Identify the 7th term of the geometric sequence in which a2 = 324 and a4 = 36
Answer:
4/3
Step-by-step explanation:
a2 = 324 and a4 = 36
second term is 324 and fourth term is 36
[tex]a_n= a_1(r)^{n-1}[/tex]
To get second term, replace n with 2
[tex]a_2= a_1(r)^{2-1}[/tex]
[tex]a_2= a_1(r)[/tex]
replace a2 with 324
[tex]324= a_1(r)[/tex] -----------> equation 1
To get fourth term , replace n with 4
[tex]a_4= a_1(r)^{4-1}[/tex]
[tex]a_4= a_1(r)^3[/tex]
Replace the value
[tex]36= a_1(r)[/tex] -----------> equation 2
divide second equation by first equation
[tex]36= a_1(r)^3[/tex] divide by [tex]324= a_1(r)[/tex]
1/9 = r^2
take square root on both sides
1/3= r
now we find a1
[tex]324= a_1(r)[/tex]
[tex]324= a_1(\frac{1}{3})[/tex]
multiply by 3 on both sides
972= a_1
So a1= 972, r= 1/3
now find out 7 term by replacing 'n' with 7
[tex]a_7= 972(\frac{1}{3})^{7-1}[/tex]
So 7th term is 4/3
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The pitch of a roof is its slope. The roof of a home rises vertically a distance of 8 ft through a horizontal distance of 15 ft. Find the pitch of the roof.
The pitch of a roof of a home rises vertically a distance of 8 ft through a horizontal distance of 15 ft is 0.53.
What is Slope?
The slope of line is a measure of its steepness.
Given that;
Vertical distance (rise) = 8 feet
Horizontal distance (running) = 15 feet
Now, To find the pitch (slope) of the roof, we would use the following formula:
Slope is the ratio of the vertical distance measured to the horizontal distance measured.
Hence, The pitch (slope) of a roof is given by the formula;
Pitch = V / R
Where:
V is the rising vertical distance of an object.
H is horizontal distance an object runs through.
Hence, Substituting the given parameters into the formula, we have;
Pitch = 8/15
= 0.53
Thus, Pitch (slope) = 0.53
So, The pitch of a roof of a home rises vertically a distance of 8 ft through a horizontal distance of 15 ft is 0.53.
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What two consecutive odd integers have a sum of 48?
to make 12 muffins, Mr. J's recipe requires 3/4 of a cup of sugar. If Mr. J wants to make 96 muffins, how much sugar will he need?
a segment has endpoints (a,b) and (c,d). The segment is translated so that its image is 6 units up and 3 units left of the preimage. Are the two segments parallel, perpendicular, or neither?
The translation of the image can be describe as
x – 3
y + 6
Since the transformation that is made is purely translation, therefore this means that the original image and the new image will never intersect and hence:
Parallel
If the two are extended we can actually see that they will never meet.
Find the constant of variation and the slope of the direct variation model
y=2x
you borrow $200 from a friend to help pay for the new laptop computer. You pay your friend $12 per week. Write and solve an inequality to find when you will owe tour friend less than $60.
You will owe your friend less than $60 if you pay them $12 per week for more than 11.67 weeks, which means you'll need to make payments for at least 12 full weeks.
Explanation:To solve the problem of when you will owe your friend less than $60, we need to set up and solve an inequality.
The amount owed after any number of weeks can be represented by the initial debt of $200 minus the total amount paid off, which is $12 times the number of weeks.
If we let x represent the number of weeks, the inequality we need to solve is 200 - 12x < 60.
To solve this inequality, we subtract 200 from both sides, getting -12x < -140.
Then, we divide both sides by -12, remembering to reverse the inequality sign because we are dividing by a negative number, which gives us x > 11.67.
Since we can't pay off part of a week, we would need to pay your friend for at least 12 full weeks to owe less than $60.
Final answer:
To find when you will owe less than $60, set up the inequality 200 - 12w < 60. After simplifying, we see that it will take just over 11.67 weeks, so you will owe less than $60 after making payments for 12 weeks.
Explanation:
To solve the problem at hand, we need to create an inequality to represent the situation where you will owe less than $60 to your friend. Let's denote the amount owed each week with w and the total amount owed with A. You start with an initial debt of $200, and each week you pay off $12. The inequality we are trying to establish is when the total amount owed will be less than $60.
The inequality will be in the form of A - 12w < 60, where A is the initial amount of $200 and w represents the number of weeks. Plugging in $200 for A, we get 200 - 12w < 60.
To solve for w, we'll perform the following steps:
Subtract $200 from both sides to isolate the variable term: -12w < -140.
Since we are dividing by a negative number, remember to flip the inequality sign: w > 140/12.
Simplify the fraction to get the minimum number of weeks: w > 11.67.
You will owe your friend less than $60 after roughly 12 weeks since fractions of a week don't apply in the context of a weekly payment schedule.
what is the limit as x is approaching 0 of the absolute value of x
The restriction of the outright worth of x as x methodologies 0 will be 0. Outright worth guarantees that the result is non-negative, and as x methodologies zero from one or the other side, the outcome stays at 0.
Explanation:The inquiry you're posing relates to the furthest reaches of the outright worth capability as the variable x methodologies are the worth of nothing. In science, explicitly in math, we assess cutoff points to comprehend the way of behaving of capabilities as they approach a specific point.
To track down the breaking point as x methodologies 0 of the outright worth of x, signified as lim x→0 |x|, we want to think about the meaning of outright worth. The outright worth of a number is the non-negative worth of that number regardless of its sign. In this manner, as x methodologies 0 from either the positive or negative side, the outright worth of x will likewise move toward 0.
Consequently, the cutoff is 0, since as x gets increasingly close to nothing, so does the outright worth of x.
( variable son both sides of an equation)
SHOW ALL WORK AND MAKE SURE IT MAKES SENSE
I WILL GIVE BRAINLIEST WITH BEST ANSWER THAT INCLUDES ALL OF THE ABOVE
Solve: 7b-20=3b+12
A line segment is different from a line in that a segment has
How many squares are along the side of a chessboard?
Which fraction is equivalent to -7/8 ?
A )8/-7
B) 7/-8
C) -7/-8
D) 8/7
Aaron bought 132 inches or wire he cut the wire into 9 pieces that were the same lenght what is the length of each piece or wire
The length of each piece of wire is about 14.7 inches.
What is division?Division is the process of dividing a number by a given number.
Given that, the length of the wire is 132 inches.
Now, the wire is cut into 9 equal pieces, therefore, the length of each piece is:
132/9
= 14.7 inches
Hence, the length of each piece of wire is about 14.7 inches.
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Plot the line for the equation on the graph.
y−4=−14(x−5)
Answer: I just did the test and the correct answer was (9,3) 9 on the x axis and 3 on the y and (4,9) 4 on the x axis and 9 on the y
Step-by-step explanation:
Adam draws three parallelograms. He measures the sides of each figure, as shown.
What is a reasonable conjecture for Adam to make by recognizing a pattern and using inductive reasoning?
In a parallelogram, all sides are congruent.
In a parallelogram, opposite sides bisect each other.
In a parallelogram, opposite sides are congruent.
In a parallelogram, all sides bisect each other.
Answer:
In a parallelogram, opposite sides are congruent.
Step-by-step explanation:
Writing the lengths of the sides of the parallelograms shows him a pattern for the side lengths of opposite sides. Doing this will show him that opposite sides are congruent.
Item 19 You pay $40 each month for satellite TV, plus $3.50 for every movie you purchase. Write and solve an equation to find the number of movies purchased during a month with a total bill of $57.50.
Find the next two terms in the sequence. 0, 1, 4, 9, ...
A. 13, 17
B. 13, 18
C. 16, 25
D 16, 23
Answer:
16, 25
Step-by-step explanation:
the next two terms in the sequence. 0, 1, 4, 9, ...
Lets find the difference between the two terms
1-0 = 1
4-1=3
9-4= 5
the terms are increasing by odd numbers
0, 1, 4, 9, ...
\/ \/ \/
+1 +3 +5
The next term will increase by +7
9+7= 16
Next term is 16
Next term will increase by 9
16 + 9 = 25
so , next two terms are 16 and 25
How do you multiply mixed negative number fractions?
If cats prowl, mice will scatter. Mice are scattering
If −5e^x^2 y=x and y(−5)=0, find y′(−5) by implicit differentiation
The diagram shows a trapezium ABCD in which BC parallel to AD
Answer:
if its the diagram i think then:
f = 6cm
g = 8cm
Step-by-step explanation:
square = 48cm²
triangle = 12cm²
24 / 4 = 6
AD = 6cm
So
BC = 6cm
CD = 48 / 6 = 8cm
CD = 8cm
f = 6cm
g = 8cm
In geometry, a quadrilateral with at least each pair of parallel sides is referred to as a trapezoid. Therefore, the length of BC is 6cm and the length of CD is 8cm.
What is trapezium?In geometry, a quadrilateral with at least each pair of parallel sides is referred to as a trapezoid both Canadian and American English, and perhaps a trapezium in British as well as other forms of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.
The bases of a trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs; if not, the trapezoid is indeed a parallelogram, with 2 sets of bases. A trapezoid without equal-sized sides is called a scalene trapezoid.
area of square = 48cm²
area of triangle = 12cm²
24 / 4 = 6
AD = 6cm
BC = 6cm
CD = 48 / 6 = 8cm
CD = 8cm
f = 6cm
g = 8cm
Therefore, the length of BC is 6cm and the length of CD is 8cm.
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Your question is incomplete but most probably your full question was,
The diagram shows a trapezium ABCD in which BC parallel to AD. What is the length of BC and CD.
Find the standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5.
The position of a particle on the x-axis at time t, t > 0, is s(t) = e^t with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for 0 ≤ t ≤ In3?
3
2/ln3
3/ln3
3/2
Also please just tell me which on it is
the equation y = 0.25x + 50 gives the cost y of renting a car if the car is driven x miles
According to the model, what is the best estimate of the cost for renting a car if you plan to drive 250 miles?
50$
62.50$
112.50$
300$
If angle m 9 =119,what is the sum of the measures of angle 11 and 16
The measures of angles ∠11 and ∠16 are 119 and 119 respectively .
How to determine the values of the named anglesUsing the parameters given for our Calculation;
∠9 = 119°From the concept of corresponding angles ;
∠9 = ∠11 = 119° (corresponding angles are equal)For ∠16 ;
∠11 and ∠16 are vertically oppositeHence,
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Find the distance between the points (4, 2) and (-8, 7).
What is the degree of the polynomial function shown in the graph?
1
2
3
4
The correct answer is
4
:)
Jada typically earns 1545 each month of which 47.20 is spent on eletricity. What percent of jadas earnings are spent on eletricity each month
Ayuda porfavor.
esto es operaciones con los numeros reales.
necesito la respuesta con procedimiento
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Answer:
y = -2/5 x - 2
Step-by-step explanation:
2x + 5y = 10
5y = -2x + 10
y = -2/5 x + 2
so slope = -2/5
passes through the point (5, −4)
y = mx + b
b = y - mx
b = -4 - (-2/5)(5)
b = -4 + 2
b = -2
equation
y = -2/5 x - 2