the following is a linear sequence. 1, 4, 7, 10, 13...

using the explicit formula 3n - 2 find the 90th term in the sequence.

A. 90
B. 270
C. 268
D. 265

​

Answer: 57

Step-by-step explanation:

53+71+89+10+62=285

285/5=57

Answer: 57

Step-by-step explanation:

Order the data least to greatest: 10, 53, 62, 71, 89

then add them to get the sum of: 285

now divide that by how many numbers are in the data set so: 285/5

= 57

Answer: 221.56

Step-by-step explanation:  (3.14)(r)^2

r = half diameter

Answer:

variable= x

x ≤ 100

Step-by-step explanation:

it would be x ≤ 100 because it says it can hold as many AS 100, making it less than or equal to 100

Answer:

g(granola bar) = $2 and a(apple) = $1

Step-by-step explanation:

This problem can be modeling as an equation systems with two unknows.

We can writting the equation systems as follows:

For Addison [tex]2g+6a=10[/tex] where "g" is a granola bar price, "a" an apple price, and 10 is the sum of both product prices in dollars.

For George [tex]2g+3a=7[/tex] where "g" is a granola bar price, "a" an apple price, and 7 is the sum of both product prices in dollars.

Ordering both equations:

[tex]\left \{ {{2g+6a=10} \atop {2g+3a=7}} \right.[/tex]

We're going to use the reduction method to solve this system of equations.

The reduction method consists of adding (or subtracting) the system equations to eliminate one of the unknowns.

1.  Make sure that adding or subtracting the equations, some of the unknowns disappears.

We can see if we substracting both equations, the "g" unknown disappears.

[tex]\left \{ {{2g+6a=10} \atop {-(2g+3a)=-(7)}} \right.[/tex]

[tex]\left \{ {{2g+6a=10} \atop {-2g-3a=-7}} \right.[/tex]

Sustracting both equations, we obtain:

[tex]0g+3a=3[/tex]

[tex]3a=3[/tex]

[tex]a=\frac{3}{3} =1[/tex] which means that the value of an apple is $1.

2. We calculate the other unknown by substituting the value obtained from "a".

Substituting the value from "a" in the first equation:

[tex]2g+6(1)=10[/tex]

[tex]2g+6=10[/tex]

[tex]2g=10-6[/tex]

[tex]g=\frac{10-6}{2}[/tex]

[tex]g=\frac{4}{2}[/tex]

[tex]g=2[/tex] which means that the value of  a granola bar is $2.

3. Finally, we verify the result by substituting the values ​​obtained for "g" and "a" to see if it satisfy the equations.

For the first equation:

[tex]2g+6a=10[/tex] with g = 2 and a = 1

[tex]2(2)+6(1)=10[/tex]

[tex]4+6=10[/tex]

For the second equation:

[tex]2g+3a=7[/tex] with g = 2 and a = 1

[tex]2(2)+3(1)=7[/tex]

[tex]4+3=7[/tex]

The problem can be solved using a system of linear equations representing the cost relationships of granola bars and apples. By forming two equations from Addison's and George's purchases, you can find the cost of a granola bar (G) and an apple (A) using substitution or elimination.

This question is a classic example of a system of linear equations where each equation represents a relationship between the cost of granola bars and apples. In this case, we have two people, Addison and George, and their respective costs for purchasing a combination of granola bars and apples.

We can set up two equations based on the information. Let's say G represents the cost of a granola bar and A represents the cost of an apple.

From Addison's purchase, we get the equation: 2G + 6A = $10

And from George's purchase, we formulate the equation: 2G + 3A = $7

You can solve this system of equations using various methods, such as substitution or elimination, to get G (cost of a granola bar) and A (cost of an apple).

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Answer:

∠2 = 80°

Step-by-step explanation:

Since BD is a diameter then

∠1 + ∠2 = 180°, that is

100° + ∠2 = 180° ( subtract 100° from both sides )

∠2 = 180° - 100° = 80°

Answer:

B. 80

Step-by-step explanation:

We have been given a circle. We are asked to find the measure of angle 2.

Since BD is diameter of our given circle, so angle 1 and angle 2 will be linear pair of angles.

We know that linear angles add up-to 180 degrees, so we can set an equation as:

[tex]m\angle 1+m\angle 2=180^{\circ}[/tex]

[tex]100^{\circ}+m\angle 2=180^{\circ}[/tex]

[tex]100^{\circ}-100^{\circ}+m\angle 2=180^{\circ}-100^{\circ}[/tex]

[tex]m\angle 2=80^{\circ}[/tex]

Therefore, measure of angle 2 is 80 degrees and option B is the correct choice.

Answer:

C

Step-by-step explanation:

1 / (cos x - sin x) = cos x + sin x

Multiply:

1 = (cos x + sin x) (cos x - sin x)

Distribute:

1 = cos² x - sin² x

Use trig identity:

sin² x + cos² x = cos² x - sin² x

2 sin² x = 0

sin x = 0

x = πk

Answer C.

Answer:

[tex]\large\boxed{A:\ 4\sqrt5}[/tex]

Step-by-step explanation:

Look at the picture.

ΔABC and ΔADB are similar. The corresponding angles are in proportion:

[tex]\dfrac{AB}{AC}=\dfrac{AD}{AB}[/tex]

We have:

[tex]AB=x,\ AC=5+11=16,\ AD=5[/tex]

Substitute:

[tex]\dfrac{x}{16}=\dfrac{5}{x}[/tex]                 cross multiply

[tex]x^2=(16)(5)\to x=\sqrt{(16)(5)}[/tex]         use √ab = √a · √b

[tex]x=\sqrt{16}\cdot\sqrt5\\\\x=4\sqrt5[/tex]

Answer:

8(2g + 1)(4g² - 2g + 1)

Step-by-step explanation:

Given

64g³ + 8 ← factor out 8 from each term

= 8(8g³ + 1) ← 8g³ + 1 is a sum of cubes and factors as

8g³ + 1 = (2g + 1)((2g)² - 2g + 1² ) = (2g + 1)(4g² - 2g + 1)

Hence

64g³ + 8 = 8(2g + 1)(4g² - 2g + 1)

Answer:

the correct answer is D

Step-by-step explanation:

trust

Answer:

Step 2: 4 ( 2 ) + 4 ( 3 x )

Step-by-step explanation:

The student didn't factorise 8 x + 12 properly

Answer:

D. g(x)=(3x)^2

Step-by-step explanation:

For function g(x), it displays the point (1,9) as part of the function. If (x,y), then we can plug those into the available answers. Plug 1 in for each x value in the function and whichever one equals 9 will be your answer. This is only true for g(x)=(3x)^2.

The equation of g(x) = (x/3)^2.

The graphs of the functions f(x) and g(x) are similiar and the difference between them is caused dilation.

g(x) = k*f(x)

It is given that f(x) = x^2

From the graph, we can see that g(3) = 1.

Therefore:

g(3) = k*f(3)

= k*3^2

= 1

k*3^2 = 1

⇒ k*9 = 1

⇒ k = 1/9

Now, substitute the value of k in the g(x)

g(x) = (1/9)*f(x)

⇒ g(x) = (1/9)*x^2

⇒ g(x) = (x/3)^2

Therefore, we have found the equation of g(x) = (x/3)^2. The correct answer is option C.

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Answer:

6 , 1 , 2

61, 62, 16, 12, 26 , 21 , 612 , 216 , 621 , 612 , 126 , 162 , 261 ,

Step-by-step explanation:

think thats it hope this helps

For this case we make a rule of three, based on the fact that 9 ounces of mushrooms cost $ 5.

9 oz --------------> 5 $

13oz ------------> x

Where "x" represents the amount of dollars that cost 13 ounces of mushrooms.

[tex]x = \frac {13 * 5} {9} = \frac {65} {9} = 7.222222[/tex]

Rounding out, we have that 13 ounces of mushrooms cost $ 7 with 22 cents.

Answer:

$ 7 with 22 cents

Answer:

Step-by-step explanation:

9 oz cost $5 therefore you want to find the cost per oz which would be $5/9oz= 0.55555556 per oz

0.55555556 x 13oz = $7.222222 which is $7.22

Answer:

means are

8th:4.5

7th:5.5

6th:4

7th is most

Step-by-step explanation:

Final answer:

4 feet is equivalent to 1 1/3 yards or 48 inches, as there are 3 feet in a yard and 12 inches in a foot.

Explanation:

The student has asked what is equivalent to 4 feet. To answer this, we must understand that feet and yards are units of measurement commonly used to measure length or distance. In the United States customary system, 1 yard is equivalent to 3 feet. Therefore, to find the equivalent of any number of feet in terms of yards, one can divide the number of feet by 3. For 4 feet, this would be calculated as follows:

4 feet ÷ 3 feet/yard = 1 1/3 yards.

Alternatively, since 4 is just 1 more than 3, we can see that 4 feet is 1 yard plus 1 additional foot, which confirms our conversion of 1 1/3 yards. Other times, feet may be converted into inches, where 1 foot equals 12 inches. In this case, 4 feet x 12 inches/foot equals 48 inches.

Final answer:

The cost of 1kg of apples is £0.45, calculated using two equations derived from the given information about the cost of oranges and apples.

Explanation:

To work out the cost of 1kg of apples, we can set up two equations based on the information given: 4.5kg of oranges and 3kg of apples cost a total of £3.87, and 2.5kg of oranges cost £1.40. Let's assume the cost per kilogram of oranges is 'O' and the cost per kilogram of apples is 'A'. The equations would be:

4.5O + 3A = 3.87 ........(1)

2.5O = 1.40 ........(2)

From equation (2), we can calculate the cost of oranges per kilogram:

O = 1.40 / 2.5

O = £0.56 per kilogram

Now substitute the value of 'O' in equation (1) to find 'A':

4.5(0.56) + 3A = 3.87

2.52 + 3A = 3.87

3A = 3.87 - 2.52

3A = 1.35

A = 1.35 / 3

A = £0.45 per kilogram

Therefore, the cost of 1kg of apples is £0.45.

Step-by-step explanation: To write 3.8 as a percent multiply 3.8 by 100 to obtain 380. Then append the percent sign (%). To learn about the spacing check out the reference section of decimal to percent.

30(3m-5)=10(m+1);

90m-150=10m+10;

90m-10m=150+10;

80m=140;

m=140/80=14/8=1.75

Answer:

m = 2

Step-by-step explanation:

If you're dividing 10 by 3m-5, please enclose the 3m - 5 inside parentheses to eliminate any ambiquity:

Solve   30/(m+1) =  10/(3m-5)

Here we have the LCD (m+1)(3m-5).  Multiply both sides of this equation by this LCD and simplify the results:

                     30                            10

(m+1)(3m-5)--------- = (m+1)(3m-5)----------

                    m+1                           3m-5

After cancelling, we have:

       30(3m-5)         = 10(m+1),

which, when expanded, comes to:

  90m - 150 = 10 m + 10

Combining like terms, we get:

80m = 160, and so m = 2.

Answer:

go back to hong kong

imma send you back to hong kong

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

In arithmetic series

[tex]\sum \limits _{k=1}^{24}(-6+0.5k)[/tex]

we have

[tex]a_1=-6+0.5\cdot 1=-5.5\\ \\a_{24}=-6+0.5\cdot 24=-6+12=6\\ \\S_{24}=\dfrac{a_1+a_{24}}{2}\cdot 24=\dfrac{-5.5+6}{2}\cdot 24=0.5\cdot 12=6[/tex]

Thus, the value of the series is equal to the value of the 24th number in the series.

Answer:

-8

Step-by-step explanation:

r=2

so multiply third term by 2

Answer: -8

Step-by-step explanation:

We must remember that, in geometric sequences, the ratio between the consecutive terms is constant.This is called "Common ratio" and is represented with "r".

We need to find the common ratio of this geometric sequence:

Divide one term by the previous term:

[tex]r=\frac{-4}{-2}\\\\r=2[/tex]

Then, the next term asked in the exercise can be found by multiplying -4 by 2.

Therefore, this is:

[tex]next\ term=(-4)(2)\\\\next\ term=-8[/tex]

Answer:

12 inches

Step-by-step explanation:

[tex]18 \times (2 \div 3)[/tex]

Answer:

27 inches

Step-by-step explanation:

We can use proportions to solve this problem.  Put the drawing size over the real life size

3 inches      x inches

------------- = -----------

2 ft                18 ft

Using cross products to solve

3 * 18 = 2 * x

54 = 2x

Divide each side by 2

54/2 =2x/2

27 =x

The stage should be 27 inches in the drawing

Answer:

[tex]\large\boxed{\dfrac{5}{10}}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{\dfrac{125}{1000}}\qquad\text{use}\ \sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}\\\\=\dfrac{\sqrt[3]{125}}{\sqrt[3]{1000}}=\dfrac{5}{10}\\\\\\\sqrt[3]{125}=5\ because\ 5^3=125\\\\\sqrt[3]{1000}=10\ because\ 10^3=1000[/tex]

Answer:

13532

Step-by-step explanation:

398 x 34 = 13532

Answer:

398 x 34 = 13532

Step-by-step explanation:

Answer:

y = -12

Step-by-step explanation:

It's a horizontal line that goes through the point (0,-12). Look up HOY VUX on Google and that should explain the special cases for lines.

Answer:

Draw a closed circle on -6 and shade to the left.

Answer:

The estimate is reasonable.

Step-by-step explanation:

Jamie's estimate seems reasonable.

We can see that there is (-24/27) in the bracket, first of all there is negative sign so there will be negative sign in the answer. Moreover, 24 is near to half of 27 so fraction will result in -0.5XXXXX and multiplying it with 1.4 will increase it around -0.75.

We can solve the given fraction for confirmation,

So,

[tex]= 1.43 * (\frac{-24}{47} )\\=1.43*(-0.5106)\\=-0.7302[/tex]

which is near to -0.75 so the estimate of Jamie was right ..

Jamie's estimate of -0.75 is reasonable given the calculated result of approximately -0.73.

The value of the expression 1.43 × (-24/47) is indeed close to -0.75. To show this, let's calculate it step by step:

Therefore, Jamie's estimate of -0.75 is reasonable given the calculated result of approximately -0.73.

-160

I'm so sorry if I get this wrong I'm still new!

Answer:

81,82 and 83

Step-by-step explanation:

X + X + 1 + X + 2 = 246

3X + 3 = 246

3X + 3 - 3 = 246 - 3

3X = 243

3X/3 = 243/3

X = 81

Which means that the first number is 81, the second number is 81 + 1 and the third number is 81 + 2. Therefore, three consecutive integers that add up to 246 are 81, 82, and 83.

81 + 82 + 83 = 246

Final answer:

To find the three consecutive integers, we can assume them as x, x+1, and x+2. By using the given sum and solving the equation, we find the values of the three integers to be 81, 82, and 83.

Explanation:

Let's assume the three consecutive integers as x, x+1, and x+2.

The sum of these three integers is given as 246, so we can write an equation:

x + (x+1) + (x+2) = 246

Combining like terms, we get:

3x + 3 = 246

Subtracting 3 from both sides:

3x = 243

Dividing both sides by 3:

x = 81

So the three consecutive integers are 81, 82, and 83.

Answer:

1440 beats

Step-by-step explanation:

Given that a doctor measured a patient's resting pulse rate at 80 beats per minute.

i.e. if no of beats in a dependent variable on time then we have a linear relationship between y - no of beats and x - no of minutes

Here slope= rate of change of y with respect to x [tex]= m=80[/tex]

And we have y intercept as 0 since when time is 0 no heart beat. i.e. (0,0) is a point on the line

The equation would be

[tex]y=80x[/tex],x≥0

When  [tex]x=18, \\y = 18(80)\\y = 1440[/tex] beats.

Graph is enclosed.

Meter :) hope this helps!

Answer:

Meters

Step-by-step explanation:

City planner should use Meter unit as the distance within the city blocks are much higher that the distances which can be measured in inches and they are much lesser than the distances which can be measured in Miles.

For instance, Two blocks of a city can not be few miles away or few inches away , but they can be few meters away from each other.

Hope that helped .