Determine the equation of a line that passes through A(2,5) and is parallel to the line defined by 3x−y+12=0. State the equation in slope y-intercept form.

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: 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

Answer:

One solution

2

Step-by-step explanation:

5(2x-3)=5

10x-15=5

10x=5+15

10x=20

x=2

Part A: 1

Part B: It has only one solution and it is 2.

Hope this helps ;) ❤❤❤

Answer:

I believe 1 solution

Step-by-step explanation:

divide both side of equation by 5= 2x-3)=1

add 3 to each side= 2x=1+3

2x=4

x=2

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:

(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:

75 meters

Step-by-step explanation:

30/50 = 45/x

x = 75

Answer:

x= 75m

Step-by-step explanation:

If we call the angle in the bottom left θ, then the sinθ=(opposite side)/(hypotenuse).

For the smaller triangle:

sinθ=30/50

And for the bigger triangle:

sinθ=45/x

So:

30/50=sinθ=45/x

30/50=45/x

x=(45•50)/30=2250/30=75

So x= 75 meters

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:

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:

(-5,0)

Step-by-step explanation:

In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number

For Decreasing:

(-8,-5)

(4,8)

For Increasing:

(-5,0)

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

#SPJ2

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:Sin

Step-by-step explanation:

right angled triangle special trig functions can be applied

Answer:

[tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex] .

Step-by-step explanation:

Since vertices lie on y-axis. So, it is a vertical parabola of the form

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where, (h,k) is center, [tex](h,k\pm c)[/tex] is focus and [tex](h,k\pm a)[/tex] is vertex.

Center is (0,0). So, h=0 and k=0.

Foci are [tex](0,\pm \sqrt{73})[/tex]. So [tex]c=\sqrt{73}[/tex].

Vertices are [tex](0,\pm 8)[/tex]. So [tex]a=8[/tex].

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex]8^2+b^2=(\sqrt{73})^2[/tex]

[tex]b^2=73-64[/tex]

[tex]b=3[/tex]

Put h=0,k=0, a=8 and b=3 in equation (1).

[tex]\dfrac{(y-0)^2}{8^2}-\dfrac{(x-0)^2}{3^2}=1[/tex]

[tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex]

Therefore, the required equation is [tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex] .

Answer:

18x-2

Step-by-step explanation:

Answer:

u=9n

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:

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:

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:

  [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:

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:

Hey there!

The additive inverse means the number opposite to five.

The additive inverse of negative five is positive five.

Hope this helps :)

Answer:

The additive inverse of negative five is positive five.

explanation:

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:

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:

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

================================================

Explanation:

Subtract straight down. The x terms subtract to 5x-2x = 3x. The y terms subtract to 3y-3y = 0y = 0, so the y terms go away and are eliminated. The terms on the right hand side subtract to 31-25 = 6.

After all that subtraction, we end up with the equation 3x = 6 which solves to x = 2 after dividing both sides by 3.

Use x = 2 to find the value of y

5x+3y = 31

5(2)+3y = 31

10+3y = 31

3y = 31-10

3y = 21

y = 21/3

y = 7

or

2x+3y = 25

2(2)+3y = 25

4+3y = 25

3y = 25-4

3y = 21

y = 21/3

y = 7

Using either equation has x = 2 lead to y = 7.

Therefore, the solution is (x,y) = (2,7)

If you were to graph the two original equations, then they would intersect at (2,7).

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]

Greetings from Brasil...

Using Cossine we will get the length L of ladder

COS 35 = 5/L

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:

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.