What is equidistant from a fixed point?

The input value that produces the same output value for f(x) and g(x) on the graph is x = 1.To find the input value that produces the same output value for both functions, we need to determine the x-coordinate of the point(s) where the two lines intersect.

These points represent the values of x where f(x) and g(x) are equal.

The line labeled f(x) passes through the points (-2, 4), (0, 2), and (1, 1). Using these points, we can determine the equation of the line using the slope-intercept form (y = mx + b). Calculating the slope, we get:

m = (2 - 4) / (0 - (-2)) = -2 / 2 = -1

Substituting the point (0, 2) into the equation, we can find the y-intercept (b):

2 = -1(0) + b

b = 2

Therefore, the equation for f(x) is y = -x + 2.

Similarly, for the line labeled g(x), we can use the points (-3, -3), (0, 0), and (1, 1) to determine the equation. The slope is:

m = (0 - (-3)) / (0 - (-3)) = 3 / 3 = 1

Substituting (0, 0) into the equation, we can find the y-intercept:

0 = 1(0) + b

b = 0

Thus, the equation for g(x) is y = x.

To find the input value that produces the same output for both functions, we can set the two equations equal to each other and solve for x:

-x + 2 = x

Simplifying the equation:

2x = 2

x = 1.

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Answer:

Comprobar explicación

Check Explanation

Step-by-step explanation:

Los números negativos son números menores que 0. Son muy importantes en la naturaleza y en cualquier trato con los números. Por lo general, se escriben con un signo menos delante de ellos.

Las situaciones en las que el uso de números negativos son absolutamente necesarios incluyen

1) En los negocios, los números negativos se utilizan para indicar la deuda y la salida de efectivo.

2) En los circuitos eléctricos, se usan números negativos para describir el voltaje nominal cuando se invierten las polaridades de la batería.

3) En mediciones de temperatura para indicar temperaturas inferiores al punto de congelación del agua, especialmente en la escala Celsius (0°C).

4) Para indicar profundidades debajo del nivel del mar. El nivel del mar generalmente se designa como nivel 0 en términos de elevación.

5) En la numeración de los pisos debajo de la planta baja para un edificio alto.

6) En el análisis económico general, se utilizan para indicar una disminución de la economía, el PIB del país o un déficit en el presupuesto.

- En el análisis matemático general, los cálculos y las manipulaciones, los números negativos se usan ampliamente y son muy importantes.

- En química, los números negativos se utilizan para indicar la carga en los aniones (iones negativos).

¡¡¡Espero que esto ayude!!!

English Translation

6 situations in which the use of negative numbers is necessary.

Solution

Negative numbers are numbers that are lesser than 0. They are very important in nature and in any dealings with numbers. They are usually written with a minus sign in front of them.

The situations in which the use of negative numbers are absolutely necessary include

1) In business, negative numbers are used to indicate debt and outflow of cash.

2) In electrical circuits, negative numbers are used to describe the rated voltage when the polarities of the battery are reversed.

3) In temperature measurements to indicate temperatures lesser than the freezing point of water especially on the Celsius scale (0°C).

4)To indicate depths below the sea level. The sea level is usually designated to be 0 level in terms of elevation.

5) In the numbering of the floors below the ground floor for a tall building.

6) In general economic analysis, they are used to indicate a decline in the economy, country's GDP or deficit in budget.

- In general mathematical analysis, calculations and manipulations, negative numbers are used very extensively and are very important.

- In chemistry, negative numbers are used to indicate the charge on anions (negative ions).

Hope this Helps!!!

Answer:

24,000

Step-by-step explanation:

first multiply 80,000 and 30 because 15 + 15 from two years is 30.

Then you get 2400000 then divide that by 100 which gives you

24,000 as your answer.

Answer:191/94 i hope this helps!!(✿◠‿◠)

Answer:

Graph b.

Step-by-step explanation:

B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.

Answer:

steps below

Step-by-step explanation:

It's easier to prove from right side to left side. If you insist to prove from left to right, you can just reverse the calculation from bottom to the top.

\(cot^{2} a * cos^{2}a \\= cot^{2} a * (1-sin^{2} a)\\= cot^{2} a - cot^{2} a*sin^{2} a\\= cot^{2} a - \frac{cos^{2} a}{sin^{2}a} *sin^{2} a\\= cot^{2} a - cos^{2} a\)

In summary, the relationships between the corresponding sides and angles of similar triangles are: Corresponding sides are proportional and congruent.

When two triangles are similar, the corresponding sides of the triangles are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles is equal. Similarly, the corresponding angles of similar triangles are congruent. This means that the angles in the two triangles that correspond to each other are equal in measure.

When two triangles are similar, it means that they have the same shape but possibly different sizes. The concept of similarity implies that the corresponding sides of the triangles have the same proportional relationship.

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Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( \(\frac{x-\mu }{\sigma}\)  > \(\frac{2.3-\mu }{\sigma}\) )

P (z  > \(\frac{2.3-1.9 }{0.3}\)  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( \(\frac{x-\mu }{\sigma }\) <  \(\frac{a-\mu }{\sigma }\) )

\(\frac{a-1.9 }{0.3 } = -1.55\)

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is

A = 1/2 × b × h

A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.

The formula to determine area of a triangle of base b and height h is

A = 1/2 × b × h

Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.

h = 2×A/ b

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Answer:

Answer is 11. You have to add the 4 and 7.

In rectangles all sides are either perpendicular or parallel, so you know that the missing side is equal to the bottom 2 horizontal sides added up.

4 + 7 = 11.

The missing side is 11cm.

Answer: x=

Step-by-step explanation:

(17x+3) and (16x+6) are alternate exterior angles, which means the measures of their angles are congruent (equal).

Therefore, 17x+3 = 16x+6

You can then solve it out.

17x+2=16x+6

-16x     -16x

x+2=6

  -2 -2

x=4.

You can check this by substituting it back into each equation and getting 70 for each.

A  conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.

The likelihood that any two events will occur is equal to the sum of the probabilities of each event separately, less the probability that the two occurrences will meet. However, if two occurrences are incompatible with one another, then there is a zero probability of the two events intersecting, therefore the likelihood that either one or the other will occur is equal to the sum of the two individual probabilities.

To calculate conditional probability, use the following formula:

p( b | a ) = p( a ∩ b )/ p(a)

It is known that if two events A and B are independent, then p(a ∩ b) = p (a) . p(b)

So, p(b | a) = [p (a) . p(b)]/p(a) = p(b)

Thus, it is concluded that a conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.

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Answer:

a) 126degrees

b) 47degrees

Step-by-step explanation:

The sum of two supplementary angles is 180 degrees.

Let the other angle be x

x  + 54 = 180

x = 180 - 54

x = 126degrees

The supplement is 126degrees

b) The sum of two complementary angles is 90 degrees.

Let the other angle be y

y  + 43 = 90

y = 90 - 43

y = 47degrees

Hence the complement is 47 degrees

In conclusion, we have shown that a vector d ∈ R^n is a feasible direction at x in the standard form polyhedron P if and only if Ad ≤ 0 and di ≤ 0 for every i such that r_i > 0.

To prove that a vector d ∈ R^n is a feasible direction at x in the standard form polyhedron P = {x | Ex ≤ l, Ax = b, x ≥ 0}, it must satisfy the condition Ad ≤ 0 and d ≥ 0 for every index i such that r_i > 0, where r_i represents the i-th row of the matrix E.

First, let's assume that d is a feasible direction at x. This means that for every feasible point x, there exists an ε > 0 such that x + εd satisfies the constraints of P.

Since x satisfies Ax = b, we have Ad = A(x + εd) = Ax + εAd = b + εAd. Since x satisfies Ex ≤ l, we have Ex + εEd ≤ l. Since x ≥ 0 and d ≥ 0, we have x + εd ≥ 0.

Now, consider the i-th row of the inequality constraint matrix E. If r_i > 0, then the i-th constraint is active at x. Since x + εd satisfies the constraints, we have E_i(x + εd) ≤ l_i, which can be rewritten as E_ix + εE_id ≤ l_i.

Since x satisfies Ex ≤ l, we have E_ix ≤ l_i. Combining this with E_ix + εE_id ≤ l_i, we obtain εE_id ≤ 0. As ε > 0, this implies E_id ≤ 0. Since ε and E_i are non-negative, we have di ≤ 0 for r_i > 0.

Therefore, we have shown that Ad ≤ 0 and di ≤ 0 for every i such that r_i > 0.

Now, let's prove the converse. Assume that Ad ≤ 0 and di ≤ 0 for every i such that r_i > 0. We need to show that d is a feasible direction at x.

Consider any feasible point x in P. Since x satisfies Ax = b and Ex ≤ l, we have Ad = A(x + εd) = Ax + εAd = b + εAd, and Ex + εEd ≤ l. As Ad ≤ 0 and di ≤ 0 for every i such that r_i > 0, we have Ad ≤ 0 and di ≤ 0 for all i, regardless of whether r_i > 0 or not.

Therefore, x + εd satisfies the constraints of P for any ε > 0. Hence, d is a feasible direction at x.

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Answer:

176.6 inches.

Step-by-step explanation:

15 is the diameter, so 15/2 is 7.5 which is the radius

A of a circle is 3.14 x r^2

7.5^2=56.25

56.25 x 3.14=176.625

rounded makes it 176.6

A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.

Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:

1. Enter the lengths of the sides of the right triangle into the calculator.

2. Select the angle for which you want to find the trigonometric ratios.

3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.

Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.

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A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.

Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:

1. Enter the lengths of the sides of the right triangle into the calculator.

2. Select the angle for which you want to find the trigonometric ratios.

3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.

Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.

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Answer:

x = - 8

Step-by-step explanation:

x - 124 = 9(2x + 3) - 15

x - 124 = 18x + 27 - 15

x - 124 = 18x + 12

x - 124 + 124 = 18x + 12 + 124

x = 18x + 136

x - 18x = 18x - 18x + 136

- 17x = 136

- 17x ÷ - 17 = 136 ÷ - 17

x = - 8

Answer:

A.32.10

Step-by-step explanation:

You have to remember to subtract the $35 then start to figure out how much he paid every month for a year.

The independent events P(AUB) = P(A) + P(B)  is C.0.55  

sincerely,

P(A) = 0.35 and P(B) =0.20

P(AUB) = P(A) + P(B)

P(AUB) = 0.55

To complete question is:

A and B are independent events with P(A) = 0.35 and P(B) =0.20,

then,

P(AUB) = Select one:

a. 0.07. b.0.62 c.0.55. d. 0.48.

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For a sample of hospitals related to shorten the average length of stay (LOS) of their patients,

A) The 90% confidence interval to estimate the population mean LOS are 3.3362 and 4.2638.

B) The Interpreted interval in terms of this application is equals to (3.3362,4.2638).

C) The meaning of phrase "90% confidence interval" is number that fall within the upper as well as lower boundaries of distribution.

We have a health insurers and federal government ordered to hospitals regarding to short or decrease the average length of stay of their patients.

population Mean of LOS = 4.5 days

Sample size of hospitals, n = 20

Sample mean, \( \bar x\) = 3.8days

Standard deviations, \( \sigma\)

= 1.2 days

A) The population estimate mean LOS for the state's hospitals at 90% confidence interval,

The degrees of freedom, df = 20 -1

= 19

90% confidence interval then the confidence interval is 0.90. So, 1 −∝

= 0.90

=> ∝ = 0.1

=> ∝/2= 0.05

The critical t value for confidence 0.05 and degree of freedom 19 is equals 1.72.

Using the confidence interval formula,

\( \bar x ± t_{(0.05, 19)} \frac{\sigma}{\sqrt{n}}\)

\( 3.8 ± 1.729\frac{1.2}{\sqrt{20}}\)

= (3.3362,4.2638)

So, required values are 3.3362 and 4.2638.

(b) In terms of this application, the interval, 90 percent confident that the populations mean length of remain (LOS) for the state’s hospitals(μ) lies among 3.3362 and 4.2638.

c) The term 90% confidence interval expresses a number that will fall within the upper as well as lower boundaries of a probability distribution.

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Answer:

1

Step-by-step explanation:

Mark as brainliest

Answer:

7k

Step-by-step explanation:

If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.

To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.

The total cost of the dryer can be calculated as follows:

Cost of dryer = $698.27

Total credit card charges = 12 x $1.25 = $15

Total late fees = 4 x $35 = $140

Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees

= $698.27 + $15 + $140

= $809.27

Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.

So, correct option is A.

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Answer:

3.2 x 10^13

Step-by-step explanation:

(8x10^4)(4x10^8)

reorder the terms using the commutative property

(8x4)x(10^4x10^8)

multiply

32x (10^4 x 10^8)

= 32 x 10^4+8

= 32 x 10^12

now convert to scientific notation

=3.2 x 10^13

Answer:

step 1. mHT = 2(74) = 148°. the arc measures twice the angle when crossing the circle.

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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The equation is x² + 11x = 12. Here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have an area of border  48 square inches.

Menu dimensions without border =  13-inch by 9-inch

The area of the border can be expressed by the equation:

area of border = area of rectangle with border—area of rectangle without

                            border

48 = (13 + 2x)(9 + 2x) - 13×9

\(\rm 48=4x^2+44x\)

After simplification:

\(\rm 4x^2+44x-48=0\)

or

x² + 11x = 12

Find the solution of the above quadratic equation:

x = 1 or x = -12(width cannot be negative)

Width should be 1 inches.

We have given x = 2.5 it is not reasonable for the border to be 2.5 inches wide. Due to the cost of printing, the border should have an area of 48 square inches.

Thus, the equation is x² + 11x = 12 here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

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The equation of the line is y = 13/6x - 5

From the question, we have the following parameters that can be used in our computation:

Points: (0, -5) and (6, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

c = -5

So, we have

y = mx - 5

Also, we have

(x, y) = (6, 8)

This means that

8 = m x 6 - 5

So, we have

6m = 13

This gives

m = 13/6

So, we have

y = 13/6x - 5

Hence, the equation is y = 13/6x - 5

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