All categories

3 years ago

If the length of AO is double the length of CO, the length of BO is?

Mathematics

1 answer:

andreev551 [17]3 years ago

7 0

BO is double that of DO. In other words, BO is two times longer than DO. The answer is choice B

For example, if DO were 3 units long, then BO would be 6 units long (2*3 = 6). This works because the triangles DCO and BAO are similar triangles. The corresponding sides are in the same ratio or proportion to one another. The larger triangle (BAO) has sides that are twice as long as the smaller triangle's (DCO) corresponding sides.

Side note: we can prove the triangles to be similar using the AA (angle angle) similarity theorem. The first pair of angles are the vertical angles DOC and BOA which are congruent to each other.The second pair is CDB and ABD which are congruent by the alternate interior angle theorem. Check out the attached image for a visual.

You might be interested in

Fernando has two equally-sized containers of clay which he is using to build a pyramid-like structure. The finished structure wi

evablogger [386]

Answer:

Fernando does not have enough clay to finish the structure since, the expressions for the volume left are not the same.

Step-by-step explanation:

Let w be the length of the longest slab. Since each slab is 2 inches less than the one beneath it, we have the width of the other 3 slabs as w - 2, w - 2 - 2 = w - 4 and w - 4 - 2 = w - 6 respectively.

Since the base of each slab is a square and has thickness 2 inches, the volume of each slab from largest to smallest is thus 2w², 2(w - 2)², 2(w - 4)² and 2(w - 6)² respectively.

We have that we have half of the container of clay left after forming the first two slabs(which are the bottom-most slabs). Let V be the volume of each clay container. Since we have half left, that is V/2, we have used 2V - V/2 = 3V/2 to make the two bottom-most slabs.

So, 3V/2 = 2w² + 2(w - 2)²

= 2w² + 2(w² - 4w + 4)

= 2w² + 2w² - 8w + 8

= 4w² - 8w + 8

= 4(w² - 2w + 2) (1)

Also we want to know if V/2 is equal to the volume of the two top-most slabs.

So, V/2 = 2(w - 4)² + 2(w - 6)²

= 2(w² - 8w + 16) + 2(w² - 12w + 36)

= 2w² - 16w + 32 + 2w² - 24w + 72

= 4w² - 40w + 104

= 4(w² - 10w + 26)

From (1) V/2 = 4(w² - 2w + 2)/3 ≠ 4(w² - 10w + 26)

<u>Since the expressions for the remaining volume are not the same, Fernando does not have enough clay to finish the structure.</u>

4 0

3 years ago

The price of a vase was increased by 10% to £22.What was the price before the increase

Anton [14]

Answer: £20.

Step-by-step explanation:

Let the old price = £x

Percent increase. = 10%

Increment. = 10% of £x

= 10x/100

Now new price = £22

To determine the old price we have

x + 10x/100. = 22

We now multiply everything by 100 to make it a linear expression

100x + 10x = 2200

110x = 2200, therefore

x. = 2200/110

= £20

Therefore, the price before the increase. = £20.

6 0

3 years ago

Plzz help its only 1 question!!!

andrew11 [14]

Answer:

D is correct

rost beef sandwich=7$

turkey sandwich=5$

Step-by-step explanation:

8 0

2 years ago

Solve the problem.

julsineya [31]

Answer:

2 dogs

Step-by-step explanation:

2 dogs at 1st plus 7 dogs added equals 9

3 0

2 years ago

List factors of 24 36 27 and 7

Helen [10]

Answer:

The factors of 7 are 1, and 7.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 27 are 1, 3, 9, and 27.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step-by-step explanation: I hope this helps :).

8 0

2 years ago