please helpp!!!!!!!!!!

Answer:

f(x) = (x - 10) (x + 10)

Step-by-step explanation:

The equation looks like the difference of squares so 5 and 20 are out

-10 x -10 = 100

-10 x 10 = - 100

so (x - 10) (x + 10)

The Mean Absolute Deviation of the top five test scores in Mr. Rhode's class (98, 92, 96, 97, and 97) is 1.6.

To find the mean absolute deviation, we first need to find the mean of the data set.

The top five test scores in Mr. Rhodes’s class were: 98, 92, 96, 97, and 97.

So, the mean is:

Mean = (98 + 92 + 96 + 97 + 97)/5 = 480/5 = 96

Now, we need to find the absolute deviation of each data point from the mean. The absolute deviation is the absolute value of the difference between the data point and the mean.

Absolute deviation of 98 from the mean: |98 - 96| = 2

Absolute deviation of 92 from the mean: |92 - 96| = 4

Absolute deviation of 96 from the mean: |96 - 96| = 0

Absolute deviation of 97 from the mean: |97 - 96| = 1

Absolute deviation of 97 from the mean: |97 - 96| = 1

Next, we find the mean of these absolute deviations.

Mean Absolute Deviation = (2 + 4 + 0 + 1 + 1)/5 = 8/5 = 1.6

Therefore, the mean absolute deviation is 1.6.

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Answer:

1.15x10 to the power of 7

Answer:

1.15×10⁷

Step-by-step explanation:

that's the answer

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method draws a relation between given data. Following the regular trend, information can be calculated. It is also called the 'Mango Method'.

At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method is only valid for regular increases or decreases. Information about unity is drawn from given data, which is multiplied as required. It is widely used in the calculation of prices, amounts, etc.

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False. The best line is the least squares line because it minimizes the sum of squared errors (SSE). This means that the least squares line provides the best fit for the data by minimizing the difference between observed and predicted values.

The least squares line is actually the line that has the smallest sum of squares error (SSE) is incorrect.

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Answer:

1.\(8x+5\)
2.\(2x^2-9\)

Step-by-step explanation:

Given the following questions:

\((2x^2+5x-2)+(-2x^2+3x+7)\)
\((2x^2+5x-2)-(5x+7)\)

In order to find the answer to these questions we have to group the terms with the same variables and then combine like terms. Of course, applying the distributive property if needing to do so.

Number one:
\((2x^2+5x-2)+(-2x^2+3x+7)\)
\((2x^2+5x-2)+(-2x^2+3x+7)=2x^2+5x-2-2x^2+3x+7\)
\(2x^2+5x-2-2x^2+3x+7\)
\(2x^2-2x^2+5x+3x-2+7\)
\(2x^2-2x^2=0\)
\(5x+3x-2+7\)
\(-2+7=5\)
\(5x+3x+5\)
\(5x+3x=8x\)
\(8x+5\)

Number two:
\((2x^2+5x-2)-(5x+7)\)
\((2x^2+5x-2)-(5x+7)=2x^2+5x-2-\left(5x+7\right)\)
\(2x^2+5x-2-\left(5x+7\right)\)
\(2x^2+5x-2-5x-7\)
\(2x^2+5x-5x-2-7\)
\(5x-5x=0\)
\(2x^2-2-7\)
\(-2-7=-9\)
\(2x^2-9\)

Hope this helps.

Answer:

no solution is the answer

Step-by-step explanation:

Using translation concepts, the coordinates of the image of the triangle are given as follows:

A'(-1,-4), B'(-2,0), C'(-3, -11).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The rule for a 90° counterclockwise rotation about the origin is given as follows:

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

Hence the coordinates of the image of the triangle are given as follows:

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Excessive punishment or negative reinforcement can harm a child's math achievement by creating fear, undermining confidence, and discouraging engagement with the subject. Positive discipline techniques and a supportive environment are crucial for fostering math success.

Excessive punishment or negative reinforcement as a discipline technique can have detrimental effects on a child's math achievement. When a child makes mistakes or struggles with math concepts, responding with punishment, criticism, or harsh consequences can create a negative association with math. This can lead to anxiety, fear, and a lack of motivation to engage with the subject.

Mathematics requires a growth mindset, where mistakes are seen as opportunities for learning and improvement. By punishing or negatively reinforcing a child's math mistakes, we discourage them from taking risks, trying new strategies, and seeking help when needed. It hampers their ability to develop problem-solving skills and critical thinking abilities.

Furthermore, negative discipline approaches can damage a child's self-esteem and confidence in their mathematical abilities. They may develop a belief that they are "bad at math" or incapable of improving, leading to a self-fulfilling prophecy where their performance suffers.

To support a child's math achievement, it is essential to employ positive discipline techniques. This includes providing constructive feedback, offering assistance and guidance, creating a safe and supportive learning environment, and promoting a growth mindset. Encouraging effort, perseverance, and celebrating small successes can foster a positive attitude towards math and enhance a child's mathematical abilities.

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Given:

A line intersects the x - axis at (-7, 0) and has slope of 5/3.

Let A be the point (-4, -2) and B be the point (x, y).

To find: The coordinates of B such that ∠A B x = 90°.

We know that, if a line is intersecting x-axis at (-7, 0) and has a slope of 5/3, then its equation is

y = mx + c where m is the slope and c is the y-intercept.

So, the equation of the given line will be: y = (5/3) x + b

Now, this line intersects the x-axis at (-7, 0), so we can put these values into the above equation to find the value of b.

0 = (5/3) (-7) + b

0 = -35/3 + b

b = 35/3

So, the equation of the given line is: y = (5/3) x + 35/3

We have to find the coordinates of point B such that ∠ABx = 90°.

It means, AB is perpendicular to x-axis and has slope of 0.

So, we can use the point-slope form of equation to find the equation of line AB that passes through point A(-4, -2) with 0 slope.

y - (-2) = 0(x - (-4))y + 2

= 0(x + 4)y = -2

Now, this line will intersect the given line at point B, so we can put the value of y from equation (2) into equation (1).

-2 = (5/3) x + 35/3(5/3) x

= -41/3x

= (-41/3) (3/5)

= -41/5

Now, we have the x-coordinate of point B as -41/5. To find the y-coordinate of point B, we can use equation (2).

y = -2

So, the coordinates of point B are (-41/5, -2).

We are given a line that intersects the x-axis at (-7, 0) and has a slope of 5/3. We are also given two points A and B and we have to find the coordinates of point B such that ∠ABx = 90°.

To solve the problem, we first found the equation of the given line using its slope and a point (-7, 0) that lies on it. Then, we found the equation of line AB that passes through point A(-4, -2) and has 0 slope because AB is perpendicular to x-axis. This line intersects the given line at point B. So, we put the value of y from equation (2) into equation (1) to find the x-coordinate of point B and then we used equation (2) to find the y-coordinate of point B.The coordinates of point B are (-41/5, -2).

Therefore, the solution of the given problem is completed. Thus, we have found the coordinates of point B such that ∠ABx = 90°, which is (-41/5, -2).

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Rounding up to the nearest whole number, we need a sample size of 15682 measurements to obtain a margin of error of ±0.001 with 98% confidence

To determine the number of measurements needed to obtain a margin of error of ±0.001 with 98% confidence, we need to use the following formula:

n = [(z-value)² * σ²] / E²

Where:

n = sample size

z-value = the critical value for the desired confidence level, which is 2.33 for 98% confidence

σ = the standard deviation of the population, which is unknown

E = the maximum error or margin of error, which is 0.001

Since the standard deviation of the population is unknown, we can estimate it using the standard deviation of the sample. Assuming that the sample standard deviation is similar to the population standard deviation, we can use the sample standard deviation of 0.03 in this case.

Substituting the given values, we have:

n = [(2.33)² * (0.03)²] / (0.001)²

n = 15681.93

Rounding up to the nearest whole number, we need a sample size of 15682 measurements to obtain a margin of error of ±0.001 with 98% confidence.

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9514 1404 393

Answer:

  3.95 in

Step-by-step explanation:

The volume is given by ...

  V = πr²h

Solving for radius, we get ...

  r = √(V/(πh))

For the given numbers, the radius is ...

  r = √(980 in³/(π·20 in)) = 7/√π in ≈ 3.95 in

The radius of the cylinder is about 3.95 inches.

The answer is 5 (x - y + 2z) (x- y - 2z)

A polynomial or integer is simply resolved into factors that, when multiplied together, produce the original or initial polynomial or integer. The factorization method allows us to simplify any algebraic or quadratic equation by representing the equations as the product of factors rather than by expanding the brackets. Any equation can have an integer, a variable, or the algebraic expression itself as a factor.

The algebraic expressions can be factored using one of four techniques.

Now, solving the following question,

= 5 [ \(x^{2}\) - 2xy + \(y^{2}\) ] - 4\(z^{2}\)

= 5 [ \((x-y)^{2}\) - \(2z^{2}\)

= 5 (x - y + 2z) (x - y - 2z)

Therefore, the factors are 5 (x - y + 2z) (x - y - 2z)

The following question is incomplete. The correct question is:

Factorize the given equation.

5\(x^{2}\) - 10xy + 5\(y^{2}\) -     \(20z^{2}\)

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there are 2 radius given and the radius extends to form a right angle triangle

6^2+ x^2 = (4+6)^2

36 + x^2 = 100

x^2=100-36

x=√44

x=6.6

hope it helps

1. Three examples of situations where consistency is important:

Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.

Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.

Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.

2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.

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Answer:

\(x=14\)

Step-by-step explanation:

1) Since we know two of the sides of that right-angled triangle, we can use the Pythagorean Theorem to find x. His theorem is: \(c^2 = a^2 + b^2\).

Substitute the values into the formula above.

Let x = c

\(c^2 = 8^2 + 11.5^2\\c^2 = 196.25\\c= \sqrt{196.25}\\c=14\)

Answer:

94.20 yds

Step-by-step explanation:

C = 2 pi r

     2 pi (15) = 94.20 yds

Answer:

x- 7.50 i think i hope i helped

Step-by-step explanation: there no explanation

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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The tangent vector of the position vector \(G(s), F(t(s)), is:F(t(s)) = (-(1/sqrt(2)) * sin((s - C) / sqrt(2)), (1/sqrt(2)) * cos((s - C) / sqrt(2)), 1/sqrt(2)).\\\)
To find the distance along curve C, we need to integrate the magnitude of the velocity vector with respect to the parameter t. The velocity vector is defined as the derivative of the position vector with respect to t.

(a) Distance along curve C, s(t):

The velocity vector v(t) is given by:

\(v(t) = (x'(t), y'(t), z'(t))\)

where \(x'(t), y'(t), and z'(t)\)are the derivatives of x(t), y(t), and z(t), respectively.

Differentiating x(t), y(t), and z(t) with respect to t, we have:

\(x'(t) = -sin(t)y'(t) = cos(t)z'(t) = 1\)

The magnitude of the velocity vector is given by:

\(|v(t)| = sqrt((x'(t))^2 + (y'(t))^2 + (z'(t))^2) = sqrt((-sin(t))^2 + (cos(t))^2 + 1^2) = sqrt(sin^2(t) + cos^2(t) + 1) = sqrt(2)\\\)
To find the distance along curve C, we integrate |v(t)| with respect to t:

\(s(t) = ∫|v(t)| dt = ∫sqrt(2) dt = sqrt(2)t + C\)

where C is the constant of integration.

(b) Tangent vector of the position vector G(s), F(t(s)):

The position vector G(s) is given by:

G(s) = (x(s), y(s), z(s))

To find the tangent vector of G(s), we need to find the derivative of G(s) with respect to s.

Since s(t) = sqrt(2)t + C, we can solve for t as a function of s:

t(s) = (s - C) / sqrt(2)

Substituting t(s) into the parametric equations for x(t), y(t), and z(t), we have:

\(x(s) = cos(t(s)) = cos((s - C) / sqrt(2))y(s) = sin(t(s)) = sin((s - C) / sqrt(2))z(s) = t(s) = (s - C) / sqrt(2)\\\)
The tangent vector F(t(s)) is given by:

\(F(t(s)) = (x'(s), y'(s), z'(s))\)

Differentiating x(s), y(s), and z(s) with respect to s, we have:

\(x'(s) = -(1/sqrt(2)) * sin((s - C) / sqrt(2))y'(s) = (1/sqrt(2)) * cos((s - C) / sqrt(2))z'(s) = 1/sqrt(2)\\\)
Therefore, the tangent vector of the position vector G(s), F(t(s)), is:

\(F(t(s)) = (-(1/sqrt(2)) * sin((s - C) / sqrt(2)), (1/sqrt(2)) * cos((s - C) / sqrt(2)), 1/sqrt(2))\\\)
Note: The constant of integration C affects the starting point along the curve, but it does not affect the direction of the tangent vector.

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Answer:

150 cm

Step-by-step explanation:

So the scale is 2 cm on the blueprint = 3.5 meters in real life.

Basically you can just divide the height of the building by 3.5 meters:

259/3.5=75

There are 75, 3.5 meters in 259 meters

Since 3.5 meters on the print is 2 cm

You need to multiply the number of 3.5 meters by 2:

75*2=150

150 cm

Answer:

y=2x+11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here you go mate

step 1

k^2+8k+22=6​  equation

step 2

k2+8k+22(-6)=6(-6)  subtract -6

k2+8k+16=0

step 3

k2+8k+16=0  factor

(k+4)(k+4)=0

step 4

(k+4)(k+4)=0  set the numbers equal to zero

answer

k=-4

Answer:

B.   16h + 15 = 111

Step-by-step explanation:

The equation should represent the initial cost plus the amount per hour (h) to equal $111 (the total amount spent).

Equation: 16h + 15 = 111

Answer:

b = 56

Step-by-step explanation:

A way to solve this is cross multiplication!

25/35 = 40/b

40 · 35 = 1400

1400/25 = 56

I hope I was able to help. Have a good new year!

Answer:

c + 2 = 16

Step-by-step explanation:

Answer:

c+2=16

Step-by-step explanation: d