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3 years ago

The expression 2700-x2 gives the area of the courtyard , in

Mathematics

1 answer:

jarptica [38.1K]3 years ago

4 0

Answer:

4x - 36 feet

Step-by-step explanation:

The area A of a square whose sides are s units is given as

A = s * s

Given that the area A = x^2-18x+81, factorizing

A = x^2-9x-9x+81

A= x(x-9)-9(x-9)

A = (x-9)(x-9)

A = (x-9)^2

This means that the size of each side of the square courtyard is x-9 feet long

Recall that the perimeter P of a square whose side is s long is given as

P = 4s hence since the side of the courtyard is x - 9 feet, the perimeter of the courtyard

P = 4(x-9)

= 4x - 36 feet

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Which of the following changes in the price index produces the greatest rate of inflation: 106 to 112, 112 to 118, or 118 to 124

boyakko [2]

Answer:

Step-by-step explanation:

firstly you have to find the rate of change of the various price index in percentage.

A, From 106 to 112:

we find the difference 112-106 = 6

then the rate of change = 6/106 * 100 = 5.66%.

B ,From 112 to 118:

we find the difference 118-112 = 6

then the rate of change = 6/118 * 100 = 5.36%.

C ,From 118 to 124:

we find the difference 124-118 = 6

then the rate of change = 6/124 * 100 = 5.08%.

we can see that the price index with the greatest percentage is A.

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3 years ago

Which statement correctly compares the function shown on this graph with

Alex

Answer:

Y=4X+2

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Step-by-step explanation:

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3 years ago

A store is offering a 20% discount on all sales over $50. If you purchase a shirt and a pair of jeans for $62.50, what is the am

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Answer:$50

Step-by-step explanation:

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3 years ago

After 1890 from where the most European immigrants come

Sergeu [11.5K]

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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