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3 years ago

A rectangle has a length of 2x 5 units and a width of , 3 units. What is the area, in square

Mathematics

1 answer:

sergey [27]3 years ago

5 0

Answer:

$2 {x}^{2} - 11x + 15$

Step-by-step explanation:

We we're given the length of the rectangle as

$l = 2 {x} - 5$

and the width of the rectangle as :

$w = x - 3$

Recall that, the area of a rectangle is

Area=l×w

We substitute the given dimensions of the rectangle into the formula to get:

$area =( 2 {x} - {5} ) \times(x - 3)$

We expand

$2 {x}^{2} - 6x - 5x + 15$

This simplifies to:

$2 {x}^{2} - 11x + 15$

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nignag [31]

Answer:

good news, the second one is relatively easy because it can be factored to (2x+1)(2x-3) which means that number two has solutions of -1/2 and 3/2

but for number one you have to either use the quadratic equation cause I've tried using synthetic division or just use the second equation to derive the first solutions so I tried move the graph up by two units and found that the intercepts are approximately (1+-√2)/2 or 1/2+-1/√2 for 4x^2-4x-1

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3 years ago

A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax 2 about the y-

Setler79 [48]

Answer:

a = $\frac{1}{2}$ . Surface Area = $\frac{4}{3}$ $ft^{2}$ . and area of the Dish = $\frac{4}{3}$ $ft^{2}$ +pi $4^{2}$ = $\frac{4}{3}$ $ft^{2}$ +50.27=51.6 $ft^{2}$

Step-by-step explanation:

(1) Constant. y(x) = a $x^{2}$ that is the curve that we need to rotate around the y axis to get the parabola with diameter of 8 feet and 2 meter depth that statement is translated in mathematics as x = -4 to 4 and y = 0 to 2.

y max = 2, x max = 4 setting up a equation with a unknown gives

2=a4 and a = $\frac{1}{2}$ .

so we have now.

y(x) = $\frac{1}{2}x^{2}$ (Done with solving for a Constant).

(2) Surface Area.

Setting Up surface integral.

(i) range in x = 0 to 4.

(ii) range in y = 0 to 2.

integral is.

Integral(0-2)[{integral[(0-4) $\frac{1}{32}$ $x^{2}$ ]}]dy

Evaluating this integral gives. $\frac{4}{3}$ $ft^{2}$ .

and area is surface area + area of the circle with 8ft diameter.

= $\frac{4}{3}$ $ft^{2}$ +pi $4^{2}$ = $\frac{4}{3}$ $ft^{2}$ +50.27=51.6 $ft^{2}$ ...

Note the Difference between area and aurface area.!

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3 years ago

0.40 - 2.55 5 please answer this

andrew-mc [135]

Answer:

-2.15

Step-by-step explanation: I was kind of confused on what you asked. If you were asking for 0.4-2.55, then that is the answer above.

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3 years ago

Paula has her own business making cakes for

djverab [1.8K]

Answer:

Since Paula has her own business of making cakes for special occasions, and the total price (P) of one of Paula's cakes is represented by the equation P = 0.75S +10, where S is the number of people the cake serves, for determine what does the 0.75 represent in this situation and what does the 10 represent in this equation, the following mathematical reasoning must be carried out:

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Therefore, 0.75 is the value of each serving, which can be variable (the number of servings can vary)

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3 years ago

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Rudik [331]

I am not so sure of this but I feel it would serve as hint

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4 years ago