Use the factor theorem to write a polynomial equation that has solutions of 2, -2, and 4. (Hint: Suppose the solutions of a quadratic equation are 3 and 5. This means that x = 3 or x = 5 which gives us x - 3 = 0 or x - 5 = 0. The expressions are the factors of the polynomial which means that the equation is (x - 3)(x - 5) = 0.)
The equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
What is the polynomial equation that has solutions of 2, -2, and 4?Roots are the points where the graph intercepts with the x-axis ( y = 0 ).
Given the roots in the question;
x = 2, -2, 3
Now, the root of x = 2 was found solving for x when x - (2) = y but y = 0.
Hence, (x - 2) is a factor.
Next, the root of x = -2 was found solving for x when x - (-2) = y but y = 0.
Hence, (x + 2) is a factor
And the root of x = 4 was found solving for x when x - (4) = y but y = 0.
Hence, (x + 2) is a factor
Now, combine all the factors into a single equation and simplify.
( x-2 )( x + 2 )( x - 4 ) = y
( x² + 2x - 2x - 4 )( x - 4) = 0
( x² - 4 )( x - 4) = 0
x( x² - 4 ) -4( x² - 4 ) = 0
x³ - 4x - 4x² + 16 = 0
x³ - 4x² - 4x + 16 = 0
x³ - 4x² - 4x + 16 = 0
Therefore, the equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
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seven and three eighths times negative one and two thirds.
Answer: -12 7/24
Step-by-step explanation:
Convert the mixed numbers to fractions (59/8 and -5/3) then multiply across to get -295/24. Simplify for -12 7/24.
Hope this helps :)
Answer: decimal -12.29 fraction -295/24
Step-by-step explanation:
A sample of copper has a mass of 15.6 g and a volume of 1.75 cm^3. Calculate the density of copper from this sample.
this is for earth science but its math :/
Given the mass and volume of the sample, the density of the copper sample is approximately 8.91 g/cm².
What is the density of copper from the given sample?The density of a substance is simply the mass of that substance per unit of its volume.
Density is expressed mathematically as;
Density = Mass / Volume.
Given the data in the question;
Mass of copper sample = 15.6 gVolume of copper sample = 1.75 cm³Density of copper sample = ?Plug the given values into the formula above and solve for density.
Density = Mass / Volume
Density = 15.6 g / 1.75 cm³
Density = 8.91 g/cm²
Given the mass and volume of the sample, the density of the copper sample is approximately 8.91 g/cm².
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A muffin recipe calls for one 3rd cup of milk and one 4th cup of oil how much liquid is needed for the recipe?
the price of the computer is 899$ the tax rate is 7% what is the sales tax on this computer in dollars and cents
The sales tax on this computer in 62 dollars and 93 cents
What is the sales tax on this computer in dollars and cents?The given parameters
Price = $899
Tax rate = 7%
The sales tax on this computer in dollars and cents is calculated as
Sales tax = Price * Tax rate
This gives
Sales tax = $899 * 7%
Evaluate
Sales tax = $62.93
Hence, the sales tax on this computer in 62 dollars and 93 cents
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36+29+14 joshua rewrote the ecpression as 36+14+29. What property fid joshua use to rewrite the expession
Answer:
Commutative property because it states that the numbers can be moved around or swapped from their position without making any difference to the answer.
it's due by 12 am. please help as soon as possible
Answer:
Step-by-step explanation:
25. 5 < x < 7
Jane bought a watch for $30 that she is going
to re-sell with a 15% markup price. How much
is Jane selling the watch for?
Step 1:
Step 2:
Step 3:
ming
What is the value of the expression (54+3³) ?
33
Answer:
Submit Answer
OL
C
Refer to the number line. Find the coordinate of point X such that the ratio of MX to XJ is 3:1.
The coordinate of point X such that the ratio of MX to XJ is 3:1 is 12
How to determine the coordinate of point X?The coordinates are given as:
M = 2
J = 18
The ratio is given as:
Ratio = 3 : 1
The location of the point X is then calculated as:
X = Ratio * (J - M)
This gives
X = 3/(3 + 1) * (18 - 2)
Evaluate
X = 3/4* 16
This gives
X = 12
Hence, the coordinate of point X such that the ratio of MX to XJ is 3:1 is 12
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Step-by-step explanation:
show how to work out the question
Algebra (4224_EOZ1)
HW Score: 88.89%, 16 of 18 points
O Points: 0 of 1
By air, the distance from city A to city B is 3003 miles less than the distance from city C to city D. If the total of these two distances is 7827 miles, find the distance from city C to city D
ework 2: 3.3 & 3.4
Brooke Conti
Question 14, 3.4.35
09/06/22 7:12
The Distance between city C and city D is 5405 miles.
Given that Distance from city a to city b is 3003 miles less than the Distance fron city c to city d, the total of these two Distance is 7807 miles and asked to find Distance between city C and city D.
Given that,
(d-c)-(b-a)=3,003 miles { (Distance between city D and city C)-(Distance between city A and city B)} Let's assume it as equation A
(d-c)+(b-a)=7,807 miles { (Distance between city D and city C)+(Distance between city A and city B)} Let's assume it as equation B
Add equation A and B
2(d-c)=10,810
(d-c)=5,405
Hence,Distance between city D and city C is 5,405
Therefore,The Distance between city C and city D is 5405 miles.
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Let f(x)=12x+7. Use algebra to find the inverse function f^-1(x).
Step-by-step explanation:
Replace x with y and y with x.
Then, try to isolate the y.
x=12y+7
x-7=12y
(x-7)/12=y
f^-1(x)=(x-7)/12
I need help please….
enter the correct letters in the boxes on the left with the negative statements on the right
E Apples make good pies A seven is not a prime number
F the sun is hot today B a line does not contain at least two points
D 3+2=7 C a right angle does not measure < 90degre
C a right angle measure < 90 D 3+2[tex]\neq[/tex]7
A seven is a prime number E apples does not make good pies
B a line contain at least two points F the sun is not hot today
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angle EFG and angle GFH are a linear pair, angle EFG=2n + 25 and angle GFH=4n + 17 what are angles EFG and GFH?
The angles EFG and GFH are 71 and 109 degrees
How to determine the angles EFG and GFH?The given parameters are:
EFG =2n + 25
GFH = 4n + 17
Linear pair angles are supplementary angles
So,we have
2n + 25 +4n + 17 = 180
Evaluate the like terms
6n= 138
Divide by 6
n = 23
Substitute n = 23 in EFG =2n + 25 and GFH = 4n + 17
EFG = 2 * 23 + 25 =71
GFH = 4 * 23 + 17 = 109
Hence, the angles EFG and GFH are 71 and 109 degrees
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what is one less than the product of seven and the difference of a number and 2 is 4 times the number?
Answer: 7x -4
Step-by-step explanation:
pleaseeee helppppp will give extra points
-2 ( 3x + 2 ) ≥ 6x – 4
Answer: x ≤ 0. Interval Notation: (-∞, 0]
"a number is no more than 26"
Answer:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25
urgent please help!
Answer: 0.05t ==> 1st blank
1 ==> 2nd blank
-0.1t+6 ==> 3rd blank
Step-by-step explanation:
could someone please help answer this.
Answer:
+ 12 yards
Step-by-step explanation:
8-3 = 5
5 + 12 - 5 = 12
In the diagram, P is a point on ST such that P is between S and T. If SP = x + 3, PT =2x-1 and ST = 17, find the length of PT
Based on the given parameters, the numerical length of PT is 9 units
How to determine the length of PT?The given parameters are:
P is a point on ST such that P is between S and T.
SP = x + 3,
PT = 2x - 1
ST = 17
The statement "P is a point on ST such that P is between S and T" implies that
ST = SP + PT
Substitute the known values in the above equation
17 = x + 3 + 2x - 1
Evaluate the like terms
17 = 3x + 2
Add 2 to both sides of the equation
3x = 15
Divide both sides of the equation by 3
So, we have
x = 5
Substitute x = 5 in PT = 2x - 1
So, we have
PT = 2 x 5 - 1
Evaluate
PT = 9
Hence, the numerical length of PT is 9 units
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Rectangle ABCD is shown on the grid.
A
(-1,4) 14
3
+2+
4
-6-5-4-312-3₁
(-3-b
B(3,3)
34
C(1-5)
X
What is the area of rectangle ABCD in square units?
O 3√17 square units
O 6√17 square units
O
17 square units
O 34 square units
well, we know it's a rectangle, so we know the opposite sides are perpendicular, so if we just get say the sides AD as its length and BA as its width, that'd give us its area, since it'll just be AD * BA.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad D(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-4}) ~\hfill AD=\sqrt{(~~ -3- (-1)~~)^2 + (~~ -4- 4~~)^2} \\\\\\ ~\hfill AD=\sqrt{( -2)^2 + ( -8)^2}\implies \boxed{AD=\sqrt{68}} \\\\\\ B(\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{4}) ~\hfill BA=\sqrt{(~~ -1- 3~~)^2 + (~~ 4- 3~~)^2}[/tex]
[tex]~\hfill BA=\sqrt{( -4)^2 + (1)^2} \implies \boxed{BA=3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Area}}{(\sqrt{68})(3)\implies (\sqrt{2^2\cdot 17})(3)}\implies (2\sqrt{17})( 3)\implies \LARGE \begin{array}{llll} 6\sqrt{17} \end{array}[/tex]
Please me with this. I got it wrong. I will give extra points and a Brainly.
Answer:
24
Step-by-step explanation:
First, we know the total number of students: 135
Then we can see that 22+31+28 students like two flavours: 81
Then we can see how many students like all three flavours: 15
Because the students who like two flavours are counted twice, we need to subtract them once.
Because the students who like three flavours are counted three times, we need to subtract them twice.
So we get 135-81-15*2
135-81-30
24
24 students do not like any of the given flavours
if this was helpful pls give me brainliest <3
Answer: 24 students dislike any of the flavors
Step-by-step explanation:
Soo since you have the diagram without any error it the other question soo at the start of the question they have told that in total there are 135 students.
so at the all the number of students with the different types of flavors then you will get the total amount of students who like 2 kinds of flavors and all three flavors.
31+22+28+15+15= 111 students (since the students who like three flavors are counted three times, we need to subtract them twice, I add it here to make it easier *15+15*)
so next you should subtract that amount from the total amount of students who likes multiple flavors in order to get the number of students who dislikes and of the flavors.
135-111= 24 students dislike any of the flavors
I hope this helped you I tried my best... I hope this is understandable and good luck!
what is the area of the rectangle?
Width;
4x-1 ,
Top length;
2x+17
Bottom Length;
6x+9 .
Please help
==============================================================
Explanation:
Recall that the opposite sides of any rectangle are the same length.
This means the top and bottom sides are the same length
top = bottom
2x+17 = 6x+9
2x-6x = 9-17
-4x = -8
x = -8/(-4)
x = 2
Then we can find each side:
width = 4x-1 = 4*2-1 = 8-1 = 7top = 2x+17 = 2*2+17 = 4+17 = 21bottom = 6x+9 = 6*2+9 = 12+9 = 21We get the same length for top and bottom (21), which confirms the correct x value.
This is a 7 by 21 rectangle with area = length*width = 7*21 = 147 square units.
Solve for x in the diagram below.
(2x+45)
Answer:
Step-by-step explanation:
you can't really solve for x because there is no equal sign to determine how much x needs to be in order to get the sum.
Given the function h(x)=-x^2-5x+11h(x)=−x
2
−5x+11, determine the average rate of change of the function over the interval -8\le x \le 4−8≤x≤4.
The average rate of change of the function over the interval is -9.25
How to determine the average rate of change of the function over the interval?The given parameters are
h(x) = x^2 - 5x + 11
−8 ≤ x ≤ 4
Calculate h(4) and h(-8)
So, we have
h(4) = (4)^2 - 5(4) + 11 = 7
h(-8) = (-8)^2 - 5(-8) + 11 = 115
The average rate of change of the function over the interval is then calculated as
Rate = [h(4) - h(-8)]/[4 - -8]
This gives
Rate = [7 - 118/[12]
Evaluate
Rate = -9.25
Hence, the average rate of change of the function over the interval is -9.25
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Tomeka is in a jump-roping contest. She hopes to be the last person jumping rope at the end of the contest. In her practice yesterday, she jumped 294 consecutive jumps. She jumped one-fourth of them in the first 5 minutes of practice. How many times did she jump after the first five minutes?
what is the plan of action to this problem?
Answer:
Answer
Step-by-step explanation:
Answer times the power of infinity
Keaton is building a rectangle tabletop and wants to put a metal border around the edge.the length of the tabletop is 1.83 meters and the width is 0.74 meter. Use the formula p=l +2w to find the permit of the tabletop. Lesson 1-1
The perimeter of the given rectangle is a 3.31 meter.
According to the statement
We have to find that the perimeter of rectangle.
So, For this purpose, we know that the
Perimeter is the distance around the edge of a shape.
From the given information:
The length of the tabletop is 1.83 meters and the width is 0.74 meter.
Then the formula to find the perimeter is a
P =l +2w
Here substitute the values then
P =l +2w
P = 1.83 +2*0.74
Now add the terms to get a perimeter of the rectangle.
Then
P = 1.83 +1.48
P = 3.31.
So, The perimeter of the given rectangle is a 3.31 meter.
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Add these fractions:
3/5 + 6/8
Answer:
[tex]\frac{27}{20}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5} + \frac{6}{8}[/tex]
adjust the denominators;
= [tex]\frac{3*8}{5*8} + \frac{6*5}{8*5}[/tex]
[tex]=\frac{24}{40} + \frac{30}{40} \\\\=\frac{24+30}{40} \\\\=\frac{54}{40} \\\\simplify\\\\=\frac{27}{20}[/tex]
PLEASE HELP IM BEIGGONG BEGGING BEGGONF YOUUUU!!! EXTRA POINTS AND BRAINLIEST I HAVE OHOTOT
Just questions 14-30 EVEN
Due to length restrictions, we kindly invite to check the explanation of this question for further details on equations.
How to clear the variables within equationsIn this problem we find equations that have got to be cleared with respect to a given variable, this can be done by taking advantage of algebra properties:
14) b / c = a → c = b / a
15) k = a - y → y = a - k
16) d · f · g = h → f = h / (d · g)
17) 2 · x + 3 · y = 12 → 3 · y = 12 - 2 · x → y = 4 - (2 / 3) · x
18) 2 · n = 4 · x + 2 · y → n = 2 · x + y
19) a · b · c = 1 / 2 → b = 1 / (2 · a · c)
20) y = 3 / (5 · u) + 5 → y - 5 = 3 / (5 · u) → 5 · u = 3 / (y - 5) → 3 / [5 · (y - 5)]
21) 8 · (x - a) = 2 · (2 · a - x) → 8 · x - 8 · a = 4 · a - 2 · x → 10 · x = 12 · a → x = (6 / 5) · a
22) 12 · (m + 3 · x) = 18 · (x - 3 · m) → 12 · m + 36 · x = 18 · x - 54 · m → 66 · m = - 18 · x → m = - (3 / 11) · x
23) V = (π / 3) · r² · h → h = [3 · V / (π · r²)]
24) V = (π / 3) · r² · (h - 1) → h - 1 = [3 · V / (π · r²)] → h = 1 + [3 · V / (π · r²)]
25) y · (a - b) = c · (y + a) → a · y - b · y = c · y + a · c → (a - b - c) · y = a · c → y = (a · c) / (a - b - c)
26) x = [3 · (y - b)] / m → (m · x) / 3 = y - b → y = b + (m · x) / 3
27) F = - (G · m) / r² → G = - (F · r²) / m
28) The area formula of the baking sheet is l · w = 117.
29) The temperature formula is T = (7 / 30) · n + 40.
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