In a soccer league with four teams, each team played four games with every other team. Each team received 3 points for a win, 1 point for a tie, and no points for a loss. After all the games, the point tallies were as follows: Team A won 22 points, team B won 19 points, team C won 14 points, and team D won 12 points. How many games ended in a tie?

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Find the volume of the wading pool

Use V = pi * r^2 * h

Givens

r = 6 feet

h = 1.5 feet

pi = 3.14

2 f^2 takes 2 minutes.

Solution

V = pr * r^2 + h

r = d/2

r = 6 / 2

r = 3 feet

Put the givens into the formula

V = 3.14 * 3 * 3  * 1.5

V = 42.39 cubic feet

Time

2 cubic feet takes 1 minutes

42.39 cubic feet takes x                  

2/42.39 = 1/x                      Cross multiply

2x =  42.39                         Divide by 2

2x/2 = 42.39/2

x = 21 rounded to the nearest whole number.

The solution to the system of equation are (0, -2) and (1, 0)

System of equations are equations that has unknown and more than 1 equations.

Given the system of equations

y = x^2 + x – 2

y = 2x – 2

Equate both expressions

x^2 + x -2 = 2x - 2
x^2 - x = 0
x(x-1) = 0
x = 0 and x - 1 = 0
x = 0 and 1

If x = 0

y = 0 - 2 = -2

If x = 1

y = 2 - 2 = 0
Hence the solution to the system of equation are (0, -2) and (1, 0)

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Answer:

[tex]\boxed{\tt = 1 2√5−24√(14)+2√(30)−8√(21)}[/tex]

Or

[tex]\boxed{ \tt \approx88.7}[/tex]

Step-by-step explanation:

Apply FOIL method to expand:

[tex] =\tt6√2(√(10)−4√7)+2√3(√(10)−4√7)[/tex]

[tex] \tt \:=6√2√(10)+6√2(−4√7)+2√3(√(10)−4√7)[/tex]

[tex] \tt \: = 6√2√(10)+6√2(−4√7)+2√3√10+2√3(−4√7)[/tex]

Simplify:

[tex] =\tt6√(20)+6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]

[tex] \tt \: = 6 \sqrt{2 {}^{2} \times 5} +6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]

[tex] \tt \: = 6(2√5)+6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]

[tex] \tt = 12√5+6√2(−4√7)+2√3√(10)+2√3(−4√7)[/tex]

[tex] \tt = 12√5−24√(14)+2√3√(10)+2√3(−4√7)[/tex]

[tex] \tt \: = 12√5−24√14+2√(30)+2√3(−4√7)[/tex]

[tex] \tt \: = 12√5−24√(14)+2√(30)−8√(21)[/tex]

or

[tex] \tt \: \approx88.7[/tex]

[tex]\rule{230pt}{2pt}[/tex]

[tex]\left( 6 \sqrt 2 + 2 \sqrt 3 \right) \left( \sqrt{10} -4 \sqrt7 \right)\\\\=\left(6\sqrt 2 \right) \left(\sqrt{10} \right) - \left(6\sqrt 2\right)\left(4\sqrt 7 \right)+\left(2\sqrt 3 \right) \left(\sqrt{10} \right)-\left(2\sqrt 3 \right) \left(4 \sqrt 7 \right)\\\\=6\sqrt{2 \cdot 10} -24\sqrt{2 \cdot 7} + 2\sqrt{10 \cdot 3} - 8 \sqrt{3 \cdot 7}\\\\=6\sqrt{4 \cdot 5}-24\sqrt{14}+2\sqrt{30} - 8 \sqrt{21}\\\\=6\cdot 2\sqrt 5-24\sqrt{14}+2\sqrt{30} - 8 \sqrt{21}\\\\[/tex]

[tex]=12\sqrt{5} -24\sqrt{14}+2\sqrt{30} - 8 \sqrt{21}\\\\\approx -88.68[/tex]

Answer:

ok , using Pythagoras theorem hyp²=opp²+adj² therefore /CB/ will be opp , Making A the angle

7²=opp²+5² which is 49=x²+25

x²=49-25=✓24

=4.9

using SOH CAH TOA

sin A = 4.9/7

=0.7 , A is then sin-¹ 0.7

=136

use cosine since you are given the adjacent side and the hypotenuse

Cos θ = [tex]\frac{adj}{hyp}[/tex]

Cos θ = [tex]\frac{5}{7}[/tex]

use the inverse of cosine to find the angle

θ = [tex]cos^{-1}(\frac{5}{7})[/tex]

θ = 44.4153086...

θ = 44.42°

Answer:

4.27985 and 14.72015

Step-by-step explanation:

4.27985 x 14.72015 = 63

4.27985 + 14.72015 = 19

Answer:

95%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let :

Finding the change in level

Answer: It would be C and D

Step-by-step explanation:

By the phythagorean theorem, the 2 legs would equal to the hypothesize.

Choice A would not form a triangle.

Choice B does not follow the pythagorean theorem. 84 plus 16 does not equal 100.

Choice C does. 8 + 121 = 129.

Choice D does. 1 + 3 = 4.

Answer:

Step-by-step explanation:

Remark

The exposed perimeter of the triangle is just the two smaller legs of the right triangle (6 + 8) + 10 units at the bottom of the rectangle + two 1/2 circles.

The area of the figure is the area of the triangle at the top + the area of the two 1/2 circles + the rectangle in the middle.

Givens

Formula

A

Perimeter = 2 legs of the triangle + 2 half circles + bottom line

B

Area = (1/2) Leg1*leg2 + pi * r^2 + L * w

Solution

A Perimeter

Perimeter = 6 + 8 + 2*pi *r + 10

Perimeter = 24 + 2*3.14*4

Perimeter = 25.12

B Area

Area = 1/2 * 8 * 6 + 3.14*4^2 + 10* 8

Area = 24 + 50.24+ 80

Area = 150.24

Answer

P = 25.12

Area = 150.24

Answer:

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex.

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Answer:

25 pizzas and 36 subs

Step-by-step explanation:

5x+3x=233 --> but there are 11 more subs that pizza, so 11x3 is 33

(5x+3x) +33 = 233

5x+3x= 200

8x=200

x=25

so then 5 dollars by 25 pizzas, and 36 (25+11) subs at 3 dollars = 233$

Answer:

use vertex form of parabola:

y=a%28x-h%29%5E2%2Bk....if vertex (0,7), we have

y=a%28x-0%29%5E2%2B7

y=ax%5E2%2B7......use point (3,2) to find a

2=a%2A3%5E2%2B7

2=9a%2B7

2-7=9a

-5=9a

a=-5%2F9

so, your equation is: y=-%285%2F9%29x%5E2%2B7

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

I think.

Answers:

The z scores are approximately:

From those scores, we can say:

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

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

z = (x - mu)/sigma

where,

Let's find the z score for the Care of Magical Creatures class

z = (x - mu)/sigma

z = (3.80 - 3.75)/(0.15)

z = 0.333 approximately

Repeat this process for the Defense Against the Dark Arts score.

z = (x - mu)/sigma

z = (3.60 - 3.25)/(0.60)

z = 0.583 approximately

And for the Transfiguration class as well

z = (x - mu)/sigma

z = (3.10 - 3.20)/(0.38)

z = -0.263 approximately

The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

z = (x - mu)/sigma

z = (2.50 - 2.90)/(0.75)

z = -0.533 approximately

This grade is below average as well.

----------------------------

To summarize, we have these z scores

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

The value of a will be 0.125. Then the value of a is positive then the parabola will be upward.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

A parabola opening up or down has vertex (0,-4) and passes through (-12,14).

The equation of the parabola is given as

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

(h, k) = (0, -4)

Then the equation of the parabola will be

y = a(x)² - 4

The parabola is passing through (-12, 14). Then the value of a will be

   14 = a(-12)² - 4

   14 = 144a - 4

144a = 18

     a = 1/8

     a = 0.125

Then the equation of the parabola will be

y = 0.125x² - 4

If the value of a is positive then the parabola will be upward.

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Answer:

4 ft 8 inches = 56 inches

Step-by-step explanation:

We know that there are 12 inches in a foot so first convert 4 ft to inches

4 ft = 4*12 = 48 inches

Add the 8 inches left over

48 inches + 8 inches

56 inches

4 ft 8 inches = 56 inches

The experimental probability is 4/5 if they randomly selected 6 blue, 4 yellow, 2 red, 3 green, and 5 purple marbles.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Total number of marbles = 6+4+2+3+5 = 20

Total number of marbles except yellow = 20 - 4 = 16

The experimental probability = 16/20

or

= 4/5

Thus, the experimental probability is 4/5 if they randomly selected 6 blue, 4 yellow, 2 red, 3 green, and 5 purple marbles.

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Answer:

He would spend $14.40 on 12 bottles.

Answer:

[tex]\huge\boxed{\bf\:30^{\circ}}[/tex]

Step-by-step explanation:

We need to find m ∠EGD.

From the given figure, we can see that, ∠BGA & ∠EGD are vertically opposite angles (opposite angles that share the same vertex ⟶ G).

Also, vertically opposite angles are equal to each other.

Given,  ∠BGA = 30°

So,  ∠EGD =  ∠BGA = 30°.

[tex]\rule{150pt}{2pt}[/tex]

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

from the given figure , we can easily see that ∠AGB = ∠EGD

this is because these angles are vertically opposite , i.e. , the angles that share the same vertex ! also , it's known that two angles that are vertically opposite are equal to each other !

[tex]\therefore \: \bold{\angle \: EGD= 30\degree}[/tex]

hope helpful ~

Answer:

144

Step-by-step explanation:

In a regular decagon like the one shown in the picture each angle is 144 degrees and it all adds up to 1,440. If you want proof search up "angle of a decagon"

"a ∝ b" means "a is proportional to b", which in turn means there is some constant k such that

a = kb

We're given that a = 18 and b = 3, so that

18 = 3k   ⇒   k = 6

Then when b = 5, we would have

a = 6 × 5 = 30

Answer:

Step-by-step explanation:

A rectangular garden has vertices at

(x = 4, y = 3), (x = 6, y = 3), (x = 6, y = 9), and (x = 4, y = 9).

To plot each vertex of the garden find on the graph the x and y coordinate of the point and mark the point.

Answer:

C

Step-by-step explanation:

-Since dot or where the line originates is at 4 we know the answer will have the number 4.

-The dot is hollow, meaning it does not include the number it is on. So it cannot be "blank and equal to."

-Since the arrow points towards the right, we know it wants all values greater than 4, so we do: x>4.

-Back to my second point, we know it is not D because the dot is open and it does not include 4, so it cannot be equal to it.

Before we continue, note that "percent increase from 43 to 78" is the same as "the percentage increase from 43 to 78". Furthermore, we will refer to 43 as the initial value and 78 as the final value.

So what exactly are we calculating? The initial value is 43, and then a percent is used to increase the initial value to the final value of 78. We want to calculate what that percent is!

Here are step-by-step instructions showing you how to calculate the percent increase from 43 to 78.

First, we calculate the amount of increase from 43 to 78 by subtracting the initial value from the final value, like this:

78 - 43

= 35

To calculate the percent of any number, you multiply the value (n) by the percent (p) and then divide the product by 100 to get the answer, like this:

(n × p) / 100 = Answer

In our case, we know that the initial value (n) is 43 and that the answer (amount of increase) is 35 to get the final value of 78. Therefore, we fill in what we know in the equation above to get the following equation:

(43 × p) / 100 = 35

Next, we solve the equation above for percent (p) by first multiplying each side by 100 and then dividing both sides by 43 to get percent (p):

(43 × p) / 100 = 35

((43 × p) / 100) × 100 = 35 × 100

43p = 3500

43p / 43 = 3500 / 43

p = 81.3953488372093

Percent Increase ≈ 81.3953

That's all there is to it! The percentage increase from 43 to 78 is 81.3953%. In other words, if you take 81.3953% of 43 and add it to 43, then the sum will be 78.

The step-by-step instructions above were made so we could clearly explain exactly what a percent increase from 43 to 78 means. For future reference, you can use the following percent increase formula to calculate percent increases:

((f - n)/n) × 100 = p

f = Final Value

n = Initial Value

p = Percent Increase

Once again, here is the math and the answer to calculate the percent increase from 43 to 78 using the percent increase formula above:

((f - n)/n) × 100

= ((78 - 43)/43) × 100

= (35/43) × 100

= 0.813953488372093 × 100

≈ 81.3953

Answer:

Step-by-step explanation:

The algebraic method for solving simultaneous linear equations is the substitution method

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The algebraic method for solving simultaneous linear equations is the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

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