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3 years ago

Which graph represents the solution to the system of inequalities?

Mathematics

2 answers:

sattari [20]3 years ago

6 0

Here is an image of that

diamong [38]3 years ago

3 0

Solution:

we are given with the system of equation:

x + y ≥ 4

2x + 3y < 12

we have been asked to find the graph representing the solution of the given system of equation.

To find the the solution of the given system of inequalities, we can draw the graph using a graphing calculator and thereafter , the point of intersection will give the solution of the given system of equation.

As we can see, the graph is intersecting at only one point at (0,4).

The given system of inequalities will have infinite number of solutions and it will fall in the region shaded with green.

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Teresa drove on monday tuesday and Wednesday. On monday her driving distance was 120 miles. The ratio of Wednesdays distance is

SSSSS [86.1K]

Answer:

Teresa drive <u>90 miles</u> on Tuesday.

Step-by-step explanation:

Given:

Teresa drove on Monday, Tuesday and Wednesday.

On monday her driving distance was 120 miles.

The ratio of Wednesdays distance is 3/5.

The ratio of Wednesdays distance to Tuesday's distance is 5/4.

Now, to find the miles Teresa drive on Tuesday:

Teresa driving distance on Monday was = 120 miles.

Her driving distance on Wednesday is = $\frac{3}{5}\ of\ 120.$

$=\frac{3}{5} \times 120\\\\=0.6\times 120\\\\=72\ miles.$

Now, her driving distance on Tuesday is:

$\frac{5}{4} \ of\ 72\\\\=\frac{5}{4} \times 72\\\\=1.25\times 72\\\\=90\ miles.$

Therefore, Teresa drive 90 miles on Tuesday.

7 0

3 years ago

During a promotional weekend, a state fair gives a free admission to every 188th person that enters the fair. On Saturday, there

damaskus [11]

Answer: 81 people

Step-by-step explanation:

Number of people that attended fair on Saturday = 6737

Number of people that got free admission = 6737/188 = 35.8.

Free admission on Saturday = 35

Number of people that attended fair on Saturday = 8669

Number of people that got free admission = 8669/188 = 46.1

Free admission on Sunday = 46

The people who received a free admission over the two days will be:

= 35 + 46

= 81 people

6 0

3 years ago

Find the length of the following curve. If you have a grapher, you may want to graph the curve to see what it looks like.

stepladder [879]

The length of the curve $y = \frac{1}{27}(9x^2 + 6)^\frac 32$ from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

$y = \frac{1}{27}(9x^2 + 6)^\frac 32$ from x = 3 to x = 6

Start by differentiating the curve function

$y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x$

Evaluate

$y' = x(9x^2 + 6)^\frac 12$

The length of the curve is calculated using:

$L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx$

This gives

$L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx$

Expand

$L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx$

This gives

$L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx$

Express as a perfect square

$L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx$

Evaluate the exponent

$L =\int\limits^6_3 {3x^2 + 1} \ dx$

Differentiate

$L = x^3 + x|\limits^6_3$

Expand

L = (6³ + 6) - (3³ + 3)

Evaluate

L = 192

Hence, the length of the curve is 192 units