[tex]x + 6 = 10 \\ x = 10 - 6[/tex]
simultaneous equations
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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.

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:

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.

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]

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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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.

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.

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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There is a reflection at the boundary between two materials if there is a change of the speed of light in the material at the boundary.

This bending is referred to as refraction. whilst a wave traveling at an angle adjusts its velocity upon crossing a boundary among materials,. This bending is known as refraction. As a wave crosses a boundary into a new medium, its pace, and wavelength exchange simultaneously as its frequency stays equal.

While light from air hits a smooth piece of glass (n = 1. five) with the ray perpendicular to the glass floor, of the subsequent will occur while light from air hits a clean piece of glass with the ray perpendicular to the glass surface, the part of the light passing into the glass: will now not exchange its frequency.

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Answer: The answer is option

Step-by-step explanation:

The solution is in the attached

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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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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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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The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.

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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]

Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

I'll take a stab at this one. if the number of dice showing a two-digit number  = the number of dice showing a one-digit number, then  2 must show a two-digit number and 2  must show a one-digit number

There are 3 two-digit numbers and 9 one-digit numbers on each die

So....the probability is

C(4,2) (3/12)^2 (9/12)^2    =  

C(4,2) (1/4)^2 (3/4)^2  =

27/128.

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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.

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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Answer:

R = 33.35%

Step-by-step explanation:

that is the solution above

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:

Step-by-step explanation:

hello :

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

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

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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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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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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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.

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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The values of the trigonometric functions are

7. [tex]sin\theta = \frac{12}{13}[/tex]

[tex]cos\theta = \frac{5}{13}[/tex]

[tex]tan\theta = \frac{12}{5}[/tex]

[tex]csc\theta =\frac{13}{12}[/tex]

[tex]sec\theta =\frac{13}{5}[/tex]

[tex]cot\theta =\frac{5}{12}[/tex]

8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]

[tex]cos\theta = \frac{12}{16}[/tex]

[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]

[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]

[tex]sec\theta =\frac{16}{12}[/tex]

[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]

From the question, we are to determine the values of the given trigonometric functions

7.

In the given triangle,

Opposite = 12

Adjacent = 5

Hypotenuse = ?

Hyp² = Opp² + Adj² (Pythagorean theorem)

∴ Hyp² = 12² + 5²

Hyp² = 144 + 25

Hyp² = 169

Hyp =√169

Hyp = 13

Using SOH CAH TOA

[tex]sin\theta = \frac{12}{13}[/tex]

[tex]cos\theta = \frac{5}{13}[/tex]

[tex]tan\theta = \frac{12}{5}[/tex]

[tex]csc\theta =\frac{1}{sin\theta} =\frac{13}{12}[/tex]

[tex]sec\theta =\frac{1}{cos\theta} =\frac{13}{5}[/tex]

[tex]cot\theta =\frac{1}{tan\theta} =\frac{5}{12}[/tex]

8.

Hypotenuse = 16

Adjacent = 12

Opposite = ?

Hyp² = Opp² + Adj² (Pythagorean theorem)

Opp² = Hyp² - Adj²

∴ Opp² = 16² - 12²

Opp² = 256 - 144

Opp² = 112

Opp =√112

Opp = 4√7

Using SOH CAH TOA

[tex]sin\theta = \frac{4\sqrt{7} }{16} = \frac{\sqrt{7} }{4}[/tex]

[tex]cos\theta = \frac{12}{16}[/tex]

[tex]tan\theta = \frac{4\sqrt{7} }{12}= \frac{\sqrt{7} }{3}[/tex]

[tex]csc\theta =\frac{1}{sin\theta} =\frac{16}{4\sqrt{7} } = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]

[tex]sec\theta =\frac{1}{cos\theta} =\frac{16}{12}[/tex]

[tex]cot\theta =\frac{1}{tan\theta} =\frac{12}{4\sqrt{7}} = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]

Hence, the values of the trigonometric functions are

7. [tex]sin\theta = \frac{12}{13}[/tex]

[tex]cos\theta = \frac{5}{13}[/tex]

[tex]tan\theta = \frac{12}{5}[/tex]

[tex]csc\theta =\frac{13}{12}[/tex]

[tex]sec\theta =\frac{13}{5}[/tex]

[tex]cot\theta =\frac{5}{12}[/tex]

8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]

[tex]cos\theta = \frac{12}{16}[/tex]

[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]

[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]

[tex]sec\theta =\frac{16}{12}[/tex]

[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]

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