Find the distance between 5 + 4i and 9 + 3i.​

Answer:

[tex]a=9[/tex]

Step-by-step explanation:

In this problem, you can use the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) to find what a is. The steps are shown below:

Steps (variables a, b, and c are in italics):

-You can rearrange the formula from the Pythagorean Theorem, which is[tex]a^{2} +b^{2} =c^{2}[/tex] to only get a because we want to know what a is.

Rearranged: [tex]a=\sqrt{c^{2}-b^{2} }[/tex] or [tex]a=-\sqrt{c^{2}-b^{2} }[/tex]  It has to ways/options for a because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.

-Since we know what c and b are, you can plug them into the new formula:

[tex]a=\sqrt{15^{2}-12^{2} }[/tex]

-Simplify it:

[tex]a=\sqrt{225-144}[/tex]

-Subtract inside the radical:

[tex]a=\sqrt{81}[/tex]  Then simplify it to get [tex]a=9[/tex].

You can check your answer by putting a back into the original Pythagorean Theorem formula ([tex]a^{2} +b^{2} =c^{2}[/tex]):

Steps

-Plug a, b, and c into the formula [tex]a^{2} +b^{2} =c^{2}[/tex]:

[tex](9)^{2} +(12)^{2} =(15)^{2}[/tex]

-Simplify to get:

[tex]81+144=225[/tex]

-Add:

[tex]225=225[/tex]  This is very true. So our answer is correct.

ANSWER: [tex]a=9[/tex]

Sorry for the long explanation, but I hope you understand and that this helps with your question! :)

Answer:

Step-by-step explanation:

lets make is short and simple

Pythagorean theorem: a² + b² = c²

a² + 12² = 15²

a² = 15² - 12²

a = √81

a = 9

Answer:

Question 2: v = 25n

Question 3: b (the output is 250 because 10 quarters is 250 cents)

Step-by-step explanation:

Each quarter is worth 25 cents. n represents the number of quarters you have. The number of quarters you have multiplied by 25 with give the value of the quarters in cents.

v = 25n

v = 25(10)

v = 250

(v represents the value in cents)

Answer:

x = 3.464 ft.

Step-by-step explanation:

To find x we use the trigonometric identity Sine.

[tex]sin\ \theta=\frac{perpendicular}{hypotenuse}\\\\sin\ 60=\frac{x}{4} \\\\4*sin60=x\\4*0.866=x\\3.464=x\\x=3.464\ ft[/tex]

Answer:

x = 3.464 ft.

Step-by-step explanation:

Answer:

x=3 C

Step-by-step explanation:

5x-13=-3x+11

8x-13=11

8x=24

x=3

Answer:

the answer is x=3

Step-by-step explanation:

i hope this help you

Answer:

f(2)= -1

Step-by-step explanation:

f(2)=-3(2)+5= -6+5= -1

Answer:

-1

Step-by-step explanation:

f(x)=-3x+5

f(2)= -3(2)+5

=-6+5 = -1

Answer:

According to the calculation, Wayra mage a mistahe in step 2 where she added 13 and 6 together instead of multiplying to get 78.

She also make a mistake in step 2 where he subtracted 5z from 4z to get z instead of -z

Step-by-step explanation:

Given the equation solved by Wayra expressed as;

Step 1: 13(z+6) = 4(z-3)-5z

She is find the value of z from the equation;

Step 2: Open the parenthesis using the distributive property;

13(z+6) = 4(z-3)-5z

13z + 13(6) = 4z - 4(3) - 5z

13z + 78 = 4z - 12 - 5z

Step 3: Simplify

13z + 78 = 4z - 5z - 12

13z + 78 = -z -12

Step 4: Collect the like terms;

13z + z = -12 - 78

Step 5: Simplify the result

14z = -90

Step 6: Divide both sides by 14

14z/14 = -90/14

z = 6.428

According to the calculation, Wayra mage a mistahe in step 2 where she added 13 and 6 together instead of multiplying to get 78.

She also make a mistake in step 2 where he subtracted 5z from 4z to get z instead of -z

Answer:

I believe it is

1) yes

2) no

3) no

4)no

Step-by-step explanation:

It can only be a solution if you put the x in from the table into the x of the equation and the y in from the same ordered pair into the equation for y and if you get 1 for the fist equation it is a solution but you also have to get 7 for the second equation for it to fully be a solution. Also, you can go to desmos and enter the equations and then substitute the x's and y's... you will have to delete the =1 and =7 in order for the website to tell you what it equals.

Answer:

It would be a obtuse triangle instead

Step-by-step explanation:

By using pythagorean and theorem (a^2 + b^2 = c^2)

So it would be 13^2___2^2 + 12^2

When you square them, you get 169___4 + 144

144 + 4 = 148, which is less than 169

SO it would be 169>148

So no, not a right triangle

9514 1404 393

Answer:

  44 inches

Step-by-step explanation:

The sides of a rhombus are all the same length, so we have ...

  AB = BC

  3x -4 = 2x +1

  x = 5 . . . . . . . . . add 4-2x

Then the side lengths are ...

  3x -4 = 3·5 -4 = 11

Four of them total 4·11 = 44 inches.

Answer:

the first one and last one are true

Step-by-step explanation:

Answer:  slope: 1/4

y-intercept: 0,3

Step-by-step explanation:

Answer:

2+10x-x^2, the last answer

Step-by-step explanation:

Answer:4 1/2  Teaspoons  of vanilla will be left in the bottle

Step-by-step explanation:

Step 1

Recipe for 1 cheesecake = 1 1/2 teaspoons of vanilla

Since she s making 5 cheesecakes, she will requite = 5 x 1 1/2 teaspoons

= 5 x 3/2= 15/2 = 7 1/2 teaspoons of vanilla.

Step 2

If a bottle of vanilla contains = 12 teaspoons of vanilla

After baking 5 cheesecakes which consumed = 7 1/2 teaspoons of vanilla

Teaspoons left of vanilla = Total teaspoons of vanilla-teaspoons of vanilla used for 5 cheesecakes= 12 - 7 1/2 =4 1/2

Therefore 4 1/2  Teaspoons  of vanilla will be left in the bottle

Answer:

2.82842712 + 2 i

Step-by-step explanation:

Answer:

[tex]C(w) = 5w + 12[/tex]

[tex]C(w) = 12+5w[/tex]

Step-by-step explanation:

Given information:

- Monthly fee of $12

- $5 fee per workout class

- [tex]w[/tex] represents the workout classes taken for a month

- - - -

With the given information, we can conclude that [tex]C(w)=[/tex] workout fee + monthly fee.

Workout fee = [tex]$5w[/tex]

Monthly fee = [tex]$12[/tex]

∴ [tex]C(w) = 5w + 12[/tex] or [tex]C(w) = 12+5w[/tex] (they are the same)

Hope this helps :)

Answer:

0.3

Step-by-step explanation:

Answer: D.

Step-by-step explanation:

the ratio of 12/4 is the same as 3

Answer:

Step-by-step explanation:

if we have 137 students, and out of this number 7 were in cars

137-7=130 students in buses

there are 5 buses

130/5=26

26 students in each bus

Answer:

c

Step-by-step explanation:

Answer:

points waisted

Step-by-step explanation:

Answer:

Yeah its parallel

Step-by-step explanation:

I would waste your points, but nah. Anyways, its parallel

Answer:

57°

Step-by-step explanation:

LHS angle=RHS angle=57° (vert. opp angles)

Answer:

first year $20 second year $20.80 Third year $21.63

Step-by-step explanation: This is for an extra money per year so after the first year that is how much extra money he gets every year.

Answer/Step-by-step explanation:

WX: 4.47

[tex]4^{2} + 2^{2} = 20\\\sqrt{20} = 4.47[/tex]

XY: 3.61

[tex]3^{2} + 2^{2} = 13\\\sqrt{13} = 3.61[/tex]

YZ: 4.12

[tex]1^{2} + 4^{2} = 17\\\sqrt{17} =4.12[/tex]

WZ: 4.24

[tex]3^{2} + 3^{2} = 18 \\\sqrt{18} = 4.24[/tex]

The slopes of the lines are:

WX = 2

XY = -1.5

YZ = 4

WZ = -1

Given is a polygon on a coordinate plane with vertices =

W = (-5, 1)

X = (-3, 5)

Y = (-1, 2)

Z = (-2, -2)

We need to find the slopes of line =

WX, XY, YZ and WZ

To find the slopes of the lines connecting the vertices of the polygon, we can use the formula for the slope between two points (x₁, y₁) and (x₂, y₂):

slope = (y₂ - y₁) / (x₂ - x₁)

Let's calculate the slopes for each line:

1) Slope of line WX:

W = (-5, 1)

X = (-3, 5)

slope(WX) = (5 - 1) / (-3 - (-5))

= 4 / 2

= 2

So, the slope of line WX is 2.

2) Slope of line XY:

X = (-3, 5)

Y = (-1, 2)

slope(XY) = (2 - 5) / (-1 - (-3))

= -3 / 2

= -1.5

So, the slope of line XY is -1.5.

3) Slope of line YZ:

Y = (-1, 2)

Z = (-2, -2)

slope(YZ) = (-2 - 2) / (-2 - (-1))

= -4 / (-1)

= 4

So, the slope of line YZ is 4.

4) Slope of line WZ:

W = (-5, 1)

Z = (-2, -2)

slope(WZ) = (-2 - 1) / (-2 - (-5))

= -3 / 3

= -1

So, the slope of line WZ is -1.

Therefore, the slopes of the lines are:

WX = 2

XY = -1.5

YZ = 4

WZ = -1

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Answer:

C.) 1 5/b boxes

Number of boxes left over

= 3 - 1/2 - 2/3

Convert each  fraction to one in terms of the LCM:

= 18/6 - 3/6 - 4/6

= 11/6

= 1 5/6 boxes.

The solution is Option B.

The number of boxes of crackers left with Eloise is 1 5/6 boxes of crackers

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of boxes of crackers left with Eloise be = A

Now , the total number of boxes of crackers be = 3 boxes

The number of boxes of crackers ate on Saturday = 1/2

The number of boxes of crackers ate on Sunday = 2/3

So , the equation will be

Number of boxes of crackers left with Eloise A =  total number of boxes of crackers - number of boxes of crackers ate on Saturday - number of boxes of crackers ate on Sunday

Substituting the values in the equation , we get

Number of boxes of crackers left with Eloise A = 3 - 1/2 - 1/3

On simplifying the equation , we get

Number of boxes of crackers left with Eloise A = 5/2 - 2/3

Number of boxes of crackers left with Eloise A = ( 15 - 4 ) / 6

Number of boxes of crackers left with Eloise A = 11/6

Number of boxes of crackers left with Eloise A = 1 5/6 boxes

Therefore , the value of A is 1 5/6 boxes

Hence , the number of boxes left is 1 5/6 boxes of crackers

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Answer:

A. 36.6

B. -94.18

C. -3.25

D. -75.01

E. -54.03

Answer:

a. 36.6

b. - 94.18

c. - 3.25

d. - 75.01

e. -54.03

Step-by-step explanation:

Hope this helps, have a great day

Answer:

17

Step-by-step explanation:

Use the Pythagorean Theorem, [tex]a^{2} +b^{2} =c^{2}[/tex]

In this situation, you would use the equation as [tex]8^{2} +15^{2} =x^{2}[/tex]