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BabaBlast [244]
3 years ago
8

In the figure below, segment AC is congruent to segment AB:

Mathematics
1 answer:
stepladder [879]3 years ago
7 0

Answer: A. "Segment AD bisects angle CAB." is the right answer.

Step-by-step explanation:

Given : In ΔABC ,AC≅AB.

⇒∠ACB=∠CBA....(1) (∵ angles opposite to equal sides of a triangle are equal )

Now in ΔACD and ΔABD

AD=AD (common)....(2)

Here we need one more statement to prove the triangles congruent that is only statement (A) fits in it.

If AD bisects ∠CAB then ∠CAD=∠BAD..(3)

Now again Now in ΔACD and ΔABD

∠ACB=∠CBA [from (1)]

AD=AD [common]

∠CAD=∠BAD [from (3)]

So by ASA congruency criteria ΔADC≅ΔABD.

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A bookstore decides to divide its space into three sections: nonfiction books, novels, and stationery. The bookstore wants to de
Colt1911 [192]

Answer:

Stationery section will be 4 feet wide.

Step-by-step explanation:

Total area of bookstore = 288 sq ft

Area to be devoted to stationery = \frac{1}6 of total area = \frac{1}{6} \times 288 = 48\ sq\ ft

Length of stationery section = 12 ft

To find:

Width of stationery section = ?

Solution:

First of all, let us have a look at the area of rectangle:

A = Length \times Width

Here, we are given the length for stationery section and area of stationery section has been calculated above.

And we have to find the Width of stationery section.

So, let us put the two values to find the third value.

\Rightarrow 48 = 12 \times Width\\\Rightarrow Width = \dfrac{48}{12}\\\Rightarrow \bold{Width = 4\ ft}

So, the answer is:

Stationery section will be 4 feet wide.

3 0
3 years ago
The Greenpoint factory produced two-fifths of the Consolidated Brick Company’s bricks in 1991. If the Greenpoint factory produce
ohaa [14]

Answer:

3500 tons

Step-by-step explanation:

The Greenpoint factory produced 2/5 of the bricks that the Consolidate Brick Company produced in 1991.

Let the amount of bricks produced by the Greenpoint factory be g and the amount of bricks produced by the Consolidated brick company be c.

Therefore:

g = 2/5 * c = 2c/5

That year, the Greenpoint factory produced 1400 tons of bricks. This implies that:

1400 = 2c/5

To find the amount that the Consolidated Brick Company produced, solve for c:

1400 = 2c/5

1400 * 5 = 2c

7000 = 2c

c = 7000 / 2 = 3500 tons

The Consolidated Brick Company had a total production output of 3500 tons in 1991.

4 0
3 years ago
2(x-2)^2+3 and 3(x+1)^2+5 rewrite in standard form
garri49 [273]

5x^2-2x+19 is the answer

6 0
3 years ago
Write the missing family fact.<br>84 + 6 = 14<br>6 x 14 = 84<br>14 x 6 = 84​
netineya [11]

Answer:

14×6=84 and 6×14=84, 84+6=90

8 0
4 years ago
In a group of 60 workers, the average (arithmetic mean) salary is $80 a day per worker. If some of the workers earn $75 a day an
Tomtit [17]
Let's let x = the number of workers making $75 per day
Then that would mean (60 - x) would be the number of workers who make $100 per day. 
Now the average salary, which needs to be 80, can be found by adding all the salaries of the 60 workers and dividing by 60.  The following equation can model this problem:
[75x + 100(60 - x)]/60 = 80  simplify the left side of the equation
(-25x + 6000)/60 = 80  multiply both sides by 60
-25x + 6000 = 4800  subtract 6000 from both sides
-25x = -1200  divide both sides by -25
x = 48  recall we set 'x' to equal the number of workers making $75 per day
And there you have it!  Hope this helps.. 

8 0
4 years ago
Read 2 more answers
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