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stepan [7]
1 year ago
5

find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point..y=x²+9

Mathematics
1 answer:
Alexandra [31]1 year ago
3 0

Explanation:

using the parabola formula:

y = a(x-h)² + k²

vertex = (h, k)

We are given a parebola equation of: y = x²+9

comparing both equations to get the vertex:

y = y

a = 1

(x-h)² = x²

x² = (x + 0)²

(x-h)² = (x + 0)²

h = 0

+k = +9

k = 9

The vertex of the parabola as (x, y): (0, 9)

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If a quadratic polynomial has an absolute minimum at (-3,-5), what is the range of the polynomial?
irga5000 [103]

Answer:

range: (-5, ∞)

domain: (-∞, ∞)

Step-by-step explanation:

given vertex, absolute minimum: (-3, -5)

Range look at y-value

(minimum, maximum) the -5 will be on the left  of the comma b/c its the min

If this was a max, you would put the y-value on the right side of the comma

3 0
3 years ago
How many kilograms of a 5% salt solution and how many kilograms of a 15% salt solution must be mixed together to make 45kg of an
JulsSmile [24]

Answer:

31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Step-by-step explanation:

Let us assume that the number of kilograms of a 5% salt solution used be x .

Let us assume that the number of kilograms of a 15% salt solution used be y .

As given

A 5% salt solution and 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Equation becomes

x + y = 45

5% is written in the decimal form .

= \frac{5}{100}

= 0.05

15% is written in the decimal form .

= \frac{15}{100}

= 0.15

8% is written in the decimal form .

= \frac{8}{100}

= 0.08

Thus

Concentration of 5% salt solution × Number of kilograms of 5% salt solution used + Concentration of 15% salt solution × Number of kilograms of  15% solution used = Concentration of 8% salt solution × Number of kilograms of 8% salt solution

Thus

0.05x + 0.15y = 0.08 × 45

Simplify the above

\frac{5x}{100} + \frac{15y}{100} = \frac{8\times 45}{100}

5x + 15y = 360

Thus two equations becomes

x + y = 45

5x + 15y = 360

Multiply x + y = 45 by 5 and subtracted from 5x + 15y = 360 .

5x - 5x + 15y - 5y = 360 - 225

10y = 135

y = \frac{135}{10}

y = 13.5 kilograms

Put value of y in the equation

x + 13.5 = 45

x = 45 - 13.5

x = 31.5 kilograms

Therefore the 31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

5 0
2 years ago
WILL GIVE BRAINLIEST
user100 [1]
I'm pretty sure the answer is SAS because it gives you one angle and the rest are sides
4 0
3 years ago
Read 2 more answers
The area of a rectangle is 105 square units. Its width measures 7 units. Find the length of its diagonal. Round to the nearest t
mezya [45]

Answer:

16.6

Step-by-step explanation:

The rectangle has an area of 105. It's width is 7.

1: Find the length

     \frac{area}{width}=length

     \frac{105}{7}= 15

      Length=15

2: Pythagorean theorem

      a^{2} +b^2=c^2

       7^{2}+15^2=c^2

       49+225=c^2

        275=c^2

         \sqrt{275} = \sqrt{c^2\\}

          16.55≈c

           Rounded to nearest tenth

              16.6

6 0
3 years ago
1/3 x (9c+12) + (4c)+6
RoseWind [281]

Answer:

7c+18

Step-by-step explanation:

FIRST

take out the parentheses so it will be

( 1/3*9c)+12+4c+6

3c+12+4c+6

Combine like terms



3 0
3 years ago
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