Find k if 3k, k-2, and k + 7 are consecutive terms of an arithmetic sequence.

Answer:

x = plus or minus 8

Step-by-step explanation:

x² - 64 = 0

x² = 64

x = [tex]\sqrt{64}[/tex]

x = ± 8

Answer: Solve  :    x2+64 = 0  

Subtract  64  from both sides of the equation :  

                     x2 = -64

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ -64  

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1  

Accordingly,  √ -64  =

                   √ -1• 64   =

                   √ -1 •√  64   =

                   i •  √ 64

Can  √ 64 be simplified ?

Yes!   The prime factorization of  64   is

  2•2•2•2•2•2  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 64   =  √ 2•2•2•2•2•2   =2•2•2•√ 1   =

               ±  8 • √ 1   =

               ±  8

Answer: the lines on the outside mean absolute value and the absolute value of -3 is 3

Step-by-step explanation:

Answer: h = 70ft

Step-by-step explanation: To find the height the ball reached after 2 seconds, substitute variable t for 2 and calculate height:

[tex]h=4+65t-16t^{2}[/tex]

[tex]h=4+65.2-16.2^{2}[/tex]

[tex]h=4+65.2-16.4[/tex]

[tex]h=4+130-64[/tex]

h = 70

After 2s, the football reached a height of 70 feet.

Answer:

if its for 3 seconds the answer is 55

Step-by-step explanation:

1 = 62° ( Vertically Opposite Angles )

10 = 62° ( Corresponding Angles )

9 = 10 = 62° ( Vertically Opposite Angles )

6 = 95° ( Vertically Opposite Angles )

7 = 180° - 95° = 85° ( Linear Pair )

8 = 7 = 85° ( Vertically Opposite Angles )

5 = 8 = 85° ( Corresponding Angles )

3 = 5 = 85° ( Vertically Opposite Angles )

4 = 180° - ( 9 + 7 )

4 = 180° - ( 62° + 85° )

4 = 180° - 147°

4 = 33° ( Angle Sum Property )

2 = 4 = 33° ( Vertically Opposite Angles )

Answer:

One real rational root

Step-by-step explanation:

x^2-4x+4=0

=>x^2-2x-2x+4=0

=>x(x-2)-2(x-2)=0

=>(x-2)(x-2)=0

=>x=2

Therefore one real rational root

Answer:

Step-by-step explanation:

Let the two numbers be x and y. If the sum of the numbers is 65, then;

x+y = 65........ 1

Given twice the smaller number is 10 more than the larger number, this can be written as 2x = 10+y (taking x as the smallest and y as the largest)

Therefore 2x = 10+y

x = 10+y/2 ....... 2

Substitute equation 2 into 1 to have;

10+y/2 +y = 65

Find the LCM

(10+y+2y)/2 = 65

10+3y/2 = 65

cross multiply

10+3y = 130

3y = 130 -10

3y = 120

y = 120/3

y = 40

Since 2x =10+y

2x = 10+40

2x = 50

x = 50/2

x = 25

Therefore the two numbers are 40 and 25

Answer:

40 and 25

Step-by-step explanation:

Correct question is;

If f(x) = x³, evaluate the difference quotient: [f(6 + h) − f(6)]/h

Answer:

h² + 108h + 18

Step-by-step explanation:

We are given f(x) = x³

Thus;

f(6 + h) = (6 + h)³ = (36 + 12h + h²)(6 + h) = 216 + 72h + 6h² + 36h + 12h² + h³ = 216 + 108h + 18h² + h³

Then, f(6) = 6³ = 216

Thus;

[f(6 + h) − f(6)]/h = [216 + 108h + 18h² + h³ - 216]/h = (h³ + 108h + 18h²)/h

This gives;

h² + 108h + 18

Answer:

fewaf

Step-by-step explanation:

fsdfadfsadfasfas

Answer:

Term in months. Number of months for this loan. Loan amount. Total amount of your loan. Interest rate. Annual ...

Step-by-step explanation:

Answer:

Alternate-exterior angles theorem.

Step-by-step explanation:

Two parallel lines are cut by a transversal, and if there are a pair of congruent angles that are outside of the parallel lines, and on opposite sides of the transversal, you will have the alternate-exterior angles theorem.

Answer: (0,3) & (0,-1)

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

(x+1)(x+2)(x+3)(x+4)=120

Split 120 in it's factors: 2x3x4x5

=>(x+1)(x+2)(x+3)(x+4)=2x3x4x5

=>x+1=2 (Take any one in order)

=>x=1

Answer:

x=1

Step-by-step explanation:

120=2^3*3*5=2*3*4*5=(x+1)(x+2)(x+3)(x+4)

so x+1=2

    -1      -1

    x=1

Answer:

54

Step-by-step explanation:

38-11= 27

27×2= 54 so he started with 54 comic books

Answer:

34,466

Step-by-step explanation:

Given:

Number of males born in 2000 = 2,086,814

Percentage of males bearing Jacob of all males born in 2000 = 1.6516%

Required:

Number of Jacobs born in 2000

Solution:

Number of Jacobs born in 2000 = 1.6516% of number of males born in 2000.

[tex] = \frac{1.6516}{100}*2,086,814 [/tex]

[tex] = 0.016516*2,086,814 = 34,465.82 [/tex]

Number of Jacobs born in 2000 is approximately 34,466.

Answer:

$375 is what i got on

Answer:

y = 8

Step-by-step explanation:

[tex]-2(3y - 6) + 4(5y - 8) = 92\\\\\mathrm{Expand\:}-2\left(3y-6\right)+4\left(5y-8\right):\quad 14y-20\\14y-20=92\\\\\mathrm{Add\:}20\mathrm{\:to\:both\:sides}\\14y-20+20=92+20\\\\Simplify\\14y=112\\\\\mathrm{Divide\:both\:sides\:by\:}14\\\frac{14y}{14}=\frac{112}{14}\\\\Simplify\\y= 8[/tex]

Answer:

Step-by-step explanation:

-6y + 12 + 20y - 32 = 92

14y -20 = 92

14y = 112

y = 8

Answer:

the answer is 6.

Step-by-step explanation:

I think they want you to skip count down by 4 and there's your anwser.

Hope I helped.

SJ

Answer:

x=1

Step-by-step explanation:

-35x+85x-24=26

Combine like terms

50x -24 = 26

Add 24 to each side

50x-24+24 =26+24

50x = 50

Divide each side by 50

50x/50 = 50/50

x=1

Answer:

x=1

Step-by-step explanation:

subtract 35 from 85 which would equal 50 and then add x

so 50x-24=26

add 24 to 26 because you want x by itself

which would equal 50

50x=50

divide by 50 on both sides

50/50=1

x=1

The statement that a clock that is set fifteen minutes fast is less precise than an identical clock that keeps correct time is false

When a time is set away from the correct time, the time on the clock would be incorrect.

However, this has nothing to do with the precision of the clock.

This is so because precision deals with closeness of the time measurement to the original time

Since the time is ten minutes fast, it would not be less precise

Hence, the statement is false

Read more about precision at:

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Answer: A.-2 that the best answer hope this help yu

Step-by-step explanation:31 - (5 - 3 • 4)^2 + 2^6 / 4

31 - (5 - 12)^2 + 2^6 / 4

31 - (-7)^2 + 2^6 / 4

31 - 49 + 64 /4

31 - 49 + 16

-2

Answer:

A. -2

Step-by-step explanation:

31 - (5 - 3 • 4)^2 + 2^6 / 4

31 - (5 - 12)^2 + 2^6 / 4

31 - (-7)^2 + 2^6 / 4

31 - 49 + 64 /4

31 - 49 + 16

-2

Easy Algebra question!

Let's use "x" as a variable.

The equation would be x+x+60 = 240 with "x" being George's weight.

Subtract 60 from both sides and you get 2x = 180.

From there you divide both sides by 2, getting x=90.

"x" is George's weight, so he weighs 90 pounds.

ANSWER: 90 POUNDS

The weight of George is 90 pounds and the weight of George's brother is 150 pounds.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

George weighs 60 pounds less than his older brother.

Together they weigh 240 pounds.

Let George weigh be x and his brother weigh be y.

x + y = 240 ...1

x = y - 60 ...2

Then from equations 1 and 2, we have

2x = 180

 x = 90

Then y will be

y = 90 + 60

y = 150

More about the linear system link is given below.

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Steps to solve:

10 + y = 3

~Subtract 10 to both sides

y = -7

Best of Luck!

Answer:

y= -7

Step-by-step explanation:

All you have to do is subtract 10 from both sides. This eliminates the 10 from the y side and leaves you with y= -7.

Answer:

18

Step-by-step explanation:

you need to get from 9 to 36 in 2 steps by multiplying, so you need to find what gets 9 to 26 in one turn. 9*4=36, and because 4 is square we know you can multiply by 2 twice to get the same effect. 9*2=18. and just to make sure we can check that 18*2=36

Bring all the equation from the right side to the left.

2x² - 2 = - 5x - 1

2x² + 5x - 2 + 1 = 0 (take note that as you bring the number over you also have to flip the sign)

Therefore,

2x² + 5x + 1 = 0 (shown)

( this ans is similar to the form of ax² + bx + c = 0 )

The equation below written in the form ax² + bx +c= 0 is 2x² + 5x + 1 = 0

In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no ax² term.

Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc.

given:

2x² - 2 = - 5x - 1

2x² + 5x + 1 = 0.

Here, the above equation is in standard form as ax² + bx +c= 0.

Learn more about quadratic equation here:

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Answer:

( x + 2) ( x - 2 )

Step-by-step explanation:

f(x) = x^2 -4x

-4 = x^2 - 4x

0 =  x^2 - 4x + 4

0 = ( x + 2) ( x - 2 )

( x + 2) ( x - 2 )

Answer:  40 peaches

Step-by-step explanation:

Let x represent (1/2) the peaches

and y represent (1/2) the strawberries

          Peaches            Strawberries               Ratio

Alice:     x - 3                        y                           1:4

Bryan:     x                        y - 8                          1:3

We can create a system of equations:

Alice: 4(x - 3) = y      -->   4x - 12 = y

Bryan: 3(x) = y - 8  

Substitute y = 4x - 12 into the Bryan equation:

3x = (4x - 12) - 8

3x = 4x - 20

-x = -20

x = 20

Therefore, Alice and Bryan each had 20 peaches, which means Bryan bought a total of 40 peaches.

Answer:

Step-by-step explanation:

[tex]-6+x-3 \\x =2\\\\-6+2-3\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:\\-6+2=-4\\\\=-4-3\\\\=-7[/tex]

Answer:

-7

Step-by-step explanation:

So we have the expression:

[tex]-6+x-3[/tex]

And we want to evaluate it when x is 2.

So, substitute in 2 for x:

[tex]=-6+(2)-3[/tex]

Add the first two terms:

[tex]=-4-3[/tex]

Subtract:

[tex]=-7[/tex]

And that's our answer :)

Answer:

a=40. b=140. c= 40

Step-by-step explanation:

b is congruent To 140 because of the vertical angles postulate that states two angles vertical from one another are congruent.

a is 40 because it is Supplementary to b Which means that the sum of a and b must add up to 180.

c is Congruent to a due to the vertical angles postulate

Answer:

16= 4²

25= 5²

36= 6²

49= 7²

64= 8²

81= 9²

so, third option is correct I.e. 49

hope it will help....

Step-by-step explanation:

Hey there!!

It's so simple.

While finding the coordinates of any point if the midpoint is there it will be much easier. You must remember the midpoint formulae.

Let's simply work with it.

Here, A (2,-1) and midpoint M(3,3) are given.

Let another coordinate be B(x,y).

By midpoint formulae,

[tex]midpoint(x.y) = \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} [/tex]

Putting their values,

[tex]m(3 , 3) = \frac{2 + x}{2} , \frac{ - 1 + y}{2} [/tex]

As they are equal, equating with their corresponding elements we get,

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

6= 2 + x

x = 6-2

Therefore, the value of a is 4.

Again,

[tex]3 = \frac{ - 1 + y}{2} [/tex]

6 = -1 + y

Therefore, the value of y is 7.

Therefore, the coordinates are B (4,7)

Hope it helps....

Answer:

The coordinates of B is (4, 7)

Step-by-step explanation:

To find the answer for B, you have to do the inverse of the midpoint formula, which is M equals (x1 multiplied by x2, over 2; y1 multiplied by y2, over 2).

If you substitute in A's coordinates for x1 and y1, you come up with (3, 3) = (2+x, over 2; and -1+y, over 2)

If the x coordinate answer for AB was 3, you can create an equation like this to solve for B's x coordinate: 2+x over 2 equals 3.

          you multiply 2 by 3 to get 6---> 2+x=6-----> x=4

If the y coordinate for AB was also three, you can create another equation to solve for B's y coordinate: -1+y over 2 equals 3.

         you multiply 2 by 3 to get 6 again---->so -1+y=6---->y=7

so the answer for B's coordinates is (4, 7).