The population of Orange County is represented by the function f(x)=87,000(0.9), where x is the number of years since 2010 The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year

How do the populations of these counties compare in 2015?

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The distance of the student from the light pole is 21.4 feet.

A student sees a bird on top of a 15 foot high light pole. The angle of elevation to the top of the light pole is 35 degrees.  

The distance of the student from the pole can be calculated as follows:

The situation forms a right angle triangle.

using trigonometric ratios,

tan 35  = opposite / adjacent

tan 35 = 15 / x

cross multiply

x tan 35 = 15

divide both sides by tan 35

x = 15 / tan 35

x = 15 / 0.70020753821

x = 21.4222201012

x = 21.4 feet

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As ΔADE and ΔABC are similar because of their slope so correct option is A.

What are similar triangles?

Similar triangles square measure triangles that have identical form, however their sizes might vary. All equal triangles, squares of any facet lengths square measure samples of similar objects.

Main Body;

let co-ordinates of the points

A = (x₁ ,y₁ ) E =(x₂, y₂)

D =( x₃,y₃) C= (x₄ ,y₄)  B =( x₅,y₅)

Now, Slope of a line = Δy/Δx

.: Slope of line AD = y₃ -y₂/x₂-x1 .

                              = DE/AE

... Slope of line AB = y₅-y₄/x₄-x₁ = BC/ AC

Since ΔADE ~ ΔABC

Now , Slope of AD = slope of AB

=> DE/ AE = BC /AC

In option A

By property of Similar triangle -

DE /BC  = BC /АC

Hence, option A is correct answer.

All other options are incorrect

Since Sides of a similar triangle may not be equal.

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Answer:

Step-by-step explanation:

2,400 consoles

Answer:

4√2

Step-by-step explanation:

hypotenuse = [tex]\sqrt{4^2 + 4^2} = \sqrt{16 + 16} =\sqrt{2*16} = 4\sqrt{2}[/tex]

Median won't change, however Mean will fall by 180.

By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.

African elephants total 555 in number.

Elephants had a 3800 kg average mass.

Elephants had a 3600 kg median mass.

Lola, the elephant that was the smallest, weighed 2700 kg.

Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.

What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.

now 2700 becomes 1800

so Median remains the same as 3600

No change in Median

The mean mass of the elephants was  3800 kg

=> total weight = 5 x 3800 = 19000 kg

2700 kg becomes 1800 kg

Hence new total mass = 19000 - 2700 + 1800 = 181000 kg

New Mean = 18100/5   = 3620  kg

Mean reduced by 3800 - 3620  = 180 kg

No change in Median weight

Mean reduced by 180 kg

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The value of the fraction expression -2 1/2 - (-4 3/5) is 2 1/10

From the question, we have the following parameters that can be used in our computation:

−2 /2/1 −(−4 3/5)

Express properly

So, we have the following representation

-2 1/2 - (-4 3/5)

Remove the brackets

This gives

-2 1/2 - (-4 3/5) = -2 1/2 + 4 3/5

Express the denominator as 10

So, we have

-2 1/2 - (-4 3/5) = -2 5/10 + 4 6/10

Evaluate the difference

-2 1/2 - (-4 3/5) = 2 1/10

Hence, the solution is 2 1/10

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Answer:

6

Step-by-step explanation:

With the help of AA similarity rule option C,D,E,F will be the answer which is C:-∠ adc is 52.8°

D:- ∠ dac is 26.7°

E:- dac/adc = 0.506

F:- cd/bc =1.8

What is AA similarity rule?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are items that feature more than two figures that are the same form but different sizes.

When two triangles are comparable, all of their matching angle pairs and sides are congruent and proportionate. However, you do not necessarily need to have information about all of the sides and angles of two triangles in order to be certain that they are identical.

AA similarity rule

So, ∠ adc is 52.8°

and ∠ dac is 26.7°

So, the ratio of dac/adc = 0.506

And the ratio of side will also be equal as well which is 1.8

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The inequality that shows how long the temperature in Round Rock  will remain colder than that in Austin is 72 - 3t > 65 - 2t and the time is less than 13 hours

From the question, we have the following parameters that can be used in our computation:

Austin

Initial temperature = 65 degrees Fahrenheit

Rate of decrement = 2 degrees Fahrenheit

Round Rock

Initial temperature = 72 degrees Fahrenheit

Rate of decrement = 3 degrees Fahrenheit

The above parameters mean that

Current temperature = Initial temperature + Rate of increment x Number of hours

So, we have

Austin: A(t) = 65 - 2t

Round Rock: B(t) = 72 - 3t

When Round Rock is colder than Austin, we have

B(t) > A(t)

Substitute the known values in the above equation, so, we have the following representation

72 - 3t > 65 - 2t

Evaluate the like terms

-t > -13

Divide both sides by -1

t < 13

Hence, the interval is less than 13 hours

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Answer:

1.3 is the common difference.

Step-by-step explanation:

The total area of the given figure is 68.56 units².

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil.

It has two dimensions.

The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

So, the total area of the given figure:
We can divide the figure into separate rectangles and circles:

Area of rectangle: l*b

14*4

56 units²

Area of circle: πr² (D = 4, R = 4/2 = 2)

πr²

3.14(2)²

3.14*4

12.56 units²

The total area of the figure:

56 units² + 12.56 units² = 68.56 units²

Therefore, the total area of the given figure is 68.56 units².

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The value of distance between points A and B is 54.4 feet.

What is the law of cosine?

The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known as the law of cosines states: c²=a²+b²−2ab cos C .

Solution:

Using the law of cosines we get:

(AB)²=(AC)²+(BC)²-2AC×BC×cos(C)

(AB)²= (45)²+(69)²-2(45)(69)cos(52°)

(AB)² = 2025 + 4761 - 3823.2577

∴ AB = 54.4 feet

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a) An exponential function to model the population of foxes in t years after 2000 is given by P(t) = 21,100 x 1.09^t.

b) From the exponential function from part (a), the estimated fox population in the year 2008 is 42,052.

An exponential function is a mathematical expression written in the form of y = ab^x.

Exponential functions can be used to model growth factors, especially the population of animals and bacteria increasing at a constant rate.

The continuous growth rate in the fox population = 9%

Estimated population of foxes in the year 2000 = 21,100

A function to model the population in t years after 2000: P(t) = 21,100 x 1.09^t

In 2008, the population function:

P(t) = 21,100 x 1.09^8

= 21,100 x 1.993

= 42,052

Thus, we can conclude that using the exponential function, the fox population growing at 9% per year reached 42,052 in 2008 from its 21,100 number in the year 2000.

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Answer: The original fraction is 8/15

Step-by-step explanation:

The part about the 7 more than the numerator is not needed. All you have to do is add 3 to the numerator and 3 to the denominator.

5+3=8

&

12+3=15

So

8/15

I hope this helps!

Answer:

Angle-Side-Angle or also known as ASA

Step-by-step explanation:

Answer:

[tex]x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]

Step-by-step explanation:

[tex](x+7)^2=11 \\ \\ (x+7)=\pm \sqrt{11} \\ \\ x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]

The elements of the required sets would be

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

What are sets?

A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Given:

Let the universal set is (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {Odd numbers}  = {1, 3, 5, 7, 9}

Q = {Prime Numbers} = {2, 3, 5, 7}

R = {1, 2, 3, 4, 5}

So by using the properties of sets we can find

P' = {2, 4, 6, 8, 10}

Q' = {1, 4, 6, 8, 9, 10}

R' = {6, 7, 8, 9, 10}

P∩Q = {3, 5, 7}

R'∪P' = {2, 4, 6, 7, 8, 9, 10}

P∪R = {1, 2, 3, 4, 5, 7, 9}

P∩R = {1, 3, 5}

P∪Q∪R = {1, 2, 3, 4, 5, 7, 9}

P'∩Q'∩R' = S - P∪Q∪R

                = {6, 8, 10}

Now we can find the elements of the required sets:

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

Hence, the elements of the required sets would be

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

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Evan's error was that he subtracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got          [tex]6\frac{1}{2}[/tex].  On adding he would be getting  [tex]1\frac{1}{2}[/tex]

What is number line?

A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.

It is given that Evan added [tex]-2\frac{1}{2}[/tex] and 4 but got [tex]6\frac{1}{2}[/tex]

The mistake that Evan did was instead of adding, he substracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got          [tex]6\frac{1}{2}[/tex]. This is because

4 -  [tex]-2\frac{1}{2}[/tex]

= 4 + [tex]2\frac{1}{2}[/tex]

=  [tex]6\frac{1}{2}[/tex]

This is wrong as he was asked to add and not to subtract.

Therefore, on adding  [tex]-2\frac{1}{2}[/tex] and 4, we get,

= 4 [tex]-2\frac{1}{2}[/tex]

= [tex]1\frac{1}{2}[/tex]

Evan's error was that he subtracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got          [tex]6\frac{1}{2}[/tex].  On adding he would be getting  [tex]1\frac{1}{2}[/tex]

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Using PEMDAS, -32 is solution of (4/5)² x (-25) - 4².

A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right). We are provided with the proper steps for solving a mathematical expression by the PEMDAS rule. Operations are carried out in parenthesis first according to the PEMDAS rule. The next step is to conduct operations on exponents or powers. Then, depending on which occurs first, the operations of multiplication and division are performed from left to right. The final step is to conduct addition or subtraction from left to right, depending on which comes first.

Given

(4/5)² x (-25) - 4²

Using PEMDAS,

Squaring the exponents,

16/25 × -25 - 16

Multiplying,

-16 - 16

Subtracting,

- 32

Using PEMDAS, -32 is solution of (4/5)² x (-25) - 4².

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Procedimiento:

Empezamos separando el problema por partes. En este caso, a "un número" le daremos el nombre "x", y al "otro número distinto" le daremos el nombre "y".

1. Entonces, "el triple de un número" significa que es el triple de "x". En otras palabras, es 3 veces "x", osea:

3x

2.Como dice "la suma", entonces sabemos que nuestro 3x se va a sumar con otro término, entonces nuestro enunciado está quedando así:

3x+

3.El segundo término de la suma es "el doble de otro número distinto al cuadrado". Si el "otro número distinto" es "y", tenemos que "el doble" de "y" es 2 veces "y", osea, "2y".

Finalmente, se explica que este término está al cuadrado, lo cual daría que nuestro segundo término sea (2y)^2.

4.Entonces, la expresión completa es:

3x+(2y)^2

Answer:

10-x

Step-by-step explanation:

Answer:

Step-by-step explanation:

mid point = a+b/2

let b(x,y)

-2 = [7+x]/2                      3 = [-6+y]/2

-4 = 7 + x                          6 = -6 + y

-11 = x                                12 = y

Hence B is at (-11,12)

The first number is -4 and the second number is 7

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

Let  first number = n

second number = n+11

2(n+n+11)= 6

expanding the bracket

2(2n+11)=6

4n+22 =6

collecting like terms

4n = -16

n=-4

The first number = n =-4

second number = n+11=-4+11=7

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Answer:

[tex]\huge{\boxed{46 \text{ or } 67 \text{ or } 88 \text{ degrees}}}[/tex]

Step-by-step explanation:

An isosceles triangle is a triangle in which two of the sides and angles are equal.  Because the sum of all of the angles in a triangle is 180°, you may setup the following equation.

46 + x + z = 180°

Depending on the following scenario, your answer may be one of two options.  If the "third angle" refers to the angle that is not at the base of the triangle, then your equation is as follows:

z = x

46 + x + x = 180

46 + 2x = 180

2x = 134

x = 67

If the third angle is one of the base angles and x is a base angle, then x is also 46, because base angles are equal.

If the third angle is one of the base angles and x is the third angle, then your equation is as follows:

z = 46

46 + 46 + x = 180

92 + x = 180

x = 88

Hope it helps :) and let me know if you want me to elaborate.

Answer: 3.62 inches

Step-by-step explanation:

Diego's cousin is too short for this ride, we know how tall he is now and what height he needs to be.

This can be solved by subtracting his needed height from his current height.

39.37-35.75=3.62 inches

Step-by-step explanation:

32^2-24^2=448

square root 448=21

the small and large parallel line is 21=21

24+9=33

33^2+21^2=1530

square root 1530=39

39-32=7

~7~=6.75

x=6.75

From the given expressions the equivalent expression is,  

8x + 4y = 4(2x + y).

What is equivalent expression?

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Consider, the given expression

8x + 4y  and 4(2x + 1)

Consider, 4(2x + 1)

Simplifying this,

4(2x + 1) = 8x + 4

8x + 4 is different from 8x + 4y.

Hence, 8x + 4y is not equivalent to 8x + 4.

Now consider, 8x + 4y = 6x(4y + 2x)

Simplifying this

8x + 4y = 24xy + 12x^2

⇒ 8x + 4y = 6x(4y + 2x) is not equivalent.

Now consider, 8x + 4y = 8(x + 4y)

(8x + 4y) = 8x + 32y

⇒ 8x + 4y = 8(x + 4y is not equivalent.

Now consider,  8x + 4y = 4(2x + y)

8x + 4y = 8x + 4y

⇒ 8x + 4y = 4(2x + y) is equivalent.

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The simplified expression of √136 is 2√34

From the question, we have the following parameters that can be used in our computation:

√136

Expand the expression

So, we have the following representation

√136 = √68 * 2

Further, expand the expression

So, we have the following representation

√136 = √34 * 2 * 2

So, we have

√136 = √34 * 4

Take the square root

√136 = 2√34

The expression cannot be further simplified

Hence, the solution is 2√34

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Answer:

  -1/2

Step-by-step explanation:

You want the slope of the line through points (8, -3) and (-6, 4) using the slope formula.

The formula for the slope of the line through points (x1, y1) and (x2, y2) is ...

  m = (y2 -y1)/(x2 -x1)

For the two given points, the slope is ...

  m = (4 -(-3))/(-6 -8) = 7/-14 = -1/2

The slope of the line is -1/2.