In 1992, the moose population in a park was measured to be 3590. By 1999, the population was measured again to be 4500. If the population continues to change linearly
A.) Find a formula for the moose population, P, in terms of t, the years since 1990.
P(t)= ____

B.) What does your model predict the moose population to be in 2006?

Answer:

54

Step-by-step explanation:

Taking into account definition of perimeter and system of equations,  the length and width of the frame is 32 inches and 21 inches respectively.

The perimeter of a two-dimensional figure is the distance around the figure. That is, the perimeter of a flat geometric figure is called the length of its contour.

So, the perimeter is the measurement obtained as a result of the sum of the sides of a flat geometric figure. So to calculate the perimeter of a figure it is necessary to know two basic variables:

A rectangle is a flat geometric figure with four sides, of which two sides that are opposite parallel to each other have the same length and the remaining two have another length. The expression to calculate the perimeter of a rectangle is:

Perimeter= 2×(length + width)

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

You know that:

So, the system of equations to be solved is

[tex]\left \{ {{2x(L+W)=106} \atop {L=2xW-10}} \right.[/tex]

From the several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first one you get:

2×(2×W - 10 + W)=106

Solving:

2×(3×W - 10)=106

2×3×W - 2×10=106

6×W - 20=106

6×W=106 + 20

6×W=126

W=126 ÷6

W= 21

Remembering that L= 2×W - 10, you get:

L= 2×21 - 10

Solving:

L= 32

Finally, the length and width of the frame is 32 inches and 21 inches respectively.

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The algebraic expression for the given statement is: 9x + 9.

Given the statement above, the unknown number can be represented with variable "x".

The number = x

"Product" means multiplication.

"Product of 9 and x" = 9x

If 9 is added to the "product of 9 and x", the algebraic expression would be: 9x + 9.

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a) The explosion does violate the town regulation

b) The values are , I = [tex]1.65 * 10^{2} W/m^{2}[/tex] and [tex]I_{0}[/tex] = [tex]10^{-12} W/m^{2}[/tex]

The values that we have been given are

        L = loudness of the sound = 10log(I/[tex]I_{0}[/tex])

        I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]

        [tex]I_{0}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]

Putting the required value in the equation of the loudness we get

      a)       L =  [tex]10*log (\frac{1.65*10^{2} }{10^{-12} } )[/tex]

             L = 10*14.217 dB = 1142.17 dB

And according to the town regulation the loudness of the construction work should not exceed 100dB.

Thus the explosion is in violation of the town regulation as it exceeds 100dB.

b)  The respective values of I and [tex]I_{0}[/tex] are

        I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]

         = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]

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Answer: associative property of adding

The measure of ∠B round to the nearest whole number is 76°.

Cosine is the trigonometric function that is equal to the ratio of the side adjacent to the acute angle in a right angled triangle.

Mathematically,

           Cos = Base/Hypotenuse

Now given that, a triangle ABC,

AB = 21

BC = 7

∠C = 90°

Thus, we have

hypotenuse = AB

Base = BC

Perpendicular = AC

So, for angle B

CosB = Base/Hypotenuse

⇒ CosB = BC/AB

Put the values we get,

⇒ CosB = 7/21

or,

CosB = Cos(75.53°)

⇒ B = 75.53°

Now the nearest whole number to 75.53° is 76°

Thus, we get

B = 76°

Thus, the measure of ∠B round to the nearest whole number is 76°.

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Answer:

-429

Step-by-step explanation:

Answer:

2751

Step-by-step explanation:

2+5 times 12 times 54 minus 10 minus 475 minus 6

2+3240-10-475-6=2751

Answer:

x= 0.31066017 rounded to 0.31

Step-by-step explanation:

first you take out the exponent (2) by getting the square root of 18 so the equation will be 4x+3=18squared rooted. the primary factors of 18 are 2*3 squared. so instead of 18 put the factors is.so now you will get

4x+3=3^2*2 square rooted.

then you apply the radical rule so square root each of the digits.that will simplify to 4x=3square rooted by 2 divide by 4 on both sides minus 3/4 and if you simplify it should give you the answer

The two numbers are 12 and 20

Let the small number be x

Let the large number be y

We have that;

y = 8 + x      (1)

But;

x + y = 32    (2)

Now, substitute the value of y as 8 + x in equation (2)

x + 8 + x = 32

collect like terms

2x + 8 = 32

2x = 32 - 8

2x = 24

Make 'x' the subject

x = 24/ 2

x = 12

But;

y = 8 + x

y = 8 + 12

y = 20

Thus, the two numbers are 12 and 20

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 10.0427.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation:  log 4 + 2 log x = 6

We are given a logarithmic expression: log 4 + 2 log x = 6  

We know that e^(log b) = b

a log b = (log b)^a

log a + log b = log (ab)

Using exponential on both sides, we have

e^(log 4 + 2 log x) = e^6

e^(log 4 + log x² ) = 403.428

e^(log 4x² ) = 403.428

4x² = 403.428

x² = 403.428 / 4

x² = 100.857

x = 10.0427

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 10.0427.

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value of x =  25

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x is the expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to given statement,

log 4x =2

now convert this equation to exponential form

=> 4x = 10²

=> 4x = 100

=> x = 100 / 4

=> x = 25

Thus solution for this equation is x =25.

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Let the number be x

x=18

if you really liked my answer, be sure to rate, thanks, and award brainliest

hope this helped :)

Answer:    X=18

Step-by-step explanation:

The factoring of the expression 3 x²-2=5 x is (x - 2) (3x +1)

By ordering the values, we get:

3x² - 5x - 2 = 0

To solve this exercise, we have to follow the rules of factoring:

1. Factor 5 from 5x:

3x² - 5x - 2 = 0

3x² + (- 6 + 1) x - 2 = 0

2. Apply the distributive b:

3x² - 6x + 1x - 2 = 0

3. Groups the first two terms and the last two terms:

(3x² - 6x) + 1x - 2 = 0

4. Factorize the greatest common denominator (GCM) of each group:

3x(x - 2) + x - 2 = 0

5. Simplify the common term (x - 2) with the distributive property:

(x - 2) (3x +1)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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The coordinates of the images of the points are B'(x, y) = (0, 2), C'(x, y) = (3, 4), Z'(x, y) = (4, 3) and X'(x, y) = (4, 1), respectively.

In this problem we find four points set on Cartesian plane, each of which has to be transformed by using the following transformation rule about the origin:

(x', y') = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

(x, y) - Coordinates of the original point.

θ - Angle of rotation, in degrees.

If we know that B(x, y) = (- 2, 0), C(x, y) = (- 4, 3), Z(x, y) = (- 3, 4), X(x, y) = (- 1, 4) and θ = 90°, then the coordinates of the resulting point:

B'(x, y) = (- 2 · cos (- 90)° - 0 · sin (- 90°), - 2 · sin (- 90°) + 0 · cos (- 90°))

B'(x, y) = (0, 2)

C'(x, y) = (- 4 · cos (- 90°) - 3 · sin (- 90°), - 4 · sin (- 90°) + 3 · cos (- 90°))

C'(x, y) = (3, 4)

Z'(x, y) = (- 3 · cos (- 90°) - 4 · sin (- 90°), - 3 · sin (- 90°) + 4 · cos (- 90°))

Z'(x, y) = (4, 3)

X'(x, y) = (- 1 · cos (- 90°) - 4 · sin (- 90°), - 1 · sin (- 90°) + 4 · cos (- 90°))

X'(x, y) = (4, 1)

Finally, we proceed to graph the locations of the points, both original and resulting, by means of a graphing tool.

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The 4 number of boxes are in the stack.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

A stack of boxes is 6/5 meters tall.

Each box is 3/10 meter tall.

According to given question we have

The number of  boxes are in the stack

[tex]\frac{6/5}{3/10} \\\\=\frac{6*10}{3*5} \\\\=4[/tex]

Therefore, the 4 number of boxes are in the stack.

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Answer:

[tex]f(x)=-x^2 + 11x - 24[/tex]

Step-by-step explanation:

Well for this problem, you want to start off by writing it in factored form.

In factored form, you can represent a quadratic as: [tex]f(x)=a(x-b)(x-c)[/tex], where x=b, and x=c are zeroes of the function, since plugging them into the function makes one of the factors zero, and multiplying zero by the other factors will just give you zero.

The "a" in front of the two factors generally defines the stretch/compression of the function.

So let's start by plugging in the zeroes into the function, and then we can solve for "a" later: [tex]f(x) = a(x-3)(x-8)[/tex]

Now let's use one point on the graph, which is not a root/zero to solve for "a". It's important to not use a zero/root since if we use that point the entire thing will be zero regardless of the value of "a"

Luckily we have one point provided that is not a zero and is: (4, 4)

So let's plug it in: [tex]4=a(4-3)(4-8)\\4=a(1)(-4)\\4=-4a\\a=-1[/tex]

So now let's plug this into the factored form to get: [tex]f(x)=-(x-3)(x-8)[/tex]

using foil to multiply these two factors you get: -[x^2 -8x - 3x + 24]

Now combine like terms

-[x^2 - 11x + 24]

distribute the negative sign

-x^2 + 11x - 24

[tex] \large \bf \implies{y = { - x}^{2} + 11x - 24}[/tex]

Let standard form of quadratic equation be

If passes through (3,0) , (8,0) and (4,4)

The numeric values of the function are given as follows:

The function is missing, and is given as follows:

It asks for the following numeric values:

f(-3), f(2), f(5).

To find the numeric value of a function, we replace each instance of the variable by the desired value.

Hence, for this function, the numeric values are:

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Answer:

3

Step-by-step explanation:

6=2*3

9=3*3

The only common factor is 3

The perimeter of triangle 8 is 41 feet and 3 inches while the area is around 81.42 feet².

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

The given object is a triangle with sides of 13 ft 4 in,13 ft 4 in, and 14 ft 7 in.

A perimeter is the sum of all sides of the triangle.

There fore,

Perimeter = 13 ft 4 in + 13 ft 4 in + 4 ft 7 in

⇒ 41 feet 3 inches.

Now the area is given as 1/2 × base × height.

Here base = 14 ft 7 in and height = 11 ft 2 inch

Now,

1 inch = 1/12 ft so 7 inch = 7/12 feet and 2 inches = 2/12 feet.

So,

Area = 1/2 × (14 + 7/12) × (11 + 2/12)

Area = 81.42 feet²

Hence "The perimeter of triangle 8 is 41 feet and 3 inches while the area is around 81.42 feet²".

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Answer:

Step-by-step explanation:

4,536

Answer:

-24

Step-by-step explanation:

-7 - 17 = -24.

Answer:

-24

Step-by-step explanation:

[tex]for~q - 7, q = -17\\-17-7\\=-24[/tex]

[tex]\sqrt{x}[/tex] = [tex]\sqrt{x+1}[/tex] has no real roots.

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

squaring both the sides

x = x+1

0 = 1

which is not true

hence false.

Therefore, no real roots.

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Answer:

it would be 1 (im not really sure what it would be, let me know if this helps)

Step-by-step explanation:

The time taken for Mel to finish mowing the yard if they have 80 minutes is 53 minutes.

It should be noted that this represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

Given that,

Michael mows = 1/3 of the yards

Mel will cut: 1 - 1/3 = 2/3

Therefore, the time taken for Mel to mow the yard will be:

= 80 × 2/3

= 53 minutes

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After Michael mows ⅓ of the yard, Write a fraction division problem that you can use to find out how long it will take Mel to finish mowing the yard if they have 80 minutes.

The output value of f(5) in the given function f(x) = -4x - 5 is -25

A function is simply a set of ordered pairs where each first element is paired with one and only second element and also no element in either pair is without a partner.

Given the data in the question;

To determine the output value of f(5), replace the variable x with 5 and simplify.

f(x) = -4x - 5

f(5) = -4(5) - 5

Perform the multiplication operation to remove the parenthesis.

f(5) = -4(5) - 5

f(5) = -20 - 5

f(5) = -25

Therefore, the output value of f(5) in the given function f(x) = -4x - 5 is -25.

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Answer:

option a 0.06 bared

Answer:

a = 10

Step-by-step explanation:

The image is showing a linear pair which equals 180°
104° is shown.

If you take 180° and subtract 104° you should get the answer to what (8a -4)° should equal to.

180° - 104° = 76°

Your equation should look like : 8a - 4 = 76°
-- Add 4 to both sides

8a - 4 = 76°
     +4    +4

= 8a = 80
-- Divide 8 on both sides

8a/8 = 80/8

a = 10

Proof:

8(10) - 4 =
80 - 4 = 76°

104° + 76° = 180°

Hope this helps!
--Blu

Answer:

hope u will be clear from the given definition

Answer:

Answer: 57 & 59

Step-by-step explanation:

Let us assume first odd integer is 'x'

Then, next consecutive integer should be 'x+2'. RIGHT?

Now, put in the form of equation:

x + (x+2) = 116

x + x + 2 = 116

2x + 2 = 116

2x = 116 - 2

2x = 114

x = 114 / 2 => 57

Now, put the value of 'x' in second step:

           x + 2 => 57 + 2 = 59

Therefore, answer would be 57 & 59