SOLVE x^4 − 15x^2 − 16 = 0
What are the roots of the equation?
Answers
Answer:
roots : 4, -4, i, -i
Step-by-step explanation:
This gets a bit tricky.
We have to substitude x^2 as u in this problem.
Now to rewrite x^4 − 15x^2 − 16 = 0 with u, we get
u^2 - 15u - 16 = 0
( u - 16) (u + 1)
U = 16
U = -1
This is not the end of the problem.
Now we have to substitute x^2 back to u.
x^2 = 16 --> we get the roots 4 and -4
x^2 = -1 --> we get the roots i and -i
tadah!
Related Questions
If ABCD is dilated by a factor of 2, the
coordinate of D' would be:
5
4
3
С
2.
B.
-8
-7
-6
-5
-4
-3
-2
-1 0
1
2
3
4
5
6
7
8
9
10
11
-1
A
-2
D
-3
D' = ([?], [ ]
=
Enter
Answers
Answer: (6, -4)
Step-by-step explanation:
Assuming the dilation is centered at the origin, you can simply double the coordinates. This gives you \(D'(3 \times 2, -2 \times 2) = (6, -4)\)
Find the perimeter of quadrilateral PQRS.
Perimeter =
(50 POINTs will give BRAINIEST FOR EFFORT)
Answers
The perimeter of the quadrilateral PQRS is calculated as:
= 180 units.
How to Find the Perimeter of the Quadrilateral?Recall that if two tangents meet outside a circle, their length will be the same based on the tangents theorem.
Therefore, note that every line segments that appear tangent and intersect each other outside the circle have the same length.
Thus, we have:
Perimeter of the quadrilateral PQRS = 52.5 + 37.5 + 23 + (37.5 - 23) + 27.1 + (52.5 - 27.1)
Perimeter of the quadrilateral PQRS = 180 units.
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I need help with this!
Answers
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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Select the correct answer.
Which number has a repeating decimal form?
b.11/25
c.3/20
d.2/6
Answers
Answer:
d.2/6 has a repeating decimal form
Answer:
[D. 2/6]
Step-by-step explanation:
For edmentum users (Please check your answers before placing the answer to avoid low grades and misconfusion.)
A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
Answers
Step-by-step explanation:
To eliminate x in the system of equations:
1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:
Equation 1: 36x -54y = 90
Equation 2: -36x - 8y = -28
2. Add the two equations together to eliminate x:
(36x - 54y) + (-36x - 8y) = 90 - 28
Simplifying, we get:
-62y = 62
3. Solve for y:
y = -1
4. Substitute y = -1 into one of the original equations, say Equation 1:
4x - 6(-1) = 10
Simplifying, we get:
4x + 6 = 10
5. Solve for x:
4x = 4
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.
I rlly need help on this badly
Answers
3.
The value of x is 20.
The value of y is 30.
4.
The value of x is 30.
The value of y is 4.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
3,
The triangle is an equilateral triangle.
Value of all the angles = 60°
All sides are equal.
Now,
46 = 16 + y
y = 46 - 16
y = 30
Now,
The sum of the three angles of the triangle is 180 degrees.
80 + 60 + (60 - x) = 180
140 + 60 - x = 180
200 - 180 = x
x = 20
4.
There is an equilateral triangle.
5y = 20
y = 4
There is an isosceles triangle.
Where two sides are equal and the angle opposite to the equal sides are also equal.
This means,
(180 - 60) + x + x = 180
120 + 2x = 180
2x = 180 - 120
x = 60/2
x = 30
Thus,
3.
The value of x and y is 20 and 30.
4.
The value of x and y is 30 and 4.
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\(\sqrt2y+3=11\)
Answers
Answer:
y = 32
Step-by-step explanation:
sqrt(2y) +3 = 11
Subtract 3 from each side
sqrt(2y) +3-3 = 11-3
sqrt(2y) = 8
Square each side
(sqrt(2y))^2 = 8^2
2y = 64
Divide by 2
2y/2 = 64/2
y = 32
Step-by-step explanation:
\(\sqrt{2y}+3=11\\\\\sqrt{2y}=11-3\\\\\sqrt{2y}=8\\\\(\sqrt{2y})^2=8^{2}\\\\2y=64\\\\y=\dfrac{64}{2}\\\\y=32\)
Using exactly four 4's and any operation or symbols [+, -, *, /, (), x to the power of __], write an expression to equal each of the following:
1 = ________________ 4 = _______________ 7 = ________________
2 = ________________ 5 = _______________ 8 = ________________
3 = ________________ 6 = _______________ 9 = ________________
Answers
Answer:
1→ (4/4) / (4/4) = 1/1 = 1
2→ (4*4) / (4+4)= 16/8 = 2
3→ (4+4+4)/4 = 12/4 = 3
4→ (4-4)*4 + 4= 0*4 + 4= 4
5→ (4*4 +4) /4 = 20/4 =5
6→ 4+(4+4)/4 = 4+ 8/4 = 4+2 =6
7→ 4+4 -4/4 = 8-1=7
8→ 4+4+4-4=12-4=8
9→ 4+4 + (4/4)= 8+1 =9
Step-by-step explanation:
The equation Y= X^2/2 - 8 and Y= 2X -2 are graphed below what are the solutions to the equation X^2/2 - 8 = 2X -2 
Answers
The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.
To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.
The equation is:
X^2/2 - 8 = 2X - 2
To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:
X^2 - 16 = 4X - 4
Next, we rearrange the equation to have all terms on one side:
X^2 - 4X - 12 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:
(X - 6)(X + 2) = 0
Setting each factor equal to zero gives us two possible solutions:
X - 6 = 0 --> X = 6
X + 2 = 0 --> X = -2
So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.
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The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet. I need to find the solution set for this.
Answers
Answer:
2x+2y=52
x*y=120
Step-by-step explanation:
Find an equation of the line between (-4,2) and (1,-8)
Answers
Given the points:
\(\mleft(-4,2\mright),(1,-8)\)You can find the slope of the line using this formula:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Where these two points are on the line:
\((x_1,y_1),(x_2,y_2)\)In this case, you can set up that:
\(\begin{gathered} y_2=-8 \\ y_1=2 \\ x_2=1 \\ x_1=-4 \end{gathered}\)Therefore:
\(m=\frac{-8-2}{1-(-4)}=\frac{-10}{1+4}=\frac{-10}{5}=-2\)By definition, the Slope-Intercept Form of the equation of a line is:
\(y=mx+b\)Where "m" is the slope and "b" is the y-intercept.
In order to find the y-intercept, substitute the slope and the coordinates of one of the points on the line into the equation, and then solve for "b":
\(undefined\)suppose that the functions s and t are defined for all real numbers x as follows. s(x)=4x-5 t(x)=x+6 write the expression for (s+t)(x) and (s•t)(x) and evaluate (s-t)(2)
Answers
Answer:
To find the expression for (s+t)(x), we simply add the two functions s(x) and t(x): (s + t)(x) = s(x) + t(x) = 4x - 5 + x + 6 = 5x + 1
To find the expression for (s•t)(x), we multiply the two functions s(x) and t(x): (s•t)(x) = s(x) * t(x) = (4x - 5) * (x + 6) = 4x^2 + 19x - 30
To evaluate (s-t)(2), we substitute 2 for x in the expression for (s-t)(x): (s-t)(2) = s(2) - t(2) = (4*2 - 5) - (2 + 6) = 3 - 8 = -5
Therefore, the expression for (s+t)(x) is 5x+1, the expression for (s•t)(x) is 4x^2+19x-30, and (s-t)(2) is -5.
Step-by-step explanation:
70 + 80 but the total of 70+80 is multiplied by 2 20 points ok fam
Answers
Answer:
300
Step-by-step explanation:
70 + 80 = 150
150 x 2 = 300
Answer:
300
Step-by-step explanation:
70+80=150
150*2=300
(copy and paste for picture)
If x = 6 units, y = 3 units, and h = 5 units, find the area of the rhombus shown above using decomposition.
A. 45 square units
B. 15 square units
C. 11 square units
D. 30 square units
Answers
Answer:
B
Step-by-step explanation:
30
Step-by-step explanation:
did it
Robert earned $300 for 6 hours of work. How much did he make in dollars per hour?
Robert earned $
per hour
Will mark brainliest
Q
Answers
Answer:
$50
Step-by-step explanation:
Kinetic energy varies jointly with the mass of an object and the square of it's velocity . A ball with a mass of rolls with a velocity of m/s and creates joules of kinetic energy. How much kinetic energy would a ball with a mass of and a velocity of m/s create?
Answers
Answer:
A. The kinetic energy is quartered.
Step-by-step explanation:
I want the inverse function pls
Answers
Therefore, the inverse function of f(x) = \(\sqrt{16-x^{2} }\) is \(f^{-1}\)(x) =\(\sqrt{16-x^{2} }\).
What is function?A function is a self-contained block of code that performs a specific task and can be reused throughout a program. It can take input parameters and return output values, and it can be called multiple times with different inputs. Functions help make code more modular and easier to maintain, as they allow programmers to break down complex problems into smaller, more manageable pieces of code. In many programming languages, functions are a fundamental building block of the language and are used extensively in both built-in libraries and user-defined code.
Given by the question.
I want the inverse function f(x)=\(\sqrt{16-x^{2} }\)
To find the inverse function of f(x) = \(\sqrt{16-x^{2} }\), we can follow these steps:
Step 1: Replace f(x) with y.
y = \(\sqrt{16-x^{2} }\)
Step 2: Swap x and y.
x = \(\sqrt{16-y^{2} }\)
Step 3: Solve for y.
Square both sides of the equation:
\(x^{2}\) =\({16-y^{2} }\)
Rearrange the terms:
\(y^{2}\) = \({16-x^{2} }\)
Take the square root of both sides (since we're looking for the positive square root, we don't need to include the ± sign):
y = \(\sqrt{16-x^{2} }\)
Step 4: Replace y with \(f^{-1}\)(x).
\(f^{-1}\)(x) = \(\sqrt{16-x^{2} }\)
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Find cos ø.
(Give your answer in lowest terms)
Answers
The value of cos ø, for the given coordinates (8, 6), is 4/5 in the lowest terms.
To find the value of cosine (cos) ø, we need the coordinates (8, 6) of a point on the unit circle.
The unit circle is a circle with a radius of 1, and the coordinates (8, 6) do not lie on the unit circle. However, we can use these coordinates to calculate the cosine value indirectly.
First, we need to find the hypotenuse (r) of the right triangle formed by the coordinates (8, 6). We can use the Pythagorean theorem:
r = √(8² + 6²) = √(64 + 36) = √100 = 10
Now, we can find the cosine value by dividing the adjacent side length (x-coordinate) by the hypotenuse:
cos ø = 8 / 10 = 4/5.
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Use Basic Probability Rules to Compute Probabilities s. A recent study found that 61% of college students purchase their textbooks online. a. If three college students are randomly selected, what is the probability that ALL three buy their textbooks online? Round to the nearest ten thousandth. b. If five college students are randomly selected, what is the probability that at least one purchases their textbooks online?
Answers
When three college students are randomly selected, the probability that ALL three buy their textbooks online is 0.227
The probability that at least one purchases their textbooks online is 1.
As per the question the probability of students purchase their textbooks online 61%.
\(=\frac{61}{100}\)
p = 0.61.
So, failure = 1 - 0.61 = 0.39
q = 0.39
When 3 students are selected(n = 3)
We know that, \($$p(x)={ }^n c_x p^x q^{n-x}$$\)
So, probability that all of them to purchase
\($$\begin{aligned}&(x=3) \\& p(3)={ }^3 c_3(0.61)^3(0.39)^{3-3} \\& p(3)=0.22698\end{aligned}$$\)
When 5 students are selected (n = 5)
And probability that at least one purchases books online
\(=P(x=1)+P(x=2)+P(x=3)$ $+P(x=4)+P(x=5)$\)
Now we know that probability of all equal to 1.
\(P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=1\)
So, we can simply write
\($$\begin{aligned}P & =1-p(x=0)+p(x=1) \\& =1-\left[{ }^5 C_0(0.61)(0.35)^{50}+{ }^5 C_1(0.61)^1(0.39)^{5-1}\right] \\& =1-0.00902-0.07056 \\P& =0.92042\end{aligned}$$\)
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Bob invested $12,350, part at 7% interest and part at 6% interest. How much money was invested at the 7% rate if each account earned the same amount of interest money?
Answers
Answer:
$5,700 was invested in the 7% account
Step-by-step explanation:
Let the amount invested in 7% interest account be x while the other account is y
Total amount invested is &12,350
Thus:
x + y = 12,350 ••••(i)
interest on 7% = 7% of x = 7/100 * x = 7x/100
Interest on 6% = 6% of y = 6/100 * y = 6y/100
Since both have same interest;
7x/100 = 6y/100
7x = 6y
y = 7x/6
Put this into equation i
x + 7x/6 = 12,350
Multiply through by 6
6x + 7x = 74,100
13x = 74,100
x = 74,100/13 = $5,700
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MULTIPLE CHOICE QUESTION
Solving Inequalities
Equations vs. Inequalities
2x+3 =15 2x+3 > 15
What is the first step for the equation?
(It'll also be the same step for the inequality)
Subtract 2 on both sides
divide both sides by 2
Subtract 3 on both sides
add 3 to both sides
Answers
Answer:
just sayin x=4
Step-by-step explanation:
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
,
,
Answers
The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3
How to determine the x-coordinates where the graphs of the equations intersect?From the question, we have the following parameters that can be used in our computation:
y = 2x
y = x² - 3
The x-coordinates where the graphs of the equations intersect is when both equations are equal
So, we have
x² - 3 = 2x
Rewrite the equation as
x² - 2x - 3 = 0
When the equation is factored, we have
(x + 1)(x - 3) = 0
So, we have
x = -1 and x = 3
Hence, the x-coordinates are x = -1 and x = 3
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Question
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
y = 2x
y = x² - 3
Find RS. Explain your reasoning.
6x + 5 9x - 4
RS=
Answers
The value of line RS is 23
How to determine the valueFrom the diagram shown, we have that line PS, line PQ, line QR and line RS form a square.
Note that the sides of a square are equal to each other.
The relationship is represented as;
Line PS = Line PQ = Line QR = Line RS
We have that;
Line PS = 6x - 5Line RS = 9x - 4Substitute the expressions
6x - 5 = 9x - 4
Now, collect like terms
6x - 9x = - 4 - 5
Subtract the like terms
-3x = -9
Make 'x' the subject of formula
-3x/-3 = -9/-3
x = 3
Then, RS = 9x - 4 = 9(3) - 4 = 27 - 2 = 23
Hence, the value is 23
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Solve for x
X^2 - y = z
Answers
Answer:
± sqrt(z+y)
Step-by-step explanation:
x^2-y=z
for x
x^2=z+y
taking sqrt on both sides
x= ± sqrt(z+y)
The dimensions of a rectangular building are given as a length of 12x + 24 feet and a width of 20x - 10 feet.
Write the expression that represents the area of the building, in terms of x.
Write the expression that represents the perimeter of the building, in terms of x.
If the perimeter is going to be 220 feet, what are the dimensions of the building.
Answers
Answer:
120(2x² + 3x - 2) or 240x² + 360x - 240
Perimeter = 64x + 28
x = 3
Length = 60ft
Width = 50ft
Step-by-step explanation:
Area = (12x + 24)(20x - 10)
= 12(x + 2).10(2x - 1)
= 120(2x² + 3x - 2)
= 240x² + 360x - 240
Perimeter = 2(12x + 24) + 2(20x - 10)
= 24x + 48 + 40x - 20
= 64x + 28
64x + 28 = 220
64x = 192
x = 3
Length = 12(3) + 24
= 36 + 24
= 60
Width = 20(3) - 10
= 60 - 10
= 50
Answer:
area: (12x +24)(20x -10)perimeter: 64x +2860 ft long by 50 ft wideStep-by-step explanation:
The area of the building is given by the formula ...
A = LW
A = (12x +24)(20x -10) . . . . . substitute given length and width
__
The perimeter is twice the sum of length and width:
P = 2(L +W)
P = 2((12x +24) +(20x -10)) = 2(32x +14)
P = 64x +28
__
If the perimeter is 220 feet, we can use that fact to find the value of x.
220 = 64x +28
192 = 64x . . . . . . . subtract 28
3 = x . . . . . . . . . . . divide by 64
Then the dimensions of the building are ...
length = 12x +24 = 12(3) +24 = 60 . . . feet
width = 20x -10 = 20(3) -10 = 50 . . . feet
The length and width of the building are 60 feet and 50 feet, respectively.
Hargray Telephone earned 155.27 interest on a $20,000 deposit in an account paying 6%.
Find the number of days that the funds were on deposit.
Answers
46 Days the number of days that the funds were on deposit on Interest rate.
What exactly does "interest rate" mean?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the total loan amount if you are a borrower.Interest earned = Principal*Interest rate*Time period
155.27 = 20,000 * 0.06 * Time period
Time period = 155.27/(20,000*0.06)
= 0.129339 years
=(0.129339 * 360)
= 46.56204 days
= 46 days(Approx)
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The charge in dollars for cab rides in one
city is modeled by f(c) = $4 + $2.5m,
when m is the number of miles traveled.
What is the charge for a 3-mile ride?
answer fast plz
Answers
f(3) = $4 + $7.5
f(3) = $11.50
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Answers
So, we know that JI and JX are perpendicular (first statement). That just means that they mean at an angle of 90*.
That means CIJ has an angle of 150*-90*=60*. Therefore, as IG bisects CIJ , both CIG and GIJ have angle 60*/2=30*.
Half a circle has 180*. GIR is just short of CIG to be a half circle.
Therefore
180*-mCIG=mGIR
We know mCIG was 30*, so
150*=mGIR
Calculate 3cm ,4cm, 10cm and 2cm
Answers
Answer:
19cm
Step-by-step explanation:
(chose one way)
1. way using commutativity
(3cm+4cm)+(10cm+2cm)=7cm+12cm=19cm
2. way just writing
3cm+4cm+10cm+2cm=19cm
The factory quality control department discovers that the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4\%4% on Tuesday, 4\%4% on Wednesday, 4\%4% on Thursday, 8\%8% on Monday, and 12\% on Friday.The Company manufactures an equal amount of ball bearings (20\ %) on each weekday. What is the probability that a defective ball bearing was manufactured on a Friday
Answers
Answer:
The probability that a defective ball bearing was manufactured on a Friday = 0.375
Step-by-step explanation:
Let the event of making a mistake = M
The event of making a precision ball bearing production on Monday = Mo
The event of making a precision ball bearing production on Tuesday = T
The event of making a precision ball bearing production on Wednesday = W
The event of making a precision ball bearing production on Thursday = Th
The event of making a precision ball bearing production on Friday = F
the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04
4% on Wednesday, P(M|W) = 0.04
4% on Thursday, P(M|Th) = 0.04
8% on Monday, P(M|Mo) = 0.08
and 12% on Friday = P(M|F) = 0.12
The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.
P(Mo) = 0.20
P(T) = 0.20
P(W) = 0.20
P(Th) = 0.20
P(F) 0.20
The probability that a defective ball bearing was manufactured on a Friday = P(F|M)
P(F|M) = P(F n M) ÷ P(M)
P(F n M) = P(M n F)
P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)
We can obtain each of these probabilities by using the expression for conditional probability.
P(Mo n M) = P(M|Mo) × P(Mo) = 0.08 × 0.20 = 0.016
P(T n M) = P(M|T) × P(T) = 0.04 × 0.20 = 0.008
P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008
P(Th n M) = P(M|Th) × P(Th) = 0.04 × 0.20 = 0.008
P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024
P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)
P(M) = 0.016 + 0.008 + 0.008 + 0 008 + 0.024 = 0.064
P(F|M) = P(F n M) ÷ P(M)
P(F n M) = P(M n F) = 0.024
P(M) = 0.064
P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375
Hope this Helps!