x³ - 10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.

Answer:

15, 60, and 61

Step-by-step explanation:

First we have to find the 3rd side length from 2 side length chosen. So let’s pick 8 meters and 11 meters, to find the third side length we use the Pythagorean theorem: c^2 = a^2 + b^2

c = 11^2 + 8^2 = 121 + 64 = 185 = 13.6

13.6 isn’t one of the answers so we can’t pick 11 & 8. Let’s try 11 & 15:

c = 15^2 + 11^2 = 225 + 121 = 346 = 18.6

18.6 isn’t one of the answers either. Let’s try 15 & 60:

c = 60^2 + 15^2 = 3600 + 225 = 3825 = 61.85

61.85 might be it but let’s try one more just in case:

c = 60^2 + 61^2 = 3600 + 3721 = 7321 = 85.6

Nope! That means 15, 60, and 61 are the answer. I hope this is correct!

The value of the function h(x) is x² -  4x +6 and 4-6 x².

Any function's x-intercept, y-intercept, and slope can be calculated using function formulas. You could also determine a quadratic function's vertex. Additionally, the function can be graphed for various x values.

Simply adding the values of the functions f(x) and g will yield the value of the function f(x) and g(x).

Therefore, we get

f(x) = x² and  we have g(x) = 4x - 6

h(x) = f(x) - g(x)

h(x) =   x² -  4x +6

h(x) = f(g(x))

     =  x²( 4x - 6)

     = 4-6 x²

h(x) is the inverse of g(x)

   = inverse of 4x - 6

   = 1/ 4x - 6

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Answer:

Step-by-step explanation:

I believe the answer is D) f(x) = 1 / (x-3)^2

I put that into my graph calculator thing and it matched it perfectly

hope this helps you

Answer:

Im guessing the top one?

Step-by-step explanation:

not sure since the questions are a bit janky, but the exponential decay formula is y=a(1-r)^x

Answer:

23.5 inches^2

Step-by-step explanation:

Area of triangle = 1/2 * base * height

area = 1/2 * (5+2) * (5+4)

area = 31.5 in^2

Area of rectangle = length * breadth

area = 4 * 2

area = 8 in^2

Area of figure = area of triangle - area of rectangle

area = 31.5 - 8

area =23.5 in^2

After constructing the frame of the sides 5.25 and sandbox, there is 10 inches of wood left over.

A square is a closed, two-dimensional shape that has four equal sides and four vertices. Parallel to one another are its opposing sides. A square is also equivalent to an equal-length and-width rectangle. A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is a two-dimensional shape with four equal-length sides. A square's opposing sides are parallel to one another, and its four internal angles are all right angles.

given,

The total amount of wood.

= 4 x 65.5

= 262 inches.

Frame:

Side = 5.25 inches

The perimeter of the frame.

= 4 x 5.25

= 21 inches

Now,

Sandbox:

The wood used for the sandbox.

= 11 x 21

= 231 inches

The remaining wood.

= 262 - (21 + 231)

= 262 - 252

= 10 inches

The wood left over after making the frame of sides 5 .25 inches and the sandbox is 10 inches.

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An equation which has one (1) solution include the following: D. |W| = 0.

In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:

|W| = 0

W = ±0

W = 0

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Answer:

18 because you use the middle section which explains how many rolls are needed

Answer:

1. 2 x 2 x 2=8

2.3x3=9

3. I'm uncertain about this one but i think maybe 12x2=24 please recheck it

Step-by-step explanation:

considering u call it easy imma assume u know how to do it

Note that equation 1 matches the Line Graph in option (B), equation 2 matches option (C), and equation 3 matches option (A).

It is a graph that depicts a line connecting many points or a line indicating the relationship between the points. The graph depicts quantitative data between two changing variables by connecting a sequence of succeeding data points with a line or curve.

With regard to the above-given graphs,

The inequalities are given as

1. 4x + 3 > 15 or —6x ≥ 12

2. —8x > —24 and —10 ≤ 2x -6

3. -29 ≤ 9x -2 < 16

Note that the way to identify the plots on the line graphs is by solving the above equations.

1) 4x + 3 > 15 or —6x ≥ 12

2) —8x > —24 and —10 ≤ 2x -6

To solve for x in  —8x > —24, divide both sides by -8

x > 3;

So solve for —10 ≤ 2x -6; add 6 from both sides and divide by 2

-4/2 ≤ x

-2 ≤ x  or x ≥ -2

3) -29 ≤ 9x -2 < 16

To solve this inequality, you can start by isolating the variable on one side of the inequality. To do this, you can add 2 to both sides to get:

-29 + 2 ≤ 9x < 16 + 2

-27 ≤ 9x < 18
Now divide both sides by 9 to get:

-3 ≤ x < 2

This means that x can be any number that is greater than or equal to -3 and less than 2.

Given the above results, it is correct to state that equation 1 matches option (B), equation 2 matches option (C), and equation 3 matches option (A).

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Full Question:

See the attached.

Answer:

34 centimetres

Step-by-step explanation:

Since the flag is made of a square white flags, then all its sides are equal in length. a diagonal of a square would divide it into two equal triangle.

Let the length of the diagonal be represented by t, such that;

[tex]/hyp/^{2}[/tex] = [tex]/adj 1/^{2}[/tex] + [tex]/adj 2/^{2}[/tex]

[tex]t^{2}[/tex]  = [tex](12)^{2}[/tex] + [tex](12)^{2}[/tex]

           = 144 + 144

[tex]t^{2}[/tex]  = 288

t = [tex]\sqrt{288}[/tex]

t = 16.9706

t = 17 centimetres

The length of a diagonal of the flag is 17 centimetres.

So that,

The centimetres of ribbon required to make the "X" = 2 x diagonal

                                                            = 2 x 17

                                                            = 34

The centimetres of ribbon required to make the "X" is 34 centimetres.

a) The probability that a person will like cake is given as follows: 0.6 = 60%.

b) The probability that a person does not like any of the two desserts is given as follows: 0.1 = 10%.

c) The events are non-mutually exclusive, as the probability of liking both is different of zero.

In a Venn probability, two events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

The events for this problem are given as follows:

The probabilities for this problem are given as follows:

P(A or B) = 0.9, P(A) = 0.42, P(A and B) = 0.12.

Hence the probability that a person likes cake is given as follows:

0.9 = 0.42 + P(B) - 0.12

0.3 + P(B) = 0.9

P(B) = 0.6.

Probability of 0.90 that people liked cake or pie, hence the probability that a person likes neither is of:

1 - 0.9 = 0.1 = 10%.

(or means at least one of them, and neither is complementary to at least one).

As P(A and B) = 0.12 is different of zero, the events are non-mutually exclusive.

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Answer:

You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle's other two sides, called the legs. You can use the Pythagorean Theorem to find a value for the length of c, the hypotenuse.

Answer:

43°

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

Answer:

  (a, b, c) = (-3, -2, -4)

Step-by-step explanation:

You want to solve the system of 3 equations in 3 variables shown in the attached figure.

The easiest solution is one provided by a suitable calculator (attached). It tells you ...

The "work" is entering the problem into the calculator.

We notice the sum of 'a' coefficients is zero, so we can add the three equations to get ...

  (4a +5b -6c) +(-3a -2b +7c) +(-a +4b +2c) = (2) +(-15) +(-13)

  7b +3c = -26 . . . . . simplify

Multiplying the third equation by 4 and adding that to the first equation gives ...

  4(-a +4b +2c) +(4a +5b -6c) = 4(-13) +(2)

  21b +2c = -50 . . . . . simplify

Now, we have two equations in two unknowns.

Multiplying the first equation above by 3 and subtracting this last equation eliminates the b term to give ...

  3(7b +3c) -(21b +2c) = 3(-26) -(-50)

  7c = -28 . . . . . simplify

  c = -4 . . . . . . . divide by 7

Using this in the first "ad hoc" equation, we can find b:

  7b +3(-4) = -26

  7b = -14 . . . . . . . . add 12

  b = -2 . . . . . . . . divide by 7

And the values of b and c can go into the last of the original equations to give ...

  -a +4(-2) +2(-4) = -13

  -a = 3 . . . . . add 16

  a = -3 . . . . . multiply by -1

The solution is (a, b, c) = (-3, -2, -4).

__

Additional comment

The given solution is "ad hoc" because we decide how we're going to approach the solution based on the coefficients we see. Here, we are solving by "elimination," performing as little arithmetic as possible.

The third equation suggests we could make a substitution for 'a':

  a = 4b +2c +13

That substitution would give a different set of equations in 'b' and 'c' than the ones shown above.

The second attachment shows a graphical solution to the system. It shows (a, b, c) = (-3, -2, -4). The graphing program requires the use of x and y instead of 'a' and 'b' for the variables.

Four methods of solving the system have been described. Take your pick. The calculator solution was the easiest, requiring each number to be entered once.

Answer:

2a + b>a-2b( just an inequality solution)

hope this helps

have a good day :)

Step-by-step explanation:

Step-by-step explanation:

50-20=30

30÷2=15

therefore the sons age is 15

Step-by-step explanation:

please refer to the sketch

Answer:

  y = -5x -19

Step-by-step explanation:

You want the equation of the line parallel to y=-5x+3 through point (-3, -4).

The equations of parallel lines differ only in their constant. We can find the new constant by using the values at the given point:

  y = -5x +b

  -4 = -5(-3) +b

  b = -4 -15 = -19 . . . . . . subtract 15

The equation is ...

  y = -5x -19

The value of x=70 and y=40

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Here, 2x+y=180

x-y= 30

Here, the coefficient of y in these two equations are equal and have opposite signs. so,

                             2x+y= 180

                             x-y= 30

     Now adding equation 1 and equation 2

We get,

               3x= 210

                  x= 210/3

                  x= 70

Now, to find y:

Putting the value of x in equation 2

          x-y= 30

         70-y= 30

          y= 70-30

           y= 40

so, the value of x and y are 70 and 40

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The probability that the area of the triangle is at most 20 is 5/9

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is

1/2×12×6=36

Now if the area of the triangle is at most 20 then the required probability is = 20/36

                      =5/9

Hence, The probability that the area of the triangle is at most 20 is 5/9

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Answer:

[tex] \frac{4x - 11}{2} \leqslant 3x - 3 < 4 \\ \\ = > \frac{4x - 11}{2} \leqslant 3x - 3 \: and \: 3x - 3 < 4 \\ \\ < = > 4x - 11 \leqslant 6x - 6 \: \: and \: \: 3x < 7 \\ \\ < = > 2x \geqslant - 5 \: \: and \: \: x < \frac{7}{3} \\ \\ < = > \frac{ - 5}{2} \leqslant x < \frac{7}{3} [/tex]

=> the greatest integer is 2

the smallest integer is -2

Answer:

Step-by-step explanation:

You want the lengths of the segments of the hypotenuse of a right triangle when an altitude of 6 m divides the hypotenuse into parts with the ratio 1:9.

The altitude to the hypotenuse of a right triangle is the geometric mean of the parts it divides the hypotenuse into. If the shorter part is x, then the longer part is 9x, and their geometric mean is ...

  6 = √(x(9x)) = 3√x² = 3x

  x = 2 . . . . . . . divide by 3

The length of the shorter segment is 2 m; the longer one, 18 m.

Answer:

I believe the answer is D