Answer:
-59.5
Step-by-step explanation:
We are given the expression
-3|t − 8| + 1.5
t = -12
Subtituting -12 for t in the expression, we have:
-3|-12 - 8| + 1.5
-3|-20| + 1.5
Note : |-20| = 20
-3 × 20 + 1.5
= -60 + 1.5
= -59.5
The value of the expression = -59.5
Consider the curve of the form y(t) = ksin(bt2) . (a) Given that the first critical point of y(t) for positive t occurs at t = 1 tells us that y '(0) = 1 y(0) = 1 y '(1) = 0 y(1) = 0 Given that the derivative value of y(t) is 3 when t = 2 tells us that y '(3) = 2 y '(0) = 2 y '(2) = 0 y '(2) = 3 (b) Find dy dt = kcos(bt2)·b2t (c) Find the exact values for k and b that satisfy the conditions in part (a). Note: Choose the smallest positive value of b that works.
Answer:
(a). y'(1)=0 and y'(2) = 3
(b). [tex]$y'(t)=kb2t\cos(bt^2)$[/tex]
(c). [tex]$ b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$[/tex]
Step-by-step explanation:
(a). Let the curve is,
[tex]$y(t)=k \sin (bt^2)$[/tex]
So the stationary point or the critical point of the differential function of a single real variable , f(x) is the value [tex]x_{0}[/tex] which lies in the domain of f where the derivative is 0.
Therefore, y'(1)=0
Also given that the derivative of the function y(t) is 3 at t = 2.
Therefore, y'(2) = 3.
(b).
Given function, [tex]$y(t)=k \sin (bt^2)$[/tex]
Differentiating the above equation with respect to x, we get
[tex]y'(t)=\frac{d}{dt}[k \sin (bt^2)]\\ y'(t)=k\frac{d}{dt}[\sin (bt^2)][/tex]
Applying chain rule,
[tex]y'(t)=k \cos (bt^2)(\frac{d}{dt}[bt^2])\\ y'(t)=k\cos(bt^2)(b2t)\\ y'(t)= kb2t\cos(bt^2)[/tex]
(c).
Finding the exact values of k and b.
As per the above parts in (a) and (b), the initial conditions are
y'(1) = 0 and y'(2) = 3
And the equations were
[tex]$y(t)=k \sin (bt^2)$[/tex]
[tex]$y'(t)=kb2t\cos (bt^2)$[/tex]
Now putting the initial conditions in the equation y'(1)=0
[tex]$kb2(1)\cos(b(1)^2)=0$[/tex]
2kbcos(b) = 0
cos b = 0 (Since, k and b cannot be zero)
[tex]$b=\frac{\pi}{2}$[/tex]
And
y'(2) = 3
[tex]$\therefore kb2(2)\cos [b(2)^2]=3$[/tex]
[tex]$4kb\cos (4b)=3$[/tex]
[tex]$4k(\frac{\pi}{2})\cos(\frac{4 \pi}{2})=3$[/tex]
[tex]$2k\pi\cos 2 \pi=3$[/tex]
[tex]2k\pi(1) = 3$[/tex]
[tex]$k=\frac{3}{2\pi}$[/tex]
[tex]$\therefore b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$[/tex]
The y'(1) =0, y'(2) = 3, and the [tex]\rm y'(t) = kb2t \ cos(bt^2)[/tex] and value of b and k are [tex]\pi/2[/tex] and [tex]3/2\pi[/tex] respectively.
It is given that the curve [tex]\rm y(t) = ksin(bt^2)[/tex]
It is required to find the critical point, first derivative, and smallest value of b.
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.
We have a curve:
[tex]\rm y(t) = ksin(bt^2)[/tex]
Given that the first critical point of y(t) for positive t occurs at t = 1
First, we have to find the first derivative of the function or curve:
[tex]\rm y'(t) = \frac{d}{dt} (ksin(bt^2))[/tex]
[tex]\rm y'(t) = k\times2bt\times cos(bt^2)[/tex] [ using chain rule]
[tex]\rm y'(t) = kb2t \ cos(bt^2)[/tex]
y(0) = 0
y'(0) = 0
The critical point is the point where the derivative of the function becomes 0 at that point in the domain of a function.
From the critical point y'(1) = 0 ⇒ [tex]\rm kb2 \ cos(b) =0[/tex]
k and b can not be zero
[tex]\rm cos(b) = 0[/tex]
b = [tex]\rm \frac{\pi}{2}[/tex]
and y'(2) =3
[tex]\rm y'(2) = kb2\times 2 \times cos(b\times2^2) =3\\\\\rm 4kb \ cos(4b) =3[/tex](b =[tex]\rm \frac{\pi}{2}[/tex])
[tex]\rm 4k\frac{\pi}{2} \ cos(4\frac{\pi}{2} ) =3\\\\\rm2 \pi kcos(2\pi) = 3[/tex]
[tex]\rm2 \pi k\times1) = 3\\\rm k = \frac{3}{2\pi}[/tex]
Thus, y'(1) =0, y'(2) = 3, and the [tex]\rm y'(t) = kb2t \ cos(bt^2)[/tex] and value of b and k are [tex]\pi/2[/tex] and [tex]3/2\pi[/tex] respectively.
Learn more about the function here:
brainly.com/question/5245372
Katya has $20.00 to spend at her college bookstore, where all students receive a 20% discount . katya wants to purchase a copy of a book that normally sells for $22.50 plus 10% sales tax. how much dose the book sell for dose katya have enough money bc bc?
Answer:
Katie is correct. You would take 20% of $22.50 (22.5 multiplied by .2). You would get $4.50 off of the book with the discount. So you would subtract 4.5 from 22.5 and get $18. Then you would take 10% of $18 for the sales tax. (18 multiplied by .1). You would get $1.80 towards sales tax. you would then add $1.80 to $18 and get $19.80
Step-by-step explanation:
The coordinates of point L on a coordinate grid are (−2, −4). Point L is reflected across the y-axis to obtain point M and across the x-axis to obtain point N. What are the coordinates of points M and N? M(2, 4), N(−2, −4) M(2, −4), N(−2, 4) M(−2, −4), N(2, 4) M(−2, 4), N(2, −4)
Answer:
M(2, −4), N(−2, 4)
Step-by-step explanation:
Transformation is the movement of a point from one place to another. If an object is transformed, all the points of the object are being changed. There are different types of transformation which are: Reflection, rotation, translation and dilation.
Reflection of a point is the flipping of a point. If a point A(x, y) is reflected across the x axis, the new point is A'(x, -y). If a point B(x, y) is reflected across the y axis, the new point is A'(-x, y).
The coordinates of point L on a coordinate grid are (−2, −4), if Point L is reflected across the y-axis to obtain point M, the coordinates of M is at (2, -4).
if Point L is reflected across the x-axis to obtain point N, the coordinates of N is at (-2, 4).
Answer: M(2, −4), N(−2, 4) So D can i get branliest
Step-by-step explanation:
Give an example of how you would solve an equation by completing the square. Describe the steps.
Answer:
Step-by-step explanation:
to solve an equation by completing the square in a quadratic formula
f(x)=ax²+bx+c
example :x²-6x-16=0
first rearrange if necessary, move the constant to one side .
x²-6x=16
second you find a new term to complete the square which is (b/2)², and add the term to both sides.(6/2)²=3²=9
x²-6x+9=16+9
x²-6x+9=25
third factorize : find the common factor between 6 and 9 which is 3
x²-6x+9=25
(x-3)²=25
last solve for x: (x-3)²=25
x-3=√25
x=3±5
x=3+5=8 or 3-5=-2
(04.02 LC)
What is the solution to the following system of equations?
X - 3y = 6
2x + 2y = 4
(-1, 3)
(3, -1)
(1, -3)
(-3, 1)
Answer:
The solution is
( 3 , - 1)Step-by-step explanation:
x - 3y = 6 ............ Equation 1
2x + 2y = 4 ............ Equation 2
Make x the subject in equation 1 and substitute it into equation 2
That's
x = 6 + 3y
2( 6 + 3y ) + 2y = 4
Expand and simplify
12 + 6y + 2y = 4
8y = - 8
Divide both sides by 8
y = - 1
Substitute y = - 1 into x = 6 + 3y
That's
x = 6 + 3(-1)
x = 6 - 3
x = 3
x = 3 y = - 1
( 3 , - 1)
Hope this helps you
Answer:
B. ( 3 , - 1)
Step-by-step explanation:
x - 3y = 6 Equation 1
2x + 2y = 4 Equation 2
x = 6 + 3y
2( 6 + 3y ) + 2y = 4
12 + 6y + 2y = 4
8y = - 8
y = - 1
x = 6 + 3(-1)
x = 6 - 3
x = 3
x = 3 y = - 1
( 3 , - 1)
An urn contains 5 white and 10 black balls. A fair die is rolled and that numberof balls are randomly chosen from the urn. What is the probability that all of theballs selected are white? What is the conditional probability that the die landed on3 if all the balls selected are white?
Step-by-step explanation:
[tex]A[/tex]- all of the chosen balls are white [tex]E_{i}-[/tex] result of the die roll is [tex]i, \quad i \in\{1,2,3,4,5,6\}[/tex]
Probabilities:
since the die is fair:
[tex] P\left(E_{i}\right)=\frac{1}{6} \quad \text { for } \quad i \in\{1,2,3,4,5,6\} [/tex]
If the die rolls [tex]i[/tex] we choose a combination of [tex]i[/tex] balls, among 10 black and five white balls, therefore
\[ \begin{array}{c}
P\left(A \mid E_{1}\right)=\frac{\left(\begin{array}{c} 5 \\
1 \end{array}\right)}{\left(\begin{array}{c} 15 \\ 1 \end{array}\right)}=\frac{5}{15}=\frac{1}{3} \\ P\left(A \mid E_{2}\right)=\frac{\left(\begin{array}{c} 5 \\ 2 \end{array}\right)}{\left(\begin{array}{c} 15 \\ 2
\end{array}\right)}=\frac{10}{105}=\frac{2}{21} \\
P\left(A \mid E_{3}\right)=\frac{\left(\begin{array}{c} 5 \\ 3
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 3
\end{array}\right)}=\frac{10}{455}=\frac{2}{91} \\
P\left(A \mid E_{4}\right)=\frac{\left(\begin{array}{c} 5 \\ 4
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 4
\end{array}\right)}=\frac{1}{273} \\
P\left(A \mid E_{5}\right)=\frac{\left(\begin{array}{c} 5 \\ 5
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 5
\end{array}\right)}=\frac{1}{3003} \\
P\left(A \mid E_{6}\right)=\frac{\left(\begin{array}{c} 5 \\ 6
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 6
\end{array}\right)}=0
\end{array} \]
Identify the two tables which represent quadratic relationships
Answer:
Option (4) and Option (5)
Step-by-step explanation:
By calculating the second difference, if the second difference in a table is equal, table will represent the quadratic relationship.
In the given option, we analyze that table given in Option (4) will represent the quadratic relationship.
x y Ist difference [tex](y_2-y_1)[/tex] IInd difference
0 4 - -
1 -4 -4 - (4) = -8 -
2 -4 -4 - (-4) = 0 0 - (-8) = 8
3 4 4 - (-4) = 8 8 - 0 = 8
Second difference of the terms in y are the same as 8.
Therefore, table of Option (4) represents the quadratic relationship.
Similarly, in Option (5) we will calculate the second difference of y terms.
x y Ist difference IInd difference
0 -4 - -
1 -8 -8 - (-4) = -4 -
2 -10 -10 - (-8) = -2 -2 - (-4) = 2
3 -10 -10 - (-10) = 0 0 - (-2) = 2
Here the second difference is same as 2.
Therefore, table of Option (5) will represent the quadratic relationship.
Answer:
Option 5 is wrong
Step-by-step explanation:
Pls help I can't understand
Answer:
A
Step-by-step explanation:
This shape is a trapezoid. We can divide into two parts: a triangle and a rectangle.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let A' be the area of the triangle.
● A'= (b*h)/2
b is the base and h is teh heigth.
b= 26-20 = 6 mm
● A'= (6*14)/2 = 42 mm^2
●●●●●●●●●●●●●●●●●●●●●●●●
Let A" be the area of the rectangle.
A"= L*w
L is the length and w is the width.
A"= 14*20
A"= 280 mm^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let A be the area of the trapezoid.
A= A'+A"
A= 42+280
A= 322 mm^2
the vertex of this parabola is at 4,-3 when the x value is 5 the y value is -6 what's the coefficient of the squared expression in the parabolas equation A-2 b2 c3 d-3
Answer:
d) -3
Step-by-step explanation:
The equation of a parabola in vertex form is given as:
y = a(x - h)² + k. Where (h, k) is the vertex of the parabola.
Given that the vertex of the parabola is at (4,-3) i.e h = 4 and k = -3.
The equation of the parabola is given as:
y = a(x - 4)² + (-3)
y = a(x² - 8x + 16) - 3
y = ax² - 8ax + 16a - 3
Given that when x = 5, y = -6. i.e:
-6 = a(5)² - 8a(5) + 16a - 3
- 6 = 25a - 40a + 16a - 3
-6 + 3 = a
a = -3
Mrs. Jones decided to buy some pencils for her class. She bought 3 packages of pencils, and each package contained 72 pencils. There are 24 students in her class and she divided up the pencils so that each student had the same amount of pencils. If there are were no pencils left over, how many pencils did each student get?
Answer:
9 pencils
Step-by-step explanation:
on a number cube (numbered 1-6) what is the probability of rolling a 3?
Answer:
1
Step-by-step explanation:
There is only one 3 on the cube
PLEASE HELP. I WILL REWARD BRAINLY TO WHO EVER ANSWERS CORRECTLY. (ignore selected answer) Recalling the SAT scores are always expressed as multiples of 10, how many points did you get on the test?
Answer:
C
Step-by-step explanation:
Can somebody please answer as many as possible?
Please and thankyou!
A quadrilateral is 360 degrees
I cant make a shape for any! Please help!
Answer:
Simply subtract the sum of the the three angles given from 360° in order to get the measure of the fourth angle!
Step-by-step explanation:
41 points * please help Write a linear equation - wil give brainlyist to first person
Answer:
C = 38n + 1750; 15,050
Step-by-step explanation:
We know that for each person, there's a fee of 38. That signifies that the n will be after 38. 1,750 is a one-time fee, so that's by itself. Plug it into the equation to get your first answer. Now, solve for b) by writing C = 38(350) + 1750; C = 15,050
Answer:
C = 38n + 1750; 15,050
Step-by-step explanation:
brainlist plzzzzzz
1)Determine que acción realiza la función definida como: f(x) = -7x - 7 a) Multiplica la variable independiente por -7 y luego resta 7 b) Multiplica la variable independiente por 7 y luego resta 7 c) Multiplica la variable dependiente por -7 y luego resta -7 d) Multiplica la variable dependiente por -7 y luego resta -7 2)Dada la funcion F(x) = -3x + 6 el valor de F(5) es
Answer:
a) Multiplica la variable independiente por -7 y luego resta 7
Step-by-step explanation:
Sea [tex]f(x) = -7\cdot x - 7[/tex], las acciones realizadas por la función sobre la variable independiente, esto es, [tex]x[/tex], son:
1) Multiplica la variable por 7.
2) Refleja el resultado anterior con eje de simetría en el eje x. (Multiplicación por -1).
3) Traslada vertical el resultado de 2) siete unidades en la dirección -y.
Por ende, la opción correcta es a).
Three triangles have sides of lengths 3, 4, and 5. Their respective perimeters are 6, 8 and 10. The triangles are similar to each other.
True or false
Answer:
'll tell you where the problem lies - it is IMPOSSIBLE to form triangles like this.
If the perimeter of the smallest triangle is 6 and one side is 3, then the sum of the other two sides can only be 6 - 3 = 3
One property to enable you to form a triangle is that NO ONE SIDE can be greater or equal to the sum of the other two sides. In the smallest triangle 1 side of length 3 equals the other two sides.
In the middle triangle one side of length "4" equals the sum of the other two sides and
In the large triangle one side of length "5" equals the other two sides.
Therefore when I say "triangle" above I am not actually correct because it is IMPOSSIBLE to form triangles with those dimensions of 1 side and with those perimeters
Problem PageQuestion Two pools are being filled with water. To start, the first pool contains 720 liters of water and the second pool is empty. Water is being added to the first pool at a rate of 19.25 liters per minute. Water is being added to the second pool at a rate of 41.75 liters per minute. After how many minutes will the two pools have the same amount of water? minutes How much water will be in each pool when they have the same amount? liters
Answer:
After 32 minutes the two pools will have the same amount of water.
There will be 1,366 liters in each pool when they have the same amount of water.
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
The first pool contains 720 liters of water, and it’s being added at a rate of 19.25 liters per minute.
First Pool = 720 +19.25 m
Where m is the number of minutes.
The second pool is empty, and Water is being added at a rate of 41.75 liters per minute
Second pool = 41.75m
Since both pools must have the same amount of water:
720 +19.25 m = 41.75m
Solving for m:
720 = 41.75m-19.25 m
720 = 22.5m
720/22.5 = m
32 = m
After 32 minutes the two pools will have the same amount of water.
Finally, we replace m=32 on any equation:
41.75m = 41.75 (32) = 1,336 liters
There will be 1,366 liters in each pool when they have the same amount of water.
Feel free to ask for more if needed or if you did not understand something.
here are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answer: 1320; 495
Step-by-step explanation:
Explanation is in the attachment file
Someone pls help me I’m struggling
Answer:
2850
Step-by-step explanation:
We know that only 19% of people prefer the sedans, so we have to find 19% of 15,000. Set up a proportion: [tex]\frac{19}{100}=\frac{x}{15000}[/tex], cross multiply and get 2850.
Answer:
2850 sedans per month
Step-by-step explanation:
19 % want sedans
They expect to sell 15000 cars
Take the number of cars and multiply by the percent sedans
19% * 15000
Change to decimal form
.19*15000
2850
What is the value of the expression
below?
675 - (15 - 12)³ ÷ 3
A 216
C 666
B 224
D 678
Plz help
Answer:
675 – (15-12) ³+3
675-3³ +3
675-27+3
651
Step-by-step explanation:
The value of the given expression is 666 which is the correct answer that would be an option (C).
What is the PEMDAS rule?PEMDAS rule states that the order of operation starts with the calculation enclosed in brackets or the parentheses first. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and then addition and subtraction.
We have been given the expression below as:
675 – (15-12)³ ÷ 3
Using the PEMDAS rule to determine the evaluation of the given expression
⇒ 675 – (15-12)³ ÷ 3
Apply the subtraction operation,
⇒ 675 - (3)³ ÷ 3
⇒ 675 - 27 ÷ 3
⇒ 675 - 27 / 3
Apply the division operation,
⇒ 675 - 9
Apply the subtraction operation,
⇒ 666
Therefore, the value of the given expression would be 666,
Learn more about the PEMDAS rule here :
https://brainly.com/question/20876480
#SPJ6
Please give me correct answer and fast answer it if know answer only
Answer:
Approximatley 5.8 units.
Step-by-step explanation:
We are given two angles, ∠S and ∠T, and the side opposite to ∠T. We need to find the unknown side opposite to ∠S. Therefore, we can use the Law of Sines. The Law of Sines states that:
[tex]\frac{\sin(A)}{a}=\frac{\sin(B)}{b} =\frac{\sin(C)}{c}[/tex]
Replacing them with the respective variables, we have:
[tex]\frac{\sin(S)}{s} =\frac{\sin(T)}{t} =\frac{\sin(R)}{r}[/tex]
Plug in what we know. 20° for ∠S, 17° for ∠T, and 5 for t. Ignore the third term:
[tex]\frac{\sin(20)}{s}=\frac{\\sin(17)}{5}[/tex]
Solve for s, the unknown side. Cross multiply:
[tex]\frac{\sin(20)}{s}=\frac{\sin(17)}{5}\\5\sin(20)=s\sin(17)\\s=\frac{5\sin(20)}{\sin(17)} \\s\approx5.8491\approx5.8[/tex]
PLEASE HELP!!
Factor the polynomial [tex]x^2+6x+5[/tex]. Your answer can be written as [tex](x+A)(x+B)[/tex] where A
Step-by-step explanation:
[tex]a + b = 6[/tex]
[tex]ab = 1 \times 5 = 5[/tex]
[tex]a = 1 \: \: \: \: \: \: \: \: b = 5[/tex]
[tex]( {x}^{2} + x) + (5x + 5)[/tex]
[tex]x(x + 1) + 5(x + 1)[/tex]
[tex](x + 1)(x + 5)[/tex]
Hope this is correct and helpful
HAVE A GOOD DAY!
Simplifying Rational Expressions: I need answers for both 7 and 8 below. Answers for just one or the other is also fine.
Answer:
1. Option A 2. Option DStep by step explanation
1. [tex] \frac{1}{1 - x} + \frac{x}{ {x}^{2} - 1} [/tex]
Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b} [/tex] to rewrite the fractions
[tex] - \frac{1}{x - 1} + \frac{x}{(x - 1)(x + 1)} [/tex]
Write all numerators above the Least Common Denominator ( X - 1 ) ( X + 1 )
[tex] \frac{ - (x + 1) + x}{(x - 1)(x + 1)} [/tex]
When there is a ( - ) in front of an expression in parentheses , change the sign of each term in the expression
[tex] \frac{ - x - 1 + x}{(x - 1)(x + 1)} [/tex]
Using [tex](a - b)(a + b) = {a}^{2} - {b}^{2} [/tex] , simplify the product
[tex] \frac{ - x - 1 + x}{ {x}^{2} - 1 } [/tex]
Since two opposites add up to zero, remove them from the expression
[tex] \frac{ - 1}{ {x}^{2} - 1} [/tex]
So, Option A is the right option.
___________________________________
2.
[tex] \frac{ {x}^{2} - x - 12}{ {x}^{2} - 16} - \frac{1 - 2x}{x + 4} [/tex]
Write - X as a difference
[tex] \frac{ {x}^{2} + 3x - 4x - 12 }{ {x}^{2} - 16 } - \frac{1 - 2x}{x + 4} [/tex]
Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression
[tex] \frac{ {x}^{2} + 3x - 4x - 12 }{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]
Factor the expression
[tex] \frac{x(x + 3) - 4(x + 3)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]
Factor out X+3 from the expression
[tex] \frac{(x + 3)(x - 4)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]
Reduce the fraction with x-4
[tex] \frac{x + 3}{x + 4} - \frac{1 - 2x}{x + 4} [/tex]
Write all the numerators above the common denominator
[tex] \frac{x + 3 - ( 1- 2x)}{x + 4} [/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \frac{x + 3 - 1 + 2x}{x + 4} [/tex]
Collect like terms
[tex] \frac{3x + 3 - 1}{x + 4} [/tex]
Subtract the numbers
[tex] \frac{3x + 2}{x + 4} [/tex]
Undefined at,
X + 4 = 0
Move constant to R.H.S and change its sign
[tex]x = 0 - 4[/tex]
Calculate
[tex]x = - 4[/tex]
So, the answer is :
[tex] \frac{3x + 2}{x + 4} [/tex] , undefined at X = -4 and 4
Hope this helps..
Best regards!!
Una máquina llena 4 baldes de helado en 30 minutos, funcionando siempre a la misma velocidad Si ante un corte de luz, solo funcionó durante 45 minutos, ¿cuántos baldes habrá llenado?
Answer:
La máquina llenó:
6 baldes
Step-by-step explanation:
Por regla de tres:
4 baldes son a 30 minutos
M baldes son a 45 minutos
M = 45*4/30
M = 180/30
M = 6
P(x) has factors (x-2), (x+1), and (x-3). Decide if there is only one polynomial that has these factors. Justify your answer.
Answer:
See explanation
Step-by-step explanation:
if multiply the 3 factors together you get
(x² - x - 2)(x - 3) - trinomial x binomial
x³ - 3x²- x² + 3x - 2x + 6 - polynomial
x³ - 4x² + x + 6, this is the polynomial with those factors.
Poly means many so it could be a bigger polynomial with more factors but if it is limited to only these factors than there is just the one polynomial.
The polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3)
What is polynomial?A polynomial is the defined as mathematical expression that have a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 12 -2 = 10
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
Given that ,
P(x) has three factors (x-2), (x+1), and (x-3).
Multiplying the 3 factors together, we get
⇒ (x-2)(x+1)(x-3)
⇒ [x(x-3) - 2(x+1)](x-3)
⇒ (x² - x - 2)(x - 3)
⇒ x³ - 3x²- x² + 3x - 2x + 6
Rearrange the terms likewise and apply arithmetic operations
⇒ x³ - 4x² + x + 6
Hence, the polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3).
Learn more about polynomial here:
https://brainly.com/question/11536910
#SPJ2
You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a Heart and the second card is a Spade. Write your answer as a decimal rounded to four places if necessary.
Answer:
The probability that the first card is a Heart and the second card is a Spade is 0.064.
Step-by-step explanation:
A standard deck of 52 cards is shuffled and two cards are drawn without replacement.
The denominations of the cards are as follows:
Spades (S) = 13
Hearts (H) = 13
Diamonds (D) = 13
Clubs (C) = 13
Compute the probability of selecting a Heart first as follows:
[tex]P(H)=\frac{13}{52}=0.25[/tex]
Compute the probability of selecting a Spade second as follows:
[tex]P(S)=\frac{13}{51}=0.255[/tex]
Since the two cards are selected without replacement the second draw is independent of the other.
Then the probability that the first card is a Heart and the second card is a Spade is:
[tex]P(1st\ H\cap 2nd\ S)=P(H)\times P(S)[/tex]
[tex]=0.25\times 0.255\\=0.06375\\\approx 0.064[/tex]
Thus, the probability that the first card is a Heart and the second card is a Spade is 0.064.
Find the area of the semicircle need help asapp
Answer:
2 pi
Step-by-step explanation:
The radius is 2
The area of a circle is
A = pi r^2
We have 1/2 of a circle so
1/2 A = 1/2 pi r^2
=1/2 pi ( 2)^2
=1/2 pi *4
= 2 pi
FIRST CORRECT ANSWER GETS BRAINLIEST 50 PTS [tex](2x-5)^{2} +3(2x-5)-18[/tex]
Answer:
4x² -14x - 8
Step-by-step explanation:
(2x - 5)² + 3(2x-5) - 18
Expand brackets.
(2x-5)(2x-5) + 6x -15 - 18
2x(2x-5)-5(2x-5) + 6x - 33
4x² - 10x - 10x + 25 + 6x - 33
Combine like terms.
4x² -14x - 8
Answer:
4x^2 -14x -8
Step-by-step explanation:
( 2x-5)^2 + 3( 2x-5) -18
Foil
(2x-5)(2x-5) = 4x^2 -10x-10x +25 = 4x^2 -20x+25
Distribute
3( 2x-5) = 6x -15
( 2x-5)^2 + 3( 2x-5) -18
Replace with the foil and distribute
4x^2 -20x+25 +6x -15 - 18
Combine like terms
4x^2 -14x -8
a blue dice and a green dice are rolled. Find the probability that the blue is either 1 or 2 and the green is 1.
Answer:
2
Step-by-step explanation:
green
Answer: 2
Step-by-step explanation:
Please answer this question now correct
Answer:
Step-by-step explanation:
cosine law
a²=b²+c²-2(bc)cos44 (c=20, b=15)
a²=15²+20²-2(15*20)cos44
a=√15²+20²-2(15*20)cos44
a=13.91