simplify [tex]\sqrt{-121}[/tex]

Answer:   [tex]\frac{x^8}{256y^{20}}[/tex]

If the font is too small, it says x^8 all over top 256y^20 as one big fraction.

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Work Shown:

[tex]\left(\frac{5x^3}{20xy^5}\right)^4\\\\\\\left(\frac{x^2}{4y^5}\right)^4\\\\\\\frac{\left(x^2\right)^4}{(4^1)^4\left(y^5\right)^4}\\\\\\\frac{x^{2*4}}{4^{1*4}y^{5*4}}\\\\\\\frac{x^{8}}{4^{4}y^{20}}\\\\\\\frac{x^{8}}{256y^{20}}\\\\\\[/tex]

Answer:

b = 5

Step-by-step explanation:

[tex]4b - 2b = 13 - 3 \\ 2b = 10 \\ b = 5[/tex]

Answer:

[tex]NK \approx 7.001[/tex], [tex]MK = 2[/tex], [tex]MF \approx 7.001[/tex], [tex]A_{AMNFD} = 49.007[/tex]

Step-by-step explanation:

According to the statement, we find the following inputs:

[tex]\angle MDK = \angle DMF = 45^{\circ}[/tex] (Due to the condition of isosceles trapezoid)

[tex]MD = 9[/tex]

[tex]NF = 5[/tex]

Given than longer base and shorter base are parallel to each other, we conclude that:

[tex]\angle KND = 180^{\circ} -\angle NKD - \angle KDN[/tex]

[tex]\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}[/tex]

[tex]\angle KND = 45^{\circ}[/tex]

[tex]\angle FND = 90^{\circ}-\angle KND[/tex]

[tex]\angle FND = 45^{\circ}[/tex] (By definition of complementary angles)

[tex]\angle FND = \angle NFM = 45^{\circ}[/tex] (Due to the condition of isosceles trapezoid)

[tex]\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}[/tex]

[tex]\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}[/tex] (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

[tex]MO = DO = \frac{\sqrt{2}}{2}\cdot MD[/tex] (By theorem for 45-45-90 Right Triangle)

[tex]NO = OF = \frac{\sqrt{2}}{2}\cdot NF[/tex] (By theorem for 45-45-90 Right Triangle)

If we know that [tex]MD = 9[/tex] and [tex]NF = 5[/tex], then we find that:

[tex]DO = MO \approx 6.364[/tex]

[tex]NO = OF \approx 3.536[/tex]

The value of MK is obtained from the following relationship:

[tex]MK = \frac{MD-NF}{2}[/tex]

[tex]MK = \frac{9-5}{2}[/tex]

[tex]MK = 2[/tex]

And the value of KD is calculated from this expression:

[tex]KD = MD-MK[/tex]

[tex]KD = 9-2[/tex]

[tex]KD = 7[/tex]

Now by the Pythagorean Theorem we find that:

[tex]NK = \sqrt{(NO+DO)^{2}-KD^{2}}[/tex]

[tex]NK = \sqrt{9.9^{2}-7^{2}}[/tex]

[tex]NK \approx 7.001[/tex]

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

[tex]MF = NO + DO \approx 7.001[/tex]

Lastly, the area of the isosceles trapezoid is determined by the following formula:

[tex]A_{AMNFD} = NF\cdot NK + MK\cdot NK[/tex]

[tex]A_{AMNFD} = NK\cdot (NF+MK)[/tex]

If we know that [tex]NK \approx 7.001[/tex], [tex]NF = 5[/tex] and [tex]MK = 2[/tex], then the area of the figure is:

[tex]A_{AMNFD} = (7.001)\cdot (5+2)[/tex]

[tex]A_{AMNFD} = 49.007[/tex]

Answer:

It was sold at $32.40.

Step-by-step explanation:

hope this helpss :))

Answer:

Today: Friday, 06 November 2020

Hour: 10.15 WIB (Indonesia)

_______________________________

so,

6c = 6 × 5 = 30

4b = 4 × (-3) = -12

Example:

4b - 6c

= 4(-3) - 6(5)

= -12 - 30

= - 42

4b + 6c

= 4(-3) + 6(5)

= -12 + 30

= 18

Answer:

An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

Usually, output refers to the dependent value of a function rule.

It is also correct that the y coordinate of ordered pairs, graphed points, and in a function table.

Answer:

An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph best disfines an output because an input can have multiple outputs like

x   y

4   5

3   5

6   5

but a function cannot have the same input with different outputs like

this example shows what is not a function

x    y

3    5

3     6

4    79

4    64

 this is not a function

Step-by-step explanation:

Answer:

Yes because they both only have one zero so the discriminant for both is 0

Step-by-step explanation:

explanation above lol

The two functions have the same discriminant b² - 4a = 0.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know, Discriminant in a quadratic equation ax² + bx + c is, b² - 4ac.

Now, From the graph the discriminant and properties here,

D = 0 as the vertex of the parabola intersect only at one point.

b² - 4ac = 0.

The blue graph intersects at (2, 0) and the red graph intersects at (- 2, 0).

So, they have the same discriminant.

learn more about quadratic equations here :

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Answer:

Your answer is:  [tex]2j^{2}(j-4)[/tex]

Factor [tex]2j^{2}[/tex]out of [tex]2j^{3} -8j^{2}[/tex]

Step-by-step explanation:

Hope this helped : )

Answer:

slope m = - 1

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 )

y = - x + 7 ← is in slope- intercept form

with slope m = - 1

Answer:

The angle of CAD is 100°.

Step-by-step explanation:

Given that total angles in a triangle is 180° so you will have to find the angle of CAB :

∠CAB + ∠ACB + ∠ABC = 180°

∠CAB + 80° + 20° = 180°

∠CAB + 100° = 180°

∠CAB = 180° - 100°

∠CAB = 80°

Next, you have to subtract it from 180° because straight line have a degree of 180°

∠CAD = 180° - 80°

∠CAD = 100°

Haha

I appreciate it I guess.

Answer:

10:7

Step-by-step explanation:

Answer:First three terms: 11,20,29 .

Step-by-step explanation:

Write a systems of equations. tn=a+(n−1)d. sn=n2 (2a+(n−1)d). So,. 110=11+(n−1)d 726=n2(22+(n−1)d).

I hope this is right

Answer:

Learn vocabulary, terms, and more with flashcards, games, and other study tools. ... The Fee that a driver pays to have automobile insurance is called a ... She receives 7% on her first $1,000 in sales and 15% on the balance of her sales. ... The Jackson's sublet their summer cottage during the winter and spring months.

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

( 6, -3 )

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

Answer:

-14/15

Step-by-step explanation:

Option c is the correct answer. A gym charges a membership fee of $50, plus a monthly charge of $20 per month.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. That constant is known as the "constant of proportionality".

So a non-proportional relationship is basically a line that does not cross the origin of a graph. So using the linear exhaustion of a line, y=mx+b, a proportional relationship would be something along the lines of y=mx+0 because b, which is the w intercept is 0. I

Having said that, here is the equation for a line:

a) would be y=1.75x (because it is only charging per drink, and nothing else, there is no b value or y-intercept). This means this is a

b) would be y=0.10x (because it is only charging per amount of texts, and nothing else, there is again no b value, so the y-intercept is 0, crossing the origin). (THIS IS ALSO NOT THE ANSWER)

c) y=20x+50 (x is the number of months, which then determine the amount of money you spend at the gym based on how many months you go there. Plus, you have to add in the cost of the gym membership as well, being 50$. So, in this case, because 50 is being added to the 20x, the b value or y-intercept would be 50.

To know more about proportional relationships follow

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Answer:

A

Step-by-step explanation:

4x - 2 and 3x + 6 are alternate angles and congruent, thus

4x - 2 = 3x + 6 ( subtract 3x from both sides )

x - 2 = 6 ( add 2 to both sides )

x = 8

Answer: The scuba diver was 35 meters below the surface of the water at the start of the ascent.

Step-by-step explanation:

Answer:that’s the answer enjoy

Step-by-step explanation:

Answer:

d = 2.8

Step-by-step explanation:

−9.76d − (−12.81d) = 8.54

~Simplify

−9.76d + 12.81d = 8.54

~Combine like terms

3.05d = 8.54

~Divide 3.05 to both sides

d = 2.8

Best of Luck!

Answer:

The temperature, in December is 47 °F

Step-by-step explanation:

The given data for the temperature are;

Month             [tex]{}[/tex]         Temp (°F)

April                   [tex]{}[/tex]          59

May               [tex]{}[/tex]               68

June             [tex]{}[/tex]                71

July                  [tex]{}[/tex]             78

August              [tex]{}[/tex]            74

Let x represent the month, and f(x) = y represent the temperature, we have;

y = a·x² + b·x + c

When x = 1, we have, f(1) = a·1² + b·1 + c = 59

f(1) = a + b + c = 59...(1)

When x = 2, we have, f(2) = a·2² + b·2 + c = 68

f(2) = 4·a + 2·b + c = 68...(2)

When x = 3, we have, f(3) = a·3² + b·3 + c = 71

f(3) = 9·a + 3·b + c = 71...(3)

When x = 4, we have, f(4) = a·4² + b·4 + c = 78

f(3) = 16·a + 4·b + c = 78...(4)

When x = 5, we have, f(5) = a·5² + b·5 + c = 74

f(3) = 25·a + 5·b + c = 74...(5)

Subtracting equation (3) from equation (5), we get;

25·a + 5·b + c - (9·a + 3·b + c) = 74 - 71

16·a + 2·b = 3...(6)

Subtracting equation (1) from equation (2), we get;

4·a + 2·b + c - (a + b + c) = 68 - 59

3·a + b = 9...(7)

Multiply equation (7) by 2 and substract from equation (6) gives;

16·a + 2·b - 2 × (3·a + b) = 3 - 2 × 9

16·a + 2·b - 6·a - 2·b = 3 - 2 × 9

16·a - 6·a + 2·b  - 2·b = 3 - 2 × 9 = -15

10·a = -15

a = -15/10 = -1.5

a = -1.5

From, 3·a + b = 9, we have;

3 × (-1.5) + b = 9

b = 9 + 4.5 =13.5

b = 13.5

From, a + b + c = 59, we have;

-1.5 + 13.5 + c = 59

c = 59 - (-1.5 + 13.5) = 47

c = 47

The quadratic equation becomes, y = a·x² + b·x + c = -1.5·x² + 13.5·x + 47

f(x) = y = -1.5·x² + 13.5·x + 47

For December, we have, x = 9, and f(x) = -1.5×9² + 13.5×9 + 47 = 47

The temperature, in December = 47 °F

Answer:

188.88

Step-by-step explanation:

Answer:

The second vendor because when you purchase 6 liters, it costs less to get it from the second vednor.

Step-by-step explanation:

Compare the price at 6 liters.

3.80(3)= $11.40

$2.70(4)= $10.80

Answer:

A.

Step-by-step explanation:

A slope is 2

B slope is -1/2

hope this helps :3

if it did pls mark brainliest

Answer:

√13

Step-by-step explanation:

length √(2^2+3^2)=√13.