Solve the equation k^2-6k=11 by completing the square

[tex] \huge\mathbb\orange{ANSWER} [/tex]

[tex] \mathsf\green{y = 6}[/tex]

[tex] \mathsf \purple{{y}^{2} - 9y + 2}[/tex]

[tex] \mathsf \pink{ {6}^{2} - 9(6) + 2}[/tex]

[tex] \mathsf \purple{36 - 54 + 2}[/tex]

[tex] \mathsf \pink{ - 16}[/tex]

[tex] \mathbb\green{Hope\:It\:Helps} [/tex]

The vertices of the hyperbola are the x-intercepts of the hyperbola

The equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

The equation of a hyperbola is represented as:

[tex]\frac{(y - k)^2}{a^2} -\frac{(x - h)^2}{b^2} = 1[/tex]

The vertices are (20,0) and (-20,0).

So, the center of the hyperbola is:

(h,k) = (0,0).

Also, we have:

a = 20

This gives

[tex]\frac{(y - 0)^2}{a^2} -\frac{(x - 0)^2}{b^2} = 1[/tex]

Evaluate

[tex]\frac{y^2}{a^2} -\frac{x^2}{b^2} = 1[/tex]

Substitute 20 for a

[tex]\frac{y^2}{20^2} -\frac{x^2}{b^2} = 1[/tex]

[tex]\frac{y^2}{400} -\frac{x^2}{b^2} = 1[/tex]

The length of the conjugate axis is:

l = 18 units

So, we have:

[tex]b = \frac{18}2 = 9[/tex]

The equation becomes:

[tex]\frac{y^2}{400} -\frac{x^2}{9^2} = 1[/tex]

[tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

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Answer:

E= -4,5

F=3,-2

Step-by-step explanation:

i think that's correct sorry if not

True:

   Area of trapezoid = [tex]\frac{1}{2}(b1 + b2) * h[/tex]

Hope that helps!

Answer:

Perimeter=25

Step-by-step explanation:

HOPE THIS HELPS YOU

Answer:

2.4 hour is  10%

Step-by-step explanation:

Because 10% is equal to 0.1 24÷ 10% =2.4

Answer:

a. 12 inches for the shorter side

b. 1050 bushels apples

c. 7/8 cups

Step-by-step explanation:

You can solve these all by the butterfly method(aka cross multiplication)

Answer:

Domain: (-∞, -5) ∪ (-1, ∞)

Step-by-step explanation:

Note:

For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.

For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.

We need to find the domain of f(x) for which f(x) < 0

From the graph, we can tell:

f(x) < 0 on (-∞, -5) ∪ (-1, ∞)

Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)

8x^5 y^8 z^9 ur welcome

Answer:

[tex]64x^6y^{12}z^{14}[/tex]

Step-by-step explanation:

[tex]\left(8x^3y^6z^7\right)^2[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]

[tex]\left(8x^3y^6z^7\right)^2=8^2\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=8^2\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]8^2=64[/tex]

[tex]=64\left(x^3\right)^2\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=64x^6\left(y^6\right)^2\left(z^7\right)^2[/tex]

[tex]=64x^6y^{12}\left(z^7\right)^2[/tex]

[tex]=64x^6y^{12}z^{14}[/tex]

~lenvy~

Answer:

choice A is correct

Step-by-step explanation:

the value of x should be 75

Answer:

x = 49º

Step-by-step explanation:

This is  right angle, and right angle's are always a 90º angle. 90º - 41º is 49.

So the basic answer is 49, but it's properly written as "49º".

Hope this helps!!

The value of x: 49 degrees

Note: All the angles in a triangle add up to 180 degrees

What we're given:

41 degrees, A right angle, and x.

A right angle is 90 degrees.

Equation:

41 + 90 + x = 180

131 + x = 180

x = 49 degrees

The the number of feet needed for the fence of the rectangular garden = its perimeter = 252 ft.

Perimeter = 2(length + width).

The number of feet needed for the fence around the rectangular garden = perimeter of teh rectangular garden.

Given the following:

Plug the values into Perimeter = 2(length + width):

Perimeter of the rectangular garden = 2(42 + 84)

Perimeter of the rectangular garden = 252 ft

Therefore, the the number of feet needed for the fence of the rectangular garden = its perimeter = 252 ft.

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Answer:

[tex]\displaystyle 600\frac{1}{2}\%[/tex]

Explanation:

Just move the decimal mark twise to the right and you will arrive at your result.

I am joyous to assist you at any time.

The domain of the function C(m) = 0.05m + 20 is (0, ∞) and the range of the function C(m) = 0.05m + 20 is (20, ∞).

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. The total cost of Haley’s monthly cell phone bill can be expressed by the function

[tex]\rm C(m) = 0.05\ m + 20[/tex]

The domain of the function is from zero to infinity because time can never be negative.

Then the range of the function will be

At m = 0, the value of C(m) will be

C(m) = 0.05(0) + 20

C(m) = 20

At m = ∞, the value of C(m) will be

C(m) = 0.05(∞) + 20

C(m) = ∞

Thus, the domain of the function is (0, ∞) and the range of the function is (20, ∞).

More about the linear system link is given below.

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Answer:

The length of river D is 2550

length of river C is 2550+500=3050

Step-by-step explanation:

Let the river D be 'x'

and the river C is (x+500)

x + x + 500 = 5600

2x + 500 = 5600

2x = 5600 - 500

2x = 5100

x = 5100/2

x = 2550

The length of river D is 2550

length of river C is 2550+500=3050

-6

Step-by-step explanation:

First we see 3 is greater than the subject so 3<x 3-9 = -6

Applying the expression for the circumference of circle, we found the diameter as 16.86 yards

Given Data

Let us apply the expression for the circumference of a circle

Circumference = 2πr----------1

But r = d/2

hence put r = d/2 in the expression above

Circumference = 2πd/2----------2

Circumference = πd

Substitute our given data

53 = 3.142*d

Make d the subject of formula we have

d = 53/3.142

d = 16.86 yards

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This equation is False.

5/6-(2/3-4/9) = 11/18

(5/6-2/3)-4 = -23/6

Showing two different answers, so no they are not equal.

Answer: 75 Degrees

Step-by-step explanation: 1. Due to the law of opposite adjacent angles, we can determine angle 1 is congruent to angle 4 and therefore is 15 degrees 2. Angle 3 is shown to be a right angle (90 degrees) 3. Since angles 1,2, and 3 are on a flat line, the sum of all 3 is 180 4. 15+90 is 105 5. 180-105 is 75 which is the measure of angle 2

Answer:

I believe it would be 73.8 or if they are rounding up 74.

Step-by-step explanation:

15% of 60 is *9* and 8% of 60 is *4.8*

9+4.8=13.8

13.8+60=73.8.

Answer:

5.025m

Step-by-step explanation:

The clothesline also creates an upside-down triangle with two sides being 5m, 0.5m, and the hypotenuse being the clothesline.

We can use the pythagorean theorem to find the length of the clothesline.

5 squared +.5 squared= the length of the clothesline squared

25+.25= the square root of 25.25

= 5.025

Answer:

Your answer would be:
5.025m

Step-by-step explanation:

5 sq + 0.5sq = the length of the clothesline sq

25 + 0.25= the square root of 25.25

= 5.025m



Have a great rest of your day
#TheWizzer

Answer:

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The given expression can be solved as shown below.

(2,3) - 3(1,1)

Multiply 3 in the second vector,

= (2,3) - (3,3)

Subtracting vectors

= (2-3, 3-3)

= (-1, 0)

Hence, the value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).

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Answer:

period = 2π

Step-by-step explanation:

the period is the distance from one point on the waveform to the corresponding point on the next wave.

there is a maximum at 2π and a corresponding maximum at 4π

period = 4π - 2π = 2π

[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}[/tex]

c=9 makes the given expression a perfect square trinomial.

The given expression is:

[tex]x^{2} +6x+c[/tex]

We can rewrite it as:

[tex]x^{2} +2*x*3 + c[/tex].....(1)

The expansion of [tex](a+b)^2[/tex] is [tex]a^{2} +2ab+b^{2}[/tex]

Comparing (1) with [tex]a^{2} +2ab+b^{2}[/tex]

We get

a=x

b=3

c=b²

So, c=3² =9.

So, c=9 makes the given expression a perfect square trinomial.

Hence,  c=9 makes the given expression a perfect square trinomial.

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Answer:

Step-by-step explanation:

Standard form: Ax + By = C

State whether each equation is in standard form.

A.) 3x + y = 8 (in standard form)

B.) x - y = 15z (not in standard form, because it has a variable(15z))

C.) x^2 + y = 11 (not in standard form, this is not a linear equation)

D.) 3xy + y^2 = 4 (not in standard form, this is not a linear equation)

E.) x + 4y = 12 (in standard form)

F.) 5x + 24y = 544 (in standard form)

Hope this helps!

The year in which the NFL voted to create a $430 million fund to help the bottom 15 clubs was 2007.

The NFL voted by a margin of 30-2 in 2007 to create a pool of funds over 3 years that would amount to $430 million.

This money would then be used to help the bottom 15 clubs who might be struggling financially. The hope was that this would make things more competitive in the NFL.

Find out more on the NFL at https://brainly.com/question/7579515.