HELP!!!!!!! LOTS OF POINTS

The two triangles ΔABC and ΔDEC are similar as the triangles follow the angle-angle axiom of similarity .

In the given triangles ΔABC and ΔDEC

In ΔABC

∠ABC = 21°

∠BAC = 36°

∠ACB = 180° - (36+21)°

or, ∠ACB = 180° - (57)° = 123°

In ΔDEC

∠CDE = 36°

∠DCE = 123°

∠CED = 21°

Therefore we can see that the two triangles are similar as all the angles are equal.

Hence the ΔABC and ΔDEC has 3 congruent angles by the angle sum property and the triangles are similar by angle-angle-angle axiom of similarity.

Two triangles are considered to be similar if their corresponding sides and angles match. Alternatively, comparable triangles may have the same shape but vary in size. The triangles are also congruent if the lengths of their respective sides are the same.

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The zeros, the polynomial x³-5x²+8x-6 are 3, (1-i) and (1+i) and factors are

(x-3)(x²-2x+2)

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

Given a polynomial (x³-5x²+8x-6)

x³-5x²+8x-6 = (x-3)(x²-2x+2)

(x²-2x+2) can't be factorized and will have imaginary roots,

Hence, The zeros, the polynomial x³-5x²+8x-6 are 3, (1-i) and (1+i) and factors are (x-3)(x²-2x+2)

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A student skipped the step  (1 minute / 60 seconds).

The time in seconds divided by 3,600 results in the time in hours.

Given:

A student skipped a step when he tried to convert 720 seconds into hours, and he got the following incorrect result;

720 seconds (1 hour / 60 minutes) = 12 hours.

In order to convert the seconds to hours:

First, we should convert the seconds to minutes.

And the rate of conversion is 1 minute per 60 seconds.

720 / 60 = 12 minutes.

Now, converting minutes to hours.

And the rate of conversion is 60 minutes per hour.

12/60 = 1/5 hours.

Therefore, student skipped the step where rate of conversion is (1 minute / 60 seconds).

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Answer:

  -6, 1

Step-by-step explanation:

You want the real roots of the quadratic x^2 + 5x = 6.

The roots are easily identified from the factored form of the equation. The factors will involve the constants that have a sum of +5 and a product of -6.

  -6 = 6·(-1) = 3·(-2)

Sums of the factor pairs are 5 and 1. We will use the constants that have a sum of 5.

  x^2 +5x = 6 . . . . . . given

  x^2 +5x -6 = 0 . . . . . standard form

  (x +6)(x -1) = 0 . . . . . . . factored form

The zero product rule tells us that a product will be zero if and only if at least one of the factors is zero. To find the values of x, we set the factors equal to zero and solve for x.

  (x +6) = 0   ⇒   x = -6

  (x -1) = 0   ⇒   x = 1

  x = -6, or x = 1 . . . . . . . . roots of the quadratic

The information in the word problem indicates that the initial total number of marbles that were given to the three of them at the beginning of the game was 40 marbles

A word problem consists of describing a situation as well as providing the necessary information to a question verbally that is to be solved by by calculations mathematically.

The initial number of marbles Brea had = 10

The number of marbles Brea had at the end = 0

Let A represent the number of marbles given to Abby, let B represent the number of marbles given to Brea and let C represent the number of marbles given to Cleo, we get;

The number of marbles Abby gave Brea and Cleo = B + C

The number of marbles Brea gave Abby and Cleo = (A - (B + C)) + 2·C

The number of marbles Brea gave Abby and Cleo = All her marbles = 2·B

Therefore;

20 = (A - (B + C)) + 2·C = (A - (10 + C)) + 2·C

20 = A - 10 + C

A + C = 20 + 10 = 30

A + B + C = A + 10 + C = A + C + 10 = 30 + 10 = 40

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The amount that Vince will be able to spend on the bike, given the amount deposited in the savings account, is $410. 29

The amount that Vince would have to spend on the bike is the future value of the amount he deposited in the savings account.

This future value is found by the formula:

= Amount deposited x ( 1 + rate) ^ number of years

= 300 x ( 1 + 11%) ³

= 300 x 1. 11 ³

= 300 x 1. 367631

= $410. 2893

= $410. 29

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If the system of equations, A·x + B·y = C and P·x + Q·y = R has infinitely many solutions, then the relationship between the values, A, B, C, P, Q, and R is; A/P = B/Q = C/R

A system of linear equations can have no solutions, only one solution or infinitely many solutions.

Part of the question that appear missing is presented as follows;

The system of equations in the question is;

If the system has infinitely many solutions, then the equations (1) and (2) represent the same equation, such that equation (1) can be obtained directly from equation (2) and vice versa

This indicates that equation (1) is a multiple of equation (2)

Let the common factor be c, we have;

A = c·P

B = c·Q

C = c·R

Which gives;

A/P = B/Q = C/R = c

The relationship between the coefficient is that; A/P = B/Q = C/R

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The smallest number of instances at which the acceleration of the plane could equal zero on the open interval 0 < c < 6 is t= 25 to t= 30.

By the mean value theorem, somewhere between t = 0 and t = 15 , v'(t) = 0, because v(15)-v(0)/15-0 = 0. Also somewhere between t=25 and t=30, v'(t) = 0, because v(30) - v(25) / 30 - 25 = 0. This means a(t) = 0 for at least two values of t.

f(t) = 6+cos(t/10)+3sin(7t/40)

a(t) = f'(t) = 1/10 sin (t/10) + 21/40 cos (7t/40)

f'(23) = -.408 miles/min²

Average Velocity = 5.916 miles per minute

Average Speed is characterized as the adjustment of position or displacement of the object (∆x) partitioned when the time interval (∆t) in which the displacement happens. The average speed can be a positive or negative sign on the indication of the displacement of the object.

The total distance that the plane flies in 40 min is 229 miles.

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Answer:

Step-by-step explanation:

As we see the two expressions are equal in value

Answer:

log3 1/3 = logb 1/b

(Both expressions are equal)

Step-by-step explanation:

Now we have to,

→ find the expression with greater value.

Then the greatest value is,

→ log3 1/3 = logb 1/b

→ log3 3^(-1) = logb b^(-1)

→ -1 = -1

→ [ LHS = RHS ]

Hence, both have same value.

Answer:

240?

Step-by-step explanation:

Answer:

24√2

Step-by-step explanation:

[tex]2 \sqrt{50} + 3 \sqrt{72} - \sqrt{32} [/tex]

[tex]2 \sqrt{25 \times 2} + 3 \sqrt{36 \times 2} - \sqrt{16 \times 2} [/tex]

[tex]2 \sqrt{25} \sqrt{2} + 3 \sqrt{36} \sqrt{2} - \sqrt{16} \sqrt{2} [/tex]

[tex]2(5 \sqrt{2} ) + 3(6 \sqrt{2} ) - 4 \sqrt{2} [/tex]

[tex]10 \sqrt{2} + 1 8\sqrt{2} - 4 \sqrt{2} [/tex]

[tex]24 \sqrt{2} [/tex]

Answer:

10%

Step-by-step explanation:

percent = part/whole × 100%

percent = 3/30 × 100%

percent = 0.1 × 100%

percent = 10%

Answer: 10%

Answer: 10%

Step-by-step explanation:

10% of 30 is the 30 divided by 10, which is 3

Answer:

Rs. 4000

Step-by-step explanation:

Profit = 80% = 180% of original price

Therefore, [tex]\frac{180}{100}x=7200\\ 180x=720000\\x=4000[/tex]

Answer:

9000

Step-by-step explanation:

80 percent *9000 =

(80:100)*9000 =

(80*9000):100 =

720000:100 = 7200

Answer:

That is a line. Here's two points that pass through the line:

Literally just graph a line that passes through those two points.

Answer:

40:60: 90

Step-by-step explanation:

interior angles of a triangle add up to 180 so...

2/9 * 180 = 40

(i got the 9 by adding the ratio)

Answer:

No

Step-by-step explanation:

listen to guy above he opened my eyes

Answer: \frac{2x^3-3x^2+5}{x-4}

Step-by-step explanation:

Answer: b

Step-by-step explanation:

It's a line, so the formula will be y = mx + b.

        [tex]-3=1(-7)+b\\7-3=b\\b=4[/tex]

So, the function would be y = x + 4. Plug the values of the coordinate in to find the missing value:

[tex]y=x+4=-1+4=3[/tex]

Answer:

Step-by-step explanation:

A*X = B

A=2x2 matrix

B= 2x1 matrix

X= 2x1 matrix of   [x1;x2]

1(x1) +3(x2) = 18

0(x1) + 1(x2) = 7

so you can probably see that x2 has to be 7, from that 2nd equation

1(x1) + 3(7) = 18

x1= -3

X = [ -3 ; 7 ]

does this make sense??

The correct option regarding the end behavior of p(x)=-9x^9+6x^6-3x^3+1 is given as follows:

B. As x -> -∞, f(x) -> ∞ and as x -> ∞, f(x) -> -∞.

The end behavior of a polynomial function is obtained by the limits of the function as x approaches infinity, meaning that only the term with the highest exponent is considered.

These limits are divided into two tails, as follows:

The function for this problem is defined as follows:

p(x)=-9x^9+6x^6-3x^3+1.

Hence the term with the highest exponent is:

-9x^9.

At the left tail of the graph, the end behavior is given as follows:

lim x -> -∞ f(x) =lim x -> -∞ -9x^9 = -9(-∞)^9 = -9 x (-∞) = ∞.

At the right tail of the graph, the end behavior is given as follows:

lim x -> ∞ f(x) =lim x -> ∞ -9x^9 = -9(∞)^9 = -9 x (∞) = -∞.

Hence option B is correct.

The problem is given by the image shown at the end of the answer.

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Answer:12 1/2

Step-by-step explanation:

Using the substitution method, the solution is: x = 31, y = -5.

To solve a system of equations by substitution, rewrite one of the equations in terms of one of the variables, then substitute its value into the other equation and solve.

Given the system:

x - 3y = 16 --> eqn. 1

4x - y = 9 ---> eqn. 2

Rewrite equation 1:

x = 16 + 3y

Substitute the value of x into eqn. 2:

4(16 + 3y) - y = 9

64 + 12y - y = 9

64 + 11y = 9

11y = 9 - 64

11y = -55

y = -5

Substitute the value of y into eqn. 1:

x - 3(-5) = 16

x + 15 = 16

x = 16 - 15

x = 1

The solution is: x = 1, y = -5

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The fourth option D is a function of the form of f(x) = ax(x-2)(x+2) where a is a constant.

We know that any function of the form y = f(x) will pass through the x axis at points such that there is only 1 value of x for a value of y.

Of all the options given the option D is in the form of polynomial expression which crosses the x-axis at points (-2,0 ) ,  (0,0) and (0,2).

The graph of the function at D will be of the form:

f(x) = ax(x-2)(x+2) a is a constant.

At y = 0 , x =-2 ,0 and 2.

Therefore for one value of y there are 3 values of x. but every value of x is mapped into one single value of y only.

For option A at x = 2 , y ahs two values -2 and 2 so it is not a function of x.

For option B  the graph is not differentiable at certain points, hence it is not a function.

For option C again y has 2 values for a single x.

The values of x are used to denote the roots and zeros of the expression, which are also on the left side of the equation, and to satisfy the equation. A quadratic problem should only have two possible solutions. One contends that if there is just one solution, the problem has numerous causes.

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To generate the overall equation A → 2C, should be B → 2C added to  

A → B gives the equation A + B → B + 2C.  

In mathematics, an equation is a method that expresses the equality of two expressions, by using connecting them with the equals signal =. The phrase equation and its cognates in other languages may also have subtly exclusive meanings; for example, in French, an equation is described as containing one or more variables, at the same time as in English, any nicely shaped formula together with expressions associated with an equal’s signal is an equation.

Solving an equation containing variables includes determining which values of the variables make the equality actual. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that satisfy the equality are referred to as solutions of the equation. Equations come in two varieties: identities and conditional equations. An identification is actual for all values of the variables. A conditional equation is handiest genuine for unique values of the variables.

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The height of the school is 8.5 m.

For a project in his Geometry class, Jacob uses a mirror on the ground to measure the height of his school building.

To find out how tall is the school:

An image is always formed at the back of a mirror. Thus, the appropriate option is -8.75 m. The flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

         = [tex]\frac{1.65}{1.7}[/tex]

Tan θ = 0.9706

θ = [tex]Tan^{-1} 0.9706[/tex]

 = [tex]44.2^{o}[/tex]

θ = [tex]44.2^{o}[/tex]

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

        = [tex]\frac{h}{8.75}[/tex]

0.9706 = [tex]\frac{h}{8.75}[/tex]

h = 0.9706 x 8.75

 = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m.

Hence the answer is the height of the school is 8.5 m.

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The table that represents g(x) is

x         g(x)

1           1

2          5

3          9

The correct option (4)

A function is defined as a relationship between a collection of inputs with one output each. In simple terms, a function is a relationship between inputs, with each input corresponding to exactly one output. Every function has a domain and a codomain or range. A function is commonly denoted by f(x), where x is the input.

From the given information, we have that

f(x) = 3x - 4 and

g(x) = f(2x)

Then,

g(x) = f(2x) becomes

g(x) = f(2x) = 3(2x) -4

g(x) = 6x - 4

Now, we'll plug x numbers ranging from 1 to 3 into the equation.

When x = 1

g(x) = 6x - 4 becomes

g(x) = 6(1) - 4

g(x) = 6 - 4

g(x) = 2

When x = 2

g(x) = 6x - 4 becomes

g(x) = 6(2) - 4

g(x) = 12 - 4

g(x) = 8

When x = 3

g(x) = 6x - 4 becomes

g(x) = 6(3) - 4

g(x) = 18 - 4

g(x) = 14

Hence, the table that represents g(x) is

x         g(x)

1          2

2          8

3          14

Therefore option (4) is correct.

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Each share of the tech company cost is $1 and 18 more shares can Josh buy with the remainder of his savings.

Given:

Josh spends of his savings to buy 48 4/5 shares in a cech company. He has $18 left.

Let x be the total savings

4/5 x = 48

x = 48*5/4

= 240/4

= $60

= 4/5*60

= 240/5

= $48.

Part A:

The cost of each share of the tech company = 48/48

= $1

Part B :

He has 18 so he can buy =18*1

= 18 shares .

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The probability that every even number appears at least once before the first occurrence of an odd is 1/20.

Given:

A fair 6-sided die is repeatedly rolled until an odd number appears.

There are 6! ways to order the 6 numbers and 3!(3!) ways to order the evens in the first three spots and the odds in the next three spots.

so the probability = 3!*3! / 6!

= 3!*3! / 6*5*4*3!

= 3*2*1 / 6*5*4

= 6*1 / 30*4

= 6/120

= 1/20

Therefore the probability that every even number appears at least once before the first occurrence of an odd is 1/20.

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If the Area= Length × Width

Then, The width of the rectangle is (x -1).

We know that area of rectangle is the number of unit square within the boundary of the rectangle.

The formula of area of rectangle is:

    Area = Length × width

⇒ Width = Length / Area

Given that,  

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = Width   ----------------- (1)

Let's simply the expression :

Note that: x=1 is a zero of the numerator since the sum of the coefficient is zero.

So, (x-1) is a factor:

Putting the values in equation (1)

(x⁴ +4x³ + 3x² -4x -4) = (x-1)  (x³ + 5x² + 8x + 4 )

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = (x-1)

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Answer:

D on Edge 23

Step-by-step explanation:

because i said so