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2 years ago

The total area of the polygon is 176 square feet. Find the value of x.

Mathematics

2 answers:

My name is Ann [436]2 years ago

5 0

Answer:

x = 6 ft

Step-by-step explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(x)(8)$

= 4x square feet

Area of rectangle 2 = Length × Width

= 16 × 8

= 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x = $\frac{48}{8}$

x = 6 ft

Serga [27]2 years ago

4 0

Answer:

The answer is six to one of the sides

Step-by-step explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 =

= 4x square feet

Area of rectangle 2 = Length × Width

= 16 × 8

= 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x =

x = 6 ft

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The New Mexico Division of Fish and Wildlife keeps track of the silvery minnow population in the Rio Grande River. They tagged 5

sattari [20]

Answer:

279 silvery minnow

Step-by-step explanation:

Number of Silvery Minnows initially tagged = 54

Number of minnows captured = 62

Number of tagged minnows in captured ones = 12

Remember that in the very beginning there were no tagged minnows. 54 minnows were captured, tagged and released. This means, there are total 54 tagged minnows in the entire population. Lets say there are x number of minnows in total.

So, in x minnows, 54 are tagged ones.

When 62 minnows are captured, only 12 are tagged ones and remaining are un-tagged. Since, the minnows were randomly captured, we can develop a proportion from this case to estimate the total population of minnows in the Rio Grande River.

Ratio of tagged minnows to total population must be equal to the ratio of captured tagged minnows in total captured minnows.

i.e.

$54 : x = 12 : 62\\\\ \frac{54}{x} = \frac{12}{62}\\\\ 62(54)=12x\\ \\ x = 279$

This means, there were 279 silvery minnows in the Rio Grande River.

3 0

2 years ago

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

anastassius [24]

Answer:

For k = 36, there is 0 solutions

For other values of k, there is 1

We never got infinite solutions on the system.

Step-by-step explanation:

We have 2 unknowns and 2 equations:

E1 8x1 + x2 = 18

E2 k*22 x1 + 9 x2 = 18

If we multiply the E1 by 9 we obtain

E3 72 x1 + 9x2 = 162

if we substract E3 with E2 we obtain

(72- 2k) x1 = 144

Thus,

x1 = 144/ (72-2k)

That is, if 72-2k = 0, otherwise there is no solution. And 72-2k = 0 when k = 72/2 = 36.

If k is not 36, then

x1 = 144/(72-2k) and we can replace this value to obtain x2 by using E1

x2 = 18-8x1 = 18- 8 * (144/72-2k)

Which is a specific number that depends only on k. Thus,

for k = 36, there is 0 solutions

for other values of k, there is unique solution.

4 0

2 years ago

A teacher reviews 4-1/2 papers per hour, how many papers will that teacher review in 6-1/3 hours

MrRa [10]

Answer:

$28\frac{1}{2}\ papers$

Step-by-step explanation:

step 1

Convert mixed numbers to an improper fractions

$4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}$

$6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}$

step 2

we know that

A teacher reviews 9/2 papers per hour

using proportion

Find how many papers will the teacher review in 19/3 hours

Let

x-----> the number of papers

$(9/2)/1=x/(19/3)$

$x=(19/3)(9/2)$

$x=28.5\ papers$

Convert to mixed numbers

$28.5=28\frac{1}{2}\ papers$

5 0

2 years ago

Choose the point-slope form of the equation below that represents the line that passes through the points (−6, 4) and (2, 0). y

Likurg_2 [28]

Y-y1=m(x-x1)
for slope=m
for point (x1,y1)
slope for 2 points (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)

points
(2,0)
(-6,4)
(0-4)/(2-(-6))=(-4)/(2+6)=-4/8=-1/2

m=-1/2

could be
y-4=-1/2(x+6)
or
y=-1/2(x-2)

6 0

2 years ago

Read 2 more answers

The mini muffins company bakes 1872 muffins the large mini muffin boxes hold a dozen muffins how many large boxes are needed to

lilavasa [31]

Answer:

To pack 1872 muffins the mini muffins company needs 156 large boxes.

Step-by-step explanation:

Number of muffins baked by the mini muffins company = 1872.

the large mini muffin boxes hold a dozen muffins that is the large box contains 12 muffins.( 1 Dozen = 12 )

We have to find the number of large boxes needed to pack 1872 muffins.

Using unitary method,