Which expressions are equivalent to the one below? Check all that apply. 21^x/3^x
The only equivalent expression is option (a) [tex]7^x[/tex].
What is expression ?
An expression in mathematics is a group of symbols that represent a statistical correlation or quantity, such as integers, variables, and operators. It may contain exponents, logarithms, and trigonometric functions in addition to mathematical operations like addition, multiplication, multiplication, and division. It may also contain constants, variables, and functions. Expressions can be used in a variety of subjects, including mathematics, calculus, geometry, and statistics, to represent mathematical models, resolve equations, and carry out calculations.
To find equivalent expressions for[tex]21^x/3^x[/tex], we can try to simplify the expression using exponent rules.
21 can be factored as 7*3, so we can write:
[tex]21^x/3^x = (7 × 3)^x/3^x = 7^x × 3^x/3^x = 7^x[/tex]
Therefore, we can see that option (a) 7^x is equivalent to the given expression.
To check the other options:
b) [tex](7/3)^x[/tex] = [tex](7^x)/(3^x)[/tex] which is not equivalent to the given expression.
c) [tex]3^(2x+1)[/tex] can be written as [tex]3^(2x)[/tex] × [tex]3^1[/tex] = [tex](3^2)^x[/tex] × 3 = [tex]9^x[/tex] × 3 which is not equivalent to the given expression.
d) [tex]7^(x-1)[/tex] can be written as [tex]7^x/7[/tex] which is not equivalent to the given expression.
e) [tex](3/7)^x[/tex] is not equivalent to the given expression.
Therefore, the only equivalent expression is option (a) [tex]7^x[/tex].
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The complete question is:
Which expressions are equivalent to [tex]21^x/3^x[/tex]? Check all that apply.
a) [tex]7^x[/tex]
b) [tex](7/3)^x[/tex]
c) [tex]3^(2x+1)[/tex]
d) [tex]7^(x-1)[/tex]
e) [tex](3/7)^x[/tex]
-(x+5)³ + 2 = 1
im supposed to be solving cubic equations but im stuck plez help
Answer: X= -4
Step-by-step explanation:
Find the expression for both A: (x+4) (2x - 1)
Answer:
2x^2+8x-4
Step-by-step explanation:
1
Type here to search
day
How many more points did Zara score than John?
i
C
Number of Points
Points Scored in Basketball Game
25
20
15
10
5
0
e g
Read and Interpret Scaled Bar Graphs - Quiz - Level C
Mateo
Zara
Player
John
Mila
DONE
7
4
1
2
0
5
points
8
9
6
3
76°F Mostly cloudy
X
Th
Answer:
yes
Step-by-step explanation:
john has 34 marbles
4 1/5 -5/3 subtract
how do i do this eqation
Answer:
38/15
Step-by-step explanation:
4 1/5 - 5/3
4 1/5 = 21/5
21/5 - 5/3 = 63/15 - 25/15 = 38/15
So, the answer is 38/15
Solve the problem in the picture please!
The answer choices are
A) 5
B) 2
C) 200
D) 100
5)
Given:
Prove:
41 and 22 are complementary.
41 = 23
22= 24
23 and 24 are complementary.
2
3
4
[tex] \angle3 \: and \: \angle4 [/tex] are complementary.
What is Complementary angle?
If sum of two angles is 90° then we can say that those angles are complementary.
For example, if [tex] \angle \: a + \angle \: b = {90}^{o} [/tex] then angle a and angle b are complementary.
Here are some examples of complementary angles:
30 degrees and 60 degrees45 degrees and 45 degrees20 degrees and 70 degrees15 degrees and 75 degrees10 degrees and 80 degrees35 degrees and 55 degrees25 degrees and 65 degrees40 degrees and 50 degrees5 degrees and 85 degrees12 degrees and 78 degrees.Here given,
[tex] \angle1 \: and \angle2[/tex] are complimentary.
So,
[tex] \angle1 + \angle2 = {90}^{o} [/tex]
It is clear that [tex] \angle1, \angle2, \angle3, \angle4[/tex] are making a straight angle.
So, we can write,
[tex] \angle1 + \angle2 + \angle3 + \angle4 = {180}^{o} \\ {90}^{o} + \angle3 + \angle4 = {180}^{o} \\ \angle3 + \angle4 = {180}^{o} - {90}^{o} \\ \angle3 + \angle4 = {90}^{o} [/tex]
Here sum of angle 3 and angle 4 is 90°.
According to definition angle 3 and angle 4 are complimentary angles.
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Screenshot, I WILL GIVE 20 POINTS AND BRAINLIST!!!!
Answer:
0.7 = 0.70, so 0.17 < 0.70
The federal government has developed the body mass index (bmi) to determine ideal weights. a person's bmi is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches. (a bmi of 19 to 25 corresponds to a healthy weight.) a 6-foot-tall person weighing 177 lb has bmi 24. find the bmi (to the nearest whole number) of a person whose weight is 176 lb and whose height is 77 in.
The BMI of a person whose weight is 176 lb and whose height is 77 inches is 21.
First, let's use the given information to find the constant of proportionality in the BMI formula:
BMI = k × (weight in pounds) / (height in inches)²
When the 6-foot-tall person weighing 177 lb has a BMI of 24, we can plug in the values and solve for k:
24 = k ₓ 177 / (72²)
k = 24 ₓ (72²) / 177
k ≈ 9.94
Now we can use this value of k to find the BMI of the person whose weight is 176 lb and whose height is 77 in:
BMI ≈ 21
BMI = 9.94 ₓ 176 / (77²)
Therefore, the BMI (to the nearest whole number) of the person is 21, which falls within the healthy weight range of 19 to 25.
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(Need help please and thank you!) :)
Step-by-step explanation:
In order to find the f(x) or y value, you have to replace x with the given one in the table:
x = -1,
[tex]y = \sqrt[3]{ - 1 - 7} = \sqrt[3]{ - 8} = - 2[/tex]
.
x = 6,
[tex]y = \sqrt[3]{ 6 - 7} = \sqrt[3]{ - 1} = - 1[/tex]
.
x = 7,
[tex]y = \sqrt[3]{7 - 7} = \sqrt[3]{0} = 0 [/tex]
.
x = 8,
[tex]y = \sqrt[3]{8 - 7} = \sqrt[3]{1} = 1 [/tex]
.
x = 15,
[tex]y = \sqrt[3]{15 - 7} = \sqrt[3]{8} = 2[/tex]
Also, the correct graph is in the 2nd photo, where the root is (7; 0)
What is the solution to x^3+4x^2 >x+4?
Answer:
Step-by-step explanation:
it’s equals 0 I think
PLS HELP ASP!!!
The state of Colorado is 4 centimeters long and 2 centimeters wide on a map. A cartographer wants to use a scale factor of 3.5 to enlarge the map. What is the area of the enlarged map?
98 cm2
42 cm2
28 cm2
8 cm2
Answer: 98 cm²
Step-by-step explanation:
When a cartographer enlarges a map with a scale factor, both the length and the width are multiplied by the scale factor. In this case, the scale factor is 3.5.
Original dimensions of Colorado on the map:
Length: 4 cm
Width: 2 cm
Enlarged dimensions using the scale factor of 3.5:
Length: 4 cm × 3.5 = 14 cm
Width: 2 cm × 3.5 = 7 cm
To find the area of the enlarged map, multiply the enlarged length and width:
Area = Length × Width
Area = 14 cm × 7 cm
Area = 98 cm²
The area of the enlarged map is 98 cm².
8a = -12 + 2a me need helpppppppppppppp
Answer: a = -2
Step-by-step explanation:
8a = -12 + 2a
8a - 2a = -12
6a = -12
a = -12/6
a = -2
Given RP = 22, RA = 6, and PQ is tangent to .R at Q, find PQ.
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{22}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{PQ} \end{cases} \\\\\\ PQ=\sqrt{ 22^2 - 6^2}\implies PQ=\sqrt{ 484 - 36 } \implies PQ=\sqrt{ 448 }\implies PQ\approx 21.17[/tex]
Please help meeee
describe an incident that shows how you were doing "selection" during the process of perception. Then, give your own example about a stereotype that you do.
The description of the incident is shown below
Describing the incidentOne incident that shows how selection works in the process of perception is when you are at a party and you hear your name being mentioned in a conversation across the room. In this situation, your attention is immediately drawn to the conversation, and you focus on it while filtering out other sounds and distractions around you.
This is an example of selective attention, where you choose to focus on a particular stimulus and ignore others.
As for an example of a stereotype that I have, it is that all people who live in a certain region or country behave in a particular way.
For instance, I may have the stereotype that people from a particular country are loud and aggressive.
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please solve this fast
Answer:
34
Step-by-step explanation:
5+5+2=12
12+6+3=21
21+8+5=34
Answer:45
Step-by-step explanation:
5+5(8)=45
In X8, Erin had the following capital gains (losses) from the sale of her investments: $2,600 LTCG, $24,400 STCG, ($9,600) LTCL, and ($15,600) STCL. What is the amount and nature of Erin's capital gains and losses?
Erin's capital gains are the sum of her long-term capital gains (LTCG) and short-term capital gains (STCG), which is $2,600 + $24,400 = $27,000.
Erin's capital losses are the sum of her long-term capital losses (LTCL) and short-term capital losses (STCL), which is ($9,600) + ($15,600) = ($25,200).
Since Erin's capital gains exceed her capital losses, she has a net capital gain of $27,000 - $25,200 = $1,800.
The nature of Erin's capital gains and losses are as follows:
LTCG: long-term capital gain, meaning the asset was held for more than one year before it was sold.STCG: short-term capital gain, meaning the asset was held for one year or less before it was sold.LTCL: long-term capital loss, meaning the asset was held for more than one year before it was sold.STCL: short-term capital loss, meaning the asset was held for one year or less before it was sold.PLS HELP :))
The property taxes on a house were $1265
. What was the tax rate if the house was valued at $115,000
? Follow the problem-solving process and round your answer to the nearest hundredth of a percent, if necessary.
The tax rate of a house valued at $115,000 with a property tax of $1265 is 110%. or $110 per $1,000 of property value.
What is property tax?The property tax is the levy imposed on the assessed value of the property of an individual or corporation.
Property tax is usually levied as a percentage of the assessed value.
Data and Calculations:Property tax = $1265
House value - $115,000
Tax rate = 110% [tex](\$1265\div\$115000 \times 100)[/tex]
Thus, the tax rate of a house valued at $115,000 with a property tax of $115,000 is 110%. or $110 per $1,000 of property value.
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127.6÷10 to the power of 5
im not sure if that is how you type it
Answer:
338262.124
Step-by-step explanation:
127.6/10 = 12.76 (depending on how many zero is how much you'll move the decimal to the left)
12.76^5 = 338262.124 because it's 12.76x12.76x12.76x12.76x12.76
Tom has $160,000 in his retirement account. It is earning an APR of 4.57%. What would be the monthly yield on the account for a 30-year period?
The monthly interest yield on Tom's retirement account for a 30-year period would be $637.71.
Assuming that the interest is compounded monthly, the monthly yield on Tom's retirement account with an APR of 4.57% for a 30-year period can be calculated using the formula:
Monthly Yield = (Principal × Monthly Interest Rate) ÷ (1 - (1 + Monthly Interest Rate[tex])^{(-Number of Months)}[/tex]
Here, Principal = $160,000
APR = 4.57%,
Number of Months = 30 years ÷ 12 months/year = 360 months.
First, we need to convert the APR to a monthly interest rate by dividing it by 12:
Monthly Interest Rate = 4.57% × 12
Monthly Interest Rate = 0.3808%
Monthly Yield = (160000 × 0.3808%) ÷ (1 - (1 + 0.3808%[tex])^{-360}[/tex]
Monthly Yield = $637.71
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Calculate the area of the shape below
Answer:
Step-by-step explanation:
Area of rectangle+area of triangle
hope the picture helps
Quadrilateral ABCD is translated 5 units up. What are the coordinates of
quadrilateral A'B'C'D?
A
D
A(-5, 5)
D(-5, 1)
B' Y
G
C₁
8(-1,5)
C(1, 2)
OA. A'(-5, 0), B'(-1,0), C'(-1, -3),
D'(-5,-4)
OB. A'(-5, 10), B'(-1, 10), C'(-1,7),
D'(-5, 6)
C. A'(-10, 10), B'(-6, 10), C'(-6, 7),
D'(-10, 6)
D. A'(-10, 5), B'(-6, 5), C'(-6, 2),
D'(-10, 1)
Answer:
it should be B but I could be wrong
Step-by-step explanation:
B
Triangle ABC aid dilated by a scale factor of 3. Which is an algebraic representation of the dilation?
Answer:
[tex](3x, 3y)[/tex]
Step-by-step explanation:
The scale factor is 3 so you multiply 3 by the (x,y) to get (3x,3y) as the scale factor
Here is another riddle:
-The sum of two numbers is less than 2
-If we subtract the second number from the first, the difference is greater than 1
The riddle can be represented by a system of inequalities. Write a inequality for each statement.
Name a possible (ordered pair) solution to the riddle.
6+r=2r+3 how to solve this
Answer:
soln
6+r =2r+3
6-3=2r-r
3=r
ans r=3Which statement best reflects how the cultural setting influences
Sigismondo's attitude in the excerpt from "The City Lost in the Snow"?
A
B
C
D
The competition between snow shovelers makes Sigismondo
excited to prove himself to Marcovaldo.
The fast-paced urban environment explains why workers like
Sigismondo must keep the city moving.
The scarcity of jobs makes Sigismondo appreciate the temporary
employment the snow provides.
The industrialization of the city leads Sigismondo to feel ambitious
about his future opportunities.
In the excerpt from "The City Lost in the Snow," the statement that best reflects how the cultural setting influences Sigismondo's attitude is: C.
The scarcity of jobs makes Sigismondo appreciate the temporary employment the snow provides. T
his statement reflects the importance of the cultural setting, as it shows that Sigismondo values the opportunity to work and earn money, even if it's temporary, due to the scarcity of jobs in the city.
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how will the product change if one number is increase by a factor of 12 and the other is decreased by a factor of 4
Using factors, we can conclude that the new product will be 48 time more than the old product.
Define factors?In mathematics, the factor of a number is a divisor of the inputted integer that entirely divides it, leaving no residue. We can use a variety of techniques, including the division method and the multiplication method, to identify a number's components.
Let the product be P.
Let the numbers be a and b.
Now,
P = a × b
According to the question.
Let a is increased by a factor of 12 and b by 4:
P = 12a × 4b
P = 48 × a × b
Hence, we can conclude that the product will increase by a factor of 48.
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1/5 of a large wall was covered in red paint, 1/10 in blue paint, and 1/4 in green paint. What
percentage of the whole wall is covered in paint (of any colour)?
19%
32%
55%
50%
68%
Answer:
55% of the whole wall is covered in paint of any color.
Step-by-step explanation:
To determine what percentage of the wall is covered in paint, we need to add the fractions of the wall covered by each color of paint and then convert the result into a percentage.
Red paint: 1/5
Blue paint: 1/10
Green paint: 1/4
First, we need to find a common denominator, which is the least common multiple (LCM) of the denominators 5, 10, and 4. The LCM of 5, 10, and 4 is 20. Now, we can convert the fractions to equivalent fractions with a denominator of 20:
Red paint: (1/5) * (4/4) = 4/20
Blue paint: (1/10) * (2/2) = 2/20
Green paint: (1/4) * (5/5) = 5/20
Now, add the fractions:
Total paint coverage = 4/20 + 2/20 + 5/20 = (4 + 2 + 5)/20 = 11/20
To convert this fraction to a percentage, we can divide 11 by 20 and multiply the result by 100:
(11/20) * 100 = 0.55 * 100 = 55%
Thus, 55% of the whole wall is covered in paint of any color.
Describe the transformations that would map the graph
of f(x) = x^2 + 1 to the graph of g(x) = (x − 3)^2 − 2.
The graph of [tex]g(x)[/tex] is the result of taking the graph of [tex]f(x)\\[/tex], shifting it right three units and down two units.
x^2-6x-16 when factored is
Answer: (x+2)(x-8)
Step-by-step explanation:
x^2-6x-16
x^2-8x+2x-16
x(x-8)+2(x-8)
(x+2)(x-8)