The polynomial remainder theorem states that the remainder of the division of a polynomial [tex]P(x)[/tex] by [tex]x-a[/tex] is equal to [tex]P(a)[/tex].
Therefore
[tex]P(-2)=4\\2\cdot(-2)^3 - 4\cdot(-2)^2 + k\cdot(-2) + 10=4\\-16-16-2k=-6\\-2k=26\\k=-13[/tex]
solve for x and y plz 12x - 5y = -20 x + 4 = y
Answer:
(0,4)
Step-by-step explanation:
System of Equations:
[tex]\left \{ {{12x-5y=-20} \atop {x+4=y}} \right.[/tex]
x= y-4 .... Change format so you can substitute to first equation
12(y-4)-5y=-20 .... Plug in x= y-4 to first equation
12y - 48 -5y = -20 ..... Distributed
7y -48 =-20 .... Added like terms
7y=28 .... Added 48 to both sides
y=4
.... Plug y into the second equation to find x
x + 4=y
x +4 = 4 .... Plugged in y
x = 4-4 .... Subtracted 4 from both sides
x=0
Your answer is (0,4)
Hope this helps:)
Un cultivo de bacterias crece y se duplica cada dos horas .¿Cu`antas veces mas grande sera el numero de bacterias en 12 horas?El numero inicial es X. Expresa usando potencias ayuda profis es para hoy ; )
Responder:
64 visitas
Explicación paso a paso:
Dado lo siguiente:
Número inicial de bacterias = x
Tasa de crecimiento = se duplica cada dos horas
¿Cuántas veces mayor será la cantidad de bacterias en 12 horas?
La cantidad de veces (n) en las que la cantidad de bacterias se duplica:
n = 12 horas / período de tasa de crecimiento
n = 12/2 = 6
Eso significa que el crecimiento de bacterias se duplicará 6 veces en 12 horas.
Por lo tanto, la cantidad de bacterias después de 12 horas será:
Después del 1er período = x * 2 = 2x
2do período = 2 ^ 2 * x = 4x
Después de n período
= 2 ^ n * x
Después de 6 períodos:
2 ^ 6 * x = 64x
Número de veces que las bacterias serán mayores en 12 horas:
Inicial = final
x = 64x
Comparando ambos
Las bacterias serán 64 veces más grandes después de 12 horas.
divide the sum of -5,-10 and -9 by the product of 2 and -3
Answer: 1/4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
=(-5)+(-10)+(-9)/2*(-3)
=-5-10-9/-6
=-24/-6
=4 ans.....
Please solve (will make brainiest)
Answer:
1a) 1/64
1b) 1/169
1c) 1/9
Step-by-step explanation:
You have to apply Indices Law :
[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]
Question A,
[tex] {4}^{ - 3} = \frac{1}{ {4}^{3} } = \frac{1}{64} [/tex]
Question B,
[tex] {13}^{ - 2} = \frac{1}{ {13}^{2} } = \frac{1}{169} [/tex]
Question C,
[tex] {( - 3)}^{ - 2} = {( - \frac{1}{3}) }^{2} = \frac{1}{9} [/tex]
Plz help me this is probably easy but im just not seeing it plz help me ASAP
Answer: is attatched to the photo I sent
Step-by-step explanation:
I admit, this is tricky, just remember to think about it as where the shapes are the most similar. I'm not exactly sure how to explain it, but where it reflects like a mirror is the "copy"
The example I'm thinking of attached too, but these over lap so its diffucult
Helpppp pleaseeeeee!!!
Answer: yes.
Step-by-step explanation:
Answer: Yes
The roll of the dice is a random process that Jon has no control over (this is assuming the dice is fair of course). Whoever is selected first is not selected again, so the probability for the second selection will increase as there is a smaller pool of people to pick from.
. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.
Answer:
The two polynomials are:
(x + 1) and (x² + x)
Step-by-step explanation:
A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.
Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.
Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.
So,
Let's multiply both numerator and denominator by (x + 1) to get;
(x + 1)/(x(x + 1))
This gives; (x + 1)/(x² + x)
Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.
Which of these relations are functions?
х
O
-2 6 2 -6
-5 21 15-15
y
11
y
4
2
O
x
4
-2
4
o
{(-5,-7), (-2,-7), (7,17), (-5,21)}
y
For each value of y, the number of value of x must be one. Then the correct options is D.
The complete question is attached below.
What is relation function?The relation function is given as, for every independent value, there is a dependent value.
Let the function be y = f(x).
For each value of x, the number of value of y may one or two.
But for each value of y, the number of value of x must be one.
Then the correct options is D.
More about the relation function link is given below.
https://brainly.com/question/2253924
#SPJ1
What is negative sqrt 64?
Answer:
8i. In real numbers only, this isnt possible, but if immagenary numbers are allowed then 8i is your answer
Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amount of space in his garden is equal to 494949 square meters. Which measurement does 494949 square meters represent?
Answer:
49 square meters represent area of the square garden
Step-by-step explanation:
Each side length=7 meters
He multiplied 7 × 7 times to find the amount of space
=49 square meters
Jack is trying to measure the area of his square garden
Area of the square garden = length^2
=Length × length
Recall,
Length=7 meters
Area of the square garden= 7 meters × 7 meters
=49 square meters
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend $
Answer:
$52.2Step-by-step explanation:
Given her total cost of ride tickets modeled by the equation c = 3.5t where c is the total cost of tickets and t is the number of tickets, If Stacy bought 15 tickets, to know the amount she would spend on 15 tickets, we will substitute t = 15 into the modeled equation as shown;
[tex]c = 3.5t\\when t = 15\\\\c = 3.5(15)\\\\c = \frac{35}{10} * 15\\ \\c = \frac{5*7}{5*2} * 15\\\\[/tex]
[tex]c = \frac{7}{2} * 15\\ \\c = \frac{105}{2}\\ \\c = \ 52.2[/tex]
Hence Stacy would spend $52.2 on 15 tickets
Answer:
I hope this helps!
Step-by-step explanation:
4.
Aliyah, Brenda and Candy share a sum of money in the ratio of 3:5:6. After
Candy gives $100 to Aliyah and $50 to Brenda, the ratio becomes 2 : 3:3.
(a) Suppose Aliyah has $3x at the start, express Candy's initial sum of money in
terms of x.
(b) Find the value of x.
(c) Hence, how much money does Brenda have in the end?
Answer:
(a) Candy's initial sum as a terms of x is $6x
(b) x = $60
(c) $350
Step-by-step explanation:
The given parameters are;
The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6
The amount Candy later gives Aliyah = $100
The amount Candy later gives Brenda = $50
The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3
(a) Whereby Aliyah has $3x at the start, we have;
Total sum of mony = Y
Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14
Therefore, Y×3/14 = $3x
x = Y×3/14 ÷ 3 = Y/14
Amount of Candy's initial share = Y × 6/14
Therefore Candy's initial sum as a terms of x = $6x
(b) Given that Aliyah's and Candy's initial sum as a function of x are $3x and $6x, therefore, in the ratio 3:5:6, Brenda's initial sum as a function of x = $5x
Which gives;
Total amount of money = $14x
With
6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3
Therefore, we have;
14·x × 2/(2 + 3 + 3) = (6·x - 150)
14·x × 2/(8) = (6·x - 150)
14·x × 1/4 = (6·x - 150)
7·x/2 = (6·x - 150)
12·x - 300 = 7·x
12·x - 7·x = 300
5·x = 300
x = $60
(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350
The final amount of money with Brenda = $350.
|3x–1|=8 please help!!!!!
Answer: -3
Add 1 to both sides
[tex]3x-1+1=8+1[/tex]
[tex]3x=9[/tex]
Divide both sides by 3
[tex]3x/3=9/3\\x=3[/tex]
10 points :) Graph this for me :P
Answer:
-2≤x≤2 f(x)=[x+3]
first the sign is ≤ it means the point is solid point and the interval is x+3
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
ху
1 | 20
3 | 10
5 | 0
7 | -10
A. Initial value: 20, rate of change: 10
B. Initial value: 30, rate of change: 10
C. Initial value: 25, rate of change: -5
D. Initial value: 20, rate of change: -10
Answer:
C, at 0/25, 1/20, 2/15, 3/10,...
Answer:
C
Step-by-step explanation:
A fish jumps out of the water at a speed of 12 feet per second. The height y (in feet) of the fish above the surface of the water is represented by the equation y=-16x^2+12x, where x is the time (in seconds) since the jump began. The fish reaches its highest point above the surface of the water after 0.375 seconds. How far above the surface is the fish at this time?
Answer:
The fish is 2.25 ft above the surface at 0.375 seconds
Step-by-step explanation:
Given:
y=-16x^2+12x
x=0.375 seconds
Substitute x=0.375 into the equation
y=-16x^2+12x
= -16(0.375)^2 +12(0.375
= -16(0.140625) + 4.5
= -2.25 + 4.5
= 2.25
y=2.25 ft
The fish is 2.25 ft above the surface at 0.375 seconds
At the Olympic games, many events have several rounds of competition. One of these events is the men's 100 100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 8 88 finishers in the final round of the 2012 20122012 Olympics. The lower dot plot shows the times of the same 8 88 swimmers, but in the semifinal round. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.) Choose all answers that apply: Choose all answers that apply:
Answer:
The center of the semifinal round distribution is greater than the center of final round distribution.
The variability in the semifinal round distribution is less than variability in the final round distribution.
Step-by-step explanation:
The mean value of each distribution set is not calculates as the center of semifinal round distribution is greater than the final round distribution. MAD Mean Absolute Deviation is calculated from the dotted graph plot, the distribution of semifinal round is less spread out than the final round distribution.
Answer:
correct answer is None of the above i understood nothing the other person was trying to say...
Step-by-step explanation:
mark me brainliest please...
find the multiplicative inverse of 3 by 4 minus 5 by 7
Answer:
28
Step-by-step explanation:
[tex]\frac{3}{4}-\frac{5}{7}[/tex]
Least Common Denominator of 4 & 7 is 4 * 7 = 28
[tex]\frac{3}{4}-\frac{5}{7}=\frac{3*7}{4*7}-\frac{5*4}{7*4}\\\\\\=\frac{21}{28}-\frac{20}{28}\\\\\\=\frac{21-20}{28}\\\\\\=\frac{1}{28}[/tex]
Multiplicative inverse of [tex]\frac{1}{28}[/tex] is [tex]\frac{28}{1} = 28[/tex]
1: The best statement for reason 6 of this proof is -∠A ≅ ∠C
-∠B ≅ ∠D
-∠B and ∠D are supplements
-∠B ≅ ∠B
2.The best reason for statements 3.5. and 7 in this proof is
- Alternate interior angles are congruent.
-Corresponding angles are congruent.
-Alternate exterior angles are congruent.
-Interior angles on the same sides of a transversal are supplements.
3. The best statement for reason 8 of this proof is
-∠B ≅ ∠B -∠A and ∠C are supplements.
-∠B ≅ ∠D
-∠A ≅ ∠C
Answer:
1) -∠B ≅ ∠D
2) -Interior angles on the same side of a transversal are supplementary
3) -∠A ≅ ∠C
Step-by-step explanation:
1) Given that ∠A and ∠B are supplements and ∠A and ∠D are supplements, we have; ∠B ≅ ∠D
2) Given that ABCD is a parallelogram, therefore ∠A and ∠B, ∠A and ∠D and ∠B and ∠C are interior angles on the same side of a transversal and are therefore supplementary
3) Given that ∠A and ∠B and ∠B and ∠C are supplementary, therefore, ∠A ≅ ∠C.
What is 12.5% of 72
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf of \ refers \ to \ multiplication.[/tex]
[tex]12.5\% \times 72[/tex]
[tex]\frac{12.5}{100} \times 72[/tex]
[tex]\sf Multiply.[/tex]
[tex]\frac{900}{100} =9[/tex]
A triangle has one side that lies along the line y=1/4x and another that lies along the line y=-1/4x. Which of the following points could be a vertex of the triangle?
Answer:
We know that our triangle has one side along the line:
y = (1/4)*x
And other side along the line:
y = -(1/4)*x.
Now, we want to find the vertex.
And we know that the vertex is the point where the two sides conect, so the vertex must be a common point of both lines.
Then we have:
y = (1/4)*x = -(1/4)*x
x = -x
The only solution to that equation is x = 0.
now we evaluate our lines in x = 0 and get:
y = (1/4)*0 = 0
y = -(1/4)*0 = 0
Then the lines intersect in the point (0, 0)
Then the vertex must be in the point (0, 0)
4x
5.
If 7:5 = (x + 2y): (x - y), find the value of
5y
Answer:
5/2 OR 2.5
Step-by-step explanation:
( x + 2y ) = 7 , ( x - 2y ) = 5
x = 7 - 2y , x = 5 + 2y
substitute the two eqns together:
7 - 2y = 5 + 2y
7 - 5 = 2y + 2y
2 = 4y
y = 1/2
when y = 1/2 ,
5y = 5(1/2)
= 5/2 OR 2.5
Which of the c-values satisfy the following inequality? 2>c/3
Answer:
[tex]\Large \boxed{{c<6}}[/tex]
Step-by-step explanation:
2>c/3
Multiply both sides of the inequality by 3.
2(3)>c/3(3)
6>c
Switch sides.
c<6
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your inequality step-by-step.
[tex]2 > \frac{c}{3}[/tex]
Step 1: Simplify both sides of the inequality.
[tex]2 > \frac{1}{3}c[/tex]
Step 2: Flip the equation.
[tex]\frac{1}{3}c < 2[/tex]
Step 3: Multiply both sides by 3.
[tex]3 * (\frac{1}{3} c) < ( 3) * (2)\\c < 6[/tex]
Answer : [tex]\boxed {c < 6}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Please please please please help
Answer:
m = 9
Step-by-step explanation:
8/12 = 6/m
8m = 72
m = 9
1.Solve by factorization method: x+1/x=11 1/11 2.Comment on the nature of roots for 4x^2-5=2(〖x+1)〗^2-7 plz, help...
Answer:
The equation
[tex]4\,x^2-5=2\,(x+1)^2-7[/tex]
can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.
Step-by-step explanation:
When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:
[tex]4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0[/tex]
We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.
LCM of x<sup>2</sup>+5x+6 and x<sup>2</sup>-x-6 is ………………………
Answer:
[tex] (x^2 - 9)(x + 2) [/tex]
Step-by-step explanation:
Given:
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 - x - 6 [/tex]
Required:
LCM of the polynomials
SOLUTION:
Step 1: Factorise each polynomial
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 + 3x + 2x + 6 [/tex]
[tex] (x^2 + 3x) + (2x + 6) [/tex]
[tex] x(x + 3) + 2(x + 3) [/tex]
[tex] (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 [/tex]
[tex] x^2 - 3x +2x - 6 [/tex]
[tex] x(x - 3) + 2(x - 3) [/tex]
[tex] (x + 2)(x - 3) [/tex]
Step 2: find the product of each factor that is common in both polynomials.
We have the following,
[tex] x^2 + 5x + 6 = (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 = (x + 2)(x - 3) [/tex]
The common factors would be: =>
[tex] (x + 2) [/tex] (this is common in both polynomials, so we would take just one of them as a factor.
[tex] (x + 3) [/tex] and,
[tex] (x - 3) [/tex]
Their product = [tex] (x - 3)(x + 3)(x +2) = (x^2 - 9)(x + 2) [/tex]
A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?
Answer:
y = -x +2
Step-by-step explanation:
y =x has a slope of 1
Perpendicular lines have slopes that multiply to -1
m* 1 = -1
The slope of the perpendicular line is -1
We have a slope and a point
y = mx+b
y= -1x+b
Substitute the point into the equation
-3 = -1(5) +b
-3 =-5 +b
Add 5 to each side
-3+5 = b
2 =b
y = -x +2
There are 9 classes of 25 students each, 4 teachers, and two times as many chaperones as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?
5 buses is the answer pls mark me brainliest
Least number of bus require for trip = 5 buses
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
Total number of classes = 9
Number of student in each class = 25
Number of teacher = 4
Number of chaperones = Double of teacher
Bus hold = 45 people
Now,
Total number of student = 9 × 25
= 225
Number of chaperones = 4 × 2
= 8
Total people = 225 + 8 + 4
= 237
Least number of bus require for trip = Total people / Bus hold
= 237 / 45
= 5.266
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
what is the sum of the interior angles of a regular hexagon
Answer:
see below
Step-by-step explanation:
The sum of the interior angles of any polygon can be found with the formula 180(n - 2) where n = number of sides. In this case, n = 6 so the answer is 180(6 - 2) = 180 * 4 = 720°.
Answer:
The sum of the interior angles of a regular hexagon is 720°
Step-by-step explanation:
As we know that the sum of interior angle is 180(n-2). So the number of sides of hexagon is 6. Now, 180(6-2)=180*4=720°
I answered all my work correctly but I don’t understand this one.
