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3 years ago

Transform the equation to isolate x: ax = bx + 1. How is the value of x related to the difference of a and b?

Mathematics

2 answers:

andrew-mc [135]3 years ago

8 0

For this case we have the following equation:

$ax = bx + 1$

From here, we must clear the value of x.

For this, we follow the following steps:

1) Place the variable on one side of the equation and the constant on the other side of the equation:

$ax - bx = 1$

2) Make common factor x:

$x (a -b) = 1$

3) Clear the value of x:

$x = \frac{1}{a-b}$

Answer:

$x = \frac{1}{a-b}$

The relationship between x and the difference of a - b is inversely proportional.

gavmur [86]3 years ago

4 0

Answer:

The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b.

Step-by-step explanation:

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Prove the circles are similar :).

Fudgin [204]

Answer:

Translate circle C 3 units towards the right and 5 units up.

Dilate this translated circle C by a factor 2.5. It will overlap (become congruent to) circle A

This is enough to prove that the two circles are similar

5 0

3 years ago

If y is a positive integer, for how many different values of y is RootIndex 3 StartRoot StartFraction 144 Over y EndFraction End

Lelechka [254]

The value of y will be 18 or 144.

Given information:

The given expression is $\sqrt[3]{\frac{144}{y} }$ .

It is required to find the values of y which are whole numbers.

Now, factorize 144 as,

$144=2\times2\times2\times2\times3\times3\\144=2^3\times2\times3\times3$

So, for the value of given expression to be a whole number, the value of y should be,

$2\times3\times3=18$ or 144.

For the above values of y, the given expression will be,

$\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{18} }\\=\sqrt[3]{8} =2\\\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{144} }\\=\sqrt[3]{1} \\=1$

Therefore, the value of y will be 18 or 144.

For more details, refer to the link:

brainly.com/question/17429689

3 0

2 years ago

5a-3b+c+(4-5b-c) ayuda

JulsSmile [24]

La respuesta es 5a - 8b + 4

5 0

3 years ago

A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30 What score is necessary to reach

nlexa [21]

Answer:

A score of 150.25 is necessary to reach the 75th percentile.

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30.

This means that $\mu = 130, \sigma = 30$

What score is necessary to reach the 75th percentile?

This is X when Z has a pvalue of 0.75, so X when Z = 0.675.

$Z = \frac{X - \mu}{\sigma}$

$0.675 = \frac{X - 130}{30}$

$X - 130 = 0.675*30$

$X = 150.25$

A score of 150.25 is necessary to reach the 75th percentile.

7 0

3 years ago

How many ways are there to select a 5-card hand from a regular deck such that the hand contains at least one card from each suit

Snezhnost [94]

Answer:

There are 685464 ways of selecting the 5-card hand

Step-by-step explanation:

Since the hand has 5 cards and there should be at least 1 card for each suit, then there should be 3 suits that appear once in the hand, and one suit that apperas twice.

In order to create a possible hand, first we select the suit that will appear twice. There are 4 possibilities for this. For that suit, we select the 2 cards that appear with the respective suit. Since there are 13 cards for each suit, then we have ${13 \choose 2} = 78$ possibilities. Then we pick one card of all remaining 3 suits. We have 13 ways to pick a card in each case.

This gives us a total of 4*78*13³ = 685464 possibilities to select the hand.

6 0

3 years ago