1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natita [175]
3 years ago
14

21. In 4 + In(4x - 15) = In(5x + 19)

Mathematics
1 answer:
Alexxx [7]3 years ago
3 0

Answer:

x=-30;\quad \:I\ne \:0

Step-by-step explanation:

In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)

\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\

\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\

\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:

\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0

You might be interested in
Problem 1: Write each expression in the form a^b, without using any radicals.
VARVARA [1.3K]

By radical do you mean the square root symbol?

7 0
3 years ago
12 out of 20 doctors agree 15 out of 30 doctors agree are the ratios equivalent
uysha [10]
No it is not because 15 out of 30 is half but 12 out of 20 is more than half
4 0
3 years ago
A professor gives her 100 students an exam; scores are normally distributed. The section has an average exam score of 80 with a
frozen [14]

Answer:

6.18% of the class has an exam score of A- or higher.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

\mu = 80, \sigma = 6.5

What percentage of the class has an exam score of A- or higher (defined as at least 90)?

This is 1 subtracted by the pvalue of Z when X = 90. So

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

Z = \frac{90 - 80}{6.5}

Z = 1.54

Z = 1.54 has a pvalue of 0.9382

1 - 0.9382 = 0.0618

6.18% of the class has an exam score of A- or higher.

4 0
3 years ago
Please help. I don’t understand and don’t know what do to.
Bingel [31]

9514 1404 393

Answer:

  72

Step-by-step explanation:

The triangles are said to be similar. (ΔNPQ ~ ΔRSQ) That means corresponding sides have the same ratio:

  NP/RS = NQ/RQ = PQ/SQ = 24/32 = 21/28 = 3/4

This ratio, or scale factor, also applies to the perimeters of the two triangles.

  perimeter NPQ / perimeter RSQ = 3/4

Using the given expressions for the perimeters, we have ...

  (7x +2)/(10x -4) = 3/4

We can solve this equation in the usual way to find the value of x. Then we can use that value to find the perimeter of ΔNPQ.

  4(7x +2) = 3(10x -4) . . . . . multiply both sides by 4(10x -4)

  28x +8 = 30x -12 . . . . . eliminate parentheses

  20 = 2x . . . . . . . . . . . add 12-28x to both sides

  10 = x . . . . . . . . . . . divide both sides by 10

The perimeter of ΔNPQ is ...

  7x +2 = 7(10) +2 = 72

The perimeter of triangle NPQ is 72 units.

7 0
3 years ago
3х - 2y = 12<br> 12x – бу = 9<br> Need help
emmasim [6.3K]

Answer:

1.  x=4+2y/3

2. x=3/4+y/2

Step-by-step explanation:

hope this helped :))

7 0
3 years ago
Read 2 more answers
Other questions:
  • Slope = 7/3, y-intercept =3
    9·2 answers
  • One gallon of of paint covers about 450 square feet how many square feet will 1.5 gallons cover?
    8·2 answers
  • Write 13 tens as a sum of hundreds and tens
    6·2 answers
  • Can you please answer this qiestion for me.
    11·1 answer
  • Ellie has 12.5 pounds of potatoes to make mashed potatoes. She uses one-tenth as many pounds of butter as potatoes. How many pou
    6·1 answer
  • Mr taylor bought back 180 euros to the uk the exchange rate was €1.2 to ?1 how kuch did he get in pounds
    10·1 answer
  • Let statements p, q, r, and s be as follow:
    9·1 answer
  • How many solutions does tan^-1 3 have?
    12·1 answer
  • Can someone help please~~!?
    9·1 answer
  • Hey can i get some help pls.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!