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3 years ago

Which relation is a function?

1 answer:

4 0

{(2, 3), (1, 5), (2, 7)} - NOT because 2->3 and 2->7
{(11, 9), (11, 5), (9, 3)} - NOT because 11->9 and 11->5
{(3, 8), (0, 8), (3, -2)} - NOT because 3->8 and 3->-2

{(-1, 5), (-2, 6), (-3, 7)} - YES

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Help me asap! I will give you marks

Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

M is the midpoint of segment GR. G has coordinates (11,-5) and M is (4,-4) Find the coordinates of R

7nadin3 [17]

Answer:

(3, -3)

Step-by-step explanation:

Given:

G = (11,-5)
M = (4,-4)
R = ?

Solution

R(x, y)

As per midpoint formula;

4 = (11 + x)/2 ⇒ x + 11 = 8 ⇒ x = 3
-4 = (-5 + y)/2 ⇒ y - 5 = -8 ⇒ y = -3
R = (3, -3)

4 0

3 years ago

The following spinner has four sections. There are equal sections for 1, 4, and 3. The section for 2 is twice as large as each o

Airida [17]

Answer:

gorge bush doesn't care

Step-by-step explanation:

about black people ~ ye

6 0

2 years ago

What are the solution of the equation 2|×+7|-3=5

marin [14]

Answer:

x = -3

Step-by-step explanation:

2(x + 7) - 3 = 5 (given)

2x + 14 - 3 = 5 (Distributive Property)

2x + 14 = 8 (Addition Property of Equality)

2x = -6 (Subtraction Property of Equality)

x = -3 (Division Property of Equality)

6 0

3 years ago

PLEASE HELP ASAP!!!!

adell [148]

The basic form of the equation is:
4p(x-h) = (y-k)2

(h,k) is the vertex

4(-0.5)(x-1.5) = (y-(-4))2
-2(x-1.5) = (y+4)2
-2(x-1.5) = y2 + 8y + 16
x - 1.5 = (-1/2)(y2 + 8y + 16)
x = (-1/2)y2 - 4y - 8 + 1.5
x = (-1/2)y2 - 4y - 6.5

4 0

3 years ago