Thus, the equation in the simplest form is found as: [(√2) *( 7√7) - 1 ]/7.
Explain about the square roots:A number can be obtained by multiplying the square root of that integer by itself.
An opposite of squaring an integer is finding its square root.
The factor of a number that, when multiplied by itself, equals the original number is known as the square root of the number. Practically speaking, determining a number's square root is the reverse of doing so to find its square (or the number multiplied by itself).
Given expression:
= (√14) - (√2)/7
The prime factor of 14 = 2 x 7
= (√2*7) - (√2)/7
Taking LCM
= [ 7*(√2*7) - (√2) ]/7
Taking (√2) common .
= [(√2) *( 7√7) - 1 ]/7
Thus, the equation in the simplest form is found as: [(√2) *( 7√7) - 1 ]/7.
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Complete question:
The question the solution in the simplest form: √14 - √2/7.
−n+(−3)+3n+5 I need helppp
Answer:
2n+2
Step-by-step explanation:
I hope this helps and can I have brainliest!
Two opposite numbers are 9 units away from each other. What are the numbers?
The two opposite numbers are given as follows:
-4.5 and 4.5.
How to obtain the opposite of a number?The opposite of a number is obtained exchanging just the signal of the number.
The opposite of a number x is then given as follows:
-x.
The two numbers in this problem are nine units away, hence the value of x is obtained as follows:
x - (-x) = 9.
2x = 9
x = 9/2
x = 4.5.
Hence the numbers are:
-x = -4.5 and x = 4.5.
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The two opposite numbers which are 9 units away are 4.5 and -4.5.
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two opposite numbers are 9 units away from each other.
Let x represent the number. Hence, x and -x are 9 units away. Therefore:
x - (-x) = 9
x + x = 9
2x = 9
x = 4.5
The two opposite numbers are 4.5 and -4.5.
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the sample space is 1,2,3,4,5,6 find p less than 0
Answer:
boom bam bam boom bam ba
When solving an equation, Drew's first step is shown
below. Which property justifies Drew's first step?
Original Equation:
2(x + - 4) = -3
First Step:
2x + -8 = -3
addition property of equality
commutative property of multiplication
distributive property of multiplication over addition
commutative property of addition
Submit Answer
Answer:
distributive property of multiplication over addition
Step-by-step explanation:
You select a marble without looking and then put it back. If you do this 12 times, what is the best prediction possible for the number of times you will pick a pink marble? there are 3 pink marbles
Answer:
6 times
Step-by-step explanation:
If there are total of 6 marbles and 3 are pink, then you will have a one half (or 50%) chance of picking a pink marble. Because you put the marble back each time, your chance of picking a pink marble remains the same every time.
So one half of 12 is 6. You are predicted to pick a pink marble 6/12 times.
How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?.
Degree of freedom for chi-square test for 10 categories will be 9.
What is chi- square test?
A test that evaluates how well a model matches real observed data is that the chi-square (χ²) statistic. A chi-square statistic can only be calculated with data that's random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a large enough sample.
The Formula for Chi-Square Is
χ(c)=²∑(Oₐ-Eₐ)₂/Eₐ²
where:
c=Degrees of freedom
O=Observed value(s)
E=Expected value(s)
Main Body:
Degree of freedom = total categories -1
so no. of categories= 10
Degree of freedom = 10 - 1
Hence degree of freedom = 9
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two people are scuba diving. one diver is 36 feet below the surface. the other river is 44 feet below the surface. what integers represent where the divers are with respect to the surface? which diver is deeper?
The correct integers are;
For first diver, the elevation = - 36 feet
For second diver , the elevation = - 44 feet
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
One diver is 36 feet below the surface.
And, The other diver is 44 feet below the surface.
Now,
Since, One diver is 36 feet below the surface.
And, The other diver is 44 feet below the surface.
Hence, The correct integers to represent the surface are;
For first diver, the elevation = - 36 feet
For second diver , the elevation = - 44 feet
Thus, The correct integers are;
For first diver, the elevation = - 36 feet
For second diver , the elevation = - 44 feet
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Co-ordinates of midpoint of A(2,2) and B(3,5) is ____
1.5 , 2.5
2.5 , 3.5
-2.5 , -3.5
-1.5 , -2.5
Kindly don't spam
\(\huge \sf༆ Answer ༄\)
Using section formula ~
\( \sf x = \dfrac{ mx_2 + nx_1}{m + n}\)
\( \sf y = \dfrac{ my_2 + ny_1}{m + n}\)
Midpoint divides a line into ratio of 1 : 1, therefore the values m and n are equal to 1
\( \sf x = \dfrac{ x_2+ x_1}{1 + 1}\)
\( \sf y= \dfrac{ y_2+ y_1}{1 + 1}\)
Next step :
Use the coordinates of given points to find the coordinates of mid point ~
that is ;
\({ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:x = \dfrac{2 + 3}{2} \)
\({ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:y = \dfrac{2 + 5}{2} \)
Next step :
\({ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:x = 2.5\)
\({ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:y = 3.5\)
So, the required option is ~
\( \large \sf {(2.5 \: , \: 3.5)}\)
find x to the nearest tenth
Answer:
x = 18.0
Step-by-step explanation:
You must memorize the definitions of the trig functions and then these types of problems are easy.
In your problem, sin of an angle = opposite side/hypotenuse
So, sin 51 = 14/x
x sin 51 = 14
x = 14/sin 51 = 18.0
Find the slope of a line that
goes through the two points
(-3, 6) and (2, -5).
Answer:
-2.2
Step-by-step explanation:
m = y2 - y1/ x2- x1
m = -5 - 6/ 2 --3
m = -11/5
m = -2.2
Which equation shows that y varies directly with x?
y = 0.8x
y = 0.8x/x
y = 0.8x - 5
y = x/8 + 5
Write a function for the height, T of the taller candle in terms of the number of hours it has burned, h.
The linear function for the height of the taller candle after t hours is given by:
h(t) = 18 - 3.1t.
What is the missing information?The missing information is that a 18 inch candle is burning at a rate of 3.1 inches an hour.
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, we have that:
The initial height of 18 inches is the intercept.The burning rate is the slope, as a negative, as burning means that the height of the candle is decreasing.Hence the linear function for the height of the taller candle after t hours is given by:
h(t) = 18 - 3.1t.
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Which real-world scenario involves a right triangle? a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet
Answer:
The bike path
Step-by-step explanation:
A right triangle has a hypotenuse that can be found using the formula
a^2 + b^2 = c^2 where c is the hypotenuse
The street sign is obviously not correct because a hypotenuse is longer than the sides. The bathroom tile isn't correct either because 6^2 + 8^2 = 100, or 10 after you take the square root. That leaves the bike path.
Checking to make sure:
5^2 + 12^2 = c^2
25 + 144 = √169
√169 = 13
The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
When do three given line segments form a right triangle?Any three line segments can form a right triangle only when they satisfy the Pythagoras Theorem, according to which, the square of the largest side in a right triangle is equal to the sum of the squares of the other two sides, that is, a² = b² + c², where a is the largest side, and b and c are the two other sides.
How to solve the given question?In the question, we are asked to identify from the given scenarios, the case that involves a right triangle.
We know that for three segments to be a right triangle, they need to satisfy the Pythagoras Theorem. So we check every scenario with the theorem:
A triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (12² = 144) ≠ (6² + 8² = 36 + 64 = 100).A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles: This is a right triangle as it satisfies the Pythagoras theorem as (13² = 169) ≠ (12² + 5² = 144 + 25 = 169).A triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (15² = 225) ≠ (10² + 10² = 100 + 100 = 200).A triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as all the sides are equal, so it is an equilateral triangle.∴ The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
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Find out the silk density in g/cc if the specific gravity of the fiber is given as 1.32. Provide your answer with two decimal positions and no unit.
The silk density in g/cc if the specific gravity of the fiber is given as 1.32 is given as 1.32 g/cc.
Density is the mass of a material substance per unit volume. d = M/V, where d is density, M is mass, and V is volume, is the formula for density. Grams per cubic centimetre are a typical unit of measurement for density.
For instance, whereas Earth has a density of 5.51 grammes per cubic centimetre, water has a density of 1 grammes per cubic centimetre. Another way to state density is in kilogrammes per cubic metre (in metre-kilogram-second or SI units). For instance, air weighs 1.2 pounds per cubic metre. In textbooks and manuals, the densities of typical solids, liquids, and gases are stated.
As we know that ,
Specific gravity = Density of object / density of water
1.32 = silk density / 1 g/cc
[Density of water is 1 g/cc]
Silk density = 1.32 x 1 g/cc
Silk density = 1.32 g/cc.
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Please help me solve the question from below. It is from IM3 Algebra
The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.
To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:
log₂(x - 1) = x³ - 4x
Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.
For the point (2, 0):
log₂(2 - 1) = 2³ - 4(2)
log₂(1) = 8 - 8
0 = 0
The equation holds true for the point (2, 0), so (2, 0) is one solution.
For the point (1.1187, -3.075):
log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)
log₂(0.1187) = 1.4013 - 4.4748
-3.075 = -3.0735 (approx.)
The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.
Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.
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8. Using only a compass and straightedge, find the image of A after a rotation by 180° counterclockwise about point B. Label the image A', please provide a picture of the answer
When a point is rotated, it must be rotated around a point.
See attachment for the image of the rotation about point K
How to construct triangles?We should note the following:
In order to construct triangles, you will need a protractor, a pair of compasses and a ruler. To draw the triangle, three properties must be taken into account: length, angle and shape
The given parameters are:
ΔEFG
The angle of rotation is
∅ = 180⁰
The above angle of rotation means that:
The translated triangle will be 180 degrees from ΔEFG about point K.
It also means that:
ΔEFG and ΔE'F'G' will be equidistant from point K
See attached image for ΔE'F'G'
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helpp!!! i don't understand this
solve x2=81/16
express your answer as a fraction.
Answer:
\(x = 2 \frac{1}{4} \)
Step-by-step explanation:
\( {x}^{2} = \frac{81}{16} \)
\(x > 0\)
\(x = \sqrt{ \frac{81}{16} } \)
\(x = \frac{ \sqrt{81} }{ \sqrt{16} } = \frac{9}{4} = 2 \frac{1}{4} \)
Answer:
x^2 = 81/16
x = +√(81/16) = +9/4
Desperate
please Hurry
Question Down Below
Answer:
4
Step-by-step explanation:
\(\frac{17 + 9}{4}\)
\(\frac{16}{4}\)
\(4\)
Answer:
1/2
Step-by-step explanation:
7 - 9 = 2
2/4 simplify to 1/2
(Its also hard to tell if that's supposed to be a plus sign or a minus sign so Im not completely sure if this is right)
5m<6m+6 pls help me
Let's solve your inequality step-by-step.
5m<6m+6
Step 1: Subtract 6m from both sides.
5m−6m<6m+6−6m
−m<6
Step 2: Divide both sides by -1.
−m / −1 < 6 / −1
m>−6
Answer:
m>−6
Do the following lengths form a right triangle? 6, 8, 9
Answer:
No
Step-by-step explanation:
Since it is a right angled triangle, we'll use the Pythagoras theorem to check If the lenghts are equal.
From the three lenghts given the longer side should be the hypotenus, that is 9, while the other two are the shorter sides. Therefore :
c² = a² + b²
9² = 6² + 8²
81 ≠ 100
Hence it is not a right angle triangle.
a box contains six green balls five red balls and eigth yellow balls how many ways are there of choosing ten balls from the bopx if the number of green balls chosen must be even
The number of ways are there of choosing ten balls from the box if the number of green balls must be in even numbers =15946 ways
To determine the number of ways of choosing ten balls from the box such that the number of green balls chosen is even, we need to consider the different possible combinations of green balls that could be chosen.
First, we can select 0 green balls, in which case we would need to choose all 10 balls from the 5 red and 8 yellow balls. This can be done in (5+8) choose 10 ways, which is 13 choose 10, or 286 ways.
Alternatively, we could choose 2, 4, or 6 green balls, and then select the remaining balls from the red and yellow balls. To count the number of ways of doing this, we can use the binomial coefficient formula.
The total number of ways of selecting 10 balls from the box is (6+5+8) choose 10, which is 19 choose 10, or 92,378 ways.
Therefore, the number of ways of choosing 10 balls from the box such that the number of green balls chosen is even is the sum of the number of ways of choosing 0, 2, 4, or 6 green balls, which is:
(6 choose 0)(13 choose 10) + (6 choose 2)(5 choose 8)(8 choose 0) + (6 choose 4)(5 choose 6)(8 choose 0) + (6 choose 6)(5 choose 4)*(8 choose 0)
Simplifying this expression gives a total of 15,946 ways.
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a cup is boiling water (212 f) is placed to cool in a room whose temperature remains constant at 68 f. suppose the difference between the water temperature and the room temperature is halved every 5 minutes. what is the water temperature in degrees fahrenheit , after 15 minutes
If the difference between the water temperature and the room temperature is halved every 5 minutes, then the water temperature in degrees fahrenheit, after 15 minutes 86 f
If a cup is boiling water (212 f) is placed to cool in a room whose temperature remains constant at 68 f. suppose the difference between the water temperature and the room temperature is halved every 5 minutes .
Temperature can be measured in degree celsius, degree fahrenheit and kelvin. so here the temperature measured in degree fahrenheit
Initially the difference between water and room temperature is,
212 - 68 = 144f
For every 5 minutes the difference of water and room temperature is halved,
After 5 minutes the difference is, 144/2 = 72 f
After 10 minutes the difference is, 72/2 = 36 f
After 15 minutes the difference is, 36/2 = 18 f
So the water temperature in degrees fahrenheit, after 15 minutes will be the sum of room temperature and difference between the temperatures of water and room after 15 minutes and it is given as, 18 f + 68 f = 86 f
Therefore, the water temperature in degrees fahrenheit, after 15 minutes is 86 f.
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Three people are using a random number generator to pick who goes first in their game the generator gives a random decimal number in hundredths between and including zero and 10 determine a fair plan for choosing who goes first and explain your reasoning
Random sampling is a fair and best plan for choosing who goes first.
Define random sampling.Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.
Name four types of random sampling.Simple, systematic, stratified and cluster are four types of random sampling.
In this instance, three players are choosing who goes first in their game using a random number generator. An impartial random sampling method can be used to choose participants in order to make the process fair.
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Which is the most accurate measurement for the line segment?
Answer:
Step-by-step explanation:
So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length. The length of a line segment can be measured either in metric units such as millimeters, centimeters, or customary units like feet or inches.
suppose that the heights, in inches, of orangutans are normally distributed with an unknown mean and standard deviation. the orangutan heights of 27 randomly sampled orangutans are used to estimate the mean of the population. what t-score should be used to find the 99% confidence interval for the population mean?
The t-score of 2.779 is used to find the 99% confidence interval for the population mean.
Given,
Assume that orangutans' heights, measured in inches, are regularly distributed with an unidentified mean and standard deviation. The population means are calculated using the orangutan heights of 27 orangutans that were randomly selected.
What t-score should be applied to determine the population mean's 99% confidence interval?
n = 27
confidence level = 0.99
We have to find a critical value for the confidence level of 0.99.
To find the critical value we need degrees of freedom and significance level.
df = n-1 = 27 - 1 = 26
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
For α/2 = 0.005 and df = 26, the critical value using the above table is,
t-critical value = 2.779
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At Lara' party, 4 gallon of fruit punch are hared equally among 18 friend. How much fruit punch will each peron get?
Answer: About 0.2 gallons
Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.
Each of her friend will get 4 and a half gallons of juice.
What is division?Division is one of the four main arithmetical operations by which we find the equal distribution of something.
Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.
To find how much each of them got, we will divide total amount of punch by total number friends
Amount of juice each of them gets, = 18/4 = 4.5
Hence, Each of her friend will get 4 and a half gallons of juice.
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A 6-pound bag of wheat costs $4.86 at the store. How much would 1 pound cost?
Answer: $1.23
Step-by-step explanation: to find the cost of one pound we need to divide 6 pounds by how much it costs so, 6 ÷ 4.86= 1.23.
Select all of the expressions that are equal to 8 × 35 . A. 8 × ( 30 + 5 ) B. 5 + 3 × 35 C. ( 8 × 30 ) + ( 8 × 5 ) D. ( 8 + 30 ) × ( 8 + 5 ) E. 8 × ( 20 + 15 )
Answer:
A,C,E
Step-by-step explanation:
Answer:
A,C,E
Sryy if wrong but im pretty sure its right
Step-by-step explanation:
a large hall has a capacity of 3200 seats. if the number of rows is equal to twice the number of seats in each row, then find the number of seats in each row.
The number of seats in each row of the hall is 40
Given that there are 3200 seats overall and that there are twice as many rows as there are seats in each row.
The total capacity of the hall=3200
Number of rows= 2 ( number of seats in each row)
Let's assume the number of seats in each row=x
⇒Number of rows=2x
The total capacity of the hall = (number of rows)( number of seats in each row)
The total capacity of the hall=3200
3200 = (2x) × (x)
[number of rows=2x, number of seats in each row=x]
3200 = 2\(x^{2}\)
1600=\(x^{2}\)
x=40
There are 80 rows with 40 seats in each row.
Hence, the Number of seats in each row=40 and the Number of rows=80
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