Which function is increasing?

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the gradient (slope) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = O (0, 0 ) and (x₂, y₂ ) = A (- 5, 2 )

[tex]m_{OA}[/tex] = [tex]\frac{2-0}{-5-0}[/tex] = [tex]\frac{2}{-5}[/tex] = - [tex]\frac{2}{5}[/tex]

(b)

the angle between a tangent and a radius at the point of contact is 90°

given a line with slope m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex]

(c)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{5}{2}[/tex] , then

y = [tex]\frac{5}{2}[/tex] x + c ← is the partial equation

to find c substitute A (- 5, 2 ) into the partial equation

2 = - [tex]\frac{25}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{25}{2}[/tex] = [tex]\frac{29}{2}[/tex]

y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{29}{2}[/tex] ← equation of tangent

Step-by-step explanation:

Equation to find the sum of the first n terms :

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] x (2[tex]a_{1}[/tex] + (n - 1)d)

- where n is the first n terms

- where [tex]a_{1}[/tex] is the first term in the sequence

- where d is the difference (To find the difference: [tex]a_{1}[/tex] - [tex]a_{2}[/tex])

How to find n for the given sum :

1. Using the previous equation, plug in all the numbers that you know

2. PEMDAS then combine all like terms

3. Distribute what's on the outside to the inside of the parenthesis

4. Move  [tex]S_{n}[/tex] to the other side to make a quadratic equation

5. Solve the quadratic, then use the positive number and round that number (term of numbers that isn't whole isn't possible ig??)

Question 1:

Sum of first 10 terms : [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] ( 2 x 2 + (10 - 1)6)

 [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] (4 + (9)6) = (4 + 54) = 58

 [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] x 58

Answer : 290

Find n for the given sum : 1704 =  [tex]\frac{n}{2}[/tex] x (2 x 2 + (n - 1)6)

distribute 6 into (n-1)

1704 =  [tex]\frac{n}{2}[/tex] x ( 4 + 6n - 6)

combine like terms

1704 =  [tex]\frac{n}{2}[/tex] x ( -2 + 6n )

Distribute  [tex]\frac{n}{2}[/tex] to ( -2 + 6n )

1704 = [tex]\frac{-2n}{2}[/tex] - [tex]\frac{6n^{2} }{2}[/tex]

Simplify fractions and move 1704 to the other side

-3[tex]n^{2}[/tex] - n + 1704 = 0

Use a quadratic calculator to find the answer and use the answer with the whole number

Answer : -24

Question 2:

(i'm just gonna show you the answers for the rest of them-)

Sum of the first 14 terms: 490

Find n for the given sum: 33.65 (I'm gonna round it to 34)

Question 3:

Sum of the first 21 terms: 483

Find n for the given sum: 11.48 (rounded: 11)

Question 4:

Sum of the first 32 terms: -1328

Find n for the given sum: -9.34 (rounded -9)

really hope this helps in any way :D

Answer: 127

Step-by-step explanation:

150 fruits times 15% = 22.5 rotten fruits

150 total -22.5 rotten=127.5 fres fruits

You can't have half a fruit so I chose to round down to 127

Answer:

5x² ( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )

Step-by-step explanation:

→ Find the highest common factor from 5 and 80

5

→ Find the highest common factor of x¹⁰ and x²

x²

→ Write the partially factored form

5x² ( x⁸ - 16 )

→ Factor down ( x⁸ - 16 )

( x⁴ + 4 ) ( x⁴ - 4 )

→ Factor down ( x⁴ + 4 ) ( x⁴ - 4 )

( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )

Answer:

Step-by-step explanation:

The greatest common factor is that factor that includes every prime factor that is found in both expressions. Once that is removed, the formula for the factorization of the difference of squares is needed.

__

Each expression factors as ...

  5x^10 = 5·x^2·x^8

  80x^2 = 5·x^2·16

The common factors in these expressions are 5, x^2, so the expression with the greatest common factor factored out is ...

  5x^2(x^8 -16)

__

The remaining factor is the difference of squares, which factors as ...

  a² -b² = (a -b)(a +b)

Here, we have a=x^4 and b=2^2, so the factors of the difference are ...

  x^8 -16 = (x^4 -4)(x^4 +4)

The first of these factors is also recognizable as a difference of squares, so it can be factored further:

  x^4 -4 = (x^2 -2)(x^2 +2)

The second factor can also be cast as the difference of squares, allowing it to be factored further:

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

  = (x^2 +2x +2)(x^2 -2x +2)

So, the complete factorization of the original expression is ...

  5x^10 -80x^2 = 5x^2(x^2 +2x +2)(x^2 -2x +2)(x^2 +2)(x^2 -2)

_____

Additional comment

We could factor to linear terms if we wanted to use radicals and complex numbers. This is the factorization in integers.

Answer:

4-4

Step-by-step explanation:

Substitute the actual values of the points into the distance formula.

The tables that can be used to show that the functions that made them are inverses of each other are the tables attached.

When functions are inverses of each other, they will give inverted x and y values.

This means that the value of x for one function, will be the value of y for the other function.

The tables that have inverse functions will therefore have a table where x values of:

627, 227, 27, 2, and 27 which will be y values in the other table.

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Answer:

y=3x+7

Step-by-step explanation:

take two points, (1,13) (2,19)

subtract using slope formula

19-13 2-1= 6/1 -> 6-> 3

find your y intercept (b) by using the first term in the 7 row (7)

Answer:

y = 3x +

Step-by-step explanation:

The equation of the line is given by:

----------------------------

The equation of a line, in slope-intercept formula, has the following format:

In which

m is the slope, that is, how much y changes when x changes by 1.

b is the y-intercept, that is, the value of y when x = 0.

----------------------------

Given two points (x,y), the slope is the change in y divided by the change in x.

We have points (-1, -1) and (3,11). Thus:

Then

----------------------------

Point (-1,-1) means that when , and we use this to find b.

Thus

A similar problem is given at brainly.com/question/13251894

Still stuck? Get 1-on-1 help from an expert tutor now.

Answer:

15cm

Step-by-step explanation:

150 meters are too long since 1 meter is about one big step.

15 meters would also be too long.

150 centimeters is the same as 1.5 meters, which is also too long.

The equation of the quadratic function is y = -1/4(x + 2)² + 4

A quadratic equation is represented as:

y = ax² +bx + c

When x = 0 and y = 3, we have:

3 = a(0)² +b(0) + c

This gives

c = 3

So, we have:

y = ax² +bx + 3

When x = 1 and y = 1.75, we have:

1.75 = a(1)² +b(1) + 3

This gives

a + b = -1.25

Make b the subject

b = -1.25 - a

When x = -2 and y = 4, we have:

4 = a(-2)² +b(-2) + 3

This gives

4a - 2b = 1

Substitute b = -1.25 - a in 4a - 2b = 1

4a - 2(-1.25 - a) = 1

Expand

4a + 2.5 + 2a = 1

Evaluate the like terms

6a = -1.5

Divide both sides by 6

a = -1/4

Substitute a = -1/4 in b = -1.25 - a

b = -1.25 + 1/4

Evaluate

b = -1

So, we have:

y = -1/4x² - x + 3

Factor out -1/4

y = -1/4(x² + 4x) + 3

-------------------------------------------------

Take the coefficient of x

k = 4

Divide by 2

k/2 = 2

Square both sides

(k/2)² = 4

-------------------------------------------------

Add and subtract 4 inside the bracket of y = -1/4(x² + 4x) + 3

y = -1/4(x² + 4x + 4 - 4) + 3

Expand

y = -1/4(x² + 4x + 4) + 1 + 3

Evaluate the sum

y = -1/4(x² + 4x + 4) + 4

Express the bracket as a perfect square

y = -1/4(x + 2)² + 4

Hence, the equation of the quadratic function is y = -1/4(x + 2)² + 4

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Answers:

P(A) = 7/12

P(B) = 1/2

=====================================================

Explanation:

To see how I calculated P(A), check out this link to this very similar question

https://brainly.com/question/27669586

--------------------

Now to calculate P(B)

If a number is divisible by 2, then the number is a multiple of 2.

In other words, the number is even.

Counting through the values in the table, you should find that there are 18 sums that are even (2, 4, 6, 8, 10 and 12). Refer to the dice chart below.

Here's a further breakdown

Side note: We have nice symmetry going on.

There are 1+3+5+5+3+1 = 18 values total that are even numbers. The other half are odd numbers of course.

P(B) = 18/36 = (1*18)/(2*18) = 1/2

Answer:

0, 2/5, 1/6,-3/4,-7/10

Step-by-step explanation:

this is just what i think i didint understand the no spaces or no commas or negatives thing but here you go i hope its right

Based on the calculation, the perimeter of the horizontal cross-section is equal to 36.13 cm.

In this scenario, the resulting geometrical shape formed when the cut is made at the middle of the height of the trapezoid and then rotated is a circle.

Given the following data:

From the middle, the diameter of this circle is given by:

D = 1/2 (10 + 13)

D = 11.5 cm.

Now, we can calculate the perimeter:

Perimeter = πD

Perimeter = 3.142 × 11.5

Perimeter = 36.13 cm.

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Answer:

True

Step-by-step explanation:

A relation is a function when each input has exactly one output. Looking at the coordinates given, none of the inputs(x-values) are repeated. Therefore, the relation is a function.

Answer:

The answers should be b=44°

Step-by-step explanation:

b=180°–90°–a

b=180°–90°–46°

b=44°

Using the hypergeometric distribution, it is found that there is a 0.3548 = 35.48% probability that she packs at least one pair of high heels.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, we have that:

The probability that she packs at least one pair of high heels is given by:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,31,2,6) = \frac{C_{6,0}C_{25,2}}{C_{31,2}} = 0.6452[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.6452 = 0.3548[/tex]

0.3548 = 35.48% probability that she packs at least one pair of high heels.

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3 yards 5 feet 6 inches X 7 is 33.833333 yards. The correct option is K- none of these.

First step

One yard is 36 inches hence:

3 yards 6 inches=(36 inches×3)+6 inches

3 yards 6 inches=108 inches+6 inches

3 yards 6 inches=114 inches

Second step

5 Feet to inches=5 ft×12

5 feet to inches=60 inches

Third step

Yards=[(114 inches+60 inches)×7]/ 36 inches

Yards=(174 inches×7)/ 36 inches

Yards=1,218 /36 inches

Yards=33.833333

Therefore the correct option is K- none of these.

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Answer:

a=646.84   c=113.04

Step-by-step explanation:

Answer:

6000

Step-by-step explanation:

Answer:

I can help, but can you label which is base, height, and length

Step-by-step explanation:

Your answer is 62.8

Have a good day

Answer:

a = 25 m²

b = 5 m

c = 7.94 m

d = 35.73 m²

Code:    H I A B

Step-by-step explanation:

Formulae

Pythagoras’ Theorem:    [tex]a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Area of a square = x²  (where x is the side length)

------------------------------------------------------------------------------------------------------

Assuming that all the quadrilaterals are squares.

Side length of blue square with area 16 m² = √16 = 4 m

Side length of yellow square with area 9 m² = √9 = 3 m

Use Pythagoras' Theorem to find the length of b:

[tex]\implies 4^2+3^2=b^2[/tex]

[tex]\implies b^2=25[/tex]

[tex]\implies b=\sqrt{25}[/tex]

[tex]\implies b=5\: \sf m[/tex]

Now we have found length b, we can find area a:

[tex]\textsf{Area a}=b^2=5^2=25\: \sf m^2[/tex]

Side length of purple square with area 144 m² = √144 = 12 m

Side length of green square with area 81 m² = √81 = 9 m

Use Pythagoras' Theorem to find the length of c:

[tex]\implies 9^2+c^2=12^2[/tex]

[tex]\implies c^2=63[/tex]

[tex]\implies c=\sqrt{63}[/tex]

[tex]\implies c=3\sqrt{7}[/tex]

[tex]\implies c=7.94\: \textsf{(nearest hundredth)}[/tex]

Now we have found length d, we can find area d:

[tex]\textsf{Area d}=\dfrac{1}{2}(9)(7.94)=35.73\: \sf m^2[/tex]

Code:    H I A B

Find b

#a

Area

H

#b

Done already

#c

A

#d

B

Code is

Answer: Month

Step-by-step explanation: x represents the number of months, and because the equation is for number of clients per something, it would be month. I hope that helps!

Answer:

[tex]x=\frac{5}{2}[/tex]     or     x= -4

Step-by-step explanation:

To solve the quadratic equation, start by factorizing it.

[tex]2x^{2} +3x-20=0[/tex]

(2x -5)(x +4)= 0

Since the equation equals to zero, either one of its factor, i.e. (2x -5) or (x +4), can be equal to zero.

2x -5= 0     or     x +4= 0

Solve for x:

2x= 5         or           x= -4

[tex]\bf{x=\frac{5}{2}}[/tex]

_______

Alternatively, the quadratic formula can be used to solve the equation.

[tex]\boxed{x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} }[/tex]

This is especially useful when the quadratic equation cannot be factorized. To use the formula, ensure that the equation is in the form of [tex]ax^{2} +bx +c=0[/tex].

Additional:

For an example on solving quadratic equations using the quadratic formula, do check out the following!

Step-by-step explanation:

........ .......... ....

Answer:

5.55 points

Step-by-step explanation:

25% reduction so its 75% of the original value

75% of 7.4 is 5.55

The system of equations and the corresponding matrix model for the following above is given and explained below.

A system of Equations refers to a set of equations that one must solve or interact with all at once.

Let's call the person who carries alleles X, Y, and Z - Xt, Yt, and Zt, respectively.

Also, lets assume that 5 percent of X alleles mutate from X to Y and 3 percent mutate from X to Z in each generation, thus the percent of X alleles remains constant at:

100 - (5 percent + 3 percent) = 92 percent.

Also, because only 0.1 percent of Y alleles evolve from Y to Z, the percentage of Y alleles remains constant at 99.9%.

We must also consider that 90 percent of Z alleles do not change from Z to X, implying that 10% of Z alleles are indifferent.

Hence, the various equations describing the system will be given as:

Xt+1 = 0.92Xt + 0.92Zt

Yt+1 = 0.05Xt + 0.999Yt

Zt+1 = 0.03Xt + 0.01Yt + 0.1Zt

or

Xt+1 = 0.92Xt + 0.000Yt + 0.9Zt

Yt+1 = 0.05Xt + 0.999Yt + 0.0Zt

Zt+1 = 0.03Xt + 0.01Yt + 0.1Zt.

The Matrix Model is given as follows:

[tex]\begin{bmatrix}X_{t+1} \\Y_{t+1} \\Z_{t+1} \end{bmatrix}[/tex]  = [tex]\left[\begin{array}{ccc}0.92&0&0.9\\0.05&0.999&0\\0.03&0.001&0.1\end{array}\right][/tex]  = [tex]\begin{bmatrix}X_{t} \\Y_{t} \\Z_{t} \end{bmatrix}[/tex]

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Answer:

18%

Step-by-step explanation:

8/44

Answer:

18% or 8/44

Step-by-step explanation:

add 12+10+14+8=44 then do 8/44