Completing the square........... (+25 points+!) Someone please help:)

Answer:

inverse = ( log(x+4) + log(4) ) / (2log(4)), or

c. y = ( log_4(x+4) + 1 ) / 2

Step-by-step explanation:

Find inverse of

y = 4^(-6x+5) / 4^(-8x+6)   - 4

Exchange x and y and solve for y.

1. exchange x, y

x = 4^(-6y+5) / 4^(-8y+6)   - 4

2. solve for y

x = 4^(-6y+5) / 4^(-8y+6)   - 4

transpose

x+4 = 4^(-6y+5) / 4^(-8y+6)

using the law of exponents

x+4 = 4^( (-6y+5) - (-8y+6) )

simplify

x+4 = 4^( 2y - 1 )

take log on both sides

log(x+4) = log(4^( 2y - 1 ))

apply power property of logarithm

log(x+4) = (2y-1) log(4)

Transpose

2y - 1  = log(x+4) / log(4)

transpose

2y = log(x+4) / log(4) + 1 = ( log(x+4) + log(4) ) / log(4)

y = ( log(x+4) + log(4) ) / (2log(4))

Note: if we take log to the base 4, then log_4(4) =1, which simplifies the answer to

y = ( log_4(x+4) + 1 ) / 2

which corresponds to the third answer.

Answer:

r=2

Step-by-step explanation:

y = k x^r  is the formula for a direct variation

y = k x^ -r is the formula for a indirect variation

20= 5 (1/2)^ -r

Divide each side by 5

4 = (1/2) ^ -r

Rewriting

2^2 = 2^ -1 ^ -r

2^2 = 2 ^ r

The bases are the same so

2 =r

Answer:

r=-2

Step-by-step explanation:

because i had this questiion and i got it right

Answer:

210

Step-by-step explanation:

Given:

Medals in sports = 40

Medals in dance = 25

Medals in music = 212

Total students that received medals = 55

Total students that received medals in all three categories = 6

Required:

How many students get medals in exactly two of these categories?

Take the following:

A = set of persons who got medals in sports.

B = set of persons who got medals in dance

C = set of persons who got medals in music.

Therefore,

n(A) = 40

n(B) = 25

n(C) = 212

n(A∪B∪C)= 55

n(A∩B∩C)= 6

To find how many students get medals in exactly two of these categories, we have:

n(A∩B) + n(B∩C) + n(A∩C) −3*n(A∩B∩C)

=n(A∩B) + n(B∩C) + n(A∩C) −3*6 ……............... (1)

n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

Thus, n(A∩B)+n(B∩C)+n(A∩C)=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)

Using equation 1:

=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)−18

Substitute values in the equation:

= 40 + 25 + 212 + 6 − 55 − 18

= 283 - 73

= 210

Number of students that get medals in exactly two of these categories are 210

Answer:

Step-by-step explanation:

To solve for BC we use sine

sin ∅ = opposite / hypotenuse

From the question

AC is the hypotenuse

BC is the opposite

So we have

sin 58 = BC / AC

sin 58 = BC / 14

BC = 14 sin 58

BC = 11.87

BC = 11.9 to one decimal place

Hope this helps you

Answer:

[tex]\boxed{BC = 11.9 \ cm}[/tex]

Step-by-step explanation:

Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]

Where A = 58°, Opposite = BC and AC = 14 cm

Sin 58 = [tex]\frac{BC}{14}[/tex]

BC = 0.848 * 14

BC = 11.9 cm

Answer:

18x-2

Step-by-step explanation:

Answer:

u=9n

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

[tex]f(x) = y[/tex] (output)

[tex]y = 16\\y = 2^x\\2^x = 16\\2^x = 2^4\\x = 4[/tex]

x = number of rounds

y = number of points

In the 4th round, 16 points will be rewarded.

The value of the function at x = 4 will be 16. Then the correct option is A.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The exponent is given as

y = a(b)ˣ

The exponent function is given below.

f(x) = 2ˣ

Then the value of the variable x when the value of the function is 16.

f(x) = 16

2ˣ = 16

2ˣ = 2⁴

x = 4

The value of the function at x = 4 will be 16. Then the correct option is A.

More about the exponent link is given below.

https://brainly.com/question/5497425

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Answer:

(i) False

(ii) Selecting a 5 or a spade are not independent.

Step-by-step explanation:

(i)

Independent events are those events that occur at the same time, i.e. the occurrence of one event does not effects the occurrence of the other.

If A and B are independent events then: [tex]P(A\cap B)=P(A)\times P(B)[/tex]

Whereas as if two events are mutually exclusive, then the probability of them both taking place at the same time is 0.

Then for events A and B: [tex]P(A\cap B)=0[/tex]

Thus, the statement is False.

(ii)

In a standard deck of 52 cards there are:

Spades = 13

Diamond = 13

Heart = 13

Clubs = 13

And each of these 13 cards are:

K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A

If a card labelled as 5 is selected then it could also be a Spade.

And if a spade is selected then the card could be labelled as 5.

So, selecting a 5 or a spade are not independent.

Answer:

This is simple! (Kind of)

Step-by-step explanation:

First, notice how HJ is tangent. HG is a radius intersecting HJ at H.

This means, (According to some theorem that I forgot the name of) that GHJ is a right angle.

Thus, we can use the 180* in a triangle theorem.

[tex]180=90+54+6x+6[/tex]

So, let's solve!

[tex]30=6x\\5=x[/tex]

So, there you go! Nice and simple!

Hope this helps!

Stay Safe!

Step-by-step explanation:

hope it helps yoy..........

Answer:

Multiply every coordinate from the old one by 0.75

Step-by-step explanation:

I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.

The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.

Answer:

x, y ----> 3/4x, 3/4y

Step-by-step explanation:

Answer:

a) 4.236 x 10^2

b) 7.194548 x 10^6

c) 5.0023 x 10^2

d) 7.123884 x 10^1

e) 5.62 x 10^-1

f) 3.48 x 10^-2

g) 1.23 x 10^-4

h)  5.603002 x 10^-1

Hopefully this helps :)

Answer:

a) 423.6=4.236*10^2

b) 7,194,548=7.194548*10^6

c) 500.23=5.0023*10^2

d) 71.23884=7.123884*10^1

e) 0.562=5.62*10^-1

f) 0.348=3.48*10^-1

g) 0.000123=1.23*10^-3

h) 0.5603002=5.603002*10^-1

Step-by-step explanation:

The numbers in which the point lies must be between 0 and 10

Hope this helps ;) ❤❤❤

Answer:

x=20

Step-by-step explanation:

3x + 2x + 80=180

5x+80=180

5x=100

x=20

Answer:

x = 20 degrees

Step-by-step explanation:

For this problem, it is important to know that the measure of a line is 180 degrees.  With this in mind, let's build an equation:

3x + 80 + 2x = 180

Now that we have this equation, let's solve for x.

3x + 80 + 2x = 180

5x + 80 = 180

5x = 100

x = 20

Hence, x is 20 degrees.

Cheers.

Answer:

4x^2 + 8x + 4

4(x^2 + 2x + 1) - remove GCF of 4

4(x + 1)(x + 1) - factor

4(x + 1)^2 - collect like terms

Step-by-step explanation:

Then also expand it out by distributing:

21x^3 + 35x²

Form 1:

21x^3 + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

Update:

You could also multiply two binomials and make a quadratic.

Example:

(7x + 2)(3x + 5)

7x(3x + 5) + 2(3x + 5)

= 21x² + 35x + 6x + 10

= 21x² + 41x + 10

The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The polynomial will be solved as below:-

21x³ + 35x²

Form 1:

21x³ + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

You could also multiply two binomials and make a quadratic.

E = (7x + 2)(3x + 5)

E = 7x(3x + 5) + 2(3x + 5)

E = 21x² + 35x + 6x + 10

E = 21x² + 41x + 10

To know more about polynomials follow

brainly.com/question/2833285

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Answer:

The quadrilateral shown is a kite, because it has two non-congruent pairs of congruent sides

x = 3

Step-by-step explanation:

The vertex angles in a kite are bisected by the diagonals.  Thus, 11x = 9x + 6.

11x=9x+6

2x=6

x=3

Hope it helps <3

Answer:

2

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( -4 - -2)/ ( 2-3)

    = ( -4+2)/( 2-3)

    = -2/ -1

    = 2

Answer:

The solution of the system of equations are;

(-2, -6) and (4, 6)

Step-by-step explanation:

-2·x + y = -2...............(1)

[tex]y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex]........(2)

Equation (1) gives;

y = 2·x - 2

From which we have;

[tex]2 \cdot x - 2 = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex]

[tex]0= -\dfrac{1}{2} \cdot x^2 + x + 4[/tex]

x² -2·x -8 = 0

(x - 4)·(x + 2) = 0

x = 4 or x = -2

The y-coordinate values are;

y = 2×(-2) - 2 = -6 and y = 2×(4) - 2 = 6

The solution points are;

(-2, -6) and (4, 6).

The points where the equation, -2·x + y = -2 and the equation [tex]y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex] intersect are  (-2, -6) and (4, 6).

Answer:

h = 7 units

Step-by-step explanation:

Jessica made an error with the [tex]\frac{1}{2}[/tex] in that she multiplied A by it instead of dividing.

Given

A = [tex]\frac{1}{2}[/tex] bh

with A = 17.5 and b = 5, then

17.5 = [tex]\frac{1}{2}[/tex] × h × 5 ( multiply both sides by 2 to clear the fraction )

35 = 5h ( divide both sides by 5 )

h = 7

it is wrong .

Jessica's mistake:

A = 1/2bh

1/2A • b = h >she should multiply the area with 2 not 1/2 and divide the area by b rather than multiply by b

1/2 (17.5)(5) = h

43.75 = h

correct answer:

A = 1/2bh

2A/b=h

h=2(17.5)/5

h=7

Answer:

C) (-4, 2)

Step-by-step explanation:

Answer:

The center is ( -4,2) and the radius is 4

Step-by-step explanation:

The equation of a circle can be written as

( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius

(x+4)^2 + (y - 2)^2 = 16

(x- -4)^2 + (y - 2)^2 = 4^2

The center is ( -4,2) and the radius is 4

Answer: the correct answer is D.

Step-by-step explanation:

Since we are given the values of angle B and side(a) we can set up an equation cos43.2=3.2/x

we will get 4.4 so c=4.4

using the paythagorion theorm (4.4)^2=x^2+(3.2)^2

we will get an approximate value of 3 so b=3

and for the finding the third angle x+43.2+90=180

x=46.8 degrees

Answer D

Step-by-step explanation:

-3x² + 2y² + 5xy -2y + 5x² - 3y²

= -3x² + 5x² +2y² -3y² + 5xy -2y

= 2x² - y² +5xy -2y

2 terms

Answer:

Total number of animals in the group = 170

Step-by-step explanation:

Let the number of sheep = a

Number of dragons in the group = 75

Number of dragons opposite dragons = 37

Number of sheep opposite to the dragon = 1

Number of sheep left = a - 1

Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]

Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,

[tex]\frac{(a-1)}{2}[/tex] = 37 + 10

[tex]\frac{(a-1)}{2}=47[/tex]

a - 1 = 94

a = 95

Then total number of animals in the group = Total number of sheep + Total number of dragons

= 95 + 75

= 170

Therefore, total number of animals in the group are 170.

Answer:

4 and 20

Step-by-step explanation:

The sum of two numbers is 24.

One of the numbers is 5 times larger than the other.

Let x be the first number.

Let y be the second number.

x + y = 24

x = 5y

Put x as 5y in the first equation.

5y + y = 24

6y = 24

y = 4

Put y as 4 in the second equation.

x = 5(4)

x = 20

Answer:

StartFraction x over 7.5 EndFraction = StartFraction 12 over 1 EndFraction

Step-by-step explanation:

Here, in this question, given that Rosa earns $12 in an hour, she earns x dollars in 7.5 hours. So we are interested in finding the value of x.

Let’s write this in terms of proportion;

$12 = 1 hour

$x = 7.5 hours

$12 * 7.5 hours = $x * 1 hour

So this can be rewritten as;

$x/7.5 = $12/1 hour

Answer: Start Fraction x over 7.5 End Fraction Start Fraction 12 over 1

explanation:

Answer:

[tex]3(6b-1)(2a-1)[/tex]

Step-by-step explanation:

[tex]36ab-18b+6a-3\\18b(2a-1)+3(2a-1)[/tex]

Taking (2a-1) as common

[tex](18b+3)(2a-1)[/tex]

=> [tex]3(6b-1)(2a-1)[/tex]

Answer:

[tex]3(6b+1)(2a-1)[/tex]

Step-by-step explanation:

[tex]36ab - 18b+6a-3[/tex]

Factor the two groups.

[tex]18b(2a-1)+3(2a-1)[/tex]

Take 2a - 1 common.

[tex](18b+3)(2a-1)[/tex]

Factor 18b + 3.

[tex]3(6b+1)(2a-1)[/tex]

Answer:

1.76m/s ; 1.76m/s ; 1.74m/s, 0.86m/s

Step-by-step explanation:

Given the following :

Distance jogged in first direction (A to B) = 300m

Time taken = 2 minutes 50s = (2*60) + 50 = 120 + 50 = 170s

Distance jogged in opposite direction (B to C) = 100m

Time taken = 1minute = 60s

Recall:

Speed = distance / time

Therefore Average speed from A to B

Average speed = 300m/ 170s = 1.764 = 1.76m/s

Average Velocity = Displacement / time

Displacement = 300m ; time = 170s

= 300m / 170s = 1.76m/s

Average speed (A to C)

Therefore, average speed = total distance / total time taken

Total distance = (300 + 100)m = 400m

Total time taken = (170 + 60)s = 230s

Average speed = 400m / 230s

= 1.739m/s = 1.74m/s

Average velocity:

Displacement = distance between initials position and final position.

Initial distance covered = 300m. Then 100m was jogged in the opposite direction.

Distance between starting and ending positions, becomes : (300 - 100)m = 200m

200 / 230 = 0.87m/s

Answer:

Step-by-step explanation:

Given the total number of games played by the softball team = 18 games

Total games won = 15 games

Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played

Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]

[tex]Ratio = \frac{15}{18}[/tex]

Expressing the ratio in its lowest term

[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]

Hence, the ratio of the softball team's wins to its total number of games played is 5:6

Answer:Sin

Step-by-step explanation:

right angled triangle special trig functions can be applied

Answer:

  [tex]\dfrac{8m^7n^6}{3}[/tex]

Step-by-step explanation:

  [tex]\dfrac{(2mn)^4}{6m^{-3}n^{-2}}=\dfrac{2^4}{6}m^{4-(-3)}n^{4-(-2)}=\boxed{\dfrac{8m^7n^6}{3}}[/tex]

__

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  1/a^b = a^-b

  (a^b)(a^c) = a^(b+c)

Answer:

A

Step-by-step explanation:

Answer:  11 units

Step-by-step explanation:

Given: On a coordinate plane, the coordinates of vertices R and T for a polygon are R(−6, 2) and T(5, 2).

To find : length of Side RT of the polygon.

Using distance formula  to find distance between (a,b) and (c,d):

[tex]d=\sqrt{(d-b)^2+(c-a)^2}[/tex]

Length of RT = [tex]\sqrt{(2-2)^2+(5-(-6))^2}[/tex]

[tex]\\\\=\sqrt{0+(5+6)^2}\\\\= \sqrt{11^2}\\\\=11[/tex]

hence, the length of RT = 11 units.

Answer:

the answer is 11 units

Step-by-step explanation:

Greetings from Brasil...

Using Cossine we will get the length L of ladder

COS 35 = 5/L