−323=x−114

What is the solution to the equation?

Enter your answer as a simplified mixed number in the box.

Answer:

1 (a f+bc)/bf

2 ac/bf

3 a f/bc

Step-by-step explanation:

Answer:

2x²+7x-4

Step-by-step explanation:

(2x-1)(x+4)

=2x(x+4)-1(x+4)

=2x²+8x-x-4

=2x²+7x-4

, the points where f(x) has a horizontal tangent line are (0, f(0)) and (-2, f(-2)).To find the points where the function f(x) has a horizontal tangent line, we need to find the values of x where the derivative of f(x) equals zero.

(a) For f(x) = (x^2 - 4x)^(3/2):

First, we find the derivative of f(x):

f'(x) = 3/2(x^2 - 4x)^(1/2) * (2x - 4)

Setting f'(x) = 0:

3/2(x^2 - 4x)^(1/2) * (2x - 4) = 0

Now we solve for x:

x^2 - 4x = 0

x(x - 4) = 0

x = 0, x = 4

Therefore, the points where f(x) has a horizontal tangent line are (0, f(0)) and (4, f(4)).

(b) For f(x) = (x^2 + 2x)^(3/1):

Similarly, we find the derivative of f(x):

f'(x) = 3(x^2 + 2x)^(2/1) * (2x + 2)

Setting f'(x) = 0:

3(x^2 + 2x)^(2/1) * (2x + 2) = 0

Now we solve for x:

x^2 + 2x = 0

x(x + 2) = 0

x = 0, x = -2

Thus, the points where f(x) has a horizontal tangent line are (0, f(0)) and (-2, f(-2)).

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Answer:

Step-by-step explanation: there you go

Let:

Op = Original price

Dp = Discount price

r = percent of discount

The discount price will be, the original price minus the product of the original price and the percent of discount, so:

The percent of discount of the item is 43%

10) Using the equation 98.4 = (12.3)8, it costs $12.30 (cost per unit) per uniform.

11) Using the equation 26.70 = k6, the cost of one bag of apples (unit rate) is $4.45.

The unit rate is the quotient of the total cost divided by the number of items contained.

The unit rate is the same as the average or mean of a data set.

We describe the unit rate as the slope of a linear equation.

The unit rate shows the constant rate of change in an equation.

The total cost of 8 uniforms = 98.4 = (12.3)8

The cost per uniform = 12.30 (98.4/8)

The total cost of 6 bags of apples = 26.70

The cost per unit = 4.45 (26.70/6)

Thus, the unit rate or cost is also described as the variable unit cost.

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Answer:

8.64

Explanation: I just did the math

Answer:

\(2.28*10^7\)

Step-by-step explanation:

\((2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7\)

Answer:

228,000

Step-by-step explanation:

(2.4x10^3) x (9.5x10^3)

(2.4x100) x (9.5x100)

240x950

228,000

Answer:

y - 7 = - 1(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 1 and (a, b) = (4, 7) , thus

y - 7 = - (x - 4)

The equation of line in the point-slope form is y = -1x + 11

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be P = P ( 4 , 7 )

Let the slope of the line be m = -1

So , the equation of line is given by the formula

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -1 ( x - 4 )

On simplifying the equation , we get

y - 7 = -1x + 4

Adding 7 on both sides of the equation , we get

y = -1x + 11

y = -x + 11

Therefore , the value of A is y = -x + 11

Hence , the equation of line is y = -x + 11

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Answer:

Step-by-step explanation:

120q(5k/13q)=600k/13

46 2/13 kents

Answer:

c

i did it on i ready

Answer:

Top left

Step-by-step explanation:

For every x value, the y values decrease by 2

Answer:

True

Step-by-step explanation:

B would be the midpoint because it is in the middle of both showing thats where both points connect.

Answer:

3.=300%

0.35=35%

4.=400%

0.812=81.2%

Answer:

30%.34  81%.02

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Answer:

y intercept is at 4, and x intercept at -2

Step-by-step explanation:

4x-2y=-8,

→The y-intercept is where the graph intersects the y axis so the x coordinate there is 0.

We substitute x= 0 in the 4x-2y=-8 and find y

4*0 -2y = -8, multiply

      -2y = -8, divide both sides by -2

          y = 4

→The x-intercept is where the graph intersects the x-axis so the y coordinate there is 0.

We substitute y = 0 in the 4x-2y=-8 and find x

4x -2*0 = -8, multiply

       4x = -8, divide both sides by 4

          x = -2

The equation of the locus of the moving point that maintains a distance of 4 units from the X-axis is y = ±4, representing two parallel horizontal lines.

To find the equation of the locus of a point that always maintains a distance of 4 units from the X-axis, let's analyze the given information.

Let P(x, y) be the moving point and Q(x, 0) be the fixed point on the X-axis. The distance between P and Q is denoted by PQ. According to the problem, PQ is always 4 units.

Using the distance formula, we have:

PQ² = (x - x)² + (y - 0)²

Since the x-coordinate of both P and Q is the same (x - x = 0), the equation simplifies to:

PQ² = y²

Substituting the value of PQ as 4 units:

4² = y²

16 = y²

Taking the square root of both sides:

\(\sqrt{16 } = \sqrt{y^2}\)

±4 = y

Therefore, the y-coordinate of the moving point P can be either positive or negative 4, giving us two possible solutions for the y-coordinate.

Hence, the locus of the moving point P that maintains a distance of 4 units from the X-axis is given by the equation:

y = ±4

This equation represents two horizontal lines parallel to the X-axis, with y-coordinates at +4 and -4. Any point (x, y) on these lines will always be at a constant distance of 4 units from the X-axis.

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The decibel level of the sound from the leaf blower is approximately 104 dB.

The decibel level of a sound is measured in logarithmic units and is defined as the ratio of the sound's intensity to a reference intensity that is just barely audible to the human ear.

The decibel level (dB) of a sound is given by the equation 10 log(I/I_0), where I is the intensity of the sound being measured and I_0 is the reference intensity.

For this problem, the intensity of the sound from the leaf blower is given as 28 × 10^-2 W/m².

The reference intensity is generally taken to be 1 × 10^-12 W/m².

Substituting these values into the formula, we get: 10 log(28 × 10^-2 / (1 × 10^-12)) = 10 log(28 × 10^10) = 10 (10.447) ≈ 104.47

Therefore, the decibel level of the sound from the leaf blower is approximately 104 dB.

Decibel (dB) is a unit used to measure the intensity or level of sound, as well as the ratio of power or amplitude of a signal. It is a logarithmic unit that compares the measured quantity to a reference level. The decibel scale is logarithmic because the human perception of sound intensity is not linear. A change of 1 dB is considered the smallest perceptible difference in sound level, while a change of 10 dB is perceived as approximately a doubling or halving of loudness.

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Using average to predict the population in 1820, the population is 10 million people

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

Population in 1810 = 7 million people

Population in 1830 = 13 million people

Using average, we have

Population in 1820 = 1/2 * (7 million people + 13 million people )

Evaluate

Population in 1820 = 10 million people

Hence, the population in 1820 is 10 million people

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Answer:

X=12

Step-by-step explanation:

X²=X×X, so 12×12=144

Answer:  \(x=12\)

Step-by-step explanation:

\(x^{2} =144\)

\(x=\sqrt{144}\)

\(x=12\)

Answer

y=3(x-2)+3

Step by step

y=m(x-h)+k

y=3(x-2)+3

The three congruence postulates are ASA, SAS, and SSS Theorems.

Two triangles are congruent if their corresponding sides are equal in length and their corresponding interior angles are equal in measure.

1) ASA Theorem (Angle-Side-Angle)

The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles.

2) SAS Theorem (Side-Angle-Side)

By applying the Side Angle Side Postulate (SAS), you can also be sure your two triangles are congruent. Here, instead of picking two angles, we pick a side and its corresponding side on two triangles.

The SAS Postulate says triangles are congruent if any pair of corresponding sides and their included angle are congruent.

3) SSS Theorem (Side-Side-Side)

Side Side Side Postulate (SSS) says triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle.

Thus, the three congruence postulates are ASA, SAS, and SSS Theorems.

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Answer:

(x - 5)² = 39

Step-by-step explanation:

Given

x² - 10x = 14

To obtain an equivalent equation use the method of completing the square.

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 5)x + 25 = 14 + 25

(x - 5)² = 39

I believe that the answer you are looking for is (x-5)²-39, if you use the completing the square method.

Solution:

x²-10x=14

Transferring 14 from the right side to the left side,

x²-10-14=0

Squaring the equation,

(x-5)²-39, or (x-5)²=39 (Depends on how you prefer to write it).

So, that is the final answer. I hope this helped. If you have any questions about the answer, please let me know. Enjoy your day and take care!

The characteristics of the correlation coefficient are A. It must be between -1 and 1. C. If the correlation is positive, the slope of the regression line is also positive. E. The correlation coefficient tells you how strong the residuals are.

The correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. Therefore, option A is correct.

Regarding option B, the correlation coefficient does not indicate the percentage of points that lie on the regression line. Instead, it measures the overall strength and direction of the relationship between the variables.

Option C is correct because if the correlation is positive, it means that as one variable increases, the other variable tends to increase as well. This positive relationship is reflected in the positive slope of the regression line.

Option D is incorrect because the correlation coefficient can be positive, negative, or zero, depending on the nature of the relationship between the variables.

Option E is correct. The correlation coefficient provides information about the strength of the relationship between the variables, which can be used to assess the strength of the residuals or the deviations from the regression line.

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The name of the polygon with the vertices at (0,0), (4,8), (12,8) and (16,0) is a Trapezoid. Option A

A trapezoid is a four-sided flat polygon.

It has two parallel sides that has different lengths. The other two sides are non-parallel and  also does have lengths.

A trapezoid has four angles, two of which are acute and two of which are obtuse.

A trapezoid's parallel sides are calld bases, while its non-parallel sides are called legs.

The height of a trapezoid is the perpendicular distance between its two bases. Trapezoids appear in a variety of sizes and forms, but its distinguishing feature is the presence of two parallel sides.

|             o                          o

|
|
|
|
|
|

|o___________________________o_

If you connect the "o" which represents the coordinates, you will draw a Trapezod.

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Answer:

40,320$.

Step-by-step explanation:

Total distance of the triathlon race is 23.34 kilometers.

Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

The total distance of the race is 23.34 kilometers.

Reg enters a triathlon race.

He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km

Total distance = 23.34 km.

The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.

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Based on the statistical analysis at the 0.01 level of significance, there is not enough evidence to show that a statistically significant linear relationship exists between the independent and dependent variables.

To determine if a statistically significant linear relationship exists between the independent and dependent variables, a statistical test such as a regression analysis can be conducted. The 0.01 level of significance indicates a high threshold for accepting the presence of a relationship.

In this case, after conducting the analysis, the results indicate that the p-value associated with the test statistic is greater than 0.01. This means that the observed relationship between the independent and dependent variables is not statistically significant. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming there is no true relationship between the variables.

Therefore, based on the data and the statistical analysis conducted, there is not enough evidence to conclude that a statistically significant linear relationship exists between the independent and dependent variables. It is important to note that this conclusion is specific to the given data set and the chosen level of significance.

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Answer:

Katie,

Once the skydiver reaches terminal velocity, then he will be falling with constant speed. The distance he falls in time t will then be d = (160 ft/s)·t. And his altitude above the ground (height h) will be his altitude when the parachute opened minus the distance he has fallen so we can write:

h = (3200 ft) - (160 ft/s)·t

As a point of interest, the time it will take him to fall all the way to the ground is t = (3200 ft)/(160 ft/s) = 20 s

Answer:

h(t) = -16t^2 + 200

Step-by-step explanation:

The success rate for the sample of 200 customers is 15%. The department store manager can compare this success rate with the established level of 20% .

To calculate the success rate for the sample, we need to determine the proportion of customers who made a purchase return out of the total number of customers in the sample.

Given that the sample size is 200 customers and 30 customers made a purchase return, we can calculate the success rate as follows:

Success Rate = (Number of Successes / Sample Size) * 100

In this case, the number of successes refers to the number of customers who made a purchase return, which is 30. The sample size is given as 200 customers.

Plugging in the values into the formula, we get:

Success Rate = (30 / 200) * 100

Success Rate = (0.15) * 100

Success Rate = 15%

Therefore, the success rate for the sample of 200 customers is 15%.

The department store manager can compare this success rate with the established level of 20% to determine if there is a significant difference between the purchase return level in their store and the established level.

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