The value of y varies directly with x. If x= 3, then y= 21. What is the value of xwhen y= 105

Answer:10

Step-by-step explanation:Use the Pythagorean theorem a^2 + b^2 = c^2, a is 8 and b is 6 so now you have 8^2 + 6^2 = C^2 this simplifies to 64 + 36 = c^2 those 2 numbers add up to 100 so C^2 is 100 then to get C you take the square root of 100 which is 10

The missing side 10.

Option C is the correct answer.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Applying the Pythagorean theorem.

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = √100

c = 10

Thus,

The missing side is 10.

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Graph: See attached image

Slope: [tex]-\frac{1}{3}[/tex]

Y- intercept: (0,5)

X-intercept: (15,0)

Domain: (-∞,∞)

Range: (-∞,∞)

I hope this helped! Good luck with your mathematics class!

Answer:

Lin’s bike travels 100 meters when her wheels rotate 55 times.

here, n = 55 rotation and D = 100 meter.

Diameter is the distance bike travel

n is the number of times rotation

C is the circumference of the wheel

Answer:

D. -11/3b > 2/3

Step-by-step explanation:

We automatically can rule out B and C because it says is more than 2/3. The greater-than sign is >. B uses the less-than sign <, and C uses the greater-than or equal to sign ≥.

This leaves us with A. and D. The equation states One-third of a number b multiplied by -11. A. only has -11/b, but D. has -11/3 b. Because of this we can rule out A. so the answer is D.

I hope that this helps! :)

Answer:

110°

Step-by-step explanation:

y = 25

Angle 5 equals Angle 4 because of the Alternate Angles Postulate.

Angle 4 equals 110°

The measure of angle ∠4 is 110 degrees.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.

Given that the measure Angle 3= (2y+20) degrees, and the measure of Angle  5= (210-4y) degree

Then ∠3 + ∠5 = 180,  By Co-interior angles are supplementary

2y + 20 + 210 - 4y = 180

2y - 4y + 20 + 210 = 180  

-2y + 230 = 180

Now Subtract 230 from both sides;

-2y = 180 - 230

-2y = -50  

Then Divide both sides by (-2);

 y = -50/-2

y = 25

Now, ∠5 = 210 - 4y

      = 210 - 100

∠5 = 110

∠4 = ∠5    { by Alternate interior angles are equal}

∠ 4 = 110°

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Answer:

A horizontal line has a gradient = 0 and only has a y-intercept.

In the standard form this would mean that  

m =0,  and c =5  So, y  = 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

You put this in the wrong place, but I'll answer it anyway.

Let's see what we can get out of it.

1. It allowed western expansion.

2. It gave the United States a southern route to enhance trade.

3. It brought America closer to the slave trade which the southern states needed at the time. I don't like posting this answer, but it is a historical fact.

4. It made things a little difficult for the Spanish who had the ports in Louisiana.

5. It made the land route to the west coast a little easier to do. Not much but some.

6. Considering the cost of the land and how it was later developed, the price paid was a steal.

Answer:

12 dimes

Step-by-step explanation:

1 dollar= 4 quarters

1 dime=10 cents

3.45-1.20=2.25

2 dollars= 8 quarters

2.25-2.20=.25

1 quarter=.25

SOOOO your answer is 12 dimes

Step-by-step explanation:

Here is your explanation:

((x4) - 3x2) - 18 = 0 Factoring  x4-3x2-18 

The first term is,  x4  its coefficient is  1 .

The middle term is,  -3x2  its coefficient is  -3 .

The last term, "the constant", is  -18 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -18 = -18 

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -3 .

     -18   +   1   =   -17     -9   +   2   =   -7     -6   +   3   =   -3   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  3 

                     x4 - 6x2 + 3x2 - 18

Step-4 : Add up the first 2 terms, pulling out like factors :

                    x2 • (x2-6)

              Add up the last 2 terms, pulling out common factors :

                    3 • (x2-6)

Step-5 : Add up the four terms of step 4 :

                    (x2+3)  •  (x2-6)

             Which is the desired factorization

Find roots (zeroes) of :       F(x) = x2+3

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  3.

 The factor(s) are:

of the Leading Coefficient :  1

 of the Trailing Constant :  1 ,3

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      4.00        -3     1      -3.00      12.00        1     1      1.00      4.00        3     1      3.00      12.00   

Factoring:  x2-6 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

         A2 - AB + BA - B2 =

         A2 - AB + AB - B2 =

         A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 6 is not a square !!(x2 + 3) • (x2 - 6) = 0 product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.Solve  :    x2+3 = 0 

 Subtract  3  from both sides of the equation : 

                      x2 = -3

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

                      x  =  ± √ -3  

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

Accordingly,  √ -3  =

                    √ -1• 3   =

                    √ -1 •√  3   =

                    i •  √ 3

The equation has no real solutions. It has 2 imaginary, or complex solutions.

                      x=  0.0000 + 1.7321 i 

                      x=  0.0000 - 1.7321 i 

Solve  :    x2-6 = 0 

 Add  6  to both sides of the equation : 

                      x2 = 6

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

                      x  =  ± √ 6  

 The equation has two real solutions  

 These solutions are  x = ± √6 = ± 2.4495  

 Solving  x4-3x2-18  = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Solve   x4-3x2-18 = 0

This equation is reducible to quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using  w , such that  w = x2  transforms the equation into :

 w2-3w-18 = 0

Solving this new equation using the quadratic formula we get two real solutions :

   6.0000  or  -3.0000

Now that we know the value(s) of  w , we can calculate  x  since  x  is  √ w  

Doing just this we discover that the solutions of

   x4-3x2-18 = 0

  are either : 

  x =√ 6.000 = 2.44949  or :

  x =√ 6.000 = -2.44949  or :

  x =√-3.000 = 0.0 + 1.73205 i  or :

  x =√-3.000 = 0.0 - 1.73205 i

so we found four answers:

 x = ± √6 = ± 2.4495

  x=  0.0000 - 1.7321 i 

  x=  0.0000 + 1.7321 i 

sorry for taking time to answer

hope its helps

The correct option is A because [tex]x=\pm\sqrt{6}i[/tex] or [tex]x=\pm\sqrt{3}[/tex].

Given:

The given equation is:

[tex]x^4+3x^2-18=0[/tex]

To find:

The real and imaginary solutions of the given equation.

Explanation:

We have,

[tex]x^4+3x^2-18=0[/tex]

Substitute [tex]x^2=t[/tex] in the given equation.

[tex]t^2+3t-18=0[/tex]

Splite the middle term.

[tex]t^2+6t-3t-18=0[/tex]

[tex]t(t+6)-3(t+6)=0[/tex]

[tex](t+6)(t-3)=0[/tex]

Using zero product property, we get

[tex]t+6=0[/tex] or [tex]t-3=0[/tex]

[tex]t=-6[/tex] or [tex]t=3[/tex]

Substituting [tex]t=x^2[/tex], we get

[tex]x^2=-6[/tex] or [tex]x^2=3[/tex]

[tex]x=\pm\sqrt{-6}[/tex] or [tex]x=\pm\sqrt{3}[/tex]

[tex]x=\pm\sqrt{6}i[/tex] or [tex]x=\pm\sqrt{3}[/tex]

Therefore, the correct option is A.

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Answer:

m<6=54 m<4=126

Step-by-step explanation:

Answer:

the 2nd, 5th and 7th are the correct ones.

Answer:

(1, 7) (2, 10) (3, 5) (4, 7) (5, 9) hope that helps

Answer:

The last one

Step-by-step explanation:

Answer:

CRTs are: heavier in weight, they consume more energy, the lifespan is 43,800 hours, and they use electron guns.

LEDs are: lighter in weight, they consume less energy, the lifespan is 60,000 hours, and they use liquid crystals.

Step-by-step explanation: i took the test :)

Answer:

Mike 270

Molly 405

Step-by-step explanation:

Let Mike be x

Let Molly be x + 135

2/3 = x/(x + 135)                        Cross Multiply

2*(x + 135) = 3x                         Remove the brackets

2x + 270 = 3x                            Subtract 2x from both sides

2x-2x + 270 = 3x - 2x

270 = x

Mike gets 270

Molly gets 270 + 135

Molly gets 405

Answer:

x= 99

Step-by-step explanation:

first we open brackets

6x+36=7x-63

transpose

6x-7x= -63-36

-x=-99

the signs cancel each other so

x= 99

the answer is 50:::::::_::::::::

Answer:

17 and 19

Step-by-step explanation:

n= lesser integer       n+2= greater integer

2(n+2) = 3n -13

2n +4  = 3n-13

n= 17

lesser number =17

The other greater  number = 19 (they are odd,so skipping 18)

19 x 2 = 38

17x3 - 13 =51-13 = 38

Answer:

(8,0)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I am pretty sure the graph is skewed to the left, because the trailing tail is on the left. Sorry for the bad explanation lol

Answer:

(-9/10, 23/10)

Step-by-step explanation:

Answer:

y = 3/4 + 3/2

Step-by-step explanation:

Slope = 3/4

Solve for y-int.

0 = 3/4(-2) + b

-3/2 + b = 0

b = 3/2

y = 3/4x +3/2

Answer:

i really am his alt

Step-by-step explanation:

Answer: (0, -2) & (1, 1)

Step-by-step explanation:

Answer:

m=-1

Step-by-step explanation:

Answer: m = -1

Step-by-step explanation: Use the slope formula to find the slope m.

Answer:

C. 35

Step-by-step explanation:

Since 34.698 is higher than 5 in it's tenths place, we give it a shove.

We then get 35 after we shove the 6.

Answer:

11.2 hours

Step-by-step explanation:

The unknown is the hour time: 120+50.30x=250+38.70x. Now solve it: Subtract 38.70 and 120 from both sides and you get 11.6x=130 x=130/11.6 or 11.2 (about)

So the answer is 11.2 hours. Hope this helps :D

Answer:

So your answer is x = 11.2068965517

or

about, X = 11.21 (to the nearest tenth)

Step-by-step explanation:

50.30x + 120 = 38.70x + 250 (Given)

Move variables to the right and constants to the left by subtracting both sides.

11.6x = 130 (subtraction Property of equaity)

x = 11.2068965517 (Division property of equality)