Ask question

Ask question

All categories

1 year ago

5

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to th

e left of the line is shaded. Which linear inequality is represented by the graph? y < Two-thirdsx + 3 y > Three-halvesx + 3 y > Two-thirdsx + 3 y < Three-halvesx + 3

2 answers:

Allushta [10]1 year ago

8 0

Answer:

$y>\frac{2}{3}x+3$

Step-by-step explanation:

step 1

Determine the slope of the dashed line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

(-3,1) and (0,3)

substitute

$m=\frac{3-1}{0+3}$

$m=\frac{2}{3}$

step 2

Find the equation of the dashed line in slope intercept form

$y=mx+b$

we have

$m=\frac{2}{3}$

$b=3$ ---> given problem

substitute

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

step 3

Find the equation of the inequality

we know that

Is a dashed line and everything to the left of the line is shaded

so

$y>\frac{2}{3}x+3$

see the attached figure to better understand the problem

Tcecarenko [31]1 year ago

5 0

Simplified Answer:

<h2>its C.</h2>

y > 2/3x + 3

Step-by-step explanation:

person above explains how you can get this answer

You might be interested in

Cheri took out a loan for $14,350. The loan term was 3 years and Cheri’s payments were $625.77 per month. Since Cheri had filed

melamori03 [73]

Answer:

You are correct.

Step-by-step explanation:

3 0

1 year ago

Read 2 more answers

Nevin made tables of values to approximate the solution to a system of equations. First he found that the x-value of the solutio

prisoha [69]

Answer:

The correct option is B.

Step-by-step explanation:

The given equation are

$y=4x-3$

$y=-5x+9$

On solving both the equation, we get

$4x-3=-5x+9$

$4x+5x=9+3$

$9x=12$

$9x=\frac{12}{9}=\frac{4}{3}$

Put this value in the given equation.

$y=4(\frac{4}{3})-3$

$y=\frac{16}{3}-3$

$y=\frac{16-9}{3}$

$y=\frac{7}{3}$

The solution of the given system of equation is

$(\frac{4}{3},\frac{7}{3})=(1.333,2.333)\approx (1.3,2.3)$

The best approximation of the exact solution is (1.3,2.3). Therefore the correct option is B.

7 0

2 years ago

Read 2 more answers

Three highways connect city A with city B. Two highways connect city B with city C.

QveST [7]

(a) The probability that there is no open route from A to B is (0.2)^3 = 0.008.
Therefore the probability that at least one route is open from A to B is given by: 1 - 0.008 = 0.992.
The probability that there is no open route from B to C is (0.2)^2 = 0.04.
Therefore the probability that at least one route is open from B to C is given by:
1 - 0.04 = 0.96.
The probability that at least one route is open from A to C is:
$0.992\times0.96=0.9523$

(b)
α The probability that at least one route is open from A to B would become 0.9984. The probability in (a) will become: $0.9984\times0.96=0.95846$

β The probability that at least one route is open from B to C would become 0.992. The probability in (a) will become:
$0.992\times0.992=0.9841$

Gamma: The probability that a highway between A and C will not be blocked in rush hour is 0.8. We need to find the probability that there is at least one route open from A to C using either a route A to B to C, or the route A to C direct. This is found by using the formula:
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$0.9523+0.8-(0.9523\times0.8)=0.99$
Therefore building a highway direct from A to C gives the highest probability that there is at least one route open from A to C.

4 0

2 years ago

Pedro has created the function f(x)= 4x-3/2 to represent the number of assingments he has completed where x represents the numbe

Law Incorporation [45]

The given function is
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments

We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:

1. Set y = f(x)
y = 4x - 3/2

2. Exchange x and y
x = 4y - 3/2

3. Solve for y
4y = x + 3/2
y = (x +3/2)/4

4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4

5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)

Answer:
Pedro needs about 8 weeks to complete 30 assignments.

6 0

1 year ago

A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10m greater than the other side.

DanielleElmas [232]

Answer:

The length of the fence needed to surround this garden is 188 meters.

Step-by-step explanation:

Given : A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10 m greater than the other side.

To find : The length of the fence needed to surround this garden if the area of the vegetable garden is 2184 m² ?

Solution :

Let the one side of rectangle be 'x'.

Then the other side is 'x+10'.

The area of the rectangle is 2184 m²,

i.e. $x(x+10)=2184$

$x^2+10x-2184=0$

Solve by middle term split,

$x^2+52x-42x-2184=0$

$x(x+52)-42(x+52)=0$

$(x+52)(x-42)=0$

$x=-52,42$

Reject negative value,

The side of the rectangle is 42 m.

The other side is 42+10=52 m

The perimeter of the rectangle is $P=2(l+b)$

$P=2(42+52)$

$P=2(94)$

$P=188$

Therefore, the length of the fence needed to surround this garden is 188 meter.

5 0

1 year ago