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Aneli [31]
3 years ago
8

A pentagon has 3 congruent sides and 2 other congruent sides. The perimeter of the pentagon is 36 centimeters. The three long co

ngruent sides are 2 centimeters longer than the two shorter congruent sides.
Let x = length of a short side
Let y = length of a long side

The system of equations can be used to represent the situation.

y = x + 22
x + 3y = 36

What is the length of one of the shorter congruent sides?
A. 2 centimeters
B. 6 centimeters
C. 8 centimeters
D. 17 centimeters
Mathematics
2 answers:
statuscvo [17]3 years ago
7 0

The answer is B. 6 centimeters.

zvonat [6]3 years ago
6 0
The answer is c. ...
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What is the cost if a $1,200 washing machine after a discount if 1/5 the original price
Fantom [35]
1/5 (or 20%) of $1,200 is $240
$1,200 - $240 = $960
The cost of a $1,200 washing machine after a discount of 1/5 (20%) is $960
3 0
3 years ago
The price of oil, in dollars per barrel, declined last week by 3.5%. If it started the week at 102.00 per barrel, at what per ba
scoray [572]

Answer:

98.57

Step-by-step explanation:

3.5% over 100% X 102=3.43

102-3.43= 98.57

6 0
3 years ago
Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen
Jobisdone [24]

Parameterize S by the vector function

\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k

so that the normal vector to S is given by

\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k

with magnitude

\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}

In this case, the normal vector is

\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k

with magnitude \sqrt{1^2+2^2+1^2}=\sqrt6. The integral of f(x,y,z)=e^z over S is then

\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx

where T is the region in the x,y plane over which S is defined. In this case, it's the triangle in the plane z=0 which we can capture with 0\le x\le8 and 0\le y\le\frac{8-x}2, so that we have

\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}

5 0
3 years ago
N.
noname [10]

Answer:

287.1 inches of the canvas.

Step-by-step explanation:

To solve this, we need to first figure out the total area of the canvas. To do that, multiply width by height.

29*33=957

Now set up your equation for solving for the area of the canvas that the rose covers.

x/957=30/100

We did it where: x is the area of the rose covers, 957 is the amount of inches that the canvas takes up, and the right side of the equation is the percent.

Now cross multiply.

100x=28,710

Now divide both sides by 100.

x=287.1

The red rose covers 287.1 inches of the canvas.

6 0
3 years ago
Given: tangent A = negative StartRoot 15 EndRoot What is the value of Tangent (A minus StartFraction pi over 4 EndFraction)?
marshall27 [118]

Answer:

( √15 + 8)/7

Step-by-step explanation:

TanA = -√15

.we are to find tan(A-π/4).

In trigonometry

Tan(A-B) = TanA - TanB/1+ tanAtanB

Hence:

tan(A-π/4) = TanA - Tanπ/4/1+ tanAtanπ/4

Substitute tan A value into the formula

tan(A-π/4) = -√15-tanπ/4 / 1+(-√15)(tanπ/4

tan(A-π/4) = -√15-1/1-√15

Rationalize

-√15-1/1-√15 × 1+√15/1+√15

= -√15-√225-1-√15/(1-√225)

= -2√15-15-1/1-15

= -2√15 -16/(-14)

= -2(√15+8)/-14

= √15 + 8/7

Hence the required value is ( √15 + 8)/7

4 0
3 years ago
Read 2 more answers
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