Determine the first 4 term of the sequence
tn=4(n - 1 )

Answer:

B. 40

Step-by-step explanation:

you would multiply 5 and 320 and then do the square root of the number

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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Answer:

[tex]6 \sqrt{8} \sqrt{2} = 6 \sqrt{16} = 6(4) = 24[/tex]

B is the correct answer.

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.

(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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Answer:

4x+1

Step-by-step explanation:

3x-1+(x+2)

3x-1+x+2

Collect Like Terms: 3x+x-1+2

= 4x+1

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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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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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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[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]

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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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.

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

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)

13) 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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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.

[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]

Answer:

5.25

Step-by-step explanation:

not much to show, go 3 topping across then up to see the price

Answer:

936m3

Step-by-step explanation:

6×6×2=72m3

9×16×6=864m3

72+864=936m3

Answer:

$3000

Step-by-step explanation:

22×10=220

15×20=300

8×10=80

220+300+80=600ft²

5×600=$3000

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.

Answer:

f : u = 12 : 9, so f : u : w = 12 : 9 : 5.

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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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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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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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.

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:

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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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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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 .

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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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