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3 years ago

If the perimeter of a rectangle is 38 cm and the area is 78 square cm, then what are the dimensions of the rectangle?

1 answer:

8 0

The length is 13 and the width is 6. The way I figured it out is: find two factors of the area (that if multiplied with each other, they equal the area) and see which ones add up and then get multiplied by two to find the perimeter. I found 6 and 13 and then added them together to get 19. Then I multiplied 19 by two and got 38. This is how I have always done it idk.

Your answer is length = 13 and width = 6.
hope this helps :)

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Neko [114]

Step-by-step explanation:

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3 years ago

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Solve for x. <br><br> x = ___

const2013 [10]

Answer:

x = 2

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{little}{big}$ .

$\frac{36}{36 + 12}=\frac{24}{24 + 6x - 4}$

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$36(24 + 6x - 4)=(36+12)(24)\\36(6x + 20)=48(24)\\216x + 720 = 1152 \\216x = 432\\\frac{216x}{216}=\frac{432}{216} \\x = 2$

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3 years ago

Evaluate function at the given value using the remainder theorem.

garik1379 [7]

Answer:

Step-by-step explanation:

$f(a)=a^4-2a^3 -10a^2 -7a \\\\f(-2) = (-2)^4-2(-2)^3 -10(-2)^2 -7(-2)\\\\~~~~~~~~~=16-2(-8)-10(4)+14\\\\~~~~~~~~~=30+16-40\\\\~~~~~~~~~=46-40\\\\~~~~~~~~~=6$

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1 year ago

What's (6+5i)(6-5i) using the foil method

I am Lyosha [343]

Answer:

Step-by-step explanation:

$Remember:\\(a+b)(a-b)=a^2-b^2\\\\(6+5i)(6-5i)=6^2-(5i)^2=36-(-1)*25=36+25=61\\$

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3 years ago

Answer ASAP. Please give correct answer. (Involves a bunch of circles and trig identities)

iren [92.7K]

Answer:

45.40

Step-by-step explanation:

First of all, the shape of rope is not a parabola but a catenary, and all catenaries are similar, defined by:

y=acoshxa

You just have to figure out where the origin is (see picture). The hight of the lowest point on the rope is 20 and the pole is 50 meters high. So the end point must be a+(50−20) above the x-axis. In other words (d/2,a+30) must be a point on the catenary:

a+30=acoshd2a(1)

The lenght of the catenary is given by the following formula (which can be proved easily):

s=asinhx2a−asinhx1a

where x1,x2 are x-cooridanates of ending points. In our case:

80=2asinhd2a

40=asinhd2a(2)

You have to solve the system of two equations, (1) and (2), with two unknowns (a,d). It's fairly straightforward.

Square (1) and (2) and subtract. You will get:

(a+30)2−402=a2

Calculate a from this equation, replace that value into (1) or (2) to evaluate d.

My calculation:

a=353≈11.67

d=703arccosh257≈45.40

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3 years ago