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3 years ago

Refer to the rectangle below. The length of the rectangle is x + 12. The width of the rectangle is x + 3.

Mathematics

1 answer:

Elis [28]3 years ago

4 0

Answer:

$x^2+15x+36$

Step-by-step explanation:

The complete question is shown in the attachment.

The length of the rectangle is x + 12. The width of the rectangle is x + 3.

Recall that area of a rectangle is $Length \times Width$

In terms of x, the area is $(x+12)(x+3)$

Recall the distributive property of real numbers: $(a+b)(c+d)=a(c+d)+b(c+d)$

We apply this property to get:

$(x+12)(x+3)=x(x+3)+12(x+3)$

We expand again to get:

$(x+12)(x+3)=x^2+3x+12x+36$

We now simplify to obtain:

$(x+12)(x+3)=x^2+15x+36$

The area of the rectangle is $x^2+15x+36$

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Instructions: The polygons in each pair are similar. Find the missing side length.

loris [4]

Answer:

missing side length is 12

Step-by-step explanation:

similar means that all correlating pairs of sides have the same ratio (old side length) / (new side length).

so, when we know the ratio of one pair, we can apply it to any other side to calculate the correlating side.

we see, when we go from small to large, that we have the ratio 32/40 = 4/5.

so, multiplying the larger side by this, we get the shorter side.

15 × 4/5 = 3 × 4 = 12

the proportion part in your picture is a bit confusing :

yes,

x/15 = 32/40 = 32/40

I don't know, why this last expression was repeated.

x/15 = 32/40

x = 15×32/40 = 15×4/5 = 3×4 = 12

as you see we get of course the same result doing it that way.

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2 years ago

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Mashcka [7]

Answer:

m = -10

Step-by-step explanation:

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3 years ago

Read 2 more answers

Use an integer to represent 15 feet and below sea level

Vitek1552 [10]

Answer:

-15 would be the answer because if it's below sea level it would have a negative sign in front of 15

Step-by-step explanation:

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1 year ago

The rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two peopl

fenix001 [56]

Answer:

between 222 and 223 days

Step-by-step explanation:

This relation includes the point (0, 2).

A proportional relation must include the point (0, 0).

This is not proportional, but it may be linear.

Points: (0, 2), (2, 20)

y = mx + b

20 = (20 - 2)/(2 - 0) × 2 + b

20 = 18/2 × 2 + b

b = 2

y = 18x + 2

When 4000 people know, y = 4000.

y = 18x + 2

4000 = 18x + 2

3998 = 18x

x = 3998/18

x = 222.111...

Answer: between 222 and 223 days

8 0

2 years ago

Solve using algebraic equation: 5sin2x=3cosx (No exponents)

DaniilM [7]

$5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x$

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

$10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0$

Now the zero product property tells us that there are two cases where this is true,

$\begin{cases}\cos x=0\\10\sin x-3=0\end{cases}$

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of $\dfrac\pi2$ , so $x=\dfrac{(2n+1)\pi}2$ where $n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}$

which occurs twice in the interval $[0,2\pi)$ for $x=\arcsin\dfrac3{10}$ and $x=\pi-\arcsin\dfrac3{10}$ . More generally, if you think of $x$ as a point on the unit circle, this occurs whenever $x$ also completes a full revolution about the origin. This means for any integer $n$ , the general solution in this case would be $x=\arcsin\dfrac3{10}+2n\pi$ and $x=\pi-\arcsin\dfrac3{10}+2n\pi$ .

6 0

3 years ago