What are the solutions of the equation x^4 - 7x^3 + 23x^3 - 29x - 60 = 0 are shown. What are the nonreal solutions to the equation?
Answers
Answer:
A.
Step-by-step explanation:
1) according to the given graph, the real roots are: -1 and 4, it means the given expression can be evaluated using (x+1)(x-4)=x²-3x-4.
2) if to divide the given expression by (x²-3x-4), then
x⁴-7x³+23x²-29x-60=(x²-3x-4)(x²-4x-15), where
3) x=-1;4 - real roots, and
[tex]x=2^+_-i\sqrt{11} \ -nonreal \ roots.[/tex]
Related Questions
How many interior angles does a 2D shape right arrow have and explain the answer?
Answers
The number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
How to determine the interior anglesIt is important that a 2D shape arrow is a shape with 8 sides
Sum of angles of a polygon = (n - 2) × 180
⇒ ( 8 - 2) × 180
⇒ 6 × 180
⇒ 1080
The number of interior angles are 8 and this is so because of the number of sides in the 2D shape right arrow
Thus, the number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
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Sets A, B, and C are subsets of the universal set U. These sets are defined as follows.
U= {f,g,h,p,q,r,x,y,z}
A={f,g,p,q}
B={g,h,q,x,y}
C={p.q.x.y.z}
Find (C ∪ B) ∩ A'.
Write your answer in roster form or as Ø.
Answers
Answer:
(C U B )=(q,x,y)
(C U B )n A=q
50 POINTS!!! Answer the question well and I will also give Brainliest.
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. Which conclusion can be made from the given information?
A) The volume of the prism is half the volume of the cylinder.
B) The volume of the prism is twice the volume of the cylinder.
C) The volume of the prism is equal to the volume of the cylinder.
D) The volume of the prism is not equal to the volume of the cylinder.
Answers
Answer:
C) The volume of the prism is equal to the volume of the cylinder.
Step-by-step explanation:
volume of triangular prism = area of base × height
volume of cylinder = area of base × height
The cross sectional area are equal, so the bases have the same area.
The heights are also equal.
The volumes must be equal.
Answer: C) The volume of the prism is equal to the volume of the cylinder.
Answer:
C) The volume of the prism is equal to the volume of the cylinder.
Step-by-step explanation:
If the cross-sectional areas of the triangular prism and the right cylinder are congruent, it means that when you look at their shapes from the top or bottom, they have the same size and shape.
Since both the triangular prism and the right cylinder have a height of 5 units, and their cross-sectional areas are the same, it implies that they have the same volume as well. So, the volume of the triangular prism is equal to the volume of the cylinder.
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Please Evaluate C(6,3)
Answers
The value of the expression C(6,3) is 20
How to evaluate the expression?The expression is given as:
C(6, 3)
This means 6 combination 3.
And it can be written as:
[tex]^6C_3[/tex]
Apply the combination formula
[tex]^6C_3 = \frac{6!}{3!3!}[/tex]
Evaluate the expression
[tex]^6C_3 = 20[/tex]
Hence, the value of the expression C(6,3) is 20
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What is the equation of the line that is perpendicular to the line defined by the equation 2y=3x+2 and goes through the point (3,2)
Answers
The equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
Equation of perpendicular linesThe equation is defined by 2y = 3x + 2
Rewrite the equation in the form y = mx + c
[tex]y=\frac{3}{2}x + 1[/tex]
The slope, m = 3/2
The y-intercept, c = 1
The equation perpendicular to the given line will be of the form:
[tex]y-y_1=\frac{-1}{m}(x-x_1 )[/tex]
Substitute [tex]x_1=3, y_1=2, and m=\frac{3}{2}[/tex] into the equation above
[tex]y-2=\frac{-2}{3} (x-3)\\\\y-2=-\frac{2}{3}x+2\\\\y=-\frac{2}{3}x+4[/tex]
Therefore, the equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
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If f(x) =2ײ+2 and g(x) =x² -1, find (f-g) (x)
Answers
Answer:
[tex]\boxed {(f-g)(x) = x^{2}+3}[/tex]
Step-by-step explanation:
Given :
f(x) = 2x² + 2g(x) = x² - 1Now, this problem can be used using a simple formula.
[tex]\fbox {(f - g)(x) = f(x) - g(x)}[/tex]
Let's solve.
(f - g)(x) = 2x² + 2 - (x² - 1)(f - g)(x) = 2x² - x² + 2 + 1(f - g)(x) = x² + 3∴ The answer will be x² + 3.
56m² = ____________ GCF =
68m² = ____________ GCF =
Answers
The greatest common factor of the expression is 4m⁴.
What is GCF?GCF simply means the greatest common factor.
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Hence,
56m⁵
68m⁴
The greatest common factor of the expression is the largest positive expression that divides evenly into all numbers with zero .
Hence, the greatest common factor is 4m⁴
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Find all primes p, q such that p^2-p=37q^2-q
Answers
The pairs of prime numbers (p,q) such that p^2-p=37q^2-q is (43, 7)
How to determine the pairs of numbers?The expression is given as:
p^2 - p=37q^2 - q
The boundary or range of numbers of p and q is not given.
So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)
i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000
Using the above range, we have the following program to determine the pairs of prime numbers (p, q).
for a in range(2,1000000):
for b in range(2,1000000):
if ((a* *2) - a) == (37 * (b* *2) - b):
print(str(a)+","+str(b))
The output of the above program is:
(43, 7)
The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q
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Which of the following statements is TRUE about rectangle ABDC.
Answers
The statement that is TRUE of the rectangle is AB + BD > AD. Option A
Facts about the rectangleWE have that a diagonal divides the rectangle into two equal triangles
line AD is the length of the diagonal
With the diagonal drawn, we have
AD = hypotenuse
AB and BD are the two other sides
From the Pythagorean theorem, we have that the square root of the square sum of the other two sides fives the hypotenuse. This mean that their sum is greater than the hypotenuse
Thus, the statement that is TRUE is AB + BD > AD. Option A
The complete question is;
Which of the following statements is TRUE about rectangle ABDC.
a. AB + BD > AD
b. AB + BD < AD
c. AB + BD = AD
d. (AB) (BD) = AD
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In London today, twice the high temperature was more than five times the high temperature minus eighty-seven. In interval form, what are the possible temperatures?
Answers
The possible temperatures are represented by (-∝, 29)
How to determine the possible temperatures?Let the high temperature be x
So, the statement can be represented as:
2x > 5x - 87
Subtract 5x from both sides
-3x > -87
Divide both sides by -3
x < 29
In interval form, we have (-∝, 29)
Hence, the possible temperatures are represented by (-∝, 29)
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A cylindrical container has a radius of 17 inches and a height of 63 inches, how many gallons will it hold?
Answers
Answer:
=57198.98
Step-by-step explanation:
Volume of Cylinder = pi x radius^2 x height
= pi x 17^2 x 63
=57198.9774439
=57198.98
Rewrite without parentheses.
−6w x5 (2w³ +7w¹x² – 5x²)
-
Simplify your answer as much as possible.
0
Answers
Step-by-step explanation:
Help me am lost somewhere
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
Answers
The equations that can be used to find the lengths of the legs of the triangle are as follows:
100 = (x + 2)² + x²24 = 0.5 × (x + 2)(x)x² + 2x - 48 = 0How to find the equation of a right triangle?The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
10² = (x + 2)² + x²
100 = (x + 2)² + x²
Therefore, using the area of a triangle,
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × (x + 2)(x)
24 = 0.5 × (x + 2)(x)
24 = x² + 2x / 2
cross multiply
48 = x² + 2x
x² + 2x - 48 = 0
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Which number has a repeating decimal form?
A. √15
B. 11/25
C. 30
D. 2/6
Answers
A theater sells 2 types of fixed-price tickets - orchestra and balcony. Peter pays $50 for 1 orchestra and 4 balcony tickets. Justine pays $150 for 3 orchestra and 12 balcony tickets. А B The cost of 1 balcony ticket. The cost of 1 orchestra ticket. The quantity under A is greater than the quantity under B. The quantity under B is greater than the quantity under A. The quantities under A and B are equal. The information given is insufficient to make the comparison.
Answers
Using a system of equations, it is found that:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Cost of an orchestra ticket.Variable b: Cost of a balcony ticket.Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:
a + 4b = 50 -> a = 50 - 4b.
Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:
3a + 12b = 150.
a + 4b = 50 -> a = 50 - 4b.
The equations are equal, hence we suppose that the costs are equal, that is:
a + 4b = 50 -> 5a = 50 -> a = 10.
Hence:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.More can be learned about a system of equations at https://brainly.com/question/24342899
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Which phrase best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)²?
O6 unit left
O6 unit right
O 1 unit left
O 1 unit right
Answers
Check the table I attached
Answer:
1 UNIT LEFT best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)².
Find the surface area of the square pyramid below if the length of the sides of the base are 10 cm, and the slant height is 15 cm.
Answers
The surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
Surface areaSurface area of the square pyramid
= a² + 2a√a²/4 + h²
where,
a = sides of base = 10 cmh = slant height = 15 cmSurface area of the square pyramid
= a² + 2a√a²/4 + h²
= 10² + 2(10)√10²/4 + 15²
= 100 + 20√100/4 + 225
= 100 + 20√25 + 225
= 100 + 20√250
= 100 + 20(15.81)
= 100 + 316.2
= 416.2 cm²
Therefore, the surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
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Solve the following system of equations.
{y=x−5
−x−3y=7
Write your answer as an ordered pair in the form (x,y).
Answers
Answer:
(2,-3)
Step-by-step explanation:
I am not sure if you meant the first equation to be y or -y. I solved it as y.
y = x-5 -x -3y =7
I am going to take the second equation and write it as x =
-x - 3y = 7 Give equation
-x = 3y +7 Add 3y to both sides
x = -3y-7 Multiplied each term in the equation by -1 so that x could be positive
I am going to substitute -3y-7 for x in the first equation up above
y = x - 5
y = -3y -7 - 5 Substitute -3y-7 for x
y = -3y -12 Combined -7-5
4y = -12 Added 3y to both sides
y = -3 Divided both sides by 4.
I now know that y is -3, I will plug that into x = -3y-7 to solve for x
x = -3(-3) -7
x = 9-7 A negative times a negative is a positive
x = 2
Please help me with this problem. Seriously desperate again !!
Answers
The dimensions are 7 inches by 17 inches.
What is the area of rectangle?
Let the length be l inches
Let the breadth be b inches
Area = l*b
We can find dimensions as shown below:
Let the length be x inches
Let the width be y inches
Area = 119 square inches
x=3+2y (1)
Area = l*w
119 = x*y
Putting value of x
119 = (3+2y) *y
119 = 3y+2y^2
2y^2+3y-119=0
2y^2-14y+17y-119=0
2y(y-7) +17(y-7) =0
(y-7) (2y+17) =0
y=7, -17/2
y cannot be negative
so, y = 7
Putting in equation (1)
x=3+2(7)
= 3+14
= 17
Hence, the dimensions are 7 inches by 17 inches.
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A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $25 . For 7 pounds of chocolate chips and 9 pounds of walnuts, the total cost is $53 . Find the cost for each pound of chocolate chips and each pound of walnuts.
Answers
Answer:
one pound of chocolate chips = $2.75
one pound of walnuts = $3.75
Step-by-step explanation:
we can solve this by first making an equation
let's write the number of chocolate chips in c
and the number of walnuts in w
5c + 3w = 25
7c + 9w = 53
let's first solve for c by multiplying the top equation by 3 and subtracting the bottom equation from it
(15c + 9w = 75) - (7c + 9w = 53)
8c = 22
c = $2.75
Let's now start to solve for w by inputting c into one of the equations.
(2.75)7 + 9w = 53
19.25 + 9w = 53
9w = 53 - 19.25
9w = 33.75
w = $3.75
a pound of chocolate chips = 2.75
a pound of walnuts = 3.75
give me brainliest, please!
Hope this helps :)
Answer:
each pound of chocolate chips costs $2.75
each pound of walnuts costs $3.75
Step-by-step explanation:
let c be the cost of a pound of chocolate chips
and w be the cost of a pound of chocolate chips
For 5 pounds of chocolate chips and 3 pounds of walnuts,
the total cost is $25 means 5c + 3w = 25
For 7 pounds of chocolate chips and 9 pounds of walnuts,
the total cost is $53 means 7c + 9w = 53
Now we have to solve the system:
[tex]\begin{cases}5c+3w=25&\\ 7c+9w=53&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 7c+9w=53&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 8c=22&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}9w=75-15 \times \frac{11}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}9w=\frac{135}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}w= \frac{15}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
1. The correlation coefficient on a scatter plot representing the variables for the amount of weight a body builder can lift in a gym and the amount of protein the body builder takes each day is 0.76. Describe the meaning of this correlation coefficient.
A
very Strong positive linear relationship between the two variables
B
very Strong negative linear relationship between the two variables
C
moderate positive linear relationship between the two variables
D
no relationship between the two variables
Answers
A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.
What does the correlation coefficient mean?Correlation is a statistical measure used to measure the linear relationship that exists between two variables.
If the sign of the correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the correlation coefficient is, the stronger the linear relationship.
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Find the missing side of the triangle.
pythagorean 4
A. 337‾‾‾‾√ km
B. 5‾√ km
C. 193‾‾‾‾√ km
D. 112‾√ km
Answers
Applying the Pythagorean theorem, the missing side of the triangle is: C. √193 km.
How to Apply the Pythagorean Theorem?To find the missing side (x) in the right triangle, based on the Pythagorean theorem, we would have the following equation:
x = √(12² + 7²)
x = √(144 + 49)
x = √193
The missing side of the triangle is: C. √193 km
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Answer:
C.) 193√ km
Step-by-step explanation:
I got it right on founders edtell
Write the equation of a parabola whose directrix is
y
=
−
1.5
y
=
-
1.5
and has a focus at
(
−
4
,
−
2.5
)
(
-
4
,
-
2.5
)
.
Answers
Answer:
y=0.5x²-4x-10.
Step-by-step explanation:
1) according to the definition of parabola:
d1=d2, then
[tex]2) \ |y+1.5|=\sqrt{(x+4)^2+(y+2.5)^2} ;[/tex]
3) after evolution:
-(2y+4)=(x+4)²; ⇔
[tex]y=-\frac{1}{2}x^2-4x-10.[/tex]
The table shows the multiplication of two linear expressions.
A 2-column table with 5 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3, Step 4. Second column is labeled Step with entries three-fourths x (negative 8 x + 6), (three-fourths x) (negative 8 x) + (three-fourths x) (6), three-fourths times (negative 8) times x times x + three-fourths times 6 times x, (three-fourths times (negative 8)) times (x times x) + (three-fourths times 6) times x, negative 6 x squared + 9 over 2 x.
What is the mathematical reasoning for Step 3?
associative property
commutative property
distributive property
simplify
Answers
The mathematical reasoning for Step 3 is a distributive property.
What is distributive property?It should be noted that the distributive property is the multiplication of the sum of two to more addends by a number that will give same result.
In this case, the mathematical reasoning for Step 3 is a distributive property.
Therefore, the correct option is C.
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Answer: C. Distributive Property
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
The value of x is 2 and the length of JK is 4
How to solve the unknown variables?The given parameters from the circle are:
Center = Point SSegment JK = 8Segment LK = 2x + 4Congruent SN = SP = 7The lines SR and SQ are the radii of the circle P
This means that lines JK and JL are congruent
So, we have:
JK = KL
Substitute LK = 2x + 4 and JK = 4
4 = 2x + 4
Rewrite the above equation as:
2x + 4 = 8
Subtract 4 from both sides
2x + 4 - 4 = 8 - 4
Evaluate the difference
2x = 4
Divide both sides by 2
2x = 4/2
This gives
x = 2
Substitute x = 2 in LK = 2x + 4
LK = 2*2 + 4
Evaluate the product of 2 and 2
LK = 4 + 4
This gives
LK = 8
The point N divides JK into 2 equal segments
So, we have
JN = JK/2
JN= 8/2
JN = 4
Hence, the value of x is 2 and the length of JK is 4
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Good recordkeeping helps protect assets and helps managers?
Answers
Answer:
yes i help yes of course he help
Bob drops a ball from a height of 400 feet. The height of the ball is given by
the function h(t) = -16t² + h, where t is the time in seconds. How long will it
take for the ball to hit the ground?
Answers
Answer: in 5 seconds it will take the ball to the ground.
Step-by-step explanation:
h=400 foot h(t)=-16t²+h
Height a ball will take for to hit the ground is 0 feet.
Hence,
-16t²+h=0
400=16t²
16*25=16*t² |:16
25=t².
t²=5²
t=5 с.
Good luck an' have a nice day!
Which of the following are equations for the line shown below? Check all that
apply.
(-2,-5)
(2,5)
A. y + 5 = 2.5(x+2)
B. y-5=2.5(x-2)
C. y-2=2.5(x - 5)
D. y+2=2.5(x+5)
Answers
Answer:
A
Step-by-step explanation:
What is the range of possible sizes for side xxx?
Answers
Answer:
1.6 < x < 9.6
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
5.6 - 4 < x < 5.6 + 4
1.6 < x < 9.6
vRichard has a red card (R) and a black card (B). He picks a card randomly from the pair and then rolls a six-sided die. The sample space of the event is listed. B-1 R-1 B-2 R-2 B-3 R-3 B-4 B-5 R-5 B-6 R-6 The missing term in the list is . If there were three cards instead of two, the sample size would be .
Answers
The Sample space for three cards is
[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)[/tex][tex]\left(B,5\right),\left(R,5\right),\left(G,5\right),\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}[/tex]
There are two cards red(R) and black(B) and a six-sided die.
The event is one card is picked randomly and then rolls the die.
So, the Sample space is as follows.
[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(B,2\right),\left(R,2\right),\left(B,3\right),\left(R,3\right),\left(B,4\right),\left(R,4\right),\left(B,5\right),\left(R,5\right),\left(B,6\right),\left(R,6\right) \right \}[/tex]
Find Sample space if there are three cards.Consider there were three cards red(R), black(B) and green(G) a six-sided die.
The event is one card is picked randomly and then rolls the die.
So, the sample space will be as follows,
[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)[/tex][tex]\left(B,5\right),\left(R,5\right),\left(G,5\right)\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}[/tex].
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