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!
I need help with this geometryyyy workkk
Answer:
Perpendicular
Step-by-step explanation:
For this problem, it is important to note two things. One line is completely vertical, and the other line is completely horizontal.
The line y=9 is completely horizontal at the y-value at 9. The line x = 2 is completely vertical at the x-value at 2.
Hence, these two lines would be perpendicular.
Cheers.
Answer:
Perpendicular.
Step-by-step explanation:
Since it makes a huge cross +, which we want it to be, we need the lines to intercept and it makes a right angle. That means it is perpendicular.
someone please help me
Approximately how many times greater is 2.3x10^-4 than 1.15x10^-8?
Answer:
2.3 × is 20,000 times greater than 1.15 ×
Step-by-step explanation:
Given as :
The first number= x = 2.3 ×
The second number= y = 1.15 ×
Let The first number is z times greater than second number
i.e x = z × y
Or, z =
Or, z =
Or, z = 2 ×
∴ z = 20,000
So,The first number is 20,000 times greater than second number
Hence, 2.3 × is 20,000 times greater than 1.15 ×
What is the value of y in the solution to the following system of equations?
5x – 3y = -11
2x - 5y = -14
Answer:
{x,y} = {33/19,-2/19}
Step-by-step explanation:
Answer: For 5x-3y=-11, the answer is y=11/3 + 5x/3.
For 2x-5y=-14, the answer is y=14/5 + 2x/5
Step-by-step explanation: Move all terms that do not contain y to the right side and then solve.
I hope this helps you out! :)
5.) Solve the equation below
X/19=4
Answer:
76
Step-by-step explanation:
multiply 19 and 4 to get 76. If you plug in 76 as x you can check to see if it's true
Simplify (9 ^ 2)/(9 ^ 7)
what can be a segment bisector
Answer: A segment bisector, always passes through the midpoint of the segment and divides a segment in two equal parts. Points, lines, segments, and rays are all types of segment bisectors. If either a ray or a line serves as a segment bisector, it will be infinite.
Hello your very welcome :)
Answer:A segment bisector, always passes through the midpoint of the segment and divides a segment in two equal parts. ... Points, lines, segments, and rays are all types of segment bisectors. It will be infinite.
Step-by-step explanation:
Find the indicated angle measurement
Answer:
by adding both the given angle we will get
78+69
Step-by-step explanation:
=141
which of these comparisons is correct?
A. -2 < -5
B. 0 > 2
C. 4 > -4
D. -6 < -5
Can you help please
Expand each expression and combine like terms if possible
2/3 (x+ 18 - 2x)
Answer:
This is the expression expanded
Step-by-step explanation:
Tell whether the lines are parallel perpendicular or neither Y=4x+5 Y=-1/4x+4
What is the slope of the line that connects the points
(-2,6) and (4,0) ?
Answer:
[tex]m=-1[/tex]
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply plug in the 2 coordinates into the slope formula to find slope m:
[tex]m=\frac{0-6}{4-(-2)}[/tex]
[tex]m=\frac{-6}{4+2}[/tex]
[tex]m=\frac{-6}{6}[/tex]
[tex]m=-1[/tex]
HEY GUYS HELP I HAVE NO CLUE AND I HAVE TO TURN IT IN AT 25 MINUETS
Answer:
elevator 1 ends at floor 23. Elevator 2 ends at floor 42.
Step-by-step explanation:
3x + 2y + -2x + 8y pls help
x+10y
Step-by-step explanation:3x+2y+(-2x)+8y
First of all you cannot substitute x with y, so what u do u make the numbers with the same letters they have,and I put -2x because + & - equals to -(minus) :-
3x-2x+2y+8y= x+10y
I don't add 1 to x coze when x alone stands for 1, I added +10y because both the y equations had + they were positive so I add a +.
Hope it helpsUse the interactive tool to find the difference.
(-4) -6? Imma give 20 brainlest
Answer:
-10
Step-by-step explanation:
Difference means to subtract
(-4) - 6
-4 - 6
-10
I hope this is what you are looking for.
Answer:
The answer to this question is -10 because when you put -4-6 you get -10 and so the answer is -10!
. If T is the midpoint of SU, what are ST, TU, and SU?
Step-by-step explanation:
We have ST=5x, TU=3x+32 and they're equal if T is the midpoint:
5x = 3x + 32
2x = 32 x = 16
ST = 5x = 80
So TU = 80
and SU=160
Answer: Second choice
Vanya drove 405 miles in 9 hours. Chuy drove 350 miles in 7 hours. Alfredo drove 330 miles in 6 hours. Who was driving at the fastest speed? (fastest MPH/ fastest Unit Rate) Question 14 options: Vanya Chuy Alfredo
Answer:
350 miles in 7 hours
Step-by-step explanation:
1. find
if 9=405
1=v(represent with a variable
2. do the same for the others and select the highest number
3m+2n=7 solve for M
It’s late night my brain is stemming. Help
Answer:
M= 7/3 hope that helps ya out
first year of high school heh need a little help
Answer:
(12 + 3x)x
Step-by-step explanation:
(12 + 3)x = 12x + 3x = 15x
(12 + 3x)x = 12x + 3x²
15x
12x + 3x = 15x
They all equal 15x except for (12 + 3x)x
5
A triangular shaped park
has side walks that are
30 feet, 40 feet, and 50
feet long. Does the
sidewalk make a right triangle
is 42 already already in simplest form.do you agree or disagree?explain
Answer:
Yes the number 42 is at its simplest form.
Step-by-step explanation:
Any whole number is already at its simplest form.
What is the simplified form of (2b2 – 6) + (4b + 7) – (b2 + 5b – 3)?
Answer:
b2−b+4
Step-by-step explanation:
Write the problem as a mathematical expression.
(2b2−6)+(4b+7)−(b2+5b−3)(2b2-6)+(4b+7)-(b2+5b-3)
Remove parentheses.
2b2−6+4b+7−(b2+5b−3)2b2-6+4b+7-(b2+5b-3)
Simplify each term.
2b2−6+4b+7−b2−5b+32b2-6+4b+7-b2-5b+3
Simplify by adding terms.
b2−b+4
(m • n) • p=m • (n • p)
what property is this
Answer:
Step-by-step explanation:
9. Whats is the equivalent fraction for 0.625
Answer:
5/8
Step-by-step explanation:
You need to convert to a simplified fraction by placing the numbers to the right of the decimal over 1000. Then reduce the fraction.
A pasta factory made 328.16 pounds of pasta in 7 minutes. How much pasta, on average, did the factory make each minute?
Answer:
46.88 lb per minute
Step-by-step explanation:
328.16/7
46.88
Point I is on line segment \overline{HJ}
HJ
. Given HI=2x,HI=2x, HJ=4x,HJ=4x, and IJ=4x-10,IJ=4x−10, determine the numerical length of \overline{IJ}.
IJ
.
Answer:
IJ = 20
Step-by-step explanation:
Point I is on the lines segment HJ. So,
HJ = HI + IJ
Putting all the given values, we get :
4x=2x+4x-10
Taking like terms together, we get :
-2x=-10
x=5
Put the value of x in IJ = 4x-10
IJ = 4(5)-10
IJ = 20
Hence, the value of IJ is 20.
Answer:
10
Step-by-step explanation:
pleaseeee help!! (click on the pic)
Find me midpoint of -9 and 6
Answer:
-3/2 or -1.5
Step-by-step explanation:
1) Write out the numbers:
-9, -8, -7, -6, -5, -4, -3, [-2, -1] 0, 1 , 2, 3, 4, 5, 6
2)-2 and -1 are in the middle
3)Add the numbers in the middle and divide by 2
Add the 2 numbers: (-2)+(-1)=-3Divide by 2: -3/2 Answer: -1.5
HELP!!! WILL GIVE BRAINLIEST!!!! 40 POINTS!!!!!! The agriculture department of a university works with individuals wanting to build greenhouses heated with only plastic. The department raised funding for 3,450 greenhouses. The program started with a group of 310 existing greenhouses. The number grew to 3,262 greenhouses 10 years after inception. Which equation can be used to model the relationship between the number of greenhouses outfitted depending on the number of years since the project began?
Answer:
Should be something along the lines of:
3,450 = 326x - 310
Step-by-step explanation:
First, let's start with the number of years. Assume the number of years is x. 3262 greenhouses amounts to about 326 greehouses/year. The other number was the existing greenhouses, but we want just how many greenhouses that were built, per the subtraction sign.
Hope this helps!! : )
Sorry if I am wrong, haven't done equations in a while.
Express this |-3x-4|