Shaggy,Velma, and Fred are camping in the woods.They each have their own tent and the tents are set up in a triangle.Shaggy and Velma are 20 meters apaart.The angle formed at Shaggy is 30 degrees and the angle formed at fred is 105 degrees.How far apart are Velma and Fred?

Answer:

x = 8

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact A is 90°

then Δ ABP is right at A

using Pythagoras' identity in the right triangle

BP² = AP² + AB² , that is

(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL

x² + 18x + 81 = x² + 225 ( subtract x² from both sides )

18x + 81 = 225 ( subtract 81 from both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Answer:

(v+8) x (v+9)

We can multiply v into the other two terms in the second bracket, then we can do the same with 8.

(v*v + v*9) + (8*v + 8*9)

v² + 9v + 8v + 72

v² + 17v + 72.

To simplify this expression, we can use the rule of exponents that states when dividing two powers with the same base, we can subtract their exponents. Therefore:

6^8/6^4 = 6^(8-4) = 6^4

So the expression 6^8/6^4 can be simplified as a single power of 6, which is 6^4.

(a) We can rewrite 32 as 2^5, so we have:

8^(2x) = (2^5)^(x+3)

Simplifying the right side, we get:

8^(2x) = 2^(5x+15)

(b) Now we can use the fact that 8 is 2^3, so we can rewrite the left side as (2^3)^(2x) = 2^(6x), giving us:

2^(6x) = 2^(5x+15)

Since the bases are equal, we can equate the exponents and solve for x:

6x = 5x + 15

x = 15

Therefore, the solution is x = 15.

The answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D, and segment AB is parallel to segment CD are;

A. Parallelogram

B. Quadrilateral

C. Rectangle

D. Rhombus

E. Square

In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.

In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).

In conclusion, a square, parallelogram, rectangle, rhombus, and quadrilateral satisfies the given conditions.

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Answer:

Step-by-step explanation:

Answer:

6 + y

Step-by-step explanation:

By BODMAS rule,

1st : Multiply

Then add,

2 + 2 x 2 + y

2 + (2 x 2) + y

= 2 + 4 + y

= 6 + y

Answer:

X = 3,2

Step-by-step explanation:

1)Expand.

[tex]x^{2}[/tex] - 8X+3X - 24 = -30

2)Simplify [tex]x^{2}[/tex]-8X+3X-24 to [tex]x^{2}[/tex]-5X - 24.

[tex]x^{2}[/tex] – 5X – 24 = –30

3)Move all terms to one side.

[tex]x^{2}[/tex] - 5X - 24+ 30 = 0

4)Simplify [tex]x^{2}[/tex]–5X-24+30 to [tex]x^{2}[/tex] - 5X + 6.

[tex]x^{2}[/tex] - 5X + 6 = 0

5)Factor [tex]x^{2}[/tex]–5X+6.

(X-3)(X-2) = 0

6)Solve for X.

X = 3,2

The function [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex] represents the same relationship.

Here given a function f(x)

When x= 0,1,2,3,4 the value of f(x) will be 648,216,72,24,8 respectively.

The function that represents the same relationship as the table is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

We can see that each successive value of f(x) is one-third of the previous value. So, we know that the function is of the form [tex]f(x) = a { (\frac{1}{3} )}^{x} [/tex] for some constant a.

To find the value of a, we can use the fact that f(0) = 648.

Substituting x = 0 into the equation gives f(0) = a(1/3)⁰ = a = 648

So, the function is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

Therefore, the correct answer is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

So, option D is the correct option.

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The probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

To find the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday, we need to multiply the probabilities of these two events occurring.

The probability of selecting a gold short sleeve top on Monday is 2/6, or 1/3. There are 2 gold short sleeve tops out of a total of 6 uniforms.

After selecting a gold short sleeve top on Monday and not replacing it, there are 5 uniforms left, of which 2 are red short sleeve tanks. Therefore, the probability of selecting a red short sleeve tank on Tuesday is 2/5.

To find the probability of both events occurring, we multiply the probabilities together:

(1/3) * (2/5) = 2/15

Therefore, the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

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Output z obtained as: multiply w with 5 and then subtract 3 from the result: w --> *5 ---> -3 ---> z.

There are only one or two variables in a linear equation.

The given expression is:

z = 5w-3

Here:

Input value : 5w-3

Output value : z

So,

Output z obtained as:

multiply w with 5 and then subtract 3 from the result:

w --> *5 ---> -3 ---> z

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The approximate value of K of the given quadratic equation is: 16.842

The general expression of a quadratic function is:

ax² + bx + c = 0

The quadratic formula to find the roots is expressed as:

x = [-b ± √(b² - 4ac)]/2a

The product of the 2 roots of the quadratic equation is equal to the constant term.

Let a and b be used to denote the roots of a given quadratic equation.

But according to given condition, one root is equal to the square of the other root. Thus: b = a²

Thus:

a + a² = k

a * a² = 48

a³ = 48

a = 2∛6

Thus:

2∛6 + (2∛6)² = k

k = 16.842

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Answer:

B) a 180° rotation about the origin

Step-by-step explanation:

Answer:simpler interest is 109.92.  Annual compounded interest is 111.98

Step-by-step explanation:

Answer: $209.2

Step-by-step explanation:
hey! i'm gonna try to make this as simple as possible;
with simple interest, the formula to this is I = PRT (Interest = Principle x Rate x Time).
we're going to take the $89 , 4.7% simple interest and the 5 years together into the same sentence like the formula.
89 (Principle, the money) x 4.7% (Interest rate)  x 5 (Time). we'll narrow down the decimal by moving the decimal forward once so we get a decimal of .47 / 0.47.
back to the equation, it is now 89 x .47 x 5. multiply all those and you'll get a sum of 209.15! by the end of the five years, patricia will have $209.15. to the nearest penny, she will have $209.2. (5 or more, it goes to the next number. 4 or less, it stays in the same place.)
hope this helped :)

Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants

If Ruby needs 2 cups of sugar to make 45 cupcakes, then we can calculate how much sugar she needs for one cupcake by dividing 2 cups of sugar by 45 cupcakes:

2 cups of sugar / 45 cupcakes = 0.0444 cups of sugar per cupcake (rounded to 4 decimal places)

To make 45 cupcakes, Ruby would need:

45 cupcakes x 0.0444 cups of sugar per cupcake = 1.998 cups of sugar (rounded to 3 decimal places)

Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants (3 cups of sugar > 1.998 cups of sugar needed for 45 cupcakes).

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Ruby wants to make 45 cupcakes.

Use your answer to b) to work out fi she has enough sugar left.

Ruby needs 2 cups of sugar to make 45 cupcakes, and she has 3 cups of sugar left.

When AB = AC and A is nonsingular, then the cancellation law holds; is, B = C. The statement is true.

In matrix algebra, the cancellation law is a crucial property to know. It states that if AB = AC, then B = C when A is a nonsingular matrix.

The given statement is true, which means that if AB = AC and A are nonsingular, then B = C. The cancellation law in matrix algebra is a property that helps in solving linear equations involving matrices. It states that if AB = AC and A is a nonsingular matrix, then B = C.

Therefore, we can say that if AB = AC and A is nonsingular, then B = C is true.

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The inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).

In mathematics, an inequality is a statement that compares two values, expressing that one value is greater than, less than, or equal to the other. It is represented by symbols such as <, >, ≤, ≥, and ≠. For example, 5 > 3 is an inequality that means "5 is greater than 3", while 2x + 3 ≤ 7x - 2 is an inequality that means "the sum of 2 times x and 3 is less than or equal to 7 times x minus 2". Inequalities are commonly used in algebra, geometry, and real analysis to express relationships between quantities and to find solutions to equations and systems of equations.

To determine the inequality shown by the graph with coordinates (0,8) and (0, 3.25), we need to find the slope-intercept form of the equation for the line passing through these points.

The slope of the line is:

(y2 - y1) / (x2 - x1) = (3.25 - 8) / (0 - 0) = -4.75 / 0 (which is undefined)

Since the line is vertical, its equation is x = 0.

Substituting this into the inequality options, we can see that only option C results in a true statement:

A) 4y+3x≤8x+6y+16 -> 4(8) + 3(0) ≤ 8(0) + 6(8) + 16 -> 32 ≤ 64 (not true)

C) 4y+3x≤8x+2y+16 -> 4(8) + 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)

B) 4y-3x≤5x+2y+16 -> 4(8) - 3(0) ≤ 5(0) + 2(8) + 16 -> 32 ≤ 32 (true)

D) 4y-3x≤8x+2y+16 -> 4(8) - 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)

Therefore, the inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).

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I'm sorry, but I don't see a question or any context for your statement. Could you please provide more information or clarify your request?

The appropriate z-value to use in the situation given in the question is 1.28.

Given,Total number of adults in the sample = 2092

Number of adults using the internet = 1318

Number of internet users who expect businesses to have websites that give product information = 1041

Probability of internet users who expect businesses to have websites that give product information as per the teacher's statement = 80% = 0.8

To find the appropriate z-value to use in this situation, we need to calculate the standard error of proportion, which is given by:

SEp = √[p(1-p)/n]

where p is the proportion of internet users who expect businesses to have websites that give product information and n is the sample size.

Substituting the given values in the formula,

SEp = √[(1041/1318)(1-1041/1318)/1318]SEp = 0.019

z-value is given by:

z = (p - P)/SEp

where P is the proportion of internet users who expect businesses to have websites that give product information as per the teacher's statement.

Substituting the given values in the formula,

z = (0.8 - 1041/1318)/0.019

z = - 1.28

The appropriate z-value to use in this situation is -1.28.

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Answer:

70

Step-by-step explanation:

Ill give it to you if you really need it its gonna take a while to explain

:)

Answer:

Step-by-step explanation:

Any value of x may be substituted into this function. So the domain is:

          [tex]D=(-\infty , \infty)[/tex]   or   D=all real [tex]x[/tex]

I am not sure the format how you have been taught to write the answer.

The value of x in the given similar triangles is 30.8.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose forms are similar to one another.

Given that the triangles are similar, thus the ratio of their sides are equal.

Here, 28/10 = x / 11

Using cross multiplication we have:

x = 28 / 10 (11)

x = 30.8

Hence, the value of x in the given similar triangles is 30.8.

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The equation of the polynomial using finite difference is y = 18x^3 - 126x^2 + 269x - 163 and other solutions are shown below

To find the equation of the polynomial table using finite difference, we need to calculate the differences.

The differences are obtained by subtracting each value of y from the next value of y and this is repeated for the differences

So, we have

x   1   2   3   4   5

y  -2  15  -4  49  282

1st 17 -19  53 233

2nd -36 72 180

3rd 108 108

Since the third differences are all the same, this indicates that the original data can be represented by a cubic polynomial.

We can use the formula for a cubic polynomial:

y = ax^3 + bx^2 + cx + d

Using the table of values, we have:

a + b + c + d = -2

8a + 4b + 2c + d = 15

27a + 9b + 3c + d = -4

64a + 16b + 4c + d = 49

Using a graphing calculator, we have

a = 18, b = -126, c = 269 and d = -163

So, we have

y = 18x^3 - 126x^2 + 269x - 163

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 3)(x + 1)(x - 2)

At (0, -12), we have

a(0 + 3)(0 + 1)(0 - 2) = -12

a = 2

So, we have

y = 2(x + 3)(x + 1)(x - 2)

Expand

y = 2x^3 + 4x^2 - 10x - 12

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 10)(x + 5)(x - 4)

At (-8, -2), we have

a(-8 + 10)(-8 + 5)(-8 - 4) = -2

a = -1/36

So, we have

y = -1/36(x + 10)(x + 5)(x - 4)

Expand

[tex]y = -\frac{x^3}{36}-\frac{11x^2}{36}+\frac{10x}{36}+\frac{200}{36}[/tex]

We have

g(x) = -9x^5 + 3x^4 + x^2 - 7

g(x) is a polynomial function of odd degree (5), so it will have at least one real root.

Also, the leading coefficient is negative;

So, g(x) has at least one root in the interval (-∞, ∞).

Since g(0) = -7 < 0 and g(1) = -12 < 0, and g(x) is continuous, there exists a root of g(x) in the interval (0, 1).

Similarly, since g(-1) = 6 > 0 and g(-2) = 333 > 0, there exists a root of g(x) in the interval (-2, -1).

Since g(x) is a polynomial of odd degree, it cannot have an even number of real roots.

Therefore, g(x) has exactly one real root.

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The trip to the campsite took 2 hours for Sami.

The total time taken by Sami on his journey = 7 hours

Let the time taken by Sami while going from his house to the campsite be 'x' hours

And, the time taken by Sami while coming back from the campsite to his house be 'y' hours

Speed while going from house to campsite = 60 miles per hour

Speed while coming back from campsite to house = 40 miles per hour

Distance from house to campsite and back will be equal as Sami will take the same route.

Let the distance be 'd'.

So, according to the question,
Distance = Speed × Time

We know that,
Time taken while going from house to campsite + Time taken while coming back from campsite = 7 hours

x + y = 7 ...(1)

Distance while going from house to campsite = Distance while coming back from campsited  = 2d ...(2)

Distance = Speed × Timex = d/60 ...(3)

y = d/40 ...(4)

Substituting (2), (3) and (4) in (1), we get,

d/60 + d/40 = 7

Solving the equation, we get d = 120

Therefore, Time taken while going from house to campsite, x = d/60 = 2 hours

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The value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

Angles are measurements created by joining two lines, also known as the vertex. Geometric forms such as triangles but also rectangles contain internal angles produced by their sides.

Using the angle bisector theorem in the given triangles:

The ratios of the sides will be equal.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, the value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

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The area of the sector with a central angle of 180° and a diameter of 5.6 cm is approximately 11.8 [tex]cm^2[/tex].

To find the area of a sector, we need to know the central angle and the radius or diameter of the circle that the sector is a part of. In this case, we are given a central angle of 180° and a diameter of 5.6 cm.

Find the radius of the circle is the first step. We can do this by dividing the diameter by 2:

radius = diameter/2 = 5.6/2 = 2.8 cm

Next, we can use the formula for the area of a sector:

Area of sector = (central angle/360°) x π x [tex]radius^2[/tex]

Plugging in the given values, we get:

Area of sector = [tex](180/360) * \pi * (2.8)^2[/tex]

= [tex](1/2) * 3.14 * 2.8^2[/tex]

= [tex]11.77 cm^2[/tex]

Rounding to the nearest tenth, we get:

Area of sector ≈ 11.8 [tex]cm^2[/tex]

Therefore, the area of the sector is approximately 11.8 [tex]cm^2[/tex].

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Statement to match the given number sentence is The absolute value of -5 is equal to the absolute value of 5.

It is the distance of a number from zero on a number line, and is always positive.

The absolute value of -5 is 5 because -5 is 5 units away from zero on the number line.

Similarly, the absolute value of 5 is 5 because 5 is also 5 units away from zero on the number line.

Therefore, the absolute value of -5 is equal to the absolute value of 5, and the statement for this number sentence is "The absolute value of -5 is equal to the absolute value of 5."

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Answer:

36

Step-by-step explanation: