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3 years ago

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

1 answer:

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 the sum of three consecutive even integers is $-78$ , therefore, you can given the variable $x
$ to the first integer, the second even integer is $x+2$ and the third one is $x+4
$ .
2. Calculate x:
 $x+(x+2)+(x+4)=-78$ 
 $3x+6=-78$
 $x=-28
$ 
 $x+2=-28+2=-26
$ 
 $x+4=-28+4=-24
$ 
Therefore, the answer is: $-28,-26,-24
$

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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:

30 gallons solution 4% and 10 gallons solution 8%

Step-by-step explanation:

4x+8y=40•5 and x+y=40

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 Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

Inessa [10]

Answer:

1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

x-intercepts:

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

y-intercept: (0, -4)

Explanation:

1. Equation:

$y=-x^2+6x-4$

2. Axis of symmetry:

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:

$x=3$

3. Vertex

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)

4. Find the x-intercepts

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:

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

5. Find the y-intercept

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.

k+150+k+s=2050

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