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3 years ago

11

Three players scored a total of 70 points during a basketball game. One player scored twice as many as one teammate and ten poin

ts fewer than the other teammate. How many points did each player score?

1 answer:

11111nata11111 [884]3 years ago

8 0

I think the answer is 23 but not sure

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Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

Using Binomial theorem,

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here, a = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

3 0

3 years ago

Graph - 9x + 6y = 18 using linear standard form

postnew [5]

Answer:

The graph is attached Below and the plotting is given below.

Step-by-step explanation:

Given:

-9x + 6y = 18

Solution:

To draw a line on a graph the required minimum two points but here we will have three points as point A, point B, and point C.

For point A

Put x = -4 in the given equation we get

-9×-4 + 6y = 18

6y = 18-36

∴ $y=\frac{-18}{3}\\ \\y=-3$

∴ Point A ≡ ( -4, -3 ).

For point B

Put x = -2 in the given equation we get

-9×-2 + 6y = 18

6y = 18 - 18

6y = 0

∴ $y=\frac{0}{3}\\ \\y=0$

∴ Point B ≡ ( -2, 0 ).

For point C

Put x = 0 in the given equation we get

-9×0 + 6y = 18

6y = 18

∴ $y=\frac{18}{3}\\ \\y=3$

∴ Point C ≡ ( 0, 3 ).

Now we have Point A ,B and C join it and you will have Line.

3 0

3 years ago

the local farm sell a 4 pound basket of apples for 5.60 each apple weighs 4 ounces. what is the price per apples

valina [46]

Because there are 16 ounces in a pound, we can multiply 16 by 4 to get 64, there are 64 ounces of apples which is also the same as 4 pounds of apples. If 64 ounces of apples equals $5.60, and each apple is 4 ounces, we have to also divide 64 by 4 to find the number of apples. 64 divided by 4 is 16, so 16 apples for $5.60. To get the price PER apple, or for one apple, we have divide $5.60 by 16, which will give us $0.35, or $.35 per apple, which is actually a good price.

4 0

3 years ago

Triangle PQR has vertices at the following coordinates : P(0,1) Q(3,2) R(5,-4) . Determine wether or not triangle PQR is a right

lord [1]

Here is my answer. Hope this help.

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3 years ago

Solve5(2x-3) = 3(x+4)

balu736 [363]

$5(2x-3)=3(x+4) \\
10x-15=3x+12 \\
10x-3x=12+15 \\
7x=27 \\
x=\frac{27}{7}=3 \frac{6}{7}$

3 0

3 years ago

Read 2 more answers