Compute (a) x₁ and (b) 2 for the iterative process defined by n+1 = 4x (3-xn) with x = 5.
(a) x₁ =???

The diagrams are shown below.

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Problem 1

We have a right triangle with horizontal leg \(a = 7\) and hypotenuse \(c = 25\) to represent the length of the ladder. Use the pythagorean theorem to find the vertical leg b.

\(a^2+b^2 = c^2\\\\7^2+b^2 = 25^2\\\\49+b^2 = 625\\\\b^2 = 625-49\\\\b^2 = 576\\\\b = \sqrt{576}\\\\b = 24\)

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Problem 2

After 1 hour, the first jet has traveled 300 miles while the other has traveled 400 miles. Use the formula

\(\text{distance = rate*time}\)

We'll have a right triangle with the two legs of \(a = 300 \text{ and } b = 400\). The order of 'a' and b doesn't matter.

Use the pythagorean theorem to find the hypotenuse c.

\(a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{300^2+400^2}\\\\c = \sqrt{90,000 + 160,000}\\\\c = \sqrt{250,000}\\\\c = 500\\\\\)

The two jets are 500 miles apart after one hour.

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Problem 3

We have a right triangle with horizontal leg 80 meters and vertical leg 30 meters. The hypotenuse is the distance you travel.

\(a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{30^2+80^2}\\\\c = \sqrt{900+6400}\\\\c = \sqrt{7300}\\\\c = \sqrt{100*73}\\\\c = \sqrt{100}*\sqrt{73}\\\\c = 10\sqrt{73}\\\\c \approx 85.440037\)

Exact Answer: \(\boldsymbol{10\sqrt{73}}\) meters

Approximate answer: 85.440037 meters

A graph that represents the solution set of the compound inequality is: graph D.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given compound inequality by making x the subject of formula as follows;

x + 3 < 1/2(4x - 12) < 20

Multiplying all through by 2, we have the following:

2x + 6 < 4x - 12 < 40

Next, we would solve the compound inequality in parts:

2x + 6 < 4x - 12

4x - 2x < 12 + 6

2x < 18

x < 18/2

x < 9.

4x - 12 < 40

4x < 40 + 12

4x < 52

x < 52/4

x < 13.

In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).

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\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)

Answer:

17x + 37

Step-by-step explanation:

looked it up

Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2

Answer:

28

Step-by-step explanation:

4x + 9x + 8x = 147

21x = 147

x = 147/21

x = 7

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The shortest side will be 4x

4*7 = 28

Answer:

Step-by-step explanation:

x^2 = 8

x=+-√8

The required coordinate of B' is B' = (4, -5), across the y-axis after reflection. Option A is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them.

here,
Given that a point B (-4, -5) is reflected across the y-axis, the Coordinate of image B' is to be determined.

Since the coordinate is reflected across the y-axis,
The equation of trasformation is given as,
(x , y) ⇒ (-x , y)

So, the image of B,

B' = (-(-4), -5)

B' = (4, -5)

Thus, the required coordinate of B' is B' = (4, -5), across the y-axis after reflection. Option A is correct.

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The value of a3 is 30.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

We are given that a_1 = 6 and \(a_n = n_a(n-1) + 2\)

Then Substitute as needed and do the arithmetic;

a_1 = 6

\(a_n = n_a(n-1) + 2\)

\(a_2 = -5a_1 +2 \\a_2= -5(6) +2 =-28\)

 \(a_ 3 = -5a_2 +2 = -(-28) +2 = 30\)

The value of a3 is 30.

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The exponential function giving the number of bacteria after x hours is given as follows:

\(y = 250(2)^x\)

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 250, b = 2.

Hence the function is given as follows:

\(y = 250(2)^x\)

The problem asks for the exponential function giving the number of bacteria after x hours is given as follows:

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Answer:

x < 7

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

5x+7<42

Step 2: Subtract 7 from both sides.

5x+7−7<42−7

5x<35

Step 3: Divide both sides by 5.

x<7

For the graph, draw an open circle at 7 and an arrow pointing left.

Hope this helps! :D

Step-by-step explanation:

5x<42-7

5x<35

5x/5<35/5

x<7

Answer:

I just guessed random numbers until I got 66 and 130.

Answer:

Step-by-step explanation:

Hi there!

Let one of the number be "x" then the next number is x+64.

According to the question,

The sum of two numbers is 196.

i.e x + (x+64) = 196

or, 2x +64 = 196

Subtract 64 from both sides,

2x +64-64 = 196 - 64

2x = 132

Divide both sides by 2,

\(\frac{2x}{2}\) = \(\frac{132}{2}\)

x = 66

And x+64 = 66+64 = 130

Therefore, the one number was 66 and another was 130.

Hope it helps!

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

The answer is A

Step-by-step explanation:

Triangle DEF was rotated and dilated so that's why is looks different than triangle ABC, but it maintained the same shape that is presented in ABC and that is why A is the answer.

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Answer:

13 sheep, 19 chicken

Step-by-step explanation:

You can start to solve this problem by assigning variables. First, let's assign the number of sheep there are as \(x\) and the number of chickens there are as \(y\).

Because each sheep has 4 legs, the number of legs for each sheep would be \(4x\). Similarly, because each chicken has 2 legs, the number of legs for each chicken would be \(2y\). Each animal would have 1 head, so the number of heads would just be \(x\) and \(y\). Because the number of legs in total are 90, \(4x + 2y=90\). Because the number of heads in total are 32, \(x+y=32.\)

There is now a system of equations with two unknown variables and two equations. There are many ways to solve this, but for me, the easiest would be elimination. First, I would double the second equation, \(2x+2y=64\). Then, I would subtract that from the first equation, eliminating \(y\). \(2x=26\). Solving for x gives 13. We can then plug that value into the second equation, making y be \(32-13=19\). This means that \(x=13\) and \(y=19\), meaning that there are 13 sheep and 19 chicken.

Answer:

Triangles in Geometry

Step-by-step explanation:

Step-by-step explanation:

3 5/6 converted to decimal form is 3.83333333

so when you round off this number to a whole number you get 4

Answer:4k

Step-by-step explanation:

2k=k+k

so

2k+k+k=k+k+k+k=4k

Answer:

En este problema se trata de una función exponencial, donde la cantidad de microbios en el recipiente se duplica cada minuto.

Si x representa el número de minutos transcurridos y y la cantidad de microbios en el recipiente, entonces se puede expresar la función exponencial como:

y = a * (2)^x

Donde "a" es la cantidad inicial de microbios en el recipiente, en este caso a = 1.

Después de 30 minutos, la cantidad de microbios en el recipiente es:

2^30 = 1,073,741,824

Esto significa que si se coloca un solo microbio en el recipiente, se tardará 30 minutos en llenarlo.

Si se colocan 2 microbios en el recipiente, entonces la cantidad inicial de la función exponencial es a = 2, y se busca el valor de x tal que:

2 * (2)^x = 1,073,741,824

Dividiendo ambos lados por 2, se tiene:

(2)^x = 536,870,912

Tomando logaritmos base 2 en ambos lados, se tiene:

x = log2(536,870,912) = 29

Por lo tanto, si se colocan 2 microbios en el recipiente, se tardará 29 minutos en llenarlo.

Step-by-step explanation:

Step-by-step explanation:

D= 104+28

= 132

x= 360-D

= 360 - 132

= 228

its ur answe

Answer:

228 degrees.

Step-by-step explanation:

m < A + m < C = 180 degrees  ( because AB || CE)

The total angles in a pentagon = 540 degrees

So m < x = 540 - 104 - 28 - 180

= 228 degrees.

Answer:

59

Step-by-step explanation:

If a number is divided by \(n\) and leaves a remainder \((n-1)\), then the number \((n+1)\) will be completely divisible by \(n\).

Therefore, when we say a number \(x\), when divided by 6, it leaves a remainder 5, then (\(x+1\)) will be a multiple of 6.

When we say a number \(x\), when divided by 5, it leaves a remainder 4, then (\(x+1\)) will be a multiple of 5.

When we say a number \(x\), when divided by 4, it leaves a remainder 3, then (\(x+1\)) will be a multiple of 4.

When we say a number \(x\), when divided by 3, it leaves a remainder 2, then (\(x+1\)) will be a multiple of 3.

So, \(x+1\) is a common multiple of 3, 4, 5 and 6.

Taking LCM of 3, 4, 5 and 6, we get 60.

So, the number 60 - 1 = 59 is the least such number.

Answer:

Option 1 <3

Step-by-step explanation:

Option 1: Not everyone might be in a sports class and not everyone might be leaving at the exact same time.

Option 2: This way of collecting information is not biased because it is random and includes a wide variation of people.

Using sampling concepts, it is found that the correct option is given by:

Option 1 is biased.

Sampling is when a group is taken from a population to estimate a parameter or a characteristic. It has to take into account the entire population to avoid bias, which generate false results.

In this question, all students have to be considering, not just the ones who like sports practice, hence Option 1 is biased.

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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On solving the provided question, we got to know that - the  cost of common equity is 11.84

Equity in mathematics education is defined by the National Council of Teachers of Mathematics as high standards and rewarding opportunities for everyone, addressing disparities to assist all kids learn mathematics, and making sure that all classrooms have resources and support for students.

here, the above question we have  -

D0 = $0.85;

P0 = $22.80;

g = 7.00%

  = 700

Answer is  -  The  cost of common equity is 11.84

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Answer:

ASA Postulate.

Explanation:

In the given diagram:

• Angle:, Angle STV is congruent to angle UVT.

• Side:, TV is congruent to TV (being a shared side).

• Angle: ,Angle TVS is congruent to angle VTU.

Therefore, triangles STV and UVT are congruent by the ASA Postulate.

Answer:

yes

Step-by-step explanation:

Answer:10 Safety razors

Step-by-step explanation:

27-12=15

15/1.50=10