The value of x for the considered algebraic equation is 4.
What are some basic properties of exponentiation?If we have [tex]a^b[/tex] then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation (the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^c \implies b = c \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
For this case, we have got the equation as:
[tex]3^{2x+1} = 3^{x+5}[/tex]
Using the property that: [tex]a^b = a^c \implies b = c \: \:(if \: a \neq 1 \: and \: a \neq -1)[/tex], we get:
[tex]2x + 1 = x + 5\\[/tex]
Solving it further:
[tex]2x + 1 = x + 5\\\\\text{Subtracting 1+x from both the sides}\\\\2x + 1 - (1+x) = x+5 - (1+x)\\x = 4[/tex]
Thus, the value of x for the considered algebraic equation is 4.
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A city starts with a population of 500,000 people in 2007. Its population declines according to the equation
P(t) = 500,000e -0.099
where P is the population in t years later. Approximately when will the population be one-half the initial amount?
A city starts with a population of 500,000 people in 2007. Its population declines according to the equation
P(t) = 500,000e -0.099t
where P is the population in t years later. Approximately when will the population be half the initial amount?
Answer:
2014
Step-by-step explanation:
Given the exponential growth function :
P(t) = 500,000e^-0.099t
Where P is population in t years later
When the population will 1/2 the initial amount
1/2 the initial amount = 1/2 * 500,000 = 250,000
P(t) = 250,000
250,000 = 500000e^-0.099t
250,000/500000 = e^-0.099t
In(0.5) = - 0.099t
t = −0.69314 / - 0.099
t = 7.0014
t = 7
Year which population = 500,000 = 2007
Hence, half the population will be attained on (2007 + 7) = 2014
After 7 years population of the city will be half of the initial amount.
Population function:
[tex]P(t) = 500000 e^{-0.099t}[/tex]
Initial population means population at t=0
P(0) = 500000
Half of initial population = 250000
So, we need to calculate the time t when the population will be half of the initial amount.
[tex]250000= 500000 e^{-0.099t}\\\\e^{-0.099t} = \frac{1}{2}[/tex]
Taking log both sides
-0.099t (log e)= log (1/2)
What is the logarithm of e?The logarithm of e is 1 when considering the base of the log as e.
So, -0.099 t= -0.693
t=7
Therefore, After 7 years population of the city will be half of the initial amount.
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What is y = -2x - 2/7 in standard form?
Answer:
14x + 7y= -2
Step-by-step explanation:
y + 2x = -2/7
↓
7y + 14x = -2
↓
14x + 7y = -2
12(8) 2x2 - 4x and g(x) = x-3, what is (p•a)(*)?
2x 4x - 12
216x + 18
216x + 30
2x16x + 15
Which economic indicator is the measure of all goods and services produced within a given economy in one year?
A. trade deficit
B. trade surplus
C. gross domestic product (GDP)
D.purchasing power parity (PPP)
Plzzz hurry!! I will give 20pts but DON’T GUESS!!!!!!
Answer:
C
(GPD)
Step-by-step explanation:
E D G E 2 0 2 0
Gross domestic product is the economic indicator to measure of all goods and services produced within a given economy in one year
What is Economic indicator ?An economic indicator is a statistic about an economic activity. Economic indicators allow analysis of economic performance and predictions of future performance.
We need to find the which economic indicator is the measure of all goods and services produced within a given economy in one year.
A trade deficit occurs when a country imports more than it exports
A trade surplus is an economic measure of a positive balance of trade, where a country's exports exceed its imports.
GDP measures the monetary value of final goods and services—that is, those that are bought by the final user—produced in a country in a given period of time
Hence, gross domestic product is the economic indicator to measure of all goods and services produced within a given economy in one year
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5
The volume of a cone is 1.782 cubic centimeters. A cylinder has the same radius and height as the cone. What is the volume of the cylinder?
Answer:
the answer of the question is 2.5
How can you tell if all the points if a linear equation are graphea correctly?
Answer:
lol
Step-by-step explanation:
Answer:
They will line up.
Step-by-step explanation:
When you graph their slopes, they will create a straight line.
Suppose the points shown on the coordinate plane are vertices of a square. Which statements are correct? A) The length of each side is 5 units. B) The perimeter of the square is 24 units. C) The perimeter of the square is 20 units. D) The coordinates for the fourth vertex of the square are (2, 7). E) The coordinates for the fourth vertex of the square are (4, 7).
Answer:
A and C for sure. I'm not sure about D and E because I can't see the picture. If you tell me the other coordinates I can figure it out.
What is the slope of y = 3? (HOY VUX)
What is the slope of x = 3? (HOY VUX)
The sum of 4 consecutive integers is 26. What is the least of 4 integers?
Answer:
5
Step-by-step explanation:
it is 5 because 5 + 6 + 7 + 8 =26
and 5 is the least
Answer:
Step-by-step explanation:
A. y=1/8x
B. y= 4x
C. y=1/4x
D. y= - 1/4
E. y= 2x
F. y= - 1/8
Answer:
C
Step-by-step explanation:
You divide first than you get ur fraction
Evaluate the expression -1/3 - 5/6 . be sure to simplify if necessary!
A: - 6/9
B: - 1/2
C: -1 and 1/3
D: - 1 and 1/6
Answer:
C: -1 and 1/3
Step-by-step explanation:
Yukon has $0.75 in her purse. Which fraction is the same as $0.75?
A. 1/4
B. 1/2
C. 3/4
D. 7/5
Answer:
C is the answer.
0.75 = 3/4
1 = 4/4, 1-0.25 = 0.75
4/4 -1/4 = 3/4
Step-by-step explanation:
Can someone please help me figure out what’s 18 3/4 as a decimal
Answer:
18.75
Step-by-step explanation:
[tex]\\ \rm\Rrightarrow 18\dfrac{3}{4}[/tex]
Break mix fraction[tex]\\ \rm\Rrightarrow \dfrac{75}{4}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{75(25)}{100}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1875}{100}[/tex]
[tex]\\ \rm\Rrightarrow 18.75[/tex]
A pair of weak earthquakes are modeled by nonlinear inequalities. One earthquake occurred roughly 15 km south and 18 km west of the center of Salt Lake City, Utah. The quake could be felt 16 km away. A couple of days later another earthquake occurred 9 km north and 4 km east of the center of Salt Lake City and could be felt 21 km away. If Salt Lake City is located at (0, 0) on a coordinate grid, the system below represents this scenario.
StartLayout Enlarged Left-brace first row (x + 18) squared + (y + 15) squared less-than-or-equal-to 256 Second row (x minus 4) squared + (y minus 9) squared less-than-or-equal-to 441 EndLayout
Which location in relation to Salt Lake City felt both earthquakes?
12 km east and 2 km north
12 km east and 2 km south
12 km west and 2 km north
12 km west and 2 km south
2 km east and 10 km north
Step-by-step explanation:
I did the activity and got the right answer.
Answer: 12km west and 2km south
Step-by-step explanation:
Just did it
Which polynomial is prime? x3 3x2 2x 6 x3 3x2 – 2x – 6 10x2 – 4x 3x 6 10x2 – 10x 6x – 6
The polynomial that is prime is given by Option C: [tex]10x^2 - 4x +3x +6[/tex]
What are prime polynomials?Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
Checking all the listed polynomials for them being prime or not:
Case 1: [tex]x^3+3x^2+2x+6[/tex]Rewriting it as:
[tex]x^3+3x^2+2x+6 = x^2(x+3) + 2(x+3) = (x^2 + 2)(x+3)[/tex]
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 2: [tex]x^3 + 3x^2 -2x -6[/tex]Rewriting it as:
[tex]x^3 + 3x^2 -2x -6 = x^2(x+3) -2(x+3) = (x^2-2)(x+3)[/tex]
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 3: [tex]10x^2 - 4x +3x +6[/tex]We can rewrite it as:
[tex]10x^2 -4x + 3x -6 = 10x^2 -x -6 = f(x) \: \rm (say)[/tex]
This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.
Case 4: [tex]10x^2 -10x + 6x - 6[/tex]
It can be factored as:
[tex]10x(x-1) + 6(x-1) = (x-1)(10x-6)[/tex]
This is not a prime polynomial.
Thus, the polynomial that is prime is given by Option C: [tex]10x^2 - 4x +3x +6[/tex]
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Answer:
The polynomial that is prime is given by Option C:
What are prime polynomials?
Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
Checking all the listed polynomials for them being prime or not:
Case 1:
Rewriting it as:
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 2:
Rewriting it as:
shows that this polynomial has factors. Thus, it isn't prime polynomial
Case 3:
We can rewrite it as:
This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.
Case 4:
It can be factored as:
This is not a prime polynomial.
Thus, the polynomial that is prime is given by Option C:
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Step-by-step explanation:
By graphing the system of constraints find the values or x and y that maximize the objective function, find the maximum value.
2x+y= 0
y=>0
Maximize for P=x+2y
A) P=100
B) P=200
C) P=400
D) P=550
Question is in the attachment
Answer:
B is the answer in the first quadrant x is positive
what is the rate of change of the cost with respect to the number of miles for the yellow cab company (yellow cab company is the dotted line)
A.$0.50
B.$2
C.$3
D.$1
Answer:
I think the answer may be option C
Ifa=12 and 120% of a is equal to 80% of b, then what is
a+b?
Rsm question
Answer:
a + b = 30
Step-by-step explanation:
If we convert the percentages to decimals (120% = 1.2 & 80% = 0.8), we can use this equation to find B: 1.2A = 0.8b
Since we know a, we then have 1.2 * 12 = 0.8b
Solving for B gives us b = 18
12 + 18 = 30
2x-y=8
3x+y=17, usingelemination method solve
What polynomial must be subtracted from 2x^3 − x^2 + 4x − 5 so that the difference is
x^3 + 2x − 9?
Answer:
-x^3 + x^2 - 2x - 4
Step-by-step explanation:
You have to subtract
Let o = the polynomial
So you know 2x^3 - x^2 + 4x + 5 - o = x^3 + 2x - 9
Now you do 2x^3 - x^3 = x^3
then you -x^2 + answer = 0
you need to cancel it out
to cancel, you found out that it is x^2
Now you need to make from 4x to 2x.
To do that, you do 4x - 2x and you get 2x
Lastly you need to change -5 to 9. To do that you add -4.
Now since it is subtraction you have to distribute
2x^3 - x^2 + 4x - 5 -(x^3 - x^2 + 2x + 4)
= 2x^3 - x^2 + 4x + 5 - x^3 + x^2 -2x -4
= x^3 -2x + 9
Please help me ASAP .......
Answer:
<3 ~= <5 - Alternate Interior Angles Theorem
<3 ~= <7 - Corresponding Angles Theorem
<5 ~= <7 - Vertical Angles Theorem
line I || line m - Transitive Property
Can someone please help me??? I’ll mark brainlist!!!
Answer: c-it’s the same price
Step-by-step explanation: 20% off 200 is 160 and 200-160=40 so it’s the same
On a coordinate plane, a triangle has points A prime (1, 2), B prime (3, negative 3), C prime (negative 1, negative 3).
Triangle ABC was translated according to the rule
T4.5, –6.2(x, y) to form A’B’C’ as shown. What are the coordinates of point C of the pre-image?
(3.5, –9.2)
(–2.7, –4.7)
(–5.5, 3.2)
(0.7, –1.3)
Answer:
(-5.5, 3.2) or the third option
Step-by-step explanation:
i did the test on edg
Answer: C: (-5.5, 3.2)
Step-by-step explanation: correct answer on edg2020. i took the quiz
Use the interactive to graph these numbers on the number line. –4, 3, 0. 5, 1 Which number is closest to zero?.
The number closest to 0 is the number whose absolute difference from 0 is the smallest
0.5 is the closest number to 0
How to determine the closest to 0The numbers are given as:
–4, 3, 0. 5, 1
Calculate their absolute difference with 0
|-4 - 0| = 4
|3 - 0| = 3
|0.5 - 0| = 0.5
|1 - 0| = 1
The smallest absolute difference is 0.5
Hence, 0.5 is the closest number to 0
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A surveyor wants to use similar triangles to determine the distance across a lake as shown at the right. What is the distance d across the lake?
A. 75ft
B. 80ft
C. 85ft
D. 90f
Base on the similarity principle of triangles, the distance d across the lake as shown is 90 ft.
Similar triangle theoremsTwo triangles are similar if they are only difference in size but have the same shape.
In similar triangles, corresponding sides are always in the same ratio.
Therefore, let's create a proportion from the triangles since they are similar.
40 / d = 20 / 45
cross multiply
45 × 40 = 20d
1800 = 20d
divide both sides by 20
1800 / 20 = 20d / 20
d = 90 ft
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good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answer:
A Trinomial expression has 3 terms.
If it has degree 2, then the exponent of the leading term will be 2.
If the leading coefficient is -5, then the leading term will be [tex]-5x^2[/tex]
Written in standard form: [tex]y=-5x^2+bx+c[/tex]
We are not given any information about the coefficients of the remaining two terms, so we can substitute any values for these:
Therefore, [tex]y=-5x^2+3x+2[/tex]
Note the standard form
ax^2+bx+c=0Here we have
a=-5So
the expression is
-5x^2+4x+2=0Safia's book has 136 pages.
She has read 1/8
of it.
How many pages has she read
Answer: 17 pages
Step-by-step explanation:
One eighth of 136:
136 divided by 8 = 17
Answer:
17 pages
Step-by-step explanation:
1/8 x 136 = 17
I need help on this question
Answer:
Step-by-step explanation:
They all give 8r so that is not the distinguishing characteristic.
The first one in column A gives
12r + t - 4r + 6t
12r - 4r + t + 6t
8r + 7t
This is the third one in column B
2nd one in Column A
12r + 2t - (4r + 10t) Remove the brackets
12r + 2t - 4r - 10t Pay close attention to 10t becoming -10t. The minus sign effects both terms inside the brackets.
12t - 4t + 2t - 10t Combine
8r - 8t Now take out the common factor (8)
8(r - t) That's the top one in column B
3rd one in column A
12(r + t) - 6(r +t) + 4(r + t) - 2(r+t) They all have r+t so r + t is a common factor)
(r+t) [12 - 6 + 4 - 2] Combine
(r + t ) [ 8 ]
This is the second one in column B
The trick here is to look out for common factors. Don't remove the brackets. But it takes a bit of practice before you know that
He ------- daily for a year now.
a) exercises b) was exercising c) has been exercising