Question 3
B
16 cm
38°
-C
Calculate the length of AB to 2 decimal places.

Answer:

C. 31.64

Step-by-step explanation:

23 = sin(36) × Hypotenuse

Hypotenuse is the baseline between the angles 36° and 54°.

Hypotenuse = 23/sin(36)

x = cos(36) × Hypotenuse

x = cos(36) × 23/sin(36) = cos(36)/sin(36) × 23 =

= 1/tan(36) × 23 = 23/tan(36) = 31.63686382... ≈

≈ 31.64

The approximate value of x in the diagram is,

⇒ x = 31.5

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now, We can formulate;

⇒ tan 36° = 23 / x

⇒ 0.73 = 23/x

⇒ x = 23 / 0.73

⇒ x = 31.5

Thus, The approximate value of x in the diagram is,

⇒ x = 31.5

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The equation of the transformed function is y = 1/2(x - 4)^3 + 5

The parent function is given as:

y = x^3

When the function is vertically compressed by 1/2, the rule is:

(x, y) ⇒ (x, 1/2y)

So, we have

y = 1/2x^3

When translated 4 units right, we have:

y = 1/2(x - 4)^3

When translated 5 units up, we have:

y = 1/2(x - 4)^3 + 5

Hence, the equation of the transformed function is y = 1/2(x - 4)^3 + 5

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The true statement about the set include:

If set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three, then the set X consists of such triples {ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE}.

The set X totally contains 10 elements.

There are three ways to form a group if persons A and C must be in it. This statement is true and these groups are ABC, ACD, ACE.

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Answer:

[tex]\frac{2 \: + \: 3 \sqrt{5} }{3} [/tex]

Step-by-step explanation:

[tex] \frac{2}{3} + \sqrt{5} = [/tex]

[tex] = \frac{2}{3} + ( \sqrt{5} \times \frac{3}{3} )[/tex]

[tex]= \frac{2}{3} + \frac{3 \sqrt{5} }{3} [/tex]

[tex]= \frac{2 \: + \: 3 \sqrt{5} }{3} [/tex]

The Domain and Range of tan(x) are mathematically given as

Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]

Range: all Real numbers

All real numbers are in the domain of the function "y=tan (x)," with the exception of the value "[tex]\pi/2+\pi n[/tex]" for all integers n, which is the case when cos(x) = 0.

It follows that "[tex]\frac{-3 \pi }{2}[/tex]" is not in the domain of "tan (x)" among the possible values.

In conclusion,

Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]

Range: all Real numbers

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Answer:

x = 9 & y = 29

Step-by-step explanation:

Since we know that 7x is next to 117, that area will be equal to 180*,

7x + 117 = 180

7x = 180-117

7x=63

x=9

to find y, you can use the same method, just by finding the other angle inside. 53+7(9) + z = 180

53+63 = 180

116+z = 180

z = 180-116

z = 64.

Then we do

4y + 64 = 180

4y = 180-64

4y=116

y = 29

Answer:

The ratio of the widths is 3:16, the ratio of the volumes is 27:4096, and the ratio of the surface areas is 9:256.

Step-by-step explanation:

In Geometry, you'll learn that when the scale factor of similar figures is a:b, then the ratio of the perimeter is a:b, the ratio of the area is a*a:b*b and the ratio of volume is a*a*a:b*b*b.

The resulting function after all transformations have been carried out is; 4log7(x+5) + 2.

The transformations which ensued on the function given are as follows;

Stretched vertically by a factor of 4; Hence, we have; 4f(x) = 4log7(x).

Shifted to the left by 5 units; 4f(x) = 4log7(x +5).

Shifted down by 2 units; 4f(x) +2 = 4log7(x+5) + 2.

On this note, it follows that the resulting function upon all the Transformations is; = 4log7(x+5) + 2.

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Answer:

B. )The graph of g(x) is a translation of the graph of f(x) right 6 units.

Step-by-step explanation:

When a positive number is directly added to an "x" variable (usually inside of parentheses), the graph is shifted to the left that many units.

When a negative number is directly added to an "x" variable, the graph is shifted to the right that many units.

A graph shifts up or down when a positive or negative number is added to the overall function. For example, if the -6 were outside of the parentheses, the graph would be translated 6 units downwards.

Answer:

• The function f is increasing to the left of -4 (-∞ , -4]

• The function f is decreasing to the right  of -4 [-4 , +∞)

Step-by-step explanation:

f(x) = -(x+6)(x+2)

     = -(x² + 2x + 6x + 12)

     = -(x² + 8x + 12)

     = -x² - 8x - 12

The leading coefficient is -1 (the coefficient of the highest term -x² of the trinomial)

Then

The parabola opens downward.

………………………………………

[tex]-\frac{b}{2a} =-\frac{-8}{2\times \left( -1\right) } =-4[/tex]

Then

The function f is increasing to the left of -4 (-∞ , -4]

The function f is decreasing to the right  of -4 [-4 , +∞)

$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the amount of fund at 10% and y represent the amount of fund at 7% interest, hence:

x + y = 160000   (1)

Also:

0.1x + 0.07y = 13750    (2)

From both equations:

x = 85000 and y = 75000

$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.

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Answer:

The answer is $0.36

Step-by-step explanation:

The equivalent expression to the given logarithm without tables is [tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]. Option A is correct.

Equivalent expressions are expressions that differ in appearance but when a value is being replaced for their unknown variable, gives an equivalent result.

From the given information:

[tex]\mathbf{(log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) )-log_{10} (6) }[/tex]

[tex]\mathbf{=log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) -log_{10} (6) }[/tex]

[tex]\mathbf{=log_{10}(9x)+ log_{10}(x^2+4) -log_{10} (6) }[/tex]

[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) }[/tex]

Apply log rule: [tex]\mathbf{log_a(x)-log_a(y) =log_a(\dfrac{x}{y})}[/tex]

[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]

[tex]\mathbf{ =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]

[tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]

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The measure of AN form the given figure is 2. 5cm. Option D

It is important to note that if from one external point, two tangents are drawn to a circle then they have equal tangent segments.

We have that,

AM ≅ AN

so, if AM  measures 2. 5cm

AN measures 2. 5cm

Thus, the measure of AN form the given figure is 2. 5cm. Option D

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The approximate value of 63000 x 200 will be 12600000.

In mathematics, multiplication is defined as the sum of the numbers to the other number given. Like if 2 is multiplied by 3 then the multiplication will be the sum of the two-three times.

Given expression is 63000 x 200 so here we need to calculate the sum of the 63000 to 200 times.

E = 63000 x 200

E = 12600000

Therefore the approximate value of 63000 x 200 will be 12600000.

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The key features of the function g(x) = (x + 3)(x + 2)(x − 3) are; Maximum Point at g(x) = 6.065; Minimum Point at g(x) = -0.879; 2.593 is the point of inflection

1) The Fundamental Theorem of Algebra states that a polynomial of degree "n" has at most "n" number of complex roots.

Since Kelsey argues the function can have as many as three zeros only, then we can say that Kelsey is correct.

2) The g(x) function that I will choose is;

g(x) = (x + 3)(x + 2)(x − 3)

Expanding this gives us;

g(x) = x³ - x² - 4x + 4

To find the key features which are critical points (maximum, minimum, point of Inflection), we will differentiate g(x) with respect to x to get;

g'(x) = 3x² - 2x - 4 = 0  

Using quadratic formula gives;

x = 1.535  and  Minimum Point; x = -0.869

Thus;

g(1.535)  = -0.879  minimum point

g(-0.869) = 6.065  maximum point

Thus;

Maximum Point occurs at g(x) = 6.065

Minimum Point occurs at g(x) = -0.879

g"(x) = 6x -2

At g"(x) = 0, we will have the point of inflection which is at;

x = 1/3

g(1/3) = 2.593 which is the point of inflection

3) The graph of the Polynomial of the function g(x) = (x + 3)(x + 2)(x − 3) is as attached.

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Answer:

Could you please provide more context to the problem

Step-by-step explanation:

There is not much context provided for us on this problem, but you can set the decimal to a percentage: 18% of customers win a prize. Now to properly solve this question we need to know either the number of people or the percentage of kids and adults.

Answer:

If i did it correctly the answer should be 255 days

Step-by-step explanation:

please mark brainliest

Answer:

They will meet at 3:04 p.m

Step-by-step explanation:

Since they are walking towards each other , that means we should add their speed together:

speed = 1.35 m/s + 1.65 m/s
           = 3 m/s

Now that we have found the speed, we can calculate the time:

time = 720 meters / 3 m/s
       = 240 seconds
       = 4 minutes ( 240 seconds is 4 minutes)

Answer:

300

Step-by-step explanation:

A pyramid with a triangle-shaped base whose three triangular faces meet at the ap/ex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid volume formula calculates the base area and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter,, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula: 

Volume= 1/3 × Base area × Height

Answer:

[tex]y = -\frac{5}{2} x + 3[/tex]

Step-by-step explanation:

We are given that a line passes through (-2, 8) and has a slope of -5/2.

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

Since we are already given the slope of this line, we can immediately plug it into the equation.

Replace m with -5/2.

[tex]y = -\frac{5}{2} x+ b[/tex]

Now we need to find b.

As the equation passes through the point (-2, 8), we can use its values to help solve for b.

Substitute -2 as x and 8 as y.

[tex]8 = -\frac{5}{2} (-2) +b[/tex]

Multiply.

8 = 5 + b

Subtract 5 from both sides.

3 = b

Replace b with 3 in the equation.

[tex]y = -\frac{5}{2} x + 3[/tex]

Topic: finding the equation of the line (slope-intercept form)

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Answer:

The last one - 256 people

Answer:

so their are three kinds of breed 2 kinds of meet and 2 kinds of cheese here the list

roll, ham,swiss

roll, turkey,american

roll,ham,american

roll, turkey,swiss

bread, ham,swiss

bread, turkey,american

bread,ham,american

bread, turkey,swiss

wrap, ham,swiss

wrap, turkey,american

wrap,ham,american

wrap, turkey,swiss

Hope This Helps!!!

Answer:

10.4

Step-by-step explanation:

So an exponential equation with a decay can be expressed as: [tex]f(x)=a(1-r)^t[/tex] where r is the decay rate. In this case is decreasing at 4% each year, this means that the r is equal to 0.04 (divide the percent by 100 to convert to decimal). So the equation is going to be: [tex]f(x)=a(0.96)^t[/tex]. The reason this works is because whenever you decrease by x%, the new value is (1-x)%, which is expressed in the formula. But the reason the exponent is there is because after 1 year it's going to be 0.96a, but after two years, it's going to be 0.96 the previous year which is 0.96a, so after two years it's going to be 0.96(0.96a), and then the next year it's 0.96 of the second year, which is then 0.96(0.96(0.96a))... and so on. So the amount of 0.96 increases as t increases. the a is going to be the initial amount, since then t=0, 0.96^0 will be equal to 1, which makes the expression a(1), which is just a. So this gives you the complete equation: [tex]p(x)=13000(0.96)^t[/tex]

Now to find when it's equal to 8,500 you need to start by setting it equal to 8,500 so I'll work through each step

Original Equation:

[tex]p(x)=13000(0.96)^t[/tex]

Set the equation equal to 8,500

[tex]8500=13000(0.96)^t[/tex]

Divide both sides by 13,000

[tex]0.653846\approx 0.96^t[/tex]

Rewrite in logarithmic form

[tex]log_{0.96}0.653846=t[/tex]

If you're calculator allows you to enter the base when calculating log, but this expression into your calculator to calculate the value of t, otherwise use the change of base formula

[tex]\text{change of base formula: }log_ba = \frac{log(a)}{log(b)}[/tex]

[tex]t=\frac{log0.653846}{log0.96}\\[/tex]

[tex]t\approx\frac{-0.1845}{-0.0177}[/tex]

[tex]t\approx10.4[/tex]

Answer:

b

Step-by-step explanation:

I did it

The approximate direction angle of v is 326°

Definition of Direction Angle

A vector's direction angle is the angle formed by the positive x-axis and the vector v. The arctangent of the ratio between the vertical and horizontal components of the vector, v=xi+yj, can be used to determine the direction angle, θ.

What is the direction angle of v?

Let θ be the direction angle of v or the angle mad by v with the horizontal line.

It is given that,

[tex]v = < 3, -2 >[/tex]

We know that,

θ = tan⁻¹([tex]\frac{y}{x}[/tex])

Here, we have y = -2 and x = 3. Hence, we get,

∴ θ = tan⁻¹[tex](\frac{-2}{3})[/tex]

⇒θ = tan⁻¹(0.66)

Hence the direction angle of v = 360 - tan⁻¹(0.66)

≈ 326°

Thus, the approximate direction angle of v is 326°.

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Answer:

15x^2y+20xy^2+28xy-9x

Step-by-step explanation:

15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x ​

First distribute the -4 to all the terms in the parentheses

15x²y +8xy² + 36xy + 12xy² - 8xy - 9x ​

Now combine like terms

15x²y       +8xy²  + 12xy²      + 36xy - 8xy     - 9x ​

15x^2y+20xy^2+28xy-9x

The comparison and contrast between a square and an equilateral triangle are stated and explained below:

What is a square? A square is a plane shape with an equal length of sides. This implies that the measure of its length is the same as that of its breadth.

What is an equilateral triangle? A triangle is a plane shape with three sides, and a sum of its internal angles to equal [tex]180^{o}[/tex]. Thus an equilateral triangle is a type of triangle with equal lengths of sides, and therefore equal internal angles.

Comparison: i. The two shapes have equal lengths of sides.

ii. An equilateral triangle and a square are examples of plane shapes.

Contrast: i. An equilateral triangle has three sides, while a square has four sides.

ii. An equilateral triangle has three internal angles, while a square has four internal angles which are right angles.

iii. The sum of internal angles of an equilateral triangle is [tex]180^{o}[/tex], while that of a square is [tex]360^{o}[/tex].

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Kindly get 1-on-1 help from an expert tutor for more explanations if required.

Answer:

A square has degrees that add up to 360 but an equilateral triangle only adds up to 180

Step-by-step explanation: