The sale price of a swimming pool after a 18.5% discount is $1189.90. Find the original list price of the pool.

The modulus of the complex number is 5.

The value of z is a complex number with a real and imaginary value. Let's assume the complex number z is given as:

[tex]z = 3 + 4i[/tex]

The modulus of the complex number is given as:

[tex]|z|=\sqrt{x^2+y^2}[/tex]

From the given complex number:

Substitute into the formula:

[tex]|z|=\sqrt{3^2+4^2}\\|z|=\sqrt{9+16} \\|z|=\sqrt{25}\\|z|=5[/tex]

Hence the modulus of the complex number is 5.

Note that the complex number was assumed.

Learn more on complex number here: https://brainly.com/question/5564133

Answer:

[tex]\sqrt{10\\[/tex]

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

-23+23= 0

0 + 23 = 23

To meet the character limit.

Answer:

0

Step-by-step explanation:

first, you need to calculate the entire distance:

23 + 23 = 46

Now divide it by half:

46 / 2 = 23

And now substract & add this

-23 + 23 = 0

23 - 23 = 0

Answer:

Well we can make a proportion in this scenario

So 3 cups of soda to 5 cups of punch

And how much soda for 18 punch.

Well we can do this

make “x” the amount of soda

And then make a proportion

3/5 = x/ 18

Now solve

You can cross multiply

54=5x

x=10.8

10.8 soda

[tex]\\ \sf\longmapsto 9\dfrac{7}{11}-(5+1\dfrac{1}{2})[/tex]

[tex]\\ \sf\longmapsto4 \dfrac{7}{11}-1\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto 4\dfrac{14}{22}-1\dfrac{11}{22}[/tex]

[tex]\\ \sf\longmapsto 3\dfrac{3}{22}[/tex]

Done

Answer:

Smallest Angle : 10 degrees

Middle Angle : 30 degrees

Biggest Angle : 50 degrees

Step-by-step explanation:

3x+5x+x=90, 9x=90, x=10

Smallest Angle : 10 degrees

Middle Angle : 30 degrees

Biggest Angle : 50 degrees

Answer:

3.14 x 10,000 equals 31,400

Step-by-step explanation:

Answer:

31415.9

Step-by-step explanation:

yeah-ya............. right?

[tex]\\ \sf\longmapsto sin10°-cos10°[/tex]

[tex]\\ \sf\longmapsto sin(90-10°)-cos10°[/tex]

[tex]\\ \sf\longmapsto cos10-cos10[/tex]

[tex]\\ \sf\longmapsto 0[/tex]

Answer:

Step-by-step explanation:

square root (3)/2 = 1.732/2 = .86603

Sin(x) = 0.86603

x = sin-1(0.86603)

x = 60

Answer:

a) 8cm

b) 19.8cm

Step-by-step explanation:

The key to these types of questions is to keep proportions in mind.

To solve the first question, you want to find the proportion of the smaller triangle to the bigger triangle. The length of AE is 6cm, but the length of AD is (6+4) = 10cm. So the proportion of the bigger triangle to the smaller triangle is 10/6. So to find the lengths of the sides of the bigger triangle, we want to keep this number in mind.

The BE side is parallel to CD, so we have to use length of BE multiplied by the proportion in order to get the length of CD.

CD = 4.8 * (10/6) = 8

CD = 8cm

For the second question, you use the same concept to find all the other side lengths. The only one you need left for the shape EBCD is side BC. Do the same thing you did before, take the length of the side of the smaller triangle that corresponds with side AC on the bigger triangle. In this case, it's AB, which is 4.5cm. Multiply this by 10/6 to get AC.

AC = 4.5 * (10/6) = 7.5

AC = 7.5

But we're not done. We just found the length of AC, but we need the length of BC to calculate the perimeter. To do this, we want to take the length of AC - the length of AB.

7.5 - 4.5 = 3

So the length of BC is 3cm. Now, to find the perimeter, just add all the sides of EBCD together.

4.8 + 4 + 8 + 3 = 19.8cm.

Hope this helps.

Answer:

a) CD = 8 cm

b) Perimeter of EBCD is 19.8 centimeters

Step-by-step explanation:

For this question, you can assume that ΔABE and ΔACD are similar. That's proven by BE ║ CD, but that's not directly relevant to the question so I won't explain it unless you would like me to.

In 2 similar triangles, all corresponding angles are congruent and all corresponding sides have the same scale factor.

For example, in ΔABC and ΔXYZ:

[tex]\frac{AB}{XY} =\frac{AC}{XZ} =\frac{BC}{YZ}[/tex]

Using those relationships, you can solve for any side in one triangle given the corresponding side in the other triangle.

A)

In the given triangles ΔABE and ΔACD, CD corresponds to BE, so:

[tex]\frac{CD}{BE} =\frac{AD}{AE}[/tex]

where AD is just 6 + 4 = 10.

[tex]\frac{CD}{4.8} =\frac{10}{6} \\\\\frac{CD}{4.8} =1.6667\\\\CD=8[/tex]

CD = 8cm

B)

Doing the same thing as above, now find the length of AC:

[tex]\frac{AC}{AB} =\frac{AD}{AE} \\\\\frac{AC}{4.5} =\frac{10}{6}\\\\\frac{AC}{4.5} =1.6667\\\\AC=7.5[/tex]

Now, to find BC:

[tex]BC=AC-AB\\BC=7.5-4.5\\BC=3[/tex]

Finally, add up the sides to find the perimeter of EBCD:

[tex]4.8+3+8+4\\19.8[/tex]

Perimeter of EBCD is 19.8 centimeters

Answer:

Step-by-step explanation:

If two triangles are congruent, then the corresponding sides and angles are congruent with each other.

Given:

The following are congruent parts:

Note Pay attention to order of vertices when comparing the congruent parts

[tex]\\ \sf\longmapsto <E\cong <U[/tex]

[tex]\\ \sf\longmapsto \overline{RE}=\overline{SU}[/tex]

[tex]\\ \sf\longmapsto ∆DRE=∆SUN[/tex]

[tex]\\ \sf\longmapsto <R\cong <S[/tex]

Hope it helps

Answer:

3x = 15

x = 15/3

x  =5

Answer:

−2.

Step-by-step explanation:

y = 4 − 2x? b is the y -intercept. Here, 4 is b and −2 is m. Therefore, the slope is −2.

Answer:

the answer is 2,430

Step-by-step explanation:

5×486=N

=2,430

Answer:

6 apples

Step-by-step explanation:

A = 0.25

P = 0.15

----------------

A + P = 10

0.25A+0.15P=2.10

----------------

I did this: 0.25*10 = 2.50

2.50-2.10=.40

0.25-0.15=0.10

0.40/0.10 = 4 so 4 peaches

10 fruits - 4 peaches = 6 apples

Answer:

the answer is d to the problem

Answer:

y-3=5/8(x-9)

Step-by-step explanation:

First, we can find the slope using the slope formula : -7-3/-7-9 = -10/-16 = 5/8

Now we can just plug in a point into point slope form

y-3=5/8(x-9)

Answer:

give me more information on this

Answer:

Quadrant 3

Step-by-step explanation:

3rd quadrant. because both x and y are negative

Answer:

10s-14

Step-by-step explanation:

Perimeter of rectangle = 2s+2(4s-7)

                                      = 2s+8s-14

                                      = 10s-14

= > Perimeter of rectangle = 2(l + b)

= > 2(s + 4s - 7)

= > 2(5s - 7)

= > 10s - 14...ans

Step-by-step explanation:

Step-by-step explanation:

a general line equation is

y = ax + b

the slope of a line is always the factor of x (a).

it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.

so, here it is -5/4.

it says, when x changes by +4, then y changes by -5.

a parallel line must have the same slope. it just crosses the y-axis at a different point. and that is what b specifies in the equation. it tells us the y value when x = 0.

and we get it by using the point coordinates in the equation and then solve for b :

1 = -5/4 × -4 + b = (-5 × -4)/4 + b = 20/4 + b = 5 + b

b = -4

so, the full equation of the parallel line is

y = -5/4x - 4

Answer:

80

Step-by-step explanation:

honestly it depends on the question but if it's addition, this is the answer

Given that f(x) is a function that represents number of hours required to travel, the domain of the function is: distance travelled in miles (x)

Recall:

Thus, given that f(x) is a function that represents number of hours required to travel, therefore:

Learn more about domain of a function on:

https://brainly.com/question/10197594

Answer:

I believe the graphing should look like this.

Step-by-step explanation:

Answer:

60 / 300 simplified 6/30 simplified 1/5 (20%)

Step-by-step explanation:

Maybe asking ratio?

Answer:

2x+10=20 so x=5

Step-by-step explanation:

Answer:

The last one

Step-by-step explanation:

The rule y times x will give the amount of money earned. After washing x cars. You'll end up with equivalent coordinates

Answer:

y=8x

Step-by-step explanation:

y=8(1)=8     (1,8)

y=8(2)=16   (2,16)

y=8(3)=24   (3,24)

y=8(4)=32   (4,32)

y=8(5)=40   (5,40)

y=8(6)=48   (6,48)

y=8(7)=56    (7,56)

Answer:

[tex]m=\frac{2}{3}[/tex]

Step-by-step explanation:

We can see that some of the points that are plotted we can tell what those plots are (-2, 0) (1, 2) (4, 4)

We use the slope formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]  for any of the two plots that are shown on the line

Answer:

2/3

Step-by-step explanation:

Answer:

luna

Step-by-step explanation:

compare the y values when x=0. looking at the table, gracey was 1 lb at week 0, and looking at the graph, Luna was 2 lbs at week 0 (y-intercept) so luna was heavier at birth

Answer:

either A or D

Step-by-step explanation: