Solve the system of equations 3x - 2y = 8 x-2y = 4​

Answer:

2

Step-by-step explanation:

first, add terms

8 + 5 + 12 + 4 + 5 + 8 + 7 = 49

seven terms, therefore we divide by 7

49/7 = 7

find distance

8-7= 1

7-5= 2

12-7=5

7-4=3

7-5=2

8-7=1

7-7=0

added together you get 14,

14/7 = 2

your answer is 2

hope this helps:)

Answer:

[tex]32\sqrt{7}-24\sqrt{2}[/tex]

Step-by-step explanation:

[tex]8(4\sqrt{7}-\sqrt{18})\\\\8(4\sqrt{7}-3\sqrt{2})\\\\32\sqrt{7}-24\sqrt{2}[/tex]

Answer:

Round off value = 500000

Step-by-step explanation:

467532  > 500

- Round up

⇒ 500,000

Step-by-step explanation:

let's explain this a bit.

when the exterior angle is a certain size, then the interior angle is 180 - that exterior angle.

in our case the exterior angle is half of a right angle, so it is 90/2 = 45°.

the corresponding interior angle is 180-45 = 135°.

the sum of all angles inside a triangle is always 180°.

so,

x + 2x + 135 = 180

3x = 45

x = 15°

2x = 30°

so, the 3 interior angles are

135°, 15°, 30°

Step-by-step explanation:

try this solution, note, the answers are underlined with green colour.

Answer:

  slope 4/5

Step-by-step explanation:

The attachment shows the rise in green (4 grid squares), and the run in red (5 grid squares). The slope is the ratio rise/run.

__

The slope is rise/run = 4/5.

The Cost of Carl's first item is 3.95. The Cost of his second item is 4.95. To find the total amount we need to add these two numbers together.

3 plus 4 is 7

95 cents plus 95 cents is 1.90

7+1.90 is 8.90

The total cost is $8.90

Hope this helps!

Using proportions, it is found that the dimensions of the reception area of of 12 feet by 20 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the scale factor is of 1 inch = 4 feet, meaning that each inch on the drawing represents a dimension of 4 feet.

The drawing is of 3 inches by 5 inches, hence the real dimensions are given by;

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The sum of the expression (x - 2) and (x+6) is 2x + 8

The sum of numbers simply means to add up the numbers.

Therefore,

(x  -2) + (x + 6)

Hence,

(x - 2) + (x + 6)

open the brackets

Therefore,

x - 2 + x + 6

combine like terms

x + x + 2 + 6

add or subtract the like terms

2x + 8

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The number of people out of 2000 expected to use the app will be 1300.

A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics.

It is given that:-

A store employee conducted a survey of 325 randomly selected customers. According to survey 212, customers often use the app to shop.

We need to find the data for 2000 people who visited the store.

So the percentage of the people who are using the app will be calculated as:-

[tex]= \dfrac{212}{3254}=65\%[/tex]

So the number of the people out of 2000 will be:-

[tex]N\ = 2000\times \dfrac{65}{100}=1300\ \[/tex]

Hence the number of people out of 2000 expected to use the app will be 1300.

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Answer:

Answer with explanation is below~

Step-by-step explanation:

We could easily obtain the formulae/formula of an equilateral triangle not only through Pythagoras Theorem, but also through Heron's formula.

INTRODUCTION:

What's equilateral triangle?

What's Heron Formula?

[tex] \boxed{\rm \: Area= \sqrt{s(s - a)(s - b)(s - c)} \: units ^{2}} [/tex]

Where,

What's Pythagoras' Theorem?

SOLVING:

Let,ABC an equilateral triangle of sides a.

Now:Draw a perpendicular straight line AM to the side BC(Name each part of triangle)

So it's clear that ∆AMB is a right angled triangle at M, BM = (1/2)BC = a/2.

Please note AM here represents the height of ∆ ABC.

[tex] \boxed{\rm \: AM = \sqrt{AB^2-BM^2}}[/tex]

[tex] \rm \: AM = \sqrt{a {}^{2} - { \bigg( \cfrac{a}{2} \bigg) }^{2} } [/tex]

[tex] \rm \: AM = 3 \: \cfrac{a {}^{2} }{4} [/tex]

[tex] \rm \: AM = \cfrac{ \sqrt{3} }{2} \: a[/tex]

Now find the area of ∆ABC:

[tex] \rm \triangle \: ABC = \cfrac{1}{2} \times \: BC \times A [/tex]

[tex] \rm \: \triangle \: ABC = \cfrac{1}{2} \times a \times \cfrac{ \sqrt{3}}{4}a [/tex]

[tex] \boxed{\rm\triangle \: ABC = \cfrac{ \sqrt{3 } }{4} a {}^{2} \: units {}^{2}} [/tex]

Hence,the formulae of equilateral triangle using Pythagoras' theorem is {√(3)/4} a^2

[tex] \rule{225pt}{2pt}[/tex]

Extras:

Now let's find the area using Heron's Formula.

Solving:

Let each side of an equilateral triangle be a.

SO, then:

s = (3a/2)

We know that, (Heron's formula)

[tex] \rm \: A = \sqrt{s(s - a)(s - b)(s - c)} [/tex]

Now the area A :

[tex]\rm AR(A)= \sqrt{ \cfrac{ 3a } 2 \bigg(\cfrac{ 3a }{2} - a \bigg)\bigg(\cfrac{ 3a }{2} - a \bigg)\bigg(\cfrac{ 3a }{2} - a \bigg)} [/tex]

[tex]\rm AR(A)= \sqrt{ \cfrac{3a}{2} \bigg( \cfrac{a}{2} \bigg)\bigg( \cfrac{a}{2} \bigg)\bigg( \cfrac{a}{2} \bigg)}[/tex]

[tex]\rm \boxed{ \rm AR(A)= \cfrac{ \sqrt{ 3a}}{4} \: a {}^{2} \: \: units {}^{2}} [/tex]

And voila! we're done!

I hope this helps! :)

[Figure of Equilateral triangle is attached, it denotes the triangle we need to draw while finding the formulae through Pythagoras' theorem. ]

44 rem

Im sorry if its wrong

Answer:

Step-by-step explanation:

Answer:

Area = 50.125 cm^2

Perimeter = 26 + 15 = 41 cm

Step-by-step explanation:

Area Rectangle = 6 * 7 = 42 cm^2

Area Triangle = 1/2 * (9.5 - 7) * 6.5

Area Triangle = 1/2 * (2.5) * 6.5 = 8.125 cm^2

Total Area = 42 + 8.125 = 50.125 cm^2

Perimeter Rectangle = 6 + 7 + 6 + 7 = 26 cm

Perimeter or Triangle = 2.5 + 6.5 + 6 = 15 cm

Total Perimeter = 26 + 15 = 41 cm

Answer:

The scale factor is 8. The model is scaled by 8 to get the sculpture.

If they want it in reverse, the answer is 1/8. The model is 1/8th of the sculpture's size.

Sculpture = scale factor * model

[we get this equation because the model must be turned into a sculpture so we want to find how much bigger the model is compared to sculpture]

Let's take the length of the sculpture and model to put in.

x

56 = scale factor * 7

56/7  = scale factor

8 = scale factor

Answer:

1/8

Step-by-step explanation:

Take the scale factor as a ratio between the model and the sculpture.

Take any of the listed dimensions (length, for example) and divide.

Answer:

See below

Step-by-step explanation:

Not sure what they are looking for here....unless there is more info

[tex]\sqrt[14]{y}[/tex]  =  [tex]y^{1/14}[/tex]     perhaps?

Answer:

3.5 centimeters

Step-by-step explanation:

75% of 2 cm = .75 x 2 = 1.5 cm

2 cm + 1.5 cm = 3.5 cm

When you use word processor functions such as spell check and thesaurus to write a second draft, you are "C. Revising."

Revising means making changes and improvements to a piece of writing to make it better. This includes making it easier to understand, organizing it well, and making sure it is good quality overall.

Using spell check helps you fix mistakes in your spelling, while using the thesaurus helps you find different words that mean the same thing and choose better words to make your writing clearer and more accurate.

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Answer:

[tex]\displaystyle \boxed{ \frac{dz}{du} = \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }[/tex]

[tex]\displaystyle \boxed{ \frac{dz}{dv} = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Multivariable Calculus

Partial Derivatives

Partial Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} \frac{\partial z}{\partial t}[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle x = 2u + v[/tex]

[tex]\displaystyle y = \frac{u}{v}[/tex]

[tex]\displaystyle z = e^{xy}[/tex]

Step 2: Find Derivatives

[tex]\displaystyle \frac{dz}{du}[/tex]:

We can find the partial derivatives by differentiating using basic differentiation rules found under "Calculus":

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial u} & = 2 \\\frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial y}{\partial u} & = \frac{1}{v} \\\end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{du} & = 2ye^{xy} + \frac{xe^{xy}}{v} \\& = \frac{2ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v} \\& = \boxed{ \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to u.

[tex]\displaystyle \frac{dz}{dv}[/tex]:

We can find the partial derivatives by using the same method(s):

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial v} & = 1 \\ \frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial x}{\partial v} & = \frac{-u}{v^2} \\ \end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{dv} & = ye^{xy} + \frac{-uxe^{xy}}{v^2} \\& = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{-u(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v^2} \\& = \boxed{ \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to v.

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Topic: Multivariable Calculus

Unit: Partial Derivatives and Applications

The Gradient of the line PQ is -5/2.

Gradient the basically the ratio between the change in vertical coordinate to change in horizontal coordinates.

Here, P (2, 7) and Q (6, -3)

Now, Gradient = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

           m = [tex]\frac{-3 -7}{6 - 2}[/tex]

           m = -10/4

         m = -5/2

Thus, the Gradient of the line PQ is -5/2.

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Answer:

a) x=loge3 ( log e base 3)

b)4=e^y

Answer:

A.) loge(x)=3

B.)  e^y =4

Step-by-step explanation:

A.) loge(x)=3

B.)  e^y =4

Answer:

$1,129.27

Step-by-step explanation:

Compounded interest formula is

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Where [tex]A[/tex] is the final amount, [tex]P[/tex] is the principal, [tex]r[/tex] is the anual interest in decimal, [tex]n[/tex] is the numer of compounded periods in one year and [tex]t[/tex] is the time in years.

[tex]P= 800\\r= 0.09\\n= 1\\t= 4[/tex]

So then we plug our numbers...

[tex]A=800(1+\frac{0.09}{1})^{1(4)}=800(1.09)^{4}[/tex]

[tex]A=$1,129.27[/tex]

After 4 years the amount would be $1,129.27

The approximate area of the triangular base of James’ tank is 3025 in²

To find the approximate area of the triangular base of James' tank, we need to know what scale is.

A scale is the ratio of two dimension. It is given by scale = New dimension/old dimension

Given that the dimensions of James’ tank are each exactly 2 3/4 times the dimensions of Julian’s tank.

The scale of the area of James' tank to the area of triangular base of Julian's tank is S = (2³/₄)²

= (11/4)²

= 121/16

Let

So, scale, S = A/A'

So, making A subject of the formula, we have

A = SA'

A = 121/16 × 400 in²

A = 121 × 25 in²

A = 3025 in²

So, the approximate area of the triangular base of James’ tank is 3025 in²

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Answer:

2:3

Step-by-step explanation:

Simplica Los dos numeros

6 ÷ 3 = 2

9 ÷ 3 = 3

Answer:

Always

Step-by-step explanation:

[tex]ax^{2} + bx + c = 0[/tex]

Answer:

m=1/7

Step-by-step explanation:

The slope of y=x/3 + 4 is 1/7.

x/3+4 = x/7 so m = 1/7.

Answer:

m = 1/3

Step-by-step explanation:

The equation given is in slope-intercept form, which has the basic structure:

y = mx + b

In this equation, "m" is the slope and "b" is the y-intercept.

The value of "b" is 4.

The value of "m" is 1/3. This is because (x/3) is the same as (1/3 times x).

A Line graph

Sure hope this helps you

Answer:

A lot

Step-by-step explanation:

So basically you learn a lot