Solve tTwo researchers are studying the decline of orangutan populations. In one study, a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year. In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year. After how many years will the two populations be the same?

he linear equation 2.25 – 11j – 7.75 + 1.5j = 0.5j – 1.

The graph has no vertical asymptote

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Explanation:

Let's simplify the function by factoring each piece.

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

In the 2nd step, I used the difference of squares rule to factor the numerator. In the 4th step, the (x-8) terms cancel.

The simplified version doesn't have any variables in the denominator. This indicates the denominator is always 8, and never 0. So it's impossible to divide by zero in this simplified form. Consequently it means this graph has no vertical asymptotes.

However, there is a hole at x = 8 because this input causes a division by zero error in the original non-simplified function. Why? Because the calculator will use PEMDAS to evaluate the expression after replacing every copy of x with 8. It likely won't attempt to simplify like shown in the steps above. This is what causes the hole at x = 8.

The value x = -8 is perfectly fine in either the original function or the simplified one. It doesn't cause the denominator to be zero.

#a

V={Vowels of English alphabets}

#b

C={cube numbers between 0 to 50}

#c

M={y:y is a multiple of 3 less than 20}

In this situation, attendee number thirty will be the first one o receive both the bobblehead and the ticket.

Bobblehead:

Ticket:

It can be concluded the attendee number 30 will be the first one to receive both the ticket and the bobblehead.

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Answer:

D.

Step-by-step explanation:

If you look at the pattern, the first shape (square) has four sides. Then, you have 5 sides, and finally, 6 sides.

Thus, a pattern of 4, 5, 6. So, the next shape must have 7 sides, leaving the only possible answer as D.

The limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1

The limit of the function given in question can also be written as:

[tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex]

To determine the required limit, we will simply substitute the value of x into the function as shown:

[tex]\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{ (-3)^2-8}\\\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{9-8}=1\\[/tex]

Hence the limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1

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Answer: the answer is b. 1

Step-by-step explanation: just got it right on edge

Answer:

A. 12 + (negative 9)

Step-by-step explanation:

8 + 4 - 9 = 3

12 - 9 = 3

-12 + 9 = -3

-4 - 9 = -13

4 - 9 = -5

this means that 8 + 4 - 9 = 12 - 9

making A the right expression

B postulates and C axioms are accepted without proof in a logical system.

A theorem is a statement that can be proven true using standard mathematical operations and reasoning. A theorem, in general, is an embodiment of a general principle that is part of a larger theory. A proof is the process of demonstrating that a theorem is correct.

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Work Shown:

yz = y(x^2+2x-5)

yz = y(x^2) + y(2x) + y(-5)

yz = x^2( y ) + 2x( y ) - 5( y )

yz = x^2( 3x+5 ) + 2x( 3x+5 ) - 5( 3x+5 )

yz = x^2*3x + x^2*5 + 2x*3x + 2x*5 - 5*3x - 5*5

yz = 3x^3 + 5x^2 + 6x^2 + 10x - 15x - 25

yz = 3x^3 + 11x^2 - 5x - 25

Answer:

22045278

Step-by-step explanation:

               5  8  2  9

                3  7  8  2

               11  6  5  8

        4  6  6  3  2  0

    4  0  8  0  3  0  0

 1  7  4  8  7  0  0  0        

2  2  0  4  5  2  7  8

Answer:

22045278

Step-by-step explanation:

It seems tricky, but if you break it down step by step it will make it a lot easier.

Hope it helped and you can do it!!

The balloon’s vertical distance above the ground is 721.7 f

In order to determine the balloon's vertical distance, we will use the SOH CAH TOA identity

Given the following parameters

Angle of depression = 30 degrees

Horizontal distance =1250 feet

Required

vertical distance H

Using the SOH CAH TOA identity

tan 30 = H/1250

H = 1250tan30
H = 721.7 feet

Hence the balloon’s vertical distance above the ground is 721.7 feet

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Answer:

721.7                                          

Step-by-step explanation:

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Answer:

432

Step-by-step explanation:

To find the volume of a rectangular prism  you multiply, L × W × H

    L = 6     W = 8    H =9  you plug that in  6 × 8 × 9= 432

     so the volume is 432in²

Answer:

You would put 11y-22+7y-6+3x+12+5x and that will give you the answer. Hope this helps!

In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."

According to the question,

Given

Length of AE=5.2

Length of  AC=11.7

Length of  CD=10.5

As shown in figure

In trapezoid ABCD,

AB is parallel to CD, AC is the transversal.

AC and BD intersect at point E.

In ΔABE and ΔCDE,

∠BAE ≅∠ECD

∠ABE ≅∠EDC

By AA theorem,

ΔABE ~ ΔCDE

Therefore,

[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]

  AE + EC = AC

⇒ 5.2 + EC = 11.7

⇒ EC = 11.7 - 5.2

⇒ EC = 6.5units

Substitute the value in the given proportion we get,

   [tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]

⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]

⇒[tex]AB = 8.4[/tex] units

Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

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Answer:

My sister is doing this, I if remember correctly graph B?

Let S be the given sum, so

[tex]S = 8 + 8 \left(\dfrac14\right) + 8 \left(\dfrac14\right)^2 + \cdots + 8 \left(\dfrac14\right)^9[/tex]

[tex]\displaystyle S = 8 \left(1 + \dfrac14 + \frac1{4^2} + \cdots + \frac1{4^9}\right)[/tex]

Multiply both sides by 1/4.

[tex]\displaystyle \frac S4 = 8 \left(\frac14 + \frac1{4^2} + \frac1{4^3} + \cdots + \frac1{4^{10}}\right)[/tex]

Subtract this from S to eliminate all the but the first term in S and the last term in S/4 :

[tex]\displaystyle S - \frac S4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

Solve for S :

[tex]\displaystyle \frac{3S}4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]

[tex]\displaystyle S = \frac{32}3 \left(1 - \frac1{4^{10}}\right) = \boxed{\frac{349,525}{32,768}}[/tex]

The value of x in both case is 17 and 10.

If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

1. As the given angle is 90 degree i.e., complementary angle.

So,

 22+4x=90

  4x= 90-22

  4x= 68

    x= 17

2. As the figure for the linear pair i.e., supplementary angle

So,

110+7x=180

7x=70

x=10

Hence the value of x in both case is 17 and 10.

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Answer:

-5 degrees is colder than -3 degrees farienheight.

Step-by-step explanation:

Let's take this and eliminate every answer-

"The lowest temperature is -3 degrees."

-5 is lower than -3.

"The highest temperature is -5 degrees."

-5 degrees is the lowest temperature, not the highest!

"-5 is warmer than 3 degrees."

-5 is the LOWEST TEMPERATURE.

This leaves us with "-5 is colder than -3 degrees," which is correct because -5 is the smallest temperature and therefore, it is the coldest.

A fraction is a way to describe a part of a whole. The fraction that can replace the question mark is 1/2.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The fraction that can replace the question mark is,

9 × ? = (3/2) + (3/2) + (3/2)

9 × ? = 3(3/2)

9 × ? = 9/2

9 × ? = 9/2

? = 9/(2×9)

? = 1/2

Hence, the fraction that can replace the question mark is 1/2.

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Answer:

430.67

Step-by-step explanation:

(4 x 100) + (3 x 10) + (6 x 1/10) + (7 x 1/100)l

(400) + (30) + (6×0.1) + (7×0.01)

400 + 30 + 0.6 + 0.07

430.67

Using the information in the diagram, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°

From the question, we are to determine the measure of [tex]\overset{\LARGE\frown}{CD}[/tex]

Consider the right triangle

The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is twice the measure of the unknown angle

Let the unknown angle in the right triangle be x

∴ The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2x

Then,

x + 90° + 45.5° = 180° (Sum of angles in a triangle)

x = 180° - 90° - 45.5°

x = 44.5°

Thus,

The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2×44.5°

The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 89°

Hence, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°

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I predict that the solid with the  greater surface area to volume ratio would be the cube.

The volume of the cube is 27in³

The surface area of the cube is

The ratio of surface area to volume for the cube is 2.

The volume of the sphere is 113.14 in³

The surface area of the sphere is 113.14 in²

The ratio of surface area to volume is 1.

The volume of a cube = side length³

3³ = 27 in³

The surface area of a cube = 6a²

a = side length

6 x (3²) = 54 inches²

Ratio of surface area to volume = 54 / 27 = 2

The volume of the sphere= 4/3πr³

4/3 x 22/7 x 3³ = 113.14 in³

The surface area of the sphere = 4πr²

4 x 22/7 x 3² = 113.14 in²

Ratio of surface area to volume = 113.14 / 113.14 = 1

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Answer and explanation:

vertex: (3,25) The vertex is the minimum/maximum of a parabola where the direction it's moving in changes. For this question, that point is (3,25).

zeroes: x=6 and x=0 The zeroes of an equation are the points that y=0. Since it doesn't look like they want the full coordinate points, I would list x=6 for the point (6,0) and x=0 for the point (0,0).

y-intercept: x=0 The y-intercept is the point at which the graph crosses the y-axis, which here happens at (0,0), or x=0.

Highest point: 25 The highest point is the maximum of the graph, meaning it's the highest y-value that the graph has. Here, this is 25 (it's also the y-value for the vertex).

Time: 3 seconds The time it takes for Simon to reach the highest point is just the x-value of the vertex, so 3.

Total air time: 6 seconds This value is the total time that the y-value of the graph is above 0. To find this, you must subtract the x-values of the zeroes from each other. Since 6-0=0, Simon is in the air for 6 total seconds.

Hope this helps! :)

Answer:

B

Step-by-step explanation:

Because it flipped over the x axis

Spot the coordinates

Yes it's reflection along x axis

Option B

#1

#2

Answer:

1. x < 2.5

2. x > 2.5

Step-by-step explanation:

Question 1

Given inequality:

-4x + 5 > -5

Subtract 5 from both sides:

⇒ -4x + 5 - 5 > -5 - 5

⇒ -4x > -10

Divide both sides by -4 (remembering to flip the sign as we are dividing by a negative):

⇒ -4x ÷ -4 > -10 ÷ -4

⇒ x < 2.5

Question 2

Given inequality:

-25 > -5(x + 2.5)

Expand the brackets:

⇒ -25 > -5x - 12.5

Add 12.5 to both sides:

⇒ -25 + 12.5 > -5x - 12.5 + 12.5

⇒ -12.5 > -5x

Divide both sides by -5 (remembering to flip the sign as we are dividing by a negative):

⇒ -12.5 ÷ -5 > -5x ÷ -5

⇒ 2.5 < x

⇒ x > 2.5

Answer:

Step-by-step explanation:

this year you earned $75500. Last year you earned $72400. What the rate of change on your earnings since last y?

Answer:

∠ABC = 39°

Step-by-step explanation:

Since ED bisects ∠CBD :

∠EBD = ∠CBE = 30°

Now, ∠ABD = ∠ABC + ∠CBE + ∠EBD = 99°

Solving :

Answer:

11

Step-by-step explanation:

2x-13=9

2x=9+13

2x=22

x=11

[tex]\dfrac{n(n-3)}{2}=44\\\\n(n-3)=88\\n^2-3n-88=0\\n^2+8n-11n-88=0\\n(n+8)-11(n+8)=0\\(n-11)(n+8)=0\\n=11 \vee n=-8[/tex]

Therefore, the number of sides is 11.

The volume of the bottom section of the figure is:

V = 48 cm³

Remember that for a rectangular prism of length L, width W, and height H, the volume is V.

V = L*W*H

For the bottom section the dimensions are:

Length = 6cm

Width = 4cm

Height = 4cm - 2cm = 2cm

Replacing these in the volume equation we get:

V = (6cm)*(4cm)*(2cm) = 48cm³

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Answer:

Step-by-step explanation:That’s t up to you STOP CHEATING!!