Answer:
n1=0 n2=4 n3=8 n4=12
Step-by-step explanation:
tn=4(n-1) is the formula to determine the value of the nth term, so all you have to do is plug in what term you want for the variable and solve.
for example
n1=4(1-1)=0
n2=4(2-1)=4
n3=4(3-1)=8
n4=4(4-1)=12
Hope you understand and have a great day.
F(x)=3x-1 and g(x)=x+2, find (f+g)(x)
Answer:
4x+1
Step-by-step explanation:
3x-1+(x+2)
3x-1+x+2
Collect Like Terms: 3x+x-1+2
= 4x+1
Please someone help me answer this
[tex]Given:\ x_{n+1}=\sqrt[3]{6x_{n}-1}\ ,\ x_{1}=4\\\\The\ iterative\ formula\ can\ be\ re-written\ as:\\x_{n}=\sqrt[3]{6x_{n-1}-1}\\\hrule\ \\x_2=\sqrt[3]{6x_{1}-1}\\x_2=\sqrt[3]{6(4)-1}\\x_2=\sqrt[3]{23}\approx 2.84\\\hrule\ \\x_3=\sqrt[3]{6x_{2}-1}}\\x_3=\sqrt[3]{17.04-1}\\x_3=\sqrt[3]{16.04}\approx 2.52\\\hrule\ \\x_4=\sqrt[3]{6x_{3}-1}}\\x_4=\sqrt[3]{15.12-1}\\x_4=\sqrt[3]{14.12}\approx 2.41[/tex]
what is the volume of a rectangular prism with a length of 4m, width of 6.5m and height of 1.2m
The volume of the rectangular prism is 31.2 [tex]m^{3}[/tex].
To find the volume of a rectangular prism, we multiply the length, width, and height of the prism.
Given that the length of the rectangular prism is 4m, the width is 6.5m, and the height is 1.2m, we can find the volume as follows:
Volume = length x width x height
= 4m x 6.5m x 1.2m
= 31.2 cubic meters
Therefore, the volume of the rectangular prism is 31.2 cubic meters.
To understand what this means, imagine filling the rectangular prism with cubic blocks, each having a volume of 1 cubic meter. We would need to place 31.2 of these blocks to completely fill the prism. Another way to think about it is that the prism could hold 31.2 cubic meters of water, if filled to the brim without any spillage.
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Restate the problem in a way that can be easily translated into an equation.
It took Dani 5 minutes longer to run the course than it did Candice.
A. Dani’s rate is slower than Candice’s rate.
B. Dani’s time is greater than Candice’s time.
C. Dani’s time equals Candice’s time plus 5
C. Candice’s time equals Dani’s time plus 5 minutes.
The relationship between Dani's time and Candice's time, taking into account the fact that Dani took 5 minutes longer to run the course. it is Reasonable time to assume that the runners' rates were constant. Option C is the correct answer.
Let "t" be the time it took Candice to run the course.
Then, according to the problem statement, Dani took 5 minutes longer than Candice to run the course. Therefore, Dani's time is equal to Candice's time plus 5 minutes, which can be expressed as:
D = C + 5
where D is Dani's time and C is Candice's time.
This equation represents the relationship between Dani's time and Candice's time, taking into account the fact that Dani took 5 minutes longer to run the course. It can be used to solve problems related to the two runners' times, such as finding their individual times or comparing their rates. Option C is the correct answer.
It is important to note that this equation assumes that both runners ran the course at a constant rate. If the runners' rates varied throughout the course, then the equation would not accurately represent their times. However, for the purposes of this problem, it is reasonable to assume that the runners' rates were constant.
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HELP ASAP PLEASE!
A bowl has 27 red M&Ms and 32 green M&Ms. John randomly chooses a M&M, eats it, and then chooses another M&M. Round to the nearest percent.
(a) What is the probability that both M&Ms are green? Show your work.
(b) What is the probability that John eats a red M&M then a green M&M? Show your work.
The probability that both M&Ms are green is 29% and the probability that John eats a red M&M then a green M&M is 25%
Here, we have
Red = 27
Green = 32
This means that
Total = 27 + 32
Total = 59
So, we have
P(Both green) = 32/59 x 31/58
Evaluate
P(Both green) = 29%
And, The probability of red M&M then a green M&M,
Here, we have
Red = 27
Green = 32
This means that;
Total = 27 + 32
Total = 59
So, we have
P(Red and green) = 27/59 x 32/58
Evaluate;
P(Red and green) = 25%
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Jim spends $16 each time he travels the toll roads. He started the month with $224 in his toll road account. The amount, (in dollars), that he has left in the account after T trips on the toll roads is given by the following function.
A(t)=224-16t
How much money does Jim have left in the account after 8 trips on the toll roads?How many trips on the toll roads can he take until his account is empty?
OMG PLEASE I BEG I NEED HELP 5th grade math
Answer: A
Step-by-step explanation:
Volume= LxWxH so we get 20x28x24 as given.
Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.
13,440-10,500= 2,940 Cubic Inches
Option A
Answer:
Part A: 13440 cubic inches.
Part B: A - 2940 cubic inches.
Step-by-step explanation:
The volume of the box = 24x20x28 = 13440 cubic inches.
The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.
13440-10500 = 2940 cubic inches. The answer is A.
Use the following information for 12 and 13: The town's city hall is located in the
center of town(origin). One block is 250 in length. The post office for the town is
located 6 blocks east and 2 blocks north. One of the postal carriers, Dave, delivers
mail for an area of 25 square blocks. (10 points total)
12) What is the equation for the circle for the area that Dave covers?
13)Millie lives 3 blocks east and 3 block south of city city hall. Does Dave deliver Millie’s mail?
The standard form of the equation of a circle and the location of where Millie lives indicates;
12) The equation of the circle is; (x - 6)² + (y - 2)² = 25/π
13) Dave does not deliver to Millie
What is the formula for the area of a circle?The equation for the area of a circle is A = π × Radius²
12) The length of a block = 250 inches
The distance of the post office = 6 blocks east and 2 blocks north
The area the postal carriers delivers mail = 25 square blocks
The coordinates of the location of the post office = (6, 2)
The radius of the circle ias therefore, r = √(25/π) ≈ 2.82
The equation of a circle is; (x - h)² + (y - k)² = r²
Where; (h, k) = (6, 2)
Therefore; The equation of the circle is; (x - 6)² + (y - 2)² = 25/π13) The coordinates of the location where Millie lives is (3, -3)
The distance of Millie's address 3 blocks south of the city hall, whereby the carrier Dave reaches about south 2.82 blocks, from 2 blocks north from the city hall, which is about 0.82 blocks south from the city hall.
Therefore, Dave's area does not extend to Millie's location and Dave does not deliver mail to Millie
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The ratio fu is 4: 3.
The ratio f: w is 12: 5.
What is the ratio fu w in its simplest
form?
Answer:
f : u = 12 : 9, so f : u : w = 12 : 9 : 5.
find an equation that passes through (1 ,2) and is parallel y=3x-9
Answer:
A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (1, 2)
Substituting the values we get:
y - 2 = 3(x - 1)
Simplifying the equation we get:
y - 2 = 3x - 3
y = 3x - 1
Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .
;>
find the geometric mean of 5 and 320
Answer:
B. 40
Step-by-step explanation:
you would multiply 5 and 320 and then do the square root of the number
Please help meeeeeeeee
Answer:
936m3
Step-by-step explanation:
6×6×2=72m3
9×16×6=864m3
72+864=936m3
Which expression is equivalent to 6√8 √√2?
A. 48√/2
B. 24
C. 24√2
D. 48
Answer:
[tex]6 \sqrt{8} \sqrt{2} = 6 \sqrt{16} = 6(4) = 24[/tex]
B is the correct answer.
What is the next step in the construction of a regular hexagon?
A. Use a compass and straightedge to continue drawing equilateral
triangles until you have six.
OB. Use a compass and straightedge to continue drawing equilateral
triangles until you have eight.
OC. Use a compass and straightedge to continue drawing equilateral
triangles until you have five.
OD. Use a compass and straightedge to continue drawing equilateral
triangles until you have four.
The next step in the construction of a regular hexagon is A. Use a compass and straightedge to continue drawing an equilateral
A circle with the required radius must first be drawn in order to make a regular hexagon. Draw a second circle whose centre is one of the spots on the first circle using the same radius. These two circles' intersection points will form the vertices of an equilateral triangle. Three of these equilateral triangles, with their vertices on the circle, must be drawn inside a circle. At the circle's centre, these three triangles will have a common vertex.
Drawing three more equilateral triangles, each of which shares a side with one of the previously drawn triangles, is necessary to finish the building of a regular hexagon. Drawing equilateral triangles keeps on until there are six of them, each of which has a side in common with a preceding triangle.
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emily has $100 extra to spend on supplies for her T-shirt-making business. she wants to buy ink, i, which costs $8 a bottle, and ne brushes, b, which are $18 each. which inequality below represents this scenario?
(c) 15i + 4b ≥ 100 inequality represents this scenario.
To represent the scenario described in the problem, we need to use an inequality that relates the amount of money Emily spends on ink and brushes to the total amount of money she has available. Let's call the amount of ink Emily buys "x" and the number of brushes "y". Then the total amount of money she spends is:
Total cost = 8x + 18y
We want to know when this total cost is less than or equal to $100, so we can write:
8x + 18y ≤ 100
This inequality means that the total cost of ink and brushes must be less than or equal to the amount of money Emily has available. Therefore, the answer is (c) 15i + 4b ≥ 100.
Correct Question :
Emily has $100 extra to spend on supplies for her T-shirt-making business. She wants to buy ink, i, which costs $8 a bottle, and ne brushes, b, which are $18 each. Which inequality below represents this scenario?
a) 4i+100 ≤ 15b
b) 15i + 4b ≤ 100
c) 15i + 4b ≥ 100
d) 4i + 15b ≤ 100
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The slope of MN¯¯¯¯¯¯¯ is −3.
Which segments are parallel to MN¯¯¯¯¯¯¯?
Select each correct answer.
Responses
WX¯¯¯¯¯¯, where W is at (2, 6) and X is at (4, 0)
segment W X, , where , W, is at , begin ordered pair 2 comma 6 end ordered pair, and , X, is at , begin ordered pair 4 comma 0 end ordered pair
RS¯¯¯¯¯, where R is at (1, 3) and S is at (4, 2)
segment R S, , where , R, is at , begin ordered pair 1 comma 3 end ordered pair, and , S, is at , begin ordered pair 4 comma 2 end ordered pair
TU¯¯¯¯¯, where T is at (8, 1) and U is at (5, 10)
segment T U, , where , T , is at , begin ordered pair 8 comma 1 end ordered pair, and, U, is at , begin ordered pair 5 comma 10 end ordered pair
PQ¯¯¯¯¯, where P is at (5, 6) and Q is at (8, 7)
TU is parallel to MN.
Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.
Therefore,
Considering the line TU, find the slope = y₂-y₁ / x₂-x₁
= 10-1 / 5-8 = -9/3 = -3
Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.
Hence TU is parallel to MN.
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the point r is a weighted average of points s and t. The weight on point t is 0.625. What is the weight on point s?
Let w be the weight on point s. Since the sum of the weights is 1, the weight on point t is 0.625, we can write:
w + 0.625 = 1
Subtracting 0.625 from both sides, we get:
w = 1 - 0.625 = 0.375
Therefore, the weight on point s is 0.375.
Select the real-world situation that can be represented by 4m+ 2.
A. Bentley swims 4 more than 2 times the laps Dan swims.
B. Grace bikes 2 more than 4 times the miles Jamie bikes.
C. An online company charges a $4 shipping fee and $2 per item for
a purchase.
OD. A music download website has a membership fee of $4 and
charges $2 for each download.
Step-by-step explanation:
The real-world situation that can be represented by 4m+2 is option D, where a music download website has a membership fee of $4 and charges $2 for each download.
Here, "4m" represents the total cost of downloading "m" songs at a cost of $2 per song, and "2" represents the fixed cost of the membership fee. So, the total cost of downloading "m" songs along with the membership fee can be represented by the expression 4m + 2.
And iron home has a listed price of $65 and the sales tax rate is 5%. How much is sales tax what is the total cost?
Convert the polar form of the complex number into rectangular form.
z=3sqrt(2)cis * 7pi / 4
Show all of your work. Show how you separately convert r and theta into a and b.
The rectangular form of the complex number z = 3√2 cis (7π/4) is
z = -3 - 3i
We have,
To convert a complex number from polar form to rectangular form, we use the following formulas:
x = r cos(theta)
y = r sin(theta)
where r is the modulus of the complex number, and theta is its argument.
In this case, we have:
r = 3√2
theta = 7π/4
So:
x = 3√2 cos(7π/4) = 3√2 (-1/√2) = -3
y = 3√2 sin(7π/4) = 3√2 (-1/√2) = -3
Therefore,
The rectangular form of the complex number z = 3√2 cis (7π/4) is
z = -3 - 3i
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If Line A has a slope of 2, what would the slope of Line B have to be in order for A and
B to be perpendicular?
The slope of Line B would have to be -1/2.
Two lines are perpendicular to each other if the product of their slopes is -1. The slope of Line A is given as 2. Therefore, the slope of Line B would have to be the negative reciprocal of 2, which is -1/2. This ensures that the product of the slopes of Line A and Line B is -1, satisfying the condition for perpendicularity.
In general, if the slope of Line A is m, then the slope of a line perpendicular to Line A would be -1/m. This relationship holds because perpendicular lines form right angles, and the slopes of perpendicular lines are negative reciprocals of each other.
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Given that log2 = x and log3 = y, express log60 in terms of x and y
can someone please do #7
The numeric value of f(a) + f(h) for f(x) = x² - 5x + 3 is given as follows:
A. f(a) + f(h) = a² + h² - 5a - 5h + 6.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is defined as follows:
f(x) = x² - 5x + 3.
Hence the numeric values are given as follows:
f(a) = a² - 5a + 3.f(h) = h² - 5h + 3.The only like term is the 3 for both expressions, hence the addition is given as follows:
f(a) + f(h) = a² + h² - 5a - 5h + 6.
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Please help and show work
Answer:
5.25
Step-by-step explanation:
not much to show, go 3 topping across then up to see the price
A restaurant automatically charges a 20% gratuity if a party has 6 or more people. How much gratuity is added to a party of 6 on a $141 bill.
Answer:
Therefore, $28.20 is added as gratuity to the $141 bill for a party of 6.
Step-by-step explanation:
If a party has 6 or more people, a 20% gratuity is automatically charged. So in this case, the gratuity is:
20% of $141 = (20/100) x $141 = $28.20
Therefore, $28.20 is added as gratuity to the $141 bill for a party of 6.
Tami has two jobs and can work at most 20 hours each week. She works as a server and makes $6 per hour. She also tutors and makes $12 per hour. She needs to earn at least $150 a week. Review the included image and choose the graph that represents the system of linear inequalities.
A.
Graph A
B.
Graph B
C.
Graph C
D.
Graph D
Graph B represents the system of linear inequalities the best.
Hence the correct option is (B).
Let Tami needs to work x hours per week as server and y hours per week as tutors.
So it is given that she can work at most 20 hours a week.
So, the suitable inequality to describe the situation:
x + y [tex]\le[/tex] 20 ............. (i)
Now the corresponding equation of this above inequality is,
x + y = 20
x/20 + y/20 = 1
comparing to inception form of straight line we can say that the equation says about a line which cuts axes at (20, 0) and (0, 20) respectively.
since (0, 0) gives 0 + 0 = 0 [tex]\le[/tex] 20 is true.
So the solution area towards origin.
It is also given that she makes $6 per hour as server and makes $12 per hour as tutor and she needs to earn at least $150.
The best suited inequality for this condition,
6x + 12y [tex]\ge[/tex] 150 .................(ii)
The corresponding equation of the above inequality:
6x + 12y = 150
6x/150 + 12y/150 = 1
x/25 + y/(12.5) = 1
So it is the line cuts the axes at (25, 0) and (0, 12.5) respectively.
since (0, 0) gives 6*0 + 12*0 = 0 [tex]\ge[/tex] 150 is not true so the solution area for this inequality towards opposite of origin along the straight line.
So Graph B represents the system of linear inequalities the best.
Hence the correct option is (B).
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Gabrielle needs several rectangular outside walls of her house repainted. The north-facing
wall is 22 feet wide by 10 feet tall, the south-facing wall is 15 feet wide by 20 feet tall, and
the wall by her patio is 8 feet wide by 10 feet tall. The painter charges $5 per square foot to
paint outside walls.
How much will it cost Gabrielle
to have the outside walls repainted?
Answer:
$3000
Step-by-step explanation:
22×10=220
15×20=300
8×10=80
220+300+80=600ft²
5×600=$3000
Suppose z varies inversely with t and that z = 10 when t = 12. What is the value of z when t = 5?
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"z" varies inversely with "t"}}{z = \cfrac{k}{t}}\hspace{5em}\textit{we also know that} \begin{cases} z=10\\ t=12 \end{cases} \\\\\\ 10=\cfrac{k}{12}\implies 120 = k\hspace{9em}\boxed{z=\cfrac{120}{t}} \\\\\\ \textit{when t = 5, what's "z"?}\qquad z=\cfrac{120}{5}\implies z=24[/tex]
A 3 1/2 inch by 5 inch photo is to be enlarged to a similar rectangle. If the width is 6 inches what should the length be?
The length of the enlarged photo should be approximately 8.57 inches.
The original photo and the enlarged photo are similar rectangles, we know that the ratio of their corresponding sides is the same.
Let's use "x" to represent the length of the enlarged photo.
We can set up a proportion to find the value of "x":
(original length) / (original width) = (enlarged length) / (enlarged width)
Substituting the given values, we get:
(5 inches) / (3.5 inches) = x / 6 inches
To solve for "x", we can cross-multiply and simplify:
5 inches × 6 inches = 3.5 inches × x
30 square inches = 3.5 inches × x
Dividing both sides by 3.5 inches:
x = 30 square inches / 3.5 inches
x = 8.57 inches (rounded to two decimal places)
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Given the expression: 12x2 + 18x − 12 Part A: What is the greatest common factor? Explain how to find it. (3 points) Part B: Factor the expression completely. Show all necessary steps. (5 points) Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)
Part A: The GCF of the expression 12x² + 18x - 12 is 6x.
Part B: The factored form of the expression 12x² + 18x - 12 is 6x(2x + 3) - 12x.
Part C: The result matches the original expression, which means our factoring is correct.
Part A: Finding the Greatest Common Factor (GCF)
To find the greatest common factor (GCF) of the given expression, we need to identify the largest term or number that can divide evenly into all the terms of the expression. In this case, we are dealing with three terms: 12x², 18x, and -12.
The coefficients of the three terms are 12, 18, and -12. The common factor of these coefficients is 6, as it can divide evenly into all of them.
The variable 'x' is present in both the first and second terms, and 'x' is also a common factor.
Combining the common factors of the coefficients and variables, we find that the GCF of the expression 12x² + 18x - 12 is 6x.
Part B: Factoring the Expression Completely
Now that we have determined the GCF of the expression, we can proceed to factor it completely.
We already found that the GCF is 6x. Factoring it out from each term, we get:
6x(2x + 3) - 6x(2)
We can simplify the expression further by multiplying the GCF with the remaining terms inside the parentheses:
6x(2x + 3) - 12x
Part C: Checking the Factoring
To check if our factoring is correct, we can multiply the factored expression back and see if it matches the original expression.
Multiplying the factored expression:
6x(2x + 3) - 12x
= 12x² + 18x - 12
The result matches the original expression, which means our factoring is correct.
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