Answer:
[tex]x=\log_3{(15+ 4\sqrt{14})}\approx3.0949\text{ or } \\x=\log_3{(15- 4\sqrt{14})}\approx-3.0949[/tex]
Step-by-step explanation:
So we have the equation:
[tex]3^{1-x}+3^{1+x}=90[/tex]
First, note that this is the same as:
[tex]3\cdot 3^{-x}+3\cdot 3^x=90[/tex]
Factor out a 3:
[tex]3(3^{-x}+3^{x})=90[/tex]
Divide both sides by 3:
[tex]3^{-x}+3^x=30[/tex]
Change the negative exponent into a fraction:
[tex]\frac{1}{3^x}+3^x=30[/tex]
Multiply both sides by 3^x:
[tex]3^x(\frac{1}{3^x}+3^x)=(30)(3^x)[/tex]
Distribute:
[tex](1)+(3^x)^2=30(3^x)[/tex]
Let u equal 3^x. So:
[tex]1+u^2=30u[/tex]
Subtract 30u from both sides:
[tex]u^2-30u+1=0[/tex]
This is a quadratic. Solve using the quadratic formula. A is 1, b is -30, and c is 1. So:
[tex]u=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute:
[tex]u=\frac{-(-30)\pm \sqrt{(-30)^2-4(1)(1)}}{2(1)}[/tex]
Simplify:
[tex]u=\frac{30\pm \sqrt{900-4}}{2}[/tex]
Subtract:
[tex]u=\frac{30\pm \sqrt{896}}{2}[/tex]
Simplify:
[tex]u=\frac{30\pm 8\sqrt{14}}{2}[/tex]
Simplify:
[tex]u=15\pm 4\sqrt{14}[/tex]
Substitute back u:
[tex]3^x=15\pm 4\sqrt{14}[/tex]
Take the log to base 3 of both sides:
[tex]\log_3{3^x}=\log_3{15\pm 4\sqrt{14}}[/tex]
The left side cancels:
[tex]x=\log_3{15\pm 4\sqrt{14}}[/tex]
So, our solutions are:
[tex]x=\log_3{(15+ 4\sqrt{14})}\approx3.0949\text{ or } \\x=\log_3{(15- 4\sqrt{14})}\approx-3.0949[/tex]
And we're done!
~**Will mark brainliest **~
For the correct answers to all three questions
a)
[tex]\dfrac{42}{65}\cdot\dfrac{25}{36}\cdot\dfrac{26}{49}=\dfrac{2\cdot3\cdot7}{5\cdot13}\cdot\dfrac{5\cdot5}{2\cdot2\cdot3\cdot3}\cdot\dfrac{2\cdot13}{7\cdot7}=\dfrac{7}{13}\cdot\dfrac{5}{2\cdot3}\cdot\dfrac{2\cdot13}{7\cdot7}=\\\\\\=\dfrac{1}{1}\cdot\dfrac{5}{2\cdot3}\cdot\dfrac{2}{7}=\dfrac{5}{3}\cdot\dfrac{1}{7}=\dfrac{5}{21}[/tex]
b)
[tex]\dfrac{21}{32}\cdot\dfrac{39}{120}\cdot\dfrac{40}{65}=\dfrac{21}{32}\cdot\dfrac{3\cdot13}{2\cdot2\cdot2\cdot3\cdot5}\cdot\dfrac{2\cdot2\cdot2\cdot5}{5\cdot13}=\\\\\\=\dfrac{3\cdot7}{32}\cdot\dfrac{13}{2\cdot2\cdot2\cdot5}\cdot\dfrac{2\cdot2\cdot2}{13}=\dfrac{21}{32}\cdot\dfrac{1}{5}\cdot\dfrac{1}{1}=\dfrac{21}{160}[/tex]
c)
[tex]\dfrac{15}{90}\cdot\dfrac{36}{75}\cdot\dfrac{27}{42}=\dfrac{3\cdot5}{2\cdot3\cdot3\cdot5}\cdot\dfrac{2\cdot2\cdot3\cdot3}{3\cdot5\cdot5}\cdot\dfrac{3\cdot3\cdot3}{2\cdot3\cdot7}=\\\\\\=\dfrac{1}{2\cdot3}\cdot\dfrac{2\cdot2\cdot3}{5\cdot5}\cdot\dfrac{3\cdot3}{2\cdot7}=\dfrac{1}{1}\cdot\dfrac{2}{5\cdot5}\cdot\dfrac{3\cdot3}{2\cdot7}=\dfrac{1}{25}\cdot\dfrac{9}{7}=\dfrac{9}{175}[/tex]
find the value of [tex]\sqrt[3]{8}[/tex]
Answer:
∛8 = 2
Step-by-step explanation:
[tex]\sqrt[3]{8}[/tex]
=2
2*2*2 = 8
This is also due tonight..
Answer: F,E,D
Step-by-step explanation: F,E,D is complementary to F,G,C because it is The angle F,E,D is a corresponding angle.
What is the y-intercept of the line that models this situation?
given b(x) = |x+4| , what is b(-10)
Answer:
6
Step-by-step explanation:
|-10+4| = |-6|= 6
inside the | | the equation is done normally. that's why it has a negative at first. then, once getting rid of the bars, you change the number to a positive
Answer:
[tex]\boxed {\tt b(-10)=6}[/tex]
Step-by-step explanation:
We are given the function:
[tex]b(x)= \mid x+4 \mid[/tex]
We want to find b(-10). Therefore, we must plug -10 in for each x.
[tex]b(-10)= \mid -10+4 \mid[/tex]
Solve inside of the absolute value symbol. Add 4 to -10 ⇒ -10+4= -6
[tex]b(-10)= \mid -6 \mid[/tex]
Absolute value represents how far away a number is from 0. It is always positive.
-6 is 6 away from 0. Therefore, the absolute value of -6 is 6.
[tex]b(-10)= 6[/tex]
b(-10) is equal to 6.
write an algebraic expression for 74 increased by 3 times y
Answer:
[tex]74+3y[/tex]
:)
Answer:
74+3y
Step-by-step explanation:
We are starting with 74
increased is addition (+)
3 times y is multiplication ×
74 + 3y
74+3y
Hope this helps :-)
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation that will represent the cost.
Find 2 equivalent ratios to 3 : 5 PLSSSSS HELP ASAP
could it be.
15:25
30:50
if its wrong, then just report me
Find the distance from each vertex on the preimage ABC to the center of rotation p enter the values in the table do the same for each vertex on the other images
Answer:
Enjoy.
Step-by-step explanation:
school
Answer:
Step-by-step explanation:
The formula for profit is P = I – E solve the formula for E I need ASAP
Answer:
Step-by-step explanation:
I - E = P
-E = P - I
E = I - P
I REALLY NEED THISSSSS
PLEASE HELP!!!!!!
can you help meew pleasee due in 5 minnn
Answer:
It's D: 3x - 12 ≤ 8x + 13
Step-by-step explanation:
The first step in this inequality is to take out the parentheses so you multiply 3 by x and -4.
What value does the 8 represent in the number 865,202 ?
The value of 8 is 800,000.
The value of each digit in a number is known as the place value. The place value of 8 in the number 865,202 is 800,000.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
How do identify the place value of a digit in a number?The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths and so on
The tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10The place value of 8 in the number 865,202 is 800,000.
Learn more about the Place Value:
https://brainly.com/question/27734142
#SPJ2
The Grand Canyon is 277 miles long and 18 miles wide. A study was completed where 17
people can fit in a sample space that is 5 feet by 6 feet. How many people can fit in the
Grand Canyon?
A child's ladder is made of 3 sections. Each section is 3/4 meters. How long is the ladder when all 3 sections are extended to make
one ladder?
O A. 1 meter
.
B. 9/4 meters
O C. 1414 meters
OD. 3/2 meters
Answer:
2 1/4
Step-by-step explanation:
Because I got it wrong and it showed me the answer. YOUR WELCOME
Answer:
2 1/4
Step-by-step explanation:
got it corrrect
-7=-x
One step equations ( Find X)
Answer:
answer of your question is
-x= -7
Solve the equation for x. –1/2x – 3 = 4
Answer:
x=−14
Step-by-step explanation:
I hope this helps you
What's the length of side b in the figure?
Answer:
the answer is 91
you have to multiply 7 and 13 to get your answer
does someone know the other endpoint
Answer:
(-10,11)
Step-by-step explanation:
x-value:
-4-2=-6
-4-6=-10
y-value:
6-1=5
6+5=11
Answer:
the new end point is (-10,11).
Find CL if TL = 6
Can y’all help me or tell me if I got this right.
Answer:
Sorry bro you are wrong .
Here CL = 2
Step-by-step explanation:
Property of triangles Centroid divides the midian of the triangle into the ratio 2:1
where is sandy mistake ive been trying for 30 mintues and still cant find it im not very good at math please help
Answer:
Sandy did not follow PEMDAS and added first instead of doing her multiplication and division and then her addition and subtraction the answer would be 18
Classify by degree of polynomial:
3x3 - 6x
Answer:
polynomial of degree 3
Step-by-step explanation:
Given
3x³ - 6x
The degree of a polynomial is given by the exponent of the term with the largest exponent.
In this case 3x³ has exponent 3 and - 6x has exponent 1
Thus this is a polynomial of degree 3
SIMPLE: 25 pts!!! Find the area A of the polygon with the given vertices:)
Hey there! I'm happy to help!
We see that points A and B are on the same horizontal line, and and they are 10 units apart. C and D are on their own horizontal line and they are also 10 apart. This means that this is a square, so we multiply one side by itself
10²=100
The area is 100 square units.
Have a wonderful day! :D
Estimation Solve the equation. First estimate using the perfect square closest to 46. Then use a
calculator
W2 = 46
Step-by-step explanation:
W^2 = 46.
We know that 6^2 = 36 and 7^2 = 49.
Therefore W should be between 6 and 7.
0.05 is 1/10 of a decimal as
Answer:
1/10 =0.1 in decimal
Step-by-step explanation:
An airplane flies with a constant speed of 920 km/h. How far can it travel and 4 hours 12 minutes?
Answer:
3,864 Km
Step-by-step explanation:
920/60=15.333333
15.33333*252=3,864
2. Is the data set "dollars of sales per week” quantitative or qualitative?
Answer:
this would be quantitative.
Step-by-step explanation:
because its an amount like dollars of sales per week so it would be quantitative or numbers
The Smith family put a rectangular garden in their back yard. The garden measured 15 34 feet long and 13 13 feet wide. Which is the best estimate of the area of the Smith's garden? Response area
Answer:
201.4 feet
Step-by-step explanation:
Area of a rectangular garden = length × width
Length of the rectangular garden = 15.34 feet
Width of the rectangular garden = 13.13 feet
Area of a rectangular garden = length × width
= 15.34 feet × 13.13 feet
= 201.4142 feet
Approximately 201.4 feet
The Area of the rectangular garden = 201.4 feet
15/49 converted into decimal
Answer:
0.30612244897959
Step-by-step explanation:
Two men are trying to carry a wooden pole. if one of them is weaker than other, how can they carry the pole hence making small load for weak man?