what is i + 6i? You have to simplify

Answer:

x = 2

y = 6

Step-by-step explanation:

y= 6x - 6

-3x- 3y= -24

to find the value of x:

- 3x - 3 (6x - 6)= -24

- 3x - 18x + 18= -24

-21x + 18 = -24

-21x= -42

x = 2

Now, to find the value of y:

(substitute x into the equation)

y = 6 x - 6

y = 6 (2) - 6

y = 12 - 6

y = 6

i think it will be B and then the second will be C

Answer:

Step-by-step explanation:

4)

30 is 60% of 50

5)

Amount Saved (Discount): $

350

Sale / Discounted Price: $

650

Answer:

10%

Step-by-step explanation:

We have been given that the manager of a store orders model railroad sets that cost $390 and sells them for $429.  

We will use markup % formula for our given problem.

[tex]\text{Markup percentage}=\frac{\text{Selling price- Cost}}{\text{Cost}}\times 100[/tex]

[tex]\text{Markup percentage}=\frac{429-390}{390}\times 100[/tex]

[tex]\text{Markup percentage}=\frac{39}{390}\times 100[/tex]

[tex]\text{Markup percentage}=\frac{1}{10}\times 100[/tex]

[tex]\text{Markup percentage}=10[/tex]

Therefore, markup is 10% of cost.

The simplified form of the rational expression 6x^2-54/5x^2+15x is 6(x - 3)/5x. This was achieved by factoring the original expressions, cancelling out common terms, and applying the difference of squares formula.

The subject here is the simplification of a rational expression. First, let's factor the numerator (6x^2 - 54) and the denominator (5x^2 + 15x). The common factor in the numerator is 6 and in the denominator is 5x. After factoring we get:

6x^2 - 54 = 6(x^2 - 9)

5x^2 + 15x = 5x(x + 3)

Now, we can use the property a^2 - b^2 = (a + b)(a - b) to further simplify x^2 - 9 to (x - 3)(x + 3). This gives our new numerator as 6(x - 3)(x + 3).

The denominator 5x(x + 3) remains the same. Therefore, the simplified form of the rational expression is 6(x - 3)(x + 3)/5x(x + 3). The (x + 3) terms can be cancelled out leaving us with the final simplified rational expression of:

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The initial y-value (or y-intercept) of the linear function that includes the points (-5, 0) and (6, -22) is -10.

The student is asking about the initial y-value of a linear function, which is also known as the y-intercept. This is the value of y when the line crosses the y-axis (where x=0). To find this, we first find the slope of the line using the formula: slope = (y2 - y1) / (x2 - x1) = (-22 - 0) / (6 - (-5)) = -22 / 11 = -2. Then we use the point-slope form of a linear equation to find the y-intercept 'b': y - y1 = m*(x - x1), substituting one of the points and the found slope: 0 - (-2)*(-5) = b gives us b = -10. This implies that the initial y-value of the linear function is -10.

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Answer:

i think it is 120

Step-by-step explanation:

4 multiplied by 30 is 120

Answer:

[tex]3x+4y=-24[/tex]

Therefore, option C is correct.

Step-by-step explanation:

We have been given the equation:

[tex]y=\frac{-3x}{4}-6[/[/tex]

We will take LCM 4 on right hand side of the above equation:

[tex]y=\frac{-3x-24}{4}[/tex]

Now, we will multiply the 4 in denominator on right hand side to the y in left hand side pof the equation we get:

[tex]4y=-3x-24[/tex]

After rearranging the terms we get:

[tex]3x+4y=-24[/tex]

Therefore, option C is correct.

Answer:

The temperature six hours ago was 13 °F

Step-by-step explanation:

Six hours ago the temperature was x degrees.

The temperature now is "6 degrees less than twice the temperature that it was six hours ago."

The temperature now is 2x - 6.

The temperature now is 20 deg.

2x - 6 = 20

2x = 26

x = 13

Answer: The temperature six hours ago was 13 °F.

Answer:

Divide 9 by 0.006 you should get 1500

Step-by-step explanation:

Answer:

0.054

Step-by-step explanation:

Velocity = wavelength times frequency

=  9 * 0.006

=  0.054

Answer:

Distance from her house to her work = 12.4 Miles

Step-by-step explanation:

Given :-

==> Automator mileage gauge read 38643.8 Miles before she left to work.

==> Automator mileage gauge read 38668.6 Miles after she came home from work.

==> She didn't drive anywhere else during the day. home to work & work to      home.

Car driven during the day = 38668.6 - 38643.8

                                           = 24.8 Miles

Let the distance from home to work be X

*It is assumed that Distance from home to work = Distance from work to home

So, Distance from work to home = X

Total distance driven during the day = Distance from home to work + Distance from work to home

Total distance driven during the day = X + X

                                                    24.8 = 2X

                                                    24.8 ÷ 2 = X

                                                    12.4 = X

Distance from her house to her work = 12.4 Miles

Answer: I think the answer is 24.8

Step-by-step explanation:

Answer:

-4< c

Step-by-step explanation:

2> -2-c

Add 2 to each side

2+2> -2+2-c.

4 > -c

Divide each side by -1.  Remember that dividing by -1 will flip the inequality.

4/-1  < -c/-1

-4< c

Answer:

C  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

30 - 14 = 16girls

ratio is : 14/16 = 7/8

Answer:

C

Step-by-step explanation:

I took the test

Answer:

inches= 342''

feet= 28.5'

yards= 9.5 yds

Step-by-step explanation:

inches= 90 +54 + 198= 342''

feet=342*(1/12)= 28.5'

yards= 9.5 yds

Convertion Rates

1'=12''

1yd = 3'

Step-by-step explanation:

inches= 342''

feet= 28.5'

yards= 9.5 yds

Answer:

The common difference would be -10.

Step-by-step explanation: If it were +10 then it would be: 9, 19, 29, 39

If it had a common ratio of -9 then it would be: 9, -81, 729, -6561

It it had a common ratio of 9, then it would be: 9, 81, 729, 6561

Answer:

A

Step-by-step explanation:

Look at the picture.

We must use the Pythagorean theorem:

[tex]AB^2+OB^2=AO^2\\\\5^2+r^2=8.6^2\\\\25+r^2=73.96\qquad\text{subtract 25 from both sides]\\\\r^2=48.96\to r=\sqrt{48.96}\\\\\boxed{r\approx7}[/tex]

Answer:

21.6 is 54% of 40.

Step-by-step explanation:

21.6 ÷ 40 = 0.54 = 54%

Method 1:

[tex]21\dfrac{3}{5}=\dfrac{21\cdot5+3}{5}=\dfrac{108}{5}\\\\\\\\\begin{array}{ccc}40&-&100\%\\\dfrac{108}{5}&-&p\%\end{array}\qquad\text{cross multiply}\\\\\\\\40p=\dfrac{108}{5}\cdot100\\\\40p=108\cdot20\\\\40p=2160\qquad\text{divide both sides by 40}\\\\\boxed{p=54}[/tex]

Method 2:

[tex]\dfrac{\frac{108}{5}}{40}\cdot100\%=\dfrac{108}{5}\cdot\dfrac{1}{4}\cdot10\%=\dfrac{108}{2}\%=54\%[/tex]

Final answer:

Using the Pythagorean theorem, the length of the shadow cast by a 30m tall building, with a diagonal distance of 36m from the top of the building to the top of the shadow, is calculated to be approximately 19.9 meters.

Explanation:

To find the length of the shadow cast by a 30m tall building, we can use the Pythagorean theorem. This theorem relates the lengths of the sides of a right triangle. Here, the building and its shadow form the two legs of a right triangle, and the line from the top of the building to the top of the shadow is the hypotenuse.

Let's denote:

The height of the building (opposite side) as O = 30m

The length of the shadow (adjacent side) as A

The distance from the top of the building to the top of the shadow (hypotenuse) as H = 36m

According to the Pythagorean theorem, we have:

O2 + A2 = H2

Plugging in the known values, we get:

302 + A2 = 362

900 + A2 = 1296

A2 = 1296 - 900

A2 = 396

A = √396

A ≈ 19.9m (rounded to one decimal place)

Therefore, the length of the shadow is approximately 19.9 meters.

Answer:

a15 = -5

Step-by-step explanation:

Let n=15 for the 15th term

a15 = -3*15 +50

a15 = -45+50

a15 = -5

To find the 15th term of the sequence an = -3n + 50, replace n with 15 in the given formula. The calculation becomes -3(15) +50 which simplifies to -45 + 50, finally giving the result 5. Therefore, the 15th term of the sequence is 5.

In mathematics, determining the nth term of a sequence involves applying the sequence formula, and substituting the specific term number, denoted as n, into the formula. For instance, consider the sequence an = -3n + 50. To find the 15th term (a15), one substitutes n = 15 into the formula: a15 = -3(15) + 50. Simplifying, a15 = -45 + 50, resulting in a15 = 5. This process showcases how a specific term in the sequence can be calculated systematically, providing a precise value for the 15th term. The formula an = -3n + 50 encapsulates the underlying pattern, allowing for the determination of any term within the sequence.

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Answer:

Perimeter of ΔAKL is, [tex]27 +9 \sqrt{3}[/tex] units.

Area of  ΔAKL is, [tex]\frac{81\sqrt{3} }{2}[/tex] square units

Step-by-step explanation:

Given: In ΔAKL , AK = 9 units , [tex]m\angle K = 90^{\circ}[/tex] and [tex]m\angle A= 60^{\circ}[/tex].

In ΔAKL

[tex]\tan (A) = \frac{KL}{AK}[/tex]

Substitute the value AK = 9 units and [tex]m\angle A =60^{\circ}[/tex] to solve for KL ;

[tex]\tan(60^{\circ}) = \frac{KL}{9}[/tex]

[tex]\sqrt{3} = \frac{KL}{9}[/tex]

⇒[tex]KL = 9\sqrt{3} units[/tex]

In right angle ΔAKL,

Using Pythagoras theorem;

[tex]AL^2 = AK^2+KL^2[/tex]                     ......[1]

Substitute AK = 9 units and [tex]KL =9\sqrt{3} units[/tex] in [1] to solve for AL;

[tex]AL^2 = 9^2+(9\sqrt{3})^2[/tex]

[tex]AL^2 = 81+(81 \cdot 3)[/tex]

[tex]AL^2 = 81+243 = 324[/tex]

[tex]AL = \sqrt{324} = 18 units[/tex]

Perimeter of triangle is the sum of all the sides.

Perimeter of triangle AKL = AK +KL +AL = [tex]9 + 9\sqrt{3} + 18 = 27 +9 \sqrt{3}[/tex] units.

Formula for Area of right angle triangle is given by:

[tex]A = \frac{1}{2} Base \times Height[/tex]

Area of triangle AKL=  [tex]\frac{1}{2} (9\sqrt{3}) \times (9)[/tex]

                                  = [tex]\frac{81\sqrt{3} }{2}[/tex] square units

Final answer:

The perimeter of triangle AKL is approximately 29.09 m, and the area is 20.25 m², calculated using the properties of a 30°-60°-90° right triangle.

Explanation:

To find the perimeter of △AKL, we need to determine the lengths of all three sides. We know that AK = 9 m, ∠K = 90° (which makes △AKL a right triangle), and ∠A = 60°. Because the angles in a triangle add up to 180°, ∠L must be 30° (180° - 90° - 60°). In a 30°-60°-90° right triangle, the lengths of the sides are in the ratio 1:√3:2. Thus, if AK is the side opposite the 60° angle, AL must be half of AK, and KL must be AK times √3.
Therefore, AL = ½ × 9 m = 4.5 m, and KL = √3 × 9 m ≈ 15.59 m. The perimeter is the sum of AK, AL, and KL: 9 m + 4.5 m + 15.59 m ≈ 29.09 m.

The area of △AKL can be found using the formula for the area of a right triangle, which is ½ × base × height. AK and AL can serve as the base and height, respectively, so the area A is ½ × 9 m × 4.5 m = 20.25 m².

Answer:

a=9

b=4

v=69

Step-by-step explanation:

Answer:

22 25/32

Step-by-step explanation:

well you just dividde the number in half and add the half and continue this and that's the seventh term. please be grateful it took me five minutes to do this

The seventh term of this sequence is 34.17875

Given : Each consecutive term is calculated by adding the half of preceding term to the preceding term.

Like : 2 + 1/2 (2) = 2 + 1 = 3

3 + 1/2 (3) = 3 + 3 / 2 =  3 + 1.5 = 4.5 or 4 1/2

4.5 + 1/2 ( 4.5 ) = 6.75

Similarly :

6.75 + 1/2 (6.75) = 10.125

10.125 + 1/2 (10.125) = 15.1875

15.1875 + 1/2 (15.1875) = 22.78125

22.78125 + 1/2 (22.78125) = 34.17875

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We know that there are about 3.785 liters in 1 gallon. From here we could pour 3 whole liters into a one-gallon container without overflowing since 3 < 3.285 liters. But if we try to pour the next whole liter( 4 liters) it would be too much since 4 is greater then 3.785 liters. So the answer is 3 liters.  

Hope this helps. <3

Answer:

Diagram attached

AJ = 8.75 in.  

Step-by-step explanation:

Since triangles HBA & HKJ are similar,    

BH/AH = KH/JH  

3 in /5.25 in = 8 in /JH  

JH = 14 in  

JA = JH - AH = JH - 5.25 in = 8.75 in

HJ = 14 in.

AJ = 14 in - 5.25 in  

AJ = 8.75 in.  

Answer:

#7 is 3,150 tickets

Step-by-step explanation:

You multiply 126 and 25 together to get 3,150, because if each of the 126 students have to sell 25 tickets, that means you have to use multiplication.

|a| = a for a ≥ 0

|a| = -a for a < 0

|-15| = -(-15) = 15

|15| = 15

Noelle bought gifts for her nine nephews and the total cost of these gifts is given. By setting up equations and solving them, we find that she purchased 6 videos and 3 CDs.

Step by Step Solution:

Noelle bought gifts for her nine nephews, which can be either videos costing $14.95 each or CDs costing $16.88 each, and spent a total of $140.34. We need to determine the number of videos and CDs she bought.

Let's denote the number of videos Noelle bought by V and the number of CDs by C. We can set up the following equations based on the given information:

V + C = 9 (as she bought gifts for nine nephews)

14.95V + 16.88C = 140.34 (total amount spent)

To solve these equations, we can use the substitution or elimination method. Let's use substitution:

From equation (1), we get:

C = 9 - V

Substitute this into equation (2):

14.95V + 16.88(9 - V) = 140.34

Expanding and simplifying:

14.95V + 151.92 - 16.88V = 140.34

-1.93V + 151.92 = 140.34

-1.93V = 140.34 - 151.92

-1.93V = -11.58

V = 6

Substitute V = 6 back into C = 9 - V:

C = 3

Therefore, Noelle bought 6 videos and 3 CDs.