Determining if the inverse is a function

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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Answer:

The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27 /125 of a volt and has been reduced 3 times.

Write the voltage in exponential form.

What was the original voltage in the circuit?

Step-by-step explanation:

voltage = v

v³ - exponential form

v³ = 27/125

make v³ a fraction so v³/1 then cross multiply

so... 125v³ = 27 then v³ = 27/125 or v³ = 0.216 if you like decimals better then to get v by it self you cube root mean v = ∛27/125

original voltage in circuit - v = ∛27/125

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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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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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??

Explanation:

In 1 month, 1.27cm grows.

So, multiply 1.27cm by 4 months to get 5.08cm

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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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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Answer:

x = 1/8

Step-by-step explanation:

divide the two from both both sides

1/4 = 2x

(1/4)/2 = x/2

1/8 = x

Answer: x = -2

Step-by-step explanation:

X is -2 because whenever you get a negative exponent you gotta make it into a fraction which is [tex]\frac{1}{4}[/tex] because I ignored the negative sign for a second and did it normally so 2 to the power of 2 is 4 put it as a fraction 1 over 4.

Normally it doesn’t happen to every problem you get. Most of the time you gotta divide the numerator by the denominator which will give you .25 in this case scenario, .25 converted to a fraction would be 1/4.

- Your Welcome.

Let's set "a number" to "x":

7*6 - x

This can be simplified to:

42 - x

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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Answer:108x10 to the 2nd power

Step-by-step explanation: Given, the diameter of the Sun is 1.4 × 10⁹ m. The diameter of the Earth is 1.2756 × 10⁷ m. We have to compare the diameters by division. Therefore, the diameter of the Sun is nearly 110 times the diameter of the Earth, So i would say 108x10 squared

That would be x+4=2x+3, so we must use substitution. Making x=1, hope that helps.

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)

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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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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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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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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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

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:

Math = 63

Step-by-step explanation:

Math = x

Eng = Math + 8

Geo = Math + 3

Math + Eng + Geo = 200

Substitute Eng and Geo with information above

Math + (Math + 8) + (Math + 3) = 200

3Math + 8 + 3 = 200

3Math + 11 = 200

3Math = 200 - 11

3Math = 189

Math = 189 ÷ 3

Math = 63

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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The probability that the mean number of hours spent playing video games is less than 42.8 hours  is   0.15866

we are  given the  mean of ( m )= 43 hours and the standard deviations (s) of  2 hours, where the sample size (n) =  100.

Obtain the Zscore ;

Z = (x - m) ÷s/sqrt(n)

Z = (42.8 - 43) ÷ 2/sqrt(100)

Z = - 0. 2 ÷ 0.2

Z = - 1

so we need the probability of P(Z < - 1), from the  table  of  z-score  the probability of a z-score of -1  is   0.15866.Hence, the probability that the mean number of hours spent playing video games is less than 42.8 hours is 0.15866

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Answer:

(i)15v=10r

Step-by-step explanation:

let no. of rice=r

let stir fry=s

let no. of veggies=v

6r=4v

then if,  v=15, r=?

if 6r=4v, then v=6/4r

v=2/3r,

1X v= 1X2/3 r

15 X v= 15X2/3r

25v=5X2r=10r

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

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:20%

Step-by-step explanation: Since 2% of x = 4, that would mean 1% would equal 2. So 2 times 100 equals 200, making 20 10% of 200

The price of one sweater is $15 and the price of one shirt is $10.

The first step is to form a set of linear equations using the information provided in the question:

s + 4p = $55 equation 1

4s + 5p = $110 equation 2

Where:

In order to determine the value of p, take the following steps:

Multiply equation 1 by 4

4s + 16p = 220 equation 3

Subtract equation 2 from equation 3:

11p = 110

Divide both sides of the equation by 11

p  = 110 / 11

p = 10

In order to determine the value of s, substitute for p in equation 1:

s + 4(10) = $55

s + 40 = 55

s = 55 - 40

s = 15

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