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inna [77]
3 years ago
10

a pool only open when the temperature is at least 72 degrees. Which inequality represents the temperature t, when the pool is op

en?
Mathematics
1 answer:
BartSMP [9]3 years ago
5 0

Answer:

t ≥ 72

Step-by-step explanation:

The pool has to be at least 72° or MORE to open, so we are going to have a greater sign with an equal sign under indicating that the temperature has to  at least be 72° or be greater than 72°. (≥)

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Y=-x^2+6x-4<br> Find the Axis of Symmetry and the Vertex, Also solve the whole equation.
Inessa [10]

Answer:

1. <em>Axis of symmetry</em>: x = 3

2. <em>Vertex:</em> (3,5)

3. <em>Solution of the equation</em>:

<u />

  • x-intercepts:

               (3-\sqrt{5},0) \\\\(3+\sqrt{5},0)

  • y-intercept: (0, -4)

Explanation:

<u>1. Equation:</u>

    y=-x^2+6x-4

<u>2. </u><em><u>Axis of symmetry:</u></em>

That is the equation of a parabola, whose standard form is:

                 y=ax^2+bx+c

Where:    

                 a=-1;b=6;c=-4

The axis of symmetry is the vertical line with equation:

               x=-b/2a

Substitute  a=-1,\text{ and }b=6

          x=-6/[(2)(-1)]=-6/(-2)=3

Thus, the axis of symmetry is:

            x=3

<em><u>3. Vertex</u></em>

<em><u /></em>

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

               y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5

Therefore, the vertex is (3, 5)

<u>4. Find the x-intercepts</u>

The x-intercepts are the roots of the equation, which are the points wher y = 0.

        y=-x^2+6x-4=0

Use the quadratic equation:

       x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}

<u>5. Find the y-intercept</u>

<u />

The y-intercet is the value of y when x=0:

         y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4

7 0
4 years ago
At a bargain store, Tanya bought 4 items that each cost the same amount. Tony bought 5 items that each cost the same amount, but
Alex_Xolod [135]

If x is the amount that Tanya paid for each item, then Tony's items would be x-2.25. So:

3x=4(x-2.25)

3x=4x-9

x=9

x-2.25=6.75

Tanya spent $9 on each item; Tony spent $6.75 on each of his items. ☺☺☺☺

6 0
3 years ago
Stuart has some 2- ounce, 3- ounce, and 4- ounce weights. How many different ways can Stuart combine the weights to make a total
podryga [215]
2,3,4
1st way: 6*2oz=12oz
2nd way: 3*2oz+2*3oz=12oz
3rd way: 4*2oz+4oz=12oz
4th way: 2*2oz+2*4oz=12oz
5th way: 4*3oz=12oz
6th way: 2*3oz+2oz+4oz=12oz
7th way: 3*4oz=12oz
Stuart can combine 2oz, 3oz and 4oz weigths 7 different ways to get 12oz.

8 0
3 years ago
Can someone help me on this problem please? I'm not sure how to figure it out. Thank you! :P
Dafna11 [192]

Answer:

They are not similar because the shape and their numbers.

Step-by-step explanation:

Pls  brainliest :/

6 0
3 years ago
Read 2 more answers
PLEASE ANSWER THE BLANKS PLEASE AND USE AN ANSWER FROM THE PARENTHESES BESIDE THE QUESTION, I'M GIVING BRAINLIEST IF YOU ANSWER
sleet_krkn [62]

Answer 1a 18 1b 36 1c 648

1a : if you look at the shape you will see its made of squares. I counted the squares, its 18.

1b : one side is 6 in. since its a square all sides are equal. so multiply 6 by 6 to get 36.

1c : this one is easy. We take the number of squares across the surface (18) by the area of each square (36) it is 648.

Also sorry I didn't make this clearer earlier.

5 0
2 years ago
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