Jaime adds equations A and B to solve this system of equations. Why is this method
generally valid for solving a system of equations?

Jaime Adds Equations A And B To Solve This System Of Equations. Why Is This Methodgenerally Valid For

Answers

Answer 1

The elimination method is valid for the system of equation because the y term cancels.

How to solve a system of equation using elimination method?

The system of equation can be solved using elimination methods.

Therefore,

x - 2y = 3

3x + 2y = 17

Hence,

x + 3x  = 4x

-2y + 2y = 0

3 + 17 = 20

Therefore,

4x = 20

The y term cancels. Therefore, we can solve for x and later solve for y.

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Answer 2

Answer:

Adding a quantity like x – 2y to one side of an equation and another quantity like 3 to the other side maintains the equality if the two quantities are equal.


Related Questions

For Rs 10,000 at 10% per annum. What will be the interest after 4 years?​

Answers

Step-by-step explanation:

please mark me as brainlest

Write an expression for the area of the trapezium below.
Expand any brackets and fully simplify your answer.

Answers

This is my hypothesis

Enter the correct answer in the box.
Consider this expression.
x² + x - 72
Replace the values of a and b to rewrite the given expression.
(x+ a)(x+b)

Answers

The answer is
(x + 9)(x - 8), where a = 9 and b = -8 or a = -8 and b = 9

The correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

Here, we have to rewrite the expression x² + x - 72 in the form (x + a)(x + b), we need to find two numbers a and b such that when multiplied,

it give us the constant term -72 and when added, it give us the coefficient of the x term, which is 1.

The expression x² + x - 72 can be factored as follows:

x² + x - 72

= x² + 9x - 8x - 72

=x(x+9) -8(x+9)

= (x + 9)(x - 8)

Therefore, the correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

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PLEASE HELP ANSWER MY QUESTION ASAP!

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: a_{33} = 1\degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

In a matrix, [tex] \sf a_{ij} [/tex] represents an element in " i " th row and " j " th column.

Henceforth, element [tex] \sf a_{33} [/tex] represents element in 3rd row and 3rd column.

[tex]\qquad \tt \rightarrow \:a_{33} = 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

After covering 4/5 of the journey, James found that he has traveled 48 km. How much of the journey is still left?

Answers

Answer:

12 km

Step-by-step explanation:

Let the total distance to be traveled = x

[tex]\sf \dfrac{4}{5} \ of \ the \ journey = 48\\\\[/tex]

        [tex]\sf \dfrac{4}{5}*x = 48\\\\[/tex]

             [tex]x = 48*\dfrac{5}{4}[/tex]

                = 12 * 5

            x = 60 Km

Distance still to traveled = 60 - 48 = 12Km

Write the quadratic equation whose roots are 3 and -3, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)

Answers

The quadratic equation is  3x² - 27.

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Given:

The roots are 3 and -3

We have

α= 3   and β=-3

So,

α+β = -b/a  and αβ = c/a

α+β = 0 =-b/a and  αβ= -9 = c/a

Comparing from above

a=1, b= 0 and c=-9

Also, the leading coefficient is 3.

Then the quadratic equation is,

= 3(ax² + bx + c)

= 3( x² +0x- 9)

Hence, the quadratic equation is 3x² - 27.

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The function f(x)= 4x + 3 represents the length of a rectangle. The function g(x)=2x-5 represents the width of the rectangle. Use ( g(4) to determine the area of the rectangle.
57
19
16
3

Answers

Answer:

57 square units

Step-by-step explanation:

Area is = Length x Width

Given:

f(x)= 4x + 3    Length

g(x)=2x-5      Width

x = 4

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

Width

g(x)=2x-5

g(4)=2(4)-5

g(4)= 3

Length

f(x)= 4x + 3

f(4) = (4)(4) + 3

f(4) = 19

Area = (length)*(width)

Area = f(x)*g(x) for x = 4

Area = (f(4))*(g(4))

Area = (19)*(3)

Area = 57 square units

the distance time graph represents a journey made by jo at the speed was jo walking for the first 15 minutes

Answers

The speed that Jo walked for the first 15 minutes is; 6 km/hr

How to Interpret Distance Time Graphs?

The distance - time graph is missing and so i have attached it.

Now, the formula for speed is;

Speed = Distance/time

The distance after 15 minutes from the graph is 1.5km.

Now, 15 minutes when converted to hours is 15/60 = ¹/₄ hr

Thus, the speed that Jo walked for the first 15 minutes is;

Speed = 1.5/(¹/₄)

Speed = 6 km/hr

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What is the closest benchmark for 99%?

Answers

The closest benchmark for 99% is 100%.

We know that benchmarks in mathematics are the norm or point of comparison that something can be measured, compared, or evaluated against. Benchmark values are values that can be used to estimate and contrast other values or quantities. Typically, benchmark figures are multiples of 10 or 100. 0 percent, 10 percent, 25 percent, 50 percent, 75 percent, and 100 percent are the most popular benchmark percentages.

Here we have to find the closest benchmark for 99%. Clearly, from the definition 100% is the required answer.

We can conclude that the closest benchmark for 99% is 100%.

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A ration of two numbers is equal to 3:8 if the smaller number is 14 find the greatest number

Answers

Answer:

34 and ⅔

Step-by-step explanation:

added in the picture

Which of the lines below is a line of symmetry?
O A. Red

B. Yellow
C. Neither
• D. Both

Answers

Answer: D) Both

Detailed Explanation:

Lines of symmetry in a figure are lines that divide the figure into equal parts.

In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.

Therefore, both the Red and Yellow lines are lines of symmetry.

Both the Red and Yellow lines are lines of symmetry, Option D is correct.

What is Coordinate system?

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Lines of symmetry in a figure are lines that divide the figure into equal parts.

The given figure is a square as we observe the four sides are equal in the given shape.

In a square, there are four lines of symmetry, each of which divides it into two identical parts.

The symmetry lines of a square are both its diagonals and the lines joining the midpoints of its opposite sides (bisectors).

In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.

Hence, both the Red and Yellow lines are lines of symmetry, Option D is correct.

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How many solutions does the following equation have?
7(y+3)=5y+8
A. No Solution
B. Exactly One Solution
C. Infinitely many solutions

Answers

B. Exactly one solution

7y +21 = 5y +8
7y +13=5y
13=-2y
-6.5=y

Answer:

B. Exactly One Solution

Step-by-step explanation:

Given:

[tex]7(y+3)=5y+8[/tex]

Expand the brackets:

[tex]\implies 7y + 21 = 5y + 8[/tex]

Subtract 21 from both sides:

[tex]\implies 7y + 21-21 = 5y + 8-21[/tex]

[tex]\implies 7y=5y-13[/tex]

Subtract 5y from both sides:

[tex]\implies 7y-5y=5y-13-5y[/tex]

[tex]\implies 2y=-13[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2y}{2}=\dfrac{-13}{2}[/tex]

[tex]\implies y=-\dfrac{13}{2}[/tex]

Therefore, the equation has exactly one solution.

Solve for x in the equation x/5 -2=11

Answers

Answer:

x = 65

Step-by-step explanation:

Solve for x in the equation

x/5 - 2 = 11

x/5 = 11 + 2

x/5 = 13

x = 5 * 13

x = 65

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

check

65/5 - 2 = 11

13 - 2 = 11

11 = 11

the answer is good

A = 1/ 7 - 4√3
B = 1/ 7+ 4√3
Find....
A) a² + b²
B) a³ + b³

Answers

The value of a2+b2 = 0.05

The value of a3+b3 = 41.73

Concept: (a+b)2 = a2+b2+2ab

(a-b)2 = a2+b2-2ab

(a+b)3 = a3+b3+3a2b+3ab2

(a-b)3 = a3-b3-3a2b+3ab2

(I) a²+b²=(1/7-4✓3)²+(1/7+4✓3)²

⇒ ( 1/49 - 48) +(1/49 + 48)=(1-2352/49) + (1+2353/49)

⇒ -47.97 +48.02= 0.05

(ii) a³+b³=(1/7-4✓3)³+(1/7+4✓3)³

⇒(-6.78)³ +(7.07)³

⇒-311.66 +353.39= 41.73

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QUESTION 10, 11, 12 and 13, 40 POINTS FOR CORRECT AWNSER AND WILL BE BRAINLIEST PLS BE FAST!! I WILL DO ANYTHING U WANT

Answers

10. The missing conversion is 20.32 inches

11. Total number of red cars is 34

12. Total number of blue cars is 36

13. Total number of silver cars is 70

What is Ratio?

Ratio is the number of times a quantity is contained more  or less than another in a whole.

Analysis:

10. If 1 inch = 2.54cm

     Then 8 inches = 8 x 2.54cm = 20.32 cm

     First car park: Total number of cars = 60

     ratio of red:blue:silver = 1:2:3

     Total ratio = 1+2+3 = 6

     number of red cars = 1/6 x 60 = 10

     number of blue cars = 2/6 x 60 = 20 cars

     number of silver cars = 3/6 x 60 = 30

   second car park: Total number of cars = 80

    ratio of blue: red: silver = 2:3:5

    total ratio = 2+3+5 = 10

    number of red cars = 3/10 x 80 = 24

    number of blue cars = 2/10 x 80 = 16

    number of silver cars = 5/10 x 80 = 40

11.  Total number of red cars = 10+24 = 34

12.  Total number of blue cars = 20+16 = 36

13.  Total number of silver cars = 30+40 = 70

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Consider a quadrilateral with vertices A(2,2) , B(2,5) , C(7,2), and D(7,5). What is the shape and area of quadrilateral ABCD

Answers

Answer:

Shape is rectangle

Area of rectangle = length * width

= 5 * 3

= 15 units²

in exponential growth functions. the base of the exponent must be greater than 1? how would the function change if the base of the exponent were between 0 and 1?

Answers

The function would become an exponential decay function.

When is the best time to round a number in a multi-step problem?

Answers

Answer:

At the end of the multi step problem

PLEASE HELP ME WITH THIS ASAP

Answers

Eddie: $10-3=$7
Marsha: $8+$3=$11

A cube has side length x. one side of the cube is increased by 4 inches, and another side is doubled. the volume of the new rectangular prism is 450 cubic inches. the equation 2 x cubed 8 x squared = 450 can be used to find x. what was the side length of the original cube? use a graphing calculator and a system of equations to find the answer.

Answers

The side length of the original cube is 1.95 inch.

Let each side length of each cube be 'x' inch.

Given : New side = (x+4 ) inch

Another new side = 2x inch

Since the sides are not equal, so it forms a cuboid in the case of new sides as given.

Also, according to question,

The volume of new rectangular prism is 450 cubic inches

= (x+4)*2x*x = 450

⇒ 2x cubed 8x squared =450

=16x5=450= 1.95 inch ( by taking out the cubic root of x3=7.5)

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Find the value of x, given that the two triangles are similar.​

Answers

Answer:

10.5 is the correct answer.

Step-by-step explanation:

Due to the fact Triangle CAB has "6" as its length, and Triangle FDE has "2" as its length, you multiply 3.5 and 3.

3.5 x 3=10.5

2 x 3=6

3.5/2=10.5/6, so the answer is 10.5.

Answer:

x = 10.5 cm

Step-by-step explanation:

Find the value of x, given that the two triangles are similar.

Given that the two triangles are similar we can solve with a proportion

6 : 2 = x : 3.5

x = 6 * 3.5 : 2

x = 21 : 2

x = 10.5

What is the median of the following data set?
(3, 4, 2, 8, 5)
02
03
04
06

Answers

Answer:

4

Step-by-step explanation:

The median is the middle number when the list is sorted from least to greatest or greatest to least.

We make this list to get 2,3,4,5,8 or 8,5,4,3,2 and the middle number in both lists is 4.

The diameter of a circle is 62cm

by first calculating the radius work out the area of the circle
give your answer in cm² to 1.d.p

Answers

Answer is 3017.5 cm^2
Reason

We know diameter is 62
Radius (r) is 1/2 of diameter so r=31

Formula for area
A= pi r^2
Fill in what we know
A= (3.14) (31^2)
Multiply
A=3017.54
Round to 1 dp
A= 3017.5

What number is the opposite of -2?
O A. ¹/2
O B. -¹/2
5
O C. - 13/
OD. /
12

Answers

Answer: 2

Step-by-step explanation:

The opposite of a negative number is the corresponding positive number.

What is the mean of the data

Answers

Answer:

hey diddle the medians the middle

you add and then divide for the mean

the mode is the one you see the most and the range is the difference between.

Hope this helps you with your question

Step-by-step explanation:

L
E
N
4
8
1
O
k
M
What is the value of k?
k=

Answers

Answer: 2

Step-by-step explanation:

By the geometric mean theorem,

[tex]\sqrt{8k}=4\\\\8k=16\\\\k=\boxed{2}[/tex]

Study the table.

x
y
–2
8
–1
2
0
0
1
2
2
8

Which best describes the function represented by the data in the table?
linear with a common ratio of 4
linear with a common second difference of 4
quadratic with a common ratio of 4
quadratic with a common second difference of 4

Answers

Answer:

quadratic with a common second difference of 4

Step-by-step explanation:

quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a[tex]x^2\\[/tex]+ b[tex]x[/tex] + c = 0.

                               [tex]\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right][/tex]

from the table it is clear that,

function is y = 2[tex]x^2\\[/tex]

so the function is not linear as the equation specifies.

formula to find second difference of a quadratic equation:

f(x + 2) - 2f(x + 1) + f(x)

therefore;

[tex]2(x+2)^2[/tex] - [tex]4(x+1)^2[/tex] + [tex]2x^2[/tex]

[tex]2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2[/tex]

[tex]2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2[/tex]

[tex]4x^2 - 4x^2 + 8x - 8x +8 - 4[/tex]

4

therefore, the answer is quadratic with a common second difference of 4

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the equation that represents the canned goods order is 24x+64y=384
x= number of minutes fruit cans
y= number minutes of for vegetable cans
explain how to calculate the x- and y- intercepts

Answers

The x-intercept is (16, 0) and y- intercept is (0, 6).

What is intercept?

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Given: 24x+64y=384

For y- intercept, put x=0

Then,

24*0+64y=384

64y= 384

y= 6

Now, for x- intercept put y=0

Then,

24x+64*0=384

24x= 384

x= 15

Hence, the x-intercept is (16, 0) and y- intercept is (0, 6).

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Answer:

Sample Answer: Substitute 0 for the x-value in the equation and solve for y. The result is y = 6, so the y-intercept is at (0, 6). Next, substitute 0 for the y-value in the equation and solve for x. The result is x = 16, so the x-intercept is at (16, 0).

Step-by-step explanation:

Equation of graph problem

Answers

The parent function y=1/x²

How horizontal shifting of the graph takes place?

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+ k) where k>0

Here, the parent function y=1/x²

Add 3 to x in the denominator as the graph is shifted to left 3.

and, Add 1 to the fraction, because the graph is shifted up 1 unit.

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bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than One-fifth? Select three options.
choosing 1 blue marble
choosing 1 red marble
choosing 1 red marble, not replacing it, and then choosing a blue marble
choosing 1 white marble, replacing it, and choosing another white marble
choosing 1 white marble

Answers

Answer:

choosing 1 red marble

choosing 1 white marble, replacing it, and choosing another white marble

choosing 1 white marble

Step-by-step explanation:

red marble has a 30 percent chance

1 white marble and then replacing and another white marble is 25% chance

1 white marble is 50% chance

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