5/12 divided by what equals 1

What is the percent increase from 2,000 to 3,000

WINSTONCH [101]

50% should be the present increase :)

3 0

3 years ago

Find x with two triangles

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

PLEASE ANSWER FOLLOWING QUESTION I’LL MARK BRAINLIST

bija089 [108]

Answer:

3rd answer

Step-by-step explanation:

If you look at the translation, each point is moved 6 to the right on the X axis, and down 4 on the y- axis. so, therefore it should be (6,-4)

3 0

3 years ago

Read 2 more answers

Victoria whit used 578 kw-hr of electricity in December the rate is 9.1 cents per kw-hr find the amount of her electric bill

MatroZZZ [7]

Answer:

The amount of electricity bill is $52.60.

Step-by-step explanation:

Given:

Victoria whit used 578 kwh of electricity.

The rate is 9.1 cents per kw-hr.

Now, to find the amount of her electric bill.

Electricity used = 578 kwh.

Rate of electricity = 9.1 cents per kw-hr.

So, to get the amount we multiply the electricity used by the rate of electricity:

$Amount\ of\ electric\ bill=Electricity\ used\times rate\ of\ electricity$

$Amount\ of\ electric\ bill=578\ kwh\times 9.1\ cents$

$Amount\ of\ electric\ bill=5259.8\ cents.$

Thus, the amount of electricity bill = 5259.8 cents.

Now, converting the amount from cents to $ by dividing:

$1 = 100 cents.

So, 5259.8 cents ÷ 100 = $52.60 .

therefore, the amount of electricity bill is $52.60.

3 0

3 years ago

Penalty Shots in World Cup Soccer A study1 of 138 penalty shots in World Cup Finals games between 1982 and 1994 found that the g

Angelina_Jolie [31]

Answer:

There is enough evidence to support the claim that the percent that the goalkeeper guessed correctly is less than 50%.

Step-by-step explanation:

We have to perform an hypothesis test on a proportion.

We have a sample of size n=138, a sample mean of p=0.41.

The standard error is SE=0.043.

We want to test the claim that the real proportion is below 50%.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.5\\\\H_a: \pi$

The significance level is α=0.05.

The z-statistic can be calculated as:

$z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.41-0.5+0.5/138}{0.043}=\dfrac{-0.086}{0.043}= -2$

The P-value (left tail test) for this z-statistic is:

$P-value=P(z$

The P-value is smaller than the level of significance, so the effect is significant. The null hypothesis is rejected.

There is enough evidence to support the claim that the percent that the goalkeeper guessed correctly is less than 50%.

5 0

3 years ago