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ollegr [7]
3 years ago
15

The sum of three consecutive even integers is -78, what are the integers ?

Mathematics
1 answer:
Digiron [165]3 years ago
5 0
First, you need to analize and understand the problem, then you must choose and strategy. There is a wide variety of strategies to solve a mathematical problem, in this case, you can use the following, which is based on the information given above:
 1. You have that t<span>he sum of three consecutive even integers is </span>-78<span>, therefore, you can given the variable </span>x&#10;<span> to the first integer, the second even integer is </span>x+2<span> and the third one is </span>x+4&#10;<span>.
 2. Calculate x:
 </span>x+(x+2)+(x+4)=-78<span>
 </span>3x+6=-78
<span> </span>x=-28&#10;<span>
 </span>x+2=-28+2=-26&#10;<span>
 </span>x+4=-28+4=-24&#10;<span>
 Therefore, the answer is:</span>-28,-26,-24&#10;
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Jim says that the square root of 200 is between 14 and 15. Do you think that is reasonable? Without using a calculator, can you
sleet_krkn [62]

Answer:

the answer is 14.14

Step-by-step explanation:

4 0
2 years ago
if there are two containers of sugar solution, the first is 4% concentration and second is 8% concentration. how much of each sh
Elina [12.6K]

Answer:

<u>30 gallons solution 4% and 10 gallons solution 8%</u>

Step-by-step explanation:

<h3>x•4%+y•8%=40•5% </h3>

<em><u>4x+8y=40•5 and x+y=40</u></em>

x=40-y

4(40-y)+8y=200

160-4y+8y=200

4y=200-160

4y=40 => y=10 (gallons solution 8%)

=> x=40-10=30 (gallons solution 4%)

30 gallons solution 4% and 10 gallons solution 8%

5 0
2 years ago
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
3 years ago
If a firm produces nothing which of the following costs will be zero?
matrenka [14]
In general when a firm produces nothing it still has to pay for the fixed costs while the variable costs are zero
3 0
3 years ago
Mathhhhhhh testtttt Add a statement, equation and concluding statement
Tom [10]

Answer:

Charlene earns $700 per week

Kristi earns $550 per week

Sascha earns $800 per week

Step-by-step explanation:

Since Kristi earns 150 less than Charlene which is 100 less than Sascha, this is equal to the value of Sascha minus 250. We put this in the equation as s-250.

Together, they all earn $2050, so we must equal this to Charlene's value k+150, plus Kristi's value k, plus Sascha's value s.

<em>k+150+k+s=2050</em>

The next step here is to put the variables on one side and to put the numeric values on the other.

2k+s=1900

Like we said before, Kristi's value is equal to s-250, so we would replace k with that expression.

2(s-250)+s=1900

2s-500+s=1900

3s=2400

s= 800

We now have Sandra's weekly pay, which we can use to find the others' pay.

c= s-100

c= 800-100

c= 700

k= c-150

k= 700-150

k= 550

7 0
3 years ago
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