The solution of the system is x = - 1 and y = 8/3.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
We have a system of equations,
2x+3y=6 {equation 1}
-4x+3y=12 {equation 2}
Subtracting equation 2 to equation 1,
2x - (-4x) = 6 - 12
6x = - 6
x = - 1.
And y = 8/3
Therefore, the solution is x = - 1 and y = 8/3.
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Which polynomial has zeros of 2, 5, and -4?
•
A. (x + 2)(x + 5)(x - 4)
B. (2x - 4)(x + 5)(x + 4)
c. 6 - 2)(x - 5)(x - 4)
D. (2x - 4)(x - 5)(x + 4)
The polynomial has zeros of 2, 5, and -4 is option (d) (2x - 4)(x - 5)(x + 4).
What is polynomial?A polynomial is a mathematical equation made up of indeterminates and coefficients and uses only addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
How to find the correct polynomial?To find a polynomial that has zeros 2, 5, and -4 substituted x = 2, 5, and -4 in a polynomial.
By substituted x = 2, 5, and -4 in a polynomial (2x - 4)(x - 5)(x + 4).
(a) For x=2.
The polynomial is
(2(2) - 4)(2- 5)(2 + 4) = (4- 4)(-3)(6)
= 0×-3×6
= 0
(b) For x=5.
The polynomial is
(2(5) - 4)(5 - 5)(5 + 4) = (10-4)(0)(9)
= 6×0×9
= 0
(c) For x=-4.
The polynomial is
(2(-4) - 4)(-4 - 5)(-4 + 4) = (-8-4)(-9)(0)
= -`12×-9×0
= 0
Since (2x - 4)(x + 5)(x + 4) has zeros of 2, 5, and -4
For incorrect options
By substituted x = 2, 5, and -4 in a polynomial (x + 2)(x + 5)(x - 4), (2x - 4)(x + 5)(x + 4) and (6x - 2)(x - 5)(x - 4) is not equal to zero therefore (a), (b) and (c)is not correct option.
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The correct polynomial with zeros of 2, 5, and -4 is represented by Option C, which is (x - 2)(x - 5)(x + 4), even though there is a typo in the option provided.
Explanation:The zeros of a polynomial are the values for which the polynomial evaluates to zero. These are also the solutions to the equation obtained by setting the polynomial equal to zero. Given the zeros of 2, 5, and -4, we can form a polynomial by finding the factors associated with each zero and then multiplying those factors together.
The factor associated with the zero 2 is (x - 2), the factor for the zero 5 is (x - 5), and the factor for the zero -4 is (x + 4). Multiplying these factors will give us the polynomial that has these zeros:
P(x) = (x - 2)(x - 5)(x + 4).
Comparing this expression with the options provided:
Option A is incorrect because it has factors of (x + 2) and (x - 4), implying zeros of -2 and 4.Option B is incorrect because it has the factor of (2x - 4), which simplifies to (x - 2), but includes the incorrect (x + 4).Option C is correctly formed with (x - 2)(x - 5)(x + 4), despite the typo, and represents the polynomial with the given zeros.Option D is incorrect, similar to option B.Therefore, the correct answer is Option C, which is (x - 2)(x - 5)(x + 4).
Luca wants to paint the back wall of his bedroom, and
he needs to know the area to determine the amount of
paint to buy What is the area of the wall?
Answer:
The answer is 75 ft^2
Step-by-step explanation:
I did it on
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d
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e
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u
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t
y
Answer:
The answer is 75
Step-by-step explanation:
the guy above me was correct
5x(f-32)divided by 9 for f = 95
Answer:
35x
Step-by-step explanation:
[tex]5x(f - 32) \div 9 \\ \\ = \frac{5x(f - 32)}{9} \\ \\ = \frac{5x(95- 32)}{9} \\ \\ = \frac{5x \times 63}{9} \\ \\ = 5x \times 7 \\ \\ = 35x[/tex]
Which answer gives statements that should be used to prove angles 4 and 6
are congruent?
Answer:
b is the answer
Step-by-step explanation:
since the vertical angles are in the same degrees
4 and 2 are vertical,
2 and 6 are in the same degrees
which means 4 and 6 are congruent.
:D
What is the answer to this
Answer:
I'm not totally sure but i want to help as best i can the graphs i narrowed it down to are a and c because the equation is less than or equal to its a dotted line and i think it would be answer c
Step-by-step explanation:
"h varies directly as u". If h = 8 when u = 40, find u when h = 25.
Answer:
125
Step-by-step explanation:
h=8
u=40
so k=5
hk-u
5*25=125
Answer: u = 25
Step-by-step explanation:
Emily purchased a couch, loveseat, in the chair for $2000. The Loveseat cost twice as much as the chair, and the couch cost $600 more than the love seat. Find the cost of the couch, loveseat, and chair.
Answer:
Chair $280
Loveseat $560
Couch $ 1,160
Step-by-step explanation:
chair = x
loveseat=2x
couch = 2x + 600
x +2x + 2x +600 = 2000
5x + 600 =2000 subtract 600 from both sides
5x =1400 divide by 5
x = $280
Chair is the value of x =$280
Loveseat is twice the value of x = 2 x $280 =$560
Couch is twice the value of x plus $600 = $560 + $600
The cost of a chair, the cost of a loveseat, and the cost of a couch are $280, $560, and $1,160 respectively.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
Emily purchased a couch, loveseat, in the chair for $2000.
The Loveseat cost twice as much as the chair, and the couch cost $600 more than the love seat.
Let
The cost of the chair is x, then the loveseat is 2x and the cost of the couch is 2x + 600.
Then
The sum of the cost of the chair, loveseat, and couch is $2000.
[tex]x + 2x + 2x + 600 = 2000\\[/tex]
On simplifying, we have
x = 280
Then
The cost of the chair = x = $280.
The loveseat = 2x = 2(280) = $560
The cost of the couch = 2x + 600 = 2(280) + 600 = $1,160
Thus, the cost of the chair, loveseat, and couch is $280, $560, and $1,160 respectively.
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Please help fast!!!
Answer:
whats the question
Step-by-step explanation:
ask the question
\
R is inversely proportional to A.
R = 12 when A = 1.5
a) Work out the value of Rwhen A= 5.
b) Work out the value of A when R = 9
Here are the answer: a) R = 3.6 and b) A = 2
Step-by-step explanation:
Given,
R is inversely proportional to A.
R ∝ [tex]\frac{1}{A}[/tex]
so, R = [tex]\frac{k}{A}[/tex] -------eq 1 where k is any constant
To find the values of a) R when A = 5 and
b) Value of A when R = 9
Now,
Putting R = 12 and A = 1.5 in eq 1 we get,
12 = [tex]\frac{k}{1.5}[/tex]
or, k = 12×1.5 = 18
From eq 1 we get,
R = [tex]\frac{18}{A}[/tex] --------- eq 2
Now,
a) Putting A= 5 in eq 2 we get,
R = [tex]\frac{18}{5}[/tex] = 3.6
b) Putting R = 9 in eq 2 we get
R = [tex]\frac{18}{A}[/tex]
or, A = [tex]\frac{18}{9}[/tex] = 2
Answer:
a.3.6
b. 2
Step-by-step explanation:
R is inversely proportional to A
Which means R=k/A
Cross multiply
k=RA
Since R=12
A=1.5
So k=12×1.5
=18
a. We are to determine the value for R
So R=k/A
=18/5
=3.6
b.we are to determine the value for A
So R=k/A
A=k/R
=18/9
=2
These box plots show daily low temperatures for a sample of days in two
different towns. Which statement is the most appropriate comparison of the spreads?
Given:
The box plots show daily low temperatures for a sample of days in two different towns.
We need to determine the most appropriate comparison of the spreads.
Interquartile range of town A:
The interquartile range can be determined by subtracting the end values of the boxes.
Thus, we have;
Interquartile range = 40 - 20
Interquartile range = 20
Thus, the interquartile range for town A is 20.
Interquartile range for town B:
The interquartile range for town B is given by
Interquartile range = 45 - 35
Interquartile range = 10
Thus, the interquartile range for town B is 10.
Hence, the interquartile range (IQR) for town A, 20° is greater than the IQR for town B, 10°
Hence, Option A is the correct answer.
Two basketball players average the same number of points per game. What information would be most helpful in determining
which player's game performances show the least variability?
the most and least points each player has scored in a game
the number of games each player has played
O the average number of points each players team scores per game
the total number of points each player has scored
Answer:
the average number of points each team scores per game
Step-by-step explanation:
Answer:
B. the number of games each player has played
Step-by-step explanation:
Lin plays a game that involves a standard number cube and a deck of ten cards numbered 1 through 10. If both the cube and card have the same number, Lin gets another turn. Otherwise, play continues with the next player. What is the probability that Lin gets another turn?
Answer:
6/60
Step-by-step explanation:
The probability that Lin gets another turn, P(E) could be 6/60
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
We are given that Lin plays a game that involves a standard number cube and a deck of ten cards numbered 1 through 10.
Therefore,
P(E) = Number of favorable outcomes / total number of outcomes
Outcomes of cube = { 1, 2, 3, 4, 5, 6}
Outcome of Card = {1, 2, 3} from each group.
when both the cube and card have the same number, then Lin gets another turn.
The probability that Lin gets another turn, P(E) =6/60
P(E) = 1/10
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The amount c in grams of a 100 gram sample of carbon-14 remaining after t years is represented by the equation c= 100 (0.99988)t use a calculator to find the amount of carbon-14 remaining after 4 years
Answer: The amount of carbon-14 remaining after 4 years is 99.95 grams.
Step-by-step explanation:
Hi, to answer this question we simply have to substitute t=4 in the equation given and solve for c.
c= 100 (0.99988)^t
c =100 (0.99988)^4
c = 100 x 0.999520086
c= 99.95200864 ≅99.95 grams (rounded)
The amount of carbon-14 remaining after 4 years is 99.95 grams.
Feel free to ask for more if needed or if you did not understand something.
The amount of carbon-14 remaining after 4 years is 99.95 grams.
Given that,
The amount c in grams of a 100-gram sample of carbon-14 remaining after t years is represented by the equation,
[tex]\rm c = 100(0.99988)^t[/tex]
We have to determine,
The amount of carbon-14 remaining after 4 years.
According to the question,
Equation; [tex]\rm c = 100(0.99988)^t[/tex]
Where the amount c in grams of a 100-gram sample of carbon-14 remaining after t years is represented by the equation,
To determine the amount of carbon-14 remaining after 4 years following all the steps given below.
Then,
The amount of carbon-14 remaining after 4 years is,
[tex]\rm c = 100(0.99988)^t\\\\\rm c = 100(0.99988)^4\\\\ c = 100 \times 0.999520086\\\\c = 99.95 \ gram[/tex]
Hence, The amount of carbon-14 remaining after 4 years is 99.95 grams.
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331 students went on a field trip. six buses were filled and 7 students travled in cars. how many students were in each bus
Answer:
54 Students in each bus
Step-by-step explanation:
331-7= 324
324/6 = 54
you have to initially subtract 7 fro 331 because they took cars. the rest of the students took the 6 buses.
now you are left with 324/6 which gives you 54 students per bus
Use elimination to solve the system of equation
4x+y=-2
3x+2y=6
Point form:
(-2,6)
Equation form:
x=-2, y=6
What is the volume?
9 m
19 m
7 m
Answer:1197m³
Step-by-step explanation:
Answer:
Volume of a triangular irregular prism=1300.16m^3 = 1300m^2
Volume of a rectangular prism two answers = 1197m^3 or 1233m^3
Step-by-step explanation:
With rectangular prism two answers we need the rectangle surface area first
A = 9 m x 19 m = 171m
or A = 7 m x 19m
The rectangle prism could be 1197m^3 or 1233m^3
depending how big the rectangle is as we calculate that first then multiply by depth. If we had the direction of measurement of the base we would just get one answer and not two.
Rectangular prism A = 171sq
V = 1197m^3 = (171sq x 7)
or V= 1233m^3 = 137sq x 9
If the prism is a irregular prism we add the surface area's
V = (a+b+c)B/3
V = (7x19)(9x7) (9x19) x B = 133 + 63 + 197 x 197 = 3900.5/3 =1300.16
Expand the following:
a) x(x + 5)
b) x(3x – 1)
c) 2x(2x + 3)
d) 5x(x – 3y)
Answer:
[tex] {x}^{2} + 5x[/tex]
[tex] {3x}^{2} - x[/tex]
[tex] {4x}^{2} + 6x[/tex]
[tex] {5x}^{2} - 15xy[/tex]
What does it mean when is says write a sequence hat plots the ordered pair if you start at the origin when you are plotting ??
Which answer choices list possible types of angles for this triangle?
Select two that apply.
Answer: the first and third one possibly but the first one for sure for sure
answer to -18x-17=-53
Hello :)
-18x - 17 = -53
-18x = -53 + 17
-18x = -36
-x = -2
x = 2
Answer = 2
Zeynoom Kopuyooz :d
-MERVE-
Answer:
Step-by-step explanation:
- 18x - 17 = - 53
- 18x =- 53 + 17
- 18x = - 36
Minus sign will be canceled
18x = 36
x = 36 / 18
x = 2
For the sides, round your answer to the nearest tenth.
DE =
EF =
DF =
Is the triangle scalene, isosceles, or equilateral?
HELPP!!
Answer:
it should be scalene
Step-by-step explanation:
DE: [tex]\sqrt{90}[/tex]
^^ [tex]\sqrt{(-1-8)^{2}+ (-3--6)^{2} }[/tex]
[tex]\sqrt{-9^{2} +3^{2}[/tex]
[tex]\sqrt{81+9}[/tex]
EF:[tex]\sqrt{65}[/tex]
^^[tex]\sqrt{(-2+1)^{2} + (5+3)^{2} }[/tex]
[tex]\sqrt{-1^{2}+8^{2}[/tex]
[tex]\sqrt{1+64}[/tex]
DF= [tex]\sqrt{101}[/tex]
^^
Consider the equation a-3 = (1/a)^5
What value(s) of a make the equation true?
Answer:
No solutions
Step-by-step explanation:
Equations are represented with the "=" sign. It means the expressions on either side are equal. The equation has no solution for a
Given that:
[tex]a^{-3} = (\frac{1}{a})^5[/tex] --- the correct equation
First, we apply the power rule of indices
[tex]a^{-3} = (a^{-1})^5[/tex]
Open the bracket
[tex]a^{-3} = a^{-1 \times 5}[/tex]
[tex]a^{-3} = a^{-5}[/tex]
Cancel out (a) on both sides
[tex]{-3} ={-5}[/tex]
The above solution is not true because
[tex]{-3} \ne {-5}[/tex]
Hence, the equation has no solution for a
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which number is a fact of 6?
Answer:
if you meant factor then 1, 2, 3 and 6
Answer:
1,2,3,6
Step-by-step explanation:
A factor of a number is any number that can go evenly into another number.
1 x 6 = 6
2 x 3 = 6
So, 1,2,3,6 are factors of 6
Tell me if I wrong.
If right, can I have brainliest
Sharon drinks 2/3 of 1/2 of lemonade. How much lemonade did Sharon drink?
Answer: The answer is 1/3 because you simplify your answer, and the answer is 1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
According to the question
Sharon drinks 2/3 of 1/2 of lemonade
So let's solve
To determine the amount Sharon's drinks
2/3 of 1/2
2/3×1/2
2/6
1/3
Therefore the final answer is 1/3
Where does
√17
belong on the Venn diagram?
A) Integers
B) Natural Numbers
C) Rational Numbers
D) Irrational Numbers
REALLY NEED HELP I HAVE 8 MORE QUESTIONS PLS HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I WILL GIVE BRAINLIEST AND 10 POINTS
A cone shaped tepee has a radius of 4 feet and a slant height of 7feet. If joe is six feet tall, determine whether joe is shorter or taller than the height of the tepee.
Answer:
Therefore Joe is taller than the height of the tepee.
Step-by-step explanation:
Cone:
Cone is three dimensional shape. It has an vertex.Slant height of an object is a height that measured along a lateral surface from the vertex to the the base. The slant height of a cone is = [tex]\sqrt{height^2+radius^2}[/tex]The height of a cone is [tex]=\sqrt{slant\ height ^2- radius^2[/tex]The volume of a cone = [tex]\frac{1}3 \pi r^2 h[/tex]Lateral surface area is [tex]=\pi r l[/tex]
Given that,
A cone shaped tepee has a radius of 4 feet and slant height of 7 feet.
The height of the cone is [tex]=\sqrt{slant\ height ^2- radius^2[/tex]
[tex]=\sqrt{7^2-4^2}[/tex]feet
[tex]=\sqrt{33}[/tex] feet
≈5.74 feet
Given that, Joe is 6 feet tall.
Since 6 feet> 5.74 feet
Therefore Joe is taller than the height of the tepee.
Answer: Joe is taller than the tepee
select all of the following that are like radicals
Answer:
READ BELOW, Answers Are: A,B,D,F
Step-by-step explanation:
If you are referring to this Edge problem here:
Answer:
A, B, D
Step-by-step explanation:
Adding and Subtracting Radicals Instruction on Edge
Write the first 5 terms of the
sequence an = 3n – 4
Answer:
- 1, 2, 5, 8, 11
Step-by-step explanation:
Substitute n = 1, 2, 3, 4, 5 into the n th term formula
a₁ = 3(1) - 4 = 3 - 4 = - 1
a₂ = 3(2) - 4 = 6 - 4 = 2
a₃ = 3(3) - 4 = 9 - 4 = 5
a₄ = 3(4) - 4 = 12 - 4 = 8
a₅ = 3(5) - 4 = 15 - 4 = 11
The first 5 terms are - 1, 2, 5, 8, 11
Final answer:
The first 5 terms of the sequence an = 3n - 4 are -1, 2, 5, 8, and 11. Each term is found by substituting the nth term number into the expression and calculating its value.
Explanation:
The student has asked to write the first 5 terms of the sequence an = 3n - 4. To find the terms of this sequence, we simply substitute the values of n (starting from 1 and going up by 1 each time) into the expression and calculate the results.
For n = 1: a1 = 3(1) - 4 = 3 - 4 = -1For n = 2: a2 = 3(2) - 4 = 6 - 4 = 2For n = 3: a3 = 3(3) - 4 = 9 - 4 = 5For n = 4: a4 = 3(4) - 4 = 12 - 4 = 8For n = 5: a5 = 3(5) - 4 = 15 - 4 = 11Therefore, the first 5 terms of the sequence are -1, 2, 5, 8, 11.
The sum of the measures of the interior angles of a convex polygon is 360 degrees? How many sides does the polygon have?
Answer: the polygon has
Four sides
Step-by-step explanation:
A square has 4 interior angles of 90° each. 4×90°=360°
2x + y = 5
x + y = 4
O A. x = 1, y = 3
O B. x = 1, y = 5
OC. x = 3, y = 1
O D. x = 9, y = -5
Answer:
A. x=1, y=3
Step-by-step explanation:
you have to isolate y in the bottom equation in order to put it into the top equation. heres what i did:
we will start with the bottom equation, x+y=4. then, subtract x on both sides of the equation. this will isolate y. now, we have the equation; y=4-x.
next, we are going to substitute our new bottom equation in where y is on the top. it looks like this: 2x+(4-x)=5. then, we are going to get rid of the parenthesis, so our equation is: 2x+4-x=5. to solve this, we have to combine like terms, so we will combine the x terms: x+4=5. now, isolate the variable. to do this, we have to take away 4 from each side so we can get x alone: x=1.
so now that we have a value for x, we can use that to find y. we can actually substitute our x-value into the bottom equation to make it easier: 1+y=4. next, we have to isolate the variable, which is y. this gives us the final answer: y=3.
i hope that this explanation helped with your struggles, it took me awhile to type out and i really tried hard. stay safe and good luck with your class!