What is the x-axis and the y-axis of -2x+2=-4

melomori [17]

Answer:

x=12

Step-by-step explanation:

Given that there is only one expression given in each triangle, if we only use the information in a single triangle, there is no way to set up an equation that we could solve to find the expression. (For this situation, at best we could use the triangle sum theorem to say that the three angles in one triangle added to 180°, but since we don't know the other two angles, that's 3 unknowns with only 1 equation... that's not solvable)

The only way to solve this problem is to make a relationship of some sort between the two triangles.

Proving a relationship between triangles - option 1

You may have a theorem about the Third angles of two triangles... "Given two arbitrary triangles, $\triangle ABC$ and $\triangle D E F$ , if $\angle A \cong \angle D$ and $\angle B \cong \angle E$ , then $\angle C \cong \angle F$ "

If you have this, then the third angles are congruent.

In a more general situation of a similar problem (one in which you don't know two of the angles to begin with), it might be easier to prove triangle congruence, or triangle similarity.

Other Relationships between triangles

There are two main relationships between triangles: similarity and congruence.

Most people learn about congruence first.

In the situation for this problem, the two triangles happen to be congruent (we'll prove it shortly), which implies that all corresponding angles between shapes are congruent (and all corresponding sides between shapes are congruent).

For the purpose of solving for things related to angles, proving that the two triangles are similar is enough to know that angles between triangles are congruent (sides wouldn't necessarily be equal, but would be proportional, and since we're not solving for anything related to side lengths, proving that the triangles are similar would be enough).

Proving a relationship between triangles - option 2 - congruence

Notice that the triangle on top has two angles with markings (a single mark, and a double mark), and one side with a marking (a single tick). These three pieces are in a configuration of ASA (the side is between the two angles).

Looking at the bottom triangle, it also has angles and sides with corresponding markings, and they are also in an ASA configuration.

Thus, by ASA congruence, these triangles are congruent triangles.

Knowing the triangles are congruent (even though we only used 3 parts), the rest of the corresponding parts (including the third angles) are also congruent.

Proving a relationship between triangles - option 3 - Similarity

For similarity, the process is similar to proving congruence, however the theorems we have for proving similarity are different.

SSS, SAS, or AA similarity.

Since the triangles in our problem do have two angles that are congruent, by AA similarity, the triangles are "similar".

Knowing the triangles are similar (even though we only used 2 parts), the last set of corresponding angles are also congruent.

Building our equation

Since the third angle of each triangle is congruent, by definition of congruent angles, the measures of each of those two angles are equal, and so we can build an equation knowing that the two expressions are equal to each other:

$3x-7=2x+5$

Solving for x

From there, we need some algebraic properties equality to solve for x.

Subtract 2x from both sides...

$(3x-7)-2x=(2x+5)-2x\\x-7=5$

add 7 to both sides...

$(x-7)+7=(5)+7\\x=12$

Extension

Knowing the value for x, we could solve for the measure of the angles, if that had been requested. Simply substitute 12 back into the expressions for the angle measure (the results should be the same for both angles, since they were congruent angles)

$3(12)-7\\36-7\\29$ $2(12)+5\\24+5\\29$

So, if we had been asked, the measure of the angle is 29°

6 0

2 years ago

A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to

valkas [14]

Answer:

Since p-value > ∝, H0 is accepted

Step-by-step explanation:

Calculating gives the following results.

ANOVA Table

Source DF Sum Mean F Statistic P-value

of Square Square

Groups 6 191.61 31.935 0.020 0.999

(b/w groups)

Error

(within 14 21736.08 1552.577

groups)

Total 20 21927.69 1096.385

1. H0 hypothesis

Since p-value > ∝, H0 is accepted.

Hence the averages of all groups considered to be equal.

Or the difference between the averages of all groups is not big enough to reject H0.

2. P-value

P-value equals 0.999. This means that if we would reject H0, the chance of type1 error (rejecting a correct H0) would be too high i.e (99.99%)

The bigger p-value supports H0.

3. The statistics

The test statistic F equals 0.020, which lies in the accepted range: [-∞ : 2.8477]

6 0

3 years ago

Molly's alarm clock fell to the floor and the glass face was broken. Molly measured the glass face so that she could order a new

lisov135 [29]

The area of the circle shaped glass is 78.54

7 0

4 years ago

Read 2 more answers

Hey factory could produce 84 toy robots in one day. The purchasing equipment. Now they can produce 105 robots in one day. What i

Finger [1]

Answer:

The answer to the question is

25 % increase in production rate

Step-by-step explanation:

To solve the question, we note that

Initial number of products = 84 toy robots per day

Present production rate = 105 robots per day

The percentage increase is given by the increase in production rate divided by the original production rate multiplied by 100

Where increase in production rate = 105 - 84 = 21

Percentage increase = 21/84 ×100 = 25 % increase

4 0

3 years ago

Plz help plz plz plz plz

Likurg_2 [28]

Answer:

4

Step-by-step explanation:

The ratio of green : pink = 32 : 56 = 4 : 7

After 7 pink are given away, then

ratio = ? : 49 = 4 : 7 ← ratio has to be the same

Using proportion

$\frac{?}{4}$ = $\frac{49}{7}$ ( cross- multiply )

7? = 196 ( divide both sides by 7 )

? = 28

Thus the ratio = 28 : 49 = 4 : 7

Thus 32 - 28 = 4 green should be given

3 0

3 years ago

What is the x-axis and the y-axis of -2x+2=-4​

What is the x-axis and the y-axis of -2x+2=-4