It is known that 1.4< square root of 2 <1.5. Find all possible values of the expression 2-square root of 2. How do I find out the second inequality?
Answer:
0.5<2-√2<0.6
Step-by-step explanation:
The original inequality states that 1.4<√2<1.5
For the second inequality, you can think of 2-√2 as 2+(-√2).
Because of the "properties of inequalities", we know that when a positive inequality is being turned into a negative, the numbers need to swap and become negative. So, the original inequality becomes -1.5<-√2<-1.4. (Notice how the √2 becomes negative, too). This makes sense because -1.5 is less than -1.4.
Using our new inequality, we can solve the problem. Instead of 2+(-√2), we are going to switch "-√2" with both possibilities of -1.5 and -1.6. For -1.5, we would get 2+(-1.5), or 0.5. For -1.4, we would get 2+(-1.4), or 0.6.
Now, we insert the new numbers into the equation _<2-√2<_. The 0.5 would take the original equation's "1.4" place, and 0.6 would take 1.5's. In the end, you'd get 0.5<2-√2<0.6. All possible values of 2-√2 would be between 0.5 and 0.6.
Hope this helped!
The possible values of 2-√2 will be in the range is 0.6 > 2 -√2 > 0.5.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have the given statement that 1.4 < √2 < 1.5
We have to determine the possible values of 2-√2 as 2+(-√2).
According to the question,
⇒ 1.4 < √2 < 1.5
Multiply by a minus sign (-) in the inequality
⇒ -1.4 > -√2 > -1.5
Adding 2 in the inequality
⇒ 2-1.4 > 2 -√2 > 2-1.5
⇒ 0.6 > 2 -√2 > 0.5
Hence, the possible values of 2-√2 will be in the range is 0.6 > 2 -√2 > 0.5.
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please i need help rn
Answer:
here u go
Step-by-step explanation:
16 /5 =3 and 1 over 53 1 /5=3.2
A function is defined by f(x) =6x+1.5. What is f(2.5)?
Answer:
16.5
Step-by-step explanation:
So we have the function:
[tex]f(x)=6x+1.5[/tex]
To find f(2.5), substitute 2.5 for x. Thus:
[tex]f(2.5)=6(2.5)+1.5[/tex]
Multiply:
[tex]f(2.5)=15+1.5[/tex]
Add:
[tex]f(2.5)=16.5[/tex]
And we're done!
Mrs. Krueger created the expression 4(h + 11) - 15 to estimate the number of hours each her students need to study each way to earn a certain grade average according to the expression how many hours per week does Lindsay needs to study if she wants to have an average of at least 90
Answer:
15.25 hours atleast.
Step-by-step explanation:
First rewrite the expression so it helps us find the answer.
4(h+11)-15=90
Distribute -> Substract from both sides -> Divide 61/4
[tex]4(h+11)-15=90\\4h+44-15=90\\4h+29=90\\4h=61\\61/4= 15.25h[/tex]
7. Three cubes of edges x cm , 6 cm, and 8 cm are melted and recast into a bigger cube of
edge 12 cm , find the value of x?
Answer:
10 cm³
Step-by-step explanation:
Volume of a cube = (Side)³
Volume of bigger cube = (12)³
(12)³ = 1728 cm³
Volume of three cubes = (x)³ + (6)³ + (8)³ = 1728
(x)³ = 1728 - (6)³ - (8)³
(x)³ = 1000
x = ∛1000
x = 10 cm³
Given: mAngleTRV = 60° mAngleTRS = (4x)° Prove: x = 30 3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees. What is the missing reason in step 3?
Answer:
the answer is angle addition postulate
Step-by-step explanation:
Given the proof for x = 30, the missing reason in step 3 is: angle addition postulate
What is Angle Addition Postulate?Angle addition postulate states that if D is the interior of ∠ABC, therefore, the sum of the smaller angles equals the sum of the larger angle, which is: m∠ABD + m∠DBC = m∠ABC.
The given diagram as shown in the image attached below alongside the proof of x = 30.
T is the interior of straight angle ∠VRS.
m∠VRS = 180° (straight line angle)
Therefore, based on the angle addition postulate, m∠TRS + m∠TRV = 180°.
Thus, given the proof for x = 30, the missing reason in step 3 is: angle addition postulateLearn more about angle addition postulate on:
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A set of three scores consists of the values 3, 7, and 2. Σ2X-2 = 22 E(x-1)2 = -41 Hint: Remember to follow the order of mathematical operations.
Answer:
Step-by-step explanation:
Given the following scores 3, 7 and 2, we are to find the expression Σ2X-2 and Σ(X-1)²
The value of X's are 3, 7 and 2. Substituting the values we will have;
Σ2X-2 = [2(3)+2(7)+2(2)] - 2
Σ2X-2 = (6+14+4) - 2
Σ2X-2 = 24-2
Σ2X-2 = 22
For Σ(X-1)²
Σ(X-1)² = (3-1)²+ (7-1)² + (2-1)²
Σ(X-1)² = 2²+6²+1²
Σ(X-1)² = 4+ 36+1
Σ(X-1)² = 41
Σ2X - 2 = 22 , Σ( X - 1 )^2 = 41
Given : X = 3 , 7 , 2
Σ2X is calculated in the image = 24
Σ2X - 2 = 24 - 2 = 22
Σ( X - 1 )^2 calculation is shown, it is = 41
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The topic is about operations on functions: composition and transformation
Answer:
5, 1, 5, 1.
Step-by-step explanation:
take it one step at a time.
for the first one f(g(1))
first do whats inside of the parenthesis.
> g(1), go to g(x) graph, go to x= 1 and your y-value is your new value (3)
> your new equation is now f(3)
→ go to f(x) graph, go to x= 3, your y-value is 5. Your final answer is 5.
Seven times the sum of a number and 2 equals 5
Answer: The number is -9/7
Step-by-step explanation:
The statement can be expressed by the equation
7(n + 2) = 5 where n is the number
Now solve for n
7(n+2) = 5 distribute on the left side
7n + 14 = 5
-14 -14
7n = - 9
n = -9 /7
Which expressions are equal to z+(z+6)
Answer:
2(z+3)
Step-by-step explanation:
2z+6
take out the 2: 2(z+3)
0.05 is 1 tenth the value of
33% 1/3 5/3 .6
which number doesn’t belong?
PLEASE HELPPP
Answer:
5/3 does'nt belong.
Step-by-step explanation:
think about it.
33% = 1/3 = .6666666 they are all the same. 5/3 doesnt belong
The number 5/3 does not belong.
what is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Given number:
33%
Now, we can write the percentage as
33/100
≈1/3
on converting the fraction in decimal
=0.666...
Hence, the which does not belong this pattern is 5/3.
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Calculate the speed of a car that traveled 425 miles in 6 hours.
Answer:
70.833333
Step-by-step explanation:
Divide 425 by 6
Step-by-step explanation:
drugs dgxln fix ezutxohcpuvpucitzkyxoh pi
the slope of the line that passes through the point (2 4) and (3 8) is
Answer:
y - 4 = 4(x - 2)
Step-by-step explanation:
Please write these points as (2, 4) and (3, 8) (use commas and parentheses).
As we move from (2, 4) to (3, 8), x increases by 1 and y increases by 4. Thus, the slope is m = rise/run = 4/1 = 4
and the equation of the line through these two points (in point-slope form) is
y - 4 = 4(x - 2)
The slope of the line that passes through the point (2 4) and (3 8) is 4
The formula for calculating the equation of a line passing through the point (x1, y1) and (x2, y2) is expressed using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the coordinate points (2 4) and (3 8), the slope is expressed as:
[tex]m=\frac{8-4}{3-2}\\m=\frac{4}{1}\\m = 4[/tex]
Hence the slope of the line that passes through the point (2 4) and (3 8) is 4
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Write the following numbers in scientific notation. (a) 291.7 (b) 0.0960
Answer:
(a)
291.7 = 2.917*10²
291.7 = 2917*10⁻³
(b)
0.0960 = 9.6*10⁻²
0.0960 = 96*10⁻³
1 liter is equivalent to a volume of 1000 cm3 (the same as 10 cm x 10 cm x 10 cm). If a beaker has a cross-section the size of the circle below, and a height of 10 cm, what is its volume
Answer:
[tex]Volume = \frac{220}{7}r^2[/tex]
Step-by-step explanation:
Given
Height = 10cm
See Attachment for complete question
Required
Determine the volume of the circle
The volume is calculated as thus;
[tex]Volume = \pi r^2h[/tex]
Take [tex]\pi[/tex] as [tex]\frac{22}{7}[/tex]
So; Volume becomes
[tex]Volume = \frac{22}{7} * r^2 * h[/tex]
Substitute 10 for h
[tex]Volume = \frac{22}{7} * r^2 * 10[/tex]
[tex]Volume = \frac{220}{7} * r^2[/tex]
Since, the value of the radius is not given;
The volume of the circle is:
[tex]Volume = \frac{220}{7}r^2[/tex]
The demand for a certain company's e-reader can be approximated byq =720p− 1 million units per year (60 ≤ p ≤ 400),where p is the price charged by the company. Assume that the company is prepared to supplyq = 0.018p − 1 million units per year (60 ≤ p ≤ 400)at a price of $p per unit.Calculate the equilibrium price and equilibrium demand.equilibrium price$equilibrium demand million e-readers per year.
Answer:
Equilibrium price P = 200 dollars
equilibrium demand of million e-readers per yer = 2.6 mi/yr
Step-by-step explanation:
Given that;
q = 720/p - 1 million units per year { 60 ≤ p ≤ 400 }
supply q = 0.018p − 1 million units per year (60 ≤ p ≤ 400)
we substitute
720/p - 1 = 0.018p − 1
720/p = 0.018p
720 = 0.018p^2
p^2 = 720/0.018 = 40000
p = sqrt(40000)
p = 200
substitute value of p
q = 0.018(200) − 1
q = 3.6 - 1 = 2.6
Therefore Equilibrium price P = 200 dollars
equilibrium demand of million e-readers per yer = 2.6 mi/yr
In a deck of 52 playing cards, are the odds favorable that you will draw a heart od a diamond?
Answer:
So theres 13 cards of heart and diamond
so 26 cards out of 52,
26/52
if ef bisects aed, aef=4x+3 and fed=7x-33 find m
Answer:
aef = fed = 51 degrees,
and the full angle aed = 102 degrees
Step-by-step explanation:
If ef bisects the angle aed, then the two angles it defines: aef and fed, must measure the same.
Therefore we can asume that aef = fed which numerically means:
4 x + 3 = 7 x - 33
so we solve for x:
33 + 3 = 7 x - 4 x
36 = 3 x
x = 36/3
x = 12 degrees
That means that the half angle aef measures:
aef = 4 x + 3 = 4 (12) + 3 = 48 + 3 = 51 degrees
Then we have that aef = fed = 51 degrees,
and the full angle aed = 51 + 51 = 102 degrees
list all number sets that apply to each number
Answer:
45
2
03
16
26
224
Step-by-step explanation:
Which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?
1. vertical translation
2. horizontal translation
3. reflection over the x-axis
4. reflection over the y-axis
Answer:
A. Vertical translation
Step-by-step explanation:
Edge test
is n/2 a rational or irrational number
Answer:
it a rational number
Step-by-step explanation:
there is always an odd exponent. So it could not have been made by squaring a rational number! This means that the value that was squared to make 2 (ie the square root of 2) cannot be a rational number. In other words, the square root of 2 is irrational.
what do i do i need help please ❤️♀️✨
I need help no one helps me never
Solve the linear equation. x - 3 = 7 x = ?
Answer: x = 10
Step-by-step explanation: You add 3 + 7 which equals 10. 10 minus 3 is 7.
3-2(x-4)= -5x-7 just the answer, also if you could can you please include the first step you would do in this equation.
Answer:
x = -4/3
Step-by-step explanation:
First, expand.
3 - 2(x - 4) = -5x - 7
Then, combine like factors.
3 - 2x + 8 = -5x + 7
11 - 2x = -5x + 7
Add 5x to both sides.
(11 - 2x) + 5x = (-5x + 7) + 5x
11 + 3x = 7
Subtract 11 from both sides.
(11 + 3x) - 11 = 7 - 11
3x = -4
Divide both sides by 3
(3x)/3 = -4/3
x = -4/3
Answer:
x = -6
Step-by-step explanation:
3-2(x-4)= -5x-7
Distribute
3 -2x +8 = -5x -7
Combine like terms
11 -2x = -5x -7
Add 5x to each side
11 -2x+5x = -5x-7+5x
11+3x = -7
Subtract 11 from each side
11+3x-11 = -7-11
3x = -18
Divide by 3
3x/3 = -18/3
x = -6
Many farmers use the height of their corn on July 4th as an indication of the entire crop. In a random sample of corn-stalk heights on July 4th in Columbia County, x⎯⎯⎯x = 25.6, s = 0.9 inch, and a histogram of the observations was bell-shaped.
Fill in the blank. (Give your answer to two decimal places.)
The approximate proportion of observations that lies between 23.8 and 27.4 is __
Answer:
0.9544
Step-by-step explanation:
Given that, his bell shapes and hence follows a normal distribution.
Mean (x) = 25.6 ; standard deviation (s) = 0.9
Approximate proportion of observation that lies between 23.8 and 27.4
Taking the Zscores of both values :
X - mean / standard deviation
(23.8 - 25. 6) / 0.9 = - 1.8/0.9 = - 2
P(Z < - 2) = 0.0228
Also;
(27.4 - 25.6) / 0.9 = 1.8 / 0.9 = 2
P(Z> 2) = 0.9772
0.9772 - 0.0228 = 0.9544
Time and Tide is the name of the question. A ship is at anchor. Over its side hangs a rope ladder with rungs a foot apart. The tide rises at the rate of 8 inches per hour. At the end of six hours how much of the rope ladder will remain above water, assuming that 8 feet were above water when the tide began to rise? Using complete sentences explain how you determined your answer.
Answer:
Hey there!
First, I converted 8 feet to inches. I knew that 12 inches were in a foot, so 96 inches are in 8 feet. If the water rises at 8 inches per hour, at the end of 6 hours, the water will rise 48 inches. Finally, subtracting 48 from 96, we get that there are 48 inches of rope above the water's surface.
Let me know if this helps :)
how do I make points
Answer:
by answering others ppl questions
Answer:
you make points by answering to others peoples questions. :)
A linear correlation scatterplot is also a direct proportionality. True or False
Answer: False
Step-by-step explanation: A linear correlation scatter plot is one which is aimed at establishing a graphical view of the relationship between two quantitative variables. A linear correlation scatter plot could either be positive which is depicted by a positive gradient which infers direct proportionality, this means an increase in variable A results in increase in variable B while a decrease in variable A results in decrease in variable B. Similarly, it could also exhibit a negative gradient which infers a inverse proportionality meaning a decrease in one variable leads to increase of the other and vice-versa. Hence, a linear scatterplot does not only exhibit direct proportionality.