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Anika
20 days ago
12

Which is the graph of the linear inequality 2x – 3y < 12? On a coordinate plane, a solid straight line has a positive slope a

nd goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded. On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.

Mathematics
2 answers:
PIT_PIT [9.1K]20 days ago
8 0

Answer: A dashed straight line with a positive slope intersects points (0, -4) and (3, -2). The area to the right of the line is shaded.

Step-by-step explanation:

AnnZ [9K]20 days ago
6 0

Answer:

A dashed straight line with a positive slope intersects points (0, -4) and (3, -2). The area to the right of the line is shaded.

Step-by-step explanation:

To graph the inequalities represented by 2x - 3y < 12, start by drawing the dashed line for 2x - 3y = 12 (the dashed signifies that the inequality excludes equality). This line passes through coordinates (0,-4) and (3,-2), which satisfy the line's equation. The slope is positive because

3y=2x-12\\ \\y=\dfrac{2}{3}x-4

with a slope calculated as 2/3.

Next, verify the position of the origin (if it lies within or outside the shaded region). Check the inequality with (0,0):

2\cdot 0-3\cdot 0=0

This implies that the origin's coordinates fulfill the inequality, meaning it is contained within the shaded area. Consequently, shade the part that includes the origin.

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For every 1 litre of water used to make a medicine, 300 ml of sucrose and 750ml of saline solution are used. Express the amount
PIT_PIT [9117]

Answer: The ratio needed will be 20:6:15.

Step-by-step explanation:

Given that

For every 1 liter of water used to create the medicine, 300 ml of sucrose and 750 ml of saline solution are required.

We should simplify the quantities of water, sucrose, and saline solution to their lowest terms.

All amounts should be converted to the same unit, which is ml.

As per the information provided,

1\ liter=1000\ milimeter\\

Thus, the ratio will be expressed as

\text{Amount of water: Sucrose: saline solution}\\\\=1000:300:750\\\\=200:60:150\\\\=40:12:30\\\\=20:6:15

Consequently, the required ratio is 20:6:15.

8 0
25 days ago
-3x + 2c = -3, solve for x
zzz [9080]

Answer:

x=2c/3+1

Step-by-step explanation:

First, subtract 2c from both sides.

−3x=−3−2c

The equation has been transformed into standard form.

−3x=−2c−3

Next, divide both sides by −3.

-3x/-3=-2c-3/-3

Dividing by −3 negates the multiplication by −3.

x=-2c-3/-3

Finally, divide −3−2c by −3.

x=2c/3+1

6 0
26 days ago
A rice merchant purchased 50 bags of rice at rupees 300 per back he spent 500 rupees towards transportation due to lack of deman
Inessa [9000]

Answer:

10500 rupees

Step-by-step explanation:

Thus, 50 bags at 300 each, which results in

300*50= 15000

15000 was his expenditure on the 50 rice bags

Additionally, he incurred a transportation cost of 500 rupees

15000 + 500 = 15500 total spent, which is extra information.

A loss of 30% translates to 30% of 15000, which is

30% of 15000 = 4500

Finally, 15000 - 4500 = 10500 rupees

8 0
1 day ago
Add and simplify 9/16=1/2=what
zzz [9080]
9 / 16 + 1/2 =?

Step 1. To add fractions, they must share the same denominator. Here the denominators are 16 and 2. Since 16 is 8 times 2, multiply 1/2 by 8 to match denominators.

(1 * 8) / (2 * 8) = 8 / 16

Step 2.  Add the numerators over the common denominator.

9/16 + 8/16 = (9+8) / 16 = 17 / 16

Step 3. Reduce the fraction if possible.

17/16 is already in simplest form. Therefore, 9/16 + 1/2 = 17/16
6 0
1 day ago
Read 2 more answers
The graphs of f(x) = 10x and its translation, g(x), are shown. On a coordinate plane, 2 exponential functions are shown. f (x) a
PIT_PIT [9117]

Answer:

g(x)=(10)^{x-3}

Detailed explanation:

* Let’s clarify the procedure for solving this problem

- An exponential function can be expressed as f(x)=a(b)^{x}, where

 a signifies the starting amount (x = 0), and b denotes the growth factor

- If b > 1, it qualifies as an exponential growth function

- If 0 < b < 1, it is categorized as an exponential decay function

- Horizontal translation to the right by h units results in the new function being g(x)=a(b)^{x-h}

- Conversely, if translated to the left by h units, the function modifies to g(x)=a(b)^{x+h}

 the new function will be

- A vertical upward shift by k units alters the function to g(x)=a(b)^{x}+k

- A vertical downward shift by k units means the new function accounts for g(x)=a(b)^{x}-k

* Now, let’s solve the problem

∵ f(x) is an exponential function

∵ The points (0, 1), (1, 10), (2, 100) are points of f(x)

- g(x) is the transformation of f(x)

∵ The points (3, 1), (4, 10), (5, 100) belong to g(x)

∵ The point (0, 1) on f(x) transforms to (3, 1) on g(x)

∵ The point (1, 10) on f(x) transforms to (4, 10) on g(x)

∵ The point (2, 100) on f(x) translates to (5, 100) on g(x)

∵ Notably, all y-coordinates of f(x) match those of g(x)

 indicating no vertical translation

∴ Hence, no vertical translation occurred

∵ The x-coordinates of f(x) are increased by

   3 units to yield the x-coordinates for g(x)

∴ This shows that f(x) is translated 3 units to the right

∵ f(x)=(10)^{x}

∴ g(x)=(10)^{x-3}

- Refer to the corresponding graph for greater clarity

# The red curve denotes f(x)

# The blue curve signifies g(x)

4 0
12 days ago
Read 2 more answers
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