Approximating square roots
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Without using a calculator, choose the statement that best describes the value of 215.
Choose 1 answer:
The value of 215 is between 13 and 13.5.
The value of 215 is between 13.5 and 14.
The value of 215 is between 14 and 1.5.
The value of v 215 is between 14.5 and 15.
Answers
Step-by-step explanation:
We know that
14^2=196, and
15^2=225
so we know that sqrt(215) is between 14 and 15.
How do we know if it is between 14.5 and 15?
we need to know the value of 14.5^2, which we can calculate in the head as follows:
The square of all numbers ending in 5 such as 15 can be calculated by breaking up the 5 and the preceding digit(s),
The preceding digit is 1. We multiply 1 by the next integer, 2 to get 2.
Attach 25 to 2 gives us 225 (as we saw above.
Example, 145*145 = 14*15 | 25 = 210 | 25 = 21025
so
14.5^2 = 210.25, which gives the more precise answer that
14.5^2 < 215 < 15^2, or
14.5 < sqrt(215) < 15 (fourth choice)
Since the third choice says sqrt(215) is between 14 and 1.5 (not 15), so the third choice is incorrect.
Note: if we eliminated the third choice, i.e. discard the likelihood of typo in the question, the only one left is the fourth choice.
Related Questions
What happens to energy that is unused?
Energy transform to heat energy.
Energy transform to potential energy.
Energy transform to kinetic energy.
Energy transform to light energy.
Answers
Energy transform to potential energy. as it is stored..I think
13. Find the area of the triangle given a = 14, b = 9, and C = 66 degrees. Round your answer to the nearest tenth.
14. Find the area of the triangle given a = 38, b = 31, and C = 29 degrees. Round your answer to the nearest tenth.
15. Find the area of the triangle given b = 17, c = 19, and A = 135 degrees. Round your answer to the nearest tenth.
Answers
Answer:
13) 57.6 units²
14) 285.6 units²
15) 114.2 units²
(All answers rounded off to the nearest tenth)
Step-by-step explanation:
Please see the attached picture for the full solution.
In a direct variation, y=9 when x=3. Write a direct variation equation that shows the relationship between x and y.
Answers
In a direct variation, y=9 when x=3. A direct variation equation that shows the relationship between x and y is y=3x
What do you mean by direct variation?
Direct variation is a type of proportionality when one quantity changes right away in reaction to a change in another variable. This implies that if one number rises, the other will follow suit in a comparable manner. Similar to the last illustration, if one quantity decreases, the other quantity also decreases. Direct variation will have a linear relationship with the graph, resulting in a straight line.
Given,
In a direct variation, y=9 when x=3.
Formulate an equation based on the conditions stated: y=kx
We put the value of the y and x in this equation
9=k*3
Subtract the coefficient of the variable from both sides of the equation
k= 3
We can write the equation of the function by putting the value of k: y=3x
Hence the correct answer is y=3x
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Need help with number 1!! Pleaseee
Answers
Answer:
Step-by-step explanation: find the circumference and then consider the shape (circle) after that get rid of options that don't make sense like 7.3 and 7.1, 8 for the radius might be too big leaving you with 7 (use a calculator if needed)
draw the dot plot of the distribution of possible data values that has the largest possible standard deviation (there were ten people at the talk, so there should be ten dots on your dot plot)
Answers
The dot plot consists of ten dots, each representing the data value of a single person at the talk. The data values are spread out as far as possible, resulting in the largest possible standard deviation.
A dot plot is a graph that is used to represent the distribution of data. It consists of dots, each of which represents a single data value. In this case, the dot plot represents the distribution of possible data values from a talk with ten people. To achieve the largest possible standard deviation, the data points should be spread out as far as possible. Each dot should be placed on the graph in such a way that the difference between any two adjacent data points is maximized. This is done by placing the highest and lowest values at opposite ends of the graph, and then evenly spacing out the remaining data points in between. All of this should result in the largest possible standard deviation of the data set.
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A man gave 5/12 of his money to his son , 3/7 of the remainder to his daughter and the remaining to his wife if his wife gets rs 8700 what is the total amount
Answers
The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.
A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?
The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.
The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'
Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).
Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.
Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200
Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.
The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.
The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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What is the area of the polygon given below?
A. 55 square units
B. 186 square units
C. 131 square units
D. 66 square units
Answers
Answer:
○ B. \(\displaystyle 186\:square\:units\)
Explanation:
All edges conjoin to form right angles, therefore you have these:
\(\displaystyle \boxed{186} \hookrightarrow 121 + 30 + 35 \Rightarrow 11^2 + 5 \times 6 + 5 \times 7\)
OR
\(\displaystyle \boxed{186} \hookrightarrow 120 + 66 \Rightarrow 24 \times 5 + 6 \times 11\)
I am joyous to assist you at any time.
Determine the number of zeros of the polynomial function.h(t) = (t − 6)2 − (t + 6)2
Answers
Answer:
Step-by-step explanation:
(t - 6)^2 = t^2 - 12t + 36
(t + 6)^2 = t^2 + 12t +36
(t - 6)^2 - (t + 6) = t^2 - 12t + 36 - (t^2 + 12t + 36)
(t - 6)^2 - (t + 6) = t^2 - 12t + 36 - t^2 - 12t - 36
(t - 6)^2 - (t + 6) = -24t The other 4 terms cancel out.
-24t = 0 Divide by - 24
t = 0
There is one root.
Find x in the given figure.
Answers
So let’s calculate “6”: 180° - 55° = 125°
Therefore x = 125°
pls help me i’ll give ty brainlist
Answers
\(\sqrt{25*7x^{4}*x^{1} } \\=\sqrt{25*x^{4}*7 *x^{1} } \\=\sqrt{25x^{4} } *\sqrt{7x}\\=5x^{2} \sqrt{7x}\)
Option B is the answer.
Answer: C
i hope you can see my handwriting
Suppose that you are checking your work on a test, and see that you have computed the cross product of
v=i+2j−3k
and
w=2i−j+2k
. You got
v×w=i+8j−5k
. Without actually redoing
v×w
, how can you spot a mistake in your work?
Answers
One way to spot a mistake in the computation of the cross product v x w = i+8j-5k without redoing the calculation is to check the orthogonality of the resulting vector to both v and w.
The cross product of two vectors v and w is a vector that is orthogonal to both v and w. In other words, the dot product of the cross product with either v or w should be zero.
To check if i+8j-5k is orthogonal to v and w, we can take the dot product of i+8j-5k with each vector. If the dot product is not zero, it means that the vector is not orthogonal to the corresponding vector, and therefore the calculation of the cross product is incorrect.
In this case, the dot product of i+8j-5k with v is 11 + 82 + (-5)(-3) = 1 + 16 + 15 = 32, which is not zero. Similarly, the dot product of i+8j-5k with w is 21 + (-1)8 + 2(-5) = 2 - 8 - 10 = -16, which is also not zero. Therefore, we can conclude that the vector i+8j-5k is not orthogonal to either v or w, and the calculation of the cross product is incorrect.
In summary, one way to spot a mistake in the computation of the cross product without redoing the calculation is to check the orthogonality of the resulting vector to both v and w. If the dot product of the cross product with either v or w is not zero, it means that the calculation is incorrect.
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Keep it simple I don’t need a explanation I will give you 5 stars Automatically just put the number to the question and answer inside of it
Answers
We will make use of the Trigonometry ratio to solve this question.
From the figure provided;
Hypotenuse side = 6
Opposite side = y
Adjacent side = x
Given angle = 60 degrees
To find side x, the suitable Trigonometry ratio to be used is the Cosine.
Thus, we have;
\(\begin{gathered} \text{Cos}\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}} \\ \text{Cos}60=\frac{x}{6} \\ \text{cross}-\text{multiply} \\ x=6\times\cos 60 \\ x=6\times0.5 \\ x=3 \end{gathered}\)To find side y, the suitable Trigonometry ratio to be used is the Sine.
Thus, we have;
\(\begin{gathered} Sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \text{Sin}60=\frac{y}{6} \\ cross-multiply \\ y=6\times\sin 60 \\ y=6\times\frac{\sqrt[]{3}}{2} \\ y=3\sqrt[]{3} \end{gathered}\)Hence, the values of x and y are:
\(x=3;y=3\sqrt[]{3}\)Find the unknown factor.
8 (5 x Blank ]= 80
![Find the unknown factor.8 (5 x Blank ]= 80](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/AWSIAMzigUqPauwsFcOUql7rbzqmrZP0.png)
Answers
Answer:
8 ( 5 × 2 ) = 80
Step by step explanation:
8 ( 5 × 2 ) = 80
8 × 10 = 80
80 = 80
what is archieves meaning
Answers
Answer:
the meaning is "a collection of historical documents or records providing information about a place, institution, or group of people."
Step-by-step explanation:
hope this helped and plz mark me as brainliest!
Answer:
a collection of historical documents or records providing information about a place, institution, or group of people
Step-by-step explanation:
A water bottle holds 120oz. Each time Anna takes a sip she drinks 10oz.a) Write a function to represent the scenario
b) How many sips can Anna take before she needs to refill?
c) Create a graph to represent this situation.
d) What is the domain of the function?
Answers
From the situation described, we have that:
a) The linear function is: f(s) = 120 - 12s.
b) She can take 10 sips before she needs to refill.
c) The graph is given at the end of the answer.
d) The domain is: 0 ≤ s ≤ 10.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the parameters are given as follows:
m = -12, b = 120.
Hence the function is:
f(s) = 120 - 12s.
She can take sips until f(s) = 0, hence:
120 - 12s = 0
12s = 120
s = 10.
She can take 10 sips before she needs to refill, and hence the domain(set that contains the input values for the function) is 0 ≤ s ≤ 10.
The graph is given at the end of the answer.
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If h(x) = -2x + 6, find x if h(x) = 12.
Answers
\(-2x+6=12\\2x=-6\\x=-3\)
The Life time in hours of a certain aircraft has the normal distribution with mean 80, Standard devation 16. What is the probability that the aircraft Will last 100 hours
Answers
1.25 is the probability that the aircraft Will last 100 hours.
What is probability?The area of mathematics described as probability concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.
Given Data
Mean = 80
Standard deviation = 16
P( x < 100)
P( x < 100) = P( Z< \(\frac{x- mean}{standard deviation}\))
P(x<100 ) = P( Z < \(\frac{100-80}{16}\))
P(x< 100) = P(Z< \(\frac{20}{16}\))
P(x < 100) = 1.25
1.25 is the probability that the aircraft Will last 100 hours.
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1. 72% of the students in Math 6 at AZVA are currently mastering their lessons. If 306 students are currently mastering their math lessons, how many students are in Math 6?
Answers
Answer:
i need help to yall help usssssssssssssssssssss pls
Step-by-step explanation:
Answer:
306/x = 72/100
72x= 306 x 100
72x = 30600
X = 425
Step-by-step explanation:
Guys what is 437x15=_____
Please Help, I Dont like Math
Thanks you guys have a good day!
Answers
Answer:
6555
Step-by-step explanation:
Again you can you Distributive property to answer this question here is how-To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Answer:
6555
Step-by-step explanation:
Question 2 (1 point)
Which equation BEST represents the line of best fit for the scatterplot?
0000
a y=-3x - 2
b
y=x-3
y=-3x + 2
с
d y = x + 3
Answers
The equation for the best fit of the scatter plot is y = x - 3
What is the scatter plot?
In a scatter plot, dots are used to represent the values of two different numerical variables. The values of each data point are represented by the position of each dot on the horizontal and vertical axes. Use scatter plots to see how different variables are related to one another.
Given data,
Let the scatter plot be represented as A
Now, the value of A is plotted below
where the slope of the plot is given by
m = y / x
m = 1
And, the y-intercept of the plot is when x = 0
So , when x = 0 , y = -3
Hence, the scatter plot is y = x - 3
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Complete the table. Answer should be T or F.
P Q
T F P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
F T P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
Answers
P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
T T T T T F F F F F T T
F T T F F T T T T T F F
P F T F F T T T T T F F
-P T T F F T T T T T F F
-Q T T T T F T F F F T T
-P V -Q T T F F T T T T T F
-P -> Q T T F F T T T T T F
-P -> -Q T T F F T T T T T F
P <-> Q T T T T F T T T T F
Here is a more detailed explanation of how I filled out the table:
P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.
P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.
-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.
-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.
-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.
-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.
-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.
P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.
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The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answers
The measure of both angles is 45.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Right triangle:
One angle = 90
Other angles:
One = 2x - 45
Another = x
Now,
The sum of the three angles = 180
90 + x + 2x - 45 = 180
Add like terms.
90 + 3x - 45 = 180
Add 45 on both sides.
90 + 3x = 180 + 45
Subtract 90 on both sides.
3x = 225 - 90
3x = 135
Divide 3 into both sides.
x = 45
Now,
Other angles:
One = 2 x 45 - 45 = 45
Another = 45
Thus,
Both angles are 45.
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Which of the following statements describes the solution to the equation 5 - d = -3?
The solution must be equal to 5.
The solution must be larger than 5.
The solution must be smaller than 5.
Answers
Answer:
The solution must be larger then 5.
Step-by-step explanation:
If the solution was smaller then 5 or equal to 5 the answer wouldn't be negative
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KG passes through the point (2, 14) and intersects HG at the point (12, 4). If the point H(18, 10) lies on HG, write the equation, in point slope form, of each line.
A. KG: y-2=-1(x-14)
HG: y-18=1(x-10)
B. KG: y-14=-1(x-2)
HG: y-10=1(x-18)
C. KG: y-10=1(x-18)
HG: y-14=-1(x+2)
D. KG: y+14=1(x+2)
HG: y+10=-1(x+18)
Answers
Answer:
B
Step-by-step explanation:
Trust
Solve for x
(3x + 2)
71
A) 28
C) 24
B) 23
D) 34
Answers
3x=71-2
3x=69
x=69/3
x=23
I need a help with this hw
Answers
The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5 d ) -25/12
What is trigonometric ratio?
Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent. Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse
the give parameters are:
tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2
a) sin(α+β)
Using the trig ratios tan = opp/adj
but from pyth. rule, 4² + 3² = h²
16+9 = h²
h = √25 = 5
Now from trig Sin(α+β)
4/5 + 3/5
=- 7/5
b) cos(α+β)
cos = ad/hypo
4/5 + 3/5
= -7/5
c) Sin(α-β)
4/5 - 3/5
-1/5
d) tan(α-β)
= -4/3 - 3/4
= (-16 - 9)/ 12
-25/12
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2. The actual tree on the left is 10 feet tall. The model tree on the right is 8 inches tall. What is the scale factor?
A: 15 B: 112 C: 1/122 D: 1/15
Answers
Answer:
D. 1/15
Step-by-step explanation:
Actual tree = 10 ft = 12 × 10 = 120 in.
Model tree = 8 in.
Scale factor = model tree/actual tree
Scale factor = 8/120
Scale factor = 1/15
Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
Answers
Answer:
\( \sqrt[4]{ {x}^{3} } \)
Step-by-step explanation:
\( \sqrt{x} \times \sqrt[4]{x} \\ = {x}^{ \frac{1}{2} } \times {x}^{ \frac{1}{4} } \\ = {x}^{ \frac{1}{2} + \frac{1}{4} } \\ = {x}^{ \frac{3}{4} } \\ = \sqrt[4]{ {x}^{3} } \)
Help?
A commercial jet liner hits an air pocket and drops 220 feet. After climbing 111 feet, it drops another 197 feet. What is its overall vertical change?
Answers
Answer:
-306 feet vertical change
Please help! I need by tomorrow
Answers
online school is hard