1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
topjm [15]
2 years ago
14

What is the area, in square feet, of the shaded part of the rectangle below?

Mathematics
1 answer:
likoan [24]2 years ago
8 0
<h3>Answer:  208</h3>

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

Work Shown:

A = area of the rectangle

A = length*width

A = 16*17

A = 272 sq ft

B = area of triangle

B = base*height/2

B = 16*8/2    ..... note that 17-9 = 8

B = 16*4

B = 64 sq ft

C = area of shaded trapezoid

C = A - B

C = 272 - 64

C = 208 sq ft

--------------------

Alternative Method:

Apply the trapezoid area formula

b1 = 17 and b2 = 9 are the parallel bases

h = 16 is the height perpendicular to either base

A = h*(b1+b2)/2

A = 16*(17+9)/2

A = 16*(26)/2

A = 16*13

A = 208 sq ft

You might be interested in
Which expression can be used to find the surface area of the following square pyramid?
telo118 [61]

Answer:

Step-by-step explanation:

The slant height of one side of this pyramid is 5, and the base of this side is 4.  Thus, the area of one slant side is (1/2)(5)(4) = 10 units^2.

There are 4 such sides.  Thus, the total slant surface area is 4(10 units^2), or 40 units^2.  

If you also want to include the base area, the total would be

40 units^2 + 16 units^2 = 56 units^2.

8 0
3 years ago
26 × (– 48) + (– 48) × (–36).
Rina8888 [55]

Answer:

480

Step-by-step explanation:

(26*-48)+(-48*-36)

-1248 + 1728

480

6 0
1 year ago
What is the measure of angle RST? Help!!
erik [133]

Answer:

62

Step-by-step explanation:

Angle Formed by Two Chords = 1/2(sum of Intercepted Arcs)

RST = 1/2 ( 47+77)

       = 1/2 (124)

       = 62

4 0
3 years ago
Read 2 more answers
Factor the four-term polynomial ab + ac - 4b - 4c
Troyanec [42]
A b + a c - 4 b - 4 c = a ( b + c ) - 4 ( b + c ) = 
= (b + c) (a - 4)
5 0
2 years ago
For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f
Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

1.

\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0

We want to find f such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)

\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C

\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}

so \vec F is conservative.

2.

\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)

\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)

\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C

\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}

so \vec F is conservative.

3.

\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0

so \vec F is not conservative.

4.

\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)

\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)

\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C

\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}

so \vec F is conservative.

4 0
3 years ago
Other questions:
  • PLS HELP I WILL MARK YOU BRAINLIEST
    9·1 answer
  • Which phrase represents the algebraic expression 5x - 9? the product of five times a number and nine the difference of nine time
    12·2 answers
  • Each sales associate at an electronics store has a choice of the two salary options shown below. • $115 per week plus 9.5% commi
    5·1 answer
  • Could ya’ll please help me???
    14·1 answer
  • How to answer this question, please I need steps​
    5·1 answer
  • Jin has pounds of birdseed. If he uses 1/8 pound a
    7·1 answer
  • Describe how the graph of y=lxl – 7 is like the graph of y=lxl and how it is different.
    8·1 answer
  • Find the slope.....<br>​
    9·1 answer
  • Whoever can answer c please help me this is for a grade
    14·1 answer
  • What is the value of the expression 2 to the third power plus 3 over 5 times 5 over 9 minus 4 plus 3.?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!