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3 years ago

I need help can you help me equation: 3x = ax +b

Mathematics

1 answer:

stepan [7]3 years ago

8 0

Answer:

a = 3

b = 0

Step-by-step explanation:

Equations that have infinite solutions are equations that equal itself.

Example: 13y = 13y has infinite solutions

We need to find the values of a and b so that it equals 3x.

Therefore, a = 3 and b = 0.

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The butterfly weighs .168, as far as the scientific notation, it's 1.68x10^2

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3 years ago

2. Factor completely<br> 16x^5 - 48x^4 + 40x²

son4ous [18]

Answer:

8x^2(2x^3 - 6x^2 + 5).

Step-by-step explanation:

The GCF is 8x^2 so we have:

8x^2(2x^3 - 6x^2 + 5)

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Prove the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus. use the distance formula

riadik2000 [5.3K]

In order to prove this, we have to put the trapezoid to the coordinate system. In the attached photo you can see how it has to be put. The coordinates for the vertices of trapezoid written according to the midpoint principle. By using the distance between two points formula, we can find the coordinates for the vertices of the rhombus.
$D_{x} = \frac{-2b-2a}{2}=-b-a$ and $D_{y}= \frac{2c+0}{2}=c$ . The coordinates of D is $(-b-a, c)$
$E_{x} = \frac{-2b+2b}{2}=0$ and $E_{y}= \frac{2c+2c}{2}=2c$ . The coordinates of E is $(0,2c)$
Since we have the reflection in this graph, the coordinates of F is $(b+a, c)$
And the coordinates of G is (0,0).

Using the distance formula, we can find that
$DE= \sqrt{(-b-a)^{2}+ c^{2}}=\sqrt{(b+a)^{2} + c^{2}}$
$EF= \sqrt{(b+a)^{2} + c^{2} }$
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$DG= \sqrt{(b+a)^{2}+ c^{2}$

Since all the sides are equal this completes our proof. Additionally, we can find the distances of EG and DF in order to show that the diagonals of this rhombus are not equal. So that it is not a square, but rhombus.

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3 years ago

Read 2 more answers

Find the number of permutations of the first 8 letters of the alphabet taking 5 letters at a time?!

Musya8 [376]

The first letter can be any one of 8. For each of those . . .
The second letter can be any one of the remaining 7. For each of those . . .
The third letter can be any one of the remaining 6. For each of those . . .
The fourth letter can be any one of the remaining 5. For each of those . . .
The fifth letter can be any one of the remaining 4.

The total number of possibilities is (8 x 7 x 6 x 5 x 4) = <em>6,720</em> .
(That's 8! / 3! .)

Note:
If you're allowed to use the same letter more than once,
then there are 8 choices for each of the 5 letters.
The total number of possibilities then is (8 x 8 x 8 x 8 x 8) = 32,768 .
(That's 8⁵ or 2¹⁵ .)

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3 years ago

A person must score in the upper 7% of the population on an admissions test to qualify for membership in society catering to hig

olya-2409 [2.1K]

Answer:

The minimum score a person must have to qualify for the society is 162.05

Step-by-step explanation:

Problems of normally distributed samples 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.

In this problem, we have that:

Test scores are normally distributed with a mean of 140 and a standard deviation of 15. This means that $\mu = 140, \sigma = 15$ .