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3 years ago

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susan is arranging coffee mugs on shelves in her shop. she wanta each shelf to have the same number of mugs.she only wants one c

olor of mug on each shelf. if she has 49 blue and 56 red mugs, what is the greatest amount vshe can put one each shelf ? how many shelves does she need for each color?

1 answer:

yaroslaw [1]3 years ago

8 0

The <em><u>correct answers</u></em> are:

7 mugs on each shelf; and 7 shelves for blue and 8 shelves for red.

Explanation:

To find the number of mugs that will fit on each shelf, we find the GCF (greatest common factor) of 49 and 56. To do this, we find the prime factorization of each:

49 = 7(7)

56 = 7(8)

8 = 2(4)

4 = 2(2)

56 = 2(2)(2)(7)

The only common factor is 7, so this is the GCF. This means that she needs to put 7 mugs on each shelf.

Since there are 49 blue mugs, she needs 49/7 = 7 shelves for them.

Since there are 56 red mugs, she needs 56/7 = 8 shelves for them.

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Find the area of the shaded region. Round the the nearest tenth.

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Answer:

226.084 sq.m.

Step-by-step explanation:

Radius of circle = 18.6 cm

Area of sector = $\frac{\theta}{360^{\circ} }\pi r^2$

Area of sector = $\frac{123}{360} \times 3.14 \times (18.6)^2$

Area of sector = $371.157 m^2$

Area of triangle = $\frac{1}{2} \times a \times b \times Sin x$

a = OA = radius = 18.6 cm

b = OB = radius = 18.6 cm

x =123 °

Substitute the values in the formula

Area of triangle = $\frac{1}{2} \times 18.6 \times 18.6 \times Sin 123$

Area of triangle = $145.073 m^2$

So, Area of shaded region = Area of sector - Area of triangle

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4 years ago

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3 years ago

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3 years ago

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B is the midpoint of ac. Ab = x+9 and bc = 3x-7 find x and ac

natali 33 [55]

To solve this problem, we need to know 2 relationships:

<h2>1. AC = AB + BC</h2>

The distance of AC is the sum of AB and BC.

$AC = AB + BC$

We know this since the distance of going from A to C (AC) is the same as going from A to B (AB), then B to C (BC).

<h2>2. AB = BC</h2>

The distance of AB is the same as AC.

$AB = BC$

We know this since B is in the middle of AC, so the distance from B to A (BA) is the same as the distance from B to C (BC).

You can see the attached image (at the bottom) for a visualization of this.

<h2>Putting them together</h2>

Since we know the values of AB and BC...

$AB = x+9\\BC = 3x-7$

...we can put these values into our 2nd equation and solve for x:

$AB = BC\\x + 9 = 3x -7$

Add 7 to both sides:

$x + 16 = 3x$

Subtract x from both sides:

$16 = 2x$

Divide both sides by 2:

$8 = x\\x = 8$

Knowing x, we can find the distance of AC using our first equation.

$AC = AB + BC$

Let's put in the values of AB and BC:

$AC = (x+9) + (3x-7)$

Before we put in x = 8, we can simplify this:

$AC = (x+9) + (3x-7)\\AC = x + 9 + 3x -7\\AC = x + 3x + 9 -7\\AC = 4x + 9 - 7\\AC = 4x+2$

We group x and 3x and add those together. Then we subtract 7 from 9.

With this equation, we can put in x = 8:

$AC = 4x +2\\AC = 4*8 + 2$

Since 4 * 8 = 32:

$AC = 4 * 8 + 2\\AC = 32 + 2\\AC = 34$

Finally, we have found both x and AC.

<h2>Answer</h2>

x = 8

AC = 34

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3 years ago

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