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Mkey [24]
3 years ago
9

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the

right of the line is shaded. Which linear inequality is represented by the graph? y ≤ One-halfx + 2 y ≥ One-halfx + 2 y ≤ One-thirdx + 2 y ≥ One-thirdx + 2

Mathematics
2 answers:
Paha777 [63]3 years ago
9 0

Answer:

y\le\dfrac{1}{2}x+2

Step-by-step explanation:

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). This line has the equation

y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\ \\y=\dfrac{1}{2}(x+4)\\ \\y=\dfrac{1}{2}x+2

The origin belongs to the shaded region, so its coordinates must satisfy the inequality. Since

\dfrac{1}{2}\cdot 0+2=2\ge 0,

then the correct inequality is

y\le\dfrac{1}{2}x+2

zzz [600]3 years ago
4 0

Answer:

A

y ≤ \frac{1}{2}x + 2

Step-by-step explanation:

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What is the answer for3+8x=4
Schach [20]

Answer: x=1/8

Step-by-step explanation:

Subtract 3 from both sides

3+ 8x=4

8x=1

Divide by 8 on both sides

x=1/8

Hope this helped! :)

3 0
3 years ago
"the life length x (in years) of a dvd player" is exponentially distributed with mean 5 years. what is the probability that a mo
loris [4]
The exponential distribution is:
\lambda e^{- \lambda x}
where \lambda = \frac{1}{mean}=\frac{1}{5}

The probability we want is how likely will a dvd player last more than 8 years, given it has already lasted 5 years
To find this, you use conditional probability.
P(A|B) = \frac{P(A and B)}{P(B)}
where A is P(x>8) and B is P(x>5)
To find these probabilities, integrate over the distribution:
P(x \ \textgreater \ N) = \int_N^{\infty} \frac{1}{5} e^{-x/5} dx = e^{-N/5}

Sub into conditional probability formula:

P(x \ \textgreater \ 8 | x\ \textgreater \ 5) = \frac{P(x\ \textgreater \ 8)}{P(x\ \textgreater \ 5)} = \frac{e^{-8/5}}{e^{-5/5}} = e^{-3/5} = 0.549

Final Answer: Given a dvd player is more than 5 years old, the probability that it will last another 3 more years is about 54.9%
3 0
3 years ago
What is the area of the parallelogram shown below in square units? 9 units 20 units
tatyana61 [14]

Answer

160

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Maths functions question!!
Marina86 [1]

Answer:

5)  DE = 7 units and DF = 4 units

6)  ST = 8 units

\textsf{7)} \quad \sf OM=\dfrac{3}{2}\:units

8)  x ≤ -3 and x ≥ 3

Step-by-step explanation:

<u>Information from Parts 1-4:</u>

brainly.com/question/28193969

  • f(x)=-x+3
  • g(x)=x^2-9
  • A = (3, 0)  and C = (-3, 0)

<h3><u>Part (5)</u></h3>

Points A and D are the <u>points of intersection</u> of the two functions.  

To find the x-values of the points of intersection, equate the two functions and solve for x:

\implies g(x)=f(x)

\implies x^2-9=-x+3

\implies x^2+x-12=0

\implies x^2+4x-3x-12=0

\implies x(x+4)-3(x+4)=0

\implies (x-3)(x+4)=0

Apply the zero-product property:

\implies (x-3)= \implies x=3

\implies (x+4)=0 \implies x=-4

From inspection of the graph, we can see that the x-value of point D is <u>negative</u>, therefore the x-value of point D is x = -4.

To find the y-value of point D, substitute the found value of x into one of the functions:

\implies f(-4)=-(-4)=7

Therefore, D = (-4, 7).

The length of DE is the difference between the y-value of D and the x-axis:

⇒ DE = 7 units

The length of DF is the difference between the x-value of D and the x-axis:

⇒ DF = 4 units

<h3><u>Part (6)</u></h3>

To find point S, substitute the x-value of point T into function g(x):

\implies g(4)=(4)^2-9=7

Therefore, S = (4, 7).

The length ST is the difference between the y-values of points S and T:

\implies ST=y_S-y_T=7-(-1)=8

Therefore, ST = 8 units.

<h3><u>Part (7)</u></h3>

The given length of QR (⁴⁵/₄) is the difference between the functions at the same value of x.  To find the x-value of points Q and R (and therefore the x-value of point M), subtract g(x) from f(x) and equate to QR, then solve for x:

\implies f(x)-g(x)=QR

\implies -x+3-(x^2-9)=\dfrac{45}{4}

\implies -x+3-x^2+9=\dfrac{45}{4}

\implies -x^2-x+\dfrac{3}{4}=0

\implies -4\left(-x^2-x+\dfrac{3}{4}\right)=-4(0)

\implies 4x^2+4x-3=0

\implies 4x^2+6x-2x-3=0

\implies 2x(2x+3)-1(2x+3)=0

\implies (2x-1)(2x+3)=0

Apply the zero-product property:

\implies (2x-1)=0 \implies x=\dfrac{1}{2}

\implies (2x+3)=0 \implies x=-\dfrac{3}{2}

As the x-value of points M, Q and P is negative, x = -³/₂.

Length OM is the difference between the x-values of points M and the origin O:

\implies x_O-x_m=o-(-\frac{3}{2})=\dfrac{3}{2}

Therefore, OM = ³/₂ units.

<h3><u>Part (8)</u></h3>

The values of x for which g(x) ≥ 0 are the values of x when the parabola is above the x-axis.

Therefore, g(x) ≥ 0 when x ≤ -3 and x ≥ 3.

8 0
1 year ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%28x%20-%201%29%28%20x%20-%20%28%20%5Cfrac%7B1%7D%7B2%7D%20%2B%203i%29%28x%20-%20%28%20%5Cfrac
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(X-1)(\frac{37}{4} -3ix+\frac{x}{2} )

Hope this helps

Mark me as brainliest pls begging u

3 0
3 years ago
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