Solving the Question
We're given:
2, 8, 14, ...First, we must identify the pattern:
The first term is 2. Add 6 each time to get the next term.This is our written pattern statement. To convert this into an expression, we can use the following format:
[tex]mn+b[/tex]
m is the number that we add each timeb is our zeroth term value, the number that comes prior the first term in the given patternn is the term numberIn this case, m is 6, and b is 2 - 6, or -4. Plug these numbers into the expression:
[tex]6n+(-4)\\6n-4[/tex]
To find the 42nd term, plug in 42 as n:
[tex]6n-4\\6(42)-4\\248[/tex]
AnswerThe 42nd term is 248.
a₄₂= 248.
An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence
This is an arithmetic sequence since there is a common difference between each term. In this case, adding
6
to the previous term in the sequence gives the next term. In other words,
aₙ= a₁+ d (n-1)
substitute in the values of a₁=2 and d=6
simplify each term
aₙ= 6n-4
substitute and calculate you will get
a₄₂= 248.
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Ahmad tutors math. For each hour that he tutors, he earns 30 dollars. His earnings, E (in dollars), after tutoring for h hours is given by the following.
E=30h
How much does Ahmad earn if he tutors for 5 hours?
Match the inequality with its line graph. 1. - x - 5 ≤ -2 2. 6 + x ≤ 3 3. x - 4 < -7 4. 2 x > -6
The inequalities and their graphs are;
1) -x - 5 ≤ -2 is represented by the third graph
2) 6 + x ≤ 3 is represented by the fourth graph
3) x - 4 < -7 is represented by the second graph
4) 2x > -6 is represented by the first graph
How to Interpret Inequality Line Graphs?
1) We are given the inequality;
-x - 5 ≤ -2
Rearranging gives us;
-x ≤ -2 + 5
- x ≤ 3
Divide both sides by -1 to get;
x ≥ -3
The graph must be a closed circle starting at -3 and pointing to the right.
It is the third graph in the link at the end of this answers.
2) We are given the inequality; 6 + x ≤ 3
Rearranging gives;
x ≤ -6 + 3
x ≤ -3
The graph must be a closed circle starting at -3 and pointing to the left. Thus, it is the fourth graph.
3) We are given the inequality; x - 4 < -7
Rearranging gives us;
x < -7 + 4
x < -3
The graph must be an open circle starting at -3 and pointing to the left.
Thus, it is the second graph.
4) We are given the Inequality; 2x > -6
Divide both sides by 2 to get;
x > -6/2
x > -3
It must be a graph with an open circle starting at -3 and then to the right.
Thus, it is the first graph as seen in the attached link
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Nicole and Daniel are splitting a pizza. Nicole eats 1/4 of the pizza and Daniel eats 2/3 of it. How much pizza is left? Write an equation to represent this situation.
The number of pizza left is 1/12
How to calculate the number of pizza left ?
Nicole and Daniel are splitting a pizza
Nicole gets 1/4 of the pizza
Daniel gets 2/3 of the pizza
let 1 represent the total amount of pizza
1- (1/4 + 2/3)
1- 11/12
= 1/12
Hence 1/12 of the pizza is left from the total amount of pizza
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find the constant of proportionality for the relationship plotted, on the graph.
please help, giving branliest. :))
The constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250
How to find the constant of proportionality for the relationship plotted, on the graph?The graph is the given parameter
On the graph, we have the following point
(x, y) = (2, 50)
The constant of proportionality for the relationship plotted, on the graph is represented with k, and the formula is
k = y/x
This gives
k = 50/2
Evaluate
k = 25
Substitute k = 25 in k = y/x
25 = y/x
When x = 10. we have
25 = y/10
This gives
y = 250
Hence, the constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250
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someone please tell me what the equation for this graph is sorry if it’s hard to see
Answer: y=3(x+3)^3-1
Step-by-step explanation:
A bag contains 11 counters five of the count as a white account is taken out of the bag at random and not replaced a second counter is taken out of the bag at random calculate the probability that only one of the counters is white
The probability that only one of the counter is white is 6/11.
So we know that there are 11 counters, 5 of them are white, 6 are not white.
Let's assume that first we take the white one, the probability is equal to the quotient between the number of white counters and the total number of counters, so we have:
p = 5/11
Now for the second one, we don't want to take a white one, so here the probability is equal to the quotient between the number of non-white counters (6) and the total number of counters (now there are 10, because we took one)
q = 6/10
The joint probability is the product of the individual probabilities, this is:
P = p*q
And, also notice that there are 2 permutations:
first white, then non-white.first non-white, then white.So we need to add a factor 2.
P = 2*p*q = 2*(5/11)*(6/10) = 6/11
The probability is 6/11
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a survey was conducted to study the relationship between the annual income of a family and the amount of money the family spends on entertainment. data were collected from a random sample of 280 families from a certain metropolitan area.
The scatterplot is the correct answer.
A scatter plot uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.
The dots in a scatter plot not only report the values of individual data points but also patterns when the data are taken as a whole.
Identification of correlational relationships is common with scatter plots. In these cases, we want to know, if we were given a particular horizontal value, what a good prediction would be for the vertical value.
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Solve each equation. 3/2log₂4- 1/2log₂x=3
The value of x using the properties of logarithm is 1.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation for x
We are given a logarithmic expression: 3/2 log₂4 - ½ log₂x = 3
Using properties of the logarithm, we have
3/2 log₂4 - ½ log₂x = 3
3/2 (2 log 2 / log 2) - ½ (log x / log 2) = 3
3 - ½ (log x / log 2) = 3
½ (log x / log 2) = 0
log x = 0
log x = log 1
On applying exponent both sides, we get,
x = 1
Hence, the value of x is 1.
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The measure of each of the
congruent angles of an isosceles
triangle is 9 less than 4 times the
vertex angle. Find the measures of all
the angles in the triangle.
Answer:
22°, 79° and 79°
Step-by-step explanation:
Let x be the vertex angle and y each of the congruent angles.
The sum of all angles =180°
So x + y + y = 180
x + 2y = 180 ·········· Equation (1)
Given "The measure of each of the congruent angles of an isosceles triangle is 9 less than 4 times the vertex angle", the equation is
y = 4x - 9
Substitute for y in terms of x in equation 1
⇒ x + 2(4x - 9) = 180
⇒ x + 8x - 18 = 180
⇒ 9x - 18 = 180
⇒ 9x = 180 + 18
⇒ 9x = 198
⇒ x = 198/9 = 22
So vertex angle is 22°
Substituting for x in Equation 1:
22 + 2y = 180
2y = 180 - 22
2y = 158
y = 158/2
y = 79°
So each congruent angle is 79°
Simplify each number. 100⁻³/₂
[tex]100^{\frac{-3}{ 2} }[/tex] can be simplified into 0.001.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 100 = 5 x 5 x 2 x 2 = [tex]10^{2}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e.,[tex](x^{m} )^{n} = x^{mn}[/tex]
According to the given condition,
∴ [tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2})^{\frac{-3}{2} }[/tex]
Applying the law of indices mentioned above,
[tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2 X}^{\frac{-3}{2} })[/tex]
= [tex]10^{-3}[/tex] = 0.001.
Thus, [tex]100^{\frac{-3}{2} }[/tex] can be simplified into 0.001.
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A company sold 1 million shares of common stock at $10 book value and the stock price then rose to $25 per share on the new york stock exchange. what amount of equity capital did the firm raise from this sale
The equity capital the firm raise from this sale is $15 million.
Equity capital refers to the funds paid into a business by investors in exchange for common or preferred stock. It can be solved by subtracting the total liabilities from the total assets.
Equity Capital = Total Assets – Total Liabilities
If a company sold 1 million shares of common stock at $10 book value, then its total liabilities is $10 million.
If the stock price then rose to $25 per share on the New York stock exchange, then the total assets is $25 million.
Equity Capital = Total Assets – Total Liabilities
Equity Capital = $25 million – $10 million
Equity Capital = $15 million
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Manipulating Positive Rational Numbers LC) What is 6 over 8 written as a decimal? 0.6 0.75 1.3 4.8
Answer:
0.75
Step-by-step explanation:
[tex]\frac{6}{8}[/tex] = 6 ÷ 8 = 0.75
Translating English to Algebra
The translations for each sentence are listed below:
x + 5 = 2y - 3 = 96 - x = y5 · x - 6 = - y2 · t < y5 · x · y = zx + y < x - y2 · (a + b) = 153 · (x - 5) > yHow to translate English sentences into algebraic language
Herein we find nine sentences that must be translated in terms of algebraic expressions, that is, combinations of constants, variables and operators. Now we proceed to present the result of each case:
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Alan is driving on a highway. He uses one gallon of gas every 25 miles he drives. The distance, D (in
miles), he travels on g gallons of gas is given by the following function.
D(g)=25g
How far does Alan drive if he uses 4 gallons of gas?
Alan drive if he uses 4 gallons of gas is 75 miles distance
The following function calculates the distance (in miles) he travels on gallons of gas. D(g)=25g
Where D(g) is the distance traveled in gallons.
and g denoted the quantity of gasoline used
We are asked to calculate the distance traveled in three gallons of gasoline. To do this, we will set the value of g to 3 in our function.
D(3)=25 x 3 = 75
As a result, Chris's automobile traveled 75 miles on three gallons of petrol.
The length of the line segment connecting two places, for example, is the distance between them. a two-dimensional plane, which may also be in a three-dimensional plane. In coordinate geometry, there are several forms of distance formulae.
Distance between two locations in a two-dimensional plane
Distance between two locations in a three-dimensional plane
Distance in 2D from a point to a line
2D distance between two parallel lines
3D distance from a point to a line
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Which equation represents inverse variation between x and y ?
(a) x=y/z (b) x=-15 z/y (c) z=-15 y/x (d) x z=5 y
The option d ,that is , x= 5y is the equation that represents inverse variation between x and y.
What is inverse variation ?1: A mathematical connection between two variables that can be described by an equation in which the sum of their products equals a fixed value.
2: an expression of inverse variation by an equation or function; contrast with direct variation.
CALCULATIONIn an inverse variation, the inverse percentage establishes the link between two quantities or variables. The inverse relationship between two quantities, x and y, is provided by:
x ∝ 1/y
or
x = k/y
xy = k
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The lengths of the sides of a triangle are 7.6 cm, 8.2cm , and 5.2cm . Find the measure of the largest angle.
Answer:
arccos(439/1976)
Step-by-step explanation:
The largest angle is opposite the longest side. So, by the Law of Cosines, if we let this angle be x,
[tex]x=\arccos \left(\frac{7.6^2 + 5.2^2 - 8.2^2}{2(7.6)(5.2)} \right) \\ \\ =\arccos(439/1976)[/tex]
Nethanel Stück receives a monthly income of $600 from a pension and some from Social Security. His wife, Lisha, also receives a monthly income from Social Security, but only 70 percent of Nethanel's amount. If their monthly income is $1,800 per month, how much is Nethanel's monthly Social Security benefit?
The Nethanel's monthly Social Security benefit is :$ 705.88
What makes the household monthly income of $1,800?
The household monthly income of $1,800 comprises the monthly income and social security of Nethanel Stuck and his wife monthly income from social security which is 70% of Nethanel's
total income=$600+x+(70%*x)
total income=$1,800
Nethanel social security=x
wife's monthly income=70%*x=0.70x
1800=600+x+0.70x
1800-600=1.70x
1200=1.70x
x=1200/1.70
x=Nethanel's monthly Social Security benefit=$ 705.88
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8+(2)((-2)-3) jjjjjjjjjj
To simplify the expression, which exponent property should you apply first?
The exponent property which must be applied first to simplify the expression as given in the task content is; The power of a power property.
Which exponent property should be applied first in a bid to simplify the expression as given in the task content?It follows from the task content that the exponent property which must be applied first in a bid to simplify the expression be determined.
Since the expression given is;
(4y)³ • (2g)² • y • g
Consequently, to solve the parentheses, the power of a power property must be used first so that we have;
4³•y³ • 2²•g² • y • g
The expression can then be further simplified by using the the product of a power property on like terms so that the simplified form is therefore;
256g³y⁴.
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Which of the statements below are correct?
select all correct statements.
2.8mm = 28cm , 1760 ml < 10 litres, 18g > 0.17 , 1.68 = 168cm
Answer:
False
True
missing info
missing info
Step-by-step explanation:
2.8mm = 28cm False since 28 cm = 280 mm
1760 ml < 10 litres True since 1760 ml = 1.76 l
18g > 0.17 missing units
1.68 = 168cm missing units
the recode for the Boston marathon wheelchair division is 1 hour 18 minutes and 27 seconds
Using the relation between velocity, distance and time, it is found that the average speed of the record winner of the wheelchair division was of 20.04 miles per hour.
What is the complete question?"The record for the Boston Marathon’s wheelchair division is 1 hour,
18 minutes, and 27 seconds.
The Boston Marathon is 26.2 miles long. What was the average speed of the record winner of the wheelchair division?"
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For this problem, we have that:
The distance is of 26.2 miles.The time in hours, considering an hour has 3600 seconds and a minute has 60 seconds, is given by: t = 1 + (18 x 60 + 27)/3600 = 1.3075.Hence the velocity is given by:
v = 26.2/1.3075 = 20.04 miles per hour.
The average speed of the record winner of the wheelchair division was of 20.04 miles per hour.
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could someone please help me on this worth 10 points 7(x+3y)=
According to the distributive property:
[tex] \alpha ( \beta + \gamma ) = \alpha \beta + \alpha \gamma [/tex]
So, applying this to our equation:
[tex]7(x + 3y) = 7 \times x + 7 \times 3y \\ 7(x + 3y) = 7x + 21y[/tex]
Greg is driving his motorhome. It uses 3 gallons of gas for every 21 miles he travels. Complete the table below showing the number of gallons used and the distance traveled
Answer:
I think the answer is 234 miles and 78 gallons.
Step-by-step explanation:
Hope this helped :)
Answer:
You didn't show the problem so ill just make it to where you can answer yourself
Step-by-step explanation:
so if he uses 3 gallons per 21 miles just divide 3 by 21(yes 3 by 21)
So 0.142 is used per mile
So because you don't show how many miles he traveled just take the number of miles he traveled and times it by 0.142
Example: 42 x 0.142 = 5.964 which when rounded is 6
Simplify each number. 4¹.⁵
The result of simplifying the number (4¹)⁵ using the exponent rules is 1024
To solve this exercise we have to resolve algebraic operations following the exponent rules.
Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(4¹)⁵ =
4 ⁽¹*⁵⁾ =
4⁵ =
4*4*4*4*4 =
1024
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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p(x)=x^3-4x^2-8x please help me solve
Answer: The value of p(x) = (-2,6) or p(x) = (-2,0)
Step-by-step explanation:
Given that,
p(x) = x^3-4x^2-8x
p(x) = [tex]x^{3}[/tex] - [tex]4x^{2}[/tex] - 8x
and replace with '0'.
x^3-4x^2-8x = 0
Now, factorizing equation is,
(x+2) ([tex]x^{2}[/tex] - 6x) = 0
(x+2) = 0
x= -2
Therefore, x = -2
and,
([tex]x^{2}[/tex] -6x) = 0
([tex]x^{2}[/tex] -6x+0) = 0
using quadratic formula = - [b ± √[tex]b^{2}[/tex]-4ac] / 2a
substitute the values,
a = 1, b = -6 , c = 0
p(x) = - [-6 ± √[tex]-6^{2}[/tex]-4.1.0] / 2.1
p(x) = - [-6 ± √36-4.1.0] / 2.1
p(x) = - [-6 ± √36-(0)] / 2.1
p(x) = - [-6 ± √36] / 2.1
p(x) = - [-6 ± 6] / 2
p(x) = [6 ± 6] / 2
p(x) = 3 ± 3
Therefore, p(x) = 3+3 = 6
p(x) = 3-3 = 0
So, that we can say the value of p(x) = (-2,6) or p(x) = (-2,0).
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Please help me with this math problem!! Will give BRAINILEST!! :) 15 points!
Using proportions and the percentage concept, it is found that:
25% of Johnny's apples are the Jonagold variety.75% of Johnny's apples are not of the Jonagold variety.63 apples are not of the Jonagold variety.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for percentage problems.
This is because a percentage of an amount a divided by a total amount b is given by the following proportion:
P = a/b x 100%.
From the image, we have that 3 out of 12 apples are of the Jonagold variety, hence:
3/12 x 100% = 0.25 x 100% = 25%.
25% of Johnny's apples are the Jonagold variety.75% of Johnny's apples are not of the Jonagold variety.Each apple in the image is equivalent to 7 apples, hence:
9 x 7 = 63.
63 apples are not of the Jonagold variety.
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find the magnitude of the sum of these two vector
please vind the direcion too
OK PLEASE I NEED HELP NOW IM RUNNING OUT OF POINTS :(
The magnitude of the sum of these two vectors is approximately 11.791 units.
How to find the magnitude of the sum of two vectors
In this question we have the representations of two vectors on a Cartesian plane, of which we must find the magnitude of the two vectors. There are different methods to find it, we decide to use a vectorial method. First, sum the two vectors:
R(x, y) = A(x, y) + B(x, y)
R(x, y) = 7.70 · (cos 27.8°, sin 27.8°) + 16.3 · (- sin 20°, - cos 20°)
R(x, y) = (6.811, 3.591) + (- 5.574, - 15.317)
R(x, y) = (1.237, - 11.726)
Second, use the Pythagorean theorem:
R = √[1.237² + (- 11.726)²]
R ≈ 11.791
The magnitude of the sum of these two vectors is approximately 11.791 meters.
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What are the solutions for the following equations 2x^2+11x+5=0
Answer:
x=-5nakalimutan ......................
......
You drove at 75 kmh-¹ for 2.25 hours Find the exact distance traveled.
Answer:
168.75 km.
Step-by-step explanation:
Distance = speed * time
= 75 * 2.25
= 168.75 km.
The greater of two numbers is 3 more than twice the smaller.Their sum is 24. Find the numbers.