Jorge's statement is partially correct. 0.029 can be written as a fraction but it is 29/1000, not 29/100 since it has three decimal places.
Explanation:Jorge's statement that 0.029 can be written as 29/1000 is indeed correct. When you convert a decimal to a fraction, we count the number of decimal places, which determines the denominator of the fraction. In the case of 0.029, it has three decimal places, therefore, the denominator would be 1000 (the first place represents tenths, the second represents hundredths and third represents thousandths). Hence 0.029 as a fraction is written as 29/1000, not 29/100.
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If f(x)=3x^2-2 and g(x)=4x+2 what is the value of f+g 2
Answer:
20
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x) = 3x² - 2 + 4x + 2 = 3x² + 4x
Substitute x = 2 into f(x) + g(x)
(f + g)(2) = 3(2)² + 4(2) = (3 × 4) + 8 = 12 + 8 = 20
Select all the equations that do NOT have a real solution.
x2 = 49
2
2x2 = - 128
3x2 - 16 = 32
2x2 + 36 = 18
*²+x+1=0
ANSWER FAST ♀️
Answer:
Second statement 2x2 + 8x – 24 = 0 Is true for the given conditions. When x = -6 2x2 + 8x – 24 = 0 Becomes 2(-6)2 + 8(-6) – 24 = 0 2(36) - 48 - 24 = 0 72 - 48 - 24 = 0 0 = 0 Which is true. When x = 2 2x2 + 8x – 24 = 0 Becomes 2(2)2 + 8(2) – 24 = 0 2(4) + 16 - 24 = 0 8 + 16 - 24 = 0 0 = 0 Which is true. So 2x2 + 8x – 24 = 0 will be answer.
The characteristics of the solutions of the polynomials are listed below:
The polynomial has two distinct real roots.The polynomial has two conjugated complex roots.The polynomial has two distinct real roots.The polynomial has two conjugated complex roots.Let be a second order polynomial of the form [tex]a\cdot x^{2}+b\cdot x + c = 0[/tex], there are no real roots if and only if [tex]b^{2}-4\cdot a \cdot c < 0[/tex]. Now we proceed to determine the nature of the roots of each polynomial:
1) [tex]x^{2} = 49[/tex]
This expression is equivalent to the polynomial [tex]x^{2}-49 = 0[/tex], then the discriminant is:
[tex]d = 0^{2}-4\cdot (1)\cdot (-49)[/tex]
[tex]d = 196[/tex]
The polynomial has two distinct real roots.
2) [tex]2\cdot x^{2} = -128[/tex]
This expression is equivalent to the polynomial [tex]2\cdot x^{2} +128 = 0[/tex], then the discriminant is:
[tex]d = 0^{2} - 4\cdot (2)\cdot (128)[/tex]
[tex]d = -1024[/tex]
The polynomial has two conjugated complex roots.
3) [tex]3\cdot x^{2}-16 = 32[/tex]
This expression is equivalent to the polynomial [tex]3\cdot x^{2}-48 = 0[/tex], then the discriminant is:
[tex]d = 0^{2}-4\cdot (3) \cdot (-48)[/tex]
[tex]d = 576[/tex]
The polynomial has two distinct real roots.
4) [tex]x^{2}+x+1 = 0[/tex]
The discriminant of this expression is:
[tex]d = 1^{2}-4\cdot (1)\cdot (1)[/tex]
[tex]d = -3[/tex]
The polynomial has two conjugated complex roots.
Nota - The original statement reports typing mistakes. Corrected form is presented below:
Select all the equations that do not have a real solution:
[tex]x^{2} = 49[/tex] [tex]2\cdot x^{2} = -128[/tex] [tex]3\cdot x^{2} - 16 = 32[/tex] [tex]2\cdot x^{2} + 36 = 18[/tex] [tex]x^{2}+x + 1 = 0[/tex]
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3 x 7 x 2 is the prime
factorization of what
number?
Answer:
42 that's ur answer u just multiply all the numbers
The multiplication of 3, 7, and 2 (which are all prime numbers) equals to 42. Therefore, 42 is the number which has a prime factorization of 2, 3, and 7.
Explanation:The product of 3 x 7 x 2 gives us the number for which this is the prime factorization. The prime factorization of a number is the breaking down of that number into its simplest factors that are prime numbers, in this case, it would be 2, 3, and 7. By multiplying these number together: 3 x 7 x 2, we get the number 42, hence, 42 is a number we are looking for.
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What is the value of the expression?
−4.2(0.35−3.5)
Enter your answer in the box as a decimal.
GUYS HELP
Answer:
Try entering 2x+3=15 @ x=6 into the text box. After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x+3=15: 2(6)+3 = 15. The calculator prints "True" to let you know that the answer is right. More Examples Here are more examples of how to check your answers with Algebra Calculator. Feel free to try them now.
Step-by-step explanation:
"The value of the expression [tex]\( -4.2(0.35 - 3.5) \) is \( 13.404 \)[/tex].
To solve the expression, we follow the order of operations, which is to first evaluate the expression inside the parentheses and then multiply the result by [tex]\( -4.2 \).[/tex]
First, we subtract [tex]\( 3.5 \)[/tex] from [tex]\( 0.35 \):[/tex]
[tex]\[ 0.35 - 3.5 = -3.15 \][/tex]
Next, we multiply this result by [tex]\( -4.2 \)[/tex]:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
However, to be precise, we should calculate this with the exact decimal values without rounding until the final step. So, let's do the multiplication with more precision:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
Now, we can round the result to the nearest ten-thousandth, as the original numbers were given to the hundredth:
[tex]\[ 13.23 \approx 13.2300 \][/tex]
But, to match the precision of the original question, we should express the answer to the same decimal place as the given numbers, which is to the hundredth:
[tex]\[ 13.2300 \approx 13.23 \][/tex]
However, the provided answer is[tex]\( 13.404 \),[/tex] which suggests that there might have been an error in the rounding process or in the original calculation. Let's re-evaluate the multiplication with exact values:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
To ensure we have the correct answer, we should not round until the final step:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
Now, rounding to the nearest hundredth:
[tex]\[ 13.23 \approx 13.23 \][/tex]
The correct answer, rounded to the nearest hundredth, is \( 13.23 \). However, if the original question or the provided answer requires more decimal places, we should calculate accordingly. Assuming the original values are exact, the precise answer calculated with more decimal places is:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
If we were to use a calculator or perform the multiplication with more precision, we would find:
[tex]\[ -4.2 \times -3.15 = 13.22999999999998 \][/tex]
Rounding this to the nearest ten-thousandth, we get:
[tex]\[ 13.22999999999998 \approx 13.2300 \][/tex]
And if we round to the nearest hundredth, we still get:
[tex]\[ 13.2300 \approx 13.23 \][/tex]
The correct final answer, rounded to the same precision as the given numbers in the question, is [tex]\[ \boxed{13.23} \][/tex]
Which pairs of triangles appear to be congruent? Check all that apply.
A. Triangles 1 and 4
O B. Triangles 1 and 3
C. Triangles 2 and 3
D. Triangles 2 and 4
E. Triangles 3 and 4
O
F. Triangles 1 and 2
SUBMIT
Answer:
Step-by-step explanation:
C,D and E
Pairs of triangles appear to be congruent are :
Triangles [tex]2[/tex] and [tex]3[/tex]Triangles [tex]2[/tex] and [tex]4[/tex] Triangles [tex]3[/tex] and [tex]4[/tex]What are congruent triangles?" Congruent triangles are defined as the pairs of triangles with same measurement."
According to the question,
Given pairs of triangles,
A. Triangles [tex]1[/tex] and [tex]4[/tex] :
After observing triangles [tex]1[/tex] and [tex]4[/tex] it appears that triangle [tex]1[/tex] is smaller than triangle [tex]4[/tex] .
Option A is not the correct answer.
B. Triangles [tex]1[/tex] and [tex]3[/tex] :
After observing triangles [tex]1[/tex] and [tex]3[/tex] it appears that triangle [tex]1[/tex] is smaller than triangle [tex]3[/tex] .
Option B is not the correct answer.
C. Triangles [tex]2[/tex] and [tex]3[/tex] :
After observing triangles [tex]2[/tex] and [tex]3[/tex] it appears that triangle [tex]2[/tex] is congruent to triangle [tex]3[/tex] .
Option C is the correct answer.
D. Triangles [tex]2[/tex] and [tex]4[/tex] :
After observing triangles [tex]2[/tex] and [tex]4[/tex] it appears that triangle [tex]2[/tex] is congruent to triangle [tex]4[/tex] .
Option D is the correct answer.
E. Triangles [tex]3[/tex] and [tex]4[/tex] :
After observing triangles [tex]3[/tex] and [tex]4[/tex] it appears that triangle [tex]3[/tex] is congruent to triangle [tex]4[/tex] .
Option E is the correct answer.
F. Triangles [tex]1[/tex] and [tex]2[/tex] :
After observing triangles [tex]1[/tex] and [tex]2[/tex] it appears that triangle [tex]1[/tex] is smaller than triangle [tex]2[/tex] .
Option F is not the correct answer.
Hence, Option(C), (D), and (E) are correct answer.
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How does the graph below change between point A and point B
The graph increases.
The graph decreases.
The graph decreases, then increases.
The graph increases, then decreases.
The nature of the graph from point A to B : The graph increases, then decreases.
Given,
Graph is x -y coordinates.
Now,
Graph is concave downwards.
Coordinates of point A : (0,0)
Coordinates of point B : (6,0)
So,
The graph firstly increases from x = 0 to x = 3.
Then,
The graph decreases from x = 3 to x = 6 .
Therefore the graph increases and then decreases.
Thus option D is correct.
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margaret is planning a wedding reception she wants to spend less than her budget of $5,323 and margaret has already spent $2,748 the meal price per guest is $25 how many quests, x, can margaret invite to the reception and stay under budget on a number line graph
Margaret can invite up to 102 guests and still stay within her budget for the wedding reception. This constraint is illustrated on a number line with a break at 103.
To find out how many guests Margaret can invite to the reception and stay under her budget of $5,323, given that she's already spent $2,748 and the meal price per guest is $25, let's determine the inequality and solve for x.
Formulate the Inequality
Margaret's remaining budget after her initial spending is:
[tex]\[ 5,323 - 2,748 = 2,575.[/tex]
If she wants to stay within this budget, and the meal price per guest is $25, the total cost for (x ) guests is:
[tex]\[ 25 \times x. \][/tex]
Margaret wants to spend less than her remaining budget, so the inequality is:
[tex]\[ 25 \times x < 2,575. \][/tex]
Solve for x :
To find x, divide by 25:
[tex]\[ x < \frac{2,575}{25}, \][/tex]
x < 103.
Since x must be a whole number (you can't invite a fraction of a guest), Margaret can invite a maximum of 102 guests to stay under budget.
Graph on a Number Line
On a number line, draw an open circle at 103, indicating that 103 is not included in the set of possible guest counts.
Extend the line leftwards to 0 (as you cannot have a negative number of guests).
|------|------|------|------|------|
0 25 50 75 100 125
The asterisk represents the open circle, indicating that the maximum number of guests is strictly less than 103.
Margaret can invite 103 guests to the reception and stay under budget. Number line A includes the largest number of guests.
In order to write a linear inequality to describe this situation, we would assign a variable to the number of guests can Margaret invite while staying within her budget, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of guests.
Since Margaret wants to spend less than her budget of $5,323, and she has already spent $2,748, and the meal price per guest is $25, a linear inequality that models this situation is given by;
2748 + 25x < 5323
25x < 5323 - 2748
25x < 2575
x < 2575/25
x < 103
In this context, we can logically deduce that the largest number of guests Margaret can invite without exceeding her budget is correctly represented by number line A, with a hollow dot located at 104.
Complete Question;
Margaret is planning a wedding reception. She wants to spend less than her budget of $5,323, and Margaret has already spent $2,748. The meal price per guest is $25. How many guests, x, can Margaret invite to the reception and stay under budget?
Select the number line that includes the largest number of guests Margaret can invite without exceeding her budget.
Jon worked x hours at the car wash on Friday and the same number of hours on Saturday. His total pay for Friday and Saturday was $175. Which expression could you use to determine Jon's hourly pay?
Answer:
[tex]\frac{175}{2x}[/tex]
Step-by-step explanation:
Jon works the same number of hours on Friday and Saturday, therefore x represents the number of hours worked on Friday and also the number of hours worked on Saturday.
So the total hours worked between Friday and Saturday is 2X
If the total for the 2X hours worked is equal to 175 $
To know how much you earn per hour, we must divide the profit by the total hours worked.
Then we have the following expression
To know how much you earn per hour, we must divide the profit by the total hours worked.
[tex]\frac{175}{2x}[/tex]
a convenience store sells two brands of orange juice. brand a contains 11 oz and costs $2.31.brand b contains 15 oz and costs $2.70. what is the difference in cost per oz between the two brands
Hey!
----------------------------------------------------------------
[tex]\boxed{ \bf 0.03~dollars~difference~per~ounce}[/tex]
----------------------------------------------------------------
Solution:
Brand A ~ 2.31 / 11 = $0.21 per ounce.
Brand B ~ 2.70 / 15 = $0.18 per ounce.
Difference ~ 0.21 - 0.18 = $0.03 per ounce.
----------------------------------------------------------------
Hope This Helped! Good Luck!
Answer:
$0.03
Step-by-step explanation:
The product of twelve and fourteen please help
Answer:
168
Step-by-step explanation:
u can eperate the 14 to 10 and 4 then multiple each to 12 then add the two answer so it would be 10×12 and 4×12 then add them so (10×12=120)+(4×12=48)
I NEED HELP
write the equation of the line parallel to the given line and passing through the given point.
y=x+5 through (8,1)
Answer:
all work is shown and pictured
7.24 divided by 7 round to the nearest tenth if necessary
Answer:
7.24/7= 1.03
1.0 is the nearest
Solve for s: 7s + 4(3-5) = 18
7s + 4(3-5) = 18
Multiply the bracket by 4
(4)(3)=12
(4)(-5)=-20
7s+12-20=18
7s-8=18
Move -8 to the other side.
Sign changes from -8 to +8
7s-8+8=18+8
7s=18=8
7s=26
Divide both sides by 7
7s/7=26/7
Answer: s=26/7 or s=3 5/7
Answer:
7s+4(3-5)=18
7s+12-20=18
7s=18-12+20
7s=26
s=3.714
Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest compounded semi-annually. How much will be in Kelly’s account at the end of four years?
The amount in Kelly's account at the end of four years will be $887.63.
Explanation:To calculate the amount in Kelly's account at the end of four years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, Kelly's principal amount is $750, the annual interest rate is 4.25%, and interest is compounded semi-annually, so n = 2. Plugging these values into the formula:
A = 750(1 + 0.0425/2)^(2*4)
A = 750(1 + 0.02125)^8
A = 750(1.02125)^8
A = 750(1.18350595645)
A = $887.63
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ba
For Exercises 5-13, write the prime factorization of each number in
expanded form.
5. 36
6. 180
7. 525
8. 165
9. 293
10. 760
11. 216
12. 231
13. 312
2011
at 10
.-
Answer:
See below.
Step-by-step explanation:
If the number is even you divide by 2 , if it is odd you try by the next prime number 3, the 5 and so on, so:
5. 36:-
36/ 2 = 18
18/2 = 9
9 / 3 = 3
We finish on the prime number 3.
So the prime factors are ( the numbers in bold ) = 2*2*3*3.
I'll do the next 3 for you, so you'll be able to do the rest on your own:
6. 180
180/ 2 = 90, 90 / 2 = 45, 45 /3 = 15, 15/3 = 5.
So 180 = 2*2*3*3*5.
7. 525
525/ 3 = 175, 175 / 5 = 35, 35 / 5 = 7.
So 525 = 3*5*5*7.
8. 165
165 / 3 = 55, 55/5 = 11.
So 165 = 3*5*11.
10. The convention center has 18 pianos. Each piano has 88 piano keys. What
is the total number of piano keys?
What we know:
The convention center has 18 pianos.
Each piano has 88 piano keys.
How to solve:
To find out the total number of of piano keys, we need to multiply the number of pianos that are at the convention center by the number of piano keys that are on each pano.
Number of pianos → 18
Number of piano keys → 88
18 × 88 = 1,584
Therefore, there are 1,584 keys at the convention center.
After several shares of the company's stock were sold, a profit of $1.320 was earned. The profit was 15%
over a 30 day period. How much were the shares worth when they were originally purchased?
Answer:
$8.8
Step-by-step explanation:
Let the original price of shares be [tex]x[/tex]
Profit earned = $1.320
percentage profit = 15%
∴ [tex]\frac{15x}{100} = 1.320\\15x = 132.0\\x = \frac{132}{15} \\x = 8.8[/tex]
Original price of shares were = $8.8
1. a. You deposit $2000 earned at a summer job in an account that pays 4.2% simple in-
terest. What is the balance in the account in 3 years?
b. Determine the balance in 3 years if the $2000 is deposited in an account that pays
4.2% compounded quarterly,
Answer:
B
Step-by-step explanation:
Answer:
25200
Step-by-step explanation:
Which of the following transformations is shown?
A.Translation 5 units up and 4 units to the right
B.Translation 5 units up and 5 units to the right
C.Reflection across the y-axis and translation 4 units up.
D.Reflection across the x-axis and translation 4 units to the right.
Answer:
A. Translation 5 units up and 4 units to the right
Step-by-step explanation:
A translation is a point-by-point movement by a prescribed number of units up/down and/or left/right.
Point A is moved from (-3,-1) up 5 and right 4 units to A prime at (1,4)
Point B is moved from (-4,-3) up 5 and right 4 units to B prime at (0,2)
Point C is moved from (-2,-3) up 5 and right 4 units to C prime at (2,2)
Answer:
A. Translation 5 units up and 4 units to the right
Step-by-step explanation:
→ Point C moves up to [-2, 2]
Transition up: → Point B moves up to [-4, 2]
→ Point A moves up to [-3, 4]
→ Point C moves to C'[2, 2]
To the right: → Point B moves up to B'[0, 2]
→ Point A moves up to A'[1, 4]
This is a genuine statement!
I am joyous to assist you anytime.
Please help do not guess please
Answer:
2x-3 = -11
Step-by-step explanation:
|2x-3| = 11
by definition of absolute numbers,
2x-3 = 11 (given)
or
2x-3 = -11 (answer)
three fractions that can be expressed as percents between 50% and 75%
Mari has 42 coins consisting of nickels, dimes, and
quarters. The total value of the coins is $9.35. The
number of dimes is one less than three times the
number of nickels. How many of each type of coin
does Mari have?
Mari has 42 coins consisting of nickels, dimes, and quarters. The total value of the coins is $9.35. The number of dimes is one less than three times the number of nickels. Mari has 17 nickels, 8 dimes, and 17 quarters.
Let's use algebraic equations to solve this problem.
Let "n" be the number of nickels, "d" be the number of dimes, and "q" be the number of quarters.
We have three pieces of information from the problem:
1. The total number of coins: n + d + q = 42
2. The total value of the coins: 0.05n + 0.10d + 0.25q = 9.35
3. The number of dimes is one less than three times the number of nickels: d = 3n - 1
Now, let's substitute the third equation into the first equation to express "d" in terms of "n":
(3n - 1) + n + q = 42
4n + q = 43
q = 43 - 4n
Next, we'll substitute the values of "q" and "d" into the second equation:
0.05n + 0.10(3n - 1) + 0.25(43 - 4n) = 9.35
0.05n + 0.30n - 0.10 + 10.75 - n = 9.35
0.35n + 10.65 = 9.35
0.35n = 9.35 - 10.65
0.35n = -1.30
n = -1.30 / 0.35
n ≈ 3.71
Since the number of coins can't be a fraction, we'll round down to the nearest whole number. Therefore, Mari has 3 nickels.
Now, let's find the number of dimes:
d = 3n - 1
d = 3(3) - 1
d = 9 - 1
d = 8
Finally, we can find the number of quarters using the equation for "q":
q = 43 - 4n
q = 43 - 4(3)
q = 43 - 12
q = 31
In conclusion, Mari has 3 nickels, 8 dimes, and 31 quarters.
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Simplify 3(2x-7y)+2(2x+3)=
Answer:25
Step-by-step explanation:Use pemdas first (2x-7y) 2-7=5 next (2x+3) 2+3=5 3•5=15 5•2=10 3•5=15 add 10+15=25
Using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation
10.0y − 4.55x = 581
where x is the number of years after 2000.
In what year is the population predicted to be 71.75 million?
Answer:
In year 2030 the population is predicted to be 71.75 million
Step-by-step explanation:
* Lets explain how to solve the problem
- Using data from 2010 and projected to 2020, the population of
the United Kingdom (y, in millions) can be approximated by the
equation 10.0 y − 4.55 x = 581
- x is the number of years after 2000
- We need to know in what year the population is predicted to be
71.75 million
* Lets substitute the value of y in the equation by 71,75
∵ The equation of the population is 10.0 y - 4.55 x = 581
∵ y = 71.75
∴ 10.0(71.75) - 4.55 x = 581
∴ 717.5 - 4.55 x = 581
- Subtract 717.5 from both sides
∴ - 4.55 x = - 136.5
- Divide both sides by - 4.55
∴ x = 30
∵ x represents the number of years after 2000
∵ 2000 + 30 = 2030
∴ In year 2030 the population is predicted to be 71.75 million
Final answer:
The population of the United Kingdom is predicted to be 71.75 million in the year 2030, calculated by substituting the given population value into the equation and solving for the year.
Explanation:
To find the year in which the population of the United Kingdom is predicted to be 71.75 million, you can use the given equation 10.0y - 4.55x = 581. Here, x is the number of years after 2000, and y is the population in millions.
First, substitute y with 71.75:
10.0(71.75) - 4.55x = 581717.5 - 4.55x = 5814.55x = 717.5 - 5814.55x = 136.5x = 136.5 / 4.55x = 30Now, add the number of years, x, to the base year, 2000:
2000 + 30 = 2030Therefore, the population of the United Kingdom is predicted to be 71.75 million in the year 2030.
When Tom found the difference −17 − (−12), he got −29. Complete the statement that explains what Tom might have done wrong.
Im so confused
Answer:
- 5
Step-by-step explanation:
Note that - (- 12) = + 12
Thus
- 17 - (- 12) = - 17 + 12 = - 5
It looks like Tom subtracted 12 from - 17, that is - 17 - 12 = - 29
Answer:-17-(-12)=-5
Step-by-step explanation:when there’s a negative number in parenthesis and there’s a minus outside the parenthesis that majestic the number inside the parenthesis a positive
The graph of y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in which direction?
Answer:
Horizontally to the left.
Step-by-step explanation:
Adding The pi/2 moves the graph pi/2 units to the left.
The graph of y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in Horizontally to the left direction.
How do we make graph of a function?Suppose the considered function whose graph is to be made is f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
We are given that the function y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in unknown direction.
Therefore, we can conclude that by Adding the pi/2 moves the graph pi/2 units to the left.
Hence, it got shifted in the Horizontally to the left.
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At the fundraiser, there were only 3 prices for books: $2. $5 and $10. There were 6 more $5 books sold than $10 books. There were 8 more
$2 books sold than $10 books. A total of $250 was raised
How many $5 books were sold?
A. 12
B. 14
C. 17
D. 18
E. 20
Answer:
Answer is 18
Step-by-step explanation:
18 x $5 = $90
12 x $10 = 120 (6 more $5 books sold than $10)
20 x $2 = $40 (8 more $2 books sold than $10)
Total $250
help asap
!!!!!!!!!!!!!!!!!!!
Answer:
The correct answer is 2 1/36.
If ƒ(x ) = 3x + 1 and ƒ -1 = , then ƒ(2) =
Answer:
f(-1)=
[tex] \frac{ - 2}{3} [/tex]
f(2)=
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
let f(x)=f(-1)
but f(x) =3x+1
substituting it into the equation
3x+1=-1
3x=-1-1
3x=-2
dividing through by 3
[tex] \frac{3x}{3} = \frac{ - 2}{3} [/tex]
[tex]x = \frac{ - 2}{3} [/tex]
f(-1) =
[tex] \frac{ - 2}{3} [/tex]
f(2)
let f( x )=f(2)
then
3x+1=2
3x=2-1
3x=1
dividing through by 3
[tex] \frac{3x}{3} = \frac{1}{3} [/tex]
[tex] x = \frac{1}{3} [/tex]
f(2)=
[tex] \frac{1}{3} [/tex]
To find ƒ(2), substitute x = 2 into the Function ƒ(x) = 3x + 1. The answer is 7.
To find ƒ(2), we need to substitute x = 2 into the function ƒ(x) = 3x + 1.
Given: ƒ(x) = 3x + 1
Step 1: Substitute x = 2 into the function:
ƒ(2) = 3(2) + 1
Step 2: Perform the calculations:
ƒ(2) = 6 + 1
Step 3: Simplify the expression:
ƒ(2) = 7
First, substitute x = 2 into the function: ƒ(2) = 3(2) + 1 = 6 + 1 = 7.Therefore, ƒ(2) = 7.
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unit 2:logic&proof homework 1: inductive reasoning
The provided statement is an example of deductive reasoning, where a specific conclusion is drawn from general observations. On the other hand, inductive reasoning forms broad generalizations from specific instances and is heavily used in scientific studies.
Explanation:The question relates to the concept of inductive and deductive reasoning in logic and proofs. The given statement “All flying birds and insects have wings. Birds and insects flap their wings as they move through the air. Therefore, wings enable flight.” is an example of deductive reasoning.
Deductive reasoning follows a logical progression from general observations to a specific conclusion, assuming the initial general statement is true. If all flying birds and insects have wings and these creatures flap their wings for flight (general observations), it logically concludes that wings enable flight (specific conclusion).
In contrast, inductive reasoning involves creating broad generalizations from specific instances. Even though conclusions from inductive reasoning may not always be accurate, they contribute significantly to the progression of scientific knowledge. Scientists often use both inductive and deductive reasoning in their scientific methods for formulating hypotheses and theories.
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