The graph of \(x^{2} +1=0\)


a) intersects x-axis at two distinct points

b) touches x-axis at a point

c) neither touches nor intersects x-axis

d) either touches or intersects x-axis

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer:

-5, 4                           10, 1

Step-by-step explanation:

The location of point G on the given number line is 4.

Given that, partitions the directed line segment from F to D into an 8:5 ratio.

A measureable path between two points is referred to as a line segment. Line segments can make up the sides of any polygon because they have a set length.

Since, the line is 13 units and 8:5 is 13 parts each proportion is 1 unit.

Which means 8 parts and 5 parts are on the line.

So, 8+(-4)

= 8-4

= 4

Therefore, the location of point G on the given number line is 4.

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The required, (a) the improper integral is convergent and (b) the exact value of the integral will depend on the specific value of the positive real number a.

(a) To show that the improper integral \(\int_0^\infty (ln(x)/(x^2 + a^2)^2) dx\) is convergent, we can analyze its behavior at the endpoints.

As x approaches 0, the integrand becomes \(ln(x)/(x^2 + a^2)^2\). The natural logarithm function ln(x) approaches negative infinity as x approaches 0. The denominator \((x^2 + a^2)^2\) approaches \(a^4\) as x approaches 0. Therefore, the entire integrand approaches \(0/ (a^4) = 0\) as x approaches 0.

As x approaches infinity, the integrand \(ln(x)/(x^2 + a^2)^2\) approaches 0 as well. The logarithm function ln(x) grows very slowly compared to any power of x, and the denominator \((x^2 + a^2)^2\) grows faster than ln(x). Hence, the entire integrand approaches 0 as x approaches infinity.

Since the integrand approaches 0 at both endpoints, the improper integral is convergent.

(b) To find the exact value of the integral, we need to evaluate it. Unfortunately, there is no simple closed-form expression for this integral. It cannot be expressed in terms of elementary functions. Therefore, the exact value of the integral will depend on the specific value of the positive real number a.

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Answer:

1050 + (150)times the amount of jobs they do for you during that winter, for A. 0 + (200)times the amount of jokes they do for you during that winter, for B.

Step-by-step explanation:

Boom I would choose B because it would be cheaper, since we do most of the snow removal ourselves.

Answer:

i is about 23.5 so you could say c)

Step-by-step explanation:

The line segment is RST.

Since RS is 1/3 of the total length, ST is 2/3.

Therefore, 2(RS) is = ST, and RS + ST = RT.

2(3x -20) = 4x - 11

6x - 40 = 4x - 11

2x = 29

x = 14.5

3(14.5) - 20 = 23.5

4x - 11 = 47

2(23.5) = 47

The length of RS is 23.5.

The length of ST is 47.

The total length of RT is 70.5.

Cleomenius.

Answer:

Its 6.3 units

Step-by-step explanation:

i took the test

Omi calculator will help u

Answer:

  see attached

Step-by-step explanation:

Relative to P, rotation 90 degrees is equivalent to the transformation ...

  (x, y) ⇒ (-y, x)

In the attached, we have labeled a couple of points so you can see how they moved.

  A(1/2, -2 1/2) ⇒ A'(2 1/2, 1/2)   . . . .   for example

\(\dfrac{\left(x^0 y^{\tfrac 23} z^{-2} \right)^{\tfrac 32}}{\left(x^2 z^{\tfrac 12} \right)^{-6}}\\\\\\=\dfrac{1\cdot \left( y^{\tfrac 23}\right)^{\tfrac 32} \cdot \left(z^{-2} \right)^{\tfrac 32}}{\left(x^2 \right)^{-6} \cdot \left( z^{\tfrac 12} \right)^{-6}}~~~~~~~~~~~~~~~~~~;\left[(ab)^m = a^m b^m\right]\\\\\\=\dfrac{y^{1} \cdot z^{-3}}{x^{-12} \cdot z^{-3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[(a^m)^n = a^{mn}\right]\\\\\\=\dfrac{y}{x^{-12}}\\\\\\\)

\(=\dfrac{y}{\tfrac 1{x^{12}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m} } \right]\\\\\\=yx^{12}\)

Answer:

\(M=\frac{280}{140} =2\)

\(C=2+5=7\)

(2 Movies and 7 Commercials)

Step-by-step explanation:

Let's represent every time Carson's songs are played in a commercial as C and in movies as M.

Set up the following equations:

\(20C+120M=380\)  (1)

\(C=M+5\)   (2)

Substitute equation 2 for equation 1:

\(20(M+5)+120M=380\)

Distribute:

\(20M+100+120M=380\)

Simplify:

\(140M=280\)

Divide both sides by 140:

\(M=\frac{280}{140} =2\)

Substitute 2 as M back into either original equation, I will use (2):

\(C=2+5=7\)

Answer:

Step-by-step explanation:

Given

Find

Greatest Common Factor

Explanation

Factors of

common factors are

Final Answer

Hence , the greatest common factor is

Answer:

72

Step-by-step explanation:

The inequality that shows the result of solving -ax/b > c - d for x is x < (b(c - d)) / a. To solve the inequality -ax/b > c - d for x, we'll perform some algebraic manipulations. Here's the step-by-step process:

Multiply both sides of the inequality by b to eliminate the denominator:

-ax > b(c - d)

Divide both sides by -a. Since a is positive, the direction of the inequality will flip:

x < (b(c - d)) / -a

Note: When dividing by a negative number, the inequality direction is reversed.

However, we want to express the result in terms of a positive coefficient for x. To achieve this, we can multiply both sides of the inequality by -1:

-x > -((b(c - d)) / a)

Finally, multiplying both sides by -1 again will reverse the inequality direction:

x < (b(c - d)) / a

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Answer:

7% sales tax

Step-by-step explanation:

If the pencils cost $6, then the sales tax costs $6.42 - $6 = $0.42. To find the rate, we must divide $0.42 by $6. $0.42/$6 = 0.07. 0.07 is 7%.

This leads to the conclusion that x=5 is the answer to the given function problem.

A link where every x is related to a distinct y variable is called a function. It's noteworthy that when utilizing the similar y and different xs, the inverse is not possible. Except for vertical and horizontal lines, all linear equations can be expressed as functions.

Here,

a function that we've provided

f(x) = 5 - 25x / x

First, the x common factor in the numerator and denominator will be removed, and the resulting fraction will be zero.

5x -25

The common factor, which is 5, will be removed once more, and we will receive 5.

5(x-5)

In this case, we'll compare the expression to zero.

5(x-5) = 0

We shall discover x's value.

x=5

As a result, x=5 is the answer to the function issue that was presented.

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The complete question is "Find the x value in the given function

f(x) = 5 - 25x / x  on the 16 pages - 9 "

Answer:

3 is the correct answer hope it helps

The system of inequalities that best models the graph is given as follows:

B. y > x - 4 and y < -2/3x - 2.

Both bounds are dashed, hence the intervals are open.

The upper bound of the solution is the decreasing line, with slope of -2/3 and intercept of -2, hence:

y < -2/3x - 2.

The lower bound of the solution is the increasing line, with slope of 1 and intercept of -4, hence:

y > x - 4.

Hence option b is correct.

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Answer:

1

Step-by-step explanation:

Answer:

Option 4

Step-by-step explanation:

This is a question on angles and their properties

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

Answer: \((x+10)(x-10)\)

Step-by-step explanation: Difference of squares is an important element in understanding square functions. In order to identify difference of squares, the equation should be given in the form a^2-b^2. You can factor it completely when b^2 can be square rooted perfectly and write the factored expression as (a-b)(a+b) as I have done above.

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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The justification for the angle will be wrong because the angle does not depend on the radius of the circle.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Jaime makes the following claim. An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches.

The justification for the angle will be wrong because the angle does not depend on the radius of the circle.

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Triangles can be formed when three angles add up to 180 degrees. Therefore, three angles with values of 25 degrees, 35 degrees, and 120 degrees cannot form a triangle as the sum of the angles is only 180 degrees.

However, if the angles are assumed to be part of a larger triangle, then it is possible to calculate the number of triangles that can be made.To begin, we need to find the total area of the triangle. The area of a triangle is equal to the base times the height divided by two. To find the base and height, we need to use trigonometry. The base of the triangle is equal to the sine of the angle of 25 degrees multiplied by the length of the side opposite to it. The height is equal to the sine of the angle of 120 degrees multiplied by the length of the side opposite to it.Once the base and height have been calculated, the area of the triangle can be found. In this case, the area of the triangle is equal to 8.6 square units.Now that the area of the triangle is known, we can calculate the number of triangles that can be made. The total area of the triangle is equal to the sum of the areas of the individual triangles. Therefore, the number of triangles that can be made is equal to the total area of the triangle divided by the area of each individual triangle. In this case, the number of triangles that can be made is equal to 8.6 divided by the area of each individual triangle. This result is equal to 2.15, which means that two and a quarter triangles can be made with the angles of 25, 35, and 120 degrees.

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The study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study, resulting in a Type I Error (false positive) of 1.67, meaning an overestimation of the true relative risk of the association by 67%.

In this case, the study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study. As a result, we can expect the relative risk to be overestimated. This is known as a Type I Error (false positive) and can be calculated using the formula:

Type I Error = (4.0 – 1.5) / 1.5 = 1.67

In other words, the study overestimated the true relative risk by 67%. This is an example of an inflated relative risk due to a lack of representativeness of the sample population.

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The request is to download a document and complete the proof of the Triangle Sum Theorem. After finishing the proof, the completed file should be saved for upload on a webpage.

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. To complete the proof, it is necessary to provide a logical and coherent argument that supports this theorem. The document provided likely contains a partially completed proof, and the task is to finish it.

The proof of the Triangle Sum Theorem typically involves using the properties of parallel lines and alternate interior angles. By extending one side of the triangle, parallel lines can be created that intersect with the other sides. This forms interior and exterior angles that can be related to the interior angles of the triangle. Through geometric reasoning and the use of angle relationships, the proof should demonstrate that the sum of the interior angles of a triangle equals 180 degrees.

Once the proof is completed, the document should be saved for upload on the webpage specified, most likely for evaluation or further review. It is important to follow any instructions provided regarding the file format or naming conventions for the upload.

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Answer:

\(\Huge \fbox{72 mph}\)

Step-by-step explanation:

Step 1:

Convert \(\bold{32 m/s}\) to \(\bold{km/h}\) by multiplying by 3.6 (since \(\bold{1 m/s}\) = \(\bold{3.6 km/h}\))

\(\large \text{32 m/s $\times$ 3.6 = 115.2 km/h}\)

Step 2:

Convert \(\bold{115.2 km/h}\) to \(\bold{mph}\) using the given conversion factor of \(\bold{8 km/h = 5 mph}\)

\(\large \text{115.2 km/h $\div$ 8 km/h = 14.4}\\\text{14.4 $\times$ 5 mph = 72 mph}\)

Therefore, \(\bold{32 m/s}\) is equivalent to \(\bold{72 mph}\).

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

In the standard conversion unit, 32 m/s equals 72 mph in mph

The conversion equation is given as

\(\sf 8 \ km/h = 5 \ mph\)

Convert 8 km to meters

So, we have the following equation

\(\sf 8 \times 1000 \ m/h = 5 \ mph\)

Evaluate the products

So, we have the following equation

\(\sf 8000 \ m/h = 5 \ mph\)

Convert 1 hour to seconds

So, we have the following equation

\(\sf 8000 \ m/3600 s = 5\ mph\)

Evaluate the quotient

So, we have the following equation

\(\sf \dfrac{20}{9} \ m/s = 5 \ mph\)

Multiply both sides by 9/20

\(\sf 1 \ m/s = \dfrac{9}{20} \times 5 \ mph\)

Multiply both sides by 32

\(\sf 32 \times 1 \ m/s = 32 \times \dfrac{9}{20} \times 5 \ mph\)

Evaluate the products

\(\sf 32 \ m/s = 72 \ mph\)

Hence, the equivalent of 32 m/s in mph is 72 mph

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Answer:

10,395

Step-by-step explanation:

Hope this helps!! :))

Answer:

\(\sqrt{88}\)

Step-by-step explanation:

The geometric mean of 11 and 8 is equal to \(\sqrt{88}\).

According to the question it is clear that we have to calculate the geometric mean of two positive numbers 11 and 8.

The geometric mean of two positive numbers a and c is the positive number b in such a way that it satisfies the condition

\(\frac{a}{b}=\frac{b}{c}\)

The geometric mean of a and b is √ab if a and b are both positive numbers and it will be −√ab if a and b are negative numbers.

The geometric mean is the positive square root of the product of two numbers.

For a square the geometric mean of two numbers a and b, is the length of one side of a square whose area is equal to the area of a rectangle with the sides of a and b lengths.

If we talk about the n numbers then the geometric mean is the nth root of the product of n numbers. If n positive values are given then the geometric mean is the nth positive root of the product of that n numbers.

So, the geometric mean is equal to \(\sqrt{a.b}\)

Here, a = 11 and b = 8

The geometric mean of this is equal to = \(\sqrt{11.8}\) = \(\sqrt{88}\)

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Answer:

80%

Step-by-step explanation:

from $25 to $45

$45/$25 = 1.8

$25 x 1.8 = $45

therefore, the increase is 80%

The type of sampling that assumes all members of a population have an equal chance of being selected for participation in the study is called Simple Random Sampling.

In Simple Random Sampling, each individual in the population has an equal probability of being chosen as a participant, and the selection process is unbiased. This method ensures that the sample is representative of the entire population, thus allowing for valid conclusions to be drawn about the population as a whole.

Here is a step-by-step explanation of how Simple Random Sampling is conducted:

1. Define the population: First, clearly identify the population you want to study.

2. Assign a unique number to each member: To ensure equal chances of selection, assign a unique number to every individual in the population.

3. Determine the sample size: Decide how many participants you need in your study based on factors like required level of accuracy and available resources.

4. Use a random selection method: Use a random selection method such as a random number generator, a lottery system, or a random number table to pick the required number of participants.

5. Collect data from the selected individuals: Once the participants are chosen, collect data from them using appropriate research methods like surveys, interviews, or experiments.

By using Simple Random Sampling, you can obtain a sample that is unbiased and representative of the entire population, which is essential for accurate and reliable research findings.

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Answer:

16 cm

Step-by-step explanation:

\(12^2+x^2=20^2\\144+x^2=400\\x^2=256\\\sqrt{x^2} =\sqrt{256} \\x=16\)

The measure of the other leg is 16 centimeters.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

The hypotenuse of a right triangle measures 20 cm and one of its legs measures 12 cm.

Applying Pythagoras' theorem,

The measure of other leg = √(20)² - (12)²

The measure of other leg = √(400-144)

The measure of other leg = 16 centimeters.

Therefore, the other leg is 16 centimeters.

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