write the following linear equations into the standard form Ax+ by=c
DETERMINE the values of A,B and C.

The expressions for the next two odd numbers after 2n -1 are; 2n +1 and 2n +3.

If follows from the task content that the expressions for the next two odd numbers after 2n-1 are required.

Since odd numbers are have difference 2, it follows that the next 2 odd numbers must be obtained by adding each time. Hence, we have, 2n +1 and 2n +3.

The sum is a multiple of 3 because; 2n -1 + 2n +1 + 2n +3 = 6n +3 = 3(2n+1).

Hence, the sum is multiples of 3.

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Answer:

To find the x-intercepts of a quadratic equation, let y = 0. Write down the new equation ax squared + bx + c = 0 and the quadratic formula that gives the solution as x = -b plus or minus the square root of (b squared - 4ac), all divided by 2a.

Step-by-step explanation:

Hope this helps.

Answer:

-3, 5

Step-by-step explanation:

The x-intercepts are the same as the zeros.

Triangle ABC was dilated to form triangle DEF, hence both triangles have the same shape and are similar.

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

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Dilation preserves the shape but not the size.

Triangle ABC was dilated to form triangle DEF, hence both triangles have the same shape and are similar.

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Hello !

[tex]5(3y + 2) + 6[/tex]

[tex] = 5 \times 3y + 5 \times 2 + 6[/tex]

[tex] = 15y + 10 + 6[/tex]

[tex] = 15y + 16[/tex]

15y + 16

Fully expanding and simplifying an expression means distributing all values and combining like terms.

Distributing

First, the 5 needs to be distributed to the values within the parentheses. Using the distribution property, the 5 can be multiplied by 3y and 2.

Then, just simplify

Combine Like Terms

Now that all values are distributed like terms need to be added together.

The terms 10 and 6 are of the same power and do not have variables. So, they can be added together.

This expression is the most expanded and simplified version.

The value of x is 2wy + y - 1.

Given: (2x + 2)/y = 4w + 2

To find: the value of x

the following steps will be used.

First, Multiply both sides by y

y * (2x + 2)/y = (4w + 2) * y

2x + 2 = 4wy + 2y

Subtract 2 from both sides

2x + 2 - 2 = 4wy + 2y - 2

2x = 4wy + 2y - 2

Multiply both sides by ½

½ * 2x = ½(4wy + 2y - 2)

x = ½(4wy + 2y - 2)

Open bracket

x = ½ * 4wy + ½ * 2y - ½ * 2

x = 2wy + y - 1

Hence, the value of x is 2wy + y - 1.

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The true equation about the functions is (d) g(2) = h(2) = 7

The graph that completes the question is added as an attachment

The function is given as:

h(x) = 2^x + 3

Calculate h(2) and h(7)

h(2) = 2^2 + 3 = 7

h(7) = 2^7 + 3 = 131

From the graph, we have:

g(2) = 7

g(7) = 610

By comparison, we have:

g(2) = h(2) = 7

Hence, the true equation is (d) g(2) = h(2) = 7

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The HCF are

This is the common factor that is the highest that a group of numbers can have in common.

1. 6 and 15

factors of 6 =  1, 2, 3, 6

factors of 15:  1, 3, 5, 15

The HCF is the number they have in common = 3

2. 12 and 18

The factors of 12:  1, 2, 3, 4, 6, 12

The factors of 18:  1, 2, 3, 6, 9, 18

The HCF = 6

3. 15 and 24

Factors of 15:  1, 3, 5, 15

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The HCF = 3

4. 24 and 36

The factors of 24:  1, 2, 3, 4, 6, 8, 12, 24

The factors of 36:  1, 2, 3, 4, 6, 9, 12, 18, 36

The HCF :  12

5. 30 and 48

The factors of 30:  1, 2, 3, 5, 6, 10, 15, 30

The factors of 48:  1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The HCF = 6

6. 36 and 54

The factors of 36:  1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 54:  1, 2, 3, 6, 9, 18, 27, 54

The hcf = 18

7. 32,40 and 56

The factors of 32:  1, 2, 4, 8, 16, 32

The factors of 40:  1, 2, 4, 5, 8, 10, 20, 40

The factors of 56:  1, 2, 4, 7, 8, 14, 28, 56

The HCF is 8

8. 28,42 and 70

The factors of 28:  1, 2, 4, 7, 14, 28

The factors of 42:  1, 2, 3, 6, 7, 14, 21, 42

The factors of 70:  1, 2, 5, 7, 10, 14, 35, 70

The HCF = 14

9. 30,75 and 90

The factors of 30:  1, 2, 3, 5, 6, 10, 15, 30

The factors of 75:  1, 3, 5, 15, 25, 75

The factors of 90:  1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The HCF is 15

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The line with a gradient of 6 is line A, and the gradient of line A is 4

The gradients are given as:

-0.5, 0, 2 and 6

A line with a negative gradient (i.e. -0.5) would decrease as the x values increase.

This is represented by line D

A line with a 0 gradient is a horizontal line

This is represented by line C

The line closer to the y-axis have a higher gradient.

This means that line A has a higher gradient than line B, because of its proximity to the y-axis

Hence, the line with a gradient of 6 is line A

The gradient of line B is given as:

Gradient = 4

Line A and line B are parallel lines

Parallel lines have the same gradient

Hence, the gradient of line A is 4

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Answer:

  x° = 43°

Step-by-step explanation:

You want the measure of the angle marked x° in the circle with arcs of 152° and 122° shown.

The arc subtended by the inscribed angle x° will be the measure of the arc that makes up the rest of the 360° circle:

  360° -152° -122° = 86°

The measure of angle x° is half the measure of the subtended arc:

  x° = 86°/2

  x° = 43°

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Answer:

B. 12x + 12 = 7x + 56

Explanation:

[tex]Given : \ \sf \dfrac{12}{ x +8} = \dfrac{7}{x + 1}[/tex]

cross multiply formula: if  [tex]\sf \dfrac{a}{b} = \dfrac{c}{d}[/tex]  then [tex]\sf ad = cb[/tex]

[tex]\sf 12(x +1) = 7(x + 8)[/tex]

distribute inside parenthesis

[tex]\sf 12x + 12= 7x + 56[/tex]

collect like terms

[tex]\sf 12x -7x = 56 - 12[/tex]

simplify the following

[tex]\sf 5x = 44[/tex]

dividing both sides by 5

[tex]\sf x = 8.8[/tex]

Answer:

Slope = 0

Step-by-step explanation:

This is a HORIZONTAL line  ....horizontal lines have slope = 0

VERTICAL lines like   x =2    have  UNDEFINED slope.

Answer:

m = 0

Step-by-step explanation:

This type of linear equation would be a horizontal line when graphed meaning that the slope would equal zero.

So in the equation y = -2, the slope is missing as the ' mx ' because it is horizontal.

Option D. The description that best fits the intercept of the graph is The initial velocity of the runner was 6 m/s, and the runner stopped after 8 seconds.

The graph has lines that would go through these points, (0,6) and pair (6,8). In the other graph, it goes through 6, 8 and 8, 0.

The initial velocity of this runner is seen to be 6m/s. As he runs this would increase and while he slows down it would fall. The stop time of the runner is going to be at 8 minutes.

Which of the following describes the intercepts on the graph?

The initial acceleration of the runner was 8 m/s2, and the runner stopped after 6 seconds.

The initial acceleration of the runner was 6 m/s2, and the runner stopped after 8 seconds.

The initial velocity of the runner was 8 m/s, and the runner stopped after 6 seconds.

The initial velocity of the runner was 6 m/s, and the runner stopped after 8 seconds.

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There are total 30 students in the piano class.

When a number can be divided by another number then they can be written as p : q , when two ratios can be equated using an equal sign then they are said to be in proportion.

It is given that the total number of girls is 40% of the total students

The ratio of total students to girls is 100 :40

= 10 :4

= 5 : 2

It is also given that in the total number of students 12 were girls

Let total students be x

Then the ratio is x : 12

As both the ratio are same and so can be equated and the proportion will be

5 : 2 = x : 12

5/2 = x /12

x = 30

Therefore there are total 30 students in the piano class.

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Answer:

The distributive property allows you multiply a sum in parenthesis by multiplying each addend separately, then add the products.

Step-by-step explanation:

How to use the distributive law example.

2(x+4) = 16

To use the distributive law in this example multiply 3 by all terms in the parenthesis. Multiply 2 and x, then 2 and 4 to open the parenthesis.

2x+8=16

That is how you use the distributive law.

To continue solving, subtract 8 from both sides.

2x+8-8=16-8

2x=8

Divide 2 from both sides.

2x/2=8/2

x=4

Hope this helps!

If not, I am sorry.

Answer:

R = 33.35%

Step-by-step explanation:

that is the solution above

When 'c' is negative both p and q would have the same sign and when opposite signs whereas when b is positive and negative, both would have positive and negative signs respectively.

The ways in which the signs of 'b' and 'c' affect the form include;

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Answer:

1. ( 0,-6 )  is y-axis

2. ( 15,4 ) is l quadrant

3. ( 100, -5 ) is lV quadrant

4. ( 0.004, .05 ) is l quadrant

5. ( -4,0 ) is x-axis

8. ( -7.5, -6.3 ) is lll quadrant

9. ( 0.1000) is y-axis.

The equation which determines the painted area is (x+15)(x+10)-5.

Given that there is a rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a given length of 5 and width of 1.

A rectangle is a two-dimensional (2D) form in which the four angles are all right angles and the opposite sides are parallel and equal to one another. The region that the rectangle's perimeter encloses is known as its area, which is equal to the product of its length and width.

Let the length of the patio be L=x+15.

The width of the patio be W=x+10.

So, the Area of the patio will be painted is, A₁=L×W

A₁=(x+15)(x+10)

Let the Length of the bench be L₁=5

The width of the bench be W₁=1

So, the Area of the bench will be painted is, A=L₁×W₁

A₂=5×1

A₂=5

The net area of the patio that will be painted is

A=A₁-A₂

A=(x+15)(x+10)-5

Hence, the equation which is used determines the area, A, of the patio that will be painted is (x+15)(x+10)-5.

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Let [tex]S_n[/tex] be the [tex]n[/tex]-th term in this sequence, so

[tex]S_1 = 1[/tex]

[tex]S_2 = 1 + 2[/tex]

[tex]S_3 = 1 + 2 + 2^2[/tex]

and so on, with general [tex]n[/tex]-th term

[tex]S_n = 1 + 2 + 2^2 + \cdots + 2^{n-1} = \displaystyle \sum_{i=1}^n 2^{i-1}[/tex]

Observe that

[tex]2 S_n = 2 + 2^2 + 2^3 + \cdots + 2^n[/tex]

and by subtracting this from [tex]S_n[/tex], we eliminate all but the outermost terms, namely

[tex]S_n - 2S_n = 1 - 2^n[/tex]

so that

[tex]-S_n = 1 - 2^n[/tex]

[tex]S_n = 2^n - 1[/tex]

Now, the sum of the first [tex]n[/tex] terms of the sequence [tex]\{S_1,S_2,S_3,\ldots,S_n\}[/tex] is

[tex]S = S_1 + S_2 + S_3 + \cdots + S_n[/tex]

[tex]S = \displaystyle \sum_{i=1}^n S_i[/tex]

[tex]S = \displaystyle \sum_{i=1}^n (2^i - 1)[/tex]

[tex]S = \displaystyle \sum_{i=1}^n 2^i - \sum_{i=1}^n 1[/tex]

[tex]S = \displaystyle 2 \underbrace{\sum_{i=1}^n 2^{i-1}}_{S_n} - n[/tex]

[tex]S = 2(2^n - 1) - n[/tex]

[tex]S = \boxed{2^{n+1} - n - 2}[/tex]

Because you make a "half circle" when you bisect an angle, neither a ruler nor a compasses are needed. Because a bisected angle wouldn't be straight, you wouldn't need either of the two.

Teams of no more than six pupils will be formed from the total group of participating students by the teachers.

Four teachers offer an after-school chess club the table shows the number of students who joined In the box, type your response. teams Part B With 18 chess sets at its beginning, the chess club. Three cases of 15 chess sets were ordered by the professors. To provide each teacher an equal number of chess sets, they will divide the total number of chess sets. Any extra sets will then be donated to the school library.

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Answer:

Step-by-step explanation:

hello :

the opposite of +(+15) is : +(-15)

the opposite of -(-24) is : +(-24)

Answer:

(1+3i)(1-3i)

Step-by-step explanation:

When these terms have the same pair of numbers in them, but one set has a PLUS and one set has a MINUS, these are called CONJUGATES.

When you multiply CONJUGATES, you will eliminate the imaginary number, i.

Remember i^2=-1

see image.

Answer:

The given lines are un-related.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (-8,-55) and (10,89). Whereas, line 2 passes through (9,-44) and (4,-14).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{89-(-55)}{10-(-8)} \\&m_{1}=\frac{144}{18} \\&m_{1}=8\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{-14-(-44)}{4-9} \\&m_{2}=\frac{30}{-5} \\&m_{2}=-6\end{aligned}$$[/tex]

Since, both slopes are neither equal nor reciprocal of each other.

Therefore, the lines are un-related.

Answer: The answer is option

Step-by-step explanation:

The solution is in the attached

The factorization of the given expression is 5x(5x - 4y) - y(21y + 10z) - z².

The factorization of an algebraic expression is the process of finding two or more factors, whose multiplication results back in the given expression.

From the information given:

The factorization of 25x^2-20xy-21y^2+10yz-z^2​ can be computed as:

= 5x(5x - 4y) - y(21y + 10z) - z²

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Answer:

For the first picture, the answer is either A or B, but I think it's A. For the second picture, the answer should also be 4, because the lines are parallel to each other and therefore have the same gradient.

The 0.375 terminating decimals are equivalent to 3/8 option second is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The fraction is:

= 3/8

After dividing with 8

= 0.375

Thus, the 0.375 terminating decimals are equivalent to 3/8 option second is correct.

The question is incomplete.

The complete question is:

Which of the following terminating decimals is equivalent to 3/8?

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