What do you think your favorite way of solving an equation will be and why?

(graphing, substitution, elimination)

Answers

Answer 1

Answer:

Elimination

Step-by-step explanation:

Elimination is a process which involves complete removal of one of the variables in a given equation, so as to first determine the value of the other variable.

For example in solving a simultaneous equation, applying the elimination method is easily understood, straight forward and simple to use. Once the logic behind the process is well understood and followed, errors can easily be avoided.

Therefore my favorite way of solving an equation would be by applying the elimination method because it is easy and direct to apply.


Related Questions

To purchase a car costing $10,000, the buyer bor-
rowed part of the money from the bank at 9% sim-
ple interest and the rest from her mother-in-law at
12% simple interest. If her total interest for the year
was $1080, how much did she borrow from the
bank?

Answers

Answer:

She borrowed 4000 from bank.

Step-by-step explanation:

Let 'y' be the amount borrowed from bank. Then 10000-y is the amount borrowed from her mother-in-law.

Let x= interest amount gained by bank . Then 1080- x = interest gained by mother-in-law

I1= interest rate by bank= 9%

I2= interest rate by mother-in-law=12%

Time(T) = 1 year

Now, By Simple Interest formula:

x=PTR/100

Or, x=(y*1*9)/100

Or,100x=9y

or,9y-100x=0...........................Equation (i)

Again 1080-x= ((10000-y)*1*12)/100

Or, 108000-100x=120000-12y

Or, 12y-100x=12000.................Equation(ii)

Solving equation (i) and (ii), we get

y= 4000, which the amount borrowed from bank.


Rationalise the denominator

Answers

Answer:

sqrt(3) /3

Step-by-step explanation:

1 / sqrt(3)

Multiply the top and bottom by sqrt(3)

1/ sqrt(3) * sqrt(3)/ sqrt(3)

sqrt(3) /  sqrt(3)*sqrt(3)

sqrt(3) /3

Answer:

[tex] = { \sf{ \frac{1}{ \sqrt{3} } }} \\ \\ { \sf{ = \frac{1}{ \sqrt{3} } . \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ = { \sf{ \frac{ \sqrt{3} }{ {( \sqrt{3}) }^{2} } = \frac{ \sqrt{3} }{3} }} [/tex]

ASAP I NEED HELP WITH THIS!!!
Find the area the sector.
A.1083pi/4in
B.38pi in
C. 57/4pi
D.1083/8pi in

Answers

Answer:

D

Step-by-step explanation:

Sector of Area=(theta/360)*pi*r^2

Sector of area=(135/360)*pi*19^2=(1083)/8 pi

Julie assembles shelves for a department store and gets paid $3.25 per shelf. She can assemble 5 per hour and works 8 hours per day. Determine Julie’s gross pay for 1 week

Answers

Pay per shelf = $3.25

No of shelfs per hour = 5

Total hours per day = 8

Total days to find pay of = 7

= 3.25×5×8×7

= 910

Therefore she is paid $910 after 1 week.

Must click thanks and mark brainliest

Hi please answer ASAP please and thank you

Answers

Answer:

1 1/4

Step-by-step explanation:

2 3/4 - 1 1/2

3 3/4 - 1 2/4

1 1/4

Determine the sum of the first 33 terms of the following series:

−52+(−46)+(−40)+...

Answers

Answer:

1320

Step-by-step explanation:

Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)

The terms increase by 6, so d is 6

a is the first term, -56

n is the terms you want to find, 33

Plug in the numbers, 33/2 (2(-56)+(32)6)

Simplify into 33(80)/2 and you get 1320


If u vector= a vector-b vector and v vector= a vector+b vector and magnitude of a = b = 2, then magnitude of u vector multiply v vector =???

Answers

Answer:

zero

Step-by-step explanation:

[tex]\overrightarrow{u} = \overrightarrow{a} - \overrightarrow{b}\\\\\overrightarrow{v}= \overrightarrow{a} + \overrightarrow{b}\\\\\overrightarrow{u} . \overrightarrow{v} = a^2 - b^2 \\\\\overrightarrow{u} . \overrightarrow{v} = 2^2 - 2^2 = 0[/tex]

So, vector u and vector v are perpendicular to each other.

PLEASE HELP I WILL GIVE BRAINLIEST

Answers

Step-by-step explanation:

A natural number is a positive whole number.

A whole number is a positive number with no fractions or decimals.

A interger is a whole number negative or positive.

A rational number is a number that terminates or continue with repeating digits.

A irrational number is a number that doesn't terminate or continue with repeating digits.

1. Rational Number

2. Natural,Whole,Interger,Rational

3. Whole,Rational,Interger

4. Rational

5.Irrational

6.Rational

7.Natural,Whole,Interger,Rational

8.Interger,Rational

9.Irrational

Determine three consecutive odd integers whose sum is 2097.

Answers

Answer:

first odd integer=x

second odd integer=x+2

third odd integer=x+4

x+x+2+x+4=2097

x+x+x+2+4=2097

3x+6=2097

3x=2097-6

3x=2091

3x/3=2091/3

x=697

therefore, x=697

x+2=697+2=699

x+4=697+4=701

How do we derive the sum rule in differentiation? (ie. (u+v)' = u' + v')

Answers

It follows from the definition of the derivative and basic properties of arithmetic. Let f(x) and g(x) be functions. Their derivatives, if the following limits exist, are

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h\text{ and }g'(x)\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]

The derivative of f(x) + g(x) is then

[tex]\displaystyle \big(f(x)+g(x)\big)' = \lim_{h\to0}\big(f(x)+g(x)\big) \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)+g(x+h)\big)-\big(f(x)+g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)-f(x)\big)+\big(g(x+h)-g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{f(x+h)-f(x)}h+\lim_{h\to0}\frac{g(x+h)-g(x)}h \\\\ \big(f(x)+g(x)\big)' = f'(x) + g'(x)[/tex]

If Sin x = -¼, where π < x < 3π∕2 , find the value of Cos 2x

Answers

Answer: 7/8

Cos2x has 3 formulas, Sinx is given in the question, we should use the formula with sinus. I guess that's the solution.

Classify the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene.​

Answers

9514 1404 393

Answer:

  (d)  Right, scalene

Step-by-step explanation:

The little square in the upper left corner tells you that is a right angle. Any triangle with a right angle is a right triangle. This one is scalene, because the sides are all different lengths.

__

Additional comment

An obtuse triangle cannot be equilateral, and vice versa.

An equilateral triangle has all sides the same length, and all angles the same measure: 60°. It is an acute triangle.

The weekly wages of employees of Volta gold are normally distributed about a mean of$1250 with a standard deviation of $120. Find the probability of an employee having a weekly wage lying 1) between $1320 and $970 2) over $1290 3) under $1400

Answers

Answer:

1) 0.7104 = 71%

2) 0.6615 = 66%

3) 0.8944 = 89%

Step-by-step explanation:

1)

Z(low)=-2.333 0.009815329

Z(upper)=0.583 0.720165536

2)

Z(low)=0.333 0.63055866

Z(upper)=8322.908 1

3)

Z(low)=-10.417 0

Z(upper)=1.25 0.894350226

help me pls??????? :)

Answers

Answer:4 in each bad 2 left over

Step-by-step explanation:

Answer:

4 in each bag and 2 left over

Step-by-step explanation:

divide 14 by 3

3 goes into 14, 4 times

14 - 12 = 2

4 in each bag and then 2 left over

Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression

Answers

Answer:

divide, 2x+9

Step-by-step explanation:

got it right

100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT

a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal

places.

Answers

Answer:

See Below (Boxed Solutions).

Step-by-step explanation:

We are given the two complex numbers:

[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]

First, convert z to polar form. Recall that polar form of a complex number is:

[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]

We will first find its modulus r, which is given by:

[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]

In this case, a = √3 and b = -1. Thus, the modulus is:

[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]

Next, find the argument θ in [0, 2π). Recall that:

[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]

Therefore:

[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]

Evaluate:

[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]

Since z must be in QIV, using reference angles, the argument will be:

[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]

Therefore, z in polar form is:

[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]

Part A)

Recall that when multiplying two complex numbers z and w:

[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]

To find the complex form, evaluate:

[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]

Part B)

Recall that when raising a complex number to an exponent n:

[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]

Therefore:

[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]

Substitute:

[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]

Simplify:

[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]

Simplify using coterminal angles. Thus, the polar form is:

[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]

And the complex form is:

[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]

Part C)

Recall that:

[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]

And the complex form is:

[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]

Part D)

Let a be a cube root of z. Then by definition:

[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

From the property in Part B, we know that:

[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]

Therefore:

[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:

[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]

The first equation can be easily solved:

[tex]r=\sqrt[3]{2}[/tex]

For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:

[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]

Solve for the argument:

[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]

There are three distinct solutions within [0, 2π):

[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]

Hence, the three roots are:

[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]

Or, approximately:

[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]

a rectangular postage stamp has a length of 3/2 inches and a width of 3/4 inch. what is the area of the stamp in square inches?

Answers

Answer:

9/8 or 1.125

Step-by-step explanation:

We want to find the area of a rectangular postage stamp

The area of a rectangle can be found by multiplying the length by the width

Given length: 3/2

Given width: 3/4

Area = 3/2 * 3/4 = 9/8 or 1.125

The area of a 2D form is the amount of space within its perimeter. The area of the stamp in square inches is 1 1/8 inches².

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given that a rectangular postage stamp has a length of 3/2 inches and a width of 3/4 inch. Therefore, the area of the stamp in square inches is,

Area of the stamp = Length × Width

                              = 3/2 inches × 3/4 inches

                              = 9/8 inches²

                              = 1 1/8 inches²

Hence, the area of the stamp in square inches is 1 1/8 inches².

Learn more about the Area here:

https://brainly.com/question/1631786

#SPJ2

Where did term “infinity” come from

Answers

the English mathematician John Wallis in 1655 invented the word infinity Infinity is from the Latin, infinitas. In general, the word signifies the state from an entity's not ending/limit.

Find the value of the sum 219+226+233+⋯+2018.

Assume that the terms of the sum form an arithmetic series.

Give the exact value as your answer, do not round.

Answers

Answer:

228573

Step-by-step explanation:

a = 219 (first term)

an = 2018 (last term)

Sn->Sum of n terms

Sn=n/2(a + an)         [Where n is no. of terms] -> eq 1

To find number of terms,

an = a + (n-1)d     [d->Common Difference] -> eq 2

d= 226-219 = 7

=> d=7

Substituting in eq 2,

2018 = 219 + (n-1)(7)

1799 = (n-1)(7)

1799 = 7n-7

1799 = 7(n-1)

1799/7 = n-1

257 = n-1

n=258

Substituting values in eq 1,

Sn = 258/2(219+2018)

    = 129(2237)

    = 228573

Find the volume of the cylinder please

ASAP

Answers

Answer:

33ft^3

Step-by-step explanation:

radius is half the diameter, half of 2=1 and 1^2=1

3(1)(11)=33

Answer: V = 33 ft³

Step-by-step explanation:

π = 3

r = (1/2)d = (1/2) (2) = 1 ft

h = 11 ft

Given Formula

V = π r² h

Substitute values into the formula

V = (3) (1)² (11)

Simplify exponents

V = (3) (1) (11)

Simplify by multiplication

V = 33 ft³

Hope this helps!! :)

Please let me know if you have any questions

What is the volume of a sphere with a diameter of 7.7 ft, rounded to the nearest tenth
of a cubic foot?

Answers

Step-by-step explanation:

V=4/3πr^3

V=4/3π(3.85)^3

V=4/3π(57.066625)

V=4/3 (179.280089865)

V=239.04011982

V=239 ft^3

what does this equal 2^3 + 6^5=

Answers

[tex]\\ \sf\longmapsto 2^3+6^5[/tex]

[tex]\\ \sf\longmapsto 2^3+(2\times 3)^5[/tex]

[tex]\\ \sf\longmapsto 8+2^5\times 3^5[/tex]

[tex]\\ \sf\longmapsto 8+32\times 243[/tex]

[tex]\\ \sf\longmapsto 40+7776[/tex]

[tex]\\ \sf\longmapsto 7784[/tex]

Answer:

2*2*2= 8

6*6*6*6*6= 7,776

7,776+8=

7,784

−30=5(x+1)

what is x?

Answers

[tex]\\ \rm\Rrightarrow -30=5(x+1)[/tex]

[tex]\\ \rm\Rrightarrow -30=5x+5[/tex]

[tex]\\ \rm\Rrightarrow 5x=-30-5[/tex]

[tex]\\ \rm\Rrightarrow 5x=-35[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-35}{-5}[/tex]

[tex]\\ \rm\Rrightarrow x=7[/tex]

Answer:

x = -7

Step-by-step explanation:

-30 = 5 (x -1 )

5 ( x + 1 ) =-30

5 (x + 1 ) = - 30

     5            5

x + 1 = -6

x + 1 -1 = -6 -1

x = - 7

Please help I’ll mark as brainlist

Answers

Answer:

Ekta and Preyal

Step-by-step explanation:

Answer: Ekta and Preyal

Originally the cubes have a perimeter of 15, both Ekta and Preyal have a perimeter of 17 which is exactly a 2 unit increase

help help help help

Answers

Answer:

abc is a triangle so ,

a is ( 9,6 )

b is ( 9,3 )

and c is ( 3,3 )

convert 10.09% to a decimal

Answers

Answer:

0.1009

Step-by-step explanation:

To convert percentage into decimal, you need to divide the percentage by 100

10.09/100

= 0.1009

To convert 10.09% to a decimal, we need to decide it by 100 like so:

10.09 ÷ 100 = 0.1009

Therefore, the answer is 0.1009

Ray is making his reward winning lemonade recipe for a party he is comparison shopping for lemons at super pioneer supermarket he can buy 4 lemons for 1.60 ray visits keyfood and found 3 lemons cost 1.80 use the table below to compare the values

Answers

Answer:

classified info jk juss use a mf calculater

Step-by-step explanation:

(√0,04-√(-1,2)²+√121)×√81

Answers

Answer:  90

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} (\sqrt{0,04}-\sqrt{(-1,2)^2}+\sqrt{121 } ) \cdot \sqrt{81} = \\\\\\(0,2-1,2+11)\cdot 9=(11-1)\cdot 9=90[/tex]

What is the perimeter of a square which has the same area as a circle with circumfrence of 4π

Answers

Answer:

Perimeter square = 8 sqrt(pi)

Step-by-step explanation:

The perimeter of a square is 4*s

The area of a circle is Area = pi * r^2

The circumference of a circle is C = 2*pi * r

C = 4 pi

4pi = 2*pi * r

r = 2

So the area of the circle is pi * r^2 = pi * 2^2 = 4pi

The square has the same area

Area = 4*pi

Square = 4*pi

s^2 = 4*pi

s = sqrt(4*pi)

s = 2*sqrt(pi)

The perimeter = 4 * 2 * sqrt(pi)

The perimeter = 8 * sqrt(pi)

Write the equation of the sinusoidal function shown?

A) y = cos x + 2

B) y = cos(3x) + 2

C) y = sin x + 2

D) y = sin(3x) + 2

Answers

Answer:

günah(3x) + 2

Step-by-step explanation:

Gösterilen sinüzoidal fonksiyonun denklemini yazınız? A) y = cos x + 2 B) y = cos(3x) + 2 C) y = günah x + 2 D) y =

Answer:

y = sin(3x) + 2

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