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3 years ago

Given the rectangles perimeter, find the unknown side lengths.

Mathematics

1 answer:

Dominik [7]3 years ago

3 0

The perimeter is just adding all the sides together.

a.) 180 = 40 + 40 + x + x

180 = 80 + 2x Subtract 80 on both sides

100 = 2x Take 1/2 of 100 to get x

x= 50cm

b.) 1000 = 150 + 150 + x + x

1000 = 300 + 2x Subtract 300 on both sides

700 = 2x Take 1/2 of 700 to get x

x = 350

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14 The straight line, L, has the equation y = 5 - 2x

diamong [38]

Answer:

When it crosses y-axis it means that x coordinate must be 0 so let substitute 0 to x, y=5-2*0

So coordinates are [0,5]

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3 years ago

What value for C will make the expression a perfect square trinomial x2-7x+c

Tom [10]

Answer:

The value of c is 12.25

Step-by-step explanation:

we know that

A perfect square trinomial is of the form

$(x-a)^{2}=x^{2}-2ax+a^{2}$

In this problem we have

$x^{2}-7x+c$

equate the equations

$x^{2}-7x+c=x^{2}-2ax+a^{2}$

we have

the following equations

$-7x=-2ax$ -----> equation A

and

$c=a^{2}$ -----> equation B

<u>Solve the equation A</u>

$-7x=-2ax$

$7=2a$

$a=3.5$

<u>Solve the equation B</u>

$c=a^{2}$

$c=3.5^{2}=12.25$

therefore

$(x-3.5)^{2}=x^{2}-7x+12.25$

The value of c is 12.25

7 0

3 years ago

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What is the result when the number 43 is decreased by 2.6%?

Darina [25.2K]

Answer:

41.882

Step-by-step explanation:

43 x 2.6% is 1.118, and when you subtract that from 43, you get 41.882.

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2 years ago

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A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10sin( t ) N(newtons) and moves in a mediu

yKpoI14uk [10]

Answer:

A) C1 = 0.00187 m = 0.187 cm, C2 = 0.0062 m = 0.62 cm

B) A sample of how the graph looks like is attached below ( periodic sine wave )

C) w = $\sqrt[4]{3}$ is when the amplitude of the forced response is maximum

Step-by-step explanation:

Given data :

mass = 5kg

length of spring = 10 cm = 0.1 m

f(t) = 10sin(t) N

viscous force = 2 N

speed of mass = 4 cm/s = 0.04 m/s

initial velocity = 3 cm/s = 0.03 m/s

Formulating initial value problem

y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m

spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m

f(t) = 10sin(t/2) N

using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion

the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)

A) finding the solution of the initial value

attached below is the solution and

B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like

C attached below

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3 years ago

A collection of five coins has a value of $1 and consists of dimes and

DENIUS [597]

For this case we propose a system of equations. We have to:

x: Let the variable that represents the number of dimes

y: Let the variable that represents the number of quaters

We know that:

One dime equals 10 cents, $0.10

A quater equals 0.25 cents, $0.25

According to the statement we have:

$x + y = 5\\0.10x + 0.25y = 1$

We multiply the first equation by -0.10:

$-0.10x-0.10y = -0.5$

We have the following equivalent system:

$-0.10x-0.10y = -0.5\\0.10x + 0.25y = 1$

We add the equations:

$-0.10x + 0.10x-010y + 0.25y = -0.5 + 1\\0.15y = 0.5\\y = \frac {0.5}{0.15}\\y = 3.33$

Approximately 3 quater coins

$x = 5-y = 5-3 = 2$

And two dimes

Answer:

3 quater

2 dimes

4 0

3 years ago