We have the sequence: 8, -2, -12...
We can prove that this is an arithmetic sequence as there is a common difference d=-10 between consecutive terms.
Then, the recursive formula (the expression where the value of a term depends on the value of the previous term) can be written as:
[tex]a_n=a_{n-1}-10[/tex]Answer: the recursive formula is a1 = 8, a(n) = a(n-1) - 10
Find the HCF and lcm of 42 72 and 90 and multiply it together
Answer:
Step-by-step explanation:
HCF of 42,72 and 90
=6
LCM of 42,72 and 90
=2520
2520 x 6 = 15120
=15120
prove why the function is even with the green highlighted formulathen show where the line of symmetry is at show all work
Here, the given function is f(x)=c.
Check whether the function is odd or even.
[tex]\begin{gathered} f(-x)=c \\ =f(x) \end{gathered}[/tex]Here, the out put of the function is constant whether it is +x or -x.
So, the function is even.
The graph of the function f(x)=c is shown below.
From, the graph, for any values of x there is a constant val;ue of y.
The function is symmetric with respect to y axis.
A certain model of TV costs 680 euros. An upgraded model of this TV costs € 782. Calculate a few percent more expensive upgraded model of this TV.
Solution
First find the difference
[tex]782-680=102[/tex][tex]\begin{gathered} \text{ \% increase=}\frac{102}{680}\times100\text{ \%} \\ \\ \operatorname{\%}\imaginaryI\text{ncrease=0.15\times100{\operatorname{\%}}} \\ \\ \operatorname{\%}increase=15\text{ \%} \\ \end{gathered}[/tex]The final answer
The few percent more expensive upgraded model of the TV is
[tex]15\text{ \%}[/tex]the segment joining (-8,1) and (11,7) is divided into four equal parts. Find the points of division nearest to ends.
Midpoint of line is:
[tex]\begin{gathered} (\frac{x_1+x_2}{2}_{},\frac{y_1+y_2}{2}) \\ (\frac{-8+11}{2},\frac{7+1}{2}) \\ (\frac{3}{2},4) \end{gathered}[/tex]Distance between two point.
x distance between F and G :
[tex]\begin{gathered} X=11-(-8) \\ =19 \end{gathered}[/tex]Y distance is:
[tex]\begin{gathered} Y=7-1 \\ =6 \end{gathered}[/tex]For 4 equal part is x and y distance is:
[tex]\begin{gathered} x\text{ distance=}\frac{19}{4}=4.75 \\ y\text{ distance=}\frac{6}{4}=1.5 \end{gathered}[/tex]so x and y coordinates is:
[tex]\begin{gathered} (-8+4.75,1+1.5)_{} \\ (-3.25,2.5) \end{gathered}[/tex]second coordinates is:
[tex]\begin{gathered} (-3.25+4.75,2.5+1.5) \\ (1.5,4) \end{gathered}[/tex]Then theird coordinates is:
[tex]\begin{gathered} (1.5+4.75,4+1.5) \\ (6.25,5.5) \end{gathered}[/tex]Fourth coordinates is:
[tex]\begin{gathered} (6.25+4.75,5.5+1.5) \\ (11,7) \end{gathered}[/tex]
Craig left his house at noon and drove 50 miles per hour until 3 p.m. Then he drove the next
5 hours at 70 miles per hour.
Graph Craig’s driving trip and calculate the average rate of change for the entire trip
Answer:
62.5 mph
Step-by-step explanation:
rate * time = distance
50 * 3 = 150 mi
70 * 5 = 350 mi
total miles = 500 mi
total time = 8 hrs
Average = 500 mi / 8hr = 62.5 mi / hr
a ramp is built to reach a doorway that is 9 feet off the ground. the ramp makes a 37 angle with the driveway. how long is the ramp
The length of the ramp from the doorway is 11.94ft
What is Trigonometric RatioIn mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry.
To solve this problem, we are going to look at SOHCAHTOA and see which of the ratios fit in this problem.
Adjacent = xOpposite = 9ftAngle = 37 degreeUsing Tangent of an angle, we can find the length of the ramp.
[tex]tan\theta = \frac{opposite}{adjacent}[/tex]
Let's substitute the values into the equation and solve.
[tex]tan 37 = \frac{9}{x} \\x = 11.94ft[/tex]
The length of the ramp is 11.94ft
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help me please
thank you
Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.
The Domain of the function is [ -8, 2].
How do you find the domain of a function?Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.The Domain of the function is [ -8, 2].
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A computer is normally $500, but is discounted to $200. By what percentage did the computer decrease?
Answer:
60%
Step-by-step explanation:
y = 3x -4
m:
b:
Proportional?
(Yes or No) j
Which formula should be used to find the circumference of a circle? C = pi dC = 2 pi dC = pi rC = StartFraction pi over d EndFraction
Solution
For this case the correct formula for the circumference of a circle is given by:
[tex]C=2\pi r=2\pi\cdot\frac{d}{2}=\pi d[/tex]Then the best option would be:
C = pi d
(02.04 MC) choose the equation that represents the line that passes through the point (2,6) and has a slope of -5
The slope intercept form of the equation that passes through the point (2,6) and has a slope of -5 is y = -5x +16
Slope intercept form:
Slope intercept form equation is used to calculate the equation of a straight line, for the given slope of the line and intercept.
The general form of slope intercept equation is,
y = mx +c
where
m represents the slope of the line
c represents the intercept.
Given
Here we have the the point (2,6) and has a slope of -5.
Now we need to find the equation of the line for this point and slope.
While we apply these value on the formula, in order to get the value of y intercept,
Then it can look like,
6 = (-5)2 + c
6 = -10 + c
c = 6 + 10
c = 16.
Therefore, the value of y intercept is 16.
Then the equation of the line is
y = -5x + 16
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Is it a function?, then state the domain and range in set notation,
It is a function.
Because none of the values of the domain is repeated
the domain in set notation
[tex]x=\lbrace1,3,5,7\}[/tex]the range in set notation is
[tex]y=\lbrace-1,4,6\rbrace[/tex]What is (2x)(3x) in words but not explaining how to get the answer?
The number (2x)(3x) in the word will be two time the variable multiplied the three times the variable.
What is termed as the variable?A variable is a property that can be assessed and has multiple values. Variables can be divided into two types: categorical and numeric. The categories are further subdivided into two subgroups: ordinal or nominal for categorical variables and discrete as well as continuous for numeric variables.For the given question,
The number in digits is given as (2x)(3x).
The 'x' is the variable part who value is not defined for the question.
Thus, twice the variable will be 2x.
Thrice the variable will be 3x.
The multiplication of both the numbers will be (2x)(3x).
Therefore, in words the number will be written as two time the variable multiplied the three times the variable.
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Please help I have trouble on these...
The value of a is 5, b is 4, c is 0, d is 3, e is 6 and R is 6 after following the long division method.
According to the question,
We have to divide 430 by 8 by following the long division method.
Note that when we follow long division method then the number by which we are dividing (divisor) is to be multiplied in such a way that the result remains less than the number in the dividend.
Now, we will solve it step by step.
In dividing 43 by 8, we have to multiply 8 by 5. Then, we get 40.
So, we have a = 5, b = 4 and c = 0.
Now, after this we have 30 and the number that we get after multiplication is 24. So, 3 has to be multiplied in 8 to get 24.
So, we have d = 3.
Now, when we will subtract 24 from 30, we will get 6.
So, we have e = 6.
And e is also the remainder, R. So, we have R = 6.
Hence, the values of a, b, c, d, e, and R are 5, 4, 0, 3, 6, and 6 respectively.
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K
What is the weight of a 35.01-carat diamond in grams and ounces? Use 1 carat = 0.2 gram, 1 carat-3.086 grains, and 1 ounce = 437.5 grains.
The weight of a 35.01-carat diamond is 9.
(Round to two decimal places as needed.)
The weight of a 35.01-carat diamond is oz.
(Round to two decimal places as needed.)
help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
The steps and answers please and thank you.
Answer:
Practical Domain: 0 ≤ g ≤ 22
Practical Range: 0 ≤ C(g) ≤ 78.32
Step-by-step explanation:
The domain is the input of the function, usually, x, but it is g in this problem.
The input here is the number of gallons you can get. The tank holds a maximum of 22 gallons, so if the tank is already full, you will get 0 gallons. If the tank is completely empty, you can get up to 22 gallons. The domain is the values of the input of the function. Since the input is from 0 gallons to 22 gallons, we get this for the domain:
Practical Domain: 0 ≤ g ≤ 22
The range is the output of the function. Usually it is f(x), but in this problem it is C(g). When you input the number of gallons into the function, the output is the cost of that number of gallons. The domain is from 0 to 22 gallons. Now we use the function to find the cost of 0 gallons and the cost of 22 gallons.
Here is the function:
C(g) = 3.56g
What is the cost of 0 gallons? In this case, g = 0.
C(0) = 3.56(0) = 3.56 × 0 = 0
0 gallons cot 0 dollars, which makes sense.
What is the cost of 22 gallons, the greatest amount of fuel you can fit in the tank?
C(g) = 3.56g
Here, g = 22.
C(22) = 3.56(22) = 3.56 × 22 = 78.32
22 gallons cost 78.32 dollars.
The range of the function is from 0 dollars to 78.32 dollars.
Practical Range: 0 ≤ C(g) ≤ 78.32
In 2006, the population of Tewksbury, Rhode Island was 25,000, and it was growing at an annual rate of 2.2%.Part AWhat is the growth factor for the town?Part BWrite an equation to model the cars value.Part CUse your equation to estimate the population of Tewksbury in 2011. round your response to the nearest whole number
Part A. To find the growth factor of the town, you can proceed like this
[tex]\begin{gathered} 2.2\text{ \% }=\frac{2.2}{100}=0.022 \\ \text{Then,} \\ 25000\cdot0.022=550\Rightarrow\text{ Population increase in one year} \\ 25000+550=25550\Rightarrow\text{ Population in 2007},\text{ adding the population in 2006 plus the increase} \\ \end{gathered}[/tex]So, the growth factor for the town will be
[tex]\frac{25550}{25000}=1.022[/tex]For part B, exponential growth is modeled by the equation
[tex]\begin{gathered} y=ab^x \\ \text{Where} \\ a\text{ is the initial amount} \\ b\text{ is the growth factor} \\ x\text{ is the time in years} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} a=25000 \\ b=1.022 \\ \text{ Then,} \\ y=(25000)(1.022)^x \end{gathered}[/tex]For part C, you need to find the population in 2011, so
[tex]2011-2006=5\text{ years}[/tex]Then, plug in the equation found x = 5
[tex]\begin{gathered} y=(25000)(1.022)^x \\ y=(25000)(1.022)^5 \\ y=27873.7 \\ \text{Rounding} \\ y=27874 \end{gathered}[/tex]Therefore, the population of Tewksbury in 2011 will be 27874 people.
Identify an inequality you can use to find the possible values of X. Perimeter <51.3 inches
Let's first get the value of x, since it's a right triangle, we use Pythagorean Theorem.
Let's make,
a = 14.2
b = 15.5
c = x
[tex]a^2+b^2=c^2[/tex][tex](14.2)^2+(15.5)^2=x^2[/tex][tex]\text{ x = }\sqrt[]{14.2^2+15.5^2}[/tex][tex]\text{ x = 21.02}[/tex]Let's try choice c if the inequality fits,
[tex]14.2\text{ }+\text{ 15.5 + x }<\text{ }51.3[/tex][tex]14.2\text{ }+\text{ 15.5 + 21.02 }<\text{ 51.3}[/tex][tex]50.72\text{ }<\text{ 51.3}[/tex]The inequality fits, therefore c is the correct answer.
1 point The $140 repair bill included $42 for parts and the rest for labor. What percent of the bill was for labor?
we must first find the price of labor
then we subtract the value of the parts from the total
[tex]140-42=98[/tex]the price of the labor was 98$
now to calculate the percent, divide the price of the labor between the total and multiply by 100
[tex]\begin{gathered} \frac{98}{140}\times100 \\ \\ 0.7\times100 \\ =70 \end{gathered}[/tex]the percent was 70%
A special commercial about Doritos is to be randomly played during the 210 minutes of the SuperBowl. If you had to leave to run an errand and miss 30 minutes of the game, what is theprobability that you would still be able to see the beginning of the commercial?A. 14.3%B. 12.5%C. 85.7%D. 75%
From the information provided;
A commercial is to be played during the 210 minutes of the super bowl. If you had to miss 30 minutes of the game, the probability of seeing beginning of the commercial would be;
[tex]\begin{gathered} \lbrack P\rbrack=\frac{Total\text{ number of successful events}}{Total\text{ number of }possibl\text{e events}} \\ \lbrack P\rbrack=\frac{30}{210} \\ \lbrack P\rbrack=0.142857\ldots \end{gathered}[/tex]The probability of seeing the beginning of the commercial would be 0.1428 (approximately), and when expressed as a percentage, this would be 14.28%.
ANSWER:
The correct answer therefore is 14.3%
Option A is the correct answer
The equation below describes a circle. What are the coordinates of the center
of the circle?
(x-4)² + (y+12)² = 17²
A. (-4,12)
B. (4,12)
C. (-4,-12)
D. (4.-12)
SUBMIT
Answer:
D. (4, -12)
Step-by-step explanation:
Given the equation of a circle is (x -4)² +(y +12)² = 17², you want to know the center.
CircleThe equation of a circle centered at (h, k) with radius r is ...
(x -h)² +(y -k)² = r²
Comparing this to the given equation, we can identify the values of the parameters as ...
(x -4)² +(y +12)² = 17²
h = 4, -k = 12, r = 17 . . . . . k = -12
This tells us the center is ...
(h, k) = (4, -12) . . . . . matches choice D
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write in summation notation 13. 20 + 22 + 24 + ... + 36
Given the expression:
20 + 22 + 24 + ..... + 36
Let's write in summation notation.
Summation notation can be said to be the addition of a sequance of numbers.
From the sequence, we have:
Common difference = 22 - 20 = 2
Number of terms = 9
Apply the formula:
[tex]\sum ^n_{i\mathop=1}a+d(i-1)[/tex]Where:
n = upper limit (number of terms)
i = 1 ==> lower limit
Initial value, a = 20
d = common difference = 2
To write in summation notation, we have:
[tex]\sum ^9_{i\mathop=1}20+2(i-1)[/tex]ANSWER:
[tex]\sum ^9_{i\mathop{=}1}20+2(i-1)[/tex]In a bag there are green, yellow and orange marbles. The ratio of green to yellow marbles is 2 to 5. The ratio of yellow to orange marbles is 3 to 4. What is the ratio of green to orange marbles?
We have to simplify the ratios to make them comparable;
If the ratio of green to yellow marbles is 2 to 5 and
The ratio of yellow to orange marbles is 3 to 4.
[tex]\begin{gathered} \text{Green to yellow = }2\colon5 \\ \text{Yellow to Orange=3 : 4} \\ \text{Multiply the gr}een\text{ yellow ratio by 3, multiply the yellow-orange ratio by 5, we obtain;} \\ \text{Green to yellow becomes = 6 : 15} \\ \text{Yellow to orange becomes = 15 : 20} \end{gathered}[/tex]Now we can rewrite the ratios of green: yellow : orange as
[tex]6\colon15\colon20[/tex]From this, we can see that the ratio of green to orange marbles is;
[tex]\begin{gathered} 6\colon20 \\ or\text{ in simplest terms} \\ 3\colon10 \end{gathered}[/tex]Therefore, the ratio of green to orange marbles is 3 : 10
solve for s1/2 s = 7/2
Solution
For this case we have the following:
1/2 s = 7/2
We can multiply both sides by 2 and we got:
s = 7
In a certain year, the annual per capita consumption of eggs was 496; that is the average person ate 496 eggs per year. Ina year many decades later, the annual per capita consumption had dropped to 255. Round each annual per capita consumption to the nearest ten. A) earlier year had (blank) eggs B) more recent year had (blank) eggs C) in more recent year, the average person ate (blank) as many eggs as the average person did in the earlier year.
Ok, so
We know that the annual per capita consumption of eggs was 496, and it dropped to 255.
So, We need to find the fraction eggs the average person eats in the first year as the average person did in the last year. We are given, per capital consumption of eggs in the first year = 496 and, per capital consumption of eggs in the last year = 255.
Then, earlier year had 496 eggs.
More recent year had 255 eggs.
We can say that in more recent year, the average person ate 0.5 as many eggs as the average person did in the earlier year.
0.5 comes from divide 255/496, that means that the average person ate 0.5 times eggs than the people who ate in the earlier year.
Two more than the quotient of a number and 6 is 4.
The algebraic equation of the English statement is (x/6) + 2 = 4 and the value of the unknown number is 12.
How to determine an algebraic equation from an English statement?Given the statement in the question;
'Two more than the quotient of a number and 6 is 4'
First, we translate into an algebraic equation;
Let the unknown number be represented by x
Two more than ⇒ + 2The quotient of a number and 6 ⇒ x/6is 4 ⇒ = 4Now, we combine;
(x/6) + 2 = 4
This is the algebraic equation of the English statement.
Next, we can solve for the unknown number 'x'
(x/6) + 2 = 4
Subtract 2 from both sides
(x/6) + 2 - 2 = 4 - 2
(x/6) = 4 - 2
(x/6) = 2
Cross multiply
x = 2 × 6
x = 12
Therefore, the numerical value of the unknown number "x" is 12.
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Write a linear equation for thw line that goes through the point (2,5) and has a slope of 2.
Given:
Point; (x, y) ==> (2, 5)
Slope, m = 2
To write a linear equation that goes through the point, apply the slop-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Take the following steps:
• Step 1:
Substitute 2 for m.
Input the points (2, 5) for the values of x and y repsectively
y = mx + b
5 = 2(2) + b
5 = 4 + b
• Step 2:
Solve for b.
Subtract 4 from both sides
5 - 4 = 4 - 4 + b
1 = b
Therefore, to write the linear equation, substitute 2 for m, and 1 for b in (y = mx + b)
y = mx + b
y = 2x + 1
Therefore, the equation for the line that goes through the point (2, 5) and has a slope of 2 is:
y = 2x + 1
ANSWER:
[tex]y=2x+1[/tex]
Find all angles 0 theta such that 0 degrees are less than or equal to 0 theta and less than or equal to 360 degrees for which the statement sin(-104) = sin 0 theta is true
Hello there. To solve this question, we'll have to remember some properties about angles and the unit circle.
First, remember the unit circle:
An angle is represented as the measure between the line joining the origin and any point of the circle with the x-axis, as follows
The full angle in this case, representing a cycle in the circle is
[tex]\theta=2\pi[/tex]So we want to determine all angles θ between 0 and 360º such that
[tex]\sin(-104^{\circ})=\sin(\theta)[/tex]For this, we have to remember about first positive determination of an angle.
Notice we can represent negative angles in the unit circle if, instead of following in the anti-clockwise orientation (we say positive orientation), we follow the other way around:
But notice that we can represent these angles with our first case if you consider:
[tex]2\pi-\alpha[/tex]Since you have the property that the full angles is 2pi, hence
Thefore you have that
[tex]360^{\circ}-104^{\circ}=256^{\circ}[/tex]In this case notice that we added 360º to the angle, since we fixed the point of which the angle was at and gave it a full rotation.
For smaller angles, for example, -1352º, you can add the biggest possible multiple of 360º, that represents the number of full rotations you have to have in order to find its first positive determination.
In this case, we found that
[tex]\theta=256^{\circ}[/tex]Satisfying the property that
[tex]0\leq\theta\leq360^{\circ}[/tex]Help me please! It’s an emergency!! A small company is selling a new board game, and theyneed to know how many to produce in the future.They sold a total of 400 games after 11 months, 800games after 21 months, and 1500 games after 36months. Is a single linear model a reasonable option for this data? Use this to estimate the number of games sold after 48 months. Explain.
Based on the data given:
400 games were sold after 11 months
800 games were sold after 21 months
1500 games were sold after 36 months
We need to plot a graph of months against the number of games:
From the graph,
Yes, a single linear model is a reasonable option for the data
The equation of the graph is given by:
[tex]y\text{ = 0. 0226x + 2.344 }[/tex]Note that y represents the number of months and x represents the number of board games.
The number of board games sold after 48months simply means that y= 48. In order to get x, we substitute y = 48 into the model
[tex]\begin{gathered} 48\text{ = 0.0226x + 2.344} \\ 0.0226x\text{ = }48-2.344 \\ 0.0226x\text{ =45.656} \\ x=\frac{45.656}{0.0226}=2020.18\text{ (to 2 d.p)} \end{gathered}[/tex]Therefore, the estimated number of games sold after 48 months is 2020.
