MATHEMATICS HIGH SCHOOL

How many leaves on a tree diagram are needed to represent all possible combinations tossing a coin 4 times?

Answers

Answer 1
Answer:

Answer with explanation:

When you toss a coin once , total possible outcome =2={H, T}

When you toss a coin twice , total possible outcome =2²=4={HT,TH,T T,H H}

When you toss a coin thrice , total possible outcome =2³=8

               ={T T T,T TH, T HT,H T T,H HT,H TH,T H H,H H H}

When you toss a coin 4 times , total possible outcome

 2^4=16

={T T T T, T T TH, H T T T,T H T T,T T HT,T T H H,H H T T,T H HT,H T TH,H TH T,T H TH, H H HT,H T H H,TH H H,H H TH,H H H H}

=16

There are 16 possible outcomes in all.

So, total number of leaves needed on the tree Diagram = 16 Leaves

       
Answer 2
Answer: 1/2 x 1/2 x 1/2 x 1/2 = 1/16

Answer: 16

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Assign two variables for each problem, and write the equations. Solve.In five years, Kate will be twice as old as Joey. Right now, Kate is 11 years older than Joey. How old is Joey right now?

I need two variables and two equations. And please solve it.

Answers

lets make k equal to Kate's age and j equal to Joey's age.  If in 5 years Kate will be twice as old as Joe, you can write the equation k+5=2(j+5) and then simplify it to make it easier to work with.
k+5=2(j+5)
k+5=2j+10
k+5-2j=10
k-2j=5
since we know that right know Kate is 11 years older than Joey, you can write the equation k+j=11.  Since you know have two equations with with the same variable, you can make a system of equations as fallows:
k-2j=5
k+j=11

Since you need to figure out how old Joey is, you need to somehow get k to cancel out.  The easiest thing to do for this problem is to is multiply the top equation by -1 to get:
-k+2j=-5   (you have to add the bottom equation to the top equation)
k+j=11     (-k+k=0, 2j+j=3j, and -5+11=6)
Since k got canceled out, you are left with the equation 3j=6 which means j=2.
Therefore, Joey's current age is 2.

I hope this helps.

Find the value of x in this polygon.

Answers

Answer:

68

Step-by-step explanation:

you have to add to 180 and 68+112=180

Final answer:

To find the value of x in the polygon, you need more information such as one of the interior angles or the total sum of the interior angles.

Explanation:

To find the value of x in this polygon, you need to use the fact that the sum of all interior angles in a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides. In this case, since it is not mentioned what polygon it is, we will assume it is a regular polygon. If the polygon is regular and has x sides, then the sum of all interior angles is also (x-2) * 180 degrees. To find the value of x, you would need more information, such as one of the interior angles or the total sum of the interior angles.

Learn more about Solving Polygon Problems here:

brainly.com/question/31620082

#SPJ2

Which ordered pair could you remove from the relation {(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)} so that it becomes a function?

Answers

Answer:

Either of (2,2) or (2,3) should be removed to get the relation as a function.

Step-by-step explanation:

We know that a relation is a function if each element of the first set is mapped to a unique element of the other set.

i.e. corresponding to each x value we have a single y-value.

We are given a relation as:

          {(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)}

As we could observe that there are two images corresponding to '2' i.e. 2 is mapped to 2 and 3 both as could be seen from the ordered pair (2,2) and (2,3).

Hence, if any one of (2,2) and (2,3) will be removed we will get our relation as a function.
Each x value should have only one y value

therefore you should remove wither (2,2) or (2,3)

Could someone help me please? I am completely lost on how to figure out this problem.Use Synthetic division to show that x is a solution for the third degree polynomial equation and use the result to Factor the Polynomial Completely. List All real solutions of the equation

x^3 - 57x - 56 = 0,    x = -1

x = _______ (smallest value)
x = _______
x = _______ (largest value)

Answers

From the factor theorem that says, "The polynomial P(x) has x-r as a factor if and only if r is a root of the equation P(x) = 0." So if you plugged -1 into the x's in the equation and get 0 back then, x+1 is a factor. Let's do it.
( -1)^(3) -57(-1)-56=-1+57-56=0
It works. When you plugged -1 into x, you got 0 back and that's what the factor theorem says. 
Now let's test it with synthetic division. If we divide x+1 into the original equation and get a remainder of 0, then we should be good. I'll write it up on Paint and upload it. 
As you can see, our remainder is 0 and our quotient is x^(2) -x-56. This is the Factor the Polynomial part that you wanted. We can factor this into (x-8)(x+7). So our 3 roots of the equation are (x+1)(x-8)(x+7)
Hope this helps and i'm so sorry for the long reply. I forgot to put 0x^2 when I was doing synthetic division. :/ and also sorry for the unclear paint image. you can zoom in if you want. it's nothing really important it just shows me doing the synthetic division part where i divide x+1 into the original equation.
x^3 - 57x - 56=0⇒ x(x^2-57)= 56

Verify if  x= - 1 is a solution of this equation.
(-1)* [(-1)^2 - 57]=56
(-1)[1 - 57] = 56
(-1)*(-56) = 56

56 =2*28 = (-2)*(-28) = 4*14 = (- 4)*(-14) = 8*7= (-8)*(-7)
x=8 ⇒ 8*(64-57)=56            ok⇒ x=8 is a solution
x= -7 ⇒ (-7)*(49-57)=56        ok  ⇒ x= - 7 is a solution

the smallest x= -7 
                    x= - 1
the largest   x= 8

The vertices of a quadrilateral ABCD are A(-3, 4), B(-4, 1), C(-7, 2), and D(-7, 6). The vertices of another quadrilateral EFCD are E(-10, 1), F(-11, 4), C(-7, 2), and D(-7, 6). Which conclusion is true about the quadrilaterals?Their corresponding diagonals are equal.

The measures of their corresponding angles are not identical.

The lengths of their corresponding sides are unequal.

Their shapes and sizes are not identical.

Answers

"Their corresponding diagonals are equal" is the one conclusion among the following choices given in the question that is true about the quadrilaterals. The correct option among all the options that are given in the question is the first option. I hope that this is the answer that has actually come to your help.

Which expression is equivalent to 5 x + 10 y minus 15?

Answers

Answer:

5(x+2y-3)

Step-by-step explanation:

5x+10y-15

Factor out 5 from the expression

5(x+2y-3)

Answer:

C

Step-by-step explanation:
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