An equivalent expression for 3^(2 · t + 3) is given by the use of algebra properties for power expressions: 27 · 9^t.
How to find an equivalent algebraic expression by power propertiesIn this problem we find a power expression whose exponent is the sum of two numbers and we are asked to determine an equivalent form by using the following properties for power expressions:
1) Product of two powers of same base
a^m · a^n = a^(m + n)
2) Power of a power
(a^m)^n = a^(m \cdot n)
First, write the expression introduced in the statement of this question:
3^(2 · t + 3)
Second, use the algebra property for the product of two powers of same base in the expression:
3^(2 · t) · 3³
27 · 3^(2 · t)
Third, use the algebra property for the power of a power in the expression:
27 · (3²)^t
27 · 9^t
Fourth, write the resulting expression after applying algebra properties:
27 · 9^t
According to algebra properties, an equivalent expression is 27 · 9^t.
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solve the system of equations by the substitution method x+10y=17 3x+6y=3
The length of a rectangular window is 5 feet more than its width. The area of the
window is 36 square feet. What are the dimensions of the window? Could a moving
company use that window to bring a standard upright piano into an apartment?
The dimensions of the window: Length = 9ft , width = 4ft
What are dimensions?
In mathematics, a dimension is the length or width of an area, region, or space in one direction.
The homes we live in and the items we use on a daily basis all have three dimensions: height, length, and width.
Here, we have
l = w + 5
Area = length × width
The linear equation of the given dimension is:
36 = (w + 5)w
w² + 5w - 36 = 0
(w + 9)(w - 4) = 0
w + 9 = 0
w = -9
We only measure positive numbers so, we disregard this value.
we take,
w - 4 = 0
w = 4
l = 4 + 5
l = 9
The length of the window is 9 ft and the width of the window is 4 ft.
Hence, the dimensions of the window: Length = 9ft , width = 4ft
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if the domain of f(x) = 2x + 3 is {-3 ≤ x ≤ 0}, which number is not in the range -1,3,0, or 6?
Answer: 6
Step-by-step explanation:
If the domain is {-3 ≤ x ≤ 0}, then we will decide which of the given values is not in the range.
6 is not between, including the values of, -3 and 0, so the number not in the range is 6.
verify that the function satisfies the three hypotheses of rolle's theorem on the given interval. then find all numbers c that satisfy the conclusion of rolle's theorem. (enter your answers as a comma-separated list.) f(x)
The c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
The three hypotheses of Rolle's theorem are:
(a) f(x) is continuous on [a,b]
(b) f(x) is differentiable on (a,b)
(c) f(a) = f(b)
i) If you graph f(x), you can see that it is continuous that is no breaks on the interval [0,81]
ii) f(x) is differentiable on (0,81)
f '(x) = 1/(2√x) - 1/9 which exists on the open interval (0,81)
iii) f(0) = f(81) = √81 - 81/9 = 9-9 = 0
Rolle's Conclusion:
f'(c) = 0
f'(c) = 1/(2√c) -1/9 = 0
(9 - 2√c)/(18√c) = 0
√c = 9/2
c = 81/4
There is one number c = 81/4, which satisfies f '(c) = 0.
Therefore the c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
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Full question:
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)
f(x) =x − 1/9 x, [0, 81].
12.0.5f-2.3g
f=12,g=2
Answer:14.1099
Step-by-step explanation:
solve for y
-8x+2y= -24
Answer:
y = -12 + 4x
Step-by-step explanation:
1. Add 8x to both sides of the equation.
2y = -24 + 8x
2. Divide each term in 2y = -24 + 8x by 2, then simplify.
• Simplify left side: cancel the common factor of 2
y = -24/2 + 8x/2
• Simplify right side: 2y/2 = -24/2 + 8x
y = -12 + 4x
Find the slope of the line shown on the graph to the right.
The slope of the line is 5/6.
From the graph:
Slope : a surface of which one end or side is at a higher level than another rising or falling surface.
Points are (-3,-2) and (3,3)
slope m = y2-y1 / x2-x1
= 3 - (-2) / 3 - (-3)
= 3 + 2 / 3 + 3
m = 5/6.
Therefore the slope of the line is 5/6.
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A student states that a triangle can be formed with side lengths 3 in, 5 in, and 9 in. Is the student correct? why, or why not? yes, because 3 + 5 < 9 yes, because 3 + 9 > 5 no, because 3 + 9 > 5 no, because 3 + 5 < 9.
Answer:
no, because 3 + 5 < 9
Step-by-step explanation:
given three sides of a triangle
For the sides to form a triangle the sum of any 2 must be greater than the third.
given sides 3, 5 and 9 , then
3 + 9 = 12 > 5
5 + 9 = 14 > 3
3 + 5 = 8 < 9
the 3 sides do not form a triangle since 3 + 5 < 9
A-1. Age of airline paenger: x = 85, μ = 49, σ = 14 (Round your anwer to 3 decimal place. )
Z-score of age of airline passenger is 2.571
Age of airline passenger when x = 85 , μ = 49 and σ = 14 .Find standardized z-score ?
Z- Score give an idea how far a data point is from mean .
z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .
Given , x = 85
mean = 49
standard deviation = 14
z-score = x- μ / σ
putting all the values ,
z-score = 85 - 49 / 14
= 36 / 14
= 2.571
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Lines j and k are parallel. m∠3 = (3x − 18)° and m∠4 = (y + 25)° and m∠7 = 75°. Find the values of x and y.
Answer:
x = 31 , y = 80
Step-by-step explanation:
∠ 3 and ∠ 7 are corresponding angles and are congruent , so
3x - 18 = 75 ( add 18 to both sides )
3x = 93 ( divide both sides by 3 )
x = 31
then
∠ 3 = 3x - 18 = 3(31) - 18 = 93 - 18 = 75°
∠ 3 and ∠ 4 are a linear pair and sum to 180° , then
75 + y + 25 = 180
y + 100 = 180 ( subtract 100 from both sides )
y = 80
Riley has saved $60 to buy a new scooter. This amount is 30% of what he needs to save. What is the total amount of money Riley needs to save to buy the new scooter?
The total amount of money Riley needs to save to buy the new scooter is $200.
What is Percentage?
Percentage is the number or ratio which is expressed as "100". It is denoted by "%". It indicates the hundredth parts of any quantity.
It is calculated by dividing the value by total value and multiplied by 100.
Formula for percentage is (Value/total value)*100
For given information,
Riley saved $60 which is 30% of the total amount.
For 1% it will be $2
So, the total amount will be $200
Thus, the total amount of money Riley needs to save to buy the new scooter is $200.
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One of the legs of a right triangle measures 11 cm and the other leg measures 14 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
∴ The measure of the hypotenuse is 20cm (to the nearest tenth).
Step-by-step explanation:
Let the length of the hypotenuse be x cm.
x² = 11² + 14²
∴ x = 20cm (to the nearest tenth)
13 out of 20 jellybeans are green what percent of jellybeans are green
Answer:
65
Step-by-step explanation:
a group of friends wnats to go to the amusement park.They have no more than $110 to spend on parking and admission.parking is $8 and tickets cost $23 per person including tax
Answer:
Step-by-step explanation:
Based on the information given in the question, the inequality which can be used to determine x, the number of people who can go to the amusement park will be:
8 + 23(x) ≤ 100
8 + 23x ≤ 100
23x ≤ 100 - 8
23x ≤ 92
x ≤ 92/23
x ≤ 4
The number of people that can go to the amusement park will be at most 4
Tavon is asked to find EF. What error does Tavon make?
EF2= DF2 + DE2-2(DF)(DE) cos D
EP2-82+102-2(8) (10) cos 44*
EF264+100-160
0.7193
EF 48.91
X
44°
10
Select the correct choice below and fill in the answer box within your choice.
Q
The error that Travon makes is
(C) Tavon forgot to take the square root to find the final answer. The correct answer is about 6.99
What is a root in mathematics?
In mathematics, a number's "root" is a number that, when multiplied by itself, equals the original number; alternatively, a number's "root" can also be an equation's solution, which is typically presented as a number or an algebraic formula.
For instance, since 7*7=49, the square root of 49 is 7. In this instance, 7 is referred to as the square root of 49 since it must be multiplied twice to produce the number. 3 because 3*3*3=27 is the cube root of 27. Since 27 is obtained by multiplying 3 by three, we refer to this as a cube root, so 3 is the cube root of 27.
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A shopper needs 48 hot dogs
Answer:
According to sources on googIe, the average price of a hot dog would be $5.22.
If a shopper needs 48 hot dogs, they would need a total of $250.56 dollars to pay.
Step-by-step explanation:
48 x 5.22 = 250.56
50 points help pls
Question: state whether the figure appears to have a line symmetry (write yes or no). If so, draw all lines of symmetry
Answer:
No, it doesn't have all lines of symmetry
Step-by-step explanation:
If you can see, the triangle's line of symmetry is from a vertex to the center of another line. So, draw a line from the bottom left vertex (corner) to the center of the right side/line. And then, draw another from the right corner to left center line.
Sarita showed the steps to solving the equation.
When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?
The option that explains Sarita's mistake is Sarita’s solution is correct. She made an error in her verification.
What was Sarita's mistake?The given equation is: 5(x - 3) + 7(x + 4) = 73
In order to determine the value of x, take the following steps:
1. Apply the Distributive property:
5x - 15 + 7x + 28 = 73
2. Add similar terms together:
12x + 13 = 73
3. Combine similar terms:
12x = 73 - 13
4. Add similar terms
12x = 60
5. Divide both sides of the equation by 12
x = 60 / 12
x = 5
In order to verify the answer, substitute for x in the given equation :
5(5 - 3) + 7(5 + 4) = 73
5(2) + 7(9) = 73
10 + 63 = 73
73 = 73
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Bijou says the following steps can be used to find 0.62 of 7:
Step 1 Change "of” to the multiplication symbol.
Step 2 62×7=434
Step 3 There are 0 decimal places in 7 and 2 decimal places in 0.62 for a total of 2 decimal places in the factors.
Step 4 Move the decimal place in the product 2 places to the right to find the solution: 0.62 of 7 is 43,400.
In which step did she make her first error?
Bijou made her first decimal place error in Step 4 because the answer is supposed to be 4.34, not 43,400.
How is the decimal place determined?The decimal place of a product of two numbers should be determined based on the number of decimal places the multiplier and the multiplicand originally have.
A decimal place error is committed when the result bears a decimal place in the wrong position.
In this situation, 0.62 of 7:
= 0.62 x 7
= 62 x 7 ... removing the two decimal places
= 434
= 4.34 ... putting back the two decimal places in the final result.
Thus, Bijou did not commit any decimal place or multiplication error in Steps 1 through 3 but in Step 4.
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3. Corey is playing a game in which he selects
all of the numbers that are less than -5 but
greater than -20. Shade the values that Corey
should choose.
-9
7 -5
6
-3 -11
-15
18
0
The numbers that will be chosen when Corey selects all of the numbers that are less than -5 but greater than -20 include -9, -11 and -15.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Based on the information, the inequality will be expressed as:
-20 < x < -5
In this case, the numbers have to be from -6 to -19. The numbers illustrated in the options are -9, -11 and -15.
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Determine which set of side measurements could be used to form a triangle. 4, 6, 12 5, 19, 24 6, 10, 17 8, 9, 15
The set of side measurements that could be used to form a triangle is 8, 9 and 15
If a, b and c are the sides of the triangle
Then a + b > c
b + c > a
c + a> b
The first set of sides are
4, 6, 12
4 + 6 > 12
10 < 12
It will not form a triangle
The second set of sides are
5, 19 and 24
5 + 19 > 24
24 = 24
It will not form a triangle
The third set of sides are
6, 10 and 17
6 + 10 > 17
16 <17
It will not form a triangle
The fourth set of sides are
8, 9 and 15
8 +9 > 15
17 > 15
8+15 > 9
23 > 9
9 + 15 > 8
24 > 8
It will from a triangle
Hence, the set of side measurements that could be used to form a triangle is 8, 9 and 15
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Find the xx-intercept of each line defined below and compare their values.
Equation of Line A:
y-2=-(x+1)
Select values from Line B:
x y
−2 0
-1− -3
0 -6
The x-intercept of line A is (1,0) and the x - intercept of line B is (-2,0).
Given:
Equation of Line A: y-2=-(x+1)
on finding x intercept put y = 0
0 - 2 = -x - 1
-2 = -x - 1
-x = -2 + 1
-x = -1
x = 1.
The x intercept is (1,0)
The x intercept for the line B is (-2,0).
Therefore the x-intercept of line A is (1,0) and the x - intercept of line B is (-2,0).
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I Given:
2x-9
5
= 1
Prove: x = 7
It is proven that the value of x in the given expression 2x-9 -5 = 1 is 7.
Given: 2x-9 -5 = 1
We need to prove that x = 7
2x - 9 - 5 = 1
2x - 13 = 1
2x = 14
x = 7
Therefore, it is proven that the value of x in the given expression 2x-9 -5 = 1 is 7.
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A jeweler is dividing 3/8 a pound of rubies among 4 lots. What part of a pound will each lot weigh?
A 1/16
B 3/32
C 1/8
D 1/4
Answer:
B 3/32
Step-by-step explanation:
3/8 divided by 4
do the keep change flip method and solve
3/8 x 1/4
a random sample of high school seniors were asked whether they were applying for college. the resulting confidence interval for the proportion of students applying for college is (0.65,0.69). what is the margin of error?
Using the confidence interval, the margin of error is 0.02.
In the given equation we have to find the margin of error.
The resulting confidence interval for the proportion of students applying for college is (0.65,0.69).
Let p = population proportion of students applying for college
P = Sample proportion of students applying for college
ME = margin of error
So the confidence interval
CI = (P-ME, P+ME)
From the given question;
(P-ME, P+ME) = (0.65,0.69)
So lower bound= P-ME = 0.65............................(1)
Upper Bound = P+ME = 0.69............................(2)
Simplifying the Equation 1 and 2
Add equation 1 and 2 we get
2P = 1.34
Divide by 2 on both side we get
P = 0.67
Putting the value of P in the equation 2
P+ME = 0.69
0.67+ME=0.69
Subtract 0.67 on both side we get
ME = 0.02
Hence, the margin of error is 0.02.
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Please help ASAP and answer the whole thing please and thank you
Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:
Year Annual Tutoring Fee
2005 $1200
2008 $1350
A. What is the rate of change and initial value for Neil's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Neil charges each year. (10 points)
The equation in slope intercept form that represent the situation is y = 50x - 99050.
How represent linear equation in slope intercept form?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptNeil charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount.
Using the table that shows the amount he charged for tutoring each year. we can find the rate of change.
The rate of change is the slope.
Therefore, (2005, 1200)(2008, 1350)
m = slope = 1350 - 1200 / 3
slope = 150 / 3
slope = 50
Therefore, let's represent the equation in slope intercept form. We will have to find the y-intercept of the equation.
Hence, using (2005, 1200)
y = 50x + b
1200 = 50(2005) + b
b = 1200 - 100250
b = - 99050
Hence, the equation is y = 50x - 99050.
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I need help with this question too here is the question.
Fiona has 212 stickers to put in her sticker book. Page holds 18 stickers. How many pages does Fiona need for all of her stickers?
Again, please give me a valid answer. And show your work. Thank you. Have a good night.
Answer:
Fiona would need 12 pages to hold all 212 stickers.
Step-by-step explanation:
Since each page holds 18 stickers, and Fiona has 212 stickers, we need to divide.
212 / 18 = 11.7777778 pages
Because that we cannot have .77777778 of a page, we round to the nearest page, getting us 12 pages.
Have a good night, I hope my answer helped you!
5. A sprinter runs at 12m/s. Convert this to km/h.
a) 2 km/h b) 12 km/h C) 3.6 km/h d) 43.2 km/h
Answer:
43.2km/h
Step-by-step explanation:
1km = 1000m
1h = 3600s
1km/h to m/s
= 1 × 1000/3600
= 1000/3600
1m/s to km/h
= 1 ÷ 1000/3600
= 1 × 3600/1000
Hence, 12m/s = 12 × 3600/1000
= 43.2km/h
4.2 = 16.7 - 5y solve for y
Answer:
y = 2.5
Step-by-step explanation:
To double check this, you can do 5 times (2.5), then do 16.7 minus that answer so you do, 16.7- 12.5 which does indeed equal 4.2
Answer:
y = 2.5
Step-by-step explanation:
[tex]4.2 =16.7-5y[/tex]
Subtract 16.7 from both sides of the equation you get:
[tex]-12.5=-5y[/tex]
Divide by -5:
[tex]2.5=y[/tex]
Hope this answers your question :)
Noah borrows \$2000$2000dollar sign, 2000 from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money. The relationship between the amount of money, aaa, in dollars that noah owes his father (including interest), and the elapsed time, ttt, in years, is modeled by the following equation. A=2000e^{0. 1t}a=2000e 0. 1t a, equals, 2000, e, start superscript, 0, point, 1, t, end superscript how long did it take noah to pay off his loan if the amount he paid to his father was equal to \$2450$2450dollar sign, 2450? give an exact answer expressed as a natural logarithm.
Two years , is the time in which Naoh had to pay off his loan when the ammount he paid to his father was equal to $2450.
In the question we have given,
Amount borrowed by Naoh from his father
= $2000
The relationship between amount of money A in dollars with interest and elapsed time t is
A = 2000 e⁽⁰·¹⁾ᵗ
let Naoh pay $2450 after elapsing "t" years .
that is A = $2450 after time t years of borrowing.
We shall calculate the time which elapsed after borrowed by Naoh for paying $2450.
So, putting A = 2450 in above equation we get
2450 = 2000 e⁽⁰·¹⁾ᵗ
=> e⁽⁰·¹⁾ᵗ= 2450/2000 = 49/40
Taking logarithm both sides
=> ln ( e⁽⁰·¹⁾ᵗ) = ln (49/40)
=> (0.1 )t = 0.203
=> t = 2.023 ~ 2
Hence, after 2 years , Naoh will pay $2450 with including interest to his father.
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