Find all complex solutions of x^2+5x+13=0

The length of the hypotenuse of a [tex]45^{\circ}-45^{\circ}-90^{\circ}[/tex] triangle with a leg length of 50 centimeters is [tex]50\sqrt{2}[/tex].

The formula to calculate the hypotenuse of [tex]45^{\circ}-45^{\circ}-90^{\circ}[/tex]  traingle is to multiply the length of the leg by [tex]\sqrt{2}[/tex].

The length of the two legs of [tex]45^{\circ}-45^{\circ}-90^{\circ}[/tex] triangle is equal.

Then the length of its hypotenuse will be calculated by multipling the length of the leg and [tex]\sqrt{2}[/tex].

Since the length of the leg is 50 centimeters,

Then its hypotenuse will be

[tex]h=50\times\sqrt{2}\\h=50\sqrt{2}[/tex]

So, the length of the hypotenuse will be [tex]50\sqrt{2}[/tex].

Learn more about hypotenuse here-https://brainly.com/question/12206865

#SPJ2

Answer:

y = 2x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

6x - 3y = 15 ( subtract 6x from both sides )

- 3y = - 6x + 15 ( divide all terms by - 3 )

y = 2x - 5 ← in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To find c substitute (- 2, 4) into the partial equation

4 = - 4 + c ⇒ c = 4 + 4 = 8

y = 2x + 8 ← equation of parallel line

The required equation of the parallel line is,

[tex]6x-3y+24=0[/tex]

Equation of parallel lines:

Parallel lines are lines that never intersect. Because of this, a pair of parallel lines have to have the same slope, but different intercepts (if they had the same intercepts, they would be identical lines).

Given, the equation of the line is [tex]6x-3y=15[/tex]

Let the equation of the parallel line be,

[tex]6x+3y+k=0[/tex]...(1)

Since, the equation (1) passes through the point (-2,4) then,

[tex]6(-2)-3(4)+k=0\\-12-12+k=0\\k=24[/tex]

Now, substituting [tex]k=24[/tex]  in equation (1) we get,

[tex]6x-3y+24=0[/tex]

Learn More information about the topic equation of the  parallel lines:

https://brainly.com/question/13517044

Answer:

Length of rectangle = 10in.

Breadth " " =x

Perimeter= 2( l+b)=30in.

Perimeter=2(10+b)=30in.

=(10+b)=30/2=15

=b=15-10

Breadth=5in.

Answer: 50 in²

Explanation: Remember that the formula for the area of a rectangle is length · width so we need to find the width of the rectangle.

To find the width of the rectangle, let's use our formula

for the perimeter of a rectangle which is 2l + 2w.

Since we know that the perimeter of the rectangle is 30 inches and the length of the rectangle is 10 inches, we have 30 = 2(10) + 2w.

Simplifying on the right side gives us 30 = 20 + 2w.

Now subtract 20 from both sides to get 10 = 2w.

Finally, dividing both sides by 2, we find that 5 = w.

So the width of the rectangle is 5 inches and remember

that the length of the rectangle is 10 inches.

So the area of the rectangle, l · w, is 10 · 5 or 50 in².

Answer:

Go to the store or get some from friends?

Step-by-step explanation:

I honestly don't know what kind of question this is but maybe it helps?

Answer:

1

Step-by-step explanation:

[tex]\frac{2^3}{2^3}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\=2^{3-3}\\2^{3-3}=1\\2^{3-3}\\\mathrm{Subtract\:the\:numbers:}\:3-3=0\\=2^0\\\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0\\=1[/tex]

Answer:

do u still need this

Step-by-step explanation:

Answer:

1) Option D is correct.

The choice that represents the number of balloons in their bags is x² - 40x + 300 ≥ 0

2) Option A is correct

If Rob had more balloons than Loretta, the least number of balloons that Rob van have before using any = 30.

Step-by-step explanation:

Complete Question

To decorate for a party, Rob and Loretta were each given a bag of balloons. There were 40 balloons between both bags. Rob used 8 balloons from his bag, and Loretta used 8 balloons from hers. The product of the number of balloons left in each bag is no more than 44.

Let x represent the number of balloons that Rob had in his bag before he used any. Which choice represents the number of balloons left in their bags?

A. x² - 40x - 300 = 0

B. x² - 40x - 300 < 0

C. x² - 40x = 300

D. x² - 40x + 300 ≥ 0

If Rob originally had more balloons than Loretta, what is the least number of balloons that Rob could have had before using any?

A.30

B.20

C.10

Solution

If x is the number of balloons that Rob had at the start, the number of balloons that Loretta would have at the start = (40 - x)

Then, they both use 8 balloons each for their designs,

The number of balloons Rob has after the design = (x - 8)

The number of balloons Lorretta has after the design = (40 - x - 8) = (32 - x)

The product of the balloons left isn't more than 44

(x - 8) × (32 - x) ≤ 44

32x - x² - 256 + 8x ≤ 44

44 ≥ -x² + 32x + 8x - 256

44 ≥ -x² + 40x - 256

44 + x² - 40x + 256 ≥ 0

x² - 40x + 300 ≥ 0

To solve the second part of the question, we just solve the expression obtained in the first part.

x² - 40x + 300 ≥ 0

Simplifying the left hand side

(x - 30)(x - 10) ≥ 0

The solutions of the inequality is

x ≤ 10 or x ≥ 30

Hence, if Rob had more balloons than Loretta, the feasible solution for x would be x ≥ 30 and the least number of balloons that Rob van have before using any = 30.

Hope this Helps!!!

Answer:

D & A

Step-by-step explanation:

Answer:

1) Option D is the right answer.

x2 - 40x + 300 0 is the option that reflects the number of balloons in their bags.

2) Option A is the right answer.

If Rob had more balloons than Loretta, the minimum number of balloons Rob could have before using any would be 30.

Step-by-step instructions:

Question in its entirety, Rob and Loretta were each handed a bag of balloons to decorate for a party. Between the two bags, there were 40 balloons. Loretta used 8 balloons from her bag, while Rob used 8 from his.The total number of balloons left in each bag cannot exceed 44. Let x be the number of balloons in Rob's bag before he utilized any of them. Which option best depicts how many balloons they still have in their bags? x2 - 40x - 300 = 0 A. x2 - 40x - 300 0 x2 - 40x - 300 0 x2 - 40x - 300 0 x2 C. 40x - x2 = 300 x2 - 40x + 300 0 x2 - 40x + 300 0 x2 - 40x + 300 0 x2 What is the smallest number of balloons that Rob has if he started with more than Loretta? What is the smallest number of balloons Rob could have had before using any if he had more than Loretta at the start? Solution A.30 B.20 C.10 If x is the number of balloons Rob had at the start, Loretta's number of balloons at the start would be = (40 - x) Then they each use eight balloons to create their creations. After the design, the number of balloons Rob possesses Equals (x - 8) Then there was (40 - x - 8) = the amount of balloons Lorretta possesses after the design (32 - x) The product of the remaining balloons is just 44. (x - 8) (32 - x) 44 x x x x x x x x x x x 32x - x2 - 256 + 8x 44 44 -x2 + 32x + 8x - 256 44 -x2 + 32x + 8x - 256 44 -x2 + 40x - 256 x2 - 40x + 256 0 x2 - 40x + 300 0 44 + x2 - 40x + 256 0 We just solve the equation acquired in the first half of the question to solve the second portion of the question. x2 - 40x + 300 ======================== Simplifying...

(x - 30)(x - 10) 0 (x - 30)(x - 10) 0 (x - 30)(x - 10) 0 (x - 30)(x - The inequality's solutions are x 10 or x 30. As a result, if Rob has more balloons than Loretta, the viable solution for x is x 30, and the smallest number of balloons Rob may have before using any is 30. I hope this information is useful!!! ⭐️

Answer:

Step-by-step explanation:

Ur not dumb I’m the dumb one XD

Answer:

2*sqrt2

Step-by-step explanation:

In right isosceles triangles, the ratios of the sides are:

1:1:sqrt(2)

1=the legs, and sqrt2 being the hypotenuse.

So, in this problem, we can simply divide the hypotenuse by sqrt2 to find the legs.

2*sqrt6/sqrt2=2*sqrt3

Therefore, the lengths of the legs are 2*sqrt2

Answer:

The answer is C

Step-by-step explanation:

Mean is more affected by the highest salary because 890 is an outlier and using mean makes middle salary inaccurate. Outliers do not affect the median because you are just counting. 

Answer:

Its the first one

Step-by-step explanation:

Answer:

The first choice (1.)

I hope I helped you! If I am correct, may I please get marked as brainiest? Thanks!

Answer:

minimum

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

The reference angle of 240° is 60°

Answer:

254

Step-by-step explanation:

I did the test on edenuity and got it right

The surface area of a rectangular prism with length = 7 inches, width = 9 inches and height = 4 inches is 254 inches square.

Surface area of a rectangular prism = 2(lw + lh + wh)

where

Therefore,

length = 7 inches

width = 9 inches

height = 4 inches

Therefore,

surface area  = 2(63 + 28 + 36)

surface area  = 2(127)

surface area  = 254 inches²

learn more on rectangular prism here: https://brainly.com/question/14987814

#SPJ2

Answer:

Okay.

Step-by-step explanation:

By the wording on this problem is can assume that is the correct answer.

Step-by-step explanation:

Please explain more easier

Answer:

[tex] \boxed{Dimensions\: of \: the \: rectangle \: are \: 15 \: and \: 10 units} [/tex]

Step-by-step explanation:

Let the length of rectangle be 'x' units

So, width of rectangle will be = x - 5 units

Area of rectangle = 150 square units

[tex]=> Area \: of \: rectangle = length × breadth \\ \\ = > 150 = x \times (x - 5) \\ \\ = > 150 =( x \times x )- (x \times 5) \\ \\ = > 150 = {x}^{2} - 5x \\ \\ = > 0 = {x}^{2} - 5x - 150 \\ \\ = > {x}^{2} - 5x - 150 = 0 \\ \\ = > {x}^{2} - (15 - 10)x - 150 = 0 \\ \\ = > {x}^{2} - 15x + 10x - 150 = 0 \\ \\ = > x(x - 15) + 10(x - 15) = 0 \\ \\ = > (x - 15)(x + 10) = 0 \\ \\ = > x - 15 = 0 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: x + 10 = 0 \\ \\ = > x = 15 \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: x = - 10[/tex]

Dimension cannot be negative so the value of x is 15

Therefore,

Length of rectangle = 15 units

Width of rectangle = 15 - 5 = 10 units

Answer: B

Step-by-step explanation:

The answer is B, because if he practices 49 times out of 100, then you know that it is a fraction of 49/100.

49/100 can also be changed into a decimal, making it 0.49.

Answer:

A: 61/100 or 0.61%

Step-by-step explanation:

He practices 49/100 days, but the question is asking us what percentage of days, he does not practice. He practices 49% of the days, but does not practice 100-49/100 days=61/100 days.

Answer:

[tex](-3)^{-2} = \frac{1}{(-3)^{2} } = \frac{1}{9} (ANS)[/tex]

Step-by-step explanation:

Answer:

The price of 1 adult ticket is $ 11 and price of 1 child ticket is $13

Step-by-step explanation:

Let x be the cost of 1 adult ticket

Let y be the cost of 1 child ticket

Cost of 8 adult tickets = 8x

Cost of 9 child tickets = 9y

We are given that A local kids play sold 8 adult tickets and 9 child tickets for a total of $205

So, 8x+9y=205 ----- 1

Cost of 4 adult tickets = 4x

Cost of 3 child tickets = 3y

We are given that 4 adult tickets and 3 child tickets for a total of $83.

4x+3y=83 ----2

Plot 1 and 2 on graph

8x+9y=205  -- Red line

4x+3y=83  -- Blue line

Intersection point provides the solution

So, Intersection point =(11,13)

So, The price of 1 adult ticket is $ 11 and price of 1 child ticket is $13

Answer:

25%

Step-by-step explanation:

We can rephrase the question like this :

2 is what percentage? of 8

let p be the percentage

then

2 = 8 × p%

  = 8 × (p/100)

then

200 = 8p

then

p = 200/8 = 25

Answer:

0.8 i think

Step-by-step explanation:

Answer: 50 percent i think

Answer:48%

Step-by-step explanation:The reason is because 50% is 25 AND lower, when it said under 25

Answer:

5133 1/3

Step-by-step explanation:

[tex]3.5 \cdot 880 = 0.6x\\3080=0.6x\\x=5133 1/3[/tex]

Hope this helps!

y = mx + b

You need to isolate m.

1. Bring b to the other side by subtracting it from both sides

y - b = mx

2. Divide out x to isolate m on the right

(y - b)/x = m

You answer is B. m = y - b / x

Answer:

Step-by-step explanation:

(-3,6)

Answer:

Step-by-step explanation:

7a - 3 = 3 + 6a

7a = 6 + 6a

a = 6

Answer:

a = 6, Nice work!

Step-by-step explanation:

7a - 3 = 3 + 6a

First step is to subtract 6a from the right, also subtracting it from the left. This will leave you with:

a -3 = 3

Now you need to isolate the variable, so to get rid of -3, you have to add 3 to both sides.

a -3 = 3

 +3   +3

a = 6

Answer:

C

Step-by-step explanation:

Figure C is correctly and exactly divided into two parts so it's a line of symmetry.

Answer:

C is divided correctly and exactly into two seperate parts.

Step-by-step explanation:

Answer:

The slope is 1

Step-by-step explanation:

Pick two points

(-1,0) and (0,1)

The slope is given by

m= (y2-y1)/(x2-x1)

   = (1-0)/( 0 - -1)

   = (1-0)/(0+1)

   = 1/1

   1

Hello there!

Y = mx + b

Looking at the graph we can find our y-intercept, which would be 0,1.

To find the slope, we can use any two coordinates on the line, such as

(-1,0) and (0,1).

Plug it into the slope formula: rise over run.

1 - 0 / 0 - - 1 = 1/1

1/1 = 1

Therefore our slope is 1x.

Lastly, we just plug the values in for our slope intercept form.

y = 1x + 1

Answer:

if the two bottles are 1 liter each then those two bottles would hold more juice because in total they would hold two liters of juice

Step-by-step explanation:

the 12 cans of 150 ml would hold a total of 1.8 liters which is less than 2 liters