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andreyandreev [35.5K]
1 year ago
7

Is (3,6) a solution of y's 3x + 4?

Mathematics
1 answer:
notka56 [123]1 year ago
3 0

Step 1:

(3,6) means x coordinate is 3 and y coordinate 6

Step 2:

We substitute the values of x = 3 and y = 6 into the inequality

\begin{gathered} y\text{ }\leq\text{ }\frac{2}{3}\text{ }x\text{ + 4} \\ 6\text{ }\leq\text{ }\frac{2}{3}\text{ x }\frac{3}{1}\text{  + 4} \\ 6\text{ }\leq\text{ 2 + 4} \\ 6\text{ }\leq\text{ 6} \end{gathered}

Conclusion:

Since 6 is equal to 6, then (3,6) is a solution of the given Inequality

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Write the equation of the line with the following characteristics.
Alika [10]

Answer:

y = 7x

y = 2x -3

y = 3

x = -2

Step-by-step explanation:

  • <em>Slope-intercept form: y= mx+b</em>
  • <em>Parallel lines have same slope</em>

a)Parallel to y=7x+2 through the point (0,0)

<u> This line will have a form:</u>

  • y= 7x + b

<u>Considering the given point of (0,0), to find the value of b:</u>

  • 0= 7*0+b ⇒ b =0

<u>The line is: </u>

  • y = 7x

b)Slope of 2 through the point (0,−3)

<u> Solving as above:</u>

  • y= 2x + b
  • -3 = 2*0 + b ⇒ b = -3
  • y = 2x -3

c)A horizontal line through the point (0,3)

<u> A horizontal line will have constant value for y for any value of x:</u>

  • y = 3

d)A vertical line through the point (−2,0)

<u>A vertical line will have constant value of x for any value of y:</u>

  • x= -2
5 0
3 years ago
8. The base of a circular cone has a diameter of 10 cm and an altitude of 10 cm. The cone is filled with water. A sphere is lowe
nataly862011 [7]

Answer:

The volume of water that remains on the cone is 523.6 cm³

Step-by-step explanation:

To solve this problem you have to keep in mind the formules that describes the volume of a cone and the volume of a sphere.

Volume of a cone = (πr²h)/3

Volume of a sphere = (4/3)πr³

So, if the base of the cone has a diameter of 10 cm, its radius is 5 cm. Its altitude is 10 cm. ⇒Volume = (πr²h)/3 ⇒ Volume = [π(5²)10) ⇒

          Volume = 785.4 cm³. This is the initial volume of water.

Now if the sphere fits in the cone and half of it remains out of the water, the other half is inside the cone. Estimating the volume of the sphere and dividing it by two, you find the volume of water that was displaced.

Volume of a sphere = (4/3)πr³, here the radius is the same of the base of the cone (5 cm).

⇒ Volume = (4/3)π(5³)  ⇒ Volume = 523.6 cm³ ⇒ The half of this volume is 261.8 cm³. This is the volume of water displaced.

⇒ The volume of water that remains on the cone is 523.6 cm³ (785.4 cm³- 261.8 cm³)

6 0
3 years ago
Veronica brought her turtle out of its aquarium for 15 minutes for 7 days.How many total minutes did she bring the turtle out of
daser333 [38]
105 minutes
15*7 = 105 
6 0
3 years ago
Find the angle complementary to the angle 80°25
Viefleur [7K]
<span>90 degrees 0 minutes is the same as 89 degrees 60 minutes.
89 degrees 60 minutes minus 80 degrees 25 minutes equals:
9 degrees 35 minutes.
-----
your answer is:
9 degrees 35 minutes</span>
5 0
3 years ago
Find the lengths of the unknown sodes
grandymaker [24]

Answer:

7

Step-by-step explanation:

24^2+x^=25^2

576+x^2+576

49=X^2

square root 49 and x

x=7

5 0
3 years ago
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