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saw5 [17]
3 years ago
14

What would the graph of 10x + 7y < 49 look ?

Mathematics
2 answers:
navik [9.2K]3 years ago
8 0

Answer: The graph is attached.

Step-by-step explanation:

1. Solve for y, as following:

10x+7y

2. The equation of the line in slope intercept form is:

y=mx+b

Where m is the slope and b is the y-intercept.

3. In this case the equation of the line is:

y=-\frac{10}{7}x+7

then:

m=-\frac{10}{7}\\\\b=7

4. Find the x-intercept. Make y=0. Then:

0=-\frac{10}{7}x+7\\\frac{10}{7}x=7\\x=4.9

5. Then, plot the line that passes through the points (0,7) and (4.9, 0).

6. The symbol of the inequality is < therefore, the line must be dashed and indicates that the region under the line must be shaded.

Then you obtain the graph attached.

larisa86 [58]3 years ago
5 0

Answer:

We need to graph the given inequality 10x + 7y < 49.

We can do that into 2 parts:

<u>Part 1:</u>

Graph the line 10x+7y=49

plug any number for x say x=0

10x+7y=49

10(0)+7y=49

0+7y=49

7y=49

y=49/7

y=7

hence it passes through point (0,7)

similarly plug y=0

10x+7(0)=49

10x=49

x=49/10

x=4.9

hence it passes through point (4.9,0)

Graph both points then join them by a straight dotted line because of < sign.

<u>PART 2:</u>

Shade the graph for inequality sign <

use any test point which is not on the given line say (0,0)

plug into original problem

10x + 7y < 49

10(0) + 7(0) < 49

0<49 is true

so shade in direction of test point

Hence final graph looks like:

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jeyben [28]

Answer:

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5 0
3 years ago
Read 2 more answers
A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the
Mashcka [7]

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

\displaystyle V(t) = 0.1(t - 10) + 4.8

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The <em>x-</em>coordinate is measured in minutes since the tank began to be filled and the <em>y-</em>coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

\displaystyle y - y_1 = m( x - x_1)

Where <em>m</em> is the slope/rate of change and (<em>x</em>₁, <em>y</em>₁) is a point.

We will substitute 0.1 for <em>m</em> and let (10, 4.8) be the point. Hence:

\displaystyle y - (4.8) = 0.1(x - 10)

Simplify:

\displaystyle y = 0.1(x-10) + 4.8

Since <em>y</em> represent how full the tank is and <em>x</em> represent the time in minutes since the tank began to be filled, we can substitute <em>y</em> for V(t) and <em>x</em> for <em>t</em>. Thus, our function is:

<em />\displaystyle V(t) = 0.1(t - 10) + 4.8<em />

<em />

The initial volume is when <em>t</em> = 0. Evaluate:

\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for <em>t</em>. Hence:

60 = 0.1(t - 10) + 4.8

Subtract:

55.2 = 0.1(t - 10)

Divide:

552 = t - 10

Add. Therefore:

t = 562\text{ minutes}

It will take 562 minutes for the tank to be completely filled.

8 0
2 years ago
I-ready test 7th grade
snow_lady [41]

Answer:

A

Step-by-step explanation:

3 0
3 years ago
Suppose you have a right triangle with congruent legs and a hypotenuse that measure (12√5)/5. What is the length of the smaller
hammer [34]

Answer:

5.4 is the length

Step-by-step explanation:

5.333 - (12√5)/5 - round to nearest hundreth (5.4)

length total 5.4

Thanks and Rate my Answer Please!

8 0
3 years ago
How many L of A 90% saline solution must be mixed with 4 L of a 50% saline solution to make a 74% solution ?
insens350 [35]

Answer:

6 L

Step-by-step explanation:

Given two solutions:

1st solution is 90% saline solution. Let the volume of this solution be x litres.

2nd solution is 50% saline solution. Volume of this solution = 4 L

Resultant solution is 74% saline.

To find:

The volume of 1st solution = ?

Solution:

Total volume of the 74% saline mixture = (4+x) Litres

We can write equation here, as per the percentage of saline in the mixtures.

90% of x L + 50% of 4 L = 74% of (x+4)

\Rightarrow \dfrac{90x}{100} + \dfrac{50}{100}\times 4 = \dfrac{74}{100}\times (x+4)\\\Rightarrow 90x + 200 = 74x+296\\\Rightarrow 90x-74x = 296-200\\\Rightarrow 16x = 96\\\Rightarrow x = \bold{6\ L}

Therefore, the volume must be <em>6 L</em>.

8 0
3 years ago
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