The owner of the course asks you to provide a scale drawing of the green section he requested that you use the length of the legs of the right triangle found in the previous step use the connect line tool to draw your green section in the grid.

The area of gs : 48.67

Length of one leg : 3.21

Length of other leg : 10.5

Length of other leg 12

The exponential equation of log(x+4) (x²+3x-7) =3 is x²+3x-7 = (x+4)³

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form a^x=b^y.

To solve exponential equations with same base, use the property of equality of exponential functions .

The law of logarithm states;

If loga b = x

b = a^x

Using the rule;

log(x+4) (x²+3x-7) = 3

x²+3x-7 = (x+4)³

therefore the exponential equation of log(x+4) (x²+3x-7) = 3 is x²+3x-7 = (x+4)³

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For the area to increase by 1. 2 square feet, the base would need to increase by 0. 4 ft.

The area of a triangle is given by the formula:

Area =  ( 1 / 2) x base x height

= 1 / 2 x 14 x 6

= 42 square feet

The new area after the increase would be :

= 42 + 1. 2

= 43. 2 square feet

The base for this to happen is:

43. 2 = 1 / 2 x base x 6

base = 14. 4 ft

The increase in base is:

= 14. 4 - 14.

= 0. 4 ft

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Answer: (5, 3)

Step-by-step explanation:

this is just basic coordinate geometry. it tells you how far to go right and up.

The graph of the inequality y ≤ (5/2)x - 5 is a downward-sloping line with shading below the line.

To graph the inequality 5x - 2y ≥ 10, we need to convert it to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's go step by step:

Step 1: Start with the original inequality:

5x - 2y ≥ 10

Step 2: Move the 5x term to the other side of the inequality by subtracting 5x from both sides:

-2y ≥ -5x + 10

Step 3: Divide the entire inequality by -2 (since we want to isolate y and have a positive coefficient for y):

y ≤ (5/2)x - 5

Now we have the inequality in the desired form. The graph of y ≤ (5/2)x - 5 represents all the points below or on the line y = (5/2)x - 5.

To graph this inequality, follow these steps:

Step 1: Plot the y-intercept, which is -5. This point is (0, -5).

Step 2: Find a second point by using the slope (5/2). The slope is the ratio of the change in y to the change in x. Starting from the y-intercept, move up 5 units (numerator of the slope) and move right 2 units (denominator of the slope). This gives us the point (2, 0).

Step 3: Draw a solid line passing through the two points (0, -5) and (2, 0). This line represents the equation y = (5/2)x - 5.

Step 4: Since the inequality is "y ≤ (5/2)x - 5," we need to shade the region below the line (including the line itself) to represent all the points that satisfy the inequality.

The graph should resemble a downward-sloping line passing through the points (0, -5) and (2, 0), with the shaded region below the line.

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Answer:

1. An ordered pair in polar coordinates (r, θ) represents a point in the plane with a distance of r from the origin and an angle of θ with respect to the positive x-axis. When r < 0, this means that the point is located on the opposite side of the origin from the positive x-axis. In other words, the angle θ is shifted by 180 degrees.

2. In polar coordinates, a point can be represented by infinitely many ordered pairs because the distance r and the angle θ are not unique. For example, the point (1, π/4) and the point (1, 9π/4) both represent the same point in the plane.

3. The component form of a vector (a, b) represents the horizontal and vertical displacement of the vector from its initial point to its terminal point. The graph of a vector in standard position is a line segment from the origin to its terminal point. The horizontal and vertical components of the vector correspond to the x- and y-coordinates of the terminal point, respectively.

4a. The velocity of the plane Vp relative to the air can be expressed as Vp = (450 cos(60°), 450 sin(60°)) - (30, 0) = (225 - 30, 389.71) = (195, 389.71) mph.

4b. The velocity of the wind V can be expressed as V = (-30, 0) mph.

4e. The true velocity of the plane vr can be expressed as vr = Vp + V = (195 - 30, 389.71) = (165, 389.71) mph. The true speed of the plane is the magnitude of the true velocity, which is approximately 414.7 mph.

Answer:

The answer is down below

Step-by-step explanation:

G={2,3,4}

W={1,5}

Total cards=1,2,3,4,5

let P(x) be G

Probability of X=G/Total

P(x)=3/5

P(not x)=2/5

X={2,3,4}

not X={1,5}

The required expression is 10000x[tex](1.1)^{t}[/tex]/(45 + 4t).

The expression representing the number of students serviced by the school system in the town of Emor, t years from 2000 is:

s(t) = 10000x[tex](1.1)^{t}[/tex]

And the expression representing the number of classrooms in the town of Emor, t years from 2000 is:

C(t) = 450 + 4t

The expression D (t) represents the average number of students per classroom in Emor's school system t years from 2000.

Then the average number of students per classroom can be computed by:

Average number of students/classroom = Number of students/Number of classrooms

D(t) = s(t)/c(t)

      = 10000x[tex](1.1)^{t}[/tex]/(45 + 4t)

Thus,

The formula = 10000x[tex](1.1)^{t}[/tex]/(45 + 4t).

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Step-by-step explanation:

One complete revolution is one circumference

circumference of a circle is found using the formula  circumf = pi * d

so    308 m = pi * d   or

                  308 m / pi = diameter = 98 m   (a VERY large bicycle wheel!)

Answer:  A. 32

Step-by-step explanation:

Rule:  That if an angle is created on the end of circle The arc that it creates is 2 times the angle.

arc AX = 2 (<B)

arc AX = 2(56)

arc AX = 112

Rule:  The angle of 2 secants = 1/2 (outer arc - inner arc)

<C =  1/2 (arc AB - arc AX)

<C = 1/2 ( 176 - 112)

<C = 1/2 (64)

<C = 32     >A

From the calculation and based on the Least common multiples, , we can tell that Maria del Carmen has a total of 36 stickers

The least common multiple is of a set of numbers is the least multiple that they have in common and is obtained by decomposing each number into prime factors and taking common and uncommon factors with their greatest exponent.

Then we break down each number to know how much is the minimum that Maria del Carmen has:

2 = 2

4 = 2*2 = 2²

6 = 2*3

9 = 3*3 = 3²

12 = 2*2*3 = 2²*3

18 = 2*3*3 = 2*3²

LCM = 2²*3² = 4*9 = 36

Now this number is between 30 and 50: so Maria del Carmen has 36 stickers

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Full Qustion:

Maria del carmen colecciona cromos de animales;tiene mas de 30 y menos de 50.los quiere organizar en un album de manera q en cada pagina guarde el mismo numero de cromos.si puede ubicar 2,4,6,9,12 o 18 cromos en cada pagina ¿cuantos cromos tiene maria del carmen?

Translation:
Maria del Carmen collects animal stickers; she has more than 30 and less than 50. She wants to organize them in an album so that on each page she keeps the same number of stickers. If she can locate 2,4,6,9,12 or 18 Stickers on each page. How many stickers does Maria del Carmen have?

Answer:

Corresponding angles is the answer to your question

The equation of line is y = -x - 9 which passes through the point Z(-4,-5)

Given data ,

To graph the line with a slope of -1 passing through the point (-4, -5), we can use the point-slope form of a linear equation:

Now , the value of A is

Let the line passes through the point P ( -4 , -5 )

The slope which is the rate of change is is m=-1

y-y₁ = m(x-x₁)

On simplifying , we get

y-(-5) = (-1)(x+4)

Expanding the brackets:

y + 5 = -x - 4

y = -x - 9

Now we have the equation in slope-intercept form. To graph the line, we can plot the given point (-4, -5) and use the slope to find additional points.

Hence , the equation of line is y = -x + 1

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P(z<2.04) is approximately 0.9793 or 97.93% (rounded to two decimal places).

We can use a table or a calculator that offers the cumulative distribution function (CDF) of the standard normal distribution to determine the area under the standard normal curve below a specified value of z.

The chance that a standard normal random variable is less than or equal to a specified value is provided by the CDF.

In this case, we want to find the value of P(z<2.04), which represents the probability that a standard normal random variable is less than 2.04. Using a table or a calculator, we can look up the value of the CDF at z = 2.04, which is approximately 0.9793.

Therefore, we can say that the value of P(z<2.04) is approximately 0.9793, or about 97.93% (rounded to two decimal places).

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The additional reason will be JK/PQ = KL/QR.

Option C is correct.

Given that are two triangles, ΔJKL and ΔPQR, where ∠K ≅ ∠Q, we need to determine a reason to show ΔJKL and ΔPQR are similar,

So, we know that the similar triangles have congruent corresponding angles and corresponding sides are in equal ratio,

So, from the options if we take JK/PQ = KL/QR we can prove that the triangles are similar by SAS rule.

Hence the option C is correct.

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The expressions that are equivalent to the one below  is [tex]2 ^{(5+x) }[/tex], option C.

Based on the definition of power multiplication properties, The Product of Powers Property serves as one that stressed that in a cae wehereby we are multiplying two exponents with the same base, then the exponents  can be multiplied and keep the base.

It shoud be noted that when  want to simplify the expressions [tex]2x^4[/tex]by [tex]6x2[/tex] , the base wil will be kept whereby  we add the exponent.

The given expression is [tex]2^5.2^x[/tex], which can be simplified as;

= [tex]2^5.2^x[/tex]

=[tex]2 ^{(5+x) }[/tex]

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Answer:

  2a. maximum: (1, 8); minimum: (3, 0)

  2b. point of inflection: (2, 4)

  3.  a = 1/4

Step-by-step explanation:

You want the extrema and the point of inflection of f(x) = 2x³ -12x² +18x, and you want the value of 'a' that makes the end behavior a horizontal asymptote at y = 1.

The cubic function f(x) = 2x³ -12x² +18x has derivative ...

  f'(x) = 6x² -24x +18 = 6(x² -4x +3) = 6(x -1)(x -3)

The derivative will be zero at x = 1 and 3. These are the x-coordinates of the extrema of f(x).

The values of f(x) at those points are ...

  f(x) = 2x((x -6)x +9)

  f(1) = 2·1((1 -6)1 +9) = 2(-5 +9) = 8

  f(3) = 2·3(3 -6)·3 +9 = 6(-9 +9) = 0

The leading coefficient is positive, so the leftmost portion of the curve is increasing. The maximum will be at the leftmost turning point. The minimum is the other one (rightmost).

The maximum is (1, 8); the minimum is (3, 0).

The point of inflection is the midpoint between the extrema of a cubic:

  ((1, 8) +(3, 0))/2 = (2, 4) . . . . point of inflection

You want the limit as x → -∞ of ((x -2)(3x² +5) -4ax³)/(8ax³ +5x -1) to be 1.

The ratio of leading terms of the numerator and denominator is ...

  (3 -4a)x³/(8ax³) = 1

This requires ...

  3 -4a = 8a   ⇒   3 = 12a   ⇒   a = 1/4

The value of 'a' that makes the limit be 1 is 1/4.

__

Additional comments

A cubic is symmetrical about its point of inflection, so the point of inflection will be equidistant from the extrema, their midpoint. When the leading coefficient is positive, the function is increasing everywhere except between the local extrema. (The first attachment has a graph of the derivative, for reference.)

The end behavior of a rational function of equal numerator and denominator degree is the ratio of the leading coefficients.

<95141404393>

Answer:

  C.  18/48 and 21/56

Step-by-step explanation:

You want to identify pairs of ratios that are proportional.

Ratios are proportional when they have the same value. We can check whether the values are the same by reducing each ratio to lowest terms.

The attached calculator display shows the proportional ratios are ...

  18/48 and 21/56 . . . . choice C

__

Additional comment

Both of these reduce to 3/8. You can remove a factor of 6 from the numbers of the first ratio, and a factor of 7 from the numbers of the second ratio to reduce both of them to 3/8.

<95141404393>

Answer: C.  18/48 and 21/56

Step-by-step explanation:  Hope it helps

The product of [tex]2\frac{4}{5}[/tex] yards, 2 yards, and [tex]\frac{3}{5}[/tex] yards comes out to be [tex]16\frac{4}{5}[/tex] yards.

Firstly we have to convert the mixed fraction into the improper fraction.

1. We multiply the denominator and the whole number

2. To the product add the numerator to get the numerator of the fraction

3. The denominator remains the same.

[tex]2\frac{4}{5}[/tex] = 2 * 5 + 4 / 5 = 14/5

To multiply the fractions:

1. We multiply the numerators to get the numerator

2. Similarly the product of the denominator is the denominator

3. We simplify the resultant fraction

= 14/5 * 2 * 3/5 = 84/5

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Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

The coefficient of a²b² in the expansion of (2a - b)⁴ is 24

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

(2a - b)⁴

When the expression is expanded, we have

(2a-b)⁴ = (2a-b)(2a-b)(2a-b)(2a-b)

So, we have

(2a-b)⁴ = 16a⁴ - 32a³b + 24a²b² - 8ab³ +b⁴

Consider an expression ax where the variable is x

The coefficient of the variable in the expression is a

Using the above as a guide, we have the following:

The coefficient of a²b² in the expansion is 24

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Answer: the answer  of mab is 72 degrees.

Answer:

146°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc.

73° = (1/2)m(arc)AB

Multiply both sides by 2.

2 × 73° = 2 × (1/2) × m(arc)AB

m(arc)AB = 146°

If 0 < θ < [tex]360^0[/tex] and sin θ = 0.3097, then θ is approximately [tex]24^0[/tex].

In order to find the value of θ given sin(θ) = 0.3907, we can use the inverse sine function, also known as arcsine or [tex]sin^{(-1)[/tex].

Using a scientific calculator or trigonometric tables, we can find the inverse sine of 0.3907:

θ= sin^(-1)(0.3907)

θ ≈ 23.576 degrees

Since 0 < θ < 360 degrees, we can conclude that θ is approximately 24 degrees.

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The linear regression equation that best fits the data is y = 3.04x + 5.8.

Using a graphing calculator, we can plot the data points and find the linear regression model that best fits the data.

The linear regression equation that best fits the data is

y = 3.04x + 5.8.

Therefore, the answer is: y=3.04x+5.8.

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Answer:

The North American Free Trade Agreement (NAFTA) among the United States, Canada and Mexico went into effect on January 1, 1994. It is the first trade agreement the United States has entered into with a geographically-close developing country and has raised concerns about its economic effect, particularly on U.S. communities and workers. Since the mid-1980s, when Mexico began reducing trade restrictions, the U.S. and Mexican economies have become more highly integrated. This is evidenced by the rapid growth in U.S. merchandise trade with Mexico, which is now 12% of all U.S. trade

Step-by-step explanation:

The value of the expression "A- 2--0.5x47" is 25.5.

Using the order of operations (PEMDAS) we first simplify the multiplication before subtracting from 2:

2 - (-0.5 x 47)

= 2 - (-23.5)

When subtracting a negative number, we can think of it as adding the positive value. Therefore, we can rewrite the expression as:

2 + 23.5

= 25.5

Therefore, the value of the expression "A- 2--0.5x47" is 25.5.

In conclusion, to determine whether a given value is a solution to an equation, we need to know what the equation is. However, given an expression, we can simplify it and then substitute a value for the variable to determine whether it is a solution.

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Question

which value is a solution  A- 2-( -0.5x47)

The amount of paint needed to cover the walls of a room, you can use the area of the walls to estimate the amount of paint required.

The area of a two-dimensional shape is the amount of space inside its boundaries, while the perimeter is the length of its outer edge.

These concepts are often related, as the perimeter of a shape can be used to calculate its area.
For example, consider a square with sides of length 5cm.

The perimeter of the square would be 4 x 5cm = 20cm, while the area would be 5cm x 5cm = 25cm².

We can see that the area is greater than the perimeter, as there is more space inside the square than around its edges.
Another way that area and perimeter can be related is through similar shapes. Similar shapes have the same shape, but different sizes.

For example, a small square and a large square are similar shapes, but the large square has longer sides and therefore a larger area and perimeter.

The ratio of the areas of two similar shapes is equal to the square of the ratio of their corresponding side lengths.

Similarly, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Understanding the relationship between area and perimeter can be helpful in a variety of situations.

For example, if you need to calculate the amount of fencing needed to enclose a rectangular garden, you can use the perimeter of the garden to determine the length of the fencing required.
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Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

We have,

Let's start by setting up an equation to represent the situation:

Profit = Revenue - Cost

We know that Peter's profit is $49, and we can find the revenue by multiplying the number of hours by the hourly rate:

Revenue = Hourly rate x Number of hours

The hourly rate is $4, and the cost includes the initial fee of $25 plus the hourly cost:

Cost = Initial fee + Hourly rate x Number of hours

Now we can substitute these equations into the profit equation and solve for the number of hours:

$49 = ($4 x Number of hours) - ($25 + $4 x Number of hours)

$49 = $4 x Number of hours - $25 - $4 x Number of hours

$49 + $25 = $4 x Number of hours - $4 x Number of hours

$74 = $4 x Number of hours

Number of hours = $74 / $4

Number of hours = 18.5

Thus,

Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

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Answer:

Area of circle = pi×r²

Where, pi =22/7 or 3.142

r = 8cm

Area =22/7 × 8²

=201.142

Approximately 201 to the nearest whole number

You're welcome

Answer:

C) F(n) = 10n-1

Step-by-step explanation:

C) F(n) = 10n-1

Try a few points

F(n) = 10n-1

= 10(20) - 1

= 200-1

= 199 >>> which matches the table

F(n) = 10n-1

= 10(5) - 1

= 50-1

= 49 >>> which matches the table

F(n) = 10n-1

= 10(1) - 1

= 10-1

= 9 >>> which matches the table

The requried domain and range of the given graph are a set of all real values i.e. (-∞, ∞).

Consider the given figure,
The domain is said to be the values of the set of dependent variables, in the given case the value on the x-axis, represents the domain.
The domain is given as all real value i.e. (-∞, ∞)

Similarly, the range is represented by the y-axis and given as (-∞, ∞).

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