7. Population Growth The population of a southern city
follows the exponential law.
(a) If N is the population of the city and is the time in
years, express N as a function of t.
(b) If the population doubled in size over an 18-month
period and the current population is 10,000, what will
the population be 2 years from now?
15

Answer:

Assuming angle 1 is 75º.

1 -> 75

2 -> 105

3 -> 75

4 -> 105

5 -> 75

6 -> 105

7 -> 75

8 -> 105

Answer:

5/8

Step-by-step explanation:

We can solve this by turning 2 1/2 into a decimal.

2 1/2 = 2.5

2.5 ÷ 4 = 0.625

0.625 = 5/8

2 1/2 divided by 4 is 5/8

Answer: t = 37.8 degree

Step-by-step explanation:

We know that a circle has 360 degrees, this is half a circle, so it total is 180 degrees.

We add 63.7 with 78.7 = 142.4 degree

Take 180 - 142.2 = 37.8 degree

Answer:  the solution to the system of equations is x = 12 and y = 16.

Step-by-step explanation: To solve this system of equations, you can use the method of substitution.

First, solve one of the equations for one of the variables. For example, you can solve the first equation for x:

2x + y = 40

2x = 40 - y

x = (40 - y)/2

Then, substitute this expression for x in the second equation:

x - 2y = -20

(40 - y)/2 - 2y = -20

Multiplying both sides by 2, we get:

40 - y - 4y = -40

-5y = -80

y = 16

Substituting this value for y in the first equation, we can solve for x:

2x + 16 = 40

2x = 24

x = 12

Therefore, the solution to the system of equations is x = 12 and y = 16.

The required function f(x) is represented by -1 + F(x + sin(x)).

To find the function f(x), you can use the formula for integration by substitution:

f(x) = F(g(x)) + C

where F is an antiderivative of f, g is a function such that g'(x) = f(x), and C is a constant.

In this case, we can take g(x) = x + sin(x). Then g'(x) = cos(x), so f(x) = F(g(x)) + C = F(x + sin(x)) + C.

We are given that f'(π) = 2 and f(π) = -1, so we can use these values to find the constants C and F.

First, we can find F by taking the derivative of F(x + sin(x)). This gives us:

F'(x + sin(x)) = f(x) = cos(x)

Substituting x = π and using the fact that F'(x + sin(x)) = f'(π) = 2, we get:

F'(π + sin(π)) = 2

Since sin(π) = 0, this simplifies to:

F'(π) = 2

Then, using the fact that F(x + sin(x)) = f(π) = -1 when x = π, we can find the value of F(π):

F(π) = -1

Now that we have found the values of F and F', we can use these to find the value of C.

Since F(x + sin(x)) = F(x) + F'(x) sin(x), we can substitute x = π to get:

F(π + sin(π)) = F(π) + F'(π) * sin(π)

Substituting the values we found above, this becomes:

F(π + 0) = -1 + 2 x 0

Which simplifies to:

F(π) = -1

Since F(π) = -1, we can conclude that C = -1.

Therefore, the function f(x) is given by:

f(x) = F(x + sin(x)) + C = F(x + sin(x)) - 1

= -1 + F(x + sin(x))

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Answer: Table

Step-by-step explanation: Hope you find it helpful!

Area of the sheep pen = 1600feet square

The amount of space occupied by a flat (2-D) surface or form of an object is known as its area.

180 feet of fence were purchased.

The perimeter of a rectangular sheep pen is equal to two times the length plus the width, or two times the length plus 180. One side of the rectangular sheep pen is covered with a barn, which equals the width.

The rectangular sheep pen's covered side:

180 =2 length + width

180 = 2 x80 +width

180 - 160 = width

20= width

Area = l*b = 80*20

Area of sheep pen = 1600 feet square

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Answer:

8m = 800cm

8m = 0.008km

Step-by-step explanation:

1 kilometer is 1000 meters

1 meter is 100 centimeters

You'd only have to multiply in the first one:

[tex]8 \times 100 = 800[/tex]

8m = 800cm

Remember that when multiplying by 100 you only have to add zeros.

For km, as it is bigger than m you have to divide by 1000, when dividing this time you only have to carry an imaginary point starting from right to left, the amount of zeros there are:

[tex]8. \\ .8 \\ .08 \\ .008 \\ 8 \div 1000 = .008[/tex]

8m = 0.008km

If you run out of numbers when carrying the point, just add zeros.

Answer:

25°

Step-by-step explanation:

We know the opposite angles must be equal when two lines intersect, so 67 = 42+t. Subtracting 42 from both sides gives t=25, which is our answer

answer:

25 degrees

step-by-step explanation:

67=42+t so using that equation the answer can be determined. hope that helps!

Answer:

(- 4, 2 )

Step-by-step explanation:

x + 5y = 6 → (1)

x + 3y = 2 → (2)

subtract (2) from (1) term by term to eliminate x

(x - x) + (5y - 3y) = 6 - 2

0 + 2y = 4

2y = 4 ( divide both sides by 2 )

y = 2

substitute y = 2 into either of the 2 equations and solve for x

substituting into (1)

x + 5(2) = 6

x + 10 = 6 ( subtract 10 from both sides )

x = - 4

solution is (- 4, 2 )

Answer:

x = 21

Step-by-step explanation:

[tex]\frac{x}{9}[/tex] = [tex]\frac{35}{15}[/tex]

[tex]\frac{35}{15}[/tex] can be simplified to [tex]\frac{7}{3}[/tex] if we divide the numerator and denominator by 5

[tex]\frac{x}{9}[/tex] = [tex]\frac{7}{3}[/tex]  cross multiply and solve for x

3x = 63  Divide both sides by 3

x = 21

Answer:

56

Step-by-step explanation:

Top line:

100% - 80% = 20%

20% of 60 = 0.2 × 60 = 12

Small piece on top is 12.

Second line:

Small piece is 12.

100% - 60% = 40%

Small piece is also 40%.

40% of x = 12

0.4x = 12

x = 12/0.4

x = 30

The entire second line is 30.

60% of 30 = 0.6 × 30 = 18

60% of second line is 18.

Third line:

30% of third line = 18

100% - 30% = 70%

30/18 = 70/x

30x = 18 × 70

x = 42

Larger part of third line is 42.

Fourth line:

75% of 4th line is 42.

100/x = 75/42

75x = 100 × 42

x = 56

Answer: 56

After evaluation of the given expression, the value obtained in mixed fraction form is equal to -4 3/10.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given expression in the question,

(-5 - (-4 1/2)) × 3 + (-2 4/5)

The expression in simplified form will be,

(-5 + 9/2) × 3 - 14/5

(-10 + 9) × 3 -14/5

-3/2 - 14/5

= (-15 - 28)/10

= -43/10

It can also be written in mixed fraction form,

= -4 3/10

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The slope is m = RISE / RUN, and the change in y is frequently referred to as "RISE."

[tex]5*x-6*y-(42)=0[/tex]

Tiger understands that this is a straight line equation. Typically, this equation is expressed as y=mx+b (or "y=mx+c" in the UK).

A straight line drawn using the Cartesian coordinate system has the formula "y=mx+b," where "y" denotes the vertical axis and "x" denotes the horizontal axis.

In this equation, y represents how high the line rises, x represents how far it travels along, m represents the slope or gradient, or how steep the line is, and b represents the Y-intercept, or the point at which the line crosses the Y axis.

The X, Y, and slope are collectively referred to as the line properties. We will now plot the line 5x-6y-42 = 0 and determine its characteristics.

x = 0 the value of y is 7/-1 so this line "cuts" the y axis at y=-7.00000

y-intercept = 42/-6 = 7/-1  = -7.00000

y = 0 the value of x is 42/5 Our line therefore "cuts" the x axis at x= 8.40000

x-intercept = 42/5  =  8.40000

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Because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.

Given,

In the question:

There are 60 minutes in an hour so use 60 as a common denominator. Then rename each opening time using another common denominator.

Explain how you found your answer.

Now, According to the question:

There are 60 min in an hour

and, 60 as a common denominator.

So, 45/60 and 10/60

Explanation: Because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.

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The solution of given equation by using the property of equality is x = 2.

An equation has been presented to us.

3(2x + 6) -4x = 2(5x -2) + 6

Our given equation has to be solved step-by-step.

Step 1: Utilize the distributive property;

3×2x + 3×6 - 4x = 2×5x -2×2 + 6

6x + 18 -4x = 10x - 4 + 6

Step 2: combine similar phrases.

6x + 18 -4x = 10x - 4 + 6

2x + 18  = 10x + 2

Step 3: Apply the equality's subtraction property

2x - 2x + 18  - 2 = 10x + 2 - 2x - 2

16 = 8x

Step 4: Apply the equality's divisional property:

16/8 = 8x/8

x = 2

As a result, is our given equation's answer is x = 2.

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The correct question is-

Follow the steps to solve this equation. 3(2x + 6) – 4x = 2(5x – 2) + 6 1. Use the distributive property: 6x + 18 – 4x = 10x – 4 + 6 2. Combine like terms: 2x + 18 = 10x + 2 3. Use the subtraction property of equality: 18 = 8x + 2 4. Use the subtraction property of equality: 16 = 8x 5. Use the division property of equality:

The image after the transformations of rotation, translation or reflection can be found by certain operation or rotation.

We can find how to know the image of certain figures after the given transformations are done.

91) Here it is translation.

x coordinates are shifted to right by 3 units and y coordinates are shifted to  down by 5 units.

So the entire graph will be shifted to right by 3 units and down by 5 units.

92) Here, the translation is by not shifting the x coordinates and shifting the y coordinates 2 units to the down.

So the entire graph will be shifted to down by 2 units.

93) When a graph is reflected across x = -2, then the graph is moved horizontally such that the original figure and the image will be at the same distance from x = -2.

94) When a graph is reflected across y = 1, then the graph is moved vertically such that the original figure and the image will be at the same distance from y = 1.

95) When a graph is rotated about the origin 180°, if it is clockwise or anticlockwise, each of the coordinates (x, y) in the graph will become (-x, -y).

96) If the rotation is 90° counterclockwise about the origin, the coordinates (x, y) in the original graph becomes (-y, x).

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Answer: 12

Step-by-step explanation:

[tex]f(9)=3+9=12[/tex]

From the given triangle diagram figure, angles are -

m∠1 = 72°

m∠2 = 114°

m∠3 = 66°

m∠4 = 66°

m∠5 = 56°

m∠6 = 32°

Depending on how many sides a polygon has, it is given a unique name. Because "tri" is a word that indicates "three," the polygon with three sides is known as a triangle. This polygon has three angles, as indicated by its name. Poly means numerous in the prefix.

Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed at a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

In the given problem,

m∠6 = 180° - (90° + 58°)

so, m∠6 = 32°

Next, m∠1 +m∠6  = 180° - (42° +34°)

                             = 104°

so, m∠1 = 104° - 32°

             = 72°

Next, m∠5 = 90° - 34°

m∠5 = 56°

Again, m∠4 = 180° - (56° + 58°)

m∠4 = 66°

Now from the figure, m∠3 and m∠4 are vertically opposite angle.

So, m∠3 = 66°

Again, m∠2 = 180° - 66° = 114°

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The coordinates of P' after the transformation are (-1, 1)

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

Point P' = (2, -4)

This point can be represented as

(x, y) =  (2, -4)

Also, from the question, we have the transformation to be:

(x-3, y-3) and reflection line y=x

Mathematically, this can be expressed as

(x, y) = (y - 3, x - 3)

So, we have

Point P' = (2, -4)

This means that

y -3 = 2

x - 3 = -4

Evaluate

y = 1

x = -1

Hence, the point P after transformation is (-1, 1)

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The value of y is -30.

Direct variation is y = kx

15 = k(-3)

Divide by -3 on both sides

-15/3 = k

-5 = k -------> 1

Substituting 1 and x = 6, in Direct Variation

y = -5*6

y = -30

Therefore, the value of y is -30.

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Answer:32

Step-by-step explanation:

To obtain an amount of 3 / 2 cups of flour, then we need three halves of cup by means of a 1 / 2 cup measuring cup.

In this problem we have the case of recipe that requires 3 / 2 cups of flour in terms of certain number of measuring cups with an amount of 1 / 2 cups. The number of measuring cups (n) is equal to the total required by the recipe (M) divided by the amount of the measuring cup (m), both in cups. That is:

n = M / m

If we know that m = 1 / 2 cup and M = 3 / 2 cup, then the number of measuring cups is:

n = (3 / 2 cup) / (1 / 2 cup)

n = 3

In other words, we need 3 halves of a cup of flour to obtain the required amount of 3 / 2 cups.

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±1/2, ±1, ±7 are the possible rational roots of the polynomial function.

The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, both the constant term (the term without a variable) and the leading coefficient (the coefficient of the highest power) must be divisible by the fraction's denominator.

An anXn+ an− 1xn − 1 + … + a1x1 + a0 = 0  is a polynomial equation in one variable (x), where a0, a1,..., and an are regular integers. Therefore, q must divide a and p must divide a0 for a polynomial equation to have a rational solution, p/q.

It is given in the question,

F(x)=2x^2-3x+7

Here, p is a 7-fold factor.

p, thus, might have a value of 1, -1, 7, or -7.

and q is a two-fold factor.

Thus, q might have a value of 1, -1, 2, or -2.

Hence, ±1/2, ±1, ±7 are the possible rational roots of the polynomial function.

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Answer:

Addition, Distributive, Addition, Multiplication, Division

Step-by-step explanation:

Answer:

g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x)

Step-by-step explanation:

Answer:

uh  nose

Step-by-step explanation:

Given polynomial equation x3 - 8 = 0

x3-8 is a cubic polynomial is in the form a3 - b3 = (a - b)(a2 + ab + b2)

x3 - 23 = (x - 2)(x2 + 2x + 4)

One root is 2

x2 + 2x + 4 = 0

x = -b ± √(b2 - 4ac) / 2a

x = -2 ± √22 - 4(4) /2

x = -2 ± √4 - 16 /2

x = -2 ± √-12 /2

x = -1 ± √3i

Therefore, x = 2, -1 ±√3i

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Given,

polynomial equation x3 - 8 = 0

x3-8 is a cubic polynomial is in the form a3 - b3 = (a - b)(a2 + ab + b2)

x3 - 23 = (x - 2)(x2 + 2x + 4)

One root is 2

x2 + 2x + 4 = 0

x = -b ± √(b2 - 4ac) / 2

x = -2 ± √22 - 4(4) /2

x = -2 ± √4 - 16 /2

x = -2 ± √-12 /2

x = -1 ± √3i

Therefore, x = 2, -1 ±√3i

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Part A

[tex](b/2)^2 =(-3/2)^2 =\boxed{9/4}[/tex]

Part B

[tex]-x^2 -3x+2\\\\=-(x^2 +3x)+2\\\\=-(x^2 +3x+2.25-2.25)+2\\ \\=-((x+1.5)^2 -2.25)+2\\\\=-(x+1.5)^2 +2.25+2\\\\\boxed{y=-(x+1.5)^2 +4.25}[/tex]