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3 years ago

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miguel is making an obstacle course for feild day.at the end of every sixth of the course is a tire.at the end of every third of

the course there is a cone.at the end of every half of the course there is a hurdle.at which locations of the course will people need to go through more than one obstacle?

1 answer:

Bogdan [553]3 years ago

8 0

I hope this helped! Good luck

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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

3 years ago

Use the compound interest formula to compute the total amount accumulated and the interest earned.

mezya [45]

A=3,500×(1+0.011÷12)^(12×4)
A=3,657.36

Interest earned
=3657.36-3500=157.36

6 0

3 years ago

A flowerbed surrounds the base of a tree. It’s enclosed by stones to form a circle that measures 25.12 feet. What is the radius

Ymorist [56]

2.83 if rounded. 2.82842712475 would be the actual.

Hope this helped!

5 0

3 years ago

Which function has the graph shown below? *

sergij07 [2.7K]

Answer:

C

Step-by-step explanation:

yeah-ya......... right?

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2 years ago

Solve this equation for x: 2x^2 + 12x - 7 = 0

zhannawk [14.2K]

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: $2x^2 + 12x - 7 = 0$

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

$2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7$

Step 2: Divide the equation all through by the coefficient of $x^2$ which is 2.

$x^2 + 6x=\frac{7}{2}$

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3= $3^2$

Therefore, we have:

$x^2 + 6x+3^2=\frac{7}{2}+3^2$

Step 4: Write the Left Hand side in the form $(x+k)^2$

$(x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\$

Step 5: Take the square root of both sides and solve for x

$x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355$

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2 years ago