(15-10)-(14+12+ (8+5)​

Let [tex]A(x_A,\ y_A),\ B(x_B,\ y_B)[/tex]. Then a slope of the line AB represent the formula:

[tex]m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]

Substitute the coordinate od the points to the formula of a slope.

[tex]A.\\(4,\ 6),\ (2,\ 2)\\\\m=\dfrac{2-6}{2-4}=\dfrac{-4}{-2}\\\\\huge\boxed{m=2}[/tex]

[tex]B.\\(8,\ 8),\ (2,\ 4)\\\\m=\dfrac{4-8}{2-8}=\dfrac{-4}{-6}\\\\\huge\boxed{m=\dfrac{2}{3}}[/tex]

[tex]C.\\(8,\ 2),\ (2,\ 4)\\\\m=\dfrac{4-2}{2-8}=\dfrac{2}{-6}\\\\\huge\boxed{m=-\dfrac{1}{3}}[/tex]

[tex]D.\\(6,\ 2),\ (2,\ 4)\\\\m=\dfrac{4-2}{2-6}=\dfrac{2}{-4}\\\\\huge\boxed{m=-\dfrac{1}{2}}[/tex]

Step-by-step explanation:

the picture and its text explain it actually already.

each block (or square) on each side represents a fraction.

the whole block is 1. the colored parts are the fraction of that whole (1).

we see the example 2/3 × 3/4

the left block with 2 out of 3 strips marked in pink shows us 2/3 (2/3 of the block is pink).

the right block with 3 out of 4 strips marked in purple shows us 3/4 (3/4 of the block is purple).

it is essential for this method to orient the strips in one block to be at a right angle with the strips of the other block.

now, to do the multiplication you overlay the strips of both blocks.

you see this creates a chess board pattern. the total number of little squares or rectangles is the denominator (bottom part) of the result. in this case 12.

the number of little squares or rectangles that are in both original strips is the numerator (the top part) of the result. in this case 6.

so, yes, 2/3 × 3/4 = 6/12, which can then be refined to 1/2.

now, you have to do the same thing with the actual examples (I cannot draw here, sorry) :

1/4 × 3/5 = 3/20

the left block with 4 strips (one in pink, or whatever color you want), the right block with 5 strips (and 3 marked in e.g. purple).

and then the result block with 4 columns and 5 rows creating 20 little squares or rectangles, and 3 of them are in all original strips.

and the same

3/5 × 2/3 = 6/15 = 2/5

1/2 × 2/5 = 2/10 = 1/5

The last  equation h(x) = 2x+4/x+1.

The pictorial representation of quantities and how the increase or decrease in one affects the other.

Analysis:

The graph cuts the x-axis and y-axis at (-2, 0) and(0, -4) respectively.

gradient of the curve = y2 - y1/x2 - x1 = -4-0/0--2 = -4/2 = -2.

The equation with a gradient equal to -2 is, h(x) = 2x+4/x+1

differentiating the equation by quotient rule,

u = 2x+4, du/dx = 2, v = x+1 dv/dx = 1

dy/dx = [tex]\frac{(x+1)(2) - (2x+4)(1)}{(x+1)^{2} }[/tex] = [tex]\frac{-2}{(x+1)^{2} }[/tex]

When x = -2, dy/dx = -2

In conclusion, 2x+4/x+1 is the equation for the curve above.

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Answer:

4x^2+3x+1

Step-by-step explanation:

4x^2+3x+1 is the answer I hope this helps

Answer:

Since the angle of EFC = 33°, DAF = 33° because DAF and EFC have the same angle.

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of y can be found as shown below.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p∝ q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

1.) The relation can be written as,

y ∝ x

y = kx

27 = k × 3

k = 9

Value of y, when x=4 is,

y = 9 × 4 = 36

2.)  The relation can be written as,

y ∝ x²

y = k x²

160 = k × 4²

160 = k × 16

k = 10

Value of y, when x=6 is,

y = 10 × 36 = 360

3.) The relation can be written as,

y ∝ (1/x)

y = k/x

16 = k × (1/2)

k = 32

Value of y, when x=17 is,

y = 32 × (1/17) = 1.8823

4.)  The relation can be written as,

y ∝ (1/x²)

y = k(1/x²)

64 = k × (1/4²)

64 = k × (1/16)

k = 1024

Value of y, when x=7 is,

y = 1024 × (1/49) = 20.8979

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According to the computations, this rhombus's value of x is equal to 55°.

The total of all the angles in a rhombus should be 360 ° because the opposing angles in a rhombus are always identical.

We may infer the preceding information from the rhombus's picture:

Neighboring angles= 2x+ 20 & 50°

Opposite angles=2x+ 20 & 50°

Combining the angles results in:

2x+20+50+2x+20+50=360

⇒4x+140= 360

⇒4x=360-140

⇒4x=220

⇒x=220/4

⇒x=55°

Hence, it is concluded that the value of x is (b) 55°.

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By using the given graph, we will see that:

Here we have a graph of function G(x), and we want to evaluate it in different values of x.

To do that, we need to look at the interval where the lines are defined. An open dot means that the endpoint does not belong to the interval, while the closed dot means that the endpoint belongs.

First, G(0).

If you look at the graph, when x = 0 we have a closed dot on the bottom line. That is the line that we need to look to do this evaluation, there we can see that when x = 0, we have G(0) = -5.

Then we have x = 2.999.

Notice that x < 3.

And the second line (the one at y = -3) is on the interval (0, 3].

Then x = 2.999 is included on that interval, it means that:

G(2.999) = -3.

Now we have x = 0.0001

Again, notice that the second line is on the interval (0, 3]

Because 3 > 0.0001 > 0, then:

0.0001 ∈ (0, 3]

From that, we conclude that:

G(0.0001) = -3

Finally:

G(3).

Again, 3 belongs to the interval (0, 3]

Then we use the second line again.

G(3) = -3

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Answer:

G(0) = -5

G(0.0001) = -3

G(2.999) = -3

G(3) = -3

Step-by-step explanation:

C- Equally likely events

Step-by-step explanation:

Equally Likely Events. Equally likely events are events that have the same theoretical probability (or likelihood) of occurring.

(｡♡‿♡｡)

Answer:

Equally Likely Events

Step-by-step explanation:

Answer:

20°

Step-by-step explanation:

Measure of QR is 180 - 108 = 72°

 then using     intercepted arc - external angle theorem:

angle RPQ then equals  1/2 ( 108 - 72) = 20 °

Answer:

Shirts are 6

Hats are 5

Step-by-step explanation:

This is a system of equations. Set up the equations first.

7s + h = 47

5s + h = 35    

-----------------------      Subtract the equations to eliminate the h variable

2s = 12                      Divide by 2 to solve

s = 6                          Each hat is 6

Plug the 6 in for s in either of the original equations

7(6) + h = 47

42 + h = 47          Subtract 42 from both sides

h = 5

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.

First Method:

∠1  + ∠2 = 180° {Supplementary angles because both lies on the line q}

∠2 = (180° - ∠1)

Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,

∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}

∠7 = 180° - ∠6

∠7 = 180° - (180° - ∠1)

∠7 = 180° - 180° + ∠1

∠7 = ∠1

OR

Second Method:

∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}

∠3 = ∠5 {Alternate Interior angles}

∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}

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When Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

One fourth of the part of a circle is said to be the quadrant of the circle.

Given the angle Ф lies in quadrant IV.

As we know, cos Ф is positive only in first and fourth quadrant i.e when Ф lies in 0<Ф<90 and 270<Ф<360.

cosФ range from [-1,1]

So, cos Ф is positive when Ф lies in 1st and 4th quadrant.

&  cos Ф is negative when Ф lies in 2nd and 3rd quadrant.

If cos ∅ lies in the quadrant IV, anything between [0, 1] can be the value of cos ∅.

Hence, when Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

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The correct expression is (82/n) - 26 ,The operations include division and subtraction , To evaluate, substitute 2 for the variable in the equation , the value of the expression is 15 , Option D, E and F is the answer.

An expression is the mathematical statement consisting of variables , constant and mathematical operators .

It is given that the expression has to be formed from the data

the quotient of 82 and a number, decreased by 26

Let the number from which it is divided is n then

quotient * divisor = 82

quotient = 82 /n

(82/n) - 26 is the expression formed from the data

When n =2

the expression value is

41 -26

15

The correct expression is StartFraction 82 Over n EndFraction minus 26.

The operations include division and subtraction.

To evaluate, substitute 2 for the variable in the equation , the value of the expression is 15.

Therefore Option D, E and F is the answer.

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Answer:D.E.F

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Answer:

48 and 37

Step-by-step explanation:

The 2 square numbers are 16 (4 squared) and 64 (8 squared)

So the difference between these 2 numbers: 64 - 16=48

The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)

64-27=37

answer:

48 and 37

step explanation:

The 2 square numbers are 16 (4 squared) and 64 (8 squared)

So the difference between these 2 numbers: 64 - 16=48

The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)

64-27=37

By the distributive property, 5(x+3) is equal to 5x + 15.

The number of possible license plates that can be issued using this system is 67600000.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.

Here, number plate contains 5 numbers and 2 letters

Total possible number (0-9) = 10

Total possible letters (A-Z) = 26

Possible number plates which contains 5 numbers and 2 letters are

          ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X ²⁶C₁ X ²⁶C₁

             10 X 10 X 10 X 10 X 10 X 26 X 26

                 10⁵ X 26²

                   676 X 10⁵

                 67600000

Thus, the number of possible license plates that can be issued using this system is 67600000.

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Answer:

y= x +4

Step-by-step explanation:

The slope-intercept form of an equation is given by y= mx +c, where m is the slope and c is the y-intercept.

Start by finding the slope of the line.

[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

Slope

[tex]=\frac{5-3}{1-(-1)}[/tex]

[tex]=\frac{2}{1+1}[/tex]

[tex]=\frac{2}{2}[/tex]

= 1

Substitute m= 1:

y= x+c

Finally, find c by substituting a pair of coordinates.

When x= 1, y= 5,

5= 1 +c

c= 5 -1

c= 4

Thus, the equation of the line is y= x +4.

Additional:

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The smallest digit of the smallest number is at the thousands place.

The system of representing numbers is called Number System.

The given numbers are 6895 , 4875 , 5689

The smallest number among these is 4875

The smallest digit in this number is 4

4 is at thousands place

Therefore , The smallest digit of the smallest number is at the thousands place.

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The correct statement regarding the box plot of the data-set is given by:

The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the right.

It shows:

In this problem, we have two unusually high values, $28 and $30, hence the right tail is longer than the left tail, hence the box plot is right-skewed, and the correct statement is:

The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the right.

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I'm assuming that the diagonals intersect at E. Since diagonals of a parallelogram bisect each other, BE=ED.

As distance must be positive, we reject the negative case, so x=8.

Thus, BE=ED=54.

The mole ratio of hydrogen to ammonia will be 3:2.

A depiction of a chemical reaction using elements' indicators to determine how much of each source and result is present-typically in moles.

The chemical equation is given below.

N₂ + 3H₂ = 2NH₃

Then the mole ratio of hydrogen to ammonia will be 3:2.

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If we double the dimension the volume will be increased by 8 times, and the volume will be 1920 cubic m.

The Volume of rectangular prism = l×b×h

The volume of a prism,

V = L x B x H

V = 4 x 6 x 10

V = 240

When all the dimensions are doubled, the new volume will become

V1 =2L x 2B x 2H

V1 = 8(4 x 6 x 10)

V1 = 8(240)

V1 = 1920 cubic m

If we double the dimension the volume will be increased by 8 times, and the volume will be 1920 cubic m.

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Answer:

33.75 Euros

Step-by-step explanation:

Trust me bro, I did the working.

Answer:

volume of cone = 1/3 volume of cylinder

according to the question, volume of cylinder =

V =

[tex]\pi \times (r) {}^{2} h[/tex]

diameter = 3 inches

radius = 3/2 inches

height = 8 inches

V = 22.7 * (3/2)²* 8

V = 22.7 * 9/4 * 8

V = 22.7 * 18

maximum volume a cone can have = 1/3 of cylinder

Volume of cone = 1/3 * 22.7 * 18

= 22.7 * 6

= 132.6

Answer:

  if the ratio allowance/chores is constant, it is proportional

Step-by-step explanation:

The values x and y are directly proportional if they satisfy the equation ...

  y = kx

for some constant k, the constant of proportionality.

__

If the relation that produces ordered pairs (chores, allowance) is directly proportional, all of the ratios (allowance)/(chores) will have the same value: the constant of proportionality (k).

If the ratios are not constant, Carlos's allowance is not directly proportional to the number of chores he completes.

The equation of the line will be y = [tex]\dfrac{1}{5}x + \dfrac{12}{5}[/tex]

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

First, we need to find the equation of the line that is given:

We can use the formula,

[tex]m = \dfrac{y_1 - y_2}{x_1-x_2}[/tex]

[tex]m=\dfrac{-3-(-4)}{0-(-5)}=\dfrac{1}{5}[/tex]

So the equation for this line is  

y = (1/5) x - 3

This means that the equation for the line we are trying to find has a slope of as well

Let's put the points in the equation and try to find the y-intercept:

2 = [tex]\dfrac{1}{5}[/tex] ( -2 ) + b

[tex]\dfrac{15}{5} = b[/tex]

So the final equation for the line we are trying to find is y = [tex]\dfrac{1}{5}x + \dfrac{12}{5}[/tex]

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