What is the value of x?

Answer:

The balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?

Answer:

6 months

A function is a relationship between inputs where each input is related to exactly one output.

x = 5,

f(5) = [tex]2^5\\[/tex] = 32

g(5) = 4 x 5 + 12 = 20 + 12 = 32

x = 6,

f(6) = [tex]2^6[/tex] = 64

g(6) = 4 x 6 + 12 = 24 + 12 = 36

At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = [tex]2^{x}[/tex]

g(x) = 4x + 12

x = number of months

Now,

x = 3,

f(3) = 2³ = 8

g(3) = 4 x 3 + 12 = 12 + 12 = 24

x = 4,

f(4) = [tex]2^4[/tex] = 16

g(4) = 4 x 4 + 12 = 16 + 12 = 28

x = 5,

f(5) = [tex]2^5\\[/tex] = 32

g(5) = 4 x 5 + 12 = 20 + 12 = 32

x = 6,

f(6) = [tex]2^6[/tex] = 64

g(6) = 4 x 6 + 12 = 24 + 12 = 36

We see that,

At x = 6,

f(5) = 64

g(5) = 36

Thus,

At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.

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Answer:

x = 0.09

Step-by-step explanation:

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

Taking Logarith both sides, we get :

Using the properties of Logarithms:

[tex](x + 2) log(3) = 3 log(2) [/tex]

[tex](x + 2) = 1.91[/tex]

(taking log2= 0.3 and log3= 0.47)

x = 0.09

Answer:

12* 12 = 144

thus 4*12 = 48 feet of fence

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Let's first find the mean and median of each class.

Class 1:

The mean is simply all the numbers added up and then divided by the number of elements. There are 9 students in Class 1. Thus, we add all the ages up and then divide by 9. Thus:

[tex]\text{Class 1 Mean }= \frac{14+15+15+16+16+16+17+17+18}{9} \\=144/9=16[/tex]

The median is simply the middle number when the data sets are placed in order. The median of Class 1 is 16, the number in the middle.

Class 2:

Again, Class 2 has 9 students. Add up all the ages and then divide:

[tex]\text{Class 2 Mean }= \frac{13+14+15+16+16+17+18+18+19}{9}\\ =146/9\approx16.2222[/tex]

The median is the middle number of the data set. The median of Class 2 is 16.

Therefore, the mean of Class 2 is larger than the mean of Class 1. The medians of the two classes are equivalent.

Of the answer choices given, only D is correct.

Answer:

The mean of class II is larger and the median is the same

Step-by-step explanation:

Class I

14,15,15,16,16,16,17,17,18

The mean is

(14+15+15+16+16+16+17+17+18)/9

144/9 = 16

The median is the middle number

14,15,15,16,    16,    16,17,17,18

median = 16

Class II

13,14,15,16,16,17,18,18,19

The mean is

(13+14+15+16+16+17+18+18+19)/9

146/9 = 16.2repeating

The median is the middle number

13,14,15,16    ,16,       17,18,18,19

median = 16

Answer:

the answer for this is 45*10^4

Answer:

33.53

Step-by-step explanation:

OB is a radius of the circle, and OC is also a radius of the circle, so both are equal length.  That makes ΔOBC an isosceles triangle.

If we cut ΔOBC in half, the angle formed is 125° / 2 = 62.5°.

Therefore:

sin 62.5 = (x/2) / 18.9

x = 37.8 sin 62.5

x ≈ 33.53

Answer:

33.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

vxcvxcvxcvxcvxcvcxvxcbcvbcvnxcgjfgjfgjghjghjghjghj

The revenue function is y₁ = –4x² + 400x, the cost function is y₁ = x² – 100x + 8000, and the break-even number of units is 20 or 80.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Jua Kali Products Ltd has been in operation for the last 10 years.

Its annual revenue and cost functions take the form of quadratic functions.

The following data was obtained from the records of the company.

Year          Unit Sold            Revenue             Cost

2017              5                        1900                 7525

2018             10                       3600                7100

2019             15                        5100                6725

We know that the quadratic equation is given as

[tex]\rm y = ax^2 + bx + c[/tex]

Let y₁ be the revenue function, y₂ be the cost function and x be the unis sold.

Then the revenue function will be

1900 = 25a + 5b + c  ...i

3600 = 100a + 10b + c  ...ii

5100 = 225a + 15b + c  ...iii

From equations (i), (ii), and (iii), we have

a = –4, b = 400, and c = 0

Then the revenue function will be

y₁ = –4x² + 400x

Similarly, the cost function will be

7525 = 25a + 5b + c  ...1

7100 = 100a + 10b + c  ...2

6725 = 225a + 15b + c  ...3

From equations 1, 2, and 3, we have

a = 1, b = –100, and c = 8000

Then the cost function will be

y₁ = x² – 100x + 8000

For the break-even units, the cost function and the revenue function will be equal. Then we have

[tex]\begin{aligned} x^2 -100x + 8000 &= -4x^2 + 400x\\\\5x^2 -500x + 8000 &= 0\\\\x^2 - 100x + 1600 &= 0\\\\x^2 - 80 x - 20x + 1600 &= 0\\\\x(x-80) - 20 (x-80) &= 0\\\\(x-80)(x-20) &= 0\\\\x &= 20, 80 \end{aligned}[/tex]

More about the quadratic equation link is given below.

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Answer:

(2,-1)

Step-by-step explanation:

Solved using math.

Answer:

The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The nth term of the sequence is

A(n) = 5n + 7

To find the (n+1)st term substitute n+1 into the general equation

That's

For (n + 1)st term

A(n+1) = 5(n+ 1) + 7

A(n+1) = 5n + 5 + 7

Hope this helps you

[tex] n^{\text{th}} \text{ term is } 5n+7 [/tex]

forget n for a while.

let's call it t .

The [tex] t^{\text{th}} \text{ term is } 5t+7 [/tex]

agreed? I don't think there should be a problem.

you're asked what's the [tex](t+1)^{\text{th}}[/tex] term.

let's call it u . so just like we did before,

[tex] u^{\text{th}} \text{ term is } 5u+7 [/tex]

but we know, [tex]u=t+1[/tex]

So, [tex]5u+7=5(t+1)+7=5t+12[/tex]

does that answer your question?

Answer:

30m^2

Step-by-step explanation:

area of parallelogram is b×h

Answer:

The area of the parallelogram is 30 square meters.

Step-by-step explanation:

The area of a parallelogram is given by the formula:

A = bh

Where b is base and h is height

The base of the parallelogram is:

6 + 4 = 10 m

The height perpendicular to the base is 3 m

Use the formula A = bh:

A = (10)(3)

= 30

So the area of the paralleogram is 30 m^2

Hope this helps!

Answer:

x = 14

y = -7

z = -3

but this is none of the provided answer options !

Step-by-step explanation:

it's really easy by principle. it's just some work to do.

we try to find equations to express one variable in terms of the others.

but one thing there is : your teacher made a mistake.

the right solution is x = 14, y = -7, z = -3

your teacher made a typo at d.

but the right answer should be d.

just to give you an idea how this can be done (and also to prove that there is a mistake by the teacher):

we can directly try to transform one expression into one that describes x by y and z.

and then another to describe e.g. z by y. and then solve the third one just for y. and then we get the other 2 by these other expressions.

or we can e.g. add or subtract one equation to/from another. this is one of these cases, because we can find really simple expressions that way :

we do

5x + 6y + 7z = 7

- (3x + 4y + 3z = 5)

- (2x + 2y + 3z = 5)

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

0x + 0y + z = -3

=> z = -3

3x + 4y - 3×3 = 5

3x = -4y + 14

x = (-4y + 14)/3

2×(-4y + 14)/3 + 2y - 9 = 5

(-8y + 28)/3 + 2y = 14

-8y + 28 + 6y = 42

-2y = 14

y = -7

x = (-4×-7 + 14)/3 = (28+14)/3 = 42/3 = 14

Answer:

(- 1, 4 )

Step-by-step explanation:

The line x + 2 = 0 can be expressed as

x + 2 = 0 ( subtract 2 from both sides )

x = - 2

This is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 2

Thus (- 3, 4 ) is 1 unit to the left of - 2

Under a reflection in the line x = - 2

The x- coordinate will be the same distance from x = - 2 but on the other side while the y- coordinate remains unchanged.

Thus

(- 3, 4 ) → (- 1, 4 )

The required value of the tanФ is given as -3/4. C option is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Tan(180 - Ф) = -tanФ = perpendicular / base

From figure,  perpendicular= 12 and  base = 16
-tanФ = 12 / 16
tanФ = -3/4

Thus, the required value of the tanФ is given as -3/4. C option is correct.

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Answer:

x=50 and y=80

Step-by-step explanation:

ATQ, x+50+y=180 and y+2x=180. x=50 and y=80

Answer:

Step-by-step explanation:

The given number is 473

The reverse number is 374

The sum is (473 + 274) =  847

The difference is (473 - 274) = 99

Answer:

The answer is D)90

Hope I helped

Answer:

A) ( -8, -32 )

Step-by-step explanation:

Given function : f (x,y) = 21 - 4x^2 - 16y^2

point p( 1,1,1 ) on surface

Gradient of F

attached below is the detailed solution

Answer:

  B) (x, y) → (x – 6, y)

Step-by-step explanation:

Each x-value in the image is 6 less than in the pre-image. Each y-value is the same. That means x gets mapped to x-6, and y gets mapped to y:

  (x, y) → (x – 6, y)

Answer:

Step-by-step explanation:

The congruence correspondence between the two given triangles is HL as one leg and hypotenuse are given equal.

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

OAmalOHopeO

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

Answer:

Δf(u) /Δx  = 92,8    ( razón de cambio promedio)

Step-by-step explanation:

La expresión de la utilidad de la empresa u(x) en función de la cantidad de unidades producidas "x" es:

u(x) = 0,04*x² + 44*x  -4000

Entonces la razón de cambio promedio en un intervalo (a ; b)  en este caso ( 620 ;  600 ) viene dada por la expresión:

Δf(x)/ Δx  =  [ f(b)  -  f(a) ]/( b - a )

en donde  f(b)  y f(a) se obtienen por sustitución de los valores a y b es decir  600 y 620 respectivamente en la función f(x) = u(x) entonces

Δf(u) /Δx  =  [ u(b)  -  u(a) ]/( b -a )        (1)

u(b) =  0,04*(620)² + 44*(620) - 4000

u(b) = 15376 + 27280 -4000

u(b) = 2656 unidades

u(a)  = 0,04* (600)²  +  44* 600  - 4000

u(a)  = 14400  +  26400  - 4000

u(a) = 800

Sustituyendo esos valores en la ecuación 1

Δf(u) /Δx  =  2656 - 800 / 620 - 600

Δf(u) /Δx  = 92,8

Answer:

A.23

maaf kalosalah !(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!

Answer:

Mean; 762,143

Median; 800,000

Step-by-step explanation:

Mean;

Add all of the numbers together, then divide by how many there are.

There are seven home prices in total, add them together then divide by 7.

5,335,000 divided by 7 = 762,142.85714285; simplified to 762,143.

Median;

Organize the numbers from least to greatest

455,000, 780,000, 795,000, 800,000, 810,000, 840,000, 855,000

Then find the number in the middle

800,000

Answer:

7

Step-by-step explanation:

First plug in the variable amounts so the expression now looks like this:

(3 × 4 - 12) + 1/2(4 × 6 - 10)

Now, start by solving the multiplication parts first, so it now looks like this:

(12 - 12) + 1/2(24 - 10)

Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)

Next, solve the multiplication part, so it now looks like this: 0 + 7

Solve that and the answer is 7.

9514 1404 393

Answer:

  108 cm²

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

where b represents the base length, and h represents the height--the perpendicular distance from the base to the opposite vertex. The area of this triangle is ...

  A = 1/2(12 cm)(18 cm) = 108 cm²

Answer:

what is the amount of money Kim earn per hour of babysitting? Also I need to know how much trip cost to find out how many hours she need to work.

Step-by-step explanation:

Answer:

[tex]\huge\boxed{7^{\frac{2}{15}}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\sqrt[3]7}{\sqrt[5]7}\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\dfrac{7^\frac{1}{3}}{7^\frac{1}{5}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=7^{\frac{1}{3}-\frac{1}{5}}\qquad\text{find the common denominator (15)}\\\\=7^{\frac{(1)(5)}{(3)(5)}-\frac{(1)(3)}{(5)(3)}}=7^{\frac{5-3}{15}}=7^{\frac{2}{15}}[/tex]

Answer:

D. 7 to the power of two fifteenths

Step-by-step explanation:

Answer:

The least possible price is  p  =  £110

Step-by-step explanation:

From the question we are told that

     The number of bracelets to be made is  [tex]n = 150[/tex]

      The length of silver require for on bracelet is  [tex]x = 26 \ cm = 0.26 \ m[/tex]

      The option of silver length packs that she buys is  a =  10.5 m  packs

                                                                                           b  =  3.7 m packs

    Generally

                   1 bracelet   [tex]\to[/tex]  0.26 m  

                   150 bracelet [tex]\to[/tex]  z

=>        [tex]z = \frac{150 * 0.26}{1}[/tex]

=>        [tex]z = 39 \ m[/tex]

Now for option a  i.e  10.5 m  per pack

    The number of packs require is

        [tex]v = \frac{z}{a}[/tex]

=>     [tex]v = \frac{39}{ 10.5}[/tex]

=>      [tex]v = 3.7 1[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase v =  4

and that 4 packs would equal  t  =  4 * 10.5 =  42 meters of  silver

 Now for option d  i.e  3.7 meters per pack  

 The number of packs requires is  

           [tex]w = \frac{z}{b}[/tex]

=>        [tex]w = \frac{39}{3.7}[/tex]

=>        [tex]w = 10.54[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase w= 11

and that 11 packs would equal  t  = 11 * 3.7 =  40.7 meters of  silver

So the comparing the option and option b we see that for her to pay as little as possible she needs to go for option b since option be will produce the 150  bracelet with a little excess while option a will produce the 150 bracelet with much excess

    Assuming the price for the 3.7 m  pack is    £10

     And the price for the 10.7 pack is  £30

The least possible amount she would pay is  

                 [tex]p = 10 * 11[/tex]

                 p  =  £110  

In a preliminary study, he observed one of his workers perform this task five times, with the following results:

Observation: Time (secs):

1 27

2 19

3 20

4 21

5 13

Answer:

100 Observations

Step-by-step explanation:

Z value = 2 (due to confidence percentage of 95.44)

S = 5

A = 1

N equals to square of (ZxS/A)

N = (ZxS/A)^2

N = (2x5/1)^2

N = 10^2 = 100

Answer:

the first term is -4

the difference is 3.

*notice how each term increases by 3:

-4 + 3 = -1

-1 + 3 = 2

2 + 3 = 5

Step-by-step explanation:

Answer:

R: {y∈R | -1 ≤ y ≤ 5}

Step-by-step explanation:

the lowest point is -1 and the highest point is 5.