Harry placed blue and green marbles in a bag. Three-quarters
of the marbles are blue. Which of the following could be the
number of blue marbles in the bag?

The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃  = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

What is a nonlinear function?

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃ = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

Answer:

×=20

Step-by-step explanation:

180-110=70

70+70=140

180-140=40

40÷2=20

Answer:

x = 20°

Step-by-step explanation:

110° and the interior angle of the triangle are a linear pair and sum to 180°

interior angle + 110° = 180° ( subtract 110° from both sides )

interior angle = 70°

the larger triangle is therefore isosceles, 2 base angle are congruent, then

2x = 180° - 140° = 40° ( sum of angles in Δ is 180° )

divide both sides by 2

x = 20°

Answer:

18

Step-by-step explanation:

The exterior angles of any regular polygon add to 360°, so the answer is 360/20 = 18

Answer:

C: 3/5.79=13/x

Step-by-step explanation:

Two ratios are said to be in proportion when the two ratios are equal

3 markers cost $5.79 in which the proportion price is unknown

13 markers cost x

markers / cost = markers / cost

3 / $5.79 = 13 / x

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The measure of angle D to the nearest tenth of a degree is 47 degrees

This theorem is used to determine the measure of sides and angles of a triangle.

According to the theorem

tan theta = opp/adj = 1.055

theta = arctan(1.055)

theta = 46.53 degrees

Hence the measure of angle D to the nearest tenth of a degree is 47 degrees

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Answer:

The difference between the Ranges in the dot plots is 2.

I've included a figure with the two-dot plots explained for easier comprehension.

The value on the far left of the numbered line that contains at least one point is the minimum value for students in Class A, and the maximum value is three (the value to the extreme right of the numbered line that contains, at least, one point).

Range = 3 - 0 = 3

The value to the far left of the numbered line that has at least one point is the minimum value for students in Class B, and the maximum value is 5. (the value to the extreme right of the numbered line that contains, at least, one point).

Range = 5 - 0 = 5

The dot plots' range differences are 5 - 3 = 2, which is a difference of two.

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Answer:

1/12

Step-by-step explanation:

dice rolling=1/6

coin flipping=1/2

Hence probability=1/6×1/2

Answer:

Dice roll = 1/6

Coin flip = 1/2

Answer:

son's present age = 30

father's present age=60

Step-by-step explanation:

his son's present age = x years

his father's present age = 2x years

before 20 years his son's age=(x-20) years

before 20 years father's age=(2x-20) years4(x-20)=(2x-20)

4x-80=2x-20

4x-2x=80-20

2x=60

x=30

Answer: 140

Step-by-step explanation:

A parallelogram means the sides are parallel, so PQM would have the same angle as MNP since they are opposite, just like NPQ and QMN.

Answer: 140°

Detailed Explanation with Figure:

In a Parallelogram, the Opposite Angles are Equal. Therefore, ∠PQM = ∠MNP, which is equal to 140°.

Here’s the Figure :-

Answer:

AAA

Step-by-step explanation:

yesss

Answer:

n=-0.769

Step-by-step explanation:

Since there is no number after the equal sign in the equation given, we can put a zero in that place.

117n+90=0

Subtract 90 from both sides.

117n=-90

Divide 117 and -90

n=-0.769

Hope this helps!

If not, I am sorry.

Answer:

8. 14

9. 14π

10. 49π

11. 1.75π

12. [tex]\frac{49}{12}[/tex] π

Step-by-step explanation:

If the radius is 7, the diameter is 14.

Circumference is pi * diameter, so 14π

Area is π r², so 49π

Arc length is [tex]\frac{n}{360}[/tex] * 2πr, so [tex]\frac{45}{360}[/tex] * 14π = 1.75π

Sector Area is [tex]\frac{n}{360}[/tex] * πr², so [tex]\frac{30}{360}[/tex] * 49π = [tex]\frac{49}{12}[/tex]π

Answer:

(a) DE = 7.5 cm

(b) Area of ΔABE = 9.33 cm2

Step-by-step explanation:

(a)   [tex]\frac{AE}{DE} =\frac{BE}{CE}[/tex]

     [tex]\frac{5}{DE} =\frac{4}{6}[/tex]

    [tex]DE=\frac{(5)(6)}{4} =\frac{30}{4} =7.5[/tex]

(b) measurements of similar triangles have a ratio of 2/3

The ratio between areas is

[tex](\frac{2}{3} )^{2} =\frac{4}{9}[/tex]

If the area of ΔCDE = 21

Then the área of ΔABE is:

[tex]21(\frac{4}{9})=\frac{(21)(4)}{9} =\frac{84}{9} =9.33[/tex]

Hope this helps

Answer:

3:1

Step-by-step explanation:

3 and 1 is not divisible by any number

Answer:

$ 63

Step-by-step explanation:

Let the new price ( price after the discount ) be x.

Old price                    Discount                     New price

 100                              30                                  70

  90                               30                                   x

Now we can make an expression like this to solve this

100  ⇒  70

90  ⇒ x

Use cross multiplication to solve for x.

100x = 70 × 90

100x = 6300

Divide both sides by 100.

x = $ 63

Answer:

Discount: $27.00

Final Price: $63.00

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 90 × 30/100

Discount = 90 x 0.3

You save = $27.00

Final Price = Original Price - Discount

Final Price = 90 - 27

Final Price = $63.00

More plainly, the sequence is defined recursively by

[tex]a_{n+1} = \begin{cases} 3a_n - 9 & \text{if } a_n \text{ is odd} \\ 2a_n - 7 & \text{if } a_n \text{ is even} \end{cases}[/tex]

and some starting value [tex]a_1[/tex].

We're given that the sequence alternates between two constants, [tex]a[/tex] and [tex]b[/tex], so that [tex]a_1 = a[/tex].

• If [tex]a[/tex] is even, then the second term [tex]b[/tex] must be odd, since

[tex]a_2 = 2a_1 - 7[/tex]

by the given rule, and 2×(even) - (odd) = (odd). So

[tex]a_2 = 2a-7 = b[/tex]

In turn, the third term is even, since we jump back to [tex]a[/tex]. From the given rule,

[tex]a_3 = 3a_2 - 9[/tex]

and so

[tex]3b-9 = 3(2a-7)-9 = a \implies 6a-30=a \implies 5a=30 \implies a=6[/tex]

[tex]3b-9 = 6 \implies 3b = 15 \implies b = 5[/tex]

Then the sum of the two integers is [tex]a+b=\boxed{11}[/tex]

• You end up with the same answer in the case of odd [tex]a[/tex], so I'll omit this part of the solution. (It's almost identical as the even case.)

Answer and Step-by-step explanation:

There is a cube with side length 3. The volume of this cube is 27.

Answer:

14

Step-by-step explanation:

to find f(value), we plug that x value into the equation

so, if..

f(x)= 3x² -x

f(-2)= 3 · (-2)² - (-2)

f (-2) = 3 · 4 + 2

f (-2) = 12 + 2

f (-2)  = 14

Answer:

14

Step-by-step explanation:

f(x) =3x^2-x

here,

f(-2)= 3(-2)^2 -(-2)

=3*4+2

=12+2

=14 Answer.

Answer:

wait lang yong tppp heheehhehe

Answer:

b is the awancer yw

Step-by-step explanation:

If we evaluate at infinity, we have:

                        [tex]\bf{\displaystyle L = \lim_{x \to \infty}{\frac{\log(x^8 - 5)}{x^2}} = \frac{\infty}{\infty} }[/tex]

However, the infinity of the denominator has a higher order. Therefore, we can conclude that  [tex]\boldsymbol{L = 0.}[/tex]

However, proving that the limit is 0 without using L'Hopital or the "order" criterion is complicated. To do so, let us denote:

                           [tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} }[/tex]

To find the limit, we must look for two functions h(x) and g(x) such that h(x)≤ f(x)≤ g(x) and

                               [tex]\boldsymbol{\displaystyle \lim_{x \to \infty}{h(x)} = 0, \qquad \lim_{x \to \infty}{g(x)} = 0}[/tex]

If we find these functions, then we can conclude that [tex]\bf{\lim_{x \to \infty}{f(x)} = 0.}[/tex]

First, let's note that when x⁸ - 5 > 1, then log(x⁸ - 5) > 0 (and this is true when x is large). Likewise, we have that x² > 0 for x > 0. Therefore, we have:

                                   [tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} \geq 0}[/tex]

when x "is big enough". Thus, we have h(x) = 0 where it is clear that [tex]\bf{\lim_{x \to \infty}{h(x)} = 0.}[/tex]

To find the second function, let's first note that \log is an increasing function, so since x⁸ ≥ x⁸ - 5, then log(x⁸) ≥ log(x⁸ - 5). So we have to

                [tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} }[/tex]

now, if we take y = e^y, then we can write

                  [tex]\boldsymbol{\displaystyle \frac{\log(x^8)}{x^2} = \frac{\log(e^{8y})}{e^{2y}} = \frac{8y}{e^{2y}}}[/tex]

A very important property about the exponential function is

                    [tex]\boldsymbol{\displaystyle e^x > \frac{x^n}{n!}}[/tex]

For any n [tex]\bf{n \in \mathbb{N}}[/tex] and x > 0. If we take n = 2, then we have

                    [tex]\boldsymbol{\displaystyle e^{2y} > \frac{(2y)^2}{2!} = \frac{4y^2}{2} = 2y^2}[/tex]

From this it follows that

                     [tex]\boldsymbol{\displaystyle \frac{1}{e^{2y}} < \frac{1}{2y^2} }[/tex]

Therefore, we have to

                    [tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} < \frac{8y}{2y^2} = \frac{4}{y} = \frac{4}{\log x} }[/tex]

yes, [tex]\bf{g(x) = 4/\log x}[/tex] where [tex]\bf{\lim_{x \to \infty}{g(x)} = 0}[/tex]. Also, [tex]\bf{h(x) \leq f(x) < g(x)}[/tex]. Therefore, [tex]\bf{\lim_{x \to \infty}{f(x)} = 0}[/tex].

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\sf{\purple{Pisces04}}}}}}}[/tex]

Answer:

2/3 + 9.26 is rational

:)

Answer:

35$

Step-by-step explanation:

You multiply $2 x 10 = 20$ then add 15$ + 20$ = 35$

Answer:

Given - Length is nine feet more

Area is 252

To find - Value of length and width

Solution-

let the width of the carpet be X

therefore length = 9 + X

Area of carpet = Length * width

252 = (9+x) * X

252 = 9x + x²

Solving the equation by splitting middle term

x² + 9x - 252 = 0

x²- 21x + 12x - 252= 0

x ( x - 21) + 12( x - 21) = 0

(x -21)( x + 12) = 0

X = 21 or X = (-12)

Length = 9 + X

= 30 or (-3)

negative is not possible so

length = 30

width = 21

Let k: y = a₁x + b₁ and l: y = a₂x + b₂. Then

We have the line y = -x + 5 ⇒ a₁ = -1.

Therefore

a₂ · (-1) = -1

-a₂ = -1     Ichange the signs

Answer:

$11,611.69

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=6000\left(1+\frac{0.045}{1}\right)^{(1 \times 15)}[/tex]

[tex]\implies \sf A=6000(1.045)^{15}[/tex]

[tex]\implies \sf A=11611.69466...[/tex]

Therefore, the value of the investment after 15 years will be $11,611.69 to the nearest cent.

Answer:

19-73 19-73 is fine thanks 70-65-46 024 465 8554 48-57

Welming's spending is $1164.8 and his savings is $291.2

The given parameters are:

Weekly pocket = $28

Save = 20%

There are 52 weeks in a year.

So, the yearly pocket is:

Yearly pocket = $28 * 52

Evaluate

Yearly pocket = $1456

He saves 20%.

So, we have:

Savings = 20% * $1456

Evaluate

Savings = $291.2

His spending is then calculated as:

Spending = $1456 - $291.2

Evaluate

Spending = $1164.8

Hence, Welming's spending is $1164.8 and his savings is $291.2

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Answer:

This answer assumes that the first equation is meant to read:

2x + y +3z = 12, and not

1.22x+y+3:= 12

Spoiler Alert:  x = 1, y=4, and z=2

Step-by-step explanation:

1.    2x + y +3z = 12

2.     x - 2y + z = -5

3.    5x - y+ 2z = 5

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

Use equations 2 and 3 to eliminate z:

2.  x - 2y + z= -5

3.  5x - y+ 2z = 5

-2(x - 2y + z) = -2(-5)   [Multiply equation 2 by -2]

             5x -   y+  2z =  5

Now subtract this new equation from equation 3:

-2x + 4y - 2z = 10  (Eq 3)

 5x -   y+  2z =  5   [

 3x +3y = 15   [Equation A]

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

Use equations 1 and 2 to eliminate z:

   2x +  y +3z = 12   (Eq. 1)

      x - 2y +  z = -5   (Eq. 2)

   2x +  y +3z = 12

(-3)(x - 2y +  z = -5)  [Multiply Eq. 2 by (-3)]

    -3x + 6y -3z = 15

Now add the resulting two equations.

   2x +   y + 3z = 12     (Eq. 1)

  -3x + 6y -3z =  15       (Eq,2 times -3)

   -x   +7y         = 27    [Equation B]

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

  Eliminate x with the 2 resulting equations (from above)

  3x +3y = 15  [Equation A]

   -x +7y = 27  [Equation B]

----

   3x +3y = 15

   3*(-x +7y = 27)  [Multiply the Equation B by 3]

  -3x +21y = 81     [Aha - this equation has a -3x term, exactly what we need to eliminate the x term in Equation A]

---

Now add the two resulting equations:

    3x +3y = 15

   -3x +21y = 81

            24y = 96  [The x term disappears.  But we'll "find x" later]

                 y = 4   [Divide both sides by 24]

Find y and z:

Since y = 4,

-x  +7y   = 27 (From above, Equation B]

-x = -7y + 27

 x = 7y - 27

x = 7(4)-27

 x = 1                  [Looking good]

=====

Find z:  (Use y = 4 and x = 1)

x - 2y + z = -5  [Equation 2]

(1) -2*(4) + z = -5

1 - 8 + z = -5

z = 2

Check:

Do the original equations work when x = 1, y = 4, and z = 2?

Results:  

1.    2x + y +3z = 12      

     (1) + (4) +3(2)    YES, this equals 12

2.     x - 2y + z = -5  

       (1)  -2*(4) + (2)   YES, this equals -5

3.    5x - y+ 2z = 5

       5(1) - (4) + 2(2)   YES, this equals 5

x = 1, y=4, and z=2

[tex] \underline{\large \bf{Required \: Answer}} : - [/tex]

[tex] \dashrightarrow \: \red{\large8}[/tex]

[tex] \sf[/tex]

[tex] \underline{ \large{ \rm \pink{SolutioN}}} \: -[/tex]

[tex] \quad \qquad\sf \: {(a + b)}^{2} = 10[/tex]

[tex] \qquad \: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2ab = 10[/tex]

[tex] \qquad\: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2(1) = 10[/tex]

[tex] \qquad\: \: \to\: \: \sf \: {a}^{2} + {b}^{2} = 10 - 2[/tex]

[tex] \qquad\: \:\bf \to\: \: \: {a}^{2} + {b}^{2} = 8[/tex]

[tex] \sf[/tex]

[tex] \sf \therefore \: 8 \: \: is \: \: the \: \: required \: \: answer[/tex]

[tex] \rule{200pt}{2pt}[/tex]