Which expressions represent purely real numbers and which expressions represent non-real complex numbers?
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-289
i9
√(-18)
4- 321² 2 √-49
3 +2i
Purely Real Number
Non-real Complex Number

Answer:

•3✓7

✓3.✓21

=✓3×✓3✓7

=3✓7

Answer:

3rd answer is correct

Step-by-step explanation:

√3 × √21

√3 × √(7 × 3)

√( 3 × 3 × 7 )

√ ( 3 × 3 ) × √7

3√7

Answer: according to my work i got

LCM - Lowest Common Factor

HCF - Highest common factor

Step-by-step explanation:

please mark brainlest!!

yw! =^.^=

Given: f(x) = 3x² -5x + 4

To find f(-2), simply substitute x = -2 in function f(x).

f(-2) = 3(-2)² -5(-2) + 4

f(-2) = 12 + 10 + 4

f(-2) = 26

Answer: 26

For an ordered pair (x, y) in a relation, the y element represents the range.

Answer: range

Answer: x = 6

Step-by-step explanation:

B(7,3) maps onto B'(5,3).

The perpendicular bisector of [tex]\overline{BB'}[/tex] is x=6, so that is also the line of reflection.

Answer:

x = 6

Step-by-step explanation:

Taking test as we speak

There are 5 nickels, 3 dimes, and 9 pennies.

Let d = The number of dimes

Let n = number of nickels

Let p = The number of pennies

As given, there are two more nickels than dimes and three times as many pennies as dimes:

d+2=n

3d=p

0.10d+0.05n+0.01p=0.64

Plug in the value to find d

[tex]0.10d+0.05(d+2)+0.01(3d)=0.64[/tex]

[tex]0.10d+0.05d+0.1+0.03d=0.64[/tex]

[tex]0.18d=0.64[/tex]

[tex]d=3[/tex]

The value of p is equal to 3d

p=3(3)=9

n=d+2

n=3+2

n=5

Hence, there are 5 nickels, 3 dimes, and 9 pennies.

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Answer:

Step-by-step explanation:

the objects which have less density than water will float

and the objects which have more density than the density of liquid will sink in liquid or will not float.

Step-by-step explanation:

(3x+6)= 48(Alternate angles)

3x=48-6

3x=42

x=14

2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)

48+9=5y-2y

57=3y

y=19

Answer:

Step-by-step explanation:

Solution

The factored form is going to be the HCF (highest common factor)

The fest way to do this is to turn this into primes.

8x^2 + 12x

8x^2 = 2*2*2*x*x

12x = 2 * 2 * x

Now bold the HCF.

8x^2 = 2*2*2*x*x

12x = 2 * 2 * x

The HCF = 2*2*x

Divide that into the original question to determine the second factor.

8x^2 / 4x = 2x

12x / 4x = 3         Notice how the x-s cancel

Answer

4x (2x + 3)

The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.

A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.

When a line divides letter T vertically, it means that two mirror images will be created.

Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.

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Answer: The base graph has been shifted down 90 units.

Step-by-step explanation:

See attached image.

Answer:

  f(x) = -5x +48

Step-by-step explanation:

A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.

In this instance, we find it convenient to leave the coefficient of y as positive.

  5y = x -10 . . . . . . original equation

  y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated

At the given point, the equation becomes ...

  8 = -5(8) +c

  48 = c . . . . . . . add 40

The equation of the line is then ...

  y = -5x +48

  f(x) = -5x +48 . . . . . . in functional notation

The slope is m=6 and length of line is 3.5√37.

The slope of a line is a measure of its steepness.

Given:

endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5

slope= 8-2/3-2= 6

Now, using distance formula,

d= √(3-2)² + (8-2)²

d= √1+ 36

d= √37

As, Line AB is dilated by a scale factor of 3.5.    

So, new d= √37*3.5

new d= 3.5√37

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Step-by-step explanation:

this is an arithmetic sequence :

a1 = 1

an = an-1 + 2 = a1 + (n-1)×2

the sum of n terms of an arithmetic sequence is

S = n×(a1 + an)/2

n = 5000

an = a1 + 4999×2 = 9999

S = 5000×(1 + 9999)/2 = 5000×5000 = 25,000,000

Answer: 3

Step-by-step explanation:

Median is a statistical measure that determines the middle value of a dataset listed in ascending order.

arranged data  is   0,1,2,3,3,5,9,12

number of data terms=8

if data is  even then

median=(3+3)/2=3

The vertical stretch of f(x) to g(x) is a factor of 5

The functions are given as:

f(x) = x

g(x) = 5x

Substitute f(x) = x in g(x) = 5x

g(x) = 5f(x)

In th above equation, the factor is 5.

5 is greater than 1 (this means vertical stretch)

Hence, the vertical stretch of f(x) to g(x) is a factor of 5

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[tex]{ \red{ \bold{option \: (d)}}} \: { \green{ \tt{ {2}^{8p} = {2}^{5p + 3}}}} [/tex]

Step-by-step explanation:

I said option (d) is correct. Because, the answer of 2^8 is 256 i.e.,

[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}}}[/tex]

[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{256}}}[/tex]

The value of 16^2 = 256.

Also, the answer of 2^5 is 32. i.e.,

[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2}}}[/tex]

[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{32}}}[/tex]

Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110

Geometric sequence are sequence that increase in an exponential manner.

Given the recursive sequence 0, 2, 14, 36, 68

From the sequence

0 + 2 = 2

2 + 12 = 14

14 + 22 = 36

36 + 32 = 68

68 + 42 = 110

Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110

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The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months

Each month, there is an increase by a factor of 0.06 of the previous months model.

From geometric sequence formula of aₙ = ar^(n - 1),

where;

a is first term

r is common ratio

aₙ is nth term

we have;

1,008.9 = 671 * 1.06^(n - 1)

1008.9/671 = 1.06^(n - 1)

In 1.504 = (n - 1) In 1.06

0.408 = (n - 1) * 0.058

n - 1 = 0.408/0.058

n = 7.03 + 1

n ≈ 8 months

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Answer:

Option (2)

Step-by-step explanation:

cos 50° = y/z

z = y/cos 50°

After 20 years of depositing and investing there will be 168474.01 dollars in your account.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

The formula for calculating how much money will your account be worth after 20 years of depositing and investing is:

P = $250, r = 9% = 0.09, t = 20 years, n = 12 and PMD = $250(per month deposit)

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]

[tex]\rm A = 250(1+\dfrac{0.09}{12})^{12\times20}+\dfrac{250((1+\dfrac{0.09}{12})^{12\times12}-1)}{\dfrac{0.09}{12}}[/tex]

A = 1502.287 + 166971.717

A = $168474.01

Thus, after 20 years of depositing and investing there will be 168474.01 dollars in your account.

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Answer:

(x+2)²+(y-4)²=36

Step-by-step explanation:

1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);

2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];

3) to make up the required equation according to the scheme:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.

4) finally, (x+2)²+(y-4)²=6².

PS. for more details see the attachment.

Answer:

182 inches

Step-by-step explanation:

1 book is 13 inches thick.

So when 14 of those books are stacked together (lets take the book cover has non-existent thickness since the question did not mention),

Height of stack of 14 books = 14 x Thickness of 1 book = 14 x 13inches

= 182 inches

The ordered pairs that represent functions are:

For a set of ordered pairs to represent a function, the following must be true:

The x value must point to only one y value

In {(-3, 10), (-2, 13), (3, 13), (8, 12)}  and {(-4,11), (5, 10), (-3, 3), (-1, 10)}, the x value point to only one y value

Hence, {(-3, 10), (-2, 13), (3, 13), (8, 12)}  and {(-4,11), (5, 10), (-3, 3), (-1, 10)} are functions

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In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.

Trigonometric Functions: SOH-CAH-TOA

Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.

tan(23) = x / 2

x = tan(23) * 2

x = 0.8489

x = 0.8

Hope this helps!

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

Slope = (y1-y2) / ( x1-x2)

            = ( f-4) / (-8 - -6)      =  6

                  (f-4) / -2    = 6

                    f-4 = -12

                     f = - 8

Answer:

f = -8

Explanation:

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given:

Inserting into slope formula:

[tex]\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6[/tex]

[tex]\sf \rightarrow \dfrac{4-f}{2 } = 6[/tex]

[tex]\sf \rightarrow 4-f = 12[/tex]

[tex]\sf \rightarrow -f = 12-4[/tex]

[tex]\sf \rightarrow -f =8[/tex]

[tex]\sf \rightarrow f =-8[/tex]

Answer:

option A: West Europe, East Europe, and Asia

Explanation: Europe and Asia as a whole are called Eurasia.

hope that helps...

The bisection method will converge to the solution after three iterations.

It should be noted that after one iteration, x1 will be:

= (1 + 9)/2

= 10/2

= 5

Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.

After the second iteration, x2 will be:

= (1 + 5)/2

= 3

Also, this is greater than 0. The third iteration will be:

m= (1 + 3)/2

= 2.

Now, f(2) = 2⁴ -2³ - 2² - 4

= 0

Therefore, the method converges exactly to the root in 3 iterations.

Complete question:

The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.

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Answer:

70

Step-by-step explanation:

【Answer】The least common multiple of 35 and 70 is 70.

                          [tex]\orange{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]                        

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{35 \ \ \ 70}\\ 35 \ \ \ 35\\ 7 \ \ \ \ 7\\ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 5\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]

                                        [tex]\sf{L.c.m.(35,70)=2\times5\times7}[/tex]

                                          [tex]\boxed{\boxed{\sf{L.c.m.(35,70)=70}}}[/tex]