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1 year ago

Find the measure of angle 6

Mathematics

2 answers:

shepuryov [24]1 year ago

4 0

angle 6 is 124

Step-by-step explanation:

(-3x+65)+(-6x+142)=180

-9x+207=180

-9x=-27

x=3

subsitute 3 for x

-6x+142

-6(3)+142

-18+142

124

SVEN [57.7K]1 year ago

4 0

X=3 because you need the two equations to equal 180

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bogdanovich [222]

Answer:

The scale factor used to go from P to Q is 1/4

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x -----> area of polygon Q

y -----> area of polygon P

$z^{2}=\frac{x}{y}$

we have

$y=72\ units^2$

Find the area of polygon Q

Divide the the area of polygon Q in two triangles and three squares

The area of the polygon Q is equal to the area of two triangles plus the area of three squares

see the attached figure N 2

Find the area of triangle 1

$A=(1/2)(1)(2)=1\ units^2$

Find the area of three squares (A2,A3 and A4)

$A=3(1)^2=3\ units^2$

Find the area of triangle 5

$A=(1/2)(1)(1)=0.5\ units^2$

The area of polygon Q is

$x=1+3+0.5=4.5\ units^2$

Find the scale factor

$z^{2}=\frac{x}{y}$

we have $y=72\ units^2$

$x=4.5\ units^2$

substitute and solve for z

$z^{2}=\frac{4.5}{72}$

$z^{2}=\frac{1}{16}$

square root both sides

$z=\frac{1}{4}$

therefore

The scale factor used to go from P to Q is 1/4

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2 years ago

Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. What is the measure of the final interior angle?

Annette [7]

Answer:

127 degrees

Step-by-step explanation:

540 degrees is what the interior of a pentagon should add up to. So you do 540-156-72-98-87=127. The measure of the final interior angle is 127 degrees.

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2 years ago

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A pan is heated to 393°F, then removed from the heat and allowed to cool in a kitchen where the room temperature is a constant 6

deff fn [24]

Answer:

The approximate temperature of the pan after it has been away from the heat for 9 minutes is 275.59°F.

Step-by-step explanation:

The formula for D, the difference in temperature between the pan and the room after t minutes is:

$D = 324\cdot e^{-0.05t}$

Compute the approximate difference in temperature between the pan and the room after 9 minutes as follows:

$D = 324\cdot e^{-0.05t}$

$=324\times e^{-0.05\times 9}\\\\=206.59$

Then the approximate temperature of the pan after it has been away from the heat for 9 minutes is:

D = P - R

206.59 = P - 69

P = 206.59 + 69

P = 275.59°F

Thus, the approximate temperature of the pan after it has been away from the heat for 9 minutes is 275.59°F.

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