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2 years ago

Hey if you're willing to help me with this, it will be very much appreciated, thanks maties and mates.

Mathematics

1 answer:

Nastasia [14]2 years ago

4 0

Answer:

Width=37in

Length=55in

Step-by-step explanation:

Let x in be the width dimension, the length dimension will be x+18 in. Area of a rectangle is calculated as A=lw. Given the area as2143 sq in, x can be calculated as:

$Area= x(18+x)\\\\=18x+x^2\\\\$

#Substitute for every x in our function to find the true value of x:

$x=37\\\\A=x^2+18x\\\\=37^2+18\times37\\\\=2035 \ in^2$ #l=37+18=55in

for x=38:

$x=38\\\\A=x^2+18x\\\\=38^2+18\times38\\\\=2128 \ in^2$ #l=38+18=56in

For x=39:

$x=39\\\\A=x^2+18x\\\\=39^2+18\times39\\\\=2223 \ in^2$ #l=39+1854in

From the calculations above, A television with a width of 37 in and length 55in has its area closest to 2143 sq in.

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Which describes these 2 figures

Sophie [7]

The answer for this is A

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2 years ago

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The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2

Bezzdna [24]

Answer:

Part 1) $2(x-3)^{2}-17=0$ (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

Part 4) x = 3.58, 0.42

Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

Part 6) 2(x − 7)2 + 118; x = $7

Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Part 8) (x + 3)^2 − 4

Part 9) 2(x − 1)^2 = 4

Part 10) 8(x − 4)^2 + 592

Step-by-step explanation:

Part 1) we have

$2x^{2} -12x+1=0$

Convert to vertex form

step 1

Factor the leading coefficient and complete the square

$2(x^{2} -6x)+1=0$

$2(x^{2} -6x+9)+1-18=0$

step 2

$2(x^{2} -6x+9)+1-18=0$

$2(x^{2} -6x+9)-17=0$

step 3

Rewrite as perfect squares

$2(x-3)^{2}-17=0$

Part 3) we have

$f(x)=-x^{2}+16x-60$

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

$f(x)+60=-x^{2}+16x$

Factor the leading coefficient

$f(x)+60=-(x^{2}-16x)$

Complete the squares

$f(x)+60-64=-(x^{2}-16x+64)$

$f(x)-4=-(x^{2}-16x+64)$

Rewrite as perfect squares

$f(x)-4=-(x-8)^{2}$

$f(x)=-(x-8)^{2}+4$

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

$-2(x-2)^{2}+5=0$

$-2(x-2)^{2}=-5$

$(x-2)^{2}=2.5$

square root both sides

$(x-2)=(+/-)1.58$

$x=2(+/-)1.58$

$x=2(+)1.58=3.58$

$x=2(-)1.58=0.42$

Part 5) we have

$f(x)=-x^{2}+50x-264$

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

$-x^{2}+50x-264=0$

$-x^{2}+50x=264$

Factor -1 of the leading coefficient

$-(x^{2}-50x)=264$

Complete the squares

$-(x^{2}-50x+625)=264-625$

$-(x^{2}-50x+625)=-361$

$(x^{2}-50x+625)=361$

Rewrite as perfect squares

$(x-25)^{2}=361$

square root both sides

$(x-25)=(+/-)19$

$x=25(+/-)19$

$x=25(+)19=44$

$x=25(-)19=6$

Part 6) we have

$-2x^{2}+28x+20$

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

Factor the leading coefficient

$-2(x^{2}-14x)+20$

Complete the square

$-2(x^{2}-14x+49)+20+98$

$-2(x^{2}-14x+49)+118$

Rewrite as perfect square

$-2(x-7)^{2}+118$

The vertex is the point (7,118)

therefore

The video game price that produces the highest weekly profit is x=$7

Part 7) we have

$f(x)=-x^{2}+8x-10$

Convert to vertex form

$f(x)+10=-x^{2}+8x$

Factor -1 the leading coefficient

$f(x)+10=-(x^{2}-8x)$

Complete the square

$f(x)+10-16=-(x^{2}-8x+16)$

$f(x)-6=-(x^{2}-8x+16)$

Rewrite as perfect square

$f(x)-6=-(x-4)^{2}$

$f(x)=-(x-4)^{2}+6$

The vertex is the point (4,6)

therefore

The maximum height of the puck is 4 feet.

Part 8) we have

$x^{2}+6x+5$

Convert to vertex form

Group terms

$(x^{2}+6x)+5$

Complete the square

$(x^{2}+6x+9)+5-9$

$(x^{2}+6x+9)-4$

Rewrite as perfect squares

$(x+3)^{2}-4$

Part 9) we have

$2x^{2}-4x-2=0$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 2 the leading coefficient

$2(x^{2}-2x)-2=0$

Complete the square

$2(x^{2}-2x+1)-2-2=0$

$2(x^{2}-2x+1)-4=0$

Rewrite as perfect squares

$2(x-1)^{2}-4=0$

$2(x-1)^{2}=4$

The vertex is the point (1,-4)

Part 10) we have

$8x^{2}-64x+720$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

$8(x^{2}-8x)+720$

Complete the square

$8(x^{2}-8x+16)+720-128$

$8(x^{2}-8x+16)+592$

Rewrite as perfect squares

$8(x-4)^{2}+592$

the vertex is the point (4,592)

The population has a minimum at x=4 years ( that is after 4 years since 1998 )

6 0

2 years ago

If the coordinates of point a are -3 and 2 and the coordinates of point B are 7 and 6 the x-intercept of CD is what

AveGali [126]

Answer:

The x-intercept of CD is -19/5

Step-by-step explanation:

If the coordinates of the first point is (-3, 2) and the coordinates of the point B are (7, 6) then we need first to find the equation of the line CD:

We know that the general equation of the line is:

y-y0 = m(x-x0) where (x0, y0) represents a point that belongs to the line and m, is the slope which can be calculated by using the following formula:

m = (x1 - x0) / (y1 - y0)

In this case:

(x1, y1) = (7, 6)

(x0, y0) = (-3, 2)

Then:

m = (7 - (-3))/(6-2) = 10/4 = 5/2.

Then, the equation of the line is:

y-y0 = m(x-x0)

y - 2 = 5/2 (x -(-3))

y = 5/2(x+3) + 2

To find the x intercept we make y=0.

Then y = 5/2(x+3) + 2 = 0

Then:

x = -4/5 - 3 = -19/5

3 0

3 years ago

I need help plz i dont get it and im trying to get my grade up

Ymorist [56]

Answer:

648

Step-by-step explanation:

(25 - 9 + 2)^2 / 3x6

= 108 x 6

= 608

follow BODMAS and you'll get it

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

4 0

3 years ago

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Use a TENS fact to subtract 13 take away 5

podryga [215]

13 - 5 8 hic fhfgghgggfdfr

5 0

2 years ago