The value of the expression, 5([tex]2^{-3}[/tex]) is expressed as: 5/8.
How to Find the Value of an Expression?We are given the expression, 5([tex]2^{-3}[/tex]), to find the value of the expression, the steps explained below should be taken.
5([tex]2^{-3}[/tex]) [given expression]
Apply the negative exponents rule to evaluate the exponent in the expression
5([tex]2^{-3}[/tex]) = 5(1/2³)
5([tex]2^{-3}[/tex]) = 5/2³
Solve the exponent to eliminate the power of minus 3
5([tex]2^{-3}[/tex]) = 5/(2 × 2 × 2)
5([tex]2^{-3}[/tex]) = 5/8
Thus, the value of the expression, 5([tex]2^{-3}[/tex]) is expressed as: 5/8.
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4. Can you prove the decimal 0.142857 is a rational number? Yea
The decimal number 0.142857 is a rational .
A rational number is defined as a number which can be written in the form p/q such that p and q are co-prime.
Co-prime numbers do not have any common factors between them other than 1.Rational numbers are a subset of real numbers.Irrational numbers are numbers which can not be written in the form p/q where p and q are both integers. Examples of irrational numbers are √2 or any non-terminating non repeating decimals.The decimal number given is 0.142857 . This number can be written in the form of a fraction of 142857/1000000 .
Now the prime factorization of 142857 gives 3³ x 11 x 13 x 37 and the Prime factorization of 1000000 is given by 2⁶ × 5⁶
So we can see that there are no common factors between the two numbers. Hence they are co-prime.
∴ 0.142857 is a rational number as it can be written in the form p/q.
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Find the surface area of D
Answer:
151 cm² (i don't know what unit you were given so im going to use cm)
Step-by-step explanation:
Part One: finding the missing side (h)
h = a² = b² + c²
13² = 12² + c²
169 = 144 + c²
169 - 145 = c²
= 25
square root of 25 = c
5 = c
area of top triangular area = ½ b × h
= ½ × 12 × 5
= 30 cm²
Part Two
area of rectangle = l × b
= 12 × 8
= 96 cm²
Part Three
area of square = l × l
= 5 × 5
= 25 cm²
total surface area = (30 + 96 + 25) cm²
= 151 cm²
How many ways can you choose 2 books from a shell of 40 books
Help please asap anyone
Answer:
x= 0 (B)
Step-by-step explanation:
hope this helps
Solve each equation. Check your answers.
log (3 x+1)=2
log ( 3x + 1 ) = 2 => x = 33, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: log (3x + 1) = 2
Raising both the sides by 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(3x+1)} = 10^{2}[/tex]
=> 3x + 1 = 100 (as [tex]a^{log_a(x)} = x[/tex])
=> 3x = 99
=> x = 33
Hence, log ( 3x + 1 ) = 2 => x = 33, by properties of logarithm.
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Fabian took a taxi from his house to an airport. The taxi company charge to pick up the fee of 4.80 plus 4 per mile . The total fare was 44.80, not including the tip. how many miles was the taxi ride?
The taxi ride was 11.2 miles
The number of miles can be calculated as follows ?Fabian took a ride from his house to the airport
The taxi company charged 4.80 and 4 per miles
The total fare amount was 44.80, the fee was not inclusive
The number of miles can be calculated as follows
= 44.80/4
= 11.2
Hence the taxi ride was 11.2 miles
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a town's january high temperatures average f with a standard deviation of , while in july the mean high temperature is and the standard deviation is . in which month is it more unusual to have a day with a high temperature of ? explain.
It is more unusual to have a day with a high temperature of 55 F. A high temerature of 55 F in July is 2.2 std deviation below the mean and a high temperature of 55 F in January is only 1.889 std deviation above the mean.
What is a temperature that's too high?103 degrees or above is considered a high fever. When your temperature reaches at least 104 degrees, a potentially hazardous fever starts to develop. You require emergency medical care if your fever is 105 degrees or greater.COVID-19 symptoms can include a fever (high temperature of 38 degrees Celsius or higher). The temperature of your body is usually between 36 and 36.8 degrees Celsius. For most people, a body temperature of 38 degrees Celsius or greater is considered to be a high temperature or fever. This may indicate that you are ill.No medication is required. If you get a strong headache, stiff neck, shortness of breath, or any other unusual signs or symptoms in addition to the temperature, call your doctor right once. Take acetaminophen (Tylenol, other), ibuprofen (Advil, Motrin IB, other), or aspirin if you're feeling uncomfortable.Which month is more unusual to have a day with a high temperature?
Here z score =(X-mean)/std deviation
Therefore for temperature 55 F ; zscore for January =(55-38)/9=1.889
And for temperature 55 F ; zscore for July =(55-77)/10=-2.2
As z score reflect that 55 F is farthest from the mean of July in terms of std deviation
It is more unusual to have a day with a high temperature of 55 F. A high temperature of 55 F in July is a 2.2 std deviation below the mean, and a high temperature of 55 F in January is only a 1.889 std deviation above the mean.
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Write the equation of a line perpendicular to 6x-7y=-4 that passes through the point (-6,5).
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]6x-7y=-4\implies 6x=7y-4\implies 6x+4=7y \\\\\\ \cfrac{6x+4}{7}=y\implies \qquad \stackrel{\stackrel{m}{\downarrow }}{\cfrac{6}{7}} x+\cfrac{4}{7}=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
now, since we know that slope, let's check for a perpendicular line to it
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{6}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{6}}}[/tex]
so we're really looking for the equation of aline whose slope is -7/6 and that it passes through (-6 , 5)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{7}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -5= -\cfrac{7}{6} (x +6) \\\\\\ y-5=-\cfrac{7}{6}x-7\implies {\LARGE \begin{array}{llll} y=-\cfrac{7}{6}x-2 \end{array}}[/tex]
Answer:
Please read and try to understand it :>
Step-by-step explanation:
[tex]6x-7y=-4[/tex] is not the standard format for a straight line so you have to rearrange it:
[tex]y=\frac{6}{7} x +\frac{4}{7}[/tex]
To find the equation of a perpendicular line to the given equation, you have to first find the negative reciprocal of the gradient:
[tex]-\frac{7}{6}[/tex]
Since you want to find the equation of a perpendicular line that passes a certain point, you have to substitute the coordinates to the equation to find the y-intercept:
[tex]5=-\frac{7}{6} (-6)+c[/tex]
Solving:
[tex]5=-\frac{7}{6} (-6) +c\\ \\ 5=\frac{42}{6} +c\\ \\-\frac{42}{6} +5=c\\ \\-7+5=c\\\\ -2=c[/tex]
Final equation: [tex]y=-\frac{7}{6} x -2[/tex]
Apolline is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus
a constant fee for each hour of work. Her fee for a 5-hour job, for instance, is $42. Her fee for a
3-hour job is $28.
Let y represent Apolline's fee (in dollars) for a single job that took a hours for her to complete.
Which of the following information about the graph of the relationship is given?
Choose 1 answer:
Slope and z-intercept
Slope and y-intercept
Slope and a point that is not an intercept
z-intercept and y-intercept
y-intercept and a point that is not an intercept
Two points that are not intercepts
The given information about the graphs of the given relationship are two points that are not intercepts.
What are intercepts ?
Intercepts of a function are the points on the x-axis or y-axis where the graph of an curve or function intersects the axes.
X intercepts are the points where the graph crosses the x-axis or where y=0
Y intercepts are the points where the graph crosses the y- axis or where
x= 0
Given that Apolline is mowing lawns and her fee for a 5 hour job is $42 and her fee for a 3 hour job is $28.
Let y represents Apolline fee in dollars for a single job that took z hours for her to complete and it is given that when z = 5 hour then y =$42 and when z= 3 hour then y= $28
Therefore these are two point (y, z) = (42,5 ) and (28, 3 ) where none of the coordinates are zero which means that none of them is intercept.
Thus, the given information about the graph of the relationship are two points (42,5 ), (28, 3 ) which are not intercepts.
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The product of 3 different positive integers is 15.
What is their sum?
A. 8
B. 9
C. 15
D. 45
I think B.9 is correct
1*3*5=15
1+3+5=9
Write each expression as a single natural logarithm. ln 3-5 ln 3
Expression as a single natural logarithm is 0.01234567901.
What is natural logarithm?Given in the question an expression
ln 3 + 5 ln 3
ln 3 + ln [tex]3^{5}[/tex]
Apply multiplication rule
ln (3/[tex]3^{5}[/tex])
[tex]3^{5}[/tex] = 243
so
expression as a single natural logarithm is 0.01234567901.
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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HELP PLS ILL MARK YOU BRAINLIST
Expand each binomial.
(9-2 x)⁵
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (9 - 2x)⁵ is expanded as 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (9 - 2x)⁵
By using binomial expansion theorem, we get
(9 - 2x)⁵ = 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.
(9 - 2x)⁵ is expanded as 59049 − 65610x + 29160x² − 6480x³ + 720x⁴ − 32x⁵.
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HELP ASAP!!!!
WRITE A finite plane is a plane that has boundaries or does not extend indefinitely. The sides of the cereal box shown are finite planes. Give a
real-life example of a finite plane. Is it possible to have a real-life object that is an infinite plane? Explain your reasoning.
Answer:
trust me a shoe box or a board game box or a small container
Express each of the following values in words.
a. 0.005
b. 11.037
c. 403.608
Answer:
a. zero point zero zero 5
b. eleven point zero three seven
c. four hundred and three point six zero eight.
I really hope this helps you!!! Have a great day :).
The sides of certain right triangles are Pythagorean triples. In some such triangles, the sum of one
of the sides of the triangle plus the hypotenuse equals 49 cm. Find the sum, in cm, of the lengths of
the third sides of all triangles that satisfy this criteria.
Using the Pythagorean Theorem, the length of the third sides in a triangle that satisfy this criteria is given by:
[tex]l_2^2 = 49 - 2l_1^2[/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, considering the description of a Pythagorean triple, we have that:
[tex]h^2 + l_1^2 = 49[/tex].[tex]h^2 = 49 - l_1^2[/tex]Hence the length of the third side can be given as follows:
[tex]49 - l_1^2 = l_1^2 + l_2^2[/tex]
[tex]2l_1^2 + l_2^2 = 49[/tex]
[tex]l_2^2 = 49 - 2l_1^2[/tex]
Hence the length of the third sides in a triangle that satisfy this criteria is given by:
[tex]l_2^2 = 49 - 2l_1^2[/tex]
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1. What is 2/7 + 1/4
2. 5/9 +3/8
3. 3 5/6- 2 7/15
[Mathematical Solutions]
1.) [tex]\frac{2}{7} + \frac{1}{4} = \frac{15}{28}[/tex]
2.) [tex]\frac{5}{9} +\frac{3}{8} = \frac{67}{72}[/tex]
3.) [tex]3\frac{5}{6} - 2\frac{7}{15} =\frac{41}{30}[/tex] as the Exact Form, or [tex]1\frac{11}{30}[/tex] as the Mixed Number Form.
Hope this helps!
what property is used in 7+(4+6)=7+n
The substitution property of equality is the property used in 7+(4+6)=7+n
What is the substitution property of equality?
The substitution property of equality refers to when a value is replaced in an equation with another value that are same or equal to the first. say AA is being used in an equation and another value say BB, replaces AA in the equation. In this case we say that AA is being substituted for BB in the equation
The equation here can be compared to see that n and ( 4 + 6 ) are the pairs that are substituted so we can say that the property used here is the substitution property of equality
Given data
7+(4+6)=7+n
n = ( 4 + 6 )
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What is the next fraction in this sequence? Simplify your answer.
4/5
13/20
1/2
, 7/20
The next fraction in this sequence 4/5, 13/20, 1/2, 7/20,.... is; 1/5
What is the next term of the sequence?Arithmetic sequence are sequence that are separated by a common difference.
We are given the sequence as;
4/5, 13/20, 1/2, 7/20,....
The fractions expressed as percentage is given as:
80%, 65%, 50%, 35%...
The general formula for the nth term of the sequence is;
Tₙ = a + (n - 1)d
where;
a is first term
d is common difference
n is position of term
Thus, the fifth term is;
T₅ = 80 + (5 - 1)(-15)
T₅ = 80 + (4)(-15)
T₅ = 80 - 60
T₅ = 20
Expressing 20% as a fraction gives us;
20% = 20/100 = 1/5
Thus the next fraction in the given sequence is 1/5
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Densità di benzina= 0,75
Qual’è il volume occupato da 1kg di benzina?
Answer:
ecdqwef
Step-by-step explanation:
Mrs. Brady purchased an item on sale and described her purchase to her students. Four students each wrote an expression to represent the cash Mrs. Brady paid for the item, in dollars, given an original price of P and the use of a five dollar gift card to help pay for the purchase. Their expressions are shown in the table below.
The variable terms in all four expression indicates that the item was on 25% off.
The expressions with more terms indicate a different sale price than the expressions with fewer terms.
The constant term in each expression indicates the original price of the item Mrs. Brady purchased.
The constant term in each expression indicates that the sale price is not dependent on the original price of the item.
The constant term in each expression indicates the amount deducted when the gift card was applied to the purchase.
The variable terms in all four expressions indicate that the item was on sale of 25 percent off.
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What is a algebraic expression of “ 5 time a number”
Answer: 5x
Step-by-step explanation:
Add or subtract if possible. ∛54x³-∛16 x³
We get that when the expression ∛ 54 x³ - ∛ 16 x³ is simplified using subtraction, we get the result as ∛ 2 x.
We are given the expression:
∛ 54 x³ - ∛ 16 x³
We need to subtract to simplify the expression.
First, we know that:
54 = 2 × 3 × 3 × 3
16 = 2 × 2 × 2 × 2
So,
∛ 54 x³ = 3 ∛2 x
∛ 16 x³ = 2 ∛2 x
So, we get the expression as:
3 ∛ 2 x - 2 ∛ 2 x
Combining the like terms, we get that:
= ∛ 2 x
Therefore, we get that when the expression ∛ 54 x³ - ∛ 16 x³ is simplified using subtraction, we get the result as ∛ 2 x.
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Write each expression as a single logarithm. Identify any properties used. log x-log y
log x-log y = log ( x/y) we use this properties Quotient in the equation.
A logarithm is defined simply?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.How does exponential growth utilise e?
e is the constant growth rate that all processes that are growing continuously share. With e, you may compare a simple growth rate—where all change occurs at the end of the year—with a compound, continuous growth rate, where growth occurs once per nanosecond or quicker.You use this properties Quotient in the equation -
log x-log y = log ( x/y)
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A car wash washes 68 vehicles in an 8 hour day.At this rate,how many vehicles are washed in 1 hour
Answer: 8 and a half vehicles (if no halves are allowed just 8)
Step-by-step explanation:
We divide 68 vehicles by 8 hours bringing us to 8 and a half vehicles an hour
Evaluate the function for the given value
f(x) = 6x − 6 use x = −6
-6
Your answer
1 point
value
Answer:
y=-42 or f(x)=-42
Step-by-step explanation:
1. Substitute x for -6. Equation: f(x)=6(-6) + -6
2. Turn f(x) into y. Equation: y=6(-6) + -6
3. Multiply 6 and -6. Equation: y=-36 + -6
4. Add -36 and -6. Equation: y=-42 or f(x)=-42
Find the inverse of each function. Is the inverse a function? f(x)=5x³+1
The inverse of the function f( x ) = 5x³ + 1 is y = ∛ [ ( x - 1) / 5 ].
A statement, rule, or regulation that establishes the relationship between an independent variable and a dependent variable is known as a function.
A function that can reverse into another function is known as an inverse function or anti-function.
Consider the function,
f(x) = 5 x³ + 1
Now, let y = 5 x³ + 1
Now, swapping the variables x, y we get;
x = 5 y³ + 1
Subtracting 1 from each side of the equation,
5 y³ + 1 - 1 = x - 1
5 y³ = x - 1
Dividing both sides by 5,
5 y³ / 5 = ( x - 1) / 5
y³ = ( x - 1) / 5
Now, take cube root on both sides of the equation,
∛ (y³) = ∛ [ ( x - 1) / 5 ]
y = ∛ [ ( x - 1) / 5 ]
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answer please scooby doO!
Answer: 1st and 3rd
Step-by-step explanation:
Answer:
A) True, B) False, C) True, D) False.
Step-by-step explanation:
A) True. Every graph on a plane is the set of solutions to the equation that defines it.
B) False. Refer to the answer for question A.
C) To know whether this is true, we should substitute [tex]x = 1[/tex] to the function's equation. If we get that [tex]y = 2[/tex], then (1, 2) lies on the graph as its a solution of the equation.
[tex]y = -2(1) + 4 \to -2 + 4 \to 2[/tex]
y = 2, therefore, (1, 2) lies on the graph. True.
D) Same here as C. Now, we should substitute [tex]x = 0[/tex] instead.
[tex]y = -2(0) + 4 \to 0 + 4 \to 4[/tex]
y = 4, therefore, (0, 2) does not lie on the graph. False.
Solve the following equation for B.
h=m+1/5rB
Solving for B in the equation gives B = 5( h - m) / r
What is subject of formula?
A subject of formula can be defined as a variable that is expressed in terms of other variables in an equation or expression.
It is also known as the variable that is being worked out in an equation or given expression.
From the information given, we have the equation;
h = m + 1/5rB
To make 'B' the subject of formula, we have to take the following crucial steps;
Take 'm' over the equality sign
h - m = rB/ 5
Now, cross multiply
5( h - m) = rB
To make 'B' stand alone, divide both sides by r
B = 5( h - m) / r
Thus, solving for B in the equation gives B = 5( h - m) / r
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please help ASAP!!!!…
From the given situation involving two parallel lines cut by transversal, we have that:
1) The value of x is of x = 20º.
2) Jenna is correct, because 3x and 120º are alternate interior angles.
What is the value of x in item 1?We have to consider two things, as follows:
Angle 6 is supplementary with of the angle of 5x + 35º, hence they add to 180º.Angle 6 and 45º are vertical, hence they are congruent, that is, m<6 = 45º.Thus:
5x + 35 + m<6 = 180º
5x + 80 = 180
5x = 100
x = 100/5
x = 20º.
The value of x is of x = 20º.
Who is correct in item 2?To solve item 2, we have to consider that 3x and 120º are alternate interior angles, hence they are congruent, and:
3x = 120º
x = 120/3
x = 40º.
Hence:
Jenna is correct, because 3x and 120º are alternate interior angles.
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