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stepladder [879]
3 years ago
15

What is the answer to this problem

Mathematics
1 answer:
Aleks04 [339]3 years ago
3 0

Answer:

14 cm^2

Step-by-step explanation:

You find the area of both triangles, and subtract by 4

6x3x1/2x2 - 2x2

18 - 4

14

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Find the area of the region bounded by the line y=3x-6 and line y=-2x+8.
Vikentia [17]

Answer:

A = 12/5 units

Step-by-step explanation:

USING ALGEBRA:

We can find the intersection point between these two lines;

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

Multiply and simplify.

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

3 0
3 years ago
PLEASEEEE 100 POINTS AND BRAINLIEST PLEASEE HELPP ASAPPPPPPPPP!!!!! THANKS <3333
castortr0y [4]

Answer:

2 5 7

Step-by-step explanation:

hopefully it helps sorry if it wrong

8 0
2 years ago
How many quarts of pure antifreeze must be added to 8 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution
anyanavicka [17]

Let <em>q</em> be the number of quarts of pure antifreeze that needs to be added to get the desired solution.

8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.

The new solution would have a total volume of 8 + <em>q</em> quarts, and it would contain a total amount of 3.2 + <em>q</em> quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means

(3.2 + <em>q</em>) / (8 + <em>q</em>) = 0.60

Solve for <em>q</em> :

3.2 + <em>q</em> = 0.60 (8 + <em>q</em>)

3.2 + <em>q</em> = 4.8 + 0.6<em>q</em>

0.4<em>q</em> = 1.6

<em>q</em> = 4

4 0
2 years ago
Find the complement of 73°<br><br>​
Nimfa-mama [501]

Answer:

18°

Step-by-step explanation:

90-72= 18

The complement of 73 is the angle that when added to 73 forms a right angle which is 90° xd

5 0
3 years ago
Write the equation of the line that passes through the points (3,5) and (-1,1). Put
dangina [55]

Given:

A line passes through the two points (3,5) and (-1,1).

To find:

The equation of the line in fully reduced point-slope form.

Solution:

If a line passes through two points, then the point slope form of the line is

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

The line passes through the two points (3,5) and (-1,1). So, the point slope form of the line is

y-5=\dfrac{1-5}{-1-3}(x-3)

y-5=\dfrac{-4}{-4}(x-3)

y-5=1(x-3)

Therefore, the  point slope form of the line in fully reduced form is y-5=1(x-3), here 1 is the slope of the line.

6 0
3 years ago
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