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jasenka [17]
3 years ago
11

Six times the sum of a number and twelve is forty.

Mathematics
1 answer:
solniwko [45]3 years ago
4 0
X-the number

6(x + 12) = 40    |use distributive property: a(b + c) = ab + ac

6x + 72 = 40    |subtract 72 from both sides

6x = -32    |divide both sides by 6

x = -32/6

x = -16/3

x = -5 1/3
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What is 7.03 as a mixed number or fraction in simplest form​
Alona [7]
7.03 can be converted to 7 3/100.

.03 is the equivalent to 3 hundredths, we know this because it in the hundredths place.
5 0
3 years ago
Pat is painting a stage backdrop for a play. The paint he is using covers 90 square feet per quart. How many quarts of paint sho
Scorpion4ik [409]
A) If you cut off half the peaks (3.5 ft down from the top), they will just fill the valleys making a rectangle 18.5 ft by 30 ft. The area is the product of these dimensions.
  A = (18.5 ft)*(30 ft) = 555 ft²

b) To determine the number of quarts of paint required, divide this number by 90 ft². Since you cannot buy a partial quart, if there is any remainder, use the next higher integer number of quarts.
  555/90 ≈ 6.2 so Pat should buy 7 quarts of paint.
4 0
3 years ago
Please Identify the congruent triangles in the figure.
Tpy6a [65]

The missing steps are each right angles and \angle R \cong \angle O.

Solution:

Step 1: Given data:

\overline {P Q} \cong \overline{M N}

\overline{Q R} \cong \overline{N O}

\overline{P R} \cong \overline{M O}

Step 2: In the two polygons,

\angle Q =90^\circ and \angle N =90^\circ

\angle Q \cong \angle N (Each right angle)

Step 3: Given

\angle P \cong \angle M

Step 4: By third angle theorem,

If two angles in one triangle are congruent to the two angles in the other triangle, then the third angles in the triangles also congruent.

\angle R \cong \angle O

Step 5: By the definition of congruent polygons,

If two same shape polygons have all the angles are congruent and all the corresponding sides are congruent then the polygons are congruent.

Hence \Delta P Q R \cong \Delta M N O.

Therefore the missing steps are each right angles and \angle R \cong \angle O.

5 0
3 years ago
There are 9 performers who are to present their acts at a variety show. How many different ways are there to schedule their appe
nika2105 [10]
For this type of question it is easiest to think about it in terms of a simple multiplication. The way we can do this is by working out how many possibilities there are for each position on the program. This is as follows:
For the first act, there are 9 possible performers we can pick
For the second act, because we have already assigned a performer to the first act, there are only 8 possible performers
For the third act, because we have already assigned a performer to the first two acts, there are only 7 possible performers
This goes on and on until we reach the final act, where we have used all the performers except one.
Therefore we can say:
For the first act there are 9 possibilities
For the second act there are 8 possibilities
For the third act there are 7 possibilities
For the fourth act there are 6 possibilities and so on
If we want to write this mathematically we can just say that there are:
9 possibilities x 8 possibilites x 7 possibilities etc right down until we are at the final act where there is 1 possibility.
To write this out as an equation we just say:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = the number of different ways
In maths however, we have a much simpler way of saying this, which we call "factorial".
That whole stream of numbers up there can just be said to be "9 factorial", or if we are writing it in an equation "9!". You may find that your calculator has a button which has an "!" on it. If you put in the number of performers and then press the "!" button, it will give you the answer to your question.
Hope this helped you :)
3 0
3 years ago
Which word phrase could represent the algebraic expression 2p + 3 where p represents Sam's age?​
s344n2d4d5 [400]

Answer:

1. 3 + 4x

2. 8/ x-y

3. X/2y

4. Four times a number m

5 let m represent months

30 + 12m

4 0
3 years ago
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