. Write the letter of each shape in the category that describes it. Shapes may fall into more than one category, and not all shapes will be used. At Least 1 Right Angle At Least 2 Sides of Equal Length At Least 1 Pair of Parallel Sides (sorry i can´t show the shapes it wont let me)
The classification of the shapes into the categories described is as follows;
At Least 1 Right Angle; Right triangle, Square and Rectangle.At Least 2 Sides of Equal Length; Rectangle, Square, isosceles triangle, Parallelogram. At Least 1 Pair of Parallel Sides; Square, Rectangle, Parallelogram.What are the characteristics of place shapes?Plane shapes have peculiar characterization in each case. A triangle can either be isosceles (2 sides of equal length) or right (90⁰ angle measure).
Rectangles, squares and Parallelograms all have parallel sides.
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Bob is throwing a party. He has 22 pints of soda. At the end of the party, there are 8
pints of soda.
How many cups of soda were drank during the party?
Answer:
14
Step-by-step explanation:
If Bob has 22 pints, and one glass is one pint, the 22-8 = 14
Answer:
14
Step-by-step explanation:
you would subtract 8 pints of soda left from the total pints which is 22 to get 14 pints used during the party
22-8=14
