The perimeter of the quadrilateral below is 119 units. Find the length of side AB.

Find an equivalent system of equations for the following system: 3x + 3y = 0 −4x + 4y = −8

Rama09 [41]

Answer:

Answer:

3x + 3y = 0

7x - y = 8

Step-by-step explanation:

3 0

3 years ago

the ratio of the sides of a certain triangle is 2:7:8 if the longest side of the triangle is 40cm how long are the other two sid

Zigmanuir [339]

The length of the other two sides is 10 and 35 respectively.

<h3>What is a ratio?</h3>

A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.

From the given information:

The sides of the triangle = 2:7:8
The total sides of the triangle = 2+7+8 = 17

We are being told that the longest side is the triangle is equal to 40.

i.e.

$\mathbf{\to\dfrac{8}{17}\times x = 40}$

$\mathbf{x = 40 \div \dfrac{8}{17}}$

$\mathbf{x = 40 \times \dfrac{17}{8}}$

x = 85

Now for the other two sides 2 and 7, their length is as follows.

$\mathbf{\dfrac{2}{17}\times 85 = 10}$

$\mathbf{\dfrac{7}{17}\times 85 = 35}$

Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.

Learn more about ratios here:

brainly.com/question/2328454

3 0

2 years ago

Consider the differential equationy′′+3y′−10y=0.(a) Find the general solution to this differential equation.(b) Now solve the in

RSB [31]

Answer:

Y= 2e^(5t)

Step-by-step explanation:

Taking Laplace of the given differential equation:

s^2+3s-10=0

s^2+5s-2s-10=0

s(s+5)-2(s+5) =0

(s-2) (s+5) =0

s=2, s=-5

Hence, the general solution will be:

Y=Ae^(-2t)+ Be^(5t)………………………………(D)

Put t = 0 in equation (D)

Y (0) =A+B

2 =A+B……………………………………… (i)

Now take derivative of (D) with respect to "t", we get:

Y=-2Ae^(-2t)+5Be^(5t) ....................... (E)

Put t = 0 in equation (E) we get:

Y’ (0) = -2A+5B

10 = -2A+5B ……………………………………(ii)

2(i) + (ii) =>

2A+2B=4 .....................(iii)

-2A+5B=10 .................(iv)

Solving (iii) and (iv)

7B=14

B=2

Now put B=2 in (i)

A=2-2

A=0

By putting the values of A and B in equation (D)

Y= 2e^(5t)

6 0

3 years ago

If an open box has a square base and a volume of 115 in.3 and is constructed from a tin sheet, find the dimensions of the box, a

Karolina [17]

Let h = height of the box,
x = side length of the base.

Volume of the box is $V=x^{2} h = 115$ .
So $h = \frac{115}{ x^{2} }$

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
$S = 2( x^{2} + hx + hx) \\ = 2 x^{2} + 4hx \\ = 2 x^{2} + 4( \frac{115}{ x^{2} } )x$
$= 2 x^{2} + \frac{460}{x}$
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

$S' = 4x- \frac{460}{ x^{2} } = 0$
$4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86$
Then $h= \frac{115}{4.86^{2}} = 4.87$
So the box is 4.86 in. wide and 4.87 in. high.

5 0

3 years ago

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Convert 0.86 into a fraction

balandron [24]

0.86= 86/100 this is because the 6 is in the hundredths place so the denominator is going to be 100<span />

5 0

3 years ago

Read 2 more answers