Graph the following system of inequalities.
y ≤2x + 1
y < -1 - 1

Answer:

\(t = 2.86 \: s\)

The ball remains in the air for 2.86 seconds.

Step-by-step explanation:

A baseball is hit into the air, and its height above the ground is described by the function

\(H(t) = -16t^2 + 45t + 2\)

Where H(t) represents the height of the ball t seconds after it is hit.

The ball remains in the air before it hits the ground.

When the ball hits the ground,

\(H(t) = 0\)

So,

\(0 = -16t^2 + 45t + 2\)

The equation may be solved using the quadratic formula.

\($t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$\)

Where

\(a = -16 \\\\b = 45 \\\\c = 2 \\\\\)

So,

\(t=\frac{-(45)\pm\sqrt{(45)^2-4(-16)(2)}}{2(-16)} \\\\t=\frac{-45\pm\sqrt{(2025 - (-128)}}{-32} \\\\t=\frac{-45\pm\sqrt{(2153}}{-32} \\\\t=\frac{-45\pm 46.4004}{-32} \\\\t=\frac{-45 + 46.4004}{-32} \: and \: t=\frac{-45 - 46.4004}{-32}\\\\t= -0.04 \: and \: t = 2.86 \\\\\)

Since the time cannot be negative, discard the negative value and accept the positive value

\(t = 2.86 \: s\)

Therefore, the ball remains in the air for 2.86 seconds.

Answer:

no

Step-by-step explanation:

Answer: your question is blurry

Step-by-step explanation:

Answer:

20 + 5x = 50

Step-by-step explanation:

Let the number of cakes Sam baked this week be x

Total amount he received this week = $50

Amount he receives each week = $20

Amount he receives for baking one cake = $5

Amount he would receive for baking x cakes = $5x

Equation: 5x + 20 = 50

Answer:

20 + 5x = 50

Step-by-step explanation:

Let x be the number of cakes

Amount paid per cake = $5

Amount paid for "x" cakes = 5*x = 5x

Basic payment per week = $20

Amount paid that week = 20 + 5x

20 + 5x = 50

Answer:

Answer option 2

Step-by-step explanation:

When a shape is rotated counterclockwise by 90°, each point of the shape is moved in a circular motion in the counterclockwise direction by 90° around the fixed point of rotation.

As the triangle is rotated about point O, the position of point O does not change (i.e. it is "fixed").

Line segment OA is horizontal in the original figure. When it is rotated 90° counterclockwise, it becomes vertical, where A is above O.

Line segment BA is vertical in the original figure. When it is rotated 90° counterclockwise, it becomes horizontal, where B is to the left of A.

Therefore, the figure that represents the image after the given rotation is the second answer option.

Answer:

Answer option number two.

If A is a symmetric matrix, then A³ is also a symmetric matrix.

To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.

Now, let's look at A³:

A³ = A * A * A

We can replace each A with A^T, since they are equal:

A³ = A^T * A^T * A^T

Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:

A³ = (A^T * A^T * A^T)^T

A³ = (A^T)^T * (A^T)^T * (A^T)^T

Since the transpose of a transpose is the original matrix, we can simplify:

A³ = A * A * A

Therefore, A³ is also a symmetric matrix.

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Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$950\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &10 \end{cases} \\\\\\ A=950e^{0.042\cdot 10}\implies A=950e^{0.42}\implies A\approx 1445.86\)

Answer:

FM and GB

Step-by-step explanation:

the angles are corresponding meaning that the lines must be parallel

Answer:

  2, 3, 5 are true statements

Step-by-step explanation:

A diagram of the geometry is helpful. Our understanding of your description is shown in the first attachment. The second attachment shows how the various angles relate to each other. An exterior angle and its adjacent interior angle are a linear pair, so are supplementary.

__

1. BEC is an exterior angle -- False, it is an interior angle

2. DEC is an exterior angle -- True

3. ABE and EBC are supplementary -- True, they are a linear pair

4. BCF and DEC are supplementary -- False, they are unrelated exterior angles

5. BEC is a remote interior angle to BCF -- True

Answer:

Step-by-step explanation:

2,3,5

Answer:

-3/7

Step-by-step explanation:

Slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\)

        \(=\frac{8-11}{10-3}\\\\=\frac{-3}{7}\\\)

Answer:

121

Step-by-step explanation:

Given

f(x) = - (x + 8)(x - 14) ← expand factors using FOIL

     = - (x² - 6x - 112) ← distribute by - 1

     = - x² + 6x + 112

Given a quadratic in standard form. y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

f(x) = - x² + 6x + 112 ← is in standard form

with a = - 1 and b = 6, thus

\(x_{vertex}\) = - \(\frac{6}{-2}\) = 3

Substitute x = 3 into f(x) for corresponding value of y

f(3) = - (3)² + 6(3) + 112 = - 9 + 18 + 112 = 121

vertex = (3, 121 ) ← with y = 121

Answer:

D. 121

Step-by-step explanation:

The y-intercept is (0,2.75), and it represents the pick-up fee

Let x represent the mile driven, and y represents the charges.

So, the given parameters can be represented using the following ordered pair

\((x,y) = \{(5,9)\ (8,12.75)\}\)

Calculate the slope (m) using:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m = \frac{12.75 - 9}{8 - 5}\)

\(m = \frac{3.75}{3}\)

\(m = 1.25\)

The equation is then calculated as:

\(y = m(x -x_1) + y_1\)

So, we have:

\(y = m(x -5) + 9\)

Substitute 1.25 for m

\(y = 1.25(x -5) + 9\)

Substitute 0 for x, to calculate the y-intercept

\(y = 1.25(0 -5) + 9\)

\(y = -6.25 + 9\)

\(y = 2.75\)

Hence, the y-intercept is (0,2.75), and it represents the pick-up fee

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The equation for the scaled version of the function f(x) = x² is g(x) = a × x²

The function g(x) can be considered a scaled version of the function f(x) = x². To create a scaled version of a function, we can multiply the original function by a scaling factor. Let's call this scaling factor "a." Now, the equation for g(x) can be written as:

g(x) = a ₓ f(x)

Since f(x) = x², we can substitute it into the equation for g(x):

g(x) = a ₓ x^2

In this equation, "a" represents the scaling factor. If "a" is greater than 1, the function g(x) will stretch vertically, meaning its parabola will be more narrow compared to f(x). If "a" is between 0 and 1, the function g(x) will be compressed vertically, resulting in a wider parabola. If "a" is negative, the parabola will be reflected over the x-axis.

In summary, the equation for the scaled version of the function f(x) = x² is g(x) = a × x², where "a" is the scaling factor. Depending on the value of "a," the resulting parabola will be either stretched or compressed vertically, and may be reflected over the x-axis if "a" is negative.

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The answer is A. The normal distribution in its standardized form has a mean of 0 and a standard deviation of 1. This means that the distribution is centered around 0, and the spread of the data is determined by the standard deviation of 1. This is useful in statistical analysis because it allows us to compare data from different distributions on a standardized scale.

The normal distribution is a continuous probability distribution that is often used in statistical analysis. It is characterized by a bell-shaped curve and is symmetrical around its mean. In its standardized form, the normal distribution has been transformed to have a mean of 0 and a standard deviation of 1. This transformation is achieved by subtracting the mean of the distribution from each data point and dividing by the standard deviation. This standardization allows us to compare data from different normal distributions on a standardized scale.

The normal distribution has many properties that make it useful in statistical analysis. It is often used as a model for many real-world phenomena, such as the distribution of human height, IQ scores, and many others. The normal distribution is also useful because it is well understood and has many mathematical properties that make it easy to work with.

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The slope of the scenario is calculated as: -250.

Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).

Given the points:

(4, 7,000) = (x1, y1)

(6, 6,500) = (x2, y2)

Plug in the values

Slope (m) = (6,500 - 7,000) / (6 - 4)

Slope (m) = (-500) / (2)

Slope (m) = -250

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Answer:

5 days

Step-by-step explanation:

There are 16 quarts in 4 gallons of milk, so if they drink 3 quarts every day just divide 16 by 3 which will give you 5.3 but rounding your answer is 5 days.

I hope this helps!!

The surface area is approximately 161.47 square units.

To find the surface area generated by revolving the curve about the x-axis, we can use the formula:

S = 2π∫[a,b] f(x)√(1+[f'(x)]^2) dx

where f(x) is the given curve.

Here, f(x) = 36 - 2√(x^2+1) and we need to revolve it about the x-axis.

To find the limits of integration, we note that the curve is symmetric about the y-axis and therefore we can find the surface area of one half of the curve and multiply it by 2. So, we need to integrate from 0 to 4.

S = 2π∫[0,4] (36 - 2√(x^2+1))√(1+((x(-2x))/((x^2+1)^2))) dx

S = 2π∫[0,4] (36 - 2√(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx

Simplifying the integrand,

S = 2π∫[0,4] (36(x^4+1) - 2(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx

S = 2π∫[0,4] (36x^4-70x^2+34)√((x^4+4x^2+1)/(x^4+1)^2) dx

This integral is difficult to evaluate analytically, but it can be approximated using numerical integration techniques. Using a calculator or software, we find that the surface area is approximately 161.47 square units.

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There is no minimum weight for the tank since the weight depends on the thickness 'h' of the tank.

Let's assume the length and width of the square base of the tank are represented by 'x', and the height of the tank (thickness) is represented by 'h'. Since the tank has an open top, we don't need to consider the thickness of the top.

The volume of the tank is given as 32 \(in^3\):

Volume = length × width × height

      = x × x × h

      =\(x^{2}\) × h

Now, we need to express the weight of the tank in terms of its dimensions. The weight of the tank can be calculated by multiplying the volume by the density of the steel. Let's assume the density of the steel is represented by 'd'.

Weight = Volume × Density

      = (\(x^{2}\) × h) × d

To find the dimensions of the tank that result in the minimum weight, we can differentiate the weight equation with respect to 'x' and 'h', and then set the derivatives equal to zero:

dWeight/dx = 2xh × d = 0    (partial derivative with respect to x)

dWeight/dh = \(x^{2}\) × d = 0    (partial derivative with respect to h)

From the first equation, we get 2xh × d = 0, which implies either x = 0 or h = 0. Since the tank cannot have zero dimensions, we can conclude that xh ≠ 0.

From the the second equation, \(x^2\) × d = 0, we get x = 0, which is not a valid solution.

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im not a mod but answers A

Answer:

The answer is A. 7x-3

Step-by-step explanation:

and what do you mean by "ok now that he mods have nothing on me since this is a math question, THERE IS A GUY WHO IS BAITING GIRLS IN TO LOOK AT THEIR.... parts.... IN A ZO.OM MEETING. HE IS MY MOST RECENT FOLLOWING. CONTACT ALL THE MODS YOU CAN​" ???

When a = 2, b = 4, c = -5, and d = -5, the expression for 1/4b^3 - 1/5d^3 is 11.

How do you evaluate this expression?

When a = 2, b = 4, c = -5, and d = -5, the expression becomes:

1/4 * 4^3 - 1/5 * (-5)^3

= 1/4 * 64 - 1/5 * -125

= 16 - 25/5

= 16 - 5

= 11

So the expression evaluates to 11.

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Answer: sqrt of 7

Step-by-step explanation:

pythagorean theorem

3^2+b^2=4^2

A) Choosing a stratified random sample might be preferable to an SRS because;

Stratified random sampling would divide the population into stratas but the

SRS would not do so. The strata would be the type of room namely those

with water view and those with golf view.

B) The reason why a cluster sample would be a simpler option is because;

It will divide the population into multiple clusters that makes it easier to

work with unlike the SRS that generalizes. The clusters would be each of

the 30 floors.

We are told that the manager wanted to select 120 rooms and carry out a survey on each registered guest by asking how satisfied they were with the hotel. He decided to use a sampling method called SRS which means Simple Random Sampling.

Simple random sampling is defined as a sampling method where individuals or objects are selected randomly from a population thereby given each person or object an equal chance of selection.

A) Stratified Random sampling is a method of sampling that divides the population into smaller groups known as objects/stata. In this case Stratified random sampling would be preferred to SRS because the hotel rooms are divided into two types namely those that can view the water and those that can view the golf course and as such the Stratified random sampling would divide the population but the SRS would not do so.

B) Cluster sampling is when the population is divided into multiple groups known for assessment. The reason why it would be a simpler option is because there are 30 floors and they can be classified as clusters and surveyed per floor.

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Answer:

7/9 to a

.62 to b

10/9 to c

The correct answer to the question is (b) The predicted Y value will be below the mean for the Y scores. The coefficient -2 represents the slope of the line, which means that for every increase of 1 unit in X, Y will decrease by 2 units. The intercept 6 represents the point where the line intersects the Y-axis.

The equation y = -2X + 6 is a linear equation that describes the relationship between X and Y.Now, if the X value is above the mean (positive deviation), that means it is further to the right of the X-axis than the mean. This also means that the predicted Y value will be lower than the mean for the Y scores. This can be seen by plugging in a value that is above the mean into the equation, which will result in a negative value for Y. Therefore, the correct answer to the question is (b) The predicted Y value will be below the mean for the Y scores.
In summary, knowing the regression equation and the deviation of the X value from the mean allows us to predict the direction and degree of change in the Y value.

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Answer:

The final balance is $16,406.01.

The total compound interest is $8,406.01

Step-by-step explanation:

take the initial balance and multiply that by the interest then take 12 and multiply that times the previous answer.

The area of the side walk is is 138.16m²

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

The area of a circle is expressed as;

A = πr²

The area of the pathway = area of big circle - area of small circle

The diameter of the big circle = 20+4 = 24m

Area of big circle = 3.14 × 12²

= 452.16m²

Area of the small circle =

3.14 × 10²

= 314m²

therefore the of the path way = 452.16 - 314m²

= 138.16m²

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Answer: 60 weeks.

Step-by-step explanation: 150 divided by 2.50 = 60