Which of the following is equivalent to the
complex number ;³¹?
Choose 1 answer:
A
B
C
D
1
i
-1
-i

Answer:

20/7

Step-by-step explanation:

5×4/7

numerator5×numerator4=20

denominator 7×denominator1=hence,answer is

20/7

Answer:

[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]

Step-by-step explanation:

Completing the square :

x² + 14x - 8y + 65 = 0

x² + 14x + 49 - 49 - 8y + 65 = 0

(x + 7)² - 8y + 16

(x + 7)² = 8y - 16

⇒ x = -7, y = 2 (Vertex)

Finding a :

⇒ x² = 4ay

⇒ (-7)² = 4(2)a

⇒ a = 49/8

Finding the focus :

⇒ (0, a)

⇒ (0, 49/8) (Focus)

Answer: y = 2x - 6

Step-by-step explanation:

   Let us turn the second given equation into slope-intercept form to match the first equation.

8x - 4y = 12

8x - 12 = 4y

4y = 8x - 12

y = 2x - 3

   Now, parallel lines have the same slope. This is the m value.

y = 2x - 3

   \/

y = mx - 6

y = 2x - 6

    Read more about your question here which includes parallel slopes:

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Answer:

x=5

Step-by-step explanation:

[tex]((x+3)/4)+(((2x-12)-1)/3)=1\\\frac{x+3}{4} +\frac{2x-12-1}{3} =1\\\frac{x+3}{4} +\frac{2x-13}{3} =1\\[/tex]

Now we have to cross multiply the denominator to progress further.

[tex]\frac{3(x+3)}{4*3} +\frac{4(2x-13)}{3*4} =1\\\frac{3x+9}{12} +\frac{8x-52}{12} =1\\\frac{3x+9+(8x-52)}{12} =1\\\frac{3x+9+8x-52}{12} =1\\\frac{11x-43}{12} =1\\11x-43=12\\11x=43+12\\11x=55\\x=\frac{55}{11} \\=5[/tex]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

[tex]x^{100}-4^x \cdot x^{98}-x^2+4^x=0[/tex]

Factor out -1:

[tex]\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0[/tex]

Divide both sides by -1:

[tex]\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0[/tex]

Rearrange the terms:

[tex]\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:[/tex]

[tex]\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0[/tex]

Factor out the common term [tex](x^{98}-1)[/tex] :

[tex]\implies (4^x-x^2)(x^{98}-1)=0[/tex]

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

[tex]\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}[/tex]

Therefore, the solutions to the given equation are: x = 1 or x = -1

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Answer:

x = ± [tex]\sqrt{2}[/tex] , x = ± i

Step-by-step explanation:

f(x) = [tex]x^{4}[/tex] - x² - 2

to find the zeros , equate f(x) to zero , that is

[tex]x^{4}[/tex] - x² - 2 = 0

using the substitution u = x² , then

u² - u - 2 = 0 ← in standard form

(u - 2)(u + 1) = 0 ← in factored form

equate each factor to zero and solve for u

u - 2 = 0 ⇒ u = 2

u + 1 = 0 ⇒ u = - 1

convert u back into terms of x

x² = 2 ( take square root of both sides )

x = ± [tex]\sqrt{2}[/tex]

x² = - 1 ( take square root of both sides )

x = ± [tex]\sqrt{-1}[/tex] = ± i

Answer: Positive or negative square root of 2, ±i

Proof o fvalidity is shown below.

Answer:

please see photo attached for detailed analysis.

Answer:

6

Step-by-step explanation:

Answer:

92 + ( -5 ) , 2+2

Step-by-step explanation:

1) 92 + ( -5 )

= 92 - 5

= 87

2) 2 + 2 = 4

Answer:

Systems of equations:

x=3

y=2

z=1

w=0

According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons. Option D is correct.

The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure. The force involved vertically to the surface of an object per unit area is pressure.

It is denoted by P. The pressure relative to the ambient pressure is known as the gauge pressure.

The complete question is:

Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question. Which cylinder pressure will Jillian need if she plans to fill 90 balloons? Tank Pressure and Balloon Quantity Pressure in the helium cylinder (psi) Number of 9-inch balloons 100 30 150 ? 200? 250? 300?

According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons (PSI.)

Simply divide the number of balloons by the total PSI to arrive at this figure.

⇒990/300

⇒3.333333 psi each.

The no of the 90-inch balloon is found as;

⇒3.33333 × 90

⇒300

According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons.

Hence option D is correct.

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If the amount of budget for media and sales combined is $25,000,000. Then the total annual budget will be $125,000,000.

The complete question is attached below.

The quantity of anything is stated as though it were a fraction of a hundred.

The pie chart below shows how the annual budget for a certain company divided by department.

If the amount of budget for media and sales combined is $25,000,000.

Then the total annual budget will be

Let x be the total annual budget.

17% + 3% = 25,000,000 / x

       20% = 25000000 / x

      0.20 = 25000000 / x

            x = $125,000,000

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Answer:

(10/3)π units

Step-by-step explanation:Mark if it is correct

Answer:

[tex]\frac{10\pi }{3}[/tex] inches

≈ 10.5 inches

Step-by-step explanation:

The formula for arc length is as follows:
Arc length = [tex]\frac{\theta}{360} * 2\pi[/tex]

[tex]\frac{120}{360} * 10\pi \\= \frac{1}{3} * 10\pi \\= \frac{10\pi}{3}[/tex]

Hope this helps and feel free to mark this as brainliest!

Answer:

30 dollars

Step-by-step explanation:

25/5 = 5 dollars per hour

so 6 hours would be 5 * 6 = 30 dollars

Answer:

It would be B

Step-by-step explanation:

First, we need to find out the unit rate

5/25=1/5

Therefore, that means in one hour the cost would be $5

Since you are going from one hour to 6 hours you need to multiply both numbers by 6

Since 5x6=30, it would be 30$ :)

The area of ABCD is 104 units²

The area of rectangle is the product of its length to its breadth.

i.e., Area of rectangle= length * breadth

As, ABCD is in the shape of rectangle.

Using distance formula,

AB = √(1-(-5)² + (6-2)²

AB = √36+16

AB = √52

AB= 2√13

BC= √(9-1)² + (-6-6)²

BC= √64+144

BC =√208

BC= 4√13

Now, area of rectangle

=length *  breadth

= 2√13 * 4√13

= 8*13

=104  units²

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AC is equal to BC by the corresponding side of a congruent triangle.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

The midpoint of a line segment means a point that lies in the mid of the given line segment.

If D is the midpoint of segment AB, then AD = BD.

So in a triangle ACD and BCD

AD = BD (by midpoint D)

angle ADC = angle BDC = 90

CD = CD (common)

Therefore, triangle ACD and BCD are congruent.

Hence, AC = BC by the corresponding side of a congruent triangle.

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If the height of the triangle will be 6.28 meters. Then the value of x will be 8.46 meters.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In the diagram shown, the area of the triangle is 44.3 m².

If b = 14.1 m and the angle at C = 48°.

Then the value of x will be

The height of the triangle will be

    A = 1/2 × B × H

44.3 = 1/2 × 14.1 × h

    h = 6.28 m

Then the value of x will be

sin 48° = 6.28 / x

x = 8.455 ≈ 8.46 m

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Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.

According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.

Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.

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If we put a=0 and b=-4.05 then the expression 4a+4b becomes -16.2 and when we put a=-4.05 and b=0 then the expression becomes -16.2.

Given  2 (a + b) = -8.1

Because no relationship between a and b is given so we can put any value of one variable to determine the value of another variable.

If we put a=0 in 2(a+b) =-8.1 then b=-4.05

If we put b=0 then a =-4.05.

We need to put these values in 4a+4b

when a=0 b=-4.05

4a+4b=4*0+4*-4.5

=-16.2

when b=0 and a=-4.05

4a+4b=4*-4.05+4*0

=-16.2

Hence for a=0,b=-4.5 the value of 4a+4b equals -16.2 and for a=-4.05 and b=0 the function equals -16.2.

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Hang on ,it is already proven through given .

So The proof is of one line only

Hence proved .

x = 2/3 , 0 .

Question :

[tex] {3x}^{2} - 2x = 0[/tex]

use quadratic formula :

[tex]x = \frac{( - b)± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

Solution :

[tex]a {x}^{2} + bx + c = 0 \\ a = 3 \\ b = - 2 \\ c = 0[/tex]

[tex]x = \frac{ - ( - 2)± \sqrt{ { (- 2)}^{2} - 4 \times 3 \times 0} }{2 \times 3} \\ \\ x = \frac{2± \sqrt{4 - 0} }{6} \\ \\ x = \frac{2± \sqrt{4} }{6} \\ \\ x = \frac{2± 2}{6} [/tex]

separate into two equations :

[tex]x = \frac{2 + 2}{6} = \frac{4}{6} = \frac{2}{3} .[/tex]

[tex]x = \frac{2 - 2}{6} = \frac{0}{6} = 0.[/tex]

the values of x are 2/3 and 0 .

Answer:

The value of the expression will be "392.79".

Step-by-step explanation:

~ The technique of dividing a quantities into equivalent portions as well as    determining however many equal components may be formed, is determined as a division.

~ It is denoted by "/".

According to the equation, the expression is:

→ 196/0.499

By applying the division, we get

→ 392.79

Answer:

392

Explanation:

Note that we are estimating, not finding the actual value. 0.499 is very close to 0.5, so to estimate this expression, we can do 196 ÷ 0.5. Dividing a number by 0.5 is the same as doubling it, so this can also be seen as
196 · 2, which is 392.

Hope this helps !! :D
The actual answer is the other one, but again, you're finding an estimate!

Answer:

Step-by-step explanation:

Equations are separated by an equal sign. The value of x is given as -6/5

Given the equations below;

5(3x + 4) = 2

Expand

5(3x) + 5(4) = 2

15x +20 = 2

Subtract 2 from both sides

15x = 2 - 20

15x = -18

x = -18/15

x = -6/5

Hence the value of x is given as -6/5

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The other name for angle 2 is ∠DBC

The correct option is (D)

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

We know that while naming the angle we have to consider the point where the angle is made should be at center.

Hence, the angle 2 can also be written as ∠DCB.

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Answer:

C

Step-by-step explanation:

Use the equation [tex]a^2 + b^2 = c^2[/tex]

Input the numbers----> [tex](2865)^2 +(4550)^2=c^2[/tex]

Simplify ----> [tex]28910725=c^2[/tex]

Find the square root------->[tex]5376.9=c[/tex]

Answer:

The answer is C (0,4)

Step-by-step explanation:

Looking at the graph we have to find a point (x,y) of D.

Find point D. It is on the y-axis, but which one? Positive/Negative y-axis.

It appears to be on the positive y-axis.

Now we have to choose either option C or D.

Option C seems like the best choice since the point is (x,y) is (0,4) on the positive y-axis.

Option D is quite the opposite of point D since the point (0, -4) is on the negative y-axis.

The answer is C. (0,4)

Answer:

1.5 is the number.

Explanation:

Let the number be 'n', this is 100% - original number.

When increased by 40%, 100% + 40% = 140%.

140% × n = 2.1

1.4n = 2.1

n = 2.1/1.4

n = 1.5

Hence, the original number is 1.5.