Why is replacement or substitution important in math?

Answers

Answer 1

The replacement or substitution approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

This makes it easier to solve by combining two linear equations into one equation with a single variable. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.

By changing the value of another variable in an equation, the variable can be eliminated. Thus, the elimination by substitution method is the name given to this technique.

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Related Questions

Fill in the table using this function rule.

Answers

The complete table is

x     y

-1     -2

0     3

1     8

2    13

How to complete the table?

The function is given as:

y = 5x + 3

On the table, we have

x = -1, 0, 1 and 2

Using the above values, we have:

y = 5(-1) + 3 = -2

y = 5(0) + 3 = 3

y = 5(1) + 3 = 8

y = 5(2) + 3 = 13

So, the complete table is

x     y

-1     -2

0     3

1     8

2    13

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2. (01.01)
Evaluate 32+(5-2)-4-
O 19
O 16
O 46
24
3
. (1 point)

Answers

32+(5-2)-4
=32+3-4
=35-4
=31

A salesman is carrying a big bag for selling a machine. In addition to the machine that the salesman wants to sell, there is some personal stuff. The weight of his machine is three kilogram and half a machine. In addition to the machine, there is a repair tool for the machine that weighs half kilogram and one-fourth of the machine. The personal stuff weighs four kilogram minus a fourth of the weight of the machine. Finally, the salesman has some supplies that weigh two-fifth of the machine and personal stuff combined. What is the total weight in the bag of salesman

Answers

The total weight of the bag that the salesman is carrying for selling a machine including some personal stuff is 13.9 Kg.

What is a fraction?

A fraction is a rational number that consists of a numerator and a denominator, used to represent a part of the whole thing.

Calculation:

It is given that,

A salesman is carrying a big bag for selling a machine.

Consider the weight of the machine = w

So,

The weight of his machine is three kilograms and half a machine. I.e.,

w = 3kg +w/2

⇒ w/2 = 3kg

w = 6kg

Thus, the weight of the machine is 6 Kg.

So, the weight of the repair tool for the machine = a half kilogram and one-fourth of the machine

⇒ 1/2Kg + 1/4w

⇒ 1/2 + 6/4

2 Kg

The personal stuff weighs - four kilograms minus a fourth of the weight of the machine.

⇒ 4Kg - w/4

⇒ 4 - 6/4

2.5 Kg

He has some supplies that weigh two-fifth of the machine and personal stuff combined.

⇒ 2/5(w + 2.5)

⇒ 2/5 × 8.5

3.4 Kg

Thus, the total weight of the bag = 6 Kg + 2 Kg + 2.5 Kg + 3.4Kg =  13.9Kg.

Therefore, the total weight of the salesman's bag is 13.9 Kg.

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A pizzeria has a choice of 15 toppings. How many ways could someone choose 3?

Select one:
a. 15
b. 455
c. 2,730
d. 3,375

Answers

Answer:

the answer is b 455

Step-by-step explanation:

15/(4×12)=455

c) tan²0 - cot²0 = sec²0 (1- cot²0)
Prove that LHS = RHS So that LHS will be the sec²0 (1- cot²0) ​

Answers

Answer:

Maybe this could help?

can someone please help me

Answers

Answer:

[tex]\frac{13\pi }{9}[/tex] radians

Step-by-step explanation:

to convert degrees to radians

degrees × [tex]\frac{\pi }{180}[/tex]

= 260 × [tex]\frac{\pi }{180}[/tex]

= 26 × [tex]\frac{\pi }{18}[/tex]

= 13 × [tex]\frac{\pi }{9}[/tex]

= [tex]\frac{13\pi }{9}[/tex]

22. What is the area of minor sector DFE?
79.3 square cm
15.2 square cm
37.9 square cm
66.1 square cm

Answers

The area of the minor sector DFE is gotten as; D: 66.1 square cm

How to find area of sector?

Formula for area of sector is;

A = (θ/360) * πr²

We are given;

minor angle; θ = 100°

radius; r = 8.7 cm

Thus;

A =  (100/360) * π(8.7²)

A = 66.1 square cm

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calculate 20% of rs 250000

Answers

Answer:

50,000

Step-by-step explanation:

20% can be rewritten as 0.2 times 250000: 0.2*250000 = 50,000

The following table shows each of Haruka's final exam scores last semester. Final exam Score on a 100100100-point scale Astronomy 727272 Biology 858585 Physics 929292 Chemistry \large

Answers

The mean calculated shows that the Chemistry score will be 87.

How to calculate the score?

From the information given, the total scores will be:

= 84 × 4

= 336

The addition of the scores given will be:

= 72 + 85 + 92

= 249

The Chemistry score will be:

= 336 - 249

= 87

Complete question:

If the mean of the data set is 84 points, find Harukas final exam score in Chemistry.

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What is the equation of the translated function, g(x), if f(x) = x2?


a.) g(x) = (x – 4)2 + 6


b.) g(x) = (x + 6)2 – 4


c.) g(x) = (x – 6)2 – 4


d.) g(x) = (x + 4)2 + 6

Answers

Answer: dfghj

Step-by-step explanation: xcfvghj

Answer: It's D

Step-by-step explanation:

Right on edge 2022

What are the answers to quick check for 13-2 equivalence with customary units of capacity in savvas

Answers

Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

According to the question,

The customary units of capacity in Sava's are 1 fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

Customary units and its equivalent  

1 Fluid ounce = 2 Tablespoons

1 Cup = 8 fluid ounces

1 Pint = 2 cups

1 Quart = 2 pints

1 Gallon = 4 quarts

Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

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x =x=x, equals
^\circ

Answers

Answer:

x = 25°

Step-by-step explanation:

Hello!

25° and x° are vertical angles, therefore they are equal to each other.

Vertical angles are angles formed by two intersecting lines that are non-adjacent.

The angle to the right of 80° would be 55°, because the sum of angles on a line is 180°.

Angle x would be 25° because the other straight line contains angles 80°, 50° and x°.

Let a and b be positive integers such that the product of all positive divisors of a equals the product of all positive divisors of b. Prove that a

Answers

The property A*B = (A' + A") * ( B'+B") is equal to each other.

According to the statement

We have given that the a and b is the positive integers and we have to prove that the product of all positive divisors of a equals the product of all positive divisors of b.

And in this statement

Now we use Distributive property

Here A and B is the positive integer and

A' and A" are the divisors of A and B' and B" are the divisors of B.

Now,

A = A' + A" and B = B'+B"

Now, Multiply both with each other then

A*B = (A' + A") * ( B'+B")

then

A*B = (A' B'+ A'B") + ( A"B'+A'B")

by this way it is equal to each other

Hence proved.

So, The property A*B = (A' + A") * ( B'+B") is equal to each other.

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Consider the equations y= |x-1 | and y = 3x + 2. The approxirate solution of this system of equations is

Answers

Answer:

Point Form: (- 1/4, 5/4)

Equation Form: x = - 1/4, y  = 5/4

Step-by-step explanation:

pls HELP Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles?

5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side

6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side

5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side

5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side

Answers

Answer:

The first choice

Step-by-step explanation:

You are setting up as you read it.  The left side has 5 x and 6 units, so you would set up 5 positive x times and 6 positive unit tiles.  On the the right you are setting up 4 positive x tiles and 3 negative unit tiles.  It is not asking you to solve with the algebra tiles, just to set it up.

b. Shawn has 42 points on his computer game. He loses the
next round though which takes away 50 points. How
many total points does Shawn now have?

Answers

Answer: -8 points

Step-by-step explanation: because he lost 50, and he originally had 42, a smaller number, the answer will go into the negatives.

42-50= -8, which is how you get the answer!

Answer:

-8

Step-by-step explanation:

42-50 is the same as 50-42, except the answer is negative

Select the correct answer.

A container is made by cutting off the bottom of a cone. The container has a diameter of 30 centimeters and a height of 20 centimeters. The
small cone that was removed has a diameter of 10 centimeters and a height of 6 centimeters.

What is the volume of the container, to the nearest cubic centimeter?

A. 6,126 cm³
B. 6,283 cm³
C. 5,812 cm³
D. 5,969 cm³

Answers

The volume of the container is 5969 cm³. The correct option is D. 5,969 cm³

Calculating Volume

From the question, we are to determine the volume of the container

Volume of the container = Volume of the cone - Volume of the small cone

The volume of a cone is given by the formula,

V = 1/3πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

For the small cone,

Diameter = 10 cm

∴ Radius, r = 10cm/ 2 = 5 cm

h = 6 cm

For the big cone

diameter = diameter of the container = 30 cm

∴ Radius = 30cm/ 2

Radius = 15cm

h = height of small cone + height of container

h = 6 cm + 20 cm

h = 26 cm

Putting the parameters into

Volume of the container = Volume of the cone - Volume of the small cone

We get,

Volume of the container = 1/3π × 15² ×26 - 1/3π × 5² × 6

Volume of the container = 1/3π (15² ×26 -  5² × 6)

Volume of the container = 1/3π (5850 -  150)

Volume of the container = 1/3π (5700)

Volume of the container = 1/3 × π × 5700

Volume of the container = 5969.026 cm³

Volume of the container ≈ 5969 cm³

Hence, the volume of the container is 5969 cm³. The correct option is D. 5,969 cm³

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find the value for the following

Answers

[tex]\sqrt{3-2\sqrt{2} }[/tex] = 0.06

(2x)ˣ = 25√5

How to solve an expression?

[tex]\sqrt{3-2\sqrt{2} }[/tex]  = [tex]\sqrt{3}-\sqrt{2\sqrt{2} }[/tex] = 1.73205080757 - 1.67428223427 = 0.06

4ˣ . 4ˣ⁻¹ = 24

4ˣ . 4ˣ / 4 = 24

4ˣ(1 - 1 / 4) = 24

4ˣ(3 / 4) = 24

multiply both sides by 4 / 3

4ˣ = 32

2²ˣ = 2⁵

2x = 5

x = 5 / 2 = 2.5

Therefore,

(2x)ˣ = 25√5

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The sum of the reciprocals of three consecutive integers is 47/60. What is the sum of the three integers

Answers

Answer:

56

Step-by-step explanation:

small brain :(

Find the area of the rhombus.
9 m
9 m
9 m
9 m

Answers

See image below! Hope this helps

PLEASE HELP I GIVE 95 POINTS

Answers

D,
3^x is positive, and the y-in. is 1.
3^0 = 1
Process of elimination.

Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −3^2 + 150 − 1200, where x is the amount he charges per tree.

1. How much does he need to charge if he wants to break even?

2. How much does he need to charge if he wants to make a profit of $600?

Answers

Solving quadratic equations, it is found that he needs to charge:

1. He needs to charge $40 to break even.

2. He needs to charge $30 for a profit of $600.

What is a quadratic function?

A quadratic function is given according to the following rule:

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

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The profit equation in this problem is:

P(x) = -3x² + 150x - 1200.

He breaks even when P(x) = 0, hence:

-3x² + 150x - 1200 = 0.

The coefficients are a = -3, b = 150, c = -1200, hence:

[tex]\Delta = 150^2 - 4(-3)(-1200) = 8100[/tex][tex]x_1 = \frac{-150 + \sqrt{8100}}{-6}[/tex][tex]x_2 = \frac{-150 - \sqrt{8100}}{-6} = 40[/tex]

He needs to charge $40 to break even.

For a profit of $600, we have that P(x) = 600, hence:

-3x² + 150x - 1200 = 600.

-3x² + 150x - 1800 = 0.

The coefficients are a = -3, b = 150, c = -1800, hence:

[tex]\Delta = 150^2 - 4(-3)(-1800) = 900[/tex][tex]x_1 = \frac{-150 + \sqrt{900}}{-6}[/tex][tex]x_2 = \frac{-150 - \sqrt{900}}{-6} = 30[/tex]

He needs to charge $30 for a profit of $600.

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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as
1
L-10log where lo-10-12
and is the least intense sound a human ear can hear. What is the approximate loudness
of a dinner conversation with a sound intensity of 10-7?

Answers

[tex]\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}[/tex]

[tex]\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\\ \rm\dashrightarrow B=10log10^5[/tex]

[tex]\\ \rm\dashrightarrow B=10\times 5log10[/tex]

[tex]\\ \rm\dashrightarrow B=10(5)[/tex]

[tex]\\ \rm\dashrightarrow B=50dB[/tex]

Answer:

50 Db

Step-by-step explanation:

Given:

[tex]L=10 \log \dfrac{I}{I_0}[/tex]

[tex]I_0=10^{-12}[/tex]

where:

L is the loudness measured in decibels (Db)I is the sound intensity measured in w/m²

To find the approximate loudness of a dinner conversation with a sound intensity of [tex]I=10^{-7}[/tex], substitute the values of I and I₀ into the given equation and solve for L:

[tex]\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies L=10 \log 10^{-7-(-12)[/tex]

[tex]\implies L=10 \log 10^5[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies L=5 \cdot 10 \log 10[/tex]

[tex]\implies L=50 \log 10[/tex]

As the given log does not have a specified base, assume the base is 10.

[tex]\implies L=50 \log_{10} 10[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies L=50 (1)[/tex]

[tex]\implies L=50\:\:\sf Db[/tex]

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What is the volume of the space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters 198.264 cubic centimeters 222.264 cubic centimeters

Answers

The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

Let l,b,h be the dimensions of small gift box V1 = Volume = l*b*h

= 24cm^3

Dimension of Large box are 2.1l , 2.1b,2.1h

Volume of large box = 2.1 l*2.1b*2.1h

= (2.1)^3*lbh

= (2.1)^3*24

V2 =222.264

Volume filled with tissue paper is V2-V1

222.264 - 24

= 198.264cm^3

Hence The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

The complete question is shown below

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?

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Clue 1
The number has three digits.
Clue 2 The number is less than 140.
Clue 3 The number has 7 as a factor.
Clue 4 The number is even.
Clue 5 The sum of the digits of the number is less than 9.

Answers

the number is 112
1. Three digits
2. Less than 140
3. 7 is a factor
4. Even
5. 1+1+2 = 4

9. Construct Arguments Write a two-column
proof for the Angle Bisector Theorem. MP.3

Answers

The angle bisector theorems is proved below.

What is the angle bisector theorems?

It should be noted that the angle bisector theorem simply states that an angle bisector of a triangle divides the opposite side into two segments which are proportional to the other sides of the triangle.

The way to proof the theorem is illustrated:

Draw a ray CX parallel to AD and then extend BA to intersect this ray at E.

In triangle CBE, DA is parallel to CE.

BD/DC == BA/AE ......... i

Now we want to prove that AE = AC

Since DA is parallel to CE, we have:

DAB = CEA (corresponding angles) ....... ii

DAC = ACE (alternate interior angles) ...... iii

Since AD is the bisector of BAC, we've DAB = DAC.

From the above, ACE makes and isosceles triangle and since the opposite sides are equal, we've AC = CE.

Substitute AC for AE in equation i

BD/DC = BA/AC

Therefore, the angle bisector theorems is proved.

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Which of the following best describes the slope of the line below?
A. Positive
B. Zero
C. Negative
D. Undefined

Answers

Answer:

Zero

Step-by-step explanation:

Since the line is a horizontal line, the slope does not change.  The slope is zero.

Answer:

Zero

Step-by-step explanation:

A zero slope is when the line is horizontal and when the slope equals to zero


I hope it helps! Have a great day!

bren~

Solve the following:
-5² + 10²
(2 × (-5) × 3) + 3³
Give your answer in simplest form.

Answers

Problem 1: -5^2 + 10^2
Work:
-5^2 + 10^2—> (-5 x -5) + (10 x 10) —> 25 + 100 = 125
Answer:
125

Problem 2: (2 x (-5) x 3) + 3^3
Work:
(2 x (-5) x 3) + 3^3 > (-25 x 3) + 3^3 —> -75 + 3^3 —> -75 + 27 —> 48
Answer:
48

describe fully the single transformation which maps triangle A onto triangle B.

Answers

The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

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Question down below about linear equations.

Answers

The system of equations is -x + y = 4 and -2x + y = 0

How to create the system of linear equations?

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The graph of the system of equations

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system

Prove that the solution is (4, 8)

The above is represented in the (a) part of this solution

Verify that the solution is (4, 8)

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

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Need serious help with this!!!!!!!!!!!!!!!!!!! 1. Compare the speed that light waves travel in air to the speed that sound waves travel in the air. How many times faster do light waves travel in air in comparison to sound waves in air?Water-1500 meters per second steel-5000 meters per second Air-335 meters per second Pls help it is due today Answer the photo below thanks El largo de una sala es 2 metros ms grande que su ancho. El rea es de 80 m?. Cunto mide de largo? Cunto mide de ancho? 4x-5y=18 determine the missing coordinate in the ordered pair (-2,?) so that it will satisfy the given equation What is the CIRCUMFERENCE of the given circle? 12.57 in30.23 in25.13 in50.27 in Help me for a cookie the dissolution of copper sulphate is Find the area of each composite figure. Signals are used whenever voice communication is_____. The graph of f(x)=x is given which graph represents g(x)=1/3x 2write neatlyI will refuse to read your work. (begin unles) Why was Lowell, Massachusetts founded in the early 1820s? What is homonationalism in simple terms? Write the symbol and charge for each individual ion:11) Beryllium and and phosphorus12) Cesium and sulfur13) lithium and Phosphorus14) Fluorine and rubidium15) Francium and oxygen Minerals and rocks have cultural value and both are used in manufacturing andtechnologic industries. Minerals and rocks improve the quality of our lives.TrueFalse 3 The formula to find the area of a rectangle is A = lw. If l = 6 in and w = 5 in, then what is the area of the blue portion of the rectangle? A. 11 sq in B. 22 sq in C. 15 sq in D. 30 sq in A force that slowly wears away mountains and other features on the surface of Earth isa. constructive.b. destructive.C. superpositiond. unnatural.Please select the best answer from the choices provided the future continuous from the