Answer:
It depends on the equation.
If the bases are equal and the variables are only in the exponents, set the exponents equal.
If there are variables in the exponents, but you cannot set the bases equal, then use logarithms.
Example 1:
[tex] 4^{2x + 5} = 4^9 [/tex]
Here you have the same base on both sides. The variables are in the exponents. Set the exponents equal and solve for x.
2x + 5 = 9
2x = 4
x = 2
Example 2:
[tex] 3^{2x} = 9^{6} [/tex]
The bases are different, but you can make the bases equal using laws of exponents. Remember that 9 = 3^2.
[tex] 3^{2x} = (3^2)^{6} [/tex]
[tex] 3^{2x} = 3^{12} [/tex]
Now you have equal bases, so the exponents must be equal.
2x = 12
x = 6
Example 3:
[tex] 10^{x + 2} = 9 [/tex]
Here you can't make the bases equal, so you take the log of both sides and use laws of logs.
[tex] \log(10^{x + 2}) = \log 3^2 [/tex]
[tex] (x + 2) \log 10 = 2 \log 3 [/tex]
Recall that: [tex] \log 10 = 1 [/tex]
[tex] x + 2 = 2 \log 3 [/tex]
[tex] x = 2 \log 3 - 2 [/tex]
Please help with this question
9514 1404 393
Answer:
4. (d) 4.38 in³
5. (b) 19 gallons
6. (a) 6.4 yd³
Step-by-step explanation:
4. The equation can be rearranged to find the compressed volume.
Multiply both sides by the compressed volume:
(compression ratio)×(compressed volume) = (expanded volume)
Divide both sides by the compression ratio:
(compressed volume) = (expanded volume)/(compression ratio)
Fill in the numbers and do the arithmetic.
compressed volume = 46.0 in³/(10.5/1) = 4.38 in³
The compressed volume is about 4.38 in³.
__
5. The area to be covered is 3170 ft². We want to cover it twice, so the total area we want to cover is 2×3170 ft² = 6340 ft². One gallon of paint covers 350 ft². We want to find the smallest integer number of gallons n such that ...
n×(350 ft²) ≥ 6340 ft²
Dividing by the coefficient of n, we have ...
n ≥ 6340/350 ≈ 18.11
The smallest integer value of n is 19. 19 gallons of paint will be needed.
__
6. The quantity of sand needed (q) is proportional to the area to be covered, so we have ...
q/(400 yd²) = (1.6 yd³)/(100 yd²)
Multiplying both sides of this equation by 400 yd² gives ...
q = (1.6 yd³)(400/100) = 6.4 yd³
6.4 yd³ of sand will be needed.
What is the equation of the curve that best fits the data? Round to the nearest hundredths, when appropriate. picture*
Answer:
.....
Step-by-step explanation:
Up and down
Brianne earns $20 for 4 hours of babysitting. Which graph shows the relationship between the number of hours and the total amount she earns?
Answer:
Can you insert a picture? and then I could help you.
Step-by-step explanation:
Answer:
Brianne would earn 5 dollars an hour so the graph should look something like this.
Anyone know this answer
Answer:
Step-by-step explanation:
1 is 60 2 i 60 and 3 is 61 ;)
Product of 32.56 and 1.4
Answer:
45.584
;)
Have a nice day
Twice a number is 14. What is the number
Answer:
7
Step-by-step explanation:
Divide 14 by 2
Cindy has a chocolate box whose length is 12 cm, height of 8 cm, and width of 6 cm. Find the volume of the box?
WITH SOLUTION PLEASE
Hello there I hope you are having a great day :) Cindy has a chocolate box whose length is 12 cm, height of 8 cm, and width of 6 cm. Find the volume of the box?
V = L x W x H
Volume = length x Width x Height.
12cm x 6cm x 8cm = V = 576cm^3
so the answer is 576cm^3
Hopefully that helps you :)
Step-by-step explanation:
VOLUME : is the quality of three deamination place enclosed by a closed surface it is the space that substance or shape or keep use or contains it is measured in cubic units
A RACTANGULAR :is a three dimensional figure it has length wind and height
to find the value of the box we need to multiply length buy it wide and by its height v=l x w x hlet us analysis the problem above
GIVEN :length =12 cm
height = 8 cm
width=6 cm
SOLUTION :v=1 x w x h
=(12 CM) x (8 CM) x (6 CM)
=576 cm³FINAL ANSWER(:the value of the box is 576 CM ³
determine the term 6 generated by the rule TN is equals to n squared minus n and over 2
Given:
Consider the rule of a sequence is:
[tex]T_n=\dfrac{n^2-n}{2}[/tex]
To find:
The 6th term generated by the given rule.
Solution:
We have,
[tex]T_n=\dfrac{n^2-n}{2}[/tex]
Substituting [tex]n=6[/tex] in the above rule, we get
[tex]T_6=\dfrac{6^2-6}{2}[/tex]
[tex]T_6=\dfrac{36-6}{2}[/tex]
[tex]T_6=\dfrac{30}{2}[/tex]
[tex]T_6=15[/tex]
Therefore, the 6th term generated by the given rule is 15.
What is the value of
(x3 x 7y÷)(10.6+5.4)for x=2 and y=6?
Step-by-step explanation:
Hope you can correct you question
can someone help me with this math problem please? One hundred ten students are assigned to four classrooms as equally as possible. How many students are in each classroom? (Write four numbers in all show how many students are in each room?
Answer:
27.5
Step-by-step explanation:
Answer:
27.5Step-by-step explanation:
110/4 is 27.5
A well-conducted opinion poll showed that 48% of voters surveyed favored the reelection of Congressman Porkbarrel. The people who conducted the survey reported that the poll had a margin of error of 3.5%. Which of the following best describes this statement
A. Based on the procedure by which this figure was generated, it is likely that the population proportion is between 44.5% and 51.5%.
B. About 3.5% of the people polled are likely to change their minds about who they will vote foir.
C. Between 44.5% and 51.5% of the voters will vote for Congressman Porkbarrel.
D. About 3.5% ofthe people interviewed refused to answer the question.
E. The probability is .48 that Congressman Porkbarrel will be reelected.
Answer:
A. Based on the procedure by which this figure was generated, it is likely that the population proportion is between 44.5% and 51.5%.
Step-by-step explanation:
Confidence interval:
We build a confidence interval from a sample proportion, to get an estimate of where the population proportion should likely be.
48% of voters surveyed favored the reelection of Congressman Porkbarrel, with a margin of error of 3.5%.
48 - 3.5 = 44.5%.
48 + 3.5 = 51.5%.
Following the concept of a confidence interval, the population proportion is likely to be between 44.5% and 51.5%, and thus, the correct answer is given by option A.
what is the solution set for this inequalty? -8x + 40> -16
Answer:
x < 7
Step-by-step explanation:
-8x + 40> -16
Subtract 40 from each side
-8x + 40-40> -16-40
-8x >-56
Divide each side by -8, remembering to flip the inequality
-8x/-8 < -56/-8
x < 7
Move each fraction to a box to make each comparison true.
solve for k. 6 = -3(k - 10)
Answer: k = 8
Step-by-step explanation:
-3k + 30 = 6
-3k = -24
k = 8
Answer:
k = 8
Step-by-step explanation:
6 = -3(k - 10)
Divide each side by -3
6/-3 = -3/-3 *(k - 10)
-2 = k-10
Add 10 to each side
-2+10 = k-10+10
8 = k
Answer for brainlest
Answer:
∠1 = ∠8
Step-by-step explanation:
Because they are ALTERNATE EXTERIOR ANGLE
Answer:
∠1 = ∠8
Step-by-step explanation:
Because alternate exterior angles are equal.
Also there is no angle given so you cant work them out.
simply put:
∠1 = ∠8
∠1 = ∠4
∠3 = ∠2
∠1 = ∠5
∠2 = ∠6
∠2 = ∠7
∠5 = ∠8
∠4 = ∠8
∠7 = ∠6
∠7 = ∠3
Let me know if I missed out on anymore! It was long that's why.
Hope this kind of explained it :)
Simplify (4a to the fifth power b to the sixth power) to the fourth power
Answer:
(4a^5b^6)^4 = 256a^20b^24
Step-by-step explanation:
Do girls read more than boys during the summer? Serena's class asked
30 parents to estimate how many pages their child read over the summer. They
collected the following data.
Girls: 10 30 230 130 110 240 150 260 60 230 100 20 50 160 90 pages
Boys: 210 100 0 40 260 240 200 220 190 150 50 100 12 140 40 pages
Make parallel box plots and compare the center, shape, spread, and outliers.
b. Do girls read more? How many IQRs more do they read? Use the box
plots to estimate.
a.
Answer:
Step-by-step explanation:
I dont know how to do the box thing, but I added all the things and boys read more.
girls:1870
boys:1952
The diffrence (when subracting) is 82
The moving company
charges extra money to move boxes weighing more than
25 pounds. Circle the packages that weigh less than 25 pounds.
Put an X on the packages that weigh more than 25 pounds.
320 ounces
480 ounces
288 ounces
368 ounces
352 ounces
432 ounces
What function equation for the input/output table

Answer: The answer would be y = x + 8
Step-by-step explanation:
For an angle to be in standard position, its vertex is at the origin and the initial side lies on the
A) positive y-axis. B) positive x-axis. C) negative x-axis. D) negative x-axis.
Answer:
B) positive x-axis.
Step-by-step explanation:
angle to be in standard position, its vertex is at the origin and the initial side lies along the positive x axis
Answer:
Positive x axis
Step-by-step explanation:
The angle lies in standard position means it begins from Q1
The first side must be x axis
Then in Q1 x>0 so it's positive x axis
PLease help!! Will mark brainliest for right answer!! NO LINKS
Let f(x)=10/x−4 . What is the average rate of change of f(x) from 2 to 8 ?
Enter your response as a decimal.
Answer:
[tex]f(x) = \frac{10}{x} - 4 \\ \delta \: f(x) = \frac{f(8) - f(2)}{2} \\ = \frac{(\frac{10}{8} - 4) - ( \frac{10}{2} - 4)}{2} \\ = \frac{ \frac{ - 11}{4} - 1}{2} \\ = \frac{ \frac{ - 15}{4} }{2} \\ = - \frac{15}{8} [/tex]
You fllp a fair coln 7 times in a row. Let X be the number of heads that come up. Which of the following cannot be a
possible value of X?
2
0
7
16
Answer:
16
Step-by-step explanation:
Given
A coin
[tex]n = 7[/tex] --- Number of flips
[tex]x \to heads[/tex]
Required
Which can't be the value of x
From the question, we understand that the coin was flipped 7 times.
This means that, the highest occurrence of head is:
[tex]x = 7[/tex]
And the list is:
[tex]x = 0[/tex]
So, the range of x is:
[tex]x = \{0,1,2,....,7\}[/tex]
In the above range, only (16) is out of range.
Hence:
[tex]x \ne 16[/tex] --- Number of heads can't be 16
Show that the transformation T defined by
T(x1, x2) = (2x1 - 3x2, X1+4, 5x2) is not linear.
Let u = (1, 0) and v = (0, 1). Then
T (u) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)
T (v) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)
=> T (u) + T (v) = (-1, 9, 5)
but
T (u + v) = T (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)
=> T (u + v) ≠ T (u) + T (v)
which means T does not preserve addition, so it is not linear.
The equation $x + {y = 2 can be rewritten in a form that reveals the y-intercept of the graph of the equatior
Drag numbers to complete the equation that is equivalent to $x + žy = 2 and show the value of the y-intercept
Answer:
[tex]y = \frac{2}{z} - \frac{x}{z}[/tex]
Step-by-step explanation:
Given
[tex]x + zy = 2[/tex]
Required
Rewrite to show y-intercept
We have: [tex]x + zy = 2[/tex]
Subtract x from both sides
[tex]zy = 2-x[/tex]
Divide both sides by z
[tex]y = \frac{2}{z} - \frac{x}{z}[/tex]
The y intercet is: [tex]\frac{2}{z}[/tex]
what is the value of x?
the answer is 35 I did a lot of work I can't show you here
Anybody know this one? I’m set that it is B but I am not too sure
Answer:
D
Step-by-step explanation:
It is D because there are only 3 sides given. I understand where you were going with B, but there is no angle given, (and you cannot prove one either), so the answer is simply D.
A - There is no angle, triangle does not matter
B - There is no angle, triangle is correct
C - It is similar, they have the same scale factor
D - There are 3 sides, and the triangle is correct
find x and y. For one point extra credit each, give the correct name for point P.
Answer:
where is the question?
Step-by-step explanation:
Suppose a fair six sided die has been relabeled so that the 6 is replaced with another 5,i.e., the sides read 1,2,3,4,5,5. If the die is rolled five times, what is the probability that we roll five distinct values
Answer:
P(rolling five distinct values) = 1/3888
Step-by-step explanation:
We are told that I the fair sided dice, 6 is replaced with 5.
Thus,the numbers are now;
1,2,3,4,5,5.
This means a total of 6 possible numbers appearing.
Now, in these 6 numbers there are only 5 distinct numbers since 5 occurs twice.
P(1) = 1/6
P(2) = 1/6
P(3) = 1/6
P(4) = 1/6
P(5) = 2/6
Thus,probability of rolling 5 distinct values = 1/6 × 1/6 × 1/6 × 1/6 × 2/6 = 1/3888
Which of the following CANNOT be true for a triangle?
A. A triangle can be equilateral and obtuse at the same time.
B. A triangle can be equilateral and equiangular at the same time.
C. A triangle can be isosceles and right at the same time.
D. A triangle can be scalene and obtuse at the same time.
Answer:
A. A triangle can be equilateral and obtuse at the same time
Step-by-step explanation:
All angles in an equilateral triangle are 60° therefore they cannot be above 90° and less than 180°
This is a 4th grade level
Ethan puts $1200 into a Certificate of Deposit (CD) account that earns 2.1% interest each year. What will be the interest of the CD account earned after 5 years? Round to the nearest cent (hundredths place).
Answer:
126
Step-by-step explanation:
1200 x .021=25.20 interest per year
25.20x5=126
assumes no compounding