The 12th term of the geometric sequence is -341796875.
The common ratio (r) is:
[tex]\frac{a_{1} }{a_{2} } =-\frac{35}{7} =-5[/tex]
[tex]\frac{a_{3} }{a_{2} } =\frac{175}{-35} =-5[/tex]
(r)=-5
The sum is :
[tex]S_{n}[/tex]=a·{[tex]\frac{1-r^{n} }{1-r^{} }[/tex]}
[tex]S_{3}[/tex]= 147
So. The general form is:
[tex]a_{n}[/tex]=7·-[tex]5^{n-1}[/tex]
Now, The nth term is:
[tex]a_{1}[/tex]=7
[tex]a_{2}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{2-1}[/tex] = 7 · [tex]-5^{1}[/tex] = 7 · -5 = -35
[tex]a_{3}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{3-1}[/tex] = 7 · [tex]-5^{2}[/tex] = 7 · 25 = 175
[tex]a_{4}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{4-1}[/tex] = 7 · [tex]-5^{3}[/tex] = 7 · -125 = -875
[tex]a_{5}[/tex] = 4375
[tex]a_{6}[/tex] = -21875
....... so, [tex]a_{12}[/tex] = - 341796875
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1. Find the equation of the line with slope 5 and y-intercept, 6.
2. Find the equation of the line that passes through the point with coordinates(0,5) and a slope of 3.
3. Determine the x-intercept and y-intercept of equation 4x+2y=16
7. Choose a method to solve the following system of equations. Then write 2-3 sentences
to why the system is set up for that method.
y = -2x + 6
y = 5x - 8
Type your 2-3 sentences in
text box below.
On solving the linear equations y = -2x + 6 and y = 5x - 8, the value for x is x = 2 and the value of y is y = 2.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first linear equation is - y = -2x + 6
The second linear equation is - y = 5x - 8
Subtracting equation (1) from (2) -
y - y = 5x - 8 - (-2x + 6)
0 = 5x - 8 + 2x - 6
0 = 7x - 14
7x = 14
x = 14/7
x = 2
Substituting the value of y in equation (1) -
y = -2x + 6
y = -2(2) + 6
y = -4 + 6
y = 2
The subtraction and substitution method is chosen to solve the system of linear equations. The linear equations are first made equal in order to find the desired variable. Then subtraction is done to find the value of one variable. Next, the found value is substituted into the equation to find the unknown variable. This method is easy to understand and gives accurate value.
Therefore, the value of x and y is 2 and 2 respectively.
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Can some help please?
Find the missing side length.
Answer:
8
Step-by-step explanation:
the side labeled 12 is equal to the sum of both of the sides its parallel to which is 4 and the missing number. Since 4+?=12 that must mean 12-4=? and 12-4=8
The quotient of a number x and 19 is 10.
An equation is [ ].
a line that includes the point (6,4) has a slope of -1/10 what is its equation in point slope form
The point Slope form equation is y = -1/10x + 26/5 , when a point (6,4) has a slope of -1/10
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
Given that the line includes the point (6,4) and has a slope of -1/10, we can substitute these values into the point-slope form to get the equation of the line:
y - 4 = -1/10(x - 6)
Simplifying this equation gives:
y = -1/10x + 26/5
So, the equation of the line in point-slope form is y = -1/10x + 26/5
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A frame designer is making a triangular frame. She has two sides of length 18 inches and 27 inches. What are the possible lengths for the third side?.
The possible lengths( in whole elevation) for the third side is
9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.
For the below question, we've a rule from the properties of triangle, the sum of the length of any two sides of the triangle must be lesser than the length of the third side.
Hence
She has two sides of length 18 elevation and 27 elevation
Let the third side = x
Hence
a) 18 27> x
45> x
b) 18 x> 27
x> 27- 18
x> 9
thus, the possible lengths( in whole elevation) for the third side is
elevation< x< 45 elevation
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What is distributive property of equality?.
The distributive property of equality states that the product of an expression and a sum is equal to the sum of the products of the expression and each term in the sum.
Distributive Property of equality : Distribution in mathematics means multiplying an element by two or more additive elements in parentheses.
Multiplying the set by the sum of two terms is the same as adding the products of the original set and each term. In other words, multiplying a quantity by the sum of two or more terms is the same as adding the product of original quantity and each term. A simpler way of expressing this is that the equality holds after the distribution of the terms. Let a, b, and c be real numbers. Then: a(b + c) = ab + ac. A more general formulation is to let be natural numbers and a, b₁, b₂, b₃,---, bₙ be real numbers. Then, a( b₁+b₂+ b₃ +---+ bₙ) = ab₁ + ab₂ + ab₃ + ----+bₙ.
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what does a square have in common with a rectangle
Answer:
They both have their four interior angles equal to 90 degrees and opposite sides parallel to each other.
Step-by-step explanation:
How do you solve 4 more than 5?.
To write 4 more than 5, we use the mathematical operation of addition and the notation 4 + 5 = 9.
To write 4 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.
In this case, we are given the number 5 and we are asked to find the number that is 4 more than it. To do this, we can use the mathematical notation: 4 + 5 = 9.
This notation means that we are adding 4 to 5, which results in N+4. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+4
Another way to write 4 more than a number is to use the phrase "4 plus 5". This phrase indicates that we are adding 4 to 5 to get 9.
Therefore, In short, to write 4 more than a number, we use the mathematical operation of addition and the notation 4 + Number = N+4. This means that we are adding 10 to a number, resulting in N+4. It can also be written as "4 plus N", indicating the same operation i.e 4 + 5 = 9.
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Part A Determine the magnitude of the resultant force. Express your answer to three significant figures and include the appropriate units. OCH Å ? O Units Fr = Value Submit Request Answer Part B Determine the direction of the resultant force, measured counterclockwise from the positive axis. Express your answer using three significant figures. IVO A ¢ vec ROO? Submit Request Answer Provide Feedback
The angles from an isosceles triangle are simple to calculate. But in order to strengthen the customary methodical approach to vector addition, we note that the angle [tex]$\overrightarrow{\mathrm{b}}$[/tex] makes with the [tex]$+\mathrm{x}$[/tex] axis is
[tex]$30^{\circ}+105^{\circ}=135^{\circ}$[/tex]
What is resultant force?The difference between the forces exerted on an item when a system of forces is at work is known as the resultant force. For instance, a force of 3 N to the left and 10 N to the right results in a force of 7 N to the right. If all of the forces are acting in the same direction, then all of the forces will be acting in the same direction. The three forces that are operating on a body in the same direction are represented by the letters F (1), F (2), and F (3) in the formula above. F(R) = [(F (1) ^2+F (2) ^2)] ^ 1/2.The combined force that two or more forces exert on an item can be calculated by adding up the component forces.It should be noted that using the cosine law for general triangles is an effective technique to solve this vector addition problem (also because
[tex]$\vec{a}[/tex], [tex]\vec{b}[/tex] and [tex]$\vec{r}$[/tex] The angles from an isosceles triangle are simple to calculate. But in order to strengthen the customary methodical approach to vector addition, we note that the angle [tex]$\overrightarrow{\mathrm{b}}$[/tex] makes with the [tex]$+\mathrm{x}$[/tex] axis is
[tex]$30^{\circ}+105^{\circ}=135^{\circ}$[/tex]
(a) The x component of
[tex]$\overrightarrow{\mathrm{r}_{\mathrm{x}}}=(10.0 \mathrm{~m}) \cos 30^{\circ}+(10.0 \mathrm{~m}) \cos 135^{\circ}=1.59 \mathrm{~m}$[/tex]
(b) the y component of
[tex]$\vec{r}$ is $r_y=(10.0 \mathrm{~m}) \sin 30^{\circ}+(10.0 \mathrm{~m}) \sin 135^{\circ}=12.1 \mathrm{~m}$[/tex].
(c) the magnitude of
[tex]\vec{r}$ is $r=|\vec{r}|=\sqrt{(1.59 \mathrm{~m})^2+(12.1 \mathrm{~m})^2}=12.2 \mathrm{~m}[/tex]
(d) The angle between
[tex]\overrightarrow{\mathrm{r}}$ and the $+\mathrm{x}$ direction is $\tan ^{-1}[(12.1 \mathrm{~m}) /(1.59 \mathrm{~m})]=82.5^{\circ}$[/tex]
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Ivan has inherited his mother's 1963 Chevrolet Corvette, which hevalues at $45,000. He decides that he might be willing to sell it so heposts it on Craigslist for $55,000. Samantha is interested and willing to pay up to $72,000
Samantha is willing to pay up to $72,000 for the 1963 Chevrolet Corvette, which is $17,000 more than Ivan's asking price of $55,000.
What do you mean by inherit?It means to receive something from a parent or ancestor through genetic transmission. It also means to receive something as a devise or legacy from an ancestor. inherit an enzyme that is flawed.
Ivan inherited the car and valued it at $45,000, therefore he would make a profit of $17,000 if he sells the car to Samantha.
It's important to note that the final price will depend on the negotiation and agreement between Ivan and Samantha.
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How to multiply 3 digit numbers by 2 digit numbers without regrouping?.
Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.
Follow along with example 343 × 32:
Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.
3 4 3
×3 2
_______
Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.
3 4 3
×3 2
________
6 8 6
Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.
3 4 3
×3 2
__________
6 8 6
10 2 9×
__________
10 976
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Help me in question b
An inequality that shows how much faster Elanor can drive without going over the speed limit is 43.5 + s ≤ 55.
Elanor can increase her speed by 2.
How to write, solve, and graph the required inequality?In order to write and solve an inequality that represents how much faster Elanor can drive without going over the speed limit, we would take note of the following important information;
The maximum speed limit is equal to 55.Elanor's speed is equal to 43.5.Let the variable s represent the safe speed.Now, we can write an inequality that represents the value of s for which the speed of Elanor is still safe as follows;
43.5 + s ≤ 55
By subtracting 43.5 from both sides of the inequality, we have the following:
43.5 - 43.5 + s ≤ 55 - 43.5
s ≤ 11.5
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What is an algebraic expression with more than 3 terms?.
An algebraic expression with more than 03 terms is known as Multinomial.
Multinomial Distribution:
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, model the probability of counting on each side of a k-sided die n tosses. For n independent trials, each succeeds in exactly one of the k categories, and each category has a certain fixed probability of success. A multinomial distribution gives the probability for each particular combination of numbers of successes in different categories.
If k is 2 and n is 1, the multinomial distribution is Bernoulli. If k is 2 and n is greater than 1, the distribution is binomial. If k is greater than 2 and n is 1, the distribution is categorical. The term "multinoulli" is sometimes used for categorical distributions to emphasize this four-way relationship (hence n determines the prefix and k determines the suffix).
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Kevin invests money in an account paying simple interest. He invests $40 and no money is added or removed from the investment. After one year, he has $42.80. What is the simple percent interest per year?
Answer:
Step-by-step explanation:
The simple percent interest per year is calculated by dividing the interest earned by the original amount invested, then multiplying by 100 to express the answer as a percentage.
In this case, Kevin earns $42.80 - $40 = $2.80 in interest.
So, the simple percent interest per year is ($2.80 / $40) * 100 = 7%
Which is the correct graph for 3y=2x−3
Answer:
D or the last graph. (I attached it)
Step-by-step explanation:
Rewrite in slope-intercept form:
[tex]y = \frac{2}{3}x - 1[/tex]
Using the slope-intercept form, the slope is [tex]\frac{2}{3}[/tex] or [tex]m = \frac{2}{3}[/tex].
Start on the graph by graphing (0, -1), then graph your slope. Up 2, over 3 & repeat!
Can someone please help me with this math problem? The math problem is listed in the picture, Thanks!
I can only use numbers, infinity symbols, etc.
You have to consider the following relation.
Answer:
Domain:
[tex] - \infty < x < \infty [/tex]
Range:
[tex] - 1 \le \: y < \infty [/tex]
Step-by-step explanation:
Domain:The Domain of a function is x values which are included in the graph. Sometimes x values will not be included because they cannot be defined at that point, but in this case the graph indicates that the graph continues to the right and left with no indication that there is an asymptote or it is undefined beyond the graph so we can assume it's defined for all real numbers. We can represent this in interval notation as:
[tex] - \infty < x < \infty [/tex]
Since if you plug in any real number, this inequality should be true.
Range:The range of a function is defined as y values which are on the graph, this is restricted when certain y values are not on the graph... but we can usually tell because functions will have a minimum/maximum. By looking at the graph it appears to reach a minimum at y = -1 and then on the right and left side is increasing, never going below this value, so the range can be defined as:
[tex] - 1 \le y < \infty [/tex]
Since the y values vary between -1 (including -1) and infinity... well that really just means there's no upper bound and it just keeps increasing and increasing.
At the grocery tore 4 pint of ice cream cot $10. 36. How much would 20 pint of ice cream cot?
Answer:$51.08
Step-by-step explanation:
What is the value of the digit 3 in 17039 write in words
The digit 3 in the number 17039 represents the value of 3 in the tens place. The place value system is a way to understand the value of each digit in a number. In this case, each digit in the number 17039 has a specific place value, starting from the rightmost digit, which is the ones place, then the tens place, followed by the hundreds place and so on. In the number 17039, the digit 3 is located in the tens place which represent 3 x 10 = 30. To understand the value of any digit in a number, you can multiply the digit by its corresponding place value.
Answer:
The digit 3 in the number 17039 represents the value of 3 in the tens place
Step-by-step explanation:
A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth
The focus of 76-inch diameter and the 42-inch deep reflecting telescope is located approximately 87.92 inches or 7.32 feet from the center of the mirror, at the prime focus.
The focus of a reflecting telescope's mirror is the point where incoming light rays converge after being reflected by the mirror. The location of the focus depends on the size and curvature of the mirror. In this case, the mirror has a diameter of 76 inches and a depth of 42 inches.
This information can be used to calculate the location of the focus, which is approximately 87.92 inches or 7.32 feet from the center of the mirror. This distance is also known as the prime focus and is the point where the image is formed. The eyepiece of the telescope, which magnifies the image formed at the prime focus, is typically located a short distance away from the prime focus, often around 0.90 inches.
The secondary mirror is positioned to reflect light from the prime focus to the eyepiece.
Complete question:
A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth.
Primary Mirror
Lighting
Prime Focus
Secondary Mirror
Eyepiece
O1.68 inches
O 87.92 inches
O 512.00 inches
O 8.60 inches
O 0.90 inches
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Pls help me with this
Answer:
Answers in attached photo.
Step-by-step explanation:
SolutionSteps are in the attached photo, do note that to ensure the inequality sign are always constant throughout the entire working, otherwise one wrong line will result incorrect answers below it.
in a group of 42 students 17 use pens for writing and 21 use pencils for writing. find the probability that a student picked from this group at random is using a pen or pencil?
(Using addition rule of probability)
The probability that a student picked from this group at random is using a pen or pencil is 19/21
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, in a group of 42 students, 17 use pens for writing and 21 use pencils for writing.
P(A or B) = P(A) + P(B)
P(A) = 17 / 42
P(B) = 21 / 42
P(A or B) = 17 / 42 + 21 / 42
P(A or B) = 38 / 42
P(A or B) = 19/21
Hence, the probability that a student picked from this group at random is using a pen or pencil is 19/21
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M) a car is travelling at 29 mph. if the tires have a diameter of 25 inches, how fast are the cars tires turning? express answer in revolutions per minute
Answer:
To calculate the speed of the car's tires turning, you need to first calculate the circumference of the tire. If the tire has a 25 inch diameter, multiply 25 by 3.1416 to find the tire circumference, which is 78.54 inches. Now, divide 63,360 inches per mile by the tire circumference (78.54) to find the revolutions per mile, which is 803.6. Finally, multiply 803.6 by 29 (the speed of the car in mph) to get the revolutions per minute, which is 23,253.6. Therefore, the car's tires are turning at a rate of 23,253.6 revolutions per minute.
the image of the point (-9,9) under a translation is (-5,13). find the coordinates of the image of the point (-6,-7) under the same translation
Answer in the photo!!
hope it's right
What type of angle is 360 degrees?.
It is called a "congruent" angle.
A full rotation, or a complete revolution, is 360 degrees. Therefore, an angle of 360 degrees is called a "full rotation" or a "complete revolution." It is also sometimes called a "congruent" angle.
A full rotation is known as a circle. A circle is a round-shaped figure that has no corners or edges.
In geometry, a circle can be defined as a closed, two-dimensional curved shape.
The entire circle completes a total of 360 degrees as it completes one rotation or what we call a complete revolution.
A circle is a congruent angle.
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The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. A random sample of 16 students will be selected and the mean number of pets for the sample will be calculated.
What is the mean of the sampling distribution of the sample mean for samples of size 16 ?
a. 1.7
b. 3.2
c. 3.216√ (The fraction 3. 2 over the square root of 16)
d. 1.716√( The fraction 1. 7 over the square root of 16)
The sampling distribution of the sample mean for samples of size 16 is made up of V3.2 pets, which is the same as the average number of pets owned by the population of high school students.
We use sampling distribution because...
The sampling distribution is the probability distribution of a statistic obtained from a larger sample size drawn from a particular population. The sampling distribution of a particular population is the frequency distribution of a set of possible outcomes for a population statistic.The sampling distribution is the probability distribution of a statistic that is created by drawing numerous samples from a particular population. Researchers use sample distributions to simplify the statistical inference process.A large high school's student population has an average of 3.2 pets per student, with a standard deviation of 1.7 pets. A random sample of 16 students will be selected, and the mean number of pets for the sample will be calculated in order to better understand this population.This will give us the sample mean for samples of size 16 and the mean of the sampling distribution.To determine this, we must first determine the standard error of the mean, which is the sample mean's standard deviation. This is calculated by multiplying the sample size (16) by the square root ofthe population standard deviation (1.7 pets), yielding a standard error ofthe mean.Learn more about Sampling distribution refer to :
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What are the steps to plotting points on a coordinate plane?.
To plot a point in a coordinate plane, first we have to define the point, then determine the coordinates, both x and y coordinates. Then plot the point in the appropriate plane.
A point is usually in a coordinate plane is described by two axis, X and Y. A point will usually be denoted as (x,y). From these values we have to determine where the point might be lying. If the x value is positive it is towards the right of 0 and negative it will be towards left. Y value become positive upwards and negative downwards.
After determining the coordinates we label as the readings the the X axis and Y-axis. In the figure given below we have plotted some points.
Point A (2,2) with x-coordinate 2 and y coordinate 2 , B(4,-2) with x coordinate 4 and y coordinate -2, C(-3,-1) with x coordinate -3 and y coordinate -1, D(-2,3) with x coordinate -2 and y coordinate 3.
So, for plotting we have to determine the coordinates and plot it.
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What is the y-intercept for the graph of this line 3x 5y 6'6 next question?.
The y-intercept for the graph of this line 3x-5y=6 is -6/5.
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
To determine the intercept of the equation, it would be helpful to write it in its slope-intercept form which is expressed as:
y = mx + b
where m is the slope and b is the y-intercept. Therefore, the value of b would be the correct answer here.
3x-5y=6
5y=3x - 6
y = 3x/5 - 6/5
Thus, the y-intercept is -6/5.
Thus, the y-intercept for the graph of this line 3x-5y=6 is -6/5.
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Please Help Asap...! :)
A) The time in minutes that it would reach 40% charge is; 48 minutes
B) The percent at 1 hr 48 minutes is; 90%
How to solve Linear Equation Word problems?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From the given parameters, we can find the slope from the formula;
m = (y2 - y1)/(x2 - x1)
m = (30 - 10)/(36 - 12)
m = 20/24
m = 5/6
Thus, for a 40% charge, we have;
5/6 = (40 - 30)/(t - 36)
Cross multiply to get;
5(t - 36) = 60
t - 36 = 12
t = 48 minutes
B) After 1 hr 48 minutes or 108 minutes, it means that;
Percentage = 5/6 * 108
= 90%
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What is the first step in solving this equation 3 2x 6 )- 4x 2 5x 2 )+ 6?.
The correct option is D. Use the distributive property on each side of the equation.
In step with this belongings, multiplying the sum of two or more addends by means of a number will deliver the identical result as multiplying each addend in my view by the quantity after which including the products together. The distributive belongings tell us how to remedy expressions in the form of a(b + c). The distributive belongings are every so often known as the distributive law of multiplication and division.
The Distributive asset is an algebraic asset that states that when an element is improved by means of the sum or difference of terms, it's far essential to multiply every one of the two numbers by means of the element, and subsequently perform the addition or subtraction operation.
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Complete Question:
What is the first step in solving this equation? 3(2x + 6) – 4x = 2(5x – 2) + 6.
A). Use the subtraction property of equality to subtract 6 from both sides. B). Use the addition property of equality to add 4x to both sides.
C). Combine the like terms on each side of the equation.
D). Use the distributive property on each side of the equation.
