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Answer:

x = -5, or x = 5

Step-by-step explanation:

First, add both sides by 8: -x^2 = -25

Then, multiply both sides by -1: x^2 = 25

Lastly, take the square root of both sides: x = -5, or x = 5

Answer:

lesser -5

greater 5

Step-by-step explanation:

khan academy

Answer:

-8/4 or -2

Step-by-step explanation:

First of all notice the graph is negative. Meaning that this will be a negative slope.

Now we can use rise over run, counting up 8 spaces, and to the left 4.

Since the graph is negative make the rise negative. -8/4.

To simplify this fraction divide -8 by 4, and receive an answer of -2.

-Hope this helped

Answer:

C

Step-by-step explanation:

ΔFDC and ΔFBA are similar          AA Similarity

The given p, α, and i using the exponentiation by squaring algorithm.

To prove that 2 is a primitive root of 11, to show that every integer a with 1 ≤ a ≤ 10 can be expressed as a ≡ 2²i (mod 11) for a unique i with 0 ≤ i ≤ 9.

verify this by checking the powers of 2 modulo 11:

2² ≡ 1 (mod 11)

2²≡ 2 (mod 11)

2² ≡ 4 (mod 11)

2³ ≡ 8 (mod 11)

2² ≡ 5 (mod 11)

2³ ≡ 10 (mod 11)

2³ ≡ 9 (mod 11)

2³ ≡ 7 (mod 11)

2² ≡ 3 (mod 11)

2³ ≡ 6 (mod 11)

The remainders obtained from the powers of 2 cover all the integers from 1 to 10 modulo 11. Additionally, each remainder is unique, express any integer between 1 and 10 as a power of 2 modulo 11.

To find log₂(9), to determine the exponent i such that 9 (mod 11). From the list of powers of 2 above, that 2³= 9 (mod 11). Therefore, log₂(9) = 6.

A given p, α, and i, where α is a primitive root of p and i is the discrete logarithm or index use the algorithm of exponentiation by squaring.

The algorithm for computing a given p, α, and i is as follows:

Set result = 1.

Initialize a binary representation of i, e.g., i = b[m]b[m-1]...b[1]b[0].

For j from m to 0:

a. Square the current result: result = result × result (mod p).

b. If bj = 1, multiply the current result by α: result = result × α (mod p).

Return the final result.

This algorithm takes advantage of the binary representation of i to compute a efficiently. By squaring the current result and multiplying by α only when necessary, compute a in logarithmic time complexity with respect to i.

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No, Etsuko is not correct. The length of the larger paper is 17.9 cm greater than the length of the smaller paper.

The smaller paper has a side length of 7.5 cm. The larger paper has a side length of 25.4 cm.

The difference between the two side lengths is 25.4 cm - 7.5 cm = 17.9 cm.

Therefore, the length of the larger paper is 17.9 cm greater than the length of the smaller paper.

Etsuko's error is likely due to the fact that she rounded the difference between the two side lengths to 32.9 cm. However, this rounding error is significant, and it results in her answer being incorrect.

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As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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Answer: (2,-3) (center), 2 (radius), (2,-1),(0,-3),(4,-3) and (2,-5) (points on the circumference).

Explanation:

The equation of a circle with center (a,b) and radius r is given by: (x-a)^2 + (y-b)^2 = r^2

The given equation is x² + y² - 4x + 6y + 9 = 0

This can be rewritten as: (x² - 4x) + (y² + 6y) = -9

Now complete the square in x and y by adding and subtracting the square of half of the coefficient of x and y respectively. (x² - 4x + 4) + (y² + 6y + 9) = -9 + 4 + 9(x - 2)² + (y + 3)² = 4

Simplify and rewrite the equation in the form of a circle equation (x - 2)² + (y + 3)² = 2²

Comparing this equation with the standard equation of a circle, we have: Center: (2,-3) Radius: 2

Now we can easily sketch the graph of the circle with the help of these details that we have found in the above steps. And for the additional points, here are four points that lie on the circumference of the circle:(2,-1),(0,-3),(4,-3) and (2,-5).

The graph of the circle is shown below:

Answer: (2,-3) (center), 2 (radius), (2,-1),(0,-3),(4,-3) and (2,-5) (points on the circumference).

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The required measure of side y = 8

Given : Triangle TUV and triangle XWV are similar

Thus \(\frac{UV}{VW} = \frac{6}{21}\)

this is further equal to \(\frac{2}{7}\)

Thus the ratio UV : VW = 2 : 7

this implies that the ratio TV : VX should also be equal to the ratio of UV : VW = 2 : 7 because of cpst or also called corresponding parts of similar triangles.

Given  UV : VW = 2 : 7

thus TV : VX = \(\frac{y}{28 }\) which on equation will give y as 8

because \(\frac{8}{28}\) when divided by 4 will give us the required ratio that is 2 : 7

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The probability of obtaining five tails in a row assuming the coin is​ fair is 1/32.

A person will have to do 5 coin tosses which means,

No. of total observations  = 25

Required outcome → 5 Heads { T , T , T , T , T }

This outcome  can occur only once so required outcome will be 1

Thus, required outcome  =1

Probability (5 Tails) = 1 / 2⁵ = 1 / 32

Hence , the probability of obtaining five tails in a row assuming the coin is​ fair is 1/32.

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Answer:

5x+6=21 is the same as 15+6=21

Step-by-step explanation:

hope this is what you wanted :)

Answer:

Solution

x=17/2

Step-by-step explanation:

Answer: x = 17/2

Step-by-step explanation: distribute 34x+95=3(14x+9)

subtract from both sides 34x+95−95=42x+27−95

34

The approximate solution of the system of equations is given as follows:

(4, 26).

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

For the point of intersection in this problem, we obtain the coordinates as follows:

This means that the correct option is given by the third option.

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Answer:

the best answer is option d

Step-by-step explanation:

4/5 x -10 = -40/5 = -8

t x t = t^2

-8t^2

Answer:

\( \sf \: d) \: - 8 {t}^{2} \)

Step-by-step explanation:

Given expression,

\( \sf \rightarrow \: \frac{4}{5}t \: ( - 10t )\)

Let's simplify the expression,

\( \sf \rightarrow \: \frac{4}{5} t \: ( - 10t) \: \)

\( \sf \rightarrow \: ( \frac{4}{5} \times - 10)( {t} \times t)\)

\( \sf \rightarrow \: ( \frac{ - 40}{ \: 5} )( {t}^{2} )\)

\( \sf \rightarrow \: - 8{t}^{2} \)

Hence, the option (d) is correct.

Using proportions, it is found that the final payment if the loan is paid off with the fifth payment is of $488.152.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, balance of $435.85 with interest rate of 12%, hence the final payment is given by:

P = 435.85 x 1.12 = $488.152.

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Answer: maybe 1 ‍♀️

Step-by-step explanation:

The stretch of an exponential decay function is y = 2(1/6)^x

An exponential function is represented as

y = ab^x

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/6)^x

Hence, the exponential decay function is y = 2(1/6)^x

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Answer:

  x = 45

Step-by-step explanation:

  0.4 + x(10%) = 4.9 . . . . . . given

  x(10%) = 4.5 . . . . . . . . . subtract 0.4

  x = 45 . . . . . . . . . . . . multiply by 10

_____

10 × 10% = 100% = 1

Hi!

I can help you, no worries!

Your answer is y = -4/5x - 3

To solve this is much easier than you think. To "solve for y" we just have to get y on one side of the equal sign all by itself. We can see that it's "1 + y" on the left instead of just the y.

To get y by itself, we just subtract "1" from both sides.

1 + y = -4/5x - 2

-1                     -1

     y = -4/5x - 3

If you don't know why we have to subtract from both sides, think of it like this (it's how I like to think of it).

Each side of the equal sign is a twin. They are equal to eachother. If you change something about one twin, such as changing their hair color (or adding a number to one side of the equal sign), you have to do it to both in order for them to be the same. Right?

Hope this helps! Have a great day! :D

Answer:

The pen is $52.50 and the cost of the pencil is $2.50.

Step-by-step explanation:

What is the answer if a pen and a pencil cost 55 dollars and the pen cost 50 more dollars than the pencil​?

—

Step 1: Let Statements

Let a be the cost of the pen

Let b be the cost of the pencil

Step 2: Write Equations

a + b = 55

a = 50 + b

Step 3: Find POI

Using substitution to find the POI of both equations:

50 + b + b = 55

50 + 2b = 55

2b = 55 - 50

2b = 5

b = 5/2 or 2.5

Substitute b = 5/2 to solve for a

a = 50 + b

a = 50 + 2.5

a = 52.5

Therefore, a = 52.5 and b = 2.5

Step 4: Concluding Sentence

The cost of the pen is $52.50 and the cost of the pencil is $2.50.

Step-by-step explanation:

2+2=4

4+6=10

12+100=112

120×670=80,400

Therefore, the function f(x) = ax + b is one-to-one, and its inverse function is given by: f1(y) = (y - b)/a.

To determine if the function f(x) = ax + b is one-to-one, we need to show that it passes the horizontal line test. That is, for any horizontal line y = k, the function intersects the line at most once.
To do this, suppose that f(x1) = f(x2), where x1 and x2 are two distinct values in the domain. Then we have:
a x₁ + b = a x2 + b
Subtracting b from both sides gives:
a x₁ = a x₂
Since a ≠ 0, we can divide both sides by a to get:
x₁ = x₂
Therefore, the function f(x) = ax + b is one-to-one, and its inverse function is given by:
f1(y) = (y - b)/a

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There are \(\frac{60!}{57!}\) ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = \(\frac{60!}{1! 59!}\)

                                                           = \(\frac{60 *59!}{1*59!}\)

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  \(\frac{60 * 59 * 58 * 57!}{57!}\)

              =  \(\frac{60!}{57!}\)

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To find this answer we have to do these steps below

1. Find the amount of money that LaShawn earns in an Hour

We have to do 60/8 which is 7.5

LaShawn earns 7.5 dollars in an hour

2. Multiply 7.5 by 35

The answer to that is 262.5 dollars

Therefore the answer is 262.5 dollars

I hope this helped, if it's wrong, blame me

Ps. Brailents would help a LOT

The required measure of the angle ∠spq of a rhombus is 110°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For rhombus,
m∠spr=(2x + 15)°
m∠qpr=(3x−5)°

And,
m∠spr = m∠qpr
2x + 15 = 3x - 5
x = 20

Now,
∠spq = m∠spr + m∠qpr
        = 2x + 15 + 3x - 5

        = 5x + 10
        = 5(20) + 10
        = 110°

Thus, the required measure of the angle ∠spq of a rhombus is 110°.

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Option (a) 1/50 The average of the 50 samples of x can be calculated as the sum of the values of x divided by the number of samples, which is 50 in this case.

Since x has a mean of 1, we know that the sum of the values of x is 50 times 1, which is 50. The variance of x is 4, which means that the standard deviation of x is 2. This means that the standard error of the mean of x, which is the standard deviation of the sample mean, is 2 divided by the square root of 50, which is approximately 0.283. Therefore, the 95% confidence interval for the mean of the 50 samples of x is [1 - 1.96(0.283), 1 + 1.96(0.283)] = [0.44, 1.56]. Since none of the answer choices fall within this interval, we cannot determine the correct answer without additional information.

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The two primary components of an angle are the limbs and the vertex. The angle sum property of a triangle is 20+21+29=180 70x=180 x=180/70.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.

According to the given question,

angle sum property of triangle-

20+21+29=180

70x=180

x=180/70.

Hence, With the angle sum property of triangle, x=180/70.

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A doctor wants to estimate the mean HDL cholesterol of a 20 to 28-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3 points with 99% confidence assuming σ = 11.5 based on earlier studies? Suppose the doctor would be content with 90% confidence. How does that decrease in confidence affect the sample size required?

To estimate the mean HDL cholesterol of a 20 to 28-year-old females, the formula for the required sample size n is given byn = [ (zα/2)^2 * σ^2 ] / E^2where zα/2 is the z-value for the level of confidence, σ is the population standard deviation, and E is the margin of error.The z-value at 99% confidence is given by z = 2.58.Rearranging the formula and substituting the values, we get;150 = [ (2.58)^2 * (11.5)^2 ] / (3)^2Therefore, the required sample size to estimate the mean HDL cholesterol within 3 points with 99% confidence assuming σ = 11.5 based on earlier studies is 150.Now, let's suppose the doctor would be content with 90% confidence, then the z-value is given by z = 1.645.The formula for the required sample size n is given by;n = [ (zα/2)^2 * σ^2 ] / E^2Substituting the values, we getn = [ (1.645)^2 * (11.5)^2 ] / (3)^2Therefore, the required sample size to estimate the mean HDL cholesterol within 3 points with 90% confidence assuming σ = 11.5 based on earlier studies is 60.

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In other words, -4 goes in the first blank and 8 goes in the second blank

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

Explanation:

Parallel lines have equal slopes, but different y intercepts.

The slope of y = -4x+1 is m = -4. So our answer will have this slope as well.

Use (x,y) = (2,0) along with that mentioned slope to get...

y = mx+b

0 = -4*2+b

0 = -8+b

0+8 = b

8 = b

b = 8 which is the y intercept

So we have m = -4 and b = 8 take us from y = mx+b to y = -4x+8

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

As a check, plugging x = 2 should lead to y = 0

y = -4x+8

y = -4*2+8

y = -8+8

y = 0

The answer is confirmed.