what is the value of x in the equation 3^(2x-1)=27?
Answers
Answer:
x=2
Explanation:
Given the equation:
\(3^{2x-1}=27\)To solve for x, begin by writing 27 as a power of 3.
\(3^{2x-1}=3^3\)Next, since both sides of the equation have the same base, 3, it follows from the law of indices that:
\(\begin{gathered} a^x=a^y\implies x=y \\ \text{Therefore:} \\ 3^{2x-1}=3^3\implies2x-1=3 \end{gathered}\)We then solve the resulting equation for x.
\(\begin{gathered} 2x-1=3 \\ \text{Add 1 to both sides} \\ 2x-1+1=3+1 \\ 2x=4 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}\)The value of x in the equation is 2.
Related Questions
The radius of a quarter circle is 4 feet. What is the quarter circle's perimeter?
r=4 ft. help
Answers
The perimeter of the quarter circle is 6.28ft
What is the perimeter of a circle ?The perimeter of a circle is called as the circumference of the circle. The circumference is the external body of a circle.
The perimeter of a circle = 2πr
where r is the radius of the circle.
The perimeter of a quarter circle will be 1/4 ×2πr
= 1/2πr
the radius of a quarter circle is still thesame as the radius of a complete circle.
Therefore the perimeter of the quarter circle = 1/2πr
= 1/2 ×3.14 × 4
= 6.28ft
Therefore the radius of the perimeter of the quarter circle is 6.28ft
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mark the x intercepts in red and mark the y intercepts in blue: which points are red and which points are blue? i will MARK AS BRAINIEST !
Answers
Consider this piecewise function.
f
(
x
)
=
{
3
,
x
≤
-
3
2
x
+
1
,
-
3
<
x
<
4
-
2
,
x
≥
4
Plot f(x) on the graph.
Answers
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The definitions in the context of this problem are given as follows:
Horizontal line at y = 3 to the left of x = -3, with a closed interval at x = -3.Increasing line y = 2x + 1 from x = -3 to x = 4, connecting the open points (-3, 5) and (4, 9).Decreasing line 4 - 2x for x to the right of x = 4, starting at the closed point (4, -4).Missing InformationThe problem asks for the graph of the following piecewise function:
y = 3, x ≤ -3.y = 2x + 1, -3 < x < 4.y = 4 - 2x, x ≥ 4.More can be learned about piece-wise functions at brainly.com/question/19358926
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What is the missing statement in the proof? Scroll down to see the entire proof.
Given: ∆ABC with m∠ABC = 90°
A right triangle A B C.
Prove: AB2 + BC2 = AC2
Statement
Reason
1. Draw view diagram.
A right triangle A B C. Point D is at the midpoint of side A C. A line runs from D to B to form two right triangles A B D and D B C.
construction
2. ∠ ABC≅ ∠BDC
Angles with the same measure are congruent.
3.
Reflexive Property of Congruence
4. ∆ABC ~ ∆BDC
AA criterion for similarity
5.
Corresponding sides of similar triangles are proportional.
6. BC2 = AC × DC
cross multiplication
7. ∠ ABC ≅ ∠ADB
Angles with the same measure are congruent.
8. ∠ BAC ≅ ∠DAB
Reflexive Property of Congruence
9. ∆ABC ~ ∆ADB
AA criterion for similarity
10.
Corresponding sides of similar triangles are proportional.
11. AB2 = AC × AD
cross multiplication
12. AB2 + BC2 = AC × AD + AC × DC
addition
13. AB2 + BC2 = AC(AD + DC)
Distributive Property
14. AB2 + BC2 = AC × AC
segment addition
15. AB2 + BC2 = AC2
multiplication
A.
∠ BDC ≅ ∠ADB
B.
∠BCA ≅ ∠DCB
C.
∠ BAC ≅ ∠BAD
D.
∠ DBC ≅ ∠BAC
Answers
Answer:
Step-by-step explanation:
Option A: ∠ BDC ≅ ∠ADB is the missing statement in the proof.
This statement is needed to complete the proof by showing that triangles ∆ABC and ∆ADB are similar by the AA criterion.
A fireman’s ladder leaning against a house makes an angle of 62 with the ground. If the ladder is 3 feet from the base of the house, how long is the ladder?
Answers
In the given scenario ladder is 6.52 feet long.
Given that,
The angle between ground and ladder = 62 degree
The distance of ladder from ground and ladder = 3 feet
We have to find the length of ladder.
Since we know that,
The trigonometric ratio
cosθ = adjacent/ Hypotenuse
Here we have,
Adjacent = 3 feet
Hypotenuse = length of ladder
Thus to find the length of ladder we have to find the value of hypotenuse.
Therefore,
⇒ cos62 = 3/ Hypotenuse
⇒ 0.46 = 3/ Hypotenuse
⇒ Hypotenuse = 3/0.46
= 6.52
Thus,
length of ladder = 6.52 feet.
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Square root of -18 ?
Answers
What is 0.17 repeating as a simplified fraction?
Answers
Answer:
If you multiply 0.17 by 100 , you get 17 . Similarly, if you divide 17 by 100 , you get 0.17 . Thus, the fraction form for 0.17 is 17100 .
Step-by-step explanation:
a) Work out the value of 10
Answers
Step-by-step explanation:
√10= 1.414×2.236
= ±3.162
hope it is helpful to you ☺️
how many terms does the sequence, 2, 5, 8, …, 332 have?
Answers
As per the details given, the sequence 2, 5, 8, …, 332 has 111 terms.
The formula for the nth term of an arithmetic series can be used to find the number of terms in the given sequence:
nth term = a + (n - 1) * d
Here,
nth term is the value of the term at position n
a is the first term of the sequence
n is the position of the term
d is the common difference between consecutive terms
In this case, the first term (a) is 2, and the common difference (d) is 3, as each term increases by 3.
We need to find the value of n when the nth term is 332. Plugging the values into the formula:
332 = 2 + (n - 1) * 3
Simplifying the equation:
330 = (n - 1) * 3
Dividing both sides by 3:
110 = n - 1
n = 111
Therefore, the sequence has 111 terms.
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The total measure of two adjacent angles is 153°. if one of the adjacent angles measures 104.7°, determine the measure of the other adjacent angle. 194.7° 257.7° 48.3° 75.3°
Answers
One of the unknown adjacent angle measures 48.3 degrees.
The adjacent angles are next to each other and hence are calculated by performing addition of the constituent angles. Let us assume the unknown adjacent angle be x.
Forming the equation based on x, adjacent angles and it's sum
104.7 + x = 153
Rewriting the equation as per the x
x = 153 - 104.7
Performing subtraction on Right Hand Side of the equation to find the value of x
x = 48.3 degrees
Thus, the measure of the adjacent angle is 48.3 degrees.
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Answer: its 48.3
Step-by-step explanation:
x+104.7= 153 -104.7 -104.7 =48.3
HELP PLS which one is least
Answers
Answer:
Option B
Step-by-step explanation:
→ Find the option with the smallest power
Option B
Find the product. Simplify your answer. (3f–1)(4f+1)
Answers
Explanation: just did it on get more math and i was right
assume that the random variable x is normally distributed with mean 80 and a standard deviation of 16. compute tjhe probabilty of p(x,100)
Answers
The probability of the random variable X being less than 100 is approximately 0.8944 or 89.44%.
Hi! Based on your question, you'd like to compute the probability P(X < 100) for a normally distributed random variable X with a mean of 80 and a standard deviation of 16.
To compute this probability, you can use the standard normal distribution table (Z-table) by first converting the given value (100) to a Z-score using the formula:
Z = (X - μ) / σ
Where X is the value (100), μ is the mean (80), and σ is the standard deviation (16).
Z = (100 - 80) / 16
Z = 20 / 16
Z = 1.25
Now, you can look up the Z-score (1.25) in a standard normal distribution table to find the probability P(X < 100):
P(X < 100) ≈ 0.8944
So, the probability of the random variable X being less than 100 is approximately 0.8944 or 89.44%.
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HELP A KID IN NEED
IM JUST A CHILD TRYING NOT TO FAIL MATH
Simplify the expression. 3z+14+5z-9
IM GIVING ALOT OF POINTS PLEASE HELP ME
please
lol sorry I'm kind of desperate
HELPPPP
Answers
Answer:
8z+5
Step-by-step explanation:
Let's split the expression into two terms- z and... not z :)
3z+5z=8z
Why? it's just 3+5 with z tacked on the end
14-9=5
simple math :)
put it together to get
8z+5
all done!
lmk if you have any more questions
What is the image of (8,7) after a reflection over the line y
x?
Answers
It’s reflected as (- 8, 7) over the y-axis and (8, -7) over the x-axis
Explanation:
I just checked it on a graph
Sorry if the pictures a little weird looking, I was in a rush .
Answers
If we write these data points in order:
2, 4, 4, 5, 5, 6, 6, 6, 6, 7, 8, 9, 10
I start crossing off numbers from one end to the other to find of the middle data point. That’s what the median is.
Remove the first 6 data points and the last 6 data points, and you have your median. If the next median problem you have to solve has an even number of data points, your average the middle two.
Let me know if you have questions.
-5 = 7 + -4/5x
I just need answer
Answers
Answer: x=15
.......
Answer:
i got 15 but im not sure if its correct :(
The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices. The Wilson family ordrs several lare pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family the equation y=10x represents the relationship where x represents the number of pizzas and y represents the number of total slices. Which statements best describe the pizzas bought by the Hernandez and Wilson familiies? Select two options.
Answers
Answer:
The CORRECT anser is B and D
Step-by-step explanation:
Hope this helps I just took the quiz!
Nicole drove 275 miles in 5 hours. At the same rate, how long would it take her to drive 605 miles?
Answers
Answer:
i think its 12 hours
Step-by-step explanation:
use calculator
There are 2 pitchers of iced tea. The iced tea in the 1st one was made with 4 tea bags and 1.25 quarts of water. The iced tea in the second pitcher was made with 5 tea bags and 2 quarts of water. Which pitcher has a higher concentration of tea? Why?
Answers
Answer:
Pitcher 2
Step-by-step explanation:
Pitcher 1 = 4 x 1.25 = 5ml concentration
Pitcher 2 = 5 x 2 = 10ml concentration
therefore, pitcher 2 has more concentration :)
hope this helped
Which one of the following best defines the notion of the significance level of a hypothesis test?
a. The probability of rejecting H_o, whether it's true or not
b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
c. The probability of the type I error
d. The probability of the type II error
Answers
C. The probability of the type I error best defines the notion of the significance position of a thesis test.
The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.
Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.
Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.
Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.
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assume that the distribution of diastolic blood pressure readings of people 30 to 39 years old in the framingham heart study is approximately normal with mean 80 and standard deviation 15. what proportion of this population has diastolic blood pressure below 70?
Answers
Approximately 2.28% of the population has a diastolic blood pressure below 70.
To find the proportion of this population with diastolic blood pressure below 70, you can use the normal distribution formula to calculate the probability that a randomly selected person from this population will have a diastolic blood pressure below 70:
P(x < 70) = P((x - mean)/standard deviation < (70 - mean)/standard deviation)
Where x is the diastolic blood pressure, mean is the average diastolic blood pressure (80 in this case), and the standard deviation is the standard deviation of diastolic blood pressure readings (15 in this case).
To calculate the probability, you can use a normal distribution calculator or table to find the probability that a standard normal random variable is less than (70 - mean)/standard deviation.
Using a normal distribution calculator or table, you can find that the probability that a person from this population will have a diastolic blood pressure below 70 is approximately 0.0228. This means that approximately 2.28% of the population has a diastolic blood pressure below 70.
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What are geometric figures?
Answers
Good morning fellow brainly users have some points and just so this doesnt get deleted what if 4+5x= if x=9?
Answers
Answer:
thanks for the points.
Step-by-step explanation:
4+5x=49 if x=9.
have a great day :)
This element orients readers by previewing the structure of the report.
O Definitions of key terms
O Organization
O Sources and methods
Answers
The element that orients readers by previewing the structure of the report is "Organization."
Organizing a report effectively helps readers understand the flow of information and the logical structure of the content. By providing an overview of the organization, readers can anticipate the main sections, their sequence, and the connections between them.
The organization element typically includes headings, subheadings, and a clear hierarchy of information. It outlines the main sections and subsections of the report, indicating how they are related and how they contribute to the overall message or argument.
In addition to the organization element, the other options listed—Definitions of key terms and Sources and methods—also play important roles in a report. Definitions of key terms clarify terminology and provide a common understanding, while Sources and methods explain the sources of information and the methods used in the report's research or analysis. However, in the context of previewing the structure, the Organization element specifically serves this purpose.
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What the experience of a polynomial give the roots:
x=scoure 3 and 2
Help me please!
Answers
Answer:
x² - (2+√3) x +2√3 = 0
Step-by-step explanation:
(x - √3)(x - 2) = 0
x² - (2+√3) x +2√3 = 0
What is a number that is 450 rounded to the nearest 10th
What is a number that is 400when rounded to the nearest hundred
Answers
Step-by-step explanation:
e.g. 452 and 397
but also e.g. 448 and 429
0:50= How much of each ingredients are needed to make 2 batches of bread? answer format: _____ tablespoons of ________ and ____cups of _____ *
Answers
Answer:
Step-by-step explanation:
2 tablespoons of yeast and four cups of flour
Answer:
A recipe for bread calls for 4 cups of flour, 1 pint of water, 2 tablespoons of yeast, and 1 teaspoon of salt. The diagram below represents 1 batch of bread.
Can someone please help me with 1,4,3
Answers
Answer:
Answer 4 = 4 / 11
Answer of 1 is ± 25
Answer of 3 is - 56
Step-by-step answer
Just take square roots
Sophia uses 334 cups of flour for each cake she makes. She has a 10-pound bag of flour that costs $8.79 and contains 152 quarter-cup servings.
Question 1
Part A
How many cakes can Sophia make with this flour?
Answers
Answer:
The number of cakes Sophia can make is 10.
Step-by-step explanation:
The bag of flour contains 152 quarter-cup servings. So, the quantity in t he bag has to be divided by four.
Number of cups = 152 / 4 = 38 cups
In order to determine the number of cakes she can make, divide the number of cups in the bag by the cups needed to make one cake.
38 ÷ 3 3/4
38 ÷ 15/4
38 × 4/15 = 10.1 cakes