Answer:
(x + 9) (x - 7)
Step-by-step explanation:
when we put x + 9 = 0 then x = -9 as it's the root of the fuction.
same thing here: x - 7 = 0 then x = 7
Nadia built a robot to filter air and water efficiently. She expects the robot to filter more than 343 liters of
air and water while using less than 49 Joules of energy.
12A + 8W > 343 represents the number of minutes the robot filters air A and water IV to hiter more
than 343 liters of air and water.
3A +41V < 49 represents the number of minutes the robot hiters air and water while using less than 49
Joules of energy
Does the robot meet both of Nadia's expectations by filtering air for 20 minutes and filtering water for 15
minutes?
Choose 1 answer.
A. The robot meets both of Nadia's expectations.
B. The robot filters the expected amount of air and water, but it doesn't use the expected amount
of energy
C. The robot uses the expected amount of energy, but it doesn't filter the expected amount of air
and water.
D. The robot doesn't meet either of Nadia's expectations.
Answer:
The correct option is;
B. The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy
Step-by-step explanation:
The given requirements are;
Volume of air and water to be filtered by the robot = 343 liters
The amount of energy consumed by the robot < 49 joules
The number of minutes the robot filters air and water to filter more than 343 liters = 12A + 8W > 343
The number of minutes the robot filters air and with less than 49 Joule of energy = 3A + 4W < 49
Given that filtering air takes 20 minutes, filtering water takes 15 minutes, we have;
To filter more than 343 liters, we have
12*20 + 8*15 = 360 > 343
The robot meets the amount of air and water requirement
To filter with less than 49 joules we have
3*20 + 4*15 = 120 > 49
Therefore, the robot does not meet the energy requirement
The correct option is the robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.
(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)
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:
-iota^5
[tex]{ - i}^{5} [/tex]
pls tell me the answer
ill mark it as the brainliest
Answer:
[tex]\boxed{-i}[/tex]
Step-by-step explanation:
[tex]-i^5[/tex]
Use identity : [tex]i^5 =i[/tex]
[tex]-(i)[/tex]
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
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:
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
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
\[ \begin{array}{c}
P\left(A \mid E_{1}\right)=\frac{\left(\begin{array}{c} 5 \\
1 \end{array}\right)}{\left(\begin{array}{c} 15 \\ 1 \end{array}\right)}=\frac{5}{15}=\frac{1}{3} \\ P\left(A \mid E_{2}\right)=\frac{\left(\begin{array}{c} 5 \\ 2 \end{array}\right)}{\left(\begin{array}{c} 15 \\ 2
\end{array}\right)}=\frac{10}{105}=\frac{2}{21} \\
P\left(A \mid E_{3}\right)=\frac{\left(\begin{array}{c} 5 \\ 3
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 3
\end{array}\right)}=\frac{10}{455}=\frac{2}{91} \\
P\left(A \mid E_{4}\right)=\frac{\left(\begin{array}{c} 5 \\ 4
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 4
\end{array}\right)}=\frac{1}{273} \\
P\left(A \mid E_{5}\right)=\frac{\left(\begin{array}{c} 5 \\ 5
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 5
\end{array}\right)}=\frac{1}{3003} \\
P\left(A \mid E_{6}\right)=\frac{\left(\begin{array}{c} 5 \\ 6
\end{array}\right)}{\left(\begin{array}{c} 15 \\ 6
\end{array}\right)}=0
\end{array} \]
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:
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
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
Finding the Area of a Trapezoid
Use the formula A= 1/2h(b^1+b^2)
What is the area of the trapezoid?_____ square units
Answer: 75 u²
Step-by-step explanation:
1/2(5)((14)+(16))
Add in parenthesis
1/2(5)(30)
Multiply
1/2(150)
Multiply
75
Hope it helps <3
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).
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.
Write a rule in function notation for each situation:
1. Sales tax is 7% of the total price
2. For f(x) = 1/4x + 10, find x such that f(x) = 14
Then,
3. Identify the independent and dependent variables.
"The essay instructions were to write three facts about each person listed."
Answer:
1. [tex]\bold{S=f(P) = 0.07P}[/tex]
2. x = 16
3. Part 1: P is the independent variable and S is the dependent variable.
Part 2: x is the independent variable and y is the dependent variable.
Step-by-step explanation:
1. To write the function notation for:
Sales tax is 7% of the total price.
Let the total price be [tex]P[/tex].
And sales tax be [tex]S[/tex].
As per the given statement:
[tex]S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P[/tex]
Writing it in the function notation:
[tex]\bold{S=f(P) = 0.07P}[/tex]
2. To find the value of x such that [tex]f(x) = 14[/tex] and
[tex]f(x) = \dfrac{1}4x + 10[/tex]
Putting the value of [tex]f(x) = 14[/tex]
[tex]14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}[/tex]
3. To find the dependent and independent variable.
Independent variables are those whose value is not dependent on the other variable's values.
Dependent variables are dependent on the value of other variables.
In question 1:
[tex]\bold{S=f(P) = 0.07P}[/tex]
P is the independent variable.
S is the dependent variable.
In question 2:
If we write it as follows:
[tex]y=f(x) = \dfrac{1}4x + 10[/tex]
x is the independent variable and y is the dependent variable.
What’s the slope???
(4, 1 2/3) and (-2, 2/3)
Answer:
1/6
Step-by-step explanation:
using this formula
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
You get 0.1666666666666666666666666666666666666666
which is 1/6
Hope this helped, if it did, please consider giving me brainliest it will help me a lot
Have a good day! :)
Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly?
Answer:
The error was made when they factored out the i, so this would be the distributive property they did not do correctly.
Factoring out the i was never needed.
Answer:
She shouldn't have factored out the i.
Step-by-step explanation:
In both parentheses, only one of the two additives had an "i" in it, so only one of them could have i factored out of it. If she wanted to factor out the i, the equation would look like this:
(4/i + 5)i + (-3/i + 7)i.
If anything, she should have done:
5i+7i + 4-3=
12i + 1.
Factoring out the i was unnecessary.
Hope this helps!
A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of digits. The first digit cannot be and the last digit must be . How many different codes are available? (Note that 0 is considered an even number.)
Answer:
4,500 Codes
Step-by-step explanation:
Given that, the access code consists of 4 digits.
Since, the First digit cannot be zero, and the last digit has to be even.
Therefore, Locks can only use numbers (0-9), which means the first digit has 9 possible outcomes ( 1-9),
the 2nd has 10 possible outcomes (0-10),
the same with the 3rd (0-10) and
finally the 4th has only 5 possible outcomes (0,2,4,6,8),
which we assume that zero is not excluded.
Finally, Mulitply 9 x 10 x 10 x 5 = 4,500.
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:
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
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
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
1. Use words to write this expression:
9 + 7x
Answer:
nine added to seven times a number.
Step-by-step explanation:
''x'' is the unknown number which is being multiplied by 7. Than 9 is added to it.
Please answer it now in two minutes
Answer:
135.5
hope this helps :)
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
1. How many terms are in the polynomial?
2. What is the degree of the polynomial?
3. How would you classify the polynomial?
Answer:
Step-by-step explanation:
A term, loosely defined, is a product of numbers and variables. Terms are separated from one another with a + or a - sign. So we have 2 terms here.
The degree of the polynomial, because it is just in terms of x and no other variable, is the highest degree'd term. Our highest degree of x is 3, so this is a third degree polynomial.
It is classified by its number of terms:
1 term is a monomial, 2 terms is a binomial, 3 is a trinomial, and anything higher is just called a "polynomial". This has 2 terms so it is a binomial.
The answer is:
⇨ a third-degree binomial.Work/explanation:
Here's how we classify polynomials based on the number of terms:
monomial - has only one term
binomial - has two terms
trinomial - has three terms
polynomial - has four terms or more
As for degrees, those are the highest exponents the polynomial.
Now, [tex]\sf{14x^3+x^2}[/tex] has 2 terms so it's a binomial; the highest exponent is 3.
Hence, this is a third-degree binomial.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
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.
I need help with this question! solve “k” -19=b-6
k = b + 13
Step-by-step explanation:k - 19 = b - 6
k = b + 19 - 6
k = b + 13
Answer:
[tex]\boxed{k=b+13}[/tex]
Step-by-step explanation:
[tex]k-19=b-6[/tex]
Add 19 on both sides.
[tex]k-19+19=b-6+19[/tex]
[tex]k=b+13[/tex]
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: