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3 years ago

Examine the following system of inequalities.

Mathematics

1 answer:

lubasha [3.4K]3 years ago

7 0

Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

$y > -x+4$ ----> inequality A

The solution of the inequality A is the shaded area above the dotted line $y=-x+4$

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

$y \leq -(1/2)^{x} +6$ -----> inequality B

The solution of the inequality B is the shaded area above the solid line $y=-(1/2)^{x} +6$

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

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Need help will give thanks and brainliest

Y_Kistochka [10]

Answer:

$y=\frac{2}{3} x-1$

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where $m$ is the slope and $b$ is the y-intercept (the value of y when the line intercepts the y-axis)

1) Find the slope of the line (m)

The equation for slope: $\frac{y_2-y_1}{x_2-x_1}$ when the given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (3,1) and (6,3)

$\frac{y_2-y_1}{x_2-x_1}$

$=\frac{3-1}{6-3}\\=\frac{2}{3}$

Now, plugging this back into $y=mx+b$ , our equation looks like this:

$y=\frac{2}{3} x+b$

2) Find the y-intercept of the line

To find the y-intercept, we take the equation that we have so far and plug in any given point to solve for b. For example, we can use the point (3,1):

$1=\frac{2}{3}*3+b\\1=2+b$

Subtract both sides by 2 to isolate b

$1-2=2+b-2\\-1=b$

3) Plug m and b into y=mx+b

$y=\frac{2}{3} x-1$

I hope this helps!

8 0

3 years ago

Solve the equation 2x^2-9x=0 by factoring

qwelly [4]

Answer: x = 0, $\frac{9}{2}$

Step-by-step explanation:

Given:

2x^2-9x=0

Rewrite:

0 = 2x² - 9x

Factor:

0 = (2x - 9)x

Solve:

x = 0, $\frac{9}{2}$

7 0

2 years ago

Read 2 more answers

Please help me out with this please!!

Monica [59]

It will be close to 15 days but don’t take my word for it

5 0

3 years ago

According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that m

tekilochka [14]

Answer:

0.0588 = 5.88% probability that a middle-aged man with diabetes is very active

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Has diabetes.

Event B: Is very active.

Probability of having diabetes:

To find this probability, we take in consideration that:

It also found that men who were very active (burning about 3,500 calories daily) were a fourth as likely to develop diabetes compared with men who were sedentary. Assume that one-fifth of all middle-aged men are very active, and the rest are classified as sedentary.

So the probability of developing diabetes is:

x of 4/5 = x of 0.8(not active)

x/4 = 0.25x of 1/5 = 0.2(very active). So

$P(A) = 0.8x + 0.25*0.2x = 0.85x$