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3 years ago

m∠3 is (3x + 4)° and m∠5 is (2x + 11)°. Angles 3 and 5 are . The equation can be used to solve for x. m∠5 = °

Mathematics

2 answers:

ratelena [41]3 years ago

7 0

I just did this question!

Answers:

1) <em>same side interior angles</em>

2) (3x+4)+(2x+11) = 180

3) 77

Sveta_85 [38]3 years ago

5 0

Answer:

Part a) consecutive interior angles

Part b) $(3x+4)\°+(2x+11)\°=180\°$

Part c) m∠5= $77\°$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

<u>Part a)</u> Angles 3 and 5 are consecutive interior angles

therefore

m∠3+m∠5= $180\°$

<u>Part b)</u> we have

m∠3= $(3x+4)\°$

m∠5= $(2x+11)\°$

substitute

$(3x+4)\°+(2x+11)\°=180\°$

<u>Part c)</u> solve for x

$(5x+15)\°=180\°$

$5x=180\°-15\°$

$x=180\°-15\°=33\°$

Find the value of m∠5

m∠5= $(2(33)+11)\°$

m∠5= $77\°$

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3 years ago

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Step-by-step explanation:

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3 years ago

You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t

rosijanka [135]

Answer:

$Height = 12cm$

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Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

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Required

Determine the values of h and r that uses the least amount of material

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Substitute 432π for V

$432\pi = \pi r^2h$

Divide through by π

$432 = r^2h$

Make h the subject:

$h = \frac{432}{r^2}$

Surface Area (A) of a cylinder is calculated as thus:

$A=2\pi rh+2\pi r^2$

Substitute $\frac{432}{r^2}$ for h in $A=2\pi rh+2\pi r^2$

$A=2\pi r(\frac{432}{r^2})+2\pi r^2$

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Factorize:

$A=2\pi (\frac{432}{r} + r^2)$

To minimize, we have to differentiate both sides and set $A' = 0$

$A'=2\pi (-\frac{432}{r^2} + 2r)$

Set $A' = 0$

$0=2\pi (-\frac{432}{r^2} + 2r)$

Divide through by $2\pi$

$0= -\frac{432}{r^2} + 2r$

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Cross Multiply

$2r * r^2 = 432$

$2r^3 = 432$

Divide through by 2

$r^3 = 216$

Take cube roots of both sides

$r = \sqrt[3]{216}$

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Recall that:

$h = \frac{432}{r^2}$

$h = \frac{432}{6^2}$

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3 years ago

Which is answer if not know please solve for mw

Vlad1618 [11]

<h3>Answers:</h3><h3>Area of parallelogram = 63</h3><h3>Area of triangle = 34</h3><h3>Area of trapezoid = 84</h3><h3>The trapezoid has the largest area</h3>

==================================================

Work Shown:

area of parallelogram = base*height

area of parallelogram = 9*7

area of parallelogram = 63

----------

area of triangle = (1/2)*base*height

area of triangle = (1/2)*10*6.8

area of triangle = 34

----------

area of trapezoid = height*(base1+base2)/2

area of trapezoid = 6*(13+15)/2

area of trapezoid = 6*(28)/2

area of trapezoid = 168/2

area of trapezoid = 84

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