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3 years ago

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The area of a rectangle is 84 square meters. The length of the rectangle is 5 meters longer than the width. What is the length,

in meters, of the rectangle?

1 answer:

Fittoniya [83]3 years ago

6 0

Answer:

7mX12m

Step-by-step explanation:

I found the factors of 84 and then figured out which one would equal 5 if subtracted from each other.

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Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length

Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola: $y=k (x-\frac13)^2$

<u />

<u>Part 1</u>

If the curve passes through point $(\frac23 ,1)$ , this means that when $x=\dfrac23$ , $y = 1$

Substitute these values into the equation and solve for $k$ :

$\implies 1=k \left(\dfrac23-\dfrac13\right)^2$

$\implies 1=k \left(\dfrac13 \right)^2$

Apply the exponent rule $\left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c}$ :

$\implies 1=k \left(\dfrac{1^2}{3^2} \right)$

$\implies 1=\dfrac{1}{9}k$

$\implies k=9$

<u>Part 2</u>

The chord of a parabola is a line segment whose endpoints are points on the parabola.

We are told that one end of the chord is at $(\frac23 ,1)$ and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:

$\implies 1=9 \left(x-\dfrac13 \right)^2$

$\implies \dfrac19 = \left(x-\dfrac13 \right)^2$

$\implies \sqrt{\dfrac19} = x-\dfrac13$

$\implies \pm \dfrac13 = x-\dfrac13$

$\implies x=\dfrac23, x=0$

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:

$\implies \dfrac23-0=\dfrac23$

**Please see attached diagram for drawn graph. Chord is in red**

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2 years ago

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Licemer1 [7]

Answer:

C

Step-by-step explanation:

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3 years ago

Which equation represents a function of x that is not linear?

AnnyKZ [126]

Answer:

y = 4x+3x^2

Step-by-step explanation:

For an equation to be linear, x must have a power of 1

y = 4x+3x^2 has a power of x that is not x ( x^2) so this is not linear ( it is quadratic)

8 0

3 years ago

Solve for x <br> (1 point)

Delicious77 [7]

It should be 13 since 13+8 = 21. 21-7 = 13

5 0

3 years ago

Akira receives a prize at a science fair for having the most informative project. Her trophy is in the shape of a

AlekseyPX

Answer:

45 square inches

Step-by-step explanation:

Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the trophy including the bottom

Total surface = surface area of the base square + area of 4 triangles

Calculate the surface area of the base square

surface area of the square = s^2

where s= side length

s=3 in

The surface area of the base =s^2

=3^2

= 9 square inches

The surface area of the side triangles

The area of the triangle = (1/2)* side length* slant height

Side length=3 in

Slant height=6 in

substituting the values,

The area of the triangle =1/2*3*6

= 18/2

= 9 square inches

There are 4 triangles

The area of 4 triangles = 4 x 9

= 36 square inches

Therefore,

Total surface = surface area of the base square + area of 4 triangles

= 9 + 36

= 45 square inches

6 0

3 years ago