There is no Real number whose square is −16.
If
a∈R then a2≥0. So there is no real square root of −16
If i is the imaginary unit, then i
i^2=-1
and we find that:
(4i)2=2⋅i2=16⋅−1=-16
So 4i is a square root of −16.
(−4i)2=(−4)2i2=16⋅−1=−16
So, −4i is a square root of −16√−16=i√16=4i
There is no Real number whose square is −16.
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Write each logarithmic expression as a single logarithm.
log₂ 15- log₂5
According to the question, write the single logarithm of the given logarithmic expression and the expression is as follows:
Expression: [tex]log_{2}15 -log_{2}5[/tex]
Using logarithmic formula that is it divide when subtraction is there: [tex]log(a)-log(b)=log(\frac{a}{b} )[/tex].
Now, the expression can be re-written as:
Expression: [tex]log_{2}15 -log_{2}5=log_{2}(\frac{15}{5} )=log_{2}(3)[/tex]
The solution for the given expression is: [tex]log_{2}(3)[/tex].
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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For the following geometric sequence find the recursive formula.
(1, -3, 9, ...)
an-3-an-1 where a₁ = 1
Oan= (-3) -1
an=-3-an-1 where a₁ = -1
an=-1-(-3) -1
Answer: the 2nd one
Step-by-step explanation: first term (a1) is -1
recursive formula goes like this
is the nth term
is the term before that
we normally have
we see each term is multipying by -3 to get next one
so that would be
where a1=-1
the 3rd option is correct except that it is the explicit formula
so answer is 2nd one.
Answer:
45
Step-by-step explanation:
run plus duck equals to the implement
Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.
a. How much will be in the account after 3 years?
There will be $ 2249.728 in the account after 3 years .
Simple Interest : Each year interest is calculated on the principal amount ( the amount that was deposited initially ) .
Simple Interest = ( P * R * T ) / 100
P ( principal amount ) = 2000
R ( Rate of Interest ) = 4
T ( No . of years for which amount is deposited ) = 3
Substituting values
Simple Interest = ( 2000 * 4 * 1 ) / 100
= 80
Amount in account after 1 yr = 2000 + 80
= $ 2080
In second year amount will be = 2080 + [ ( 2080 * 4 * 1 ) / 100 ]
= 2080 + 83.2
= $ 2163.2
After three yrs . amount in account = 2163.2 + [ ( 2163.2 * 4 * 1 ) / 100 ]
= 2163.2 + 86.528
= $ 2249.728
Hence , there will be $ 2249.728 in the account after 3 yrs .
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In the following diagram, a is parallel to b and m is parallel n.
m<2=x^2+5x
m<4=11x+16
Note: the diagram may not be drawn to scale.
The is a parallel to b and m is parallel n.
The values of x is -2 and 8.That both values not work in geometric problem.Given that
a is parallel to b and m is parallel n.m∠2=x²+5xm∠4=11x+16To find
The value of x.That both values of x are working with this problem.So, according to the question
We have,
a is parallel to b and m is parallel n.and the value of two angles m∠2 and m∠4.
m∠2=x²+5xm∠4=11x+16From diagram we can see a is parallel to b and m is parallel to n.
So, we can say that
m∠4 = m∠3 { they are vertical congruent angles } and
m∠3 = m∠2 { they are congruent angles}
∴ m∠4 = m∠2 -------------(1)
Now, putting the values in equation(1)
So, will be get
m∠4 = m∠2 -------------(1)
11x+16 = x²+5x
x²+5x - 11x-16 = 0
x²- 6x-16 = 0
x²-8x+2x-16 = 0
x(x-8)+2(x-8) = 0
(x-8)(x+2) = 0
If (x+8) = 0
x = 8
And if (x+2) = 0
x = -2
The values of x is -2 and 8.
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What is the simplified form of each expression?
b. 11¹/² . 11¹/²
The simplified form of the expression is 11.
Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term."
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like terms
Factoring
Increasing (the opposite of factoring)
Clean out fractions by multiplying
Recognizing a pattern you have seen earlier, just like the difference between squares
Simplify the following:
sqrt(11) * sqrt(11)
sqrt(11) * sqrt(11) = 11:
Answer: 11
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Simplify each radical expression. Use absolute value symbols when needed. ∛64 x⁶
The correct answer of the given expression is 4x².
A formula is a statement containing at least two numbers/variables and at least one mathematical operation. An expression is a combination of terms combined by mathematical operations such as subtraction, addition, multiplication, and division. The terms that appear in the formula are:Constant: A constant is a fixed number.Variables: Variables are symbols that do not have fixed values.Term: A term can be a single constant, a single variable, or a combination of variables and constants combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.It is given that ∛64 x⁶
On simplifying , we get
= ∛4³(x²)³
= 4x²
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translate the equation into a sentence: 3/5 t + 2 = t
Answer:
6t
Step-by-step explanation:
Samwell bought a packet of pens. His receipt is shown above. Assume that sales tax is rounded to the nearest cent. If the 6% sales tax had been computed on the sale price instead of on the regular price, how much lower would the tax have been?
If the 6% sales tax had been computed on the sale price instead of on the regular price, the tax will be $0.04 lower.
How to calculate the difference?It should be noted that from the information, Samwell bought a packet of pens and his receipt is shown above as $2.04.
Assume that sales tax is rounded to the nearest cent, If the 6% sales tax had been computed on the sale price instead of on the regular price, the difference will be:
Sales price = $1.89
Tax = $1.89 × 0.06 = $0.11
Therefore, the difference will be:
= Former tax amount - New tac amount
= $0.15 - 0.11
= $0.04
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8y - 9y = -8 hhhhhhhh
Answer:
-y
Step-by-step explanation:
i did the test
Answer:
Y=8
Step-by-step explanation:
Move all terms that don't contain y to the right side and solve.
Elena elaboró un prisma de plástilina cuya base mide 4cm de largo por 2 cm de ancho, y su altura es de 8cm cual es el volumen del prisma que construyó? Porfis me urge
Answer:
elena
Step-by-step explanation:
Answer:
Step-by-step explanation:
The product of 15 and √2 can be expressed as
15√2. Which of these is a true statement
about the expression 15√2?
Answer:
The alternative form would be ≈ 21.213203
Step-by-step explanation:
Determine whether each logarithm is a common logarithm.
C. (log₁₀100)
Yes , the given logarithm is a common logarithmic.
A base 10 logarithm is a common logarithm.It is also known as decimal logarithm and is named after its base. It is also known as the Briggs logarithm, and the "standard logarithm", after Henry Briggs, the English mathematician who pioneered its use.Calculators usually say "logarithm", but mathematicians usually mean the natural logarithm (the logarithm with base e ≈ 2.71828), not the common logarithm when writing "logarithm". To reduce this ambiguity [tex]log_{10}x[/tex] should be written lg(x) and [tex]log_ex[/tex] must be ln(x).We have given an logarithm function which is [tex]log_{10}100[/tex] ..... (1)
As , we can see that this log has a base of 10 so , it is a common logarithm.
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Find the sum of E = [3 4 7] and the additive inverse of G = [-2 0 5].
Answer:
[ 5 4 2 ]
Step-by-step explanation:
4(5x+1)-3x
i need help solving this
Answer:
17x + 4
Step-by-step explanation:
Distribute: 4(5x + 1) - 3x
20x + 4 - 3x
Combine like terms: 20x + 4 - 3x --> 17x + 4
Hope this helps! :')
A square has an area of 90 square inches. Which two consecutive integers does a side length of the square fall between?
The two consecutive integers in which the side length of the square fall between is 9 and 10
The formula for the area of a square is given as follows:
A = (s)²
where A = area of square
s = length of side of a square
According to the question we have been given that
the area of square = 90 inch²
Now putting the required values in the formula of area we get
(s)² = 90
Taking square root both sides we get
s = √90
As 90 is not a perfect square but it lies between two perfect squares which are 81 and 100.
As √81 = 9 and √100 = 10
Now, √81 ≤ √90 ≤ √100
⇒ 9 ≤ √90 ≤ 10
Hence two consecutive integers such that the side length of the square fall between is 9 and 10
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Help how do I do this ???
Answer:
A.) 2(-2) -y=10
-4-y= 10
+4 +4
-y=14
/-1 /-1
y= -14
B.) 2(0)-y=10
-y=10
/-1 /-1
y=-10
C.) 2(2)-y=10
4-y=10
-4 -4
-y = 6
/-1 /-1
y=-6
PLEASE HELP QUICK
Use function notation to write the equation of the line.
Answer:
Step-by-step explanation:
Answer: f(x) = x
Step-by-step explanation:
Find the midpoint and distance for each:
1. A(0, 0) & B(8,4)
The midpoint between two points A(0,0) and B(8,4) is (4,2)
The distance between two points A(0,0) and B(8,4) is 4√5
To find the midpoint of two points,
We need to take an average of both the x and y components of both points
Two points A(x ₁,y₁) and B(x₂ ,y₂) are (0,0) and (8,4) respectively
Let M be the mid-point M(x, y),
x = x₁+x₂/2
= 0+8/2
= 8/2
= 4
Similarly
y = y₁+y₂/2
= 0+4/2
= 4/2
= 2
So, the midpoint of the two points A(0,0) and B(8,4) is (4,2)
To find the distance between two points,
We need to take the square root of the difference square of x and y, which is
d² = Δx² + Δy²
d = √(Δx²+Δy²)
Δx = x₂-x₁
= 8-0
= 8
Δy = y₂-y₁
= 4-0
= 4
Thus,
d = √(8²+4²)
d = √(64 + 16)
d = √80
d = 4√5
So the distance between the two points is 4√5
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3/9 a rational number
Answer:
1 : 3 and/or 3 : 9.Step-by-step explanation:
3/9 can be a rational number.
Let me show you:
3/9= 1 : 3= 3 : 9The Answer and/or 1 : 3 or 3 : 9.
In the picture below, which line segment is parallel to AD.
a. BC
b. EB
c. EH
d. CD
In the cuboid, the line segment parallel to AD is BC as they both lie on same plane and are directed in same direction.
What are parallel lines?Two lines are said to be parallel if they lie on the same plane and are directed towards the same direction.
Given in the question is a labelled cuboid.
From the definition of parallel lines, they should lie on the same plane. Therefore, we will eliminate EB and EH because they don't lie in the plane of AB. CD lies in the plane of AB, but is directed perpendicular to AB. BC is in the same plane in which AB lies and is also directed in the direction of AB.
Therefore, in the cuboid, the line segment parallel to AD is BC.
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find the compound interest 316,000 naira in 3yrs if the interest rate is 5% per annum
Answer:
the compound interest will be 365,809.5 naira.
A salt-water tank needs to contain 5 gallons of water for each 1-inch fish. If Ian has a 30-gallon tank, predict how many inch-long fish he can have.
inch-long fish
Question
Write in scientific notation.
215 × 107
Responses
2.15 × 1092.15 × 109
2.15 × 1052.15 × 105
2.15 × 1072.15 × 107
2.15 × 1014
It should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴
How to illustrate the information?It should be noted that from the information, we want to calculate 215 * 107 in scientific notation.
It should be noted that 215 = 2.15 × 10²
It should be noted that 107 = 1.07 × 10²
Therefore, calculating 215 * 107 in scientific notation will be:
= 215 × 107.
= 2.15 × 10² × 1.07 × 10²
= 2.15 × 10⁴
Therefore it should be noted that calculating 215 * 107 in scientific notation will be 2.15 × 10⁴
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When making lasagna, Mr. Singleton uses 1 pound of sausage for every 3/4 of a pound of mozzarella cheese. For a dinner party, Mr. Singleton wants to make an extra lasagna with 1 pound of mozzarella cheese. How much sausage will he need?
Using ratio we can calculate that Mr. Singleton used approximately 1.33 pounds of sausage .
A ratio demonstrates how frequently one number is found within another. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
A ratio can therefore be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value represented by this fraction. Ratios of counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of two numbers is a dimensionless number when they are measured using the same unit, which happens frequently. A rate is the product of two quantities that are divided by their respective units of measurement.He uses 1 pound sausage for every 3/4 pound of cheese.
Ratio of sausage to cheese = 1 : 0.75 = 4 : 3 .
Now he uses 1 pound of cheese therefore let he uses x pounds of sausage.
Now using ratio:
x : 1 = 4 : 3
or , x / 1 = 4 / 3
or, x = 1.333..
or, x ≈ 1.33 pounds
Hence he uses 1.33 about pounds of sausage
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In your own words, explain why solving 4 = 2x uses the division property of equality. Provide an example with your explanation
In the given particular sum we have to give reason why asolving 4 = 2x uses the division property of equality.
The reason for that why it is using division property of equality we wneed to know what is division property of equality : It states that when both side of the equation is divided by a real number other than 0 then the quotients remain same . It can be written as following : if a,b,c are real numbers where a = b , c ≠ 0 then ac = bc
for example suppose we have two breads of same size . We cut each of them into halfs and give it to our friends , if we measure the remaining portions we will see that we are left with same portions of bread . Here at initial both the breads were same and we divide it by 2 and find that they are still same.
Solving 4 = 2x using the division property because in order to get the last portion that answer we have divide the both sides by 2 to get x by itself .
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nfs anyone ig lah.cj2x ??????????????????????????????????
Answer:
huh?
Step-by-step explanation:
10 is at least the product of a number h and 5
Answer:
h =2
Step-by-step explanation:
10=h ×5
10=h5
DBS by 5
10÷5=h5÷5
h=2
The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex? What are coordinates of the fourth vertex?
The fourth coordinate for the given parallelogram are going to be (5, 7).
According to the statement
We have to find that the coordinate of the parallelogram.
So, For this purpose, we know that the
A parallelogram is a quadrilateral with opposite sides parallel
From the given information:
The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1).
Then
Now,
The slope of AB = Slope of CD
(y - 5)/(x - 11) = (1 - 3)/(8 - 2)
6(y - 5) = -2(x - 11)
⇒ 6y + 2x = 52 are going to be the primary equation.
Now,
The slope of BC = Slope of AD
[(y - 3)/(x - 2)] = [(5 - 1)/(11 - 8)]
[(y - 3)/(x - 2)] = 4/3
3(y - 3) = 4(x - 2)
⇒ 3y - 4x = 1 are the second equation.
Now, By substitution
x = 5 and y = 7
Hence, The fourth coordinate for the given parallelogram are going to be (5, 7).
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Simplify m^9m^−3??? thanks need this answer asapppp
Answer:
[tex]\sf \bf m^6[/tex]
Step-by-step explanation:
Exponent law:In exponent multiplication, if bases are same, add the powers.
[tex]\sf \boxed{\bf a^m*a^n =a^{m+n}}[/tex]
[tex]\sf m^9 * m^{-3}=m^{9 +(-3)}[/tex]
[tex]\sf = m^{6}[/tex]
Question in florida, 55% of adults live in a house, 25 of adults live in an apartment, 4.6% of adults live in a condo and the rest live on a boat. what percent of people live on a boat? write the equivalent decimal and fraction to represent the percent you solved for.
The percentage of people living on boat in Florida is 15.4%. The equivalent of this percentage to decimal is 0.154 and to fraction is 77/500.
55% live in a house, 25% live in an apartment, 4.6% in condo while the rest live on a boat. If all the percentages are summed up, they must be equal to 100%.
Let a% equals to the percentage of adult living on boat
55+25+4.6+a = 100
84.6 + a = 100
Collect like terms
a = 100 - 84.6
a = 15.4%
Therefore, the percentage of adult living on boat is 15.4%
To convert the percentage to decimal equivalence, one must divide it by 100%
15.4%/100%
= 15.4/100
= 0.154
To convert the percentage to fraction equivalence, one have to divide it by 100%
15.4%/100%
= 15.4/100
One has to make both the numerator and denominator of the fraction whole numbers, to do that one has to shift the decimal place behind the last digit, for a number without decimal point a 0 is added to the back of the number.
= 154/1000
Reducing the fraction to its lowest term, this is done by diving the numerator and denominator by a common factor
= 77/500
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