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3 years ago

What is the reciprocal of each mixed number? Drag and drop the answer into the box to match each number.

1 answer:

5 0

Hi there!!

First, we are going to find the improper fraction of each mixed number.

10 1/3 >>>>> 10*3+1=31 31/3

2 2/3 >>>>> 2*3+2=8. 8/3

5 1/3 >>>>>> 5*3+1 = 16. 16/3

TO find the reciprocal, we switch the numerator with the denominator.

31/3 changes to 3/31, 8/3 changes to 3/8, and finally 16/3 changes to 3/16.

Your answer is:

3/31
3/8
3/16

Hope this helps! Let me know if you have any questions:)

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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:

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

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Distance traveled in 3 hrs was (speed in mph)(3 hrs)

Then s(3 hrs) + 12 mi = 132 mi.

Therefore, 3s = 120, and s = 120 miles / 3 hrs = 40 mph (answer)

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3 years ago

The product of two numbers is 10 times the value of 8 × 7. Which expression shows the two numbers?

Aleonysh [2.5K]

Answer: 7 x 80 i think

Step-by-step explanation:\

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3 years ago

Please help solve quick

RoseWind [281]

Answer:

see below

Step-by-step explanation:

3x^2 + 17x +10 =0

(3x+ ) ( x+ ) =0

We need to factor 10 = 2*5 or 1*10

They are positive since we have all positive terms

3*5 = 15+2 = 17

The 5 needs to multiply the 3 so it goes on the outside

(3x+ ) ( x+ 5 ) =0

That leaves the 2 on the inside

(3x+ 2 ) ( x+ 5 ) =0

Using the zero product property

3x+2 =0 x+5=0

3x = -2 x=-5

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3 years ago