Is (1, -3) a solution of f (x) = |x + 2|?​

Answer:

p = 19 ft

hope it's helpful

The value of the discriminant when a quadratic equation has exactly one real number solution is zero.

If a quadratic equation has exactly one real number solution, it means that the discriminant of the quadratic equation is equal to zero. The discriminant is a value calculated from the coefficients of the quadratic equation and determines the nature of its solutions.

For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant (D) is given by the formula:

D = b^2 - 4ac

When a quadratic equation has exactly one real number solution, it means that the discriminant is equal to zero:

D = 0

Setting the discriminant to zero, we can solve for the value of the discriminant:

b^2 - 4ac = 0

Therefore, the value of the discriminant when a quadratic equation has exactly one real number solution is zero.

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The interval containing the middle 95% of the simulation data is approximately 0.3426 to 0.5374.

To create an interval containing the middle 95% of the data based on the simulation results, we can use the concept of confidence intervals. Since the simulation was repeated 100 times, we can calculate the proportion of tails in each set of 100 flips and then find the range that contains the middle 95% of these proportions.

Let's calculate the interval:

Calculate the proportion of tails in each set of 100 flips:

Proportion of tails = 44/100 = 0.44

Calculate the standard deviation of the proportions:

Standard deviation = sqrt[(0.44 * (1 - 0.44)) / 100] ≈ 0.0497

Calculate the margin of error:

Margin of error = 1.96 * standard deviation ≈ 1.96 * 0.0497 ≈ 0.0974

Calculate the lower and upper bounds of the interval:

Lower bound = proportion of tails - margin of error ≈ 0.44 - 0.0974 ≈ 0.3426

Upper bound = proportion of tails + margin of error ≈ 0.44 + 0.0974 ≈ 0.5374

Therefore, the interval containing the middle 95% of the simulation data is approximately 0.3426 to 0.5374.

Now, we can compare the observed proportion of 44 tails in 100 flips with the simulation results. If the observed proportion falls within the margin of error or within the calculated interval, then it can be considered consistent with the simulation results. If the observed proportion falls outside the interval, it suggests a deviation from the expected result.

Since the observed proportion of 44 tails in 100 flips is 0.44, and the proportion falls within the interval of 0.3426 to 0.5374, we can conclude that the observed proportion is within the margin of error of the simulation results. This means that the result of 44 tails in 100 flips is reasonably likely to occur with a fair coin based on the simulation.

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Expressing x² + 4x – 7 in the form (x + p)² - q, where p and q are integers, we get p = 2 and Q= 11

Integer:

An integer is the number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). A negative number is the additive inverse of the corresponding positive number. In the language of mathematics, sets of integers are usually denoted by a bold Z.

To find: To express x² + 4x - 7 in the form (x+ p)² - q and determine the values of p and q.

The values of p and q are 2 and 11 respectively.

By completing the square method;

⇒ p = (4/2) = 2.

Therefore,

by expanding (x+ p)² i.e., (x+2)²

By expanding the above (x+2)² We have;

x² + 4x + 4

However,

The question is given as x²+4x-7

Therefore, by comparison between;

x² + 4x + 4 and x²+4x-7; we have:

x² + 4x + 4 = x²+4x-7

⇒ 4 - q = -7,

and, q = 7+4

⇒ q = 11

The values are p =2 and q = 11.

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Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

The volume of the rectangular prism is, \(\(105 in^3\)\).

What is the volume of rectangular prism?
The amount of three-dimensional space that an object takes up is its volume. Cubic units are used to measure volume. When calculating the volume of a rectangular prism, we multiply the prism's length, width, and height.

Rectangle prism volume = length x width x height.

The given rectangular prism has length 7, width 3 and height 5.

So, Volume = length x width x height = 7 x 3 x 5.

Volume = 105 cubic units.

Therefore, the volume of the given rectangular prism is 105 cubic units.

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Answer:

105 in

explanation:

did the same test.

The addition inequality 37 + x ≥ 42 can be used to determine how much taller William must be to ride the coaster, where x represents the additional height he needs to meet the height requirement.

To write an addition inequality to determine how much taller William must be to ride the coaster, we first need to convert his height to inches. Since he is 3 feet 1 inch tall, his height is (3 x 12) + 1 = 37 inches.

Let x be the amount of additional height William needs to ride the roller coaster. The inequality can be written as:

37 + x ≥ 42

This inequality ensures that William's total height after adding x must be greater than or equal to the required height of 42 inches to ride the roller coaster.

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9514 1404 393

Answer:

Step-by-step explanation:

The value in square brackets is evaluated using the product of powers rule:

  (7^5)(7^3) = 7^(5+3) = 7^8

Then the overall value is found using the power of a power rule:

  [7^8]^-4 = 7^(8(-4)) = 7^-32

Finally, the expression value is found using the negative exponent rule:

  7^(-32) = 1/7^32 = 1/1104427674243920646305299201

Answer:

512,000,000,000

Step-by-step explanation:

2*10 =

20

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

for this problem, try to put paraphasis in between each (20*20) then you'd get 400. So, put this in paraphasis (400*20) then you will get 8000. Next you would put the 8000 in paraphasis like this (8000*20). Do you get the pattern? If you do just do this nine times! Ik very confusing but this was the best way I learned w/out a calculator lol

20*20*20*20*20*20*20*20*20 =

512000000000

Answer:

2

Step-by-step explanation:

Scale factor tells how much the size of the figure increases or decreases. Part A shows that the larger figure is twice the size of the smaller figure. So, the scale factor of this dilation is 2.

Answer:

C

Step-by-step explanation:

If you plug the coordinate pairs in, C is the only one in which keeps both equations true.

Answer:

Step-by-step explanation:

Have the cash register print a pink arrow on a receipt every 15 minutes. Survey customers with a pink arrow on their receipts.

Its correct I got it right!!

The approach which is most likely to represent a sample that is representative of the population is option C. Have the cash register print a pink arrow on a receipt every 15 minutes. Survey customers with a pink arrow on their receipt.

Sampling methods are methods used to select a sample using specific methods. This includes various types of probability sampling and non probability sampling methods.

The random sample we need here is the sample of customers coming to a shop.

If we select the customers by the other options other than the third one, it will lead to various bias issues like sampling bias and research bias.

Hence the most appropriate method is to use option c.

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Answer: I think 288

Step-by-step explanation:

The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Answer:

The required equation is: \(\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}\)

Step-by-step explanation:

We need to find equation from the table given

x     f(x)

3     -5

7     -2

11     1

15    4

We can write equation in the form of \(y=mx+b\)

where m is slope and b is y-intercept.

Finding Slope

We can used the slope formula to find slope: \(Slope=\frac{y_2-y_1}{x_2-x_1}\)

From the table we have: \(x_1=3, y_1=-5, x_2=7, y_2=-2\)

Putting values and finding slope

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}\)

So, we get slope \(m=\frac{3}{4}\)

Now, finding y-intercept

Using the slope \(m=\frac{3}{4}\) and point (3,-5) we can find y-intercept

\(y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}\)

The y-intercept is \(b=\frac{-29}{4}\)

So, the equation having slope \(m=\frac{3}{4}\) and y-intercept \(b=\frac{-29}{4}\) will be:

\(y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}\)

The required equation is: \(\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}\)

Answer:

You buy the following from Best Buy:

1 new Chromebook for $550, 1 wireless mouse for $20, 1 wireless keyboard for $20

What is the Subtotal:

You use your Elite Members Best Buy credit card to save 6%, how much do you save:

What is the new Subtotal: $

Sales tax is 5%: $

What is the total: $

Step-by-step explanation:

Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

Answer:

800m

Step-by-step explanation:

If 100cm is equivalent to a meter (1 Meter). 8 Meters would be equivalent to 8 Meters multiplied by 100cm and divided by a meter (1 Meter)

Answer:  π

Step-by-step explanation:

The standard form of a secant equation is: y = A sec(Bx - C) + D   where

Given: F(x) = 2 sec(2x + 3)

                               ↓

                             B=2

Period = 2π/B

           = 2π/2

           = π

Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

The  small angle approximation is a mathematical technique used to simplify calculations involving angles that are close to zero.

It is used when the angle is so small that sine and cosine can be approximated by their linear terms. This is represented by the formula sinθ ≈ θ and cosθ ≈ 1.

For example, if we have an angle of θ = 0.1 radians, then we can use the small angle approximation to calculate the sine and cosine of the angle as follows:

sinθ ≈ θ = 0.1

cosθ ≈ 1 = 1

This approximation can be seen graphically by plotting the sine and cosine functions. On the graph, the small angle approximation is the line tangent to the curve at the origin. This line can be used to approximate the sine and cosine of small angles near the origin.

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Answer:

its simple.it is 20.

The statement a base class cannot contain a pointer to one of its derived classes is false because a base class can indeed contain a pointer to one of its derived classes.

In object-oriented programming, a base class can have a pointer to one of its derived classes. This is known as upcasting or polymorphism. Upcasting allows for the flexibility of treating derived class objects as instances of the base class.

By using pointers, a base class can refer to derived class objects and access their member functions and variables. This enables the base class to work with different derived classes without needing to know their specific types.

Pointers to derived classes can be stored in base class member variables or passed as function parameters. This allows for dynamic binding and the ability to invoke overridden functions based on the actual derived class type at runtime.

This concept is fundamental to achieving polymorphism and code reusability in object-oriented programming languages like C++ and Java. It facilitates the implementation of inheritance hierarchies and the ability to work with objects of different derived classes through a common base class interface.

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The correct radius of the cylinder is given by: Option B: 3.04 cm

The formula for the volume of a cylinder is given by the formula:

V = πr²h

where:

V is volume

r is radius

h is height

We are given the parameters as:

Height: h = 12.25 cm

Volume: V = 355 cm³

Thus:

355 = π * r² * 12.25

r² = (355)/(12.25π)

r² = 9.2245

r = √9.2245

r = 3.04 cm

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Answer:

Step-by-step explanation:

Given the dimension in feet

Width = 60 ft

Height = 20 ft

Given the dimension in inches

Width = 9in

Height = ?

To get the height in inches, we will use the equality postulate:

60 ft = 9in

20ft = x

Cross multiply

60x = 9*20

60x =180

x = 180/60

x = 3in

Hence the height of the screen will be 3inches

Answer:

1/2000

Step-by-step explanation:

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

The height of the beam is: \(h=12\: feet\)

Step-by-step explanation:

The radius of the tunnel is r = 15 feet

The distance of the beam from the center of the tunnel is:

\(d_{beam}=15-6=9\: feet\)

We have a right triangle, where:  

Let's use Pythagoras theorem.

\(15^{2}=9^{2}+h^{2}\)

\(h^{2}=15^{2}-9^{2}\)

\(h=\sqrt{15^{2}-9^{2}}\)

Therefore, the heigh of the beam is:

\(h=12\: feet\)

I hope it helps you!