Use the drop-down menus to complete each statement to show why √65 is between 12 and 18.
Answers
Answer:
12 < 6√5 < 18
Step-by-step explanation:
It has been given in the question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3) ⇒ 6×2 < 6×√5 < 6×3
Therefore final answer is 6×2 < 6×√5 < 6×3 ⇒ 12 < 6√5 < 18
The square root of 65 (√65) falls between 8 and 9, as these are the square roots of the closest perfect square numbers (64 and 81 respectively). The range of 12 to 18 provided in the question seems incorrect.
Explanation:The student's question is referring to the mathematical concept of square roots of numbers. The square root of a number is a value which, when multiplied by itself, yields the original number. In the case of √65, we need to locate it between two perfect square numbers, which are 64 (8^2) and 81(9^2). As a result, √65 should fall between 8 and 9.
However, the interval of 12 and 18 as stated in the question seems to be a mistake, as they are not the correct boundaries for the value of √65. Please verify the numbers in your question.
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Related Questions
what is 67912 to the nearest 10
Answers
the last digit is the ones place, if it is 5 or higher you would round up
under 5 you round down
so to the nearest 10 the number would be 67910
Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = eight divided by square root of quantity two x plus four.
Answers
recursive function f(n+1)=1/3 f(n) if f (3)=9 what is f(1)
Answers
In which expression should the exponents be multiplied?
a. (5^3)-4
b. (1/3)^4*(1/3)^7
c. 3^7/3^15
d. 4^5*4^2
Answers
(1/3)^4*(1/3)*7 = (1/3)^(4+7) = (1/3)^11
3^7/3^15 = (3^7)*(3*(-15)) = 3^(7 + (-15)) = 3^(-8) = 1/(3^8)
4^5*4^2 = 4^(5+2) = 4^7
Option b is the correct answer. Exponents should be multiplied in the expression (1/3)^4*(1/3)^7, resulting in (1/3)^11.
The expression where the exponents should be multiplied is Option b. (1/3)^4*(1/3)^7. This is because when you multiply two expressions that have the same base, you add their exponents. In this case, you have the base (1/3) raised to the 4th power and then to the 7th power, so you add the exponents 4 + 7, which equals 11. Therefore, (1/3)^4*(1/3)^7 simplifies to (1/3)^11.
Another case where you multiply exponents would be when raising a power to another power, like in (5^3)^4. Here the exponents 3 and 4 are multiplied, resulting in (5^12).
(30 points) Enter numbers to write 0.000328 in scientific notation.
Answers
Which is a factor of 54xy + 45x + 18y + 15?
Answers
54xy+18y+45x+15 now factor 1st and 2nd pair of terms
18y(3x+1)+15(3x+1) which is equal to
(18y+15)(3x+1) and you can further factor the first binomial factor
3(6y+5)(3x+1)
(6.04)The scatter plot shows the relationship between the number of hours spent jogging and the number of minutes spent stretching, by the students on a track team:
What is the y-intercept of the line of best fit and what does it represent?
1 minute; the number of minutes students stretch when they do not jog
1 hour; the number of hours students jog when they do not stretch
4 hours; the number of hours students jog when they do not stretch
4 minutes; the number of minutes students stretch when they do not jog
Answers
1 minute, the number of minutes students stretch when they do not jog
James is four years younger than Austin. If 2 times James age is increased by the square of austins age, the result is 28. Find the 2 ages. Use an algebraic solution
Answers
"If 2 times James age is increased by the square of Austins age, the result is 28."
means: [tex]2(a-4)+ a^{2} =28[/tex]
rearrange the quadratic equation and solve it:
[tex]a^{2}+2(a-4)-28=0[/tex]
[tex]a^{2}+2a-8-28=0[/tex]
[tex]a^{2}+2a-36=0[/tex]
add and subtract 1 to complete the square:
[tex]a^{2}+2a+1-1-36=0[/tex]
[tex](a+1)^{2} =37[/tex]
a+1=root 37 = 6 (approximately), so a=5
or a+1=root 37 = -6 (approximately), so a=-7, which is not possible
The age of Austin is 5, and the age of James is 1.
Solve this quadratic equation. x ^2 + 2x - 22 = 0
Answers
Answer:
[tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
Step-by-step explanation:
Roots of quadratic equations [tex]ax^{2}+bx+c=0[/tex] calculated as:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
First, compare [tex]ax^{2}+bx+c=0[/tex] with [tex]x^{2}+2x-22=0[/tex]
here a = 1 , b = 2 and c = -22
Now, plug the value of a,b and c in [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x=\frac{-2\pm \sqrt{2^{2}-4(1)(-22)}}{2(1)}[/tex]
[tex]x=\frac{-2\pm \sqrt{4+88}}{2}[/tex]
[tex]x=\frac{-2\pm \sqrt{92}}{2}[/tex]
[tex]x=\frac{-2\pm 2\sqrt{23}}{2}[/tex]
[tex]x=-1\pm \sqrt{23}[/tex]
Hence, [tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
Let $s$ be the set of points with polar coordinates $(r,\theta)$ such that $ 2 \le r \le 6$ and $\frac{\pi}{3} \le \theta \le \frac{5 \pi}{6} $. find the area of $s$.
Answers
2 ≤ r ≤ 6 and π/3 ≤ θ ≤ (5π)/6 is shown in the figure below.
An element of area is
dA = r dr dθ
Therefore the total area is
[tex]A=\int _{ \frac{ \pi }{3}} ^{ \frac{5 \pi }{6} } \,d\theta \int_{2}^{6} \,rdr \\ A= [ \frac{5 \pi }{6}- \frac{ \pi }{3}]*[ \frac{6^{2}}{2} - \frac{2^{2}}{2}] = 8 \pi [/tex]
Answer: 8π
A cell phone company charges a basic rate of $19.99 per month for 300 minutes of local usage. Any local usage over 300 minutes is charged at $.10 per minute. All long distance calls are charged at $.25 per minute. Write and simplify an expression that gives the total monthly bill if x is the number of local minutes and y is the number of long distance minutes. Evaluate the expression if local usage totals 375 minutes and long distance usage totals 54 minutes.
Answers
total = 19.99 + 0.10(x-300) + 0.25y
x = 375
y=54
total = 19.99 +0.10(375-300) +0.25(54)
total = 19.99 + 0.10(75) + 0.25(54)
total = 19.99 + 7.50 + 13.50
total = $40.99
The total monthly bill is $40.99 for 375 local minutes and 54 long distance minutes, given the cell phone company's rates.
The total monthly bill can be expressed as the sum of the basic rate, the extra charge for local minutes beyond the included 300, and the charge for all long distance minutes. The expression can be written as:
Total Monthly Bill = Basic Rate + (Local Extra Charge x Extra Local Minutes) + (Long Distance Rate x Long Distance Minutes)
Where:
Basic Rate = $19.99Local Extra Charge = $0.10 per minuteExtra Local Minutes = x - 300 (only if x > 300)Long Distance Rate = $0.25 per minuteLong Distance Minutes = yFor x = 375 local minutes and y = 54 long distance minutes, the total monthly bill is calculated as follows:
Total Monthly Bill = $19.99 + ($0.10 x (375 - 300)) + ($0.25 x 54)
Total Monthly Bill = $19.99 + $7.50 + $13.50
Total Monthly Bill = $40.99
Vanessa typically works 8 hours per day in a normal 5 day work week. last week, however, vanessa had to take 90 minutes off on tuesday, 45 minutes off on thursday, and she left two and a half hours early on friday. how many hours did vanessa work last week?
Answers
The total number of hours Vanessa work in a week is:
total work hours = (8 hours / day) * 5 day / week
total work hours = 40 hours per week
The total number of hours she did not work:
total hours did not work = (90 minutes)(1 hour / 60 minutes) + (45 minutes)(1 hour / 60 minutes) + 2.5 hours
total hours did not work = 4.75 hours
The amount of hours Vanessa work last week can be calculated using the formula:
work hours = total work hours - total hours did not work
work hours = 40 hours – 4.75 hours
work hours = 35.25 hours
.help me with this please
Answers
-4x + 8y + 4x + 8y
16y ← answer
Perform the operation(s) and write the answer in simplest from.
2 2/5+3 1/4
A.)5 1/3
B.)25/9
C.)5 13/20
D.)12 5/9
Answers
What is the value of x?
x =
Answers
Answer: The value of x is 2 units.
Explanation:
Since we have given that
AB and CD are two chords that are intersected externally at point E.
As we know the relation regarding the above i.e.
[tex]EA\times EB=EC\times ED[/tex]
Here,
EB=x+1
EA=x+1+11 = (x+12)
EC=x+4
ED=x+4+1 = (x+5)
Now, we put the values in the relation given above :
[tex](x+1)(x+12)=(x+4)(x+5)\\\\x^2+13x+12=x^2+9x+20\\\\12+13x=20+9x\\\\13x-9x=20-12\\\\4x=8\\\\x=\frac{8}{4}=2\\\\x=2\ units[/tex]
Hence, the value of x is 2 units.
Answer:
x = 2 is the answer.
Step-by-step explanation:
When two chords AE and ED are drawn from an external point E to a circle then by theorem we know the relation
AE×BE = DE×CE
AE = x + 1 + 11 = x + 12
BE = x + 1
CE = x + 4
DE = x + 4 + 1 = x + 5
Now putting these values in the formula
(x + 12)(x + 1) = (x + 4)(x + 5)
x² + 12x + x + 12 = x² + 5x + 4x + 20
13x + 12 = 9x + 20
13x - 9x = 20 - 12
4x = 8
x = 2
x = 2 is the answer.
The distance of saturn from the sun is 1507 million kilometers express this distance in standard form
Answers
Brian is waiting at a park across the street from the hockey arena for his dad to pick him up. It rained most of the morning, and the streets still have puddles. At which point should Brian stand to be as far as possible from each street to avoid getting splashed? Explain your answer.
Answers
To avoid getting splashed from puddles on the street, Brian should stand in the middle of the park. This would distance him completely from the immediate spray zone of passing vehicles, like being further away from the shore reduces the impact of sprays from waves.
Explanation:To avoid getting splashed by cars driving through the puddles, Brian should stand in the middle of the park. By doing so, he establishes the maximum possible distance between himself and any part of the street. Staying as far away from the streets reduces the risk of any water reaching him when cars pass by.
Think of it like Jill delivering her flyers and retracing her steps: the farthest spot from her house during her journey was at the midpoint of her travel route.
Also consider Peter's driving scenario: The farther he is from other cars, the less likely he is to get affected by their maneuvers. In a similar way, Brian, being in the middle of the park would keep him away from the splash zone of passing cars.
Lastly, akin to Julian and his father on their surfboards, being away from the impact point of the waves (which is near the shore) they get least affected by the spray. This analogy can be compared to Brian's situation with the puddles.
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How do you simplify squats roots
Answers
[tex]\sqrt{ab} = \sqrt{a} * \sqrt{b}[/tex]
Knowing this, we can choose two factors where one of the factors is a perfect square.
Examples:
[tex]\sqrt{12} = \sqrt{4} * \sqrt{3} = 2\sqrt{3}[/tex]
Notice in this example if we used the factors 2 and 6 we wouldn't be able to simplify the square root.
[tex]\sqrt{32} = \sqrt{16} * \sqrt{2} = 4\sqrt{2}[/tex]
We could have also used the factors 4 and 8 because 4 is a perfect square.
every evening jenna empties her pockets and puts the changein a jar. at the end of the week she had 50 coins, all of them dimes and quarters. when she added them up, she had a totals of $10.25
d=number of dimes q=number of quarters
how many dimes did jenna have?
Answers
A box with a square base and open top must have a volume of 32,000 cm3. find the dimensions of the box that mini- mize the amount of material used.
Answers
squaer base so length=width, nice
v=lwh
but in this case, l=w, so replace l with w
V=w²h
and volume is 32000
32000=w²h
the amount of materials is the surface area
note that there is no top
so
SA=LW+2H(L+W)
L=W so
SA=W²+2H(2W)
SA=W²+4HW
alrighty
we gots
SA=W²+4HW and
32000=W²H
we want to minimize the square foottage
get rid of one of the variables
32000=W²H
solve for H
32000/W²=H
subsitute
SA=W²+4WH
SA=W²+4W(32000/W²)
SA=W²+128000/W
take derivitive to find the minimum
dSA/dW=2W-128000/W²
where does it equal 0?
0=2W-1280000/W²
128000/W²=2W
128000=2W³
64000=W³
40=W
so sub back
32000/W²=H
32000/(40)²=H
32000/(1600)=H
20=H
the box is 20cm height and the width and length are 40cm
If the following object is translated right two units and down three units. Where will the translation be located?
Answers
The coordinate H (0, -4) will be translated to H' (2, -7)
The coordinate T (5, -1) will be translated to T' (7, -4)
The coordinate A (4, 5) will be translated to A' (6, 2)
The quadrilateral M'H'T'A' is shown in the diagram below
How do you convert .444444444 to a fraction?
Answers
[tex]x=0.444\ldots=0.\overline4[/tex]
Then
[tex]10x=4.444\ldots=4.\overline4[/tex]
It follows that
[tex]10x-x=4.\overline4-0.\overline4[/tex]
[tex]\implies 9x=4[/tex]
[tex]\implies x=\dfrac49[/tex]
Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281
Answers
Final answer:
To find the nth term equation of an arithmetic sequence, we first determined the common difference to be 92 by given terms, and then found the first term by using the formula for arithmetic sequences. The nth term equation for the sequence is: an = -1489 + (n-1)(92).
Explanation:
To find the nth term equation of the arithmetic sequence, we need to determine the common difference and the first term of the sequence. Since we know the 18th term, a18 = 97, and the 20th term, a20 = 281, we can find the common difference, d, by subtracting the two given terms and dividing by the number of terms between them:
d = (281 - 97) / (20 - 18) = 184 / 2 = 92.
Once we have the common difference, we can use the following formula to find the first term (a1):
an = a1 + (n-1)d.
Let's substitute n = 18 and d = 92 into the formula:
97 = a1 + (18-1)(92)
a1 = 97 - (17)(92) = -1489.
Now we can write the equation for the nth term of the arithmetic sequence:
an = -1489 + (n-1)(92).
Anderson has $50 in his savings account. He deposits $5 every week. His father also deposits $20 into the account every time Anderson mows the lawn. His savings account balance can be shown with the following expression:
50 + 5w + 20m
Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)
Part B: If Anderson saves for 10 weeks and mows the lawn 2 times, how much will he have in his account? Show your work to receive full credit. (4 points)
Part C: If Anderson had $85 in his savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)
Answers
We are given the equation of the savings (s) as:
s = 50 + 5 w + 20 m
Part A.
Coefficient = 5 and 20
Variable = w and m
Constant = 50
Part B.
w = 10
m = 2
Therefore the total savings is:
s = 50 + 5 (10) + 20 (2)
s = $140
Part C.
The coefficient and the constant values are considered as fixed value because they do not change. Therefore only the variable value would change, however the expression 50 + 5 w + 20 m would still be the same. That is only the values of the variable change.
Conjectures can always be proven true.
True or False
Answers
basically if you start with a crazy wrong conjecture, then it can't be proven true
a conjecture is a guess based on incomplete information
some examples are when you have some special cases and assume they are true for all cases
example:
this rectangle is 4 by 16
this square is 8 by 8
they have the same area
therfor I think that all squares have the same area as rectangles
(that's obviously false)
so you can't prove that true
Solve 2x2 + 20x = −38.
a. −5 ± square root 14
b.−5 ± square root 51
c. −5 ±square root 6
d.−5 ± square root 13
Answers
x^2+10x=-19, halve the linear coefficient, square it, than add that value to both sides of the equation, in this case add (10/2)^2=25...
x^2+10x+25=6 now the left side is a perfect square
(x+5)^2=6 take the square root of both sides
x+5=±√6 subtract 5 from both sides
x=-5±√6 (so answer c.)
Answer:
c
Step-by-step explanation:
−5 ±square root 6
which one of the following sets of numbers represents the lengths of the sides of a right triangle ?
a. 13 35 37
b. 6 9 10
c. 5 12 13
d. 9 40 42
Answers
a. 13 35 37
13² + 35² = 1394 and 37² = 1369
1394 ≠ 369
b. 6 9 10
6² + 9² = 117 and 10² = 100
117 ≠ 100
c. 5 12 13
5² + 12² = 169 and 13² = 169
169 = 169 ← right triangle
d. 9 40 42
9² + 40² = 1681 and 42² = 1764
1681 ≠ 1784
The answer is c. 5 12 13
5, 12, 13 are the sides representing lengths of sides of a right triangle.
What is Pythagoras theorem?The theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Given that, lengths of sides of triangles.
If a triangle is a right triangle, then it should follow Pythagoras theorem,
Using Pythagoras theorem,
13² = 169
12² + 5² = 144 + 25 = 169
Therefore, 13² = 12² + 5² is following Pythagoras theorem.
Hence, 5, 12, 13 are the sides representing lengths of sides of a right triangle
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HELPPPPPPPPPPPP ASAP!!!!!!!!!!
Answers
(rounded is 24.5.)
Copy and complete the table on the previous page into a Word document. Title your journal "Pythagorean Theorem". Discuss any relationships you see in the table? Then, look at the equation below and calculate whether a2 + b2 is >, <, or = to c2 based on the numbers you recorded in your table.
I attached the chart (in blue) and the assignment! Can someone please help, I don't understand!
Answers
Row 1:
3² + 4² ? 5²
25 ? 25
25 = 25
Row 2:
5² + 12² ? 13²
169 ? 169
169 = 169
Row 3:
9² + 12² ? 15²
225 ? 225
225 = 225
Therefore, all of the given values conform to a² + b² = c².
How many roots does y+x^2-6x+9 have?
A. One
B. Two
C. Zero
D. Three