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The roots of the function  x⁴+ x² = 4 x²  + 4 are ±2 or x = ±i.

A Complex number is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a function as x⁴+ x² = 4 x²  + 4

x⁴+ x² - 4 x²  - 4 = 0

x⁴+ - 3 x²  - 4 = 0

Assume u = x²

x⁴+ - 3 x²  - 4 = 0

Now using the substitution u = x² , then

u² - 3u - 4= 0 ← in standard form

(u - 4)(u + 1) = 0 ← in factored form

Then equate each factor to zero and solve for u

u - 4 = 0 ⇒ u = 4

u + 1 = 0 ⇒ u = - 1

Then convert u back into terms of x

x² = 4 ( take square root of both sides )

x = ± 2

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

⇒ x = ±i

Thus, The roots of the function  x⁴+ x² = 4 x²  + 4 are ±2 or x = ±i.

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Answer: [tex]3^{14}[/tex]

Step-by-step explanation:

[tex]\frac{3^{9} }{3^{-5} }[/tex]

Properties of exponents (negative exponent) says that a term can be moved from the numerator to the denominator and vice versa by flipping the sign.

So,

[tex]\frac{1}{3^{-5} } =3^{5}[/tex]

Properties of exponents (Product Rule) also say that

[tex]a^{x} *a^{y} = a^{x+y}[/tex]

So,

[tex]3^9*3^5=3^{9+5} =3^{14}[/tex]

Another way to solve this is simply using the Properties of exponents (Quotient Rule) which states

[tex]a^{x} /a^{y} =a^{x-y}[/tex]

So,

[tex]\frac{3^{9} }{3^{-5} }=3^{9-(-5)} =3^{14}[/tex]

Answer:

[tex]m∠1 = 64°[/tex]

[tex]m∠2 = 26°[/tex]

[tex]m∠3 = 36°[/tex]

Step-by-step explanation:

[tex]m∠1→75° + 41° + m∠1 = 180° \\ m∠1 = 180 - 116[/tex]

[tex]m∠1 = 64°[/tex]

[tex]m∠2→64° + m∠2 = 90° \\ m∠2 = 90 - 64[/tex]

[tex]m∠2 = 26°[/tex]

[tex]m∠3→m∠3 + 54° = 90° \\ m∠3 = 90 - 54[/tex]

[tex]m∠ 3 = 36°[/tex]

Answer:

The volume of a cube is the edge length cubed (S^3)

To find the edge length when the volume is known find the cubic root of the volume.

Step-by-step explanation:

Edge = ∛1/27

Edge = 1/3 ft.

Answer:

==============================

Let the number of adult tickets be x and student tickets be y.

When the storage unit is 8 ft high, the volume of the storage unit is C. 192ft³

To determine the volume, V,

= Area of the rectangle ABCG + Area of the rectangle CDEF

Area of the rectangle ABCG =2 x 2 = 4 square feet.

Area of the rectangle CDEF = 6 x 3 = 18 square feet.

So, the area of the base ABCDEFG, A = 18+4 = 22 square feet.

The given height, h= 8 feet

Volume = 22 x 8 = 192 cubic feet.

Therefore, it should be noted that when the storage unit is 8 ft high, the volume of the storage unit is 192ft

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Bank account with an interest rate of r% per year = 2.5%

Simple Interest :

Simple interest paid or received over a certain period is a fixed percentage of the principal amount.

Simple Interest=P×[tex]\frac{r}{100} }[/tex]×T

where:

P=Principal

r= interest rate on a certain period

T= Time

Given :

Principal(P)=  £1000

Time (T)= 1 Year

Find :

the interest rate per year = r%

Now,  

Interest earned on account =  £1025 - £1000

Simple Interest= £ 25

Simple Interest=P×[tex]\frac{r}{100}[/tex]×T

25= 1000×[tex]\frac{r}{100}[/tex]×1

25×100=1000r

2500=1000r

[tex]\frac{2500}{1000} =r\\\frac{25}{10} =r\\\frac{5}{2} =r\\2.5=r[/tex]

r= 2.5%

the interest rate of r% per year. after one year the value of the account=2.5%

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​

y + 1/4x - 9/4 is an equation of a line passing through the point (-1, 2) that is parallel to the line y = -4x + 5

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that y = -4x + 5

Here -4 is the slope and 5 is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 1/4, x₁ = -1 and y₁ = 2

y - 2 = 1/4(x - (-1))

y - 2 = 1/4(x + 1)

y - 2 = 1/4x + 1/4

y + 1/4x - 9/4

You can use the point-slope form calculator to determine the equation of a line given its slope and a point on the line. You will soon understand what the point-slope form equation is and how it differs from the slope-intercept form equation.

The point-slope formula is expressed as

y - y₁ = m(x - x₁)

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The percentage saved if the customer purchases the shirt today will be 18%.

The percentage of the original price which is the sale price will be 82%.

The percent discount offered on the shirt is 18%.

From the information, the men’s dress shirt costs $45, but it is $8.1 off today, the percentage saved if the customer purchases the shirt today will be:

= Amount off / Cost × 100

= 8.1/45 × 100

= 18%

The percentage of the original price that is the sale price will be:

= ($45 - $8.1) / $45 × 100

= 36.9/45 × 100

= 82%

The percent discount offered on the shirt is 18%.

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Answer:

$30.00

Step-by-step explanation:

$25.50 = y(1 - 0.15)

$25.50 = y(0.85)

($25.50) / (0.85) = y

y = $30

Answer:

$30

Step-by-step explanation:

let x = the original price

x - .15x = 25.50  

The original price - .15 of the original price is 25.25

.85x = 25.25  Divide both sides by .85

x = 30

Check:

30 - .15(30) = 25.25

30 - 4.50 = 25.25

25.25 = 25.25

The equation of the CD in slope-intercept form is: C. y = -4x + 2.

The equation of a line in slope-intercept form can be written as y = mx + b. In this form, m represents the slope and b represents the y-intercept.

The slopes of lines that are parallel are equal, while the slopes of the lines that are perpendicular to each other are negative reciprocals of each other.

The slope (m) of the graph y = 1/4x - 3 is 1/4. Since AB of rectangle ABCD is perpendicular to the graph, then the slope (m) of AB would be the negative reciprocal of 1/4 which is: -4.

Also, since CD is parallel to AB, they would have the same slope, m = -4.

To find the equation of CD that is parallel to AB, substitute m = -4 and (a, b) = (-1, 6) into y - b = m(x - a):

y - 6 = -4(x - (-1))

y - 6 = -4(x + 1)

y - 6 = -4x - 4

y = -4x - 4 + 6

y = -4x + 2

Therefore, the equation of the CD in slope-intercept form is: C. y = -4x + 2.

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Answer: solve for x

x=[tex]\frac{y-2}{3}[/tex]

solve for y

y=3x+2

Step-by-step explanation:

solve for x

2y=6x+4

Swap sides so that all variable terms are on the left hand side.

6x+4=2y

Subtract 4 from both sides.

6x=2y−4

Divide both sides by 6.

6

6x

Dividing by 6 undoes the multiplication by 6.

[tex]x=\frac{2y-4}{6}[/tex]

Divide −4+2y by 6.

x=[tex]\frac{y-2}{3}[/tex]

solve for y

2y=6x+4

The equation is in standard form.

2y=6x+4

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide 6x+4 by 2.

y=3x+2

​

The addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.

Given 3 1/2 + 2 3/4

= 7/2 + 11/4

= (14+11) / 4

= 25/4

= 6 1/4

Given 3 1/2 - 2 3/4

= 7/2 - 11/4

Find the LCM of both denominators

= (14-11) / 4

= 3/4

Therefore, the addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.

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Answer:

[tex](x-6)^2=-1[/tex]

Step-by-step explanation:

Given equation:

[tex]-6x^2+64x-222=-8x[/tex]

When completing the square, first move the terms in x to the left and the constant to the right of the equation:

[tex]\implies -6x^2+64x-222=-8x[/tex]

[tex]\implies -6x^2+64x-222+222=-8x+222[/tex]

[tex]\implies -6x^2+64x=-8x+222[/tex]

[tex]\implies -6x^2+64x+8x=-8x+222+8x[/tex]

[tex]\implies -6x^2+72x=222[/tex]

Factor out the leading coefficient -6 from the left side, then divide both sides by -6:

[tex]\implies -6(x^2-12x)=222[/tex]

[tex]\implies \dfrac{-6(x^2-12x)}{-6}=\dfrac{222}{-6}[/tex]

[tex]\implies x^2-12x=-37[/tex]

Add the square of half the coefficient of the term in x to both sides, forming a perfect square trinomial on the left side:

[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2=-37+\left(\dfrac{-12}{2}\right)^2[/tex]

[tex]\implies x^2-12x+\left(-6\right)^2=-37+\left(-6\right)^2[/tex]

[tex]\implies x^2-12x+36=-37+36[/tex]

[tex]\implies x^2-12x+36=-1[/tex]

Factor the perfect square trinomial on the left side:

[tex]\implies (x-6)^2=-1[/tex]

To solve:

[tex]\implies \sqrt{(x-6)^2}=\sqrt{-1}[/tex]

[tex]\implies x-6=\pm i[/tex]

[tex]\implies x-6+6=\pm i+6[/tex]

[tex]\implies x=6 \pm i[/tex]

Therefore, the solutions are:

[tex]x=6+i, \quad x=6-i[/tex]

Answer:

-1 or -3/3

Step-by-step explanation:

Average rate of change = slope

x = 2 x = 5

(2,3) (5,0)

Slope formula: y₂-y₁/x₂-x₁

(0-3)/(5-2) = -3/3 or -1

The values of the required parameters based on the analysis of the dataset are as follows;

X MIN = 0

X MAX = 2

X Scl = 0.5

Y MIN = 0

Y MAX = 110

Y Scl = 20

A dataset is a presentation of a collection of data. In a tabular form, a dataset is arranged such that each column of the table presents the data of a specific variable.

The table of values in the question are presented as follows;

d   [tex]{}[/tex]              p

0   [tex]{}[/tex]             110

0.25  [tex]{}[/tex]        90

0.5  [tex]{}[/tex]           80

0.75  [tex]{}[/tex]         75

1  [tex]{}[/tex]         [tex]{}[/tex]      75

1.25  [tex]{}[/tex]          40

1.5  [tex]{}[/tex]            40

1.75  [tex]{}[/tex]           10

2  [tex]{}[/tex]               0

Please find attached a plot of the data in the table presented in the question

X MIN is the minimum x-value obtained from the set of x-values, which is the minimum value of the domain of the data in the table.

From the table in the question; X MIN = 0

X MAX is the maximum x-value obtained from the set of x-values of the data in the table, which is also the maximum x-value of the range of input values in the table.

The maximum x-value in the table, X MAX = 2

X scl is the scale the specification of the distance between consecutive tick marks on the x-axis.

The distance between tick marks on the x-axis of the attached graph, X Scl = 0.5

Y MIN is the minimum y-value obtained from the set of y-values, which is the minimum value of the range of the data presented in the table

The Y MIN obtained from the table is 0

Y MAX is the maximum y-value obtained from the y-values of the data in the table, which is the maximum value of the range of the data in the table

The maximum y-value, Y MAX = 110

Y Scl is the distance between consecutive tick marks on the y-axis of the graph of the data

The Y Scl of the y-axis of the attached graph Y Scl = 20

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Answer:

The first option

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

to solve this you should first write it out

-8 * -3

now multiply them

the negatives cancel each other out

so

you can just do 8 * 3

and get 24

The length of each sides of the right triangle are as follows:

The shape of the city lot is a right triangle.

The hypotenuse side is 4 ft longer than one of the other side.

The perimeter of the lot is 440 ft.

Therefore, using Pythagoras theorem,

let

x = the other side

y = the second leg

x² + y² = (x + 4)²

x² + y² = (x + 4)(x + 4)

x² + y² = x² + 4x + 4x + 16

x² + y² = x² + 8x + 16

y² = 8x + 16

Hence,

x + x + 4 + y = 440

2x + y + 4 = 440

2x + y = 436

2x + y = 436

y = 436 - 2x

y² = 8x + 16

(436 - 2x)(436 - 2x) = 8x + 16

190096 - 872x - 872x - 4x² = 8x + 16

190096 - 1744x - 4x² = 8x + 16

4x² + 1752x -190080 = 0

4(x² + 438x - 47520) = 0

x² + 438x - 47520 = 0

Therefore,

x = 90 and x = - 528

Therefore, the hypotenuse side is 94 ft.

94² - 90² = y²

y = √8836 - 8100

y = √736

y = 27.1293199325

y = 27 ft

Therefore, the short leg, long leg and hypotenuse are 27 ft, 90 ft and 94 ft.

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Using the given information, the value of the variable x is equal to -0.125.

The given question can easily be solved using the constraints given in the question. It is given that B is between A and C. Also, the given question is in the form of Linear equation in one variable. Linear equation in one variable is the one which is of the form ax+b=0 where a and b are real numbers and x is the variable.

So, this implies that AB+BC=AC

Also, AB=4x-7 and BC=20x-5 and it is given that AB=BC

Thus, this implies that:

AB=BC

4x-7=20x-5

Taking 20x from Right hand side to Left hand side and -7 from Left hand side to Right hand side.

4x-20x=-5+7

-16x=2

x=-2/16

=>x=-1/8

=>x=-0.125

Thus, the value of x is equal to -0.125.

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Usando la fórmula del valor futuro, se encuentra que el valor acumulado en su cuenta al final de los dos años es de $110,615.

La formula es dada por:

[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]

En que:

En este problema, hay que:

Así:

[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]

[tex]V(24) = 1600\left[\frac{(1 + 0.02625)^{23}}{0.02625}\right][/tex]

V(24) = $110,615.

El valor acumulado en su cuenta al final de los dos años es de $110,615.

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The original price is $623.51.

Let the original price be represented by x.

Since the appliance store decreases the price of a 19-In television set 29%, that means the percentage of the sales price will be:

= 100 - 29

= 71%

Therefore, the original price will be:

= 71% of x = $442.69

0.71x = $442.69

x = $442.69/0.71

x = $623.51

The price is $623.51.

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The flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.

From the information, it was stated that the recipe for cookies calls for 3 cups of flour for every 4 cups of oatmeal.

Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be:

= 3/4 × 16

= 12

Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.

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Answer:

VAT = R239.85

Step-by-step explanation:

VAT = 15%

15/100 = 0.15

R1599 × 0.15 = 239.85

VAT = R239.85

Answer:

It's C, a function cannot have an x paired with 2 different y's