Which inequality is graphed below?

A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).

Allushta [10]

Answer:

y= (3/2)x-3

Step-by-step explanation:

We need two points to find the equation of a line. Let's take (2,0) and (4, 3).

In the equation y=mx+b, m represents the slope. To find the slope, we can calculate the change in y/change in x. For (2,0) and (4,3), the change in y is 3-0=3 and the change in x is 4-2=2. Therefore, our slope is 3/2.

Then, in the equation y=mx+b, we can plug 3/2 in for m to get y = (3/2)x+b. To find b, we can plug one point in, such as (2.0), to get 0=(3/2)(2) + b, 0=3+b, and b=-3, making our equation

y= (3/2)x-3

8 0

3 years ago

Solve the simultaneous equation y-2x+1=0 and 4x^2+3y^2-2xy=7

Lapatulllka [165]

The first equation is $y-2x+1=0$

$y=2x-1$ (Equation 1)

The second equation is $4x^{2}+3y^{2}-2xy=7$ (Equation 2)

Putting the value of x from equation 1 in equation 2.

we get,

$4x^{2}+3(2x-1)^{2}-2x(2x-1)=7$

$4x^{2}+3(4x^{2}+1-4x)-4x^{2}+2x=7$

by simplifying the given equation,

$12x^{2}-10x-4=0$

$6x^{2}-5x-2=0$

Using discriminant formula,

$D=b^{2}-4ac$

$D=25-4 \times 6 \times -2 = 73$

Now the formula for solution 'x' of quadratic equation is given by:

$x=\frac{-b+\sqrt{D}}{2a} and x=\frac{-b-\sqrt{D}}{2a}$

$x=\frac{5+\sqrt{73}}{12} and x=\frac{5-\sqrt{73}}{12}$

Hence, these are the required solutions.

8 0

3 years ago

A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the

forsale [732]

<h3>The probability of student passing the quiz with at least 50% of the questions correct is 0.05457.</h3>

Step-by-step explanation:

Here, the total number of T/F question = 10

The minimum answers needed correctly answered = 8

So, student needs to answer at least 8 questions correctly.

Here, the possibility of answering a question correctly = $(\frac{1}{2})$ = p = 0.5

Also, the possibility of answering a question wrong = $(\frac{1}{2})$ = q = 0.5

Now, to pass he needs to answer 8 or more ( 8 , 9 or 10) answers correctly.

P(answering 8 correct answer) = $^{10}C_8(p)^8(q)^2 = ^{10}C_8(0.5)^8(0.5)^2 = 0.0439$

P(answering 9 correct answer) = $^{10}C_9(p)^9(q)^1 = ^{10}C_9(0.5)^9(0.5)^1 = 0.0097$

P(answering 10 correct answer) = $^{10}C_{10}(p)^{10}(q)^0 = ^{10}C_{10}(0.5)^{10}(0.5)^0 = 0.00097$

So, the total Probability = P(8) + P(9) + P(10)

= (0.0439) + (0.0097) + (0.00097)

= 0.05457

Hence, the probability that the student passes the quiz with at least 8 of the questions correct is 0.05457.

6 0

4 years ago

REPOST!!!!!! 20 POINTS!!!!!!

kkurt [141]

Answer:

A

Step-by-step explanation:

according to tangent property

we get

AM=BM
AN=CN
BK=CK

Given that

AM=6
BK=4

Thus our equation is

$\rm \displaystyle 2AM + 2AN + 2BK = 34$

substitute the given values

$\rm \displaystyle 2.6+ 2AN+ 2.4 = 34$

simplify multiplication:

$\rm \displaystyle 12+ 2AN+ 8 = 34$

simplify addition:

$\rm \displaystyle 2AN+ 20= 34$

cancel 20 from both sides:

$\rm \displaystyle 2AN=14$

divide both sides by 2:

$\rm \displaystyle AN=7$

AN=CN

hence,CN=7

therefore our answer is A

6 0

3 years ago

What are the x-intercepts of the function f(x) = –2x2 – 3x + 20?

lesya [120]

Answer:

F27

Step-by-step explanation:

5 0

3 years ago