Don't answer this.
A, B, and C are equal in length; each one is 4.47 units long. ABC is an isosceles triangle since two of its sides are congruent.

The factoring the equation (a + 1)² - 4b² we get (a+1+2b)(a+1-2b).

Given:  (a + 1)² - 4b²

Apply Perfect Square Formula, and we get

(a + b)² = a² + 2 a b + b²

(a + 1)² = a² + 2a1+1²

= a² + 2a1 + 1² - 4 b²

simplifying the equation, we get

a² + 2a1 + 1² = a² + 2a + 1

= a² + 2a + 1 - 4b²

Factor, a² + 2a + 1 = (a + 1)²

= (a + 1)² - 4 b²

Simplify 4 b² = (2 b)²

= (a + 1)² - (2b)²

Apply the Difference of Two Squares Formula, and we get

x² - y² = (x + y)(x - y)

(a + 1)² - (2b)² = ((a + 1) + 2b)((a + 1) - 2 b)

simplifying the equation, we get

= ((a + 1) + 2b)(a + 1) - 2 b)

= (a + 1 + 2b)(a + 1 - 2b)

Therefore, the correct answer is (a+1+2b)(a+1-2b).

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The critical values of the function are x = 0 and x = 64

The critical values of a function f(x) are the values of x for which f'(x) = 0.

Given,

f(x) = [tex]\frac{x^{4} }{5(x-8)^{2} }[/tex]

The derivative is found as follows, applying the quotient rule:

f'(x) = [tex]\frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2} }[/tex]

     = [tex]\frac{2x^{3}(x-64) }{5(x-8)^{3} }[/tex]

The zeros of the function are the zeros of the numerator, thus:

[tex]2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\[/tex]

x - 64 = 0------------->x = 64

The critical values are x = 0 and x = 64

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By using what we know about right triangles, we conclude that the height is 11ft.

We can think of this as a right triangle.

Where the length of the escalator is the hypotenuse

We know that the angle of depression is 42.51°, then the top angle of our right triangle is:

90° - 42.51° = 47.49°

Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Replacing what we know:

cos(47.49°)  = height/16ft

cos(47.49°) *16ft = height = 10.8ft

Rounding to the nearest foot, we get:

height = 11ft

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Answer:

area = 10

Step-by-step explanation:

Triangle BOC is a right triangle. You can see this because the slope of BO and OC are negative reciprocals (opposite sign and flipped over) You can calculate the slope, m.

m = (y-Y)/(x-X)

Slope of BO is 4/2,

slope of OC is -2/4.

see image.

So then you can use BO and OC as the base and height in an area calculation.

But first you have to calculate the length of each. Luckily they are the same length. You can use distance formula, but when you have a picture, you can just see to use Pythagorean theorem (distance formula comes from PythagThm anyway)

Both BO and OC have legs length 2 and 4. See image. They are both length sqrt20.

Use Area= 1/2bh to find the area. See image.

Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  [tex]\frac{1}{3}[/tex].

A linear equation o line can be expressed in the form y = mx + b.

where

Perpendicular lines are lines that intersect at right angles or 90° angles.

Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -3. So:

(-3)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-3)

slope perpendicular line=  [tex]\frac{1}{3}[/tex]

Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  [tex]\frac{1}{3}[/tex].

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the interval in which g(x) is positive is [3, ∞].

Here we have the function:

g(x) = ∛(x - 3)

The interval in which the function is positive is defined by:

g(x) > 0.

Then we have:

∛(x - 3) > 0.

We need to solve that inequality for x.

∛(x - 3) > 0

The cube root respects the sign of the argument, then:

x - 3 > 0

x > 3

Then the interval in which g(x) is positive is [3, ∞].

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Answer:

30°

Step-by-step explanation:

To make sure it's complete

The height is changing by 0.5 units per minute as evident in the given table.

It follows from the task content that the table given indicates that at, 0min, the height was 150.

While at 1 min, the height is 150.5. On this note, it follows that the height increases by 0.5 units for after every minute.

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Answer:

B

Step-by-step explanation:

if an angle is congruent, it is the same measurement

The pair of the line together that could be perpendicular to RS and should be considered will be EA and FG.

It should be noted that in terms of elementary geometry, two geometric objects should be considered as perpendicular when they intersect at a right angle.

In such a case, a line is treated to be perpendicular to another line in the case when the two lines intersect at a right angle.

Therefore, based on the information, the pair of the line together that could be perpendicular to RS and should be EA and FG.

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Answer:

1053

Step-by-step explanation:

To fill in the values we have the following

a. log6⁰, log 2 . 1, log 8/3

b. log 1 .4 , 1 , log 4. 6

c. log 9/2, log 3. 5 , log 5⁷

To do this, you have to decide on that particular number that you want to find the logarithm on. Next you have to find the base of that number.

The logarithm of the number is the power that it would have to be raised for us to obtain a different number. You have to note that the logarithm of the number is the exponent that a base would have to be raised up to in order to get a particular number.

Log6⁰ for instance would give us the solution of 1 as the answer. While telling us that we have that the exponent is 0 while the base is 6.

One good property of logarithm is that log m/n = log m - log n also when we have log mn, it is the same as log m * log n

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Answer:

Step-by-step explanation:

1. yes

2. 0.048955

3. equal, not equal, less than and equal to, less than, greater than and equal to, greater than

4. 9 51/250

5. 387.5%

Answer:

To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction.

Answer:

84m

Step-by-step explanation:

The perimeter of a triangle is the sum of the length of the external sides.

Therefore, the perimeter of the triangle = 21m + 28m + 35m = 84m.

Hey there!

What is the formula for finding the perimeter of a triangle?
a + b + c = perimeter

What does the labels mean?
a = side 1

b = base

c = side 2

What should the equation look like?
21m + 28m + 35m = perimeter

How do should it be solve?
21m + 28m + 35m = perimeter

49m + 35m = perimeter

84m = perimeter

What is the answer to the question?

84m

Good luck on your assignment and enjoy your day!

~Amphitrite1040

Using a quadratic regression equation, it is found that the prediction of the number of songs that Kimberly will download on Month 9 is of:

c. 16.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially decreases, then it increases , which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(1,8), (2,6), (4,5), (6,7), (7,9)

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = 0.391x² - 2.937x + 10.455

Hence, when x = 9, the prediction is:

y = 0.391 x 9² - 2.937 x 9 + 10.455

y = 15.69

Rounded to 16, hence option c is correct.

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Answer: [tex]\Large\boxed{z=57}[/tex]

Concept:

Here, we need to know how to expand expressions like (a - b)(a + b).

For expressions like (a - b)(a + b), the expanded form must be:

                                                  a² - b²

For checking whether it is true:

 (a - b)(a + b)

= a² - ab + ba - b²

= a² - b²

Solve:

Given equation

[tex](\sqrt{z}+\sqrt{22})(\sqrt{z}-\sqrt22)}=35[/tex]

Expand the parenthesis by the concept

[tex](\sqrt{z})^2-\sqrt{22}^2=35[/tex]

Simplify the exponents

[tex]z-22=35[/tex]

Add 22 on both sides

[tex]z-22+22=35+22[/tex]

[tex]\Large\boxed{z=57}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

1413.86 ft^2.

Step-by-step explanation:

The diameter of the circle = 50 - 2(18)

= 50-36

=  14 ft.

So its radius is 7 ft.

The total area of the blue shape

= 2(35 * 18) + 3.14*7^2

= 1413.86 ft^2.

Answer:

11.25

77.85

Step-by-step explanation:

1.6x + 3 = 21

use inverse operation (+ = -, x = ÷) by taking 3 to the opposite side and changing it's integer to negative

1.6x = 21 - 3

divide 2 sides by 1.6

1.6x = 18

1.6x/1.6 = 18/1.6

x = 11.25//

2.15(x-5)=75

inverse operation

x= 75 - 2.15 + 5

x= 77.85//

Answer:

b

Step-by-step explanation:

Answer:

B. Monday

Step-by-step explanation:

Monday, Tuesday, Wednesday, Monday, Tuesday, Wednesday, Monday

hope it helps

Answer:

g(1) = 1

Step-by-step explanation:

Since 1 ≠ -2  and  1 ≠ -1

Then we must use the expression:

g(x) = x³ - x² + 1  ,to calculate g(1).

Therefore

g(1) = (1)³ - (1)² + 1

     = 1 - 1 + 1

     = 0 + 1

     = 1

Answer: 120

Step-by-step explanation:

Answer:

B. 60°

Step-by-step explanation:

Angle 4 and angle 8 are equal. Find the measure of angle 4 to know the measure of angle 8.

∠4=∠8

180-120=60

∠4=60°

Since angle 4 equals 60 degrees, angle 8 also equals 60 degrees.

Hope this helps!

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

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Answer:

17

Step-by-step explanation:

the pattern

x is the blank

1+5 = 6

5+6 = 11

6+11 = x

11 + x = 28

so x = 17

Answer: 1547.10

Step-by-step explanation: Since you are not in a physics class, in which case requires the usage of the radioactive decay formula, definite integrals, and natural logarithms) but an Algebra class which deploys the usage of percentages, this should be rather simple.

I believe they want you to find 27% of the half life of Carbon-14 since it is below 50%. To find the percent of a number (in this case 27%), you multiply the number by 0.27.

5730 * 0.27 = 1547.10

Hope this helped! And if I'm wrong, please don't hesitate to correct me.

Answer:

  (a)  (f +g)(x) = √(x-2) +√(x)

Step-by-step explanation:

The sum of two functions is the sum of their definitions.

  (f +g)(x) = f(x) +g(x)

  (f +g)(x) = √(x -2) +√(x)

Note: the radicals can only be combined if they can be reduced to a form that has the same expression under the radical. Here, that is not the case, so there is no way to simplify the sum.

The solution to the equation is x = 1.62

The equation is given as:

[tex]x =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we split the equations as follows:

y = x

[tex]y =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we graph the equations (see attachment)

From the attached graph, the equations intersect at

(x, y)= (1.62, 1.62)

Remove the y value

x = 1.62

Hence, the solution to the equation is x = 1.62

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Rationalize the right side first. Expand and simplify.

[tex]x = \sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}\right) \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x}\right)^2 - \left(\sqrt{1 - \dfrac1x}\right)^2[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(x - \dfrac1x\right) - \left(1 - \dfrac1x\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = x - 1[/tex]

Rearrange terms as

[tex]\dfrac{x - 1}x = \sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}[/tex]

[tex]\dfrac{x - 1}x + \sqrt{\dfrac{x - 1}x} = \sqrt{x - \dfrac1x}[/tex]

Substitute

[tex]y = \sqrt{\dfrac{x-1}x} = \sqrt{1 - \dfrac1x} \\\\ \implies y^2 = 1 - \dfrac1x \implies x = \dfrac1{1-y^2}[/tex]

(noting that [tex]y>0[/tex]) so that

[tex]x - \dfrac1x = \dfrac1{1-y^2} - (1-y^2) = \dfrac{2y^2 - y^4}{1-y^2}[/tex]

and the equation transforms to

[tex]y^2 + y = \sqrt{\dfrac{2y^2 - y^4}{1-y^2}}[/tex]

[tex]y + 1 = \sqrt{\dfrac{2 - y^2}{1-y^2}}[/tex]

Solve for [tex]y[/tex].

[tex](y+1)^2 = \left(\sqrt{\dfrac{2-y^2}{1-y^2}}\right)^2[/tex]

[tex]y^2 + 2y + 1 = \dfrac{2 - y^2}{1 - y^2}[/tex]

[tex]-y^4 - 2y^3 + 2y + 1 = 2 - y^2[/tex]

[tex]y^4 + 2y^3 - y^2 - 2y + 1 = 0[/tex]

[tex]\left(y^4 + 2y^3 + y^2\right) - 2y^2 - 2y + 1 = 0[/tex]

[tex](y^2 + y)^2 - 2(y^2 + y) + 1 = 0[/tex]

[tex]\left(y^2 + y - 1\right)^2 = 0[/tex]

[tex]y^2 + y - 1 = 0[/tex]

[tex]y = \dfrac{-1 \pm \sqrt5}2[/tex]

Since [tex]y>0[/tex], we take the positive root. Then

[tex]y = \sqrt{\dfrac{x-1}x} = \dfrac{-1 + \sqrt5}2[/tex]

Solve for [tex]x[/tex].

[tex]\left(\sqrt{\dfrac{x-1}x}\right)^2 = \left(\dfrac{-1 + \sqrt5}2\right)^2[/tex]

[tex]\dfrac{x-1}x = \dfrac{6 - 2\sqrt5}4 = \dfrac{3 - \sqrt5}2[/tex]

[tex]x - 1 = \dfrac{3-\sqrt5}2x[/tex]

[tex]\dfrac{-1+\sqrt5}2 x = 1[/tex]

[tex]x = \dfrac2{-1+\sqrt5}[/tex]

Rationalize to clean up the answer.

[tex]x = \dfrac2{-1+\sqrt5}\cdot\dfrac{-1-\sqrt5}{-1-\sqrt5} = \boxed{\dfrac{1+\sqrt5}2} \approx 1.6108[/tex]

i.e. the golden ratio constant.