An approximate solution to an equation is found using this iterative process.
(x₂)³-1
and x₁ = -1
4
Xn+1 =
4/34
a) (i) Work out the value of x₂
(ii) Work out the value of x3
b) Work out the solution to 6 decimal places.

Answer:

b, c, and e

Step-by-step explanation:

a. 3^9 = 3 × 3 × 3× 3 × 3 × 3 × 3 × 3 × 3

= 27 × 27 × 27 => 19683

b. 3^4 = 3 × 3 × 3 × 3

= 9 × 9 => 81

c. -9² =>  81

d. 9^9 = 9 × 9 ×  9 × 9 × 9 × 9 × 9 × 9 ×  9

= 729 × 729 × 729 =>  387420489

e. 81¹ => 81

b, c, and e are all equal to 81

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

[tex]\LARGE\begin{gathered}\sf{Evaluate \ All \ Expressions \ First} \\ \sf{ 3^9=19683} \\ \sf{ 3^4=81} \\ \sf{-9^2=81, \ or \ -81, \because} \\ \sf{there's \ a \ difference \ between (-9)^2 \ and \ -(9)^2} \\ \sf{(-9)^2=81 \ and -(9)^2=-81} \\ \sf{ 9^9=387,420,489} \\ \sf{0.81^1=0.81\end{gathered}[/tex]

Now, can you see the expressions that are equivalent?

⊰______________________________________________________⊱

[tex]f(1)=1^2+4\cdot1+6=1+4+6=11\\f(5)=5^2+4\cdot5+6=25+20+6=51[/tex]

x is 45° (45 degrees.)

To find this out, we first need to understand the properties of a rectangle. A rectangle has opposite sides that are equal, but more importantly, all 4 interior angles of a rectangle are right angles, meaning they are all 90 degrees. These can also be denoted by 4 square boxes in each corner.

When a rectangle is cut diagonally, the rectangle becomes two right triangles, but when joined together, of course make a rectangle. When they are cut diagonally, the triangles are congruent triangles by the Hypotenuse-Leg (HL) Congruence property.

To find the missing x in this angle, we must know that x is apart of a right angle, and if 45 is next to it, x must also be 45 degrees (90-45 = 45)

Hope this helped!

Answer:

A. -7

Step-by-step explanation:

Answer:

x = 1 19/21 the one is in front of the 19/21

Step-by-step explanation:

Exact form: x = 40/21

Decimal form: x = 1.90476190

Mixed number form: x = 1 19/21.

Answer:

Let's solve your equation step-by-step.

[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]

Step 1: Simplify both sides of the equation.

[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]

[tex]\tt{ 14 = \dfrac{3}{5}(7) + \dfrac{3}{5}(10)}[/tex]

(Distribute)

[tex]\tt{ 14 = \dfrac{21}{5} x + 6 }[/tex]

Step 2: Flip the equation.

[tex]\tt{ \dfrac{21}{5} x + 6 = 14}[/tex]

Step 3: Subtract 6 from both sides.

[tex]\tt{ \dfrac{21}{5} x + 6 - \blue{6} = 14 - \blue{6}}[/tex]

[tex]\tt{ \dfrac{21}{5} = 8}[/tex]

Step 4: Multiply both sides by 5/21.

[tex]\tt{ \left( \dfrac{5}{21}\right) \times \left(\dfrac{21}{5}x \right) = \left(\dfrac{5}{21}\right) \times (8)}[/tex]

[tex]\\[/tex]

[tex]\large\tt\purple{ x = \dfrac{40}{21}}[/tex]

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The two pairs of polar coordinates for the given point (3, -3) with 0° ≤ θ < 360° are (3√2, 135°) and (3√2, 315°).

A polar coordinate is a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

Next, we would determine the distance (r) and angle (θ) as follows:

r = √(3² + (-3)²)

r = √(9 + 9)

r = 3√2.

θ = tan⁻¹(-3/3)

θ = tan⁻¹(-1)

θ = 3π and 7π/4 (second and fourth quadrants).

Converting to degrees, we have:

θ = 135° and 315°.

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Complete Question:

Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°

The rational expression that satisfies x = y +-2 is 2xy/(x + y)(x² - 4).

It should be noted that non permissible value is the value of the variable which make the denominator of the rational expression equal to zero.

Based on the information, x + y gives x - y = 0.

x = 2 gives x - 2 = 0

x = -2 gives x + 2 = 0

Ths denominator according to the condition illustrated will be (x - y)(x - 2)(x + 2) = (x - y)(x² - 4)

Then, the rational expression can be written by taking the numerator and denominator. An example will be 2xy/(x + y)(x² - 4).

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Answer:

-1468955

Step-by-step explanation:

please don't forget to write down the correct questions and formula.

find f(x) of g(x)

f(x)=2x+1 and g(x)=x²-7

F of G = 2(x²-7)+1

= 2x²-14+1

= 2x²-13

according to the question x=-1212

so there for f(x) of g(x)=2(-1212)²-13

=-1468955

Answer: Circumcenter

Step-by-step explanation: The circumcenter is the point where all perpendicular bisectors of a triangle meet. The 3 perpendicular bisectors of the 3 sides of the triangle meet at the point which is labeled in this triangle as H.

Answer:

1.) & 2.) BC and AD are congruent and parallel because in parallelogram opposite sides are equal and parallel

4.) <BCE≅<DAF because they are alternating interior angles bisected by line CA

5.) & 6.) The line BE/DF which bisects the <B/<D iS perpendicular to diagonal CA which forms the right angle

7.) Because sum of any two adjacent angles are 180
8.) This follows ASA Postulate which means that if 2 pair of angles is congruent given that they share a same side, the triangle formed will also be congruent.

Step-by-step explanation:

Take the side CA as the same side of both triangles. This side also participates on the aforementioned angles on the given. The angles <BCE≅<DAF shares the side CA which makes the angles <DFA and <BEC congruent to each other. Therefore, the two right triangles are congruent

See below for the demonstration of (e) graphing a line using x- and y-intercepts

To solve this question, we make demonstrate (e) graphing a line using x- and y-intercepts

At the end of this exercise, you should be able to graph a line using x- and y-intercepts

A linear equation is represented as:

Ax + By = C

Where:

This means that we plot the points (0,C/B) and (C/A, 0) on a graph and then connect the points using a straight line.

Once this is done, the line has been graphed.

For instance, a line parallel to 3x + 8y = 16 will have a slope of -3/8

Plot the graph of the following equation using the intercepts

2x + 4y = 10

We have:

2x + 4y = 10

Set x = 0 to determine the y-intercept

4y = 10

Divide by 4

y = 2.5

Set x = 0 to determine the x-intercept

2x = 10

Divide by 2

x = 5

So, we have:

(5, 0) and (0, 2.5)

Plot the above points and connect the points (see attachment for graph)

Plot the graph of the following equation using the intercepts

3x + 6y = 18

We have:

3x + 6y = 18

Set x = 0 to determine the y-intercept

6y = 18

Divide by 6

y = 3

Set x = 0 to determine the x-intercept

3x = 18

Divide by 3

x = 6

So, we have:

(6, 0) and (0, 3)

Plot the above points and connect the points (see attachment for graph)

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Simple

Sum of all three

Sum of first two

Divide by

Yes Verified

Answer:

AB - Diameter

DA - Tangent

BC - Chord

OA - Radius

CAB - Inscribed Angle

Answer:

[tex]\sqrt{16} = 4\\[/tex]

Step-by-step explanation:

the distance formula for graph = [tex]\sqrt{x^{2} + y^{2} }[/tex]

(simplified version)

[tex]\sqrt{0^{2} + (-4)^{2} } \\\\\\\sqrt{0 + 16} \\\\\\\sqrt{16}\\\\= 4[/tex]

I hope its right TT I just looked it up here:

https://byjus.com/maths/distance-between-two-points-formula/

you should double check here as well

Based on the geometric figures shown, the three collinear points are:

Collinear points can be defined as three or more points that all lie on the same straight line (single line). Based on the geometric figures shown in the image below, the three collinear points include:

Another name for line AB is line segment BA, AT, BT, TA, TB. Also, a line in plane Z is line segment AT or line l.

Based on the image shown, the intersection of planes Z and W is line segment AT.

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Answer:

a) 25% are bad

b) 75% are good

Step-by-step explanation:

We know that there are 300 oranges total and that 75 are bad. That means that the rest are good (implied).

300 - 75 = 225 good oranges.

So to find the percentage we have to take the selected amount divided by the total amount.

Bad Apples:                               Good Apples:

75 / 300 = 0.25                          225/300 = 0.75

However, that's a decimal or a number out of 1, we need a percent or a number out of 100. So we have to multiply both numbers by 100.

Bad Apples = 25%

Good Apples = 75%

The different ways that the students can elect a president and a vice president will be 13110.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

Given data;

Total no of students =  115

The total number of ways to elect a president = 115

If one person is elected as the president the total number of ways to elect a president  = 114

The different ways that the students can elect a president and a vice president are found as;

⇒ 115 ways × 114 ways

⇒ 13110 ways

Hence the different ways that the students can elect a president and a vice president will be 13110.

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Answer:

C is the right answer I think

Answer:

the top one as highlighted

Step-by-step explanation:

y=Mx+c is the equation for a straight line

C is the intercept as it is at 0 it can be dropped from the expression as adding or taking away 0 makes no difference to the end value.

m is the slope

[tex]\huge\boxed{y-5&=-\frac{1}{3}(x+9)}[/tex]

First, we'll find the slope of the new line. The first line has a slope of [tex]3[/tex]. Take the negative reciprocal of this (Flip the numerator and denominator, then multiply by [tex]-1[/tex]) to get [tex]-\frac{1}{3}[/tex] for the new slope.

Then, we'll use the point-slope form to make the new equation, where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-5&=-\frac{1}{3}(x-(-9))\\y-5&=-\frac{1}{3}(x+9)\end{aligned}[/tex]

Lou Ann needed 25 packages that contains all the 150 invitations.

Lou Ann needed to mail 150 invitations to her school play. The invitations came 6 to a package.

The statistic is the study of mathematics which deal with relations between comprehensive data.

Here, 1 package contains 6 invitation
so 1 package = 6 invitations
total invitation= 150 invitations
now number of packages = Total invitation/ 6 invitation = 150/6
=25

Thus the required number of packages is 25.

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Answer:

38%

Step-by-step explanation:

2.3/5.98 x 100

= 0.38 x 100

= 38%

The area of the similar triangle named ∆DEF is; 4 square centimeters.

We are given that ∆ABC is similar to ∆DEF.

The perimeter of ∆ABC is five times the perimeter of ∆DEF.  Thus;

(Perimeter of ΔABC) = 5(Perimeter of ΔDEF)

Thus;

(Perimeter of ΔABC)/(Perimeter of ΔDEF) = 5

Thus, we can say that;

Scale factor, K = 5.

Since the area of ∆ABC is 100 square centimeters, Then;

(area of ∆ABC)/(area of ∆DEF) = K²

100/(area of ∆DEF) = 5² = 25.

(area of ∆DEF) = 100/25 = 4.

Thus, the area of ∆DEF is 4 square centimeters.

Complete Question is;

∆ABC is similar to ∆DEF. The perimeter of ∆ABC is five times the perimeter of ∆DEF. The area of ∆ABC is 100 square centimeters. The area of ∆DEF is square centimeters

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Using translation concepts, the vertices of the rectangle after the translation about the origin by 180° will be as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The rule for a rotation of 180º about the origin is:

(x,y) -> (-x,-y).

Hence, for triangle EFG, the vertices after the translation will be given as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

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Answer:

Step-by-step explanation:

Hello,

8(6x-7) <5(9x - 4)

48x - 56 < 45x - 20

48x - 45x < -20 + 56

3x < 36

x < 36/3

x < 12

[tex]\huge\boxed{8\ \text{bags of oranges}}[/tex]

Let's first find how many ounces the basket can hold.

1 pound is equal to 16 ounces. Multiply that to find how many ounces the basket can hold.

[tex]6\cdot16=96[/tex]

Now, divide the weight held by the basket by the weight of each bag of oranges.

[tex]96\div12=\boxed{8}[/tex]