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2 years ago

How do I do this Q11

Mathematics

1 answer:

SashulF [63]2 years ago

5 0

Look at one of the vertices of the heptagon where two squares meet. The angles within the squares are both of measure 90 degrees, so together they make up 180 degrees.

All the angles at one vertex must clearly add up to 360 degrees. If the angles from the squares contribute a total of 180 degrees, then the two remaining angles (the interior angle of the heptagon and the marked angle) must also be supplementary and add to 180 degrees. This means we can treat the marked angles as exterior angles to the corresponding interior angle.

Finally, we know that for any convex polygon, the exterior angles (the angles that supplement the interior angles of the polygon) all add to 360 degrees (recall the exterior angle sum theorem). This means all the marked angles sum to 360 degrees as well, so the answer is B.

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What is the expression for "the difference between 5 times a number and twice that number"?

ycow [4]

Hey there :)

Before translating the sentence into mathematics, let r represent 'a number'

5 times a number = 5r
2 times that number = 2r

The difference between them = 5r - 2r

* Your equation
5r - 2r

* Solving the equation
= 5r - 2r
= 3r

3 0

3 years ago

Please select all that apply

sergij07 [2.7K]

Answer:

ceg and cfg

Step-by-step explanation:

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2 years ago

Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder

vitfil [10]

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be $x$ and $y$ the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>

$4\cdot x +5\cdot y = 32\,oz$ (Eq. 1)

ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>

$x + 8\cdot y = 35\,oz$ (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

$x = 35 - 8\cdot y$

(Eq. 2) is (Eq. 1):

$4\cdot (35-8\cdot y) + 5\cdot y = 32$

$140-32\cdot y +5\cdot y = 32$

$32\cdot y - 5\cdot y = 140-32$

$27\cdot y = 108$

$y = 4\,oz$

From (Eq. 2):

$x = 35 - 8\cdot (4)$

$x = 35 - 32$

$x = 3\,oz$

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

4 0

2 years ago

4. Small Town USA has a population of 3 x 102, Big Town has a population of 6 x 105,

zvonat [6]

Answer:

2.06

Step-by-step explanation:

3x102=306

6×105=630

630 ÷ 306 = 2.0588235294

round it to 2.06

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2 years ago

In how many ways can 3 Americans, 4 Frenchmen, 4 Danes and 2 Italians be seated in a row so that those of the same nationality s

kaheart [24]

Answer (13 of the original arrangements are duplicates now, as AAAF F F FDDDDCC, AAF F F FDDDDCCA, ..., CAAAF F F FDDDDC are identical): 900900/13 = 69300.

4 0

3 years ago

Read 2 more answers