f(n) = n2 - 3n; Find f(2)

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

5. Your track coach is letting you choose between two different workouts.

A: Run 10 minutes on Monday and double that time every day through Friday.

B: Run 30 minutes on Monday and add 10 minutes every day through Friday.

What type of function is represented by plan A? By plan B? Which plan should you choose if you have plans Friday night and want a short workout on Friday? Why? Create a table to justify your answer.

Plan A: Geometric function

Plan B: Arithmetic function

I would choose plan B because Plan A has me working out for 160 minutes on Friday, but I want a short workout that day because I have plans.

Plan A minutes

Plan B minutes

Monday

10

30

Tuesday

20

40

Wednesday

40

50

Thursday

80

60

Friday

160

70

Brainliest plz

To have lesser workout on Friday, You must choose plan B.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

There are 2 plans.

Plan A : run 10 min on Monday and double that time everyday through Friday.

Here the function is going on as,

10, 2 × 10 = 20, 2 × 20 = 40, 2 × 40 = 80, 2 × 80 = 160

10, 20, 40, 80, 160

This is a geometric Function since the ratio of minutes on two consecutive days is constant which is 2.

Plan B : Run 30 minutes on Monday and add 10 min everyday through Friday.

Here the function is going on as,

30, 30 + 10 = 40, 40 + 10 = 50, 50 + 10 = 60, 60 + 10 = 70

30, 40, 50, 60, 70

This is a arithmetic function since the difference of minutes between two consecutive days is constant which is 10.

If I need shorter workout on Friday, I would choose plan B, since there is only 70 minutes of workout on Friday.

Hence plan B is better in order to keep shorter workout on Friday.

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given that m is parallel to n,

the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.

using the corresponding angle rule we know that:

2x + 16 = 96

2x = 80

so x = 40

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer:

6 red tiles in the box

Step-by-step explanation:

Let's represent the red tiles as "R" and the blue tiles as "B". According to the given information, the ratio of red tiles to blue tiles is 3:5, which means for every 3 red tiles, there are 5 blue tiles.

Let's use a tape diagram to represent this situation:

R R R B B B B B

This represents 3 red tiles and 5 blue tiles, as per the given ratio.

It is also given that there are 12 more blue tiles than red tiles. So, we can add 12 more blue tiles in the tape diagram:

R R R B B B B B B B B B

Now, we can see that the difference between the number of blue tiles and red tiles is 12. Since the ratio of red tiles to blue tiles is 3:5, the difference between the two should be 2 (5 - 3 = 2). Therefore, 2 represents 12 tiles in the tape diagram.

Now, to find out how many red tiles are there, we can divide 12 by 2 (since the difference between the ratio is 2).

12 ÷ 2 = 6

So, there are 6 red tiles in the box.

The inequality that represents the given graph is: D. y ≥ 2/3x + 2.

Using two points on the line, (0, 2) and (-3, 0), find the slope (m).

Slope (m) = change in y / change in x

Slope (m) = (2 - 0)/(0 - (-3))

Slope (m) = 2/3

The y-intercept (b) is the y-value of the point where the line intercepts the y-axis = 2.

Substitute m = 2/3 and b = 2 into y ≥ mx + b:

y ≥ 2/3x + 2

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answer is here about stem and leaf

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Survey research method is used to  do researchers use to systematically collect data from respondents through questionnaires or interviews.

It can be used for descriptive, exploratory, or explanatory research. This method is best suited for studies that have individual people as the unit of analysis. Although other units of analysis, such as groups, organizations or dyads, are also studied using surveys, such studies often use a specific person from each unit as a “key informant” or a “proxy” for that unit, and such surveys may be subject to respondent bias if the informant chosen does not have adequate knowledge or has a biased opinion about the phenomenon of interest. For instance, Chief Executive Officers may not adequately know employee’s perceptions or teamwork in their own companies, and may therefore be the wrong informant for studies of team dynamics or employee self-esteem.

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

YES

Step-by-step explanation:

For example, in the figure displayed in the attachment, the length of \( YM = MS + SY \)

\( MS = 3 \)

\( SY = 10 \)

Therefore, \( YM = 3 + 10 = 13 \).

The lengths of segments MS and SY sums up to give you the length of YM.

Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.

Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.

So the expression becomes:

-14 + 8

To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:

(-14) + (8) = -14 * 1 + (-14) * 8

This can be simplified as:

-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)

Finally, we can add the two negative numbers to get the result:

-14 + (-112) = -126

Therefore, the expression -14 - (-8) factors completely as -126.

Answer:

1

Step-by-step explanation:

3x² +24x = -48

3x² +24x + 48 = 0

x² +8x + 16 = 0

By using cross multiplication,

(x-4)² = 0

Therefore,

x-4 = 0

x = 4 (repeated)

Answer:

Only one real solution

Step-by-step explanation:

\({ \tt{ {3x}^{2} + 24x = - 48}} \\ { \tt{ {3x}^{2} + 24x + 48 = 0 }} \\ { \tt{ {x}^{2} + 8x + 16 = 0}} \\ { \tt{(x + 4) = 0}}

The main belt is not located between these all planets.

What is orbit?

A route that an object in space follows around another is known as an orbit. A satellite is a thing that orbits the earth. An Earth- or moon-like natural satellite is one possibility. Moons are satellites that orbit many planets. A man-made satellite is also possible, such as the International Space Station.

The belt of asteroids is located between the orbits of Mars and Jupiter. The asteroids in this region, known as the main belt, are made up of small rocky bodies that orbit the sun in a region between about 2.2 and 3.2 astronomical units (AU) from the sun.

The distance from the sun to the Earth is about 1 AU, and the distance from the sun to Venus is about 0.7 AU, so the main belt is located beyond the orbits of both Venus and Earth.

The orbits of Saturn and Uranus are much farther out from the sun, at distances of about 9.5 and 19.2 AU, respectively, so the main belt is not located between these planets.

Hence, The main belt is not located between these all planets.

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The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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Answer:

The equation is found to be: \(y = 50.6e^{0.16x}\)

y(20) = 1241.34

Step-by-step explanation:

The given data is:

x:   3          7         11        14          17

y: 83      142      301     450      722

Now, we find sum summation values, relevant to the formula of exponential regression model, using calculator:

∑ ln y = 27.77305, ∑x ln y = 308.1494, ∑x = 52, ∑ x² = 664

and, n = no. of data points = 5

Now, we use formulae of exponential regression model to find out values of constant:

b = (n∑x lny - ∑x ∑ln y)/[n∑x² - (∑x)²]

b = [(5)(308.1494) - (52)(27.77305)]/[(5)(664) - (52)²]

b = 0.16

Now, for a;

a = (∑ln y - b∑x)/n

Therefore,

a = [(27.77305) - (0.16)(52)]/5

a = 3.9

For, α:

α = e^a = e^3.9

α = 50.6

So, the final equation of exponential regression model is given as:

\(y = \alpha e^{bx}\\ y = 50.6e^{0.16x}\)

Now, we find value of y for x = 20:

y(20) = (50.6) e^(0.16*20)

y(20) = 1241.34

Answer:

5/6 ÷ 3/4 = 20/18 as simplified as 10/9 in fraction form. 5/6 ÷ 3/4 = 1.1111 in decimal form.

Step-by-step explanation:

The value of 5/6 divided by 3/4 is 10/9.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

5/6 divided by 3/4

as, fraction does not perform proper division

So,  5/6 ÷ 3/4

= 5/6 x 4/3

= 20 / 18

= 10 / 9

Hence, the resultant value is 10/9

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The graph of f(x) = 100(0.7)^x is represented by On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100)

Using the exponential function f(x) = 100(0.7)^x the graph is plotted and attached

Other information that can be abstracted from the equation directly

f(x) = 100(0.7)^x

at x = 2

f(x) = 100(0.7)^2

f(x) = 100(0.49)

f(x) = 49

hence the ordered pair is written as (2, 49)

f(x) = 100(0.7)^x

at x = 0

f(x) = 100(0.7)^0

f(x) = 100(1)

f(x) = 100

hence the ordered pair is written as (0, 100)

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The answer is A. its correct on EDGE 2022

The amount is 4.8, base is 12 and the precent of the given condition is unknown.

Define base:

In mathematics, the term "base" refers to a fixed number or symbol used as a point of reference for counting, measuring or representing a quantity.

In the decimal system, for example, the base is 10, because there are 10 possible digits (0-9) that can be used to represent a number. In binary system, the base is 2, because there are only 2 possible digits (0 or 1) that can be used to represent a number.

What about precent?

In mathematics, percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred," so a number expressed as a percent represents a fraction of 100.

To convert a number to a percent, we multiply it by 100. For example, if we want to express the number 0.25 as a percent, we can multiply it by 100 to get:

⇒ 0.25 x 100 = 25%

According to the given information:

Percent: The precent is the number with the % symbol

Base: The base is the whole amount which in this case is 12.

Amount: The amount based on the precent is 4.8

So, from overall condition we have that option 'a' is correct.

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Answer:  426

Step-by-step explanation:

221 - 33 = 288

288 - 4 = 284

284 / 2 = 142

284 + 142 = 426

Answer:

The value of k that makes the relationship shown in the table below proportional is \(\mathbf{\frac{1}{2}}\)

Step-by-step explanation:

The relation is proportional if \(y=kx \:or\:k=\frac{y}{x}\)

Putting values of x and y to find k.

For x =2 and y =1 k is: \(k=\frac{y}{x}=\frac{1}{2}\)

For x =4 and y =2 k is: \(k=\frac{y}{x}=\frac{2}{4} =\frac{1}{2}\)

For x =6 and y = 3 k is: \(k=\frac{y}{x}=\frac{3}{6} =\frac{1}{2}\)

For x = 8 and y = 4 k is: \(k=\frac{y}{x}=\frac{4}{8} =\frac{1}{2}\)

For x =10 and y = 5 k is: \(k=\frac{y}{x}=\frac{5}{10} =\frac{1}{2}\)

So, The value of k that makes the relationship shown in the table below proportional is \(\mathbf{\frac{1}{2}}\)

20 miles per hour converted to feet per second is 88/3 feet per second.

It is given in the question that there are 60 minutes in one hour and 60 seconds in one minute.

We have to convert 20 miles per hour in feet per second.

We know that,

1 mile = 5280 feet

1 hour = 60 minutes

1 minute = 60 seconds

Hence, we can write,

1 hour = 60*60 = 3600 seconds

1 mile per hour = 5280/3600 feet per second = 22/15 feet per second

Using unitary method, we can write,

20 miles per hour = 20*(22/15) = 88/3 feet per second or 29.3334 feet per second.

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Answer:

130

Step-by-step explanation:

if wrong sorry

have a great day