ANSWER>> DETERMINE THE RANGE OF THE FUNCTION.
.
y = 1/4x^2 - 5
.
A) All real numbers.
B) All integers less than or equal to -5.
C) All integers greater than or equal to -5.
D) All real numbers greater than or equal to -5.

Answers in bold:

S9 = 2

i = 20

R = -2

=====================================================

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

--------------------

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

Answer:

\(y=-2x+13\)

Step-by-step explanation:

For reference, slope-intercept form is:

\(y=mx+b\)

\((m=slope)\)

\((b=y-intercept)\)

For the equation \(2x+y=13\) to be written in slope-intercept form, all we must do is subtract \(2x\) from both sides of the equation:

\(2x+y=13\)

\(y=-2x+13\)

Answer: 4, 2

Step-by-step explanation:

The offer percentage on that online site on the book  is 20%

What is the dollar amount of discount?

The dollar value of the discount given by the online site is difference between the normal price of the  book which is $25 and the offer price of the online site of $20 as shown below:

discount offered=$25-$20

discount offered=$5

Now that the offer discount has been ascertained, the discount offer in percentage terms relates the dollar value of the discount to the normal price to arrive at the percentage given off the normal price

offer percentage=discount offered/normal selling price

offer percentage=$5/$25

offer percentage=20%

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Answer:dang bro amma take points

Step-by-step explanation:

To prove this identity, we start with Fermat's Little Theorem, which states that if p is a prime number and a is any integer coprime to p, then a^(p-1) ≡ 1 (mod p).

Using this theorem, we can rewrite the given identity as a^(p-1) * a(p-2) ≡ 1 (mod p^2).

Next, we can multiply both sides by a to get a^(p-1) * a(p-1) ≡ a (mod p^2).

Since a and p are coprime, we can use Euler's Totient Theorem, which states that a^φ(p) ≡ 1 (mod p) where φ(p) is the Euler totient function. Since p is prime, φ(p) = p-1, so a^(p-1) ≡ 1 (mod p).

Using this result, we can rewrite our identity as a^(p-1) * a(p-1) * a^-1 ≡ a^(p-1) ≡ 1 (mod p), which implies that a^(p-1) ≡ 1 (mod p^2).

Therefore, we have proven the identity a p(p−1) ≡ 1 (mod p 2 ), where a is coprime to p, and p is prime.

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Londyn can tell that 18(x + 3) = 3(6x + 18) by factorization

factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and (x – 2)(x + 2) is a factorization of the polynomial x2 – 4.

6(x + 3) = 6x + 18 which is true as a result of multiplying each term in the bracket by 6 otherwise say expansion.

But in 18(x + 3) + 32 = 3(6x + 18) +32, can be done by expansion and then  factoring out 3. She can tell that both are equal by expanding the two expression at the left and right which will give the same result.

In conclusion expanding both terms of the equation will yield the same result.

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To measure an overbought or oversold market level, a technical analyst would typically c)use one or more price oscillators.

When assessing whether a market is overbought or oversold, technical analysts often turn to price oscillators. Price oscillators are technical indicators that provide insights into the momentum and potential reversal points in a market. These indicators are derived from price data and offer a visual representation of the relationship between current prices and historical price movements.

Price oscillators, such as the Relative Strength Index (RSI), Stochastic Oscillator, or Moving Average Convergence Divergence (MACD), measure the speed and magnitude of price changes. They help identify when a market has moved too far in one direction, signaling potential reversal or exhaustion. An overbought condition indicates that prices have risen too steeply and may be due for a pullback, while an oversold condition suggests that prices have declined excessively and could potentially rebound.

By analyzing the readings and patterns of these price oscillators, technical analysts can identify overbought or oversold levels. This information helps traders make more informed decisions, such as entering or exiting positions, adjusting risk management strategies, or looking for potential trading opportunities based on anticipated market reversals. However, it is important to note that technical analysis is just one approach to market analysis, and it should be used in conjunction with other forms of analysis and risk management techniques.

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The value of n in 1/5n+3/5n=7/9 is 35/36

The equation is given as:

1/5n+3/5n=7/9

Multiply through by 5

n + 3n = 35/9

Evaluate the sum

4n = 35/9

Divide both sides by 4

n = 35/36

Hence, the value of n in 1/5n+3/5n=7/9 is 35/36

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The basis for the null space of A is {(-5,0,-1,1)}.

Given matrix A = [1 0 -4 -6, -2 1 13, 5 0 1 5 -7] ~ [1 0 -4 -6, 0 1 5 -7, 0 0 0 0]The basis for the column space of matrix A is {(1,-2,5),(0,1,0),(-4,13,1),(-6,5,5)}. We can obtain the basis for the column space of matrix A by selecting the pivot columns. In this case, the pivot columns are columns 1 and 2. The non-zero columns in the row echelon form are columns 1, 2 and 3. To obtain the basis, we take columns 1 and 2 from the original matrix A, then write them in order followed by columns 3 and 4 of the original matrix A. So the basis for the column space of A is as shown below{(1,-2,5),(0,1,0),(-4,13,1),(-6,5,5)}.The basis for the row space of matrix A is {(1,0,-4,-6),(0,1,5,-7)}.

In order to find the basis for the row space, we take the nonzero rows from the row echelon form of A, which are rows 1 and 2. Then we select the corresponding rows of the original matrix A. The result is {(1,0,-4,-6),(0,1,5,-7)}.The basis for the null space of matrix A is {(-5,0,-1,1)}. We can obtain the basis for the null space of matrix A by solving the system Ax = 0. By writing this system in the form Rx = 0 where R is the row echelon form of A,

we get$$\begin{bmatrix}1&0&-4&-6\\0&1&5&-7\\0&0&0&0\end{bmatrix} \begin{bmatrix}x_1\\x_2\\x_3\\x_4\end{bmatrix} = \begin{bmatrix}0\\0\\0\end{bmatrix}.$$ Solving this system, we get the general solution as x = (-5t, 0, -t, t) where t is a scalar. Therefore, the basis for the null space of A is {(-5,0,-1,1)}.

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Answer:

x=0.2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

-a + 7x

-7 + 7(-6)

-7 + (-42)

-7-42

= -49

Step-by-step explanation:

Answer:

-55

Step-by-step explanation:

-a+8x

=-7+8*(-6)

=-55

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Answer:

x ≤ -4

Step-by-step explanation:

-7x + 13 ≥ 41

Rearrange the terms

-7x ≥ 41 - 13

Calculate

-7x ≥ 28

Divide both sides

x ≤ -28/7

Simplify

x ≤ -4

HOPE THIS HELPS AND HAVE A NICE DAY <3

Answer:

It should take about 4.75 min.

Step-by-step explanation:

Hope this helps and could you mark me as the brainliest

Answer:A

Step-by-step explanation:

Step-by-step explanation:

Example 1

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution

f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2

f(2) = 23 − 3×22 – 2×2 + 4 = −4

f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

f(4) = 43 − 3×42 – 2×4 + 4 = 12

f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.

Now we can factorise our expression as follows:

x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0

It now remains for us to solve the quadratic equation.

x2 − 2x − 4 = 0

We use the formula for quadratics with a = 1, b = −2 and c = −4.

We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:

x = 1

x = 1 + Ö5

x = 1 − Ö5

Example 2

We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.

First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.

f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution

f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4

f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4

f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.

The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.

First divide by x + 2

Now divide the resulting cubic factor by x − 1.

We have now factorised

f(x) = x4 − x3 − 5x2 + 3x + 2 into

f(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation

x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1.

Now we have found a total of four solutions. They are:

x = 1

x = −2

x = 1 +

x = 1 −

Sometimes we can solve a third degree equation by bracketing the terms two by two and finding a factor that they have in common.

Step-by-step explanation:

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Commutative law under addition says- p + q = q + p. Commutative law under multiplication says p x q = q x p. Note- Rational numbers, integers and whole numbers are commutative under addition and multiplication. Rational numbers, integers and whole numbers are non commutative under subtraction and division.0

Answer:

D) x=6

Step-by-step explanation:

8/2=4

4²+x²=(√52)²

16+x²=52

x²=52-16

x²=36

x=√36

x=6

The horse that can be fed with 44 bales of hay is 110 horses.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Given that the average adult horse needs 2/5 bale of hay each day to meet dietary requirements and a horse farm has 44 bales of hay.

The number of horses that can be fed will be:

= Total number of hay / Fraction needed

= 44 ÷ 2/5

= 44 × 5/2

= 22 × 5

= 110

100 horses can be fed.

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Answer:

B , D and E is one answer

Step-by-step explanation:

Answer:

B,D,E

Step-by-step explanation:

Using Trigonometric ratios, we can conclude the length of the indicated side is 12.70m.

It can be solved using Trigonometric ratios and Pythagoras theorem

Firstly using Trigonometric ratios

Using Sinθ,

Sinθ = perpendicular / hypotenuse(h)

Sin 39 = 8 / h

0.63 = 8 / h

h = 8 / 0.63

h = 12.70

∴ The length of indicated side is 12.70m

Secondly, using Pythagoras theorem,

(hypotenuse)² = (Altitude)² + (Base)²

⇒ (H)² = 8² + 10²

⇒ (H)² = 64 + 100

⇒ (H)² = 164

⇒ H = √164

⇒ H = 12.80

∴ The length of indicated side is 12.80m

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\(-4-4(-x-1)=-4(6+2x)\\\\-4+4x+4=-24-8x\\\\4x=-24-8x \ \ /+8x\\\\12x=-24 \ \ /:12\\\\\huge\boxed{x=-2}\)

Answer:

The probability that the customer finds exactly one defective light bulb among the eight purchased is approximately 0.042 or 4.2%.

Step-by-step explanation:

To find the probability that the customer finds exactly one defective light bulb among the eight they purchased, we can use the formula for combinations and probability.

1. Calculate the number of ways to choose one defective light bulb and seven non-defective light bulbs: -

Number of ways to choose 1 defective light bulb:

C(5,1) = 5! / (1! * (5-1)!) = 5

Number of ways to choose 7 non-defective light bulbs:

C(45,7) = 45! / (7! * (45-7)!) = 453,024

2. Multiply the number of ways together: -

5 (number of ways to choose 1 defective) * 453,024 (number of ways to choose 7 non-defective) = 2,265,120 (total ways to choose exactly 1 defective and 7 non-defective light bulbs)

3. Calculate the total possible ways to choose any 8 light bulbs from the 50 available: - C(50,8) = 50! / (8! * (50-8)!) = 53,907,800

4. Divide the favorable outcomes (exactly 1 defective and 7 non-defective) by the total possible outcomes: -

Probability = 2,265,120 (favorable outcomes) / 53,907,800 (total outcomes) ≈ 0.042

Therefore, the probability that the customer finds exactly one defective light bulb among the eight purchased is approximately 0.042 or 4.2%.

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The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer:

  \(\textbf{A. }0.25^{3/2}\)

Step-by-step explanation:

Perhaps your answer choices are ...

  \(\textbf{A. }0.25^{3/2}\\\textbf{B. }(\sqrt[3]{4})^2\\\textbf{C.}\sqrt[3]{16}\\\textbf{D. }0.25^{-2/3}\)

Of these, the one that is not equivalent to 4^(2/3) is ...

  \(\boxed{\textbf{A. }0.25^{3/2}}\)

The value of this is ...

  \(\left(\dfrac{1}{4}\right)^{3/2}=\sqrt{\dfrac{1}{4^3}}=\dfrac{1}{8}\ne4^{2/3}=\sqrt[3]{16}=(\sqrt[3]{4})^2\)

Answer:     a1=1/2;an=-4an-1

Step-by-step explanation: The last one

SOLUTION

The diagram below would be very helpful in answering the question

(a) to find f'(-2), we find the slope m of the line that I have made in red.

We use the points (-1, 0) and (-3, 1) we have

Hence the answer is

(c) We should determine x, where f'(x) = 0

Now f'(x) = 0 at a where we call the maximum point. That is the highest point of the graph curved as "n" From the figure above we can see that at this point, y is 3, also tracing down to the x-axis plane, can see that x = 3

Hence the answer is x = 3

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

R (- 3, 3 ) → R' (3, 3 )

S (- 3, 8 ) → S' (3, 8 )

T (- 2, 7 ) → T' (2, 7 )

50

Step-by-step explanation:

Because at the beginning samuel score was 14 points but when he continue buiding a high-rise-apartment building then his score rose to 36 point, then we add the two together then it give us 50

50

Step-by-step explanation: