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zhannawk [14.2K]
2 years ago
9

He statement below describes a situation in which opposite quantities combine to make zero:

Mathematics
1 answer:
kozerog [31]2 years ago
3 0
False I’m pretty sure
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Volume is equal mass by density
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Alex has a grid in the shape of a rectangle. he has right triangles. each right triangle has an area of 25 square millimeters an
Maurinko [17]
First you have to find the area of the rectangular grid. The area of a rectangle is length•width.
So:
A= 20•12
A= 240cm
Then you need to convert 240cm into mm.
240cm is 2400mm.

Then you need to figure out how many triangles can fit into the rectangle if all the triangles have an area of 25mm. So you divide 2400 by 25.
2400:25= 96

So Alex can fit 96 triangles into the grid.
4 0
3 years ago
Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence?: f(1) = 6, f(4) = 12, f(7)
Gala2k [10]
A = 6
tn = a + (n - 1)d
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A problem states: "There are 5 more girls than boys at the party. There are 27 children at the party in all. How many boys are t
Sever21 [200]
As there is 5 more girls than boys and b is the number of boys, the expression b + 5 represents the number of girls. 
total there are 27 childrens
b + (b+5) = 27
b + b + 5 = 27
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6 0
3 years ago
Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the
Bond [772]

Answer:

1) Vertex point (-1.5,-20.25)

2) axis of symmetry: x=-1.5

3) x-intercepts: (-6,0) and (3,0)

4) y-intercept: (0,18)

5) Graph in attachment.

Step-by-step explanation:

1) The given parabola has equation:

y =  {x}^{2}  + 3x - 18

We need to complete the square.

y =  {x}^{2}  + 3x + {1.5}^{2}   -  {1.5}^{2} - 18

y = ( {x + 1.5)}^{2}  - 20. 25

This function is in the vertex form:

y = a( {x - h)}^{2}  + k

where (h,k) is the vertex, x=h is the axis of symmetry.

By comparing our equation to the general vertex form:

The vertex point is (-1.5,-20.25)

2) The axis of symmetry divides the parabola into two congruent halves.

Since this is a vertical parabola, the axis of symmetry occuring at x=h is a vertical line.

The axis of symmetry is x=-1.5

3) Y-INTERCEPT.

The y-intercept is the point where the graph cross the y-axis.

At this point, the value of x is zero.

To find the y-intercept, we substitute x=0 in the equation of the parabola and simplify.

when x=0,

y =  {(0)}^{2}  + 3(0) - 18 =  - 18

The y-intercept is (0,-18).

4) X-INTERCEPT

The x-intercepts are the points where the graph touches or intersect the x-axis.

To find the x-intercept, we substitute y=0.

( {x + 1.5)}^{2}  - 20.25 = 0

Add 20.25 to both sides;

( {x + 1.5)}^{2}   =  20.25

Take square root.

(x + 1.5)=  \pm \sqrt{20.25}

x =   - 1.5\pm 4.5

x =   - 1.5 -  4.5 \:  \:  or \:  \: x =  - 1.5 + 4.5

x =  - 6 \: or \: x = 3

The x-intercepts are(-6,0) and (3,0).

4) GRAPH

To graph this function, we can use transformation.

To graph the function,

y =  {(x + 1.5)}^{2}  - 20.25

We shift the parent quadratic function 1.5 units left and 20.25 units down.

See attachment for graph.

5 0
3 years ago
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