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Basile [38]
3 years ago
13

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credi

t:
x^2 + 4x + y^2 − 6y = −4
Mathematics
1 answer:
Nitella [24]3 years ago
5 0

Answer:

Circle with center at (-2,3) and radius r=3.

Step-by-step explanation:

Rewrite equation in standard form.

(x-a)^2+(y-b)^2=r^2

(x-(-2))^2+(y-3)^2=3^2

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What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?
AfilCa [17]

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

4 0
3 years ago
A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to t
velikii [3]

Answer:

B

Step-by-step explanation:

To answer this, we need to see the to see to the fact that they are both in the same unit before we can take the ratio.

Firstly, we know that 1 foot = 12 inches. 9 feet would this be 9 * 12 = 108 inches.

Now we are told to get the ratio of length of car to length of model.

This means 108:6 = 18:1

5 0
3 years ago
Read 2 more answers
If A/B and C/D<br> are rational expressions, then<br> AxC/BxD = AxD/BxC<br> A. True<br> B. False
sdas [7]

Answer:

True

Step-by-step explanation:

If A/B and C/D are rational expression then

A/B*C/D

Or

A/B*C/D=A/C*B/D

It means that if A/B and C/D are rational expression then their product with each other will also be a rational expression.

6 0
3 years ago
PLS HELP ! Will give brainliest
Darina [25.2K]

Answer:

Step-by-step explanation:

The quadratic formula would be the following...

x = \frac{-b (+-)\sqrt{b^{2} - 4ac } }{2a}

where the original quadratic equation would be represented as follows

ax^{2} + bx +c = 0

Using this information and the information provided in the image we can plug in the quadratic equation values in the image to form the quadratic formula.

\frac{-(-20)±\sqrt{(-20)^{2} - 4(16)(-6) } }{2(16)}

That would be the correct order for the values.

3 0
3 years ago
Draw a 6 × 6 grid. Colour 1
attashe74 [19]

Answer:

Step-by-step explanation:

there are 36 squares

red takes 1 of 4 so red has 9

blue takes 1 of 3 so blue has 12

5 of 12 of the grid is yellow

3 0
3 years ago
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