Answer: An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. We can call this constant difference "d".
In this sequence, we can see that the difference between consecutive terms is -6x - 5.
The 9th term of an arithmetic sequence can be found by using the formula:
a_n = a_1 + (n-1)d
Where a_n is the nth term of the sequence, a_1 is the first term of the sequence and d is the common difference.
Given the sequence -5x + 2, -11x - 3, -17x -8, ...
The 9th term is:
-5x + 2 + (9-1) (-6x-5) = -5x + 2 - 48x - 40 = -53x -38
Therefore the 9th term of the arithmetic sequence is -53x -38.
Step-by-step explanation:
at an entertainment center, two groups of people bought batting tokens and miniature golf games. the first group bought 16 tokens and 3 golf games for $30. the second group bought 22 tokens and 5 golf games for $43. find the cost of a battling token and the cost of a miniature golf game.
An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.
The system's answer is: what is it?An equation system's solution is a collection of values for the variable that concurrently fulfill each equation. Finding all of the possible sets of variable values that make up the system's solutions is necessary to solve an equation system. However, the second equation does not have a solution at (5, 4).An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.There are an endless number of ordered pairs that satisfy both of the equations if both variables are removed and you are left with a true assertion. Actually, the lines of the equations are identical.To lean more about system's solution refer to:
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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.
The system's answer is: what is it?The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).
The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.
If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.
Let cost token be x and golf games be y, i.e.
16x + 3y = 30
22x + 5y = 43
Lets Solve by using Elimination method both the expression in equal terms
80x + 15y = 150
- 66x + 15y = 129
14x = 21
x = 21/14
x = 1.5
Then, for y
16(1.5) + 3y = 30
y = 2
Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.
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Annie is helping you graph the line y - 3 = 2(x + 1).
She tells you to follow the steps below.
Step 1: Plot the point (1, -3).
Step 2: Plot more points by moving up 2 and right 1.
Step 3: Draw a line through the points and put arrows on the ends..
Annie made a mistake.
What was her mistake? How should she fix her mistake?
Answer: Annie made a mistake in step 1 by plotting the point (1, -3) instead of (1, 0) which is the x-intercept of the given equation.
Step-by-step explanation:
She should have used the x-intercept of the equation instead of just any point.
To fix her mistake, Annie should find the x-intercept of the equation by setting y to 0, and solve for x. Then she can plot the point (1,0) and proceed with step 2 and 3.
Create a diagram based on the given symbolic statement. Be sure enough information is provided in the diagram to validate each statement. △FUN≅△CAR
The triangle △FUN is congruent to the triangles △CAR. And the diagram is given below.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles △FUN and △CAR, then we have
∠FUN = ∠CAR = 90°
∠UFN = ∠ACR
FN = CR
Then the triangles △FUN and △CAR are congruent triangles. And the diagram is given below.
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Which is the y-intercept of the relationship represented in the table?
x y
-8 -3
-5 0
-2 3
1 6
-3
-5
5
3
how to solve 66 divided by 7 using standard algorithm
Answer: The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers. To solve 66 divided by 7 using the standard algorithm, you can follow these steps:
Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:
66 | 7
--- |
Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.
66 | 7
--- | 0
Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).
66 | 7
--- | 0
0 |
Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.
66 | 7
--- | 0
0 | 6
Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).
66 | 7
--- | 0
0 | 6
| 66
Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.
66 | 7
--- | 09
0 | 6
| 66
Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).
66 | 7
--- | 09
0 | 6
--- | 63
Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
So, 66 divided by 7 = 9 with a remainder of 3
So the answer is 9 R 3
Step-by-step explanation:
The solution is: 66 divided by 7 is 9 with a remainder of 3.
The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers.
To solve 66 divided by 7 using the standard algorithm, you can follow these steps:
Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:
66 | 7
--- |
Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.
66 | 7
--- | 0
Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).
66 | 7
--- | 0
0 |
Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.
66 | 7
--- | 0
0 | 6
Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).
66 | 7
--- | 0
0 | 6
| 66
Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.
66 | 7
--- | 09
0 | 6
| 66
Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).
66 | 7
--- | 09
0 | 6
--- | 63
Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
So, 66 divided by 7 = 9 with a remainder of 3
So the answer is 9 R 3.
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the activity of a radioactive isotope is found to decrease by 40% in one week. what are the values of its: a) decay constant, b) half-life, c) mean lifetime?
Answer: A) The decay constant (λ) is a measure of the rate at which a radioactive isotope decays. It is defined as the probability per unit time that an atom of the isotope will decay. The decay constant can be calculated using the formula:
λ = -ln(1 - x) / t
Where x is the fraction of the original activity that has decayed (in this case, 0.40), and t is the time over which the decay occurred (in this case, one week).
B) The half-life (T1/2) is the amount of time it takes for half of the original activity of a radioactive isotope to decay. It can be calculated using the formula:
T1/2 = ln(2) / λ
C) The mean lifetime (τ) is the average amount of time an atom of a radioactive isotope will survive before it decays. It can be calculated using the formula:
τ = 1 / λ
It's important to note that the above formulas are based on the exponential decay model, which assumes that the decay process is random and that the decay constant is constant over time. If the isotope does not decay in this way, these formulas may not give accurate results.
Step-by-step explanation:
Suppose the diameter of a circle is 8 units. What is its circumference? Use 3.14 for ππpi and enter your answer as a decimal.
The circumference of a circle with diameter 8 units is equal to 25.14 units.
How to calculate the circumference of a circle
Circumference is the perimeter of a circle, circles are featured solely by diameter. The formula for circumference is described below:
s = π · D
Where D is the diameter, in units.
If we know that D = 8 units, then the circumference of the circle is:
s = π · 8
s = 8π
s = 25.14
The circle (diameter: 8 units) has a circumference of 25.14 units.
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100 POINTS ANSWER QUICKLY Question 3 Part C (4 points): Based on what you learned about causation in lesson 5. 07, give a real world scenario that would represent a causal relationship
The real world scenario that would represent a causal relationship in causation:
Example 1: Shark attacks and sales of ice cream
Example 2: Box Office Income and Master's Degrees
Example 3: Nuclear Energy Production vs. Pool Drownings
Example 4: Marriage Rate versus. Measles Cases
The concept of causation states that one occurrence results in another event. Just a test with a correct engineering can demonstrate correlation. Similar groups are given various treatments in these trials, and the results of each group are examined. Only when there is a discernible difference between the groups' results can we say that a treatment had an impact.
People frequently misunderstand and misuse the concept of causality in statistics because they believe that just because data reveals a correlation, there must definitely be an underlying causal relationship.
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Which is a correct solution for the following system of Inequalities
The solution for given linear inequalities is (-0.5,4.25) from the given graph.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
As we know the solution for the lines which intersect at a certain point is that point or the coordinates of that point i.e. (-0.5,4.25).
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Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
The surface area of the rectangular prism is 100m²
How to determine the surface areaThe formula for calculating the surface area of a rectangular prism is expressed as;
Surface area = 2(wl + hw + lh)
Given that;
w is the width of the rectangular primsh is the height of the rectangular prisml is the length of the rectangular prismFrom the diagram shown, let's substitute the values, we have;
Surface area = 2(2× 7 + 4× 2 + 7 × 4)
multiply the values, we get;
Surface area = 2(14 + 8 + 28)
Add the values
Surface area = 2(50)
Expand the bracket
Surface area = 100m²
Hence, the value is 100m²
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convert 6 2/5 to a fraction greater than 1
Answer:
Step-by-step explanation:
6 2/5
Number 5 is denominator, keep it for denominator.
Numerator will be 6x5+2 =32
so, a fraction of 6 2/5 greater than 1 is 32/5
PLEASE HELP ASAP!!!!
The inverse matrix of the given matrix is
[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
What is meant by inverse matrix?
If A is a non-singular square matrix, then A^-1, often known as the inverse matrix of A, must exist if it is to satisfy the following property:
AA^-1 = A^-1A = I, Where I is the Identity matrix
Now, we will first find the determinant of the given matrix, whichis as follows:
Determinant = 6-4 = 2
Since, the determinant is not zero, this means that the inverse matrix exists.
Now, let's find the inverse matrix i.e. A^-1
[tex]A^{-1} = \frac{1}{D} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{2} \left[\begin{array}{ccc}3&-4\\-1&2\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-4/2\\-1/2&2/2\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
Hence, the inverse matrix of the given matrix is as under
[tex]\left[\begin{array}{ccc}3/2&-2\\-1/2&1\end{array}\right][/tex]
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HELP ASAP!!! GIVING 50 POINTS!!
Answer:
200,000 times
Step-by-step explanation:
80 km × (1000 m)/(1 km) × (100 cm)/(1 m) = 8,000,000 cm
8,000,000 cm / 40 cm = 200,000
Answer: 200,000 times
Ben and tom each take driving test. The probability that ben and tom will pass is 0. 87 and 0. 7 respectively
The probability that ben and tom will pass is 0. 87 and 0. 7 respectively will be 0.38
The answers to the questions are as follows:
Please refer to the attached file for point a.
Since both of them pass their driving tests at the same time, we double the odds of each one passing, which results in a probability of "56%".
Tom passes but Ben fails, or Tom passes but Ben succeeds. Therefore, the likelihood and the response is "38%."
(a)The tree diagram is attached.
P(Ben Fails)=1-0.8=0.2
P(Tom Fails)=1-0.7=0.3
(b)Probability that both will pass their driving test.
P(both will pass)=0.8 X 0.7 =0.56
(c)Probability that only one of them will pass their driving test.
P(Tom Bass, Ben Fails OR Ben Pass, Tom Fails)
=(0.7 X 0.2)+(0.8 X 0.3)
=0.14+0.24
=0.38
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A toy store had 4 boxes that weighed a total of 34 kilograms. If each box had the
same amount of weight, how much did each box weigh? Between what two whole
numbers does your answer lie?
The weight lies between the whole numbers 8 and 9.
The length, breadth, and height of a package are multiplied using the longest point on each side to determine the dimensional (DIM) weight.
If each of the 4 boxes has the same weight, the weight of each box can be found by dividing the total weight by the number of boxes. Given that the total weight is 34 kilograms, the weight of each box is:
w = 34 kg / 4 boxes = 8.5 kg
So, each box weighs 8.5 kilograms. The weight lies between the whole numbers 8 and 9.
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the maller of 2 conecutive number i x3
a.find the um of the two number
b.find their difference
c.ubtract their um for x8
The sum of the two consecutive numbers is 31.
Let the two consecutive number are n and n+1.
Given the difference between square of two consecutive Numbers is 31.
(n + 1)² - n² = 31n² + 2n + 1 – n² = 312n + 1 = 312n = 30n = 15Then, two consecutive number = n, n+1 = 15, 16
Therefore
( A ): the sum of two consecutive number = 15 + 16 = 31
( B ): Their difference = 16 – 15 = 1
( C ): Subtract their sum by 8 = 31 – 8 = 23
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Change 9 out of 20 to a percentage.
Answer:
45%
Step-by-step explanation:
Answer:
45%
Step-by-step explanation:
[tex]\frac{9*5}{20*5}[/tex] = [tex]\frac{45}{100}[/tex]
What is
√12x8/√3x²
in simplest form, where x>0?
The simplest form of √12x⁸/√3x² is 2x³.
What is simplification?
Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.
Here, we have
Given: √12x⁸/√3x²
We have to simplify this function.
We combine both terms in one and we get
= √12x⁸/3x²
= √4x⁶
= 2x³
Hence, the simplest form of √12x⁸/√3x² is 2x³.
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You are going on vacation and need to rent a car. You must chose between Hertz and Enterprise.
At Hertz you will be charged a one-time insurance fee of $80, plus $60 per day.
At Enterprise you will be charged a one-time insurance fee of $100, plus $55 per day.
Answer:
what's the question? how many days? 4 day is the breakeven mark.
Step-by-step explanation:
80+60x = 100+55x
5x =20
x=4
for a 4-day rental, it'll be the same.
if longer than 4 days, go with enterprise. shorter than 4 days go with hertz.
Sentence letter are ingle letter P,Q, R, etc. tranlated to Englih entence that are either true or fale.
The English sentences that are translated from single letters, such as P, Q, R, etc., can either be true or false depending on the context in which they are used.
For example, if P is translated as "the sky is blue," then this sentence is true. However, if P is translated as "the sky is orange," then this sentence is false. In order to determine the truth value of the translated sentence, we must first identify the context in which the letter is being used. Then, we can decide whether the translation is true or false by using logic and reasoning. For example, if we know that the sky is not orange, then the translation of P can be determined to be false.
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2 5/12 + 4 1/4 please help
Answer: 6 2/3
Step-by-step explanation: 2 5/12 + 4 1/4 29/12 + 4 1/4 29/12 + 17/4 (3/3) 29/12 + 51/12 80/12/4/4 20/3 6 2/3
Makayla leans a 26-foot ladder against a wall so that it forms an angle of 69
∘
∘
with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.
A right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.
What are right triangles?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides.
The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
So, the parameters listed are:
69-degree angle.
Ladder length (l) equals 26 feet.
The following cosine ratio is used to compute the horizontal distance (h).
cos(θ) = h/l
Replace known values:
cos(69) = h/26
Make the topic "h":
h = 26 * cos(69)
Consider the product:
h = 9.3
Therefore, a right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.
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what is y=12x-35 domain and range
The domain and the range of y = 12x - 35 are the set of all real numbers
How to determine the domain and the range?from the question, we have the following parameters that can be used in our computation:
y = 12x - 25
There is no restriction on the input values, x
So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).
The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).
This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.
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Nelson earned $379.25 in net pay for working 40 hours. He paid $56.64 in federal and state taxes, and $36.11 in FICA tax. What was Nelson's hourly wage?
Nelson hourly wage is $11.8
How to calculate Nelson hourly wage ?Nelson earned $379.25 in net pay for working 40 hours
He paid $56.64 in federal and state taxes
He also paid $36.11 in FICA tax
Therefore Nelson hourly wage can be calculated as follows
The first step is to calculate the total earnings
= 379.25 + 56.64 + 36.11
= 472
The next step is to calculate the hourly wage
472/40
= 11.8
Hence Nelson hourly wage is $11.8
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(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division
(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division
The synthetic division for the polynomial (x^4+10x^3+10x^2-15x-6) divided by (x+2) would be:
x^3 + 8x^2 - 19x - 12 + (R)
Where R is the remainder.
The quotient is x^3 + 8x^2 - 19x - 12
What is a synthetic division for the polynomial?A synthetic division, also known as long division of polynomials or polynomial synthetic division, is a method of dividing polynomials that is faster and simpler than the traditional polynomial long division method. It is particularly useful for dividing a polynomial by a linear factor of the form (x - a), where a is a real number.
Synthetic division allows you to divide a polynomial by a linear factor without having to perform the traditional long division algorithm, by using the polynomial's coefficients instead of the polynomial itself. Synthetic division is also useful for finding the remainder of a polynomial division. The quotient and the remainder are written in a form of simplified polynomials.
Therefore, the correct answer is as given above
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What number is 24 less than 3 times itself?
Answer:
3x - 24
Step-by-step explanation:
24 less is the same as: - 24
3 times itself is: 3x
3. Which represents the least percent of change?
A. A $125 watch selling for $90.
B. The speed limit changing from
40 mph to 55 mph.
C. The stock market dropping from
250 to 175 points.
D. Marissa's math grade increasing
from 75 to 99.
Answer: B. The speed limit changing from 40 mph to 55 mph represents the least percent of change.
In A, a watch selling for $90 from $125 represents a 28% decrease,
In C, the stock market dropping from 250 to 175 points represents a 30% decrease,
In D, Marissa's math grade increasing from 75 to 99 represents a 32% increase.
While in B, the speed limit changing from 40 mph to 55 mph represents a 37.5% increase.
So, B represents the least percent of change.
Step-by-step explanation:
DJ is riding in the passenger seat of a car that is going 40 miles per hour
when it passes Jabari, who is standing on the street. From Jabari's
perspective, how quickly is DJ moving?
A
DJ does not appear to be moving at all.
B. DJ appears to be moving more slowly than the car.
C. DJ appears to be moving more quickly than the car.
D. DJ appears to be moving at the same speed as the car.
Answer: DJ appears to be moving at the same speed as the car
Step-by-step explanation:
DJ is inside of the car, so he moves with it. Jabari is outside of the car and is standing still, so both DJ and the car he is in seems to be moving at 40 miles per hour at the same time
imagine you are painting a series of towers built from cubes. You are going to paint only the exposed faces of the cubes. If the tower you paint has 25 exposed faces, how many cubes are in the tower?
Answer:
101 Faces
Step-by-step explanation:
Hope it helps + get it right
The scatter plot shows a hiker's elevation above sea level during a hike from the base to the top of a mountain. The equation of a trend line for the hiker's elevation is y=9.54x+694, where x represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of the trend line to estimate the hiker's elevation after 145 minutes.
By using the equation of the trend line, the hiker's elevation after 145 minutes is equal to 2,077.3 feet.
How to determine the hiker's elevation after 145 minutes?In order to determine the hiker's elevation after 145 minutes, we would have to substitute the value representing the number of minutes (x) into the linear equation that models the hiker's elevation in feet and then evaluate as follows;
y = 9.54x + 694
When the value of x = 145 minutes, the hiker's elevation (y) in feet is given by;
Hiker's elevation (y) = 9.54x + 694
Hiker's elevation (y) = 9.54(145) + 694
Hiker's elevation (y) = 1,383.3 + 694
Hiker's elevation (y) = 2,077.3 feet.
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