MATHEMATICS HIGH SCHOOL

Solve using logs 5^(3x-6)=125

Answers

Answer 1
Answer: 5 ^(3x-6) =125 \n \n 5 ^(3x-6) =5^3 \n \n3x-6 =3 \ \ |+6 \n \n3x=3+9 \n \n3x=12 \ \ /:3 \n \nx=(12)/(3) \n \nx= 3

Related Questions

Monique collects data from a random sample of seventh graders in her school and finds that 8 out of 16 seventh graders participate in​ after-school activities. Write and solve a proportion to estimate the number of seventh graders n who participate in​ after-school activities if 136 seventh graders attend​ Monique's school. Write the proportion used to solve this problem. Choose the correct answer below.
14(0.89)^x+4.5 =162
Please help the answers are A) AB) BC) DD) E
Rewrite 0.8 as a fraction in simplest form.
What two numbers multiply to get 77 but add up to 18?

Which fraction can be represented with a repeating decimal?3/20
12/5
7/16
4/11

Answers

Answer:

Thanks for asking!

Step-by-step explanation:

The answer would be 4/11. 3/20 in decimal form is 0.15. 12/5 is 2.4. 7/16 is 0.4375. 4/11 is 0.36 repeating.

Answer:

4/11

Step-by-step explanation:

=0.363636....

Tom's Tent Rental charges a flat rate of $100 per day plus $10 for each hour the tent is used. If the number of hours is represented by "h," which algebraic expression represents the overall rate for the day using "h"?100 + 10h

10h

100 + h

90h

Answers

100 + 10h

The 100 represents the $100 and the 10h represents the $10 times the hours 

Final answer:

The algebraic expression that represents the overall rate for a day's tent rental from Tom's Tent Rental, considering both the flat rate and the hourly charges, is '100 + 10h'.

Explanation:

To solve the problem, we need to express the situation in algebraic form. In this case, Tom's Tent Rental charges a flat rate of $100 per day, so we have '100'. Additionally, it costs $10 for each hour the tent is used. If we denote the number of hours as 'h', then the charge for the hours used would be '10h'.

Therefore, the total cost or the algebraic expression representing the overall rate for the day, considering both the flat rate and the hourly charges would be '100 + 10h'.

Learn more about Algebraic Expression here:

brainly.com/question/34192827

#SPJ11

Given the figure below, solve for x:

Answers

Answer:

46uusuhdhuduhsbsu7sheheususysyw7wuwuw

Answer:

x=12

Step-by-step explanation:

70+50= 120

180-120= 60

60/5=12

I need help with this question Two different professors teach an introductory statistics class at a local college. The table below shows the distribution of final grades they reported. We wonder if one of the professors is an “easier” grader.
Professor Jones Professor Smith
A 3 9
B 11 12
C 14 8
D 9 4
F 8 4

B. What are the conditions required to use this test? Have the conditions been satisfied? Explain.

Answers

We use a chi-square test of homogeneity, as we have a single categorical variable measured within two different populations.

The requirements for this test are that we have two simple random samples (this is clearly satisfied, given that we are sampling all students who take the class that year) and that the expected value for each cell, defined as the cell's row sum multiplied by the column sum divided by the sum of all values in the dataset, is greater than 5.  This is satisfied simply by testing for each value in the table.

Which set of data of temperatures has the largest dispersion as measured by its interquartile range?1) 15,17,19,21,21,22,28
2) 21,23,36,37,44,48,50
3) 10,19,22,23,23,29,44
4) 42,47,49,50,52,59,60

Answers

1) 22-17= 5
2) 48-23= 25
3) 29-19= 10
4) 59-47= 12

The planets in our solar system do not travel in circular paths. Rather, their orbits are elliptical. The Sun is located at a focus of the ellipse. The perihelion is the point in a planet’s orbit that is closest to the Sun. So, it is the endpoint of the major axis that is closest to the Sun.

The aphelion is the point in the planet’s orbit that is furthest from the Sun. So, it is the endpoint of the major axis that is furthest from the Sun.

The closest Mercury comes to the Sun is about 46 million miles. The farthest Mercury travels from the Sun is about 70 million miles.


1. What is the distance between the perihelion and the aphelion?


2. What is the distance from the center of Mercury’s elliptical orbit and the Sun?


3. Write the equation of the elliptical orbit of Mercury, where the major axis runs horizontally. Allow a and b to be measured in millions of miles. Use the origin as the center of the

Answers

Answer:

(1) 83.764 million miles

(2) 52.766 million miles

(3) (x^2)/(4900)+(y^2)/(2116)=1.

Step-by-step explanation:

Let the origin C(0,0) be the center of the elliptical path as shown in the figure, where the location of the sun is at one of the two foci, say f.

The standard equation of the ellipse having the center at the origin is

(x^2)/(a^2)+(y^2)/(b^2)=1\;\cdots(i)

where a and b are the semi-axes of the ellipse along the x-axis and y-axis respectively.

Let the points P and A represent the points of perihelion (nearest to the sun) and the aphelion (farthest to the sun) of the closest planet Mercury.

Given that,

CP=46 million miles and

CA=70 million miles.

So, CP=b is the semi-minor axis and CA=a is the semi-major axis.

Let the distances on the axes are in millions of miles. So, the coordinates of the point P and A are P(0,46) and A(70,0) respectively.

(1) From the distance formula, the distance between the perihelion and the aphelion is

PA=√((0-70)^2+(46-0)^2)=83.764 million miles.

(2) Location of the Sun is at focus, f, of the elliptical path.

From the standard relation, the distance of the focus from the center of the ellipse, c, is

c=ae\;\cdots(ii)

where a and e are the semi-major axis and the eccentricity of the ellipse.

The eccentricity of the ellipse is

e=\sqrt{1-(b^2)/(a^2)}

\Rightarrow e=\sqrt{1-(46^2)/(70^2)}=0.7538.

Hence, from the equation (i) the distance of the Sun from the center of the elliptical path of the Mercury is

c=70*0.7538=52.766 million miles.

(3) From the equation (i), the equation of the elliptical orbit of Mercury is

(x^2)/(70^2)+(46^2)/(b^2)=1

\Rightarrow (x^2)/(4900)+(y^2)/(2116)=1.
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