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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The sport of korfball is played by teams of eight players. Each team has fourmen and four women on it. Halliday High School has seven men and 11 women interested in playing korfball.In how many ways can they form a korfball team from their 18 interested students
Answer:
There are 11550 possible selections
Step-by-step explanation:
Given
[tex]Men = 7[/tex]
[tex]Women = 11[/tex]
Required
How many ways can 4 men and 4 women be selected
The keyword in the question is SELECTION and it means COMBINATION;
So, number of selection is:
[tex]Number = Men * Women[/tex]
[tex]Number = ^7C_4 * ^{11}C_4[/tex]
This gives
[tex]Number = \frac{7!}{(7-4)!4!} * \frac{11!}{(11-4)!4!}[/tex]
[tex]Number = \frac{7!}{3!4!} * \frac{11!}{7!4!}[/tex]
[tex]Number = \frac{7 * 6 * 5 * 4!}{3!4!} * \frac{11 * 10 * 9 * 8 * 7!}{7!4!}[/tex]
[tex]Number = \frac{7 * 6 * 5}{3!} * \frac{11 * 10 * 9 * 8}{4!}[/tex]
[tex]Number = \frac{7 * 6 * 5}{3 * 2 * 1} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = \frac{7 * 6 * 5}{6} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = 7 * 5 * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = 7 * 5 * \frac{7920}{24}[/tex]
[tex]Number = 7 * 5 * 330[/tex]
[tex]Number = 11550[/tex]
Hence;
There are 11550 possible selections
one more than seven times the difference of a number and 4 is equivalent to twice the difference of the number and 1
Answer:
the number is 5
Step-by-step explanation:
We have to find the equation to solve the problem.
Let the number be x
lets write one more than seven times the difference of a number and 4 in mathematical form
1. Difference of number and 4 will be written as x - 4
now
2. seven times the difference of a number and 4 will be written as
7*( x - 4)
3. one more than seven times the difference of a number and 4 is expressed as
1 + 7*( x - 4)
_____________________________________________
1 + 7*( x - 4) is equal to twice the difference of the number and 1
4. difference of the number and 1 is x - 1
5. twice the difference of the number and 1 is 2*(x-1)
Thus,
1 + 7*( x - 4) = 2*(x-1)
=> 1 + 7x - 28 = 2x -2
=> 7x - 27 = 2x - 2
adding 27 both sides
=> 7x - 27 + 27 = 2x - 2 + 27
=> 7x = 2x + 25
subtracting 2x from both sides
7x -2x = 2x + 25 - 2x
=> 5x = 25
dividing both side by 5
5x/5 = 25/5
x = 5
Thus, the number is 5 answer
If 26.97 ÷ 6.3 is written in long division form as long division set up where 63 is on the outside of the division symbol and 26970 is on the inside so that the divisor is written as a whole number, where should the decimal point be placed in the dividend?
Between the 2 and the 6
Between the 6 and the 9
Between the 9 and the 7
Between the 7 and the 0
The decimal point should be placed between digits 9 and 7 in the dividend. i.e the dividend becomes 269.7
Step-by-step explanation:
Dividend = 26.97 [numerator]
Divisor = 6.3 [denominator]
If 26.97 ÷ 6.3 is written in long division form so that the divisor is written as a whole number, we have the following;
(i)First convert the divisor to a whole number by multiplying by 10 i.e
6.3 x 10 = 63
(ii) Since the divisor (denominator) has been multiplied by 10, to make sure the division expression stays the same, we need to multiply the dividend(numerator) too by 10. i.e
26.97 x 10 = 269.7
(iii) The division expression then becomes;
269.7 ÷ 63
Therefore, the decimal point should be placed between digits 9 and 7 in the dividend.
can you give me Brainliest
Answer:
9 and 7
Step-by-step explanation:
26.6.3 is long division set up 63 is out of the division symbol and 26970.
In a game, the two players scored a total of 121 points. One player had 13 more points than the other player. How many points did the player with the fewer points score? Group of answer choices 67 54 108 52
Answer:
Answer is 54 . IT is the correct answer
Step-by-step explanation:
Hope it is helpful for you
Simplify (2^3)^–2 ment to put this
Answer:
[tex]\frac{1}{64}[/tex]
Step-by-step explanation:
[tex]\left(2^3\right)^{-2}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\left(2^3\right)^{-2}=2^{3\left(-2\right)}\\\\3\left(-2\right)=-6\\=2^{-6}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\2^{-6}=\frac{1}{2^6}\\\\2^6=64\\\\=\frac{1}{64}[/tex]
Answer:
1/64
Step-by-step explanation:
[tex]\left(2^3\right)^{-2}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\\\left(2^3\right)^{-2}=2^{3\left(-2\right)}\\\\3\left(-2\right)=-6\\\\=2^{-6}\\\\=\frac{1}{2^6}\\\\2^6=64\\\\=\frac{1}{64}[/tex]
What is the value of x in 3x-9
Answer:
x could be anything. you have to have a equation to solve for x.
Step-by-step explanation:
What is equal to 4 1/2 dividend by 2 2/3
Answer:
Step-by-step explanation:
9/2 / 8/3
9/2 x 3/8
27/16 = 1 13/16
Answer:
9/2 / 8/3
IS THE POSSIBLE ANSWER TO THIS EQUATION.
Solve for x.
2x/3 + 1 = 3
x = 1
x = 2
x = 3
x = 6
Answer:
The correct answer is x=3 trust me. Im good at math got 1st place on 1v1 equations in my school hope this helped.
Step-by-step explanation:
Answer:
[tex]\boxed {\tt x=3}[/tex]
Step-by-step explanation:
We want to solve for x, therefore we must isolate the variable.
We are given the equation:
[tex]\frac{2x}{3} +1=3[/tex]
1 is being added to 2x/3. The inverse of addition is subtraction. Subtract 1 from both sides of the equation.
[tex]\frac{2x}{3}+1-1=3-1[/tex]
[tex]\frac{2x}{3} =2[/tex]
2x is being divided by 3. The inverse of division is multiplication. Multiply both sides by 3.
[tex]3*\frac{2x}{3} =2*3[/tex]
[tex]2x=2*3[/tex]
[tex]2x=6[/tex]
x is being multiplied by 2. The inverse of multiplication is division. Divide both sides of the equation by 2.
[tex]\frac{2x}{2} =\frac{6}{2}[/tex]
[tex]x=\frac{6}{2}[/tex]
[tex]x=3[/tex]
The solution to the equation is x=3.
The quotient of 4 and five times t
Answer:
[tex]\frac{4}{5t}[/tex]
Step-by-step explanation:
Quotient means division, and 5 times t is 5t, as we are simplifying. Since 4 comes first in the question or sentence, 4 must be the nominator; therefore, 5t is the denominator.
The answer would then be [tex]\frac{4}{5t}[/tex].
Hope this helped!
-9 would be a part of which group(s)? *
Natural
Whole
Integer
Rational
What is the answer
Answer:
Integer, Rational
Step-by-step explanation:
Natural numbers are the basic counting numbers (1,2,3...) and does not include negatives.
Whole numbers are natural numbers with the addition of zero, and still does not include negatives.
Integers are all whole numbers and their negative counterparts, which includes -9.
Rational numbers are numbers that can be expressed as a fraction and -9 can be expresses as -9/1, so -9 is a rational number.
Hope this helps!
Need help quick Solve each equation for x. x to the power of 2= 1/100
Answer:
x=1/10
Step-by-step explanation:
x^2=1/100
x=root(1/100)
x=1/10
Answer:
[tex]x = \frac{1}{10}[/tex]
Step-by-step explanation:
If x squared gets us [tex]\frac{1}{100}[/tex], then we can create the equation [tex]x^2 = \frac{1}{100}[/tex].
To solve for x, we find the square root of both sides.
[tex]\sqrt{x^2} = \sqrt{\frac{1}{100}}[/tex]
The square root of [tex]\frac{1}{100}[/tex] is [tex]\frac{1}{10}[/tex], since [tex]10\cdot10=100[/tex].
This means [tex]x = \frac{1}{10}[/tex].
Hope this helped!
What next three numbers come in this sequence 1/4, 1/2, 3/4
Answer:
4/4, 1 1/4, 1 1/2, 1 3/4
Step-by-step explanation:
It moves by fourths so it goes 1/4, 2/4, 3/4, and so on.
Hope This Helps :)
4/4, 5/4, and 6/4 will come in the given sequence of the pattern.
What is the pattern?A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.
The hint which is present in a given pattern hides in the pattern only.
For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.
Another example is 2,4,16,256 in this pattern each term is the square of the previous term and this will become its specific pattern.
Given the pattern,
1/4, 1/2, 3/4
Now if we look then we will get to know that if we add 1/4 consecutively then the next term will come.
For example
1/4 + 1/4 = 1/2
1/4 + 1/4 + 1/4 = 3/4
So,
The next three terms will be
4/4,5/4 and 6/4.
Hence "4/4, 5/4, and 6/4 will come in the given sequence of the pattern".
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5/6 equals 1/3 plus d what does d equal
It equals 1 1/6 + d.
In other words, one and one sixth plus d.
What are the features of the quadratic function graphed in the figure? Question 14 options: A) Vertex = (–4,3), y-intercept = (5,0), x-intercepts = (0,1) and (0,5), axis of symmetry is x = –4 B) Vertex = (3,–4), y-intercept = (0,5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = 3 C) Vertex = (3,–4), y-intercepts = (1,0) and (5,0), x-intercept = (0,5), axis of symmetry is x = 3 D) Vertex = (–3,4), y-intercept = (0,5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = –3
Answer:
B
Step-by-step explanation:
The vertex is the bottom-most point of the curve located at the halfway point. The x coordinate of the point is 3, and the y coordinate is -4. The places at which the quadratic hits the x axis are at (1,0) and (5,0), and it hits the y axis at (0,5).
Vertex = (3,–4), y-intercept = (0,5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = 3. Therefore, option B is the correct answer.
We need to find the features of the quadratic function graphed in the figure.
What is a vertex in the graph?"Vertex" is a synonym for a node of a graph, i.e., one of the points on which the graph is defined and which may be connected by graph edges.
The features of the quadratic function are as follows:
The vertex is the bottom-most point of the curve located at the halfway point. The x -coordinate of the point is 3, and the y -coordinate is -4. The places at which the quadratic hits the x-axis are at (1,0) and (5,0), and it hits the y-axis at (0,5).
Therefore, option B is the correct answer.
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Solve 10-5x+1=7x+11-12
Answer:
x=1
Step-by-step explanation:
Let's solve your equation step-by-step.
10−5x+1=7x+11−12
Step 1: Simplify both sides of the equation.
10−5x+1=7x+11−12
10+−5x+1=7x+11+−12
(−5x)+(10+1)=(7x)+(11+−12)(Combine Like Terms)
−5x+11=7x+−1
−5x+11=7x−1
Step 2: Subtract 7x from both sides.
−5x+11−7x=7x−1−7x
−12x+11=−1
Step 3: Subtract 11 from both sides.
−12x+11−11=−1−11
−12x=−12
Step 4: Divide both sides by -12.
−12x
−12
=
−12
−12
x=1
Is -5/13 a rational number
Answer:
yes -5/13 is a rational number
-8=x+11/2 please help me
Answer:
Hey there!
-8=x+11/2
-16/2=x+11/2
-27/2=x
Let me know if this helps :)
Answer: -27/2 or -27
Step-by-step explanation:
You didn't use parentheses so the equation isn't clear.
I answered for both possibilities.
[tex]-8=x+\dfrac{11}{2}\\\\\\-8-\dfrac{11}{2}=x\\\\\\-\dfrac{16}{2}-\dfrac{11}{2}=x\\\\\\\large\boxed{-\dfrac{27}{2}=x}[/tex]
[tex]-8=\dfrac{x+11}{2}\\\\\\-8(2)=\dfrac{x+11}{2}(2)\\\\\\-16=x+11\\\\\\-16-11=x\\\\\\\large\boxed{-27=x}[/tex]
Which of the following are quadratic functions A. Y =5x-3/2+x^2 B. Y=x^2+5x-2 C. Y=-x+2 D. Y=x-1/x
Answer:
A and B
Step-by-step explanation:
Quadratic Equations: f(x) = a(bx - h)² + k
Quadratic equations always have a degree of 2. That means that we will always have an x² term. Of the 4 choices, only A and B offer a term of x², making them a quadratic.
Answer:
Y = 5x - 3/2 + x^2
Y = x^2 + 5x - 2
Step-by-step explanation:
The function must contain x^2.
That is have a degree of 2.
If a house is worth $125,000 and depreciates by 7.5% per year, how much is it worth in two
years?
Answer:
18750
Step-by-step explanation:
so since it's 2 years we have to double 7.5 which is 15%. Then we multiply 15 x 125,000 which is 18,750
After two years of depreciation the house would be worth approximately $106,953.
To calculate the worth of the house after two years of depreciation, you need to apply the depreciation rate for each year.
After the first year, the value of the house would decrease by 7.5%.
So, the worth of the house after one year is:
125,000 - (7.5% of 125,000)
= 125,000 - (0.075 × 125,000)
= 125,000 - 9,375
= $115,625.
Now, to find the worth of the house after the second year, you need to apply the depreciation rate again:
115,625 - (7.5% of 115,625)
= 115,625 - (0.075 × 115,625)
= 115,625 - 8,671.88
= 106,953.
So, the house would be worth approximately $106,953 after two years of depreciation.
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A 47-inch piece of steel is cut into three pieces so that the second piece is twice as
long as the first piece, and the third piece is two inches more than six times the
length of the first piece. Find the lengths of the pieces
2x
6x+2
First, find an equation that represents the total length of the piece of steel in terms of x by adding the three pieces together,
Answer:
first piece: 5 in second piece: 10 in third piece: 32 inStep-by-step explanation:
x - the length of the first piece
2x - twice the length of the first piece (the length of the second piece)
6x - six times the length of the first piece
two inches more:
6x+2 - the length of the third piece
first + second + third = 47 in {total length of the pieces of steel}
x + 2x + 6x + 2 = 47
9x + 2 = 47
9x = 45
x = 45:9
x = 5 in
first piece: 5 in
second piece: 2×5 = 10 in
third piece: 6×5 + 2 = 30 + 2 = 32 in
What values of X make the two expressions below equal?
Answer:
A
Step-by-step explanation:
they dont come out the same
In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB=AO, what is the degree measure of∠ABO?
(A) 15°
(B) 30°
(C) 45°
(D) 60°
what is the sum of 0.64 and 0.28
Answer:
0.92
Here is my work:
+1
0.64
+ 0.28
__________
0.92
(the +1 is the carrying of the one)
Hope this helps!!
The answer would be 0.92 after adding 0.64 and 0.28 and applying the arithmetic operation.
What are arithmetic operations?The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.
It is given that:
The numbers are 0.64 and 0.28
= 0.64 + 0.28
After applying arithmetic operations,
= 0.92
Thus, the answer would be 0.92 after adding 0.64 and 0.28 and applying the arithmetic operation.
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A group incoming first-year students at Major University were surveyed in order to determine the factors that influenced their decisions to choose to attend Major U. The survey revealed the following information. 55 said "great football team" (F) 51 said "excellent party reputation" (P) 61 said "it was the only place that would accept me" (O) 9 said "great football team" but didn't say "excellent party reputation" and didn't say "it was the only place that would accept me" 26 said "it was the only place that would accept me" and "great football team" and "excellent party reputation" 31 said "excellent party reputation" and "great football team" 8 said only "excellent party reputation" 4 said none of the above reasons Required:a. How many said "it was the only place that would accept me" and "excellent party reputation"? b. How many said "great football team "or "it was the only place that would accept me"? c. How many said "great football team "but no "excellent party reputation"? d. How many were surveyed?
Answer:
Step-by-step explanation:
This is a problem of SETS.
Start by listing out important data:
1. Total that said F = 55
2. Total that said P = 51
3. Total that said O = 61
4. F only = 9
5. F ∩ P ∩ O = 26 [NOTE: If you were to draw a Venn Diagram, 26 would be in the innermost circle because it comprises all three categories]
6. F ∩ P = 31
7. P only = 8
8. Students that said none of the 3 reasons = 4
QUESTIONS
1. How many said O and P? In other words, find the intersect of O and P. Find O ∩ P
2. How many said either F or O? [Answer to be gotten using a venn diagram] Find F ∪ P which translates to "F union P"
3. How many said F without saying P? [Answer to be gotten from the venn diagram as well]
4. How many students in total were surveyed? [HINT: Remember to include the 4 students that had none of the three options]
A) 12 said "it was the only place that would accept me" and "excellent party reputation"; B) 17 said "great football team" or "it was the only place that would accept me"; C) 24 said "great football team" but no "excellent party reputation"; and D) 87 students were surveyed.
Given that a group incoming first-year students at Major University were surveyed in order to determine the factors that influenced their decisions to choose to attend Major U, and the survey revealed that 55 said "great football team" (F), 51 said " excellent party reputation "(P), 61 said" it was the only place that would accept me "(O), 9 said" great football team "but didn't say" excellent party reputation "and didn't say" it was the only place that would accept me ", 26 said" it was the only place that would accept me "and" great football team "and" excellent party reputation ", 31 said" excellent party reputation "and" great football team ", 8 said only "excellent party reputation", and 4 said none of the above reasons, to determine:
A) How many said "it was the only place that would accept me" and "excellent party reputation"?
B) How many said "great football team" or "it was the only place that would accept me"?
C) How many said "great football team" but no "excellent party reputation"?
D) How many were surveyed?
The following calculations must be performed:
F = 55 (F = 9 + FP = 5 + FO = 15 + FPO = 26) = 55 - (26 + 9) = 20 - (31 - 26) = 15 = 9 + 5 + 15 + 26 = 55 // / FO = 15 /// FP = 5 P = 51 (P = 8 + PF = 5 + PO = 12 + PFO = 26) = 51 - 8 - 5 - 26 = 12 /// PO = 12 O = 61 (O = 8 + OP = 12 + OF = 15 + OPF = 26) = 61 - 12 - 15 - 26 = O = 8 None = 4 4 + 9 + 8 + 8 + 5 + 12 + 15 + 26 = X 87 = X
Therefore, A) 12 said "it was the only place that would accept me" and "excellent party reputation"; B) 17 said "great football team" or "it was the only place that would accept me"; C) 24 said "great football team" but no "excellent party reputation"; and D) 87 students were surveyed.
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if you could generate energy by fusing the hydrogen in solution a, how much of the solution would you need to generate the electrical energy used daily in a certain home? energy released by fusion of hydrogen in 1 liter of solution A = 7.6*10^10 Electrical energy used daily in a certain family home = 3*10^4
Answer:
We know that:
Energy released by fusion of hydrogen in 1 liter of solution A = 7.6x10^10 J
Energy used daily in a certain family home = 3x10^4 J
(you did not write the units, so i suppose that are the same in both cases)
Then, if x is the number of liters of solution A used, the energy produced will be:
E(x) = x*7.6x10^10 J
And we want this equal to 3x10^4
then:
E(x) = x*7.6x10^10 J = 3x10^4 j
now we solve this for x.
x = (3x10^4 j)/(7.6x10^10 j) = 3.9x10^-7
Then you need to use 3.9x10^-7 L of solution a.
Josie found a job with an annual salary of $67.3K. What is her monthly pay, rounded to the nearest dollar?
Answer:
$5,608
Step-by-step explanation:
Since there are 12 months in one year, divide her annual salary by 12.
$67,300/12 = $5,608.33 ≈ $5,608
Josie makes $5,608 per month.
Answer:
5608
Step-by-step explanation:
annual salary=$67.3k
it is annual
so
monthly salary=$67.3÷12
=$5608.33333333
rounded off top the nearest dollar= $5608
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A bicycle is traveling at 20 miles per hour.
How many feet will it cover in 25 seconds?
Round your answer to the nearest tenth of a foot.
Answer:
Distance= 73.333 feet
Step-by-step explanation:
Speed of the bicycle= 20 miles per hour
1 mile =
5280 feet
I hour= 3600 seconds
Speed in feet/seconds=( 20*5280)/(3600)
Speed in feet/second= 29.333 feet/s
Distance= speed*Time
Distance= 29.333*25
Distance= 73.333 feet
A group of 37 families will share the cost of building a new playground in their neighborhood  The playground Will cost 3,145 how much will each family have to pay
Answer:
37÷3,145
=85+5
=90-37
=53
two poles 8m and 13m high
are placed opposite to each other across a 12
metre long road find the distance
between their tops
Answer:
13 m
Step-by-step explanation:
The distance x is:
x = √12² + (13 -8)² = √144 + 25 = √169 = 13 m
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 1 + sec(x), −π 3 ≤ x ≤ π 3 , y = 3; about y = 1
Using the washer method, the volume is given by the integral
[tex]\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx[/tex]
where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.
So the volume is
[tex]\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}[/tex]