Choose all the true statements.
A. √√-2= √2
B. √-2=√√2i
C. √-8=2i√/2
D. √√-8=-2√2
E. √-16=4i
F. √-16=-4

By substitution, the solution of the system of equations, 3c + 2d = 2 and d = 4, is (c , d) = (-2 , 4).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in variables c and d,

3c + 2d = 2     (equation 1)

d = 4     (equation 2)

Since the second equation is already expressed in d in terms of a constant, substitute the second equation to the first equation.

3c + 2d = 2     (equation 1)

3c + 2(4) = 2

3c + 8 = 2

Combining all terms containing the variable c on one side and the constants on the other side of the equality, and solving for c.

3c + 8 = 2

3c = 2 - 8

3c = -6

c = -6/3

c = -2

Hence, the solution of the given system of equations is (c , d) = (-2 , 4).

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The baseball field mark up its organic hotdogs from $2.00 to $6.50 each by 225%.

The markup on cost is defined as the amount added to the original cost of a product or service to arrive at the new selling price. It can also be a percentage of the original cost.

mark up = selling price - original price

If organic hotdogs at the grocery store cost $2.00 each and at a major league baseball game, an organic hotdog cost $6.50, then the mark up price is the difference between the two.

mark up = selling price - original price

mark up = $6.50 - $2.00

mark up = $4.50

To get the percentage of the mark up from the original price, divide the mark up price by the original selling price and multiply by 100%.

percent mark up = (mark up price/original price) x 100%

percent mark up = ($4.50/$2.00) x 100%

percent mark up = 2.25 x 100%

percent mark up = 225%

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Answer:

Step-by-step explanation:

solve by factoring

you get x=3/2

Answer: a) y=x²+6x+2   b) x=-3-√7, -3+√7

Step-by-step explanation:

(0,2)    (-6,2)     (-3,-7)

a)

y=ax²+bx+c

(0,2)

x=0   y=2

⇒ 2=a(0²)+b(0)+c

⇒ 2=0+0+c

⇒ 2=c

(-6,2)

x=-6   y=2

⇒ 2=a(-6)²+b(-6)+2

⇒ 2=36a-6b+2

⇒ 2-2=36a-6b+2-2

⇒ 0=36a-6b

⇒ 0+6b=36a-6b+6b

⇒ 6b=36a

Divide both parts of the equation by 6:

b=6

(-3,-7)

⇒ -7=a(-3)²+6(-3)+2

⇒ -7=9a-18+2

⇒ -7=9a-16

⇒ -7+16=9a-16+16

⇒ 9=9a

Divide both parts of the equation by 9:

1=a

Hence,

y=x²+6x+2

b)

x²+6x+2=0

D=(-6)²-4*1*2

D=36-8

D=28

√D=√28

√D=√(4*7)

√D=2√7

x=(-6±2√7)/2

x=-3-√7

x=-3+√7

Answer: f = 10

Step-by-step explanation:

        An undefined slope means it's graphed as a straight vertical line. There is no change in x, so the x value will be the same for both points.

       Here, f = x as coordinate points are written as (x, y);

       f = 10

The number of the text messages where it will result in the exact same charge from both companies is 500 messages

Number systems are mathematical systems that allow computers to understand and express numbers in various ways. A number is a mathematical value that is used to count and measure items as well as execute arithmetic calculations.

Natural numbers, whole numbers, rational and irrational numbers, and so on are all types of numbers. Similarly, different number systems with differing properties exist, such as the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.

Let the number calls be x where the messages will result in the exact same charge

So, Cell phone company A charges $20 per month plus $0.05 per text

message is 20 + 0.05x

And, Cell phone company B charges $10 per month plus $0.07 per text message is 10 + 0.07x

As we want the numbers to be equal, following equation is obtained

20 + 0.05x = 10 + 0.07x

Lets find x

20 + 0.05x = 10 + 0.07x

0.07x - 0.05 = 20 -10

0.02x = 10

x = 10/0.02

x = 500

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The probability that the number spun is a 3 given that it was less than 4 is 1/6.

Let A is the event of a number less than 4.

P(A) is the probability of getting a number less than 4.

The total number less than 4 is 3

Here, the total numbers in the game are 6.

By the Formula for the probability of an event E can be observed as:

P(A)= no of favorable cases/total no. of cases  = 3/6 = 1/2

B is the event of getting the number  3

P(B) be the probability of getting 3

The total  possible cases  is 1

Therefore , P(B)= 1/6

Now, P(B/A) is the probability of getting 3 which is an odd number.

P(B/A)= P(A ∩ B) / P(A)

          =1/6 / 1/2

   = 1/3

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The result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70

Given,

The expression = -5(x+2y)+15(x+2y)

The value of the variables

x=7 and y= -7

Substitute the values in the expression

-5(7+2(-7))+15(7+2(-7))= -5(7-14)+15(7-14)

=-5(-7)+15(-7)

=35-105

=-70

Hence, the result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70

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Answer:

Step-by-step explanation:

where?

ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

The right angle triangle JKL with base JL and perpendicular KJ has been drawn.

Height = KJ = a

Since J(0,0) so K(0,a)

Hence "ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units".

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The average rate of change between the given values of the variable is 21

A function can be defined as an expression or rule showing the relationship between a dependent and an independent variable.

Given the function;

h(t) = 2t^{2}[/tex] − t

For t =2

Substitute the value of t as 2 in the function, we have;

h(2) = 2 (2)² - (2)

Find the square

h(2) = 2(4) - 2

h(2) = 8 - 2

h(2) = 6

For t = 9

Substitute the value of t as 9 in the function, we have;

h(9) = 2(9)² - 9

Find the square

h(9) = 2(81) - 9

h(9) = 153

The average change = 153 - 6 = 147/ 9 -2 = 147/ 7 = 21

Thus, the average rate of change between the given values of the variable is 21

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Yes, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5  ,both are equals to (-1/5).

As given in the question,

Given number is 5

Case 1 : First find reciprocal of 5

Reciprocal of 5 =1/5

Then, opposite of the reciprocal of 5 =(-1/5)

Case 2. First find the opposite of 5

Opposite of 5 =-5

Reciprocal of the opposite of 5 =(1/ -5)

                                                =(1/-5) × (-1/-1)

                                                =(-1/5)

Therefore, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5  ,both are equals to (-1/5).

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Answer:

26 and 32 are the two numbers, the product is 832

Step-by-step explanation:

The line segment FG can be represented as expression 4x whose midpoint is N

We are provided with that Point N is the midpoint of FG and FN = 2x and We need to find expression that  represents FG

As N is the midpoint of line segment FG than FN = NG

Also it could be written as FG = FN + NG because FG is the broken into two different line segment FN and NG because of the midpoint N

Therefore, FN = 2x which means FN= NG=2x

So, we can write an expression that could represent FG

FG = FN + NG

FG = 2x + 2x

FG = 4x

Hence, The line segment FG can be represented as expression 4x

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Based on the number of votes that the two finalists received, the number of votes that Luke received was 2,875 votes

Assuming that the number of Sean's votes could be shown as x, the expression for the votes would be:

x + (x + 25%) = 5,175

2.25x = 5,175

x = 5,175 / 2.25

= 2,300 votes

Luke's votes were:

= 2,300 x (1 + 25%)

= 2,875 votes

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Answer:

5X2 + 2X + 3 orr 10x + 2

Step-by-step explanation:

The value of A in the 4-digit number, 3A5A is 5.

The 4-digit number provided in the question has to be a multiple of 15 given the information in the question. A multiple of a number is divisible by that number. A multiple of 10 is 100 because when 100 is divided by 10 , the value gotten is 10.

A multiple of a number is the product of an integer and that number. For example, a multiple of 2 is 100. This is because 2 multiplied by 50 is equal to 100.

The multiplies of 15 either have a unit value of 5 or 0.

If A is 5, the number becomes 3555.

3555 / 15 = 237

If A is 0, the number becomes 3050

3050 / 15 = 203.33

Thus, the value of A is 5 because 3555 is divisible by 15.

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Answer:

Pencils = 35

Notebooks = 15

Step-by-step explanation:

15 cents = 15/100 = $0.15

85 cents = 85/100 = $0.85

p + n = 50                    Eq. 1

0.15p + 0.85n = 18       Eq. 2

p = number of pencils

n = number of notebooks

From Eq. 1

p = 50 - n               Eq. 3

Replacing Eq. 3 in Eq. 2:

0.15(50-n) + 0.85n = 18

(0.15*50 + 0.15*-n) + 0.85n = 18

(7.5 - 0.15n) + 0.85n = 18

7.5 + 0.7n = 18

0.7n = 18 - 7.5

0.7n = 10.5

n = 10.5 / 0.7

n = 15

From Eq. 3:

p = 50 - n

p = 50 - 15

p = 35

Check:

From Eq. 2

0.15p + 0.85n = 18

0.15*35 + 0.85*15 = 18

5.25 + 12.75 = 18

e

Answer:

-1/10 - 7i/24

Step-by-step explanation:

Answer: M(-4.75,-6.25)

Step-by-step explanation:

C(-3,-8)    D(-6.5,-4,5)

Let the midpoint of C(-3,-8) and D(-6.5, -4.5) is M(x,y)

[tex]\displaystyle\\M(x,y)=(\frac{-3+(-6.5)}{2} ,\frac{-8+(-4.5)}{y} )\\\\M(x,y)=(\frac{-9.5}{2},\frac{-12.5}{2})\\\\M(x,y)=(-4.75,-6.25)\\\\Thus, \ M(-4.75,-6.25)[/tex]

Coordinates of point G is ( 10 , 2) in this equation.

What do mathematical point coordinates mean?

M is the mid points of FG.

coordinates of M is ( 8,5)

coordinates of F is ( 6,8 )

Let coordinates of G point is ( x₂, y₂)

[tex]x = \frac{x_{1} + y_{1} }{2} , y = \frac{x_{2}+ y_{2} }{2}[/tex]

[tex]8 = \frac{6 + x_{2} }{2} , 5 = \frac{8 + y_{2} }{2}[/tex]

[tex]16 = 6 + x_{2} , 10 = 8 + y_{2}[/tex]

x₂ = 10  ,  y₂ = 2

So, coordinates of point G is ( 10 , 2)

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The climbing steps have parallel planes for the treads. Although each step may appear to be a line, it is actually a plane.

Considering it as a staircase; a moving stairway that transports people between levels of a building or structure is known as an escalator. It is made up of a motor-driven chain of individually connected steps on a track that cycles along a pair of tracks that maintain them horizontal.

The climbing stair treads are parallel planes. Each step appears to be a line, but it is actually a plane.

The top two steps of the inclination are on the same plane. They are parallel.

These tires are twisted. They are neither parallel, nor do they share the same plane.

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If you are looking to solve the inequality for y:

_____________________________________

Inequality Form:

[tex]-12 < y < -6[/tex]

Interval Notation:

[tex](-12, -6)[/tex]

Hope this helps!

Answer:

{y|y≥0}

Step-by-step explanation:

The parent absolute value function is

This is a V-shaped function whose vertex is at the origin.

This means that, the least y-value is 0 and there is no highest y-value.

The range refers to all y-values for which the function exists.

Therefore the range is

Or

{y|y≥0}

Answer:

{y | y is a real number}

Step-by-step explanation:

because yxy=y=2

1,200 is not a viable solution to this problem as B.

No; 1,200 will cause her to exceed 1,500

It should be noted that Luna has consumed 900 calories so far today and has also burned 500 calories in dance class.

Therefore, the amount left will be:

= 1500 - (900 - 500)

= 1500 - 400

= 1100

Therefore, 1,200 is not a viable solution to this problem

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We get the absolute value inequality as | x - 88 | > 38.

We are given that:

Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and can occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of 88mg. We need to write an inequality for it.

We know that the blood sugar level should not be less than:

88 mg - 38 mg = 50 mg

Also, the blood sugar level should not be higher than:

88 mg + 38 mg = 126 mg

The inequality then will become:

50 mg ≤ Blood sugar level ≤ 126 mg.

The absolute value inequality will be:

| x - 88 | > 38

Therefore, we get the absolute value inequality as | x - 88 | > 38.

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The given pattern 5/7, 8/7, 11/7, 2, ....... is in the form of the arithmetic progression AP. The next 3 terms are  17/7, 20/7, 23/7.

An arithmetic progression is a sequence whose terms continue to increase and otherwise decrease by a constant number. The common difference is the set amount through which they either increase or decrease.

The following arithmetic progression formulas are frequently utilized to solve various AP problems for the initial term 'a' of an AP and the common difference 'd'-

Now, as per the stated question;

The AP given as; 5/7, 8/7, 11/7, 2, ...........

The series consists of four given terms.

Consider the initial term be 'a₁' = 5/7.

Then, the second term be 'a₂' = 8/7.

And, the third term be 'a₃' = 11/7.

And, the fourth term is 'a₄' = 2.

The AP have the same common difference. so,

d = a₃ - a₂

Substitute the values.

d = 11/7 - 8/7

d = 3/7

Thus, the common difference is 3/7.

or d = a₄ - a₃ (Put the values)

d = 2 - 11/7

d = 3/7

As, a₃ - a₂ = a₄ - a₃

Thus, we can conclude that the given sequence is in AP.

The fifth term will be; a₅ = a₄ + d = 2 + 3/7

a₅ = 17/7

Now, the 6th term will be; a₆ = a₅ + d = 17/7 + 3/7

a₆ = 20/7

Similarly, the 7th term will be; a₇ = a₆ + d = 20/7 + 3/7

a₇ = 23/7

Therefore, it can be said that the given sequence is in AP next three terms be 17/7, 20/7, 23/7.

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