Quadratic Equation Question

The value of f(1) is 81

Recursive Function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms

Given:

f(n + 1) = 1/3* f(n)

f(3) = 9

let n=0

f(0+1) = 1/3 * f(0)

f(1) = 1/3 * f(0)

Let n=1

f(1+1) = 1/3 * 1/3*f(0)

f(2) = 1/9 * f(0)

let n=2

f(2+1) = 1/3 * 1/9* f(0)

f(3) = 1/27 * f(0)

Also, f(3) =9

So,

9 = 1/27 * f(0)

f(0) = 27 * 9

f(0) = 243

Now,

f(1) = 1/3 * f(0)

f(1) = 1/3/ 243

f(1) = 81

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The approximate distance in km between her house and her job is 9 km.

The map is a scale drawing of the places mentioned. A scale drawing is a smaller image of a larger place or diagram.

The scale of the map = 8cm : 12km

Distance between the house and the job = (12 x 6) / 8 = 9m

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 23 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 5x - x - 8 = 15 + 3x[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 8 = 15 + 3x[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 3x = 15 + 8[/tex]

[tex]\qquad \tt \rightarrow \: x = 23[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

x = 23

Explanation:

⇒ 5x - x - 8 = 15 + 3x

collect like terms

⇒ 5x - x - 3x = 15 + 8

add or subtract like terms

⇒ x = 23

Checking:

5(23) - 23 - 8 = 15 + 3(23)

115 - 23 - 8 = 15 + 69

84 = 84

Answer:

See attached graph.

Step-by-step explanation:

Each situation can be expressed as an equation:

Jerzy: Total Cost (y1) is the $25 membership fee plus $0.80/golf ball (x):

y1 = $25 + $0.90x

Rick and Tom's:  Total Cost (y2) is $1.25 per golf ball, x.

y2 = $1.25x

See the attached graphs of these two equations.  Jerzy's cost less after 56 balls are purchased.

Answer: y+6 = 1/3(x-4

The equation of line perpendicular to the given line and passes through the point P ( 4 , -6 ) is y + 6 = ( 1/3 ) ( x - 4 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y + 1 = -3 ( x - 5 )

So , the slope of the line is m = -3

Now , the lines are perpendicular , so the slope of the line m₂ is

m₂ = 1/3

Let the first point be P ( 4 , -6 )

And , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - ( -6 ) = ( 1/3 ) ( x - 4 )

y + 6 = ( 1/3 ) ( x - 4 )

Hence , the equation of line is y + 6 = ( 1/3 ) ( x - 4 )

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The figures Сone Z and Cylinder Y have the same volume.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

Similarly, the volume of a cylinder can be calculated by using this formula:

V = πr²h

In this context, we can infer and logically deduce that Сone Z and Cylinder Y have the same volume because they both have the same base area, while the cone's height is three (3) times the height of Cylinder Y.

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Answer:

g(-0.0001) = -9

g(0.0001) = -1

g(0) = -1

g(9) undefined

Step-by-step explanation:

g(9) undefined .because the graph have an empty circle

at (9 , 0) which means g is not defined at 9.

1 hamper box, curated by Jithu can be contained 5 cupcakes.

The total amount of cupcakes =665 nos.

Jithu wants to create a gift box, each of which contains 6 cupcakes.

We have to see first, whether 665 could be equally distributed or not.

Hence, 665/6= 110.84 unit

It is seen that the number is in a fraction.so, It can be said that 665 cakes cannot be equally distributed to each gift pack carrying 6 cakes.

Hence, 110*6=660 cupcakes.

∴665-660= 5 cupcakes in one box

So, it is concluded that Jithu could be prepared 110 gift boxes containing 6 cakes each & 1 box containing 5 cupcakes.

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The range of possible heights is given by the inequality:

d ≥ 300.125 m

We know that the time that it takes for an object to fall from a distance d is:

[tex]t = \frac{\sqrt{2d} }{4.9}[/tex]

In this case, we know that t ≥ 5s.

Then we can solve for the minimum distance, which is given when t = 5s.

[tex]5 = \frac{\sqrt{2d} }{4.9}\\\\(5*4.9)^2/2 = d = 300.125[/tex]

So the minimum height of the building is 300.125 meters, then the range of possible heights is:

d ≥ 300.125 m

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Answer:

Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.

Step-by-step explanation:

Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.

Perimeter of polygon C = 60in

Perimeter of polygon D = 12in

Length of side of polygon C = 4in

Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.

First equation, 4n = 60

Second equation, xn = 12

Dividing second by first

(xn) / (4n) = 12 / 60

x / 4 = 1 / 5

x = 4 / 5 = 0.8in

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Answer:

Step-by-step explanation:

Answer:

∠ 2 = 75° , ∠ 1 = 105°

Step-by-step explanation:

∠ 2 and 75° are alternate angles and are congruent , then

∠ 2 = 75°

∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is

∠ 1 + ∠ 2 = 180°

∠ 1 + 75° = 180° ( subtract 75° from both sides )

∠ 1 = 105°

Answer:

Every ordered pair within this region will satisfy the inequality y ≥ x. Incorrect. The boundary line here is y = x, and the correct region is shaded, but remember that a dotted line is used for < and >. The inequality you are graphing is y ≥ x, so the boundary line should be solid.

The graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3

The equation of the line will be:

y = mx + b

In this case, we can observe that both lines have the same y intercept and that the lines are solid.

Hence, graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3. The graph is attached.

When the coordinate grid shows points A through, the point that is a solution to the system of inequalities is negative 6 point G at negative 3, negative 10 point H at negative 4.

Finally, the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 is the graph of two intersecting lines where both lines are solid.

One line of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.

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Answer: 21 sqrt(43)/43

Step-by-step explanation: The tangent identity states that tanx = sinx/cosx. Thus, we get 21/22 / sqrt(43)/22. We can simplify this to 21 sqrt(43)/43

Please mark my answer as brainliest if this helped you.

Answer:

16hr

Step-by-step explanation:

distance= time x speed

250mi/min=250x60mi/hr =15000mi/hr

239000/15000≈15.9333hr

Round up to 16hr

a) At this point, the grade is 27.1

b)  The lowest possible grade is 81

a) At this point the student has 81 in homework and 95 on the first project.

Remember that the homework is worth 10% of the final grade, and each project is worth 20%, then at this point the final grade is:

F = 0.10*81 + 0.20*95 = 27.1

b) The student gets 72 on the second project and 71 on the third project, at this point the final grade is:

F = 27.1 + 0.20*72 + 0.20*71 = 55.7

Now the student wants to get a final grade of 80, then if we define x as the grade on the final exam (which is worth 30%) we must have that:

55.7 + 0.30*x = 80

Now we can solve this for x:

x = (80 - 55.7)/0.30 = 81

The lowest possible grade that he must get is 81.

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Answer: x(5) = 10 has the multiplication property.

Step-by-step explanation:

To verify the multiplication property of equality , We need to put  the value of x= 2

1.  x(5) = 10

Solution = 2(5) = 10     ✔

2.  x(1.5) = 2(2)

Solution = 2 (1.5) = 3    X

3.  x(0.5) = 2(0.5)

Solution = 2 (0.5) = 1    X

4.  x(12) = 12

Solution = 2 (12) = 24    X

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Answer:

Step-by-step explanation:

answer B and D

I got it right and didnt spell the entire constitution

Answer:

1936

Step-by-step explanation:

We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.

AOPS ANSWER:

Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.

The equation of the parabola is y = 2(x - 2)^2 + 4

The given parameters are:

A parabola is represented as:

y = a(x - h)^2 + k

Substitute (h,k) = (2,4)

y = a(x - 2)^2 + 4

Substitute (x,y) = (3,6)

6 = a(3 - 2)^2 + 4

Evaluate the difference

6 = a(1)^2 + 4

This gives

6 = a + 4

Subtract 4 from both sides

a = 2

Substitute a = 2 in y = a(x - 2)^2 + 4

y = 2(x - 2)^2 + 4

Hence, the equation of the parabola is y = 2(x - 2)^2 + 4

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Answer:

228 cm

Step-by-step explanation:

the average is calculated as

average = [tex]\frac{sum}{count}[/tex] , then

[tex]\frac{sum}{10}[/tex] = 140 ( multiply both sides by 10 to clear the fraction )

sum = 1400

let the height of new pupil be x , then

[tex]\frac{sum+x}{11}[/tex] = 148 ( multiply both sides by 11 )

sum + x = 1628 , that is

1400 + x = 1628 ( subtract 1400 from both sides )

x = 228

height of new pupil is 228 cm

Answer:

11:12

Step-by-step explanation:

You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio

Step-by-step explanation:

hope you can understand

Answer:

Positive Linear Association

Step-by-step explanation:

A positive/negative association can be determined by seeing if the slope of the line of best fit is positive or negative. A positive slope indicates a positive relationship and a negative slope indicates a negative relationship.

If y increases as x increases => positive

If y decreases as x increases => negative

In the graph, the line of best fit clearly has a positive slope. I.e. as x increases, y also increases. Therefore, the association is positive.

Next determine if the relationship is linear or nonlinear. A linear relationship can be modeled strongly with a straight line. Anything else is nonlinear. In the graph, a straight line can be draw through the points with a strong correlation, therefore the association is linear.

Therefore, the best answer is Positive Linear Assosciation

Answer:

$ 1805

Step-by-step explanation:

2000 × 95%

= 1900

1900 × 95%

= 1805