The graphs of f(x)=-10x-1 and g(x)=2^x are shown. Create a new function h(x) by reflecting f(x) over the x-axis. How many times do the graphs of h(x) and g(x) intersect?

Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

give me thanks for more! your welcome bud!

The exponential function of the graph is y = 2 ( 0.5 )ˣ

Given data ,

Let the exponential function be represented as f ( x )

Now , f ( x ) = y

where y = 2 ( 0.5 )ˣ

And , the base of the exponential function is 0.5, and the coefficient or amplitude is 2. The base of an exponential function determines how fast the function grows or decays, and the coefficient or amplitude determines the vertical stretch or compression of the function.

Hence , the function is y = 2 ( 0.5 )ˣ and the graph is plotted

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Answer: june is in the second quarter

The range of the function is -8 < y < -3(option c)

What is range?

The set of all the outputs for a certain inputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outputs of the dependent variable.

Given points on the graph is given by:

(x, y) = (-5, -3)

(x, y) = (10, -8)

A diagonal curve connecting both points.

Removing the x values to determine the range

y = -3

y = -8

-8 is less than -3

So, the range can be represented as

-8 less than y less than -3

So, we have

Range: -8 < y < -3

Hence, the range of the given data is -8 < y < -3.

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x-intercept :(- 4, 0) . The given function is not a example of exponential decay.

We can determine the increase in pollution or the number of deaths using the exponential growth as well as decay equation, respectively. The exponential decay equation is used to calculate the radioactive elements' rate of decay.

There are two categories in which to classify exponential functions. Exponential growth as well as exponential decay are these. The formula for both of these functions is f = abˣ, but only varies in b's value.

The stated function:

f (x) = –3(–x – 3) + 3

x-intercept occurs when, f(x) = 0

0 = –3(–x – 3) + 3

–3(–x – 3) = - 3

-x - 3 = 1

x = -3 - 1

x = -4

x-intercept :(- 4, 0)

The graph for the function is plotted using the graphing tool.

Now, from the graph its is seen that the function forms a straight line in creasing order.

x → ∞, f (x) → 3 linearly.

Thus, the given function is not a example of exponential decay.

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The algebraic expression for Desmond's height is x + 5.

If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.

So the algebraic expression for Desmond's height is x + 5.

Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).

They can contain one or more variables and can be evaluated for different values of the variables.

For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.

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[tex]D=\cfrac{1}{2}t(s2-s1)\implies D=\cfrac{t(s2-s1)}{2}\implies 2D=t(s2-s1) \\\\\\ 2D=ts2-ts1\implies 2D+ts1=ts2 \\\\\\ ts1=ts2-2D\implies s1=\cfrac{ts2-2D}{t}[/tex]

The volume of the rectangular prism is: 567 cubic inches

The volume of the triangular prism is: 183.6 cubic yards

The volume of the rectangular prism is:

Volume = length x width x height

Volume = 9 in x 7 in x 9 in

Volume = 567 cubic inches

It should be noted that to find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism. In this case, the triangular prism has a base that is a triangle with dimensions of 9 yards by 3.4 yards, and a height of 12 yards. So the volume of the triangular prism is:

Volume = (base area) x height

Volume = (1/2 x base x height) x height

Volume = (1/2 x 9 yd x 3.4 yd) x 12 yd

Volume = 183.6 cubic yards

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[tex](\stackrel{x_1}{36}~,~\stackrel{y_1}{-35})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{12} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-35)}=\stackrel{m}{- \cfrac{7}{12}}(x-\stackrel{x_1}{36}) \implies y +35 = - \cfrac{7}{12} ( x -36) \\\\\\ y+35=- \cfrac{7}{12}x+21\implies {\Large \begin{array}{llll} y=- \cfrac{7}{12}x-14 \end{array}}[/tex]

Answer:

1) true

2) false

Step-by-step explanation:

1) area of a square is s²

in this case s²=144. by taking the square root of 144 to solve for s, you get s=12

√144=s=12

2) False because the area for a square is s², and if you plug in 72 into this equation, you get 72²=5184, which isn't the area given in the problem

The equation s^2=144 can be used to find the length of one side of a pyramid with a square base and an area of 144 ft^2, which is true. However, the length of one side is not 72 feet, but rather it is 12 feet.

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By answering the presented question, we may conclude that Therefore, the volume of the rectangular solid is 6 cubic units.

In geometry, a coordinate system is a method that uses one or more numbers or coordinates to determine the precise location of points or other geometrical objects on a manifold, such as Euclidean space. Coordinates are pairs of numbers used to locate a point or object on a two-dimensional plane. T

he x and y coordinates of a point on a 2D plane are two numbers that define its location. a set of digits that represent precise locations. In most cases, the figure has two numbers. The first number represents the front-to-back distance, while the second number represents the top-to-bottom distance. As in (12.5), there are 12 units below and 5 units above.

The rectangular solid in the first octant bounded

0 ≤ x ≤ 1, 0 ≤ y ≤ 2, 0 ≤ z ≤ 3

∫[0,1] ∫[0,2] ∫[0,3] 1 dz dy dx

∫[0,2] ∫[0,1] ∫[0,3] 1 dz dx dy

∫[0,3] ∫[0,2] ∫[0,1] 1 dx dy dz

∫[0,3] ∫[0,1] ∫[0,2] 1 dy dx dz

∫[0,2] ∫[0,3] ∫[0,1] 1 dx dz dy

∫[0,1] ∫[0,3] ∫[0,2] 1 dy dz dx

Let's evaluate the first integral:

∫[0,1] ∫[0,2] ∫[0,3] 1 dz dy dx

= ∫[0,1] ∫[0,2] [z]3 dy dx

= ∫[0,1] ∫[0,2] 3 dy dx

[tex]= ∫[0,1] [3y]0^2 dx[/tex]

= ∫[0,1] 6 dx

= [6x]1

= 6

Therefore, the volume of the rectangular solid is 6 cubic units.

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The digits from 0-9 should Jimmy use to represent him winning is 6-9.

We are given that;

Hockey games won against brother=60%

Now,

Since Jimmy wins 60% of his games, we can assign 0-5 to him winning and 6-9 to him losing. This way, each digit has an equal chance of being selected and the probability of Jimmy winning matches his actual win rate. To simulate two games, we can look at two digits from the random number table and see if they are 0-5 or 6-9. For example, if we see 37, that means Jimmy won the first game and lost the second game. If we see 01, that means Jimmy won both games.

Therefore, by probability the answer will be 6-9.

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(m + n) has a magnitude of approximately 25.8.

We have,

Consider the two vectors as m and n.

To find (m + n), we need to add the two vectors.

To do this, we first need to determine the components of each vector.

Let's call the angle between vector m and the x-axis α, and the angle between vector n and the x-axis β.

Then we have:

|m| = 10, so the x-component of vector m is m_x = 10 cos α and the

y-component is m_y = 10 sin α.

|n| = 15, so the x-component of vector n is n_x = 15 cos β and the

y-component is n_y = 15 sin β.

We also know that the angle between vectors m and n is 75 degrees. Using the dot product, we can find the cosine of this angle:

m · n = |m| |n| cos 75

m · n = 10 * 15 * cos 75

m · n = 37.32

We also know that the dot product is equal to the sum of the products of the corresponding components:

m · n = (m_x) x (n_x) + (m_y) x (n_y)

37.32 = 10 cos α x 15 cos β + 10 sin α * 15 sin β

Now we have two equations with two unknowns:

m_x + n_x = (10 cos α) + (15 cos β)

m_y + n_y = (10 sin α) + (15 sin β)

We can solve for α and β using the equations we just derived:

m_x + n_x = (10 cos α) + (15 cos β)

10 cos α = (m_x + n_x - 15 cos β)

cos α = (m_x + n_x - 15 cos β) / 10

α = arccos[(m_x + n_x - 15 cos β) / 10]

m_y + n_y = (10 sin α) + (15 sin β)

10 sin α = (m_y + n_y - 15 sin β)

sin α = (m_y + n_y - 15 sin β) / 10

α = arcsin[(m_y + n_y - 15 sin β) / 10]

Now we can substitute these values into the equations for m_x + n_x and m_y + n_y to find (m + n):

m_x + n_x = 10 cos α + 15 cos β

m_y + n_y = 10 sin α + 15 sin β

We can use a graphical method to estimate the values of α and β. Start by drawing vector m with length 10 and angle α with respect to the x-axis. Then draw vector n with length 15 and angle β with respect to the x-axis, starting the tail of n at the head of m.

The parallelogram formed by the two vectors will have a diagonal that represents (m + n). Use a ruler to measure the length of this diagonal to the nearest hundredth.

We can use the law of cosines to find the magnitude of (m + n):

|(m + n)|² = |m|² + |n|² + 2|m||n| cos 75

|(m + n)|² = 10² + 15² + 2(10)(15) cos 75

|(m + n)|² = 665.19

|(m + n)| = 25.8 (to the nearest hundredth)

Therefore,

(m + n) has a magnitude of approximately 25.8.

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If sin(tetha) = √5/3, then the value of cos (tetha) =2/3

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

If sin(tetha) = √5/3, therefore the hypotenuse is 3 and the opposite is √5

Using Pythagoras theorem,

3² = √5)²+x²

x² = 9-5

x² = 4

x = 2

adjascent = 2

therefore the value of cos(tetha) = adj/hyp

= 2/3.

therefore the value of cos(tetha) = 2/3

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The length of the arc is 12π units.

The area of a sector is given by the formula:

Area of sector = θ/360 × πr²

Where θ is the angle subtended and r is the radius

Substituting:

16π = θ/360 × π × 8²

θ = 90° = 0.5π (in radian)

m∠WYX = 2π - m∠WX

m∠WYX = 2π - 0.5π

m∠WYX = 1.5π

Length of arc = θ/360 ×  2πr

Length of m∠WYX = (1.5π)/2π × 2πr

Length of m∠WYX = (1.5π)/2π × 2π × 8

Length of m∠WYX = 12π units.

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Answer:

about 149 ft

Step-by-step explanation:

cosine of 43 degrees is about 0.73 (can be found using calculator)

cosine is the adjacent side divided by the hypotenuse, so:

adjacent/hypotenuse=0.73

we know the adjacent is 109 so

109/hypotenuse=0.73

solve for hypotenuse

109/0.73=149.3

so the hypotenuse is about 149 ft

The new coordinates of the image of the shape are

The picture of the graph showing the image is attached

The rule for 90 degrees clockwise rotation is

(x, y) becomes (y, -x)

The rule involves interchanging the coordinates of the ordered pair such that x takes the place of y and y tales the place of x and a change of sign

performing the rotation we have the new coordinates as below

(2, 3) becomes (3, -2)

(2, 2) becomes (2, -2)

(4, 2) becomes (2, -4)

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Answer: 249.06

Step-by-step explanation: the area of the circle is 201.06

The area of the rectangle is 48 because 8*6 is 48. Add and you get 249.06

The vertices of the resulting image A'B'C'D'E' are A' = (2, -2), B' = (4, -2), C' = (6, -4), D' = (4, -6) and E' = (2, -6)

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

A = (2, 2), B = (2, 4), C = (4, 6), D = (6, 4) and E = (6, 2)

Rule: 90 degrees rotation

The rule of 90 degrees rotation is

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

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

A' = (2, -2), B' = (4, -2), C' = (6, -4), D' = (4, -6) and E' = (2, -6)

Hence, the image = A' = (2, -2), B' = (4, -2), C' = (6, -4), D' = (4, -6) and E' = (2, -6)

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Answer:

75cm2 is right I think

Step-by-step explanation:

Hope this helps

The area of the given circle with radius 4 feet is 50.24 square feet.

From the given figure, radius of a circle is 4 feet.

The formula for the area of a circle is A = πr², where r is the radius of the circle.

Here, area of a circle = 3.14×4²

= 3.14×16

= 50.24 square feet

Therefore, the area of the given circle with radius 4 feet is 50.24 square feet.

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Answer:

500 miles

Step-by-step explanation:

if an inch equals 125 miles (m) and a map is 4 inches you can use the equation 4m=x and 4x125=500.

Answer:

The slope of the graph is 8

Step-by-step explanation:

For a function to have a slope or gradient, it must be represented in this format as y= mx+c.

Where in this case 8 is m, y is said to be f(x) and c is -11

Answer:

my friend will help you with this :)

Step-by-step explanation:

the expression 9 log2x + 1/2log2x - 5 log2(x+1) can be written as a single logarithm, log2[x²(19/2) / (x+1)²5].

Why is it?

We can use the logarithmic identities to simplify this expression and write it as a single logarithm:

9 log2x + 1/2 log2x - 5 log2(x+1)

= log2(x²9) + log2(x²(1/2)) - log2(x+1)²5 (using the product and power rules of logarithms)

= log2[x²9 ×x²(1/2) / (x+1)²5] (using the quotient rule of logarithms)

= log2[x²(19/2) / (x+1)²5] (simplifying the expression)

Therefore, the expression 9 log2x + 1/2log2x - 5 log2(x+1) can be written as a single logarithm, log2[x²(19/2) / (x+1)²5].

A logarithm is a mathematical function used to determine how many times a particular number, called the base, must be multiplied by itself to produce a given value. The most commonly used base for logarithmic functions is 10, but other bases such as 2 and e (the base of the natural logarithm) can also be used.

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Answer:

67.678

Step-by-step explanation:

Answer:

  1a. increasing. It is increasing for all values of t.

  1b. no. The population asymptotically approaches 40,000.

  2. the sign of the slope of a reciprocal function is opposite the sign of the function's slope

Step-by-step explanation:

Given the population function P(t) = 20(4t+3)/(2t+5), you want to know if the population is increasing or decreasing, and if the population will reach 50,000. You want to have an explanation of why the reciprocal of an increasing linear function is decreasing.

The population function can be expanded to ...

  P(t) = 40 -140/(2t+5)

As we know from question 2, the second term is increasing, hence the population function is increasing. (The basic reciprocal function is decreasing, but it is subtracted here, so the overall effect is an increasing function.)

The magnitude of the second term of the above version of the population function starts at 28 for t=0 and decreases asymptotically to zero. Hence the population starts at 12000 and increases to an asymptote of 40,000. It will never reach 50,000.

The basic reciprocal function is f(x) = 1/x. It is decreasing everywhere it is defined. It is the reciprocal of a linear function with positive slope (an increasing function).

Translation or vertical or horizontal scaling of the basic function (using positive scale factors) does not change the sign of the slope, either of the original linear function or of its reciprocal. Hence the reciprocal of an increasing function is decreasing.

Looking at derivatives, if f'(x) is positive, then the derivative of g(x) = 1/f(x) is ...

  g'(x) = (-1/f(x)^2)f'(x)

That is, f(x)^2 is non-negative, and -f'(x) is negative, so the derivative g'(x) must be negative (wherever f(x)≠0). The reciprocal function is decreasing.