Answers
Answer:
[tex]x = 0.68[/tex]
Step-by-step explanation:
We would like to find out the value of x using logarithms of the given equation .The equation is ,
[tex]\longrightarrow 25^x - 3(5^x)=0\\[/tex]
Add [tex]3(5^x)[/tex] on both sides,
[tex]\longrightarrow 25^x = 3(5^x) [/tex]
Using log to the base 10 on both sides, we have;
[tex]\longrightarrow log_{10}(25^x) = log_{10}\{3(5^x)\}[/tex]
Recall that [tex] log(ab ) = log\ a + log\ b [/tex] .
[tex]\longrightarrow log_{10}(25^x)=log_{10}3 + log_{10}5^x [/tex]
Recall the properties of logarithm as [tex] log\ a^b = b\ log\ a [/tex] .
[tex]\longrightarrow xlog25 = log_{10}3 + xlog_{10}5 [/tex]
Again we can rewrite it as ,
[tex]\longrightarrow xlog(5^2)=log_{10}3+xlog_{10}5\\ [/tex]
[tex]\longrightarrow 2x\ log_{10}5 = log_{10}3+xlog_{10}5 \\ [/tex]
[tex]\longrightarrow 2x\ log_{10}5-x\ log_{10}5 = log_{10}5 [/tex]
Simplify,
[tex]\longrightarrow x\ log_{10}5=log_{10}3 [/tex]
Divide both sides by log5 ,
[tex]\longrightarrow x =\dfrac{log_{10}3}{log_{10}5} [/tex]
Put on the values of log 3 and log5 ,
[tex]\longrightarrow x =\dfrac{0.47}{0.69} [/tex]
Simplify,
[tex]\longrightarrow \underline{{\underline{\boldsymbol{ x = 0.68}}}}[/tex]
And we are done!
Related Questions
Which graph represents f(x)=−2cos(4πx)?
Answers
Answer:
the last one (bottom right)
Step-by-step explanation:
4×pi is the same as twice around the whole circle to the beginning. it is the same as 0°, and cos(0) = 1, and then -2×cos(0) = -2
so, we only need to look, where the function reaches -2.
it should be at x = 0, x = 0.5 and x = 1.
I would love the pleasure of someone helping me with the answer
Answers
Answer:
A, B, E, and F
Step-by-step explanation:
Will give brainliest if you find the mean
10, 10, 20, 40, 70
Answers
Answer:
30
Step-by-step explanation:
10+10+20+40+70=150
150/5=30
hope this helps!
Answer:
ok so find the average first we have to add up
10+10=20
20+40=60
70+20=90
90+60=150
then we have to divide by the number so 5 since their is 5 number in the date set
150/5=30
30
Hope This Helps!!!
100 points! please help meeee.
find the missing dimensions on the figure
Answers
Answer:
r = 2 and n = 3
Step-by-step explanation:
9 = r + 3+ 4
9 = r + 7
r = 2
10 = n +2 + 5
10 = n + 7
n = 3
Answer:
r = 2 ft
n = 3 ft
area = 61 ft²
explanation:
total length : 10 fttotal width : 9 ft-------------------------------
n + 2 + 5 = 10 n = 10 - 7n = 3 ft-------------------------------
r + 3 + 4 = 9 r = 9 - 7r = 2 ft-----------------------------
Area of the entire figure:
length * width9 ft * 10 ft90 ft²Area of the missing side:
5 * (3+2) + 2 * 229 ft²So area of the shape:
90 ft² - 29 ft²61 ft²You earn $17.50/hour, if you work 28 hours week 1 and 25 hours week 2 determine how much you will make for the two weeks before deductions?
Answers
Answer:
$122.50
Step-by-step explanation:
17.50
x25
437.50
x 28
$122.50
when the legs of a triangle are both 6 cm. what is the hypotenuse
Answers
Answer:
72
Step-by-step explanation:
to find the hypotenuse you need to do (Hypotenuse)^2 = (Base)^2 + (Altitude)^2, which is the Pythagorean theorem (a^2+b^2=c^2)
if the bases are both 6, you need to do 6^2+6^2= hypotenuse
6*6+6*6=?
36+36=72
so the hypotenuse is 72 cm
100 POINTS! CORRECT ONLY!! HELP ASAP!!
Match the graph with its function. Which is an example of growth decay?
What type of sequence is shown below:
3,6,9,12,15 1,3,9,27,81
The first sequence has a common:
The second sequence has a common:
Answers
The first sequence has a common difference( arithmetic progression)
The second sequence has a common ratio( geometric progression)
Brainliest plss !!!
Have a good day :)
Suppose the monthly charges for cell phone plans in the U. S. Are normally distributed with a mean of $62 and a standard deviation of $10. What is the proportion of cell phone plans charging less than $42 a month for service?
Answers
Using the normal distribution, it is found that 0.0228 = 2.28% of cell phone plans charge less than $42 a month for service.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X.In this problem, the mean and the standard deviation are given by, respectively: [tex]\mu = 62, \sigma = 10[/tex].
The proportion of cell phone plans charging less than $42 a month for service is the p-value of Z when X = 42, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{42 - 62}{10}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.0228 = 2.28% of cell phone plans charge less than $42 a month for service.
More can be learned about the normal distribution at https://brainly.com/question/24663213
The Panthers did not score more points than the Tigers. The Tigers scored fewer points than the Lions. The Lions scored fewer points than the Wolverines but more points than the Panthers. Which team scored more points, the Wolverines or the Panthers?
Answers
Answer:Wolverines
Step-by-step explanation:
The panthers < tigers Tiger 1
Tigers < Lions Lions 2
Lions< wolverines Panthers 0
Lions> Panthers Wolverines 1
Even though the lions scored more wolverines scored more than the panthers since the panthers didn't score a single point according to my calculations
Calculate the volume. Round your answers to the nearest tenth if necessay
Answers
Answer:
384 cm^3
Step-by-step explanation:
Use the formula to find the volume.
Volume = Area of the base x the height
V = Bh
V = 32(12)
V = 384 cm^3
In parallelogram rstu, what is su? 10 m 13 m 23 m 26 m.
Answers
Answer:
26
Step-by-step explanation:
none
The length of SU is 26.
What is Parallelogram?Opposite sides are parallel and congruentOpposite angles are congruentConsecutive angles are supplementaryDiagonals bisect each otherAs, we know the diagonal of parallelogram bisect each other.
So, UV = VS
x+ 3 = 2x- 7
Now, solve for we get
x - 2x = - 7 - 3
-x = -10
x = 10
Then, the length of SU
= UV + VS
= 10 + 3 + 2(10)-7
= 13 + 13
= 26
Thus, the required value is 26.
Learn more about Parallelogram here:
https://brainly.com/question/29147156
#SPJ7
Your class has 28 students if 25 of them play soccer how many students play soccer?
Answers
Answer:
7 students
Step-by-step explanation:
"Of" in math most of the time means multiplication.
28 x 25% = 7
That also means that 21 students DO NOT play soccer.
Find all numbers whose absolute value is -9.
If there is more than one, separate them with commas.
If there are no such numbers, click on "None".
Answers
Answer:
-9 and 9
Step-by-step explanation:
|-9| = 9
|9| = 9
Only -9 and 9 can have an absolute value of 9
PLEASE HELP ILL GIVE BRAINLIEST TO FIRST ANSWER
Answers
Answer:
x =11
Step-by-step explanation:
6x +1 + 5x -17 + 9x - 24 = 180
x =11
PLEASE HELP!!!!!
4. A cube has a volume of 64 m². What is the cube's surface area?
12 points!!! <333
Answers
Answer:
Surface area = 96 m^2
Step-by-step explanation:
Let's cube root the volume to find the length of one side of the cube.
[tex]64^\frac{1}{3} = 4[/tex]
Therefore each side is 4 m.
Surface area of one side = 4x4 = 16
A cube has 6 sides.
Total surface area of the cube = 16*6 = 96 m^2
The box below represents some data set what is the range of the data
Answers
Answer:
Maximum value-minimum value=answer
what is the distributive property of 6(2x + 5y).
Answers
Answer:
12x+30y
Step-by-step explanation:
6*2x+6*5y
12x+30y
Answer:
12x+30y
Step-by-step explanation:
6(2x+5y)
The distributive property is used if a number is in the form
[tex]a(b+c)[/tex]
To solve this problem, you need to multiply b and c by a.
[tex]=ab+ac[/tex]
Now, let's plug in your numbers.
a = 6
b = 2x
c = 5y
[tex]6(2x+5y)\\=(6)2x+(6)5y\\=12x+30y[/tex]
What is the standard notation for the distance of 8.512 x 10^10 miles (10 to the tenth power)
Answers
I'm not sure what the answer can be for this
Answer:
85120085120000000
Explanation
What is the slope of the line that passes through the points (9, -10) and (14,5)?
Write your answer in simplest form.
Answers
Answer:
3
Step-by-step explanation:
so you have to use the equation
y2 - y1 / x2 - x1
to find the slope
now all you have to do is substitute
-10 - 5 / 9 - 14
-15/ -5
3
Answer:
[tex]m=3[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(9,\:-10\right),\:\left(x_2,\:y_2\right)=\left(14,\:5\right)[/tex]
[tex]m=\frac{5-\left(-10\right)}{14-9}[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]m=3[/tex]
Hurry please!
What is the slope of a line perpendicylar to the line whose equation is
5x + 6y = -54. Fully simplify your answer.
Answers
Answer:
[tex]\frac{6}{5}[/tex]
Step-by-step explanation:
*Perpendicular lines have negative reciprocals slopes*
First, find the slope-intercept form of 5x + 6y = -54:
5x + 6y = -54
-5x -5x
6y = -5x - 54
/6 /6
y = [tex]-\frac{5}{6}x[/tex] - 9
y = mx + b
So, the reciprocal slope of m = [tex]-\frac{5}{6}[/tex] is m = [tex]\frac{6}{5}[/tex]
Hope this helps!
Triangle F GH is formed by connecting the midpoints of the side of triangle CDE.
The lengths of the sides of triangle DE are shown. Find the perimeter of triangle
FGH. Figures not necessarily drawn to scale.
Answers
Answer: 6
Step-by-step explanation:
Factor. 15x-9 how do i solve and get the correct answer
Answers
Answer:
[tex]{ \rm{15x - 9}} \\ = { \rm{(5 \times 3)x - (3 \times 3)}} \\ = { \boxed{ \rm{3(5x - 3)}}}[/tex]
Answer:
15x-9 = 3(5x-9)
above answer is correct
5. Three jars of crushed ginger costs $2.00. How many jars can you buy for $6.00?
Answers
Answer:
9 jars
Step-by-step explanation:
If 3 jars cost $2
and 3 times 2 is $6 then just multiply 3 by 3 to get 9 jars.
Hope this helped.
A brainliest is always appreciated.
16 x + 5y when x = 1/4 and y = 8
Answers
Answer:
44
Step-by-step explanation:
16x + 5y
16( 1/4 ) + 5( 8 )
4 + 40
44
I hope this helps!
The Phi Theta Kappa fraternity has 160 sweatshirts and 60 pairs of sweatpants available to sell. During rush week, they decided to offer two package deals to students. Package A has two sweatshirt and one pair of sweatpants for $40. Package B has four sweatshirts and one pair of sweatpants for $20. The fraternity wants to sell at least 10 of Package A and at least 10 of Package B. How many of each package type must they sell in order to maximize their revenue?
Answers
Answer:
is this high school
Step-by-step explanation:
srry cant help
please help me! geometry help needed.
Answers
Answer: Choice D
181 grams
======================================================
Explanation:
First we need to find the volume of the tennis ball
Since the diameter is d = 6 cm, it divides in half to a radius of r = 3 cm.
[tex]V = \text{volume of a sphere}\\\\V = \frac{4}{3}\pi*r^3\\\\V \approx \frac{4}{3}*3.14*3^3\\\\V \approx 113.04 \ \text{ cm}^3\\\\[/tex]
This leads to
[tex]\text{density} = \frac{\text{mass}}{\text{volume}}\\\\D = \frac{M}{V}\\\\M = D*V\\\\M \approx 1.6*113.04\\\\M \approx 180.864\\\\M \approx 181 \text{ grams}\\\\[/tex]
Zach's zoo has two elephants. The male elephant weighs 3/5 of a ton and the female elephant weighs 1/5 of a ton. How much more does the male weigh than the female?
Answers
Step-by-step explanation:
I think 3/5 - 1/5 = 2/5 of a ton
Triangle ABC has vertices A(-4, 3), B(2, 3), and C(-5, 1). A
dilation with a scale factor of 5 and center at the origin is applied to this triangle.
What are the coordinates of C' in the dilated image?
Enter your answer by filling in the boxes.
C' has a coordinate pair of (O
Answers
Answer: (-25, 5)
Step-by-step explanation:
Answer:
-25 5
Step-by-step explanation:
THIS IS DUE IN 5 mins i need help .Rewrite the fraction in the sentence below as a percentage. In , 2012 a fire destroyed 11/20 of the farmer's crops.
Answers
Answer:
55%
Step-by-step explanation:
first, you have to divide 11 by 20
11 divided by 20 = 0.55
then you multiply the resulting decimal value by 100 and add the percent symbol (%)
(0.55*100% = 55%
so that's how you get a percentage of 55%
you're welcome
A
1080
B
Reflex Angle B =
degrees.
Answers
Answer:
A reflex angle is an angle greater than a straight angle and less than a circle. ... Some examples of the measures of reflex angles in degrees are:.
Step-by-step explanation:
hope it helps!