Solve the equation formed when f ( x ) = g ( x ).

f ( x ) = 4 x − 4

g ( x ) = 1 2 x + 3

Group of answer choices

A. x = -4

B. x = 4

C. x = 2

D. x = -2

Answer:

Step-by-step explanation:

The slope-intercept form:

The slope refers to the steepness of the line and is same as the rate of change.

The y- intercept is the starting point or the point of the intersection of the line with the y- axis.

Answer:

Check the screenshot

Step-by-step explanation:

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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The quotient using compatible numbers for 2252 divided by 7 is 321 remainder 5.

Compatible numbers are those that are simple to mentally add, subtract, multiply, or divide. Compatible numbers are close in value to the actual numbers, making it easy to estimate the answer and solve problems.

The following steps are required:

Step 1: Take the dividend's first digit from the left.

Step 2: Next, divide it by the divisor and write the result as the quotient on top.

Step 3: Subtract the result from the digit and record the difference.

Step 4: Subtract the dividend's next digit (if present).

Step 5: Write the value gotten.

A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio. In this case, the value gotten after the division is 321 remainder 5.

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The blue shaded portion on the top left side is described as forming lines pass through (6, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion W. D.

To graph the system of inequalities y ≥ 1/3x - 2 and y ≤ -4x - 2, we will plot the lines corresponding to each inequality and shade the region that satisfies both inequalities.

First, let's graph the line y = 1/3x - 2.

We can find two points on this line and connect them with a straight line:

Using (6, 0):

y = 1/3(6) - 2

y = 2 - 2

y = 0

So we have the point (6, 0).

Using (0, -2):

y = 1/3(0) - 2

y = -2

So we have the point (0, -2).

Plotting these two points and drawing a line through them, we get a line labeled as Line 1.

Next, let's graph the line y = -4x - 2 using the same process:

Using (0.5, 0):

0 = -4(0.5) - 2

0 = -2 - 2

0 = -4

So we have the point (0.5, 0).

Using (0, -2):

-2 = -4(0) - 2

-2 = -2

So we have the point (0, -2).

Plotting these two points and drawing a line through them, we get a line labeled as Line 2.

Now, we need to shade the region that satisfies both inequalities.

The shaded region will be the region where Line 1 is above Line 2.

Based on the given descriptions of the shaded portions W, X, Y and Z we can determine the correct option.

The blue shaded portion on the top left side is described as forming when lines pass through (0.5, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion X.

The blue shaded portion on the left side is described as forming when lines pass through (0.5, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion Y.

The blue shaded portion on the bottom left side is described as forming when lines pass through (6, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion Z.

Based on this information, we can determine the correct option:

A. X

B. Y

C. Z

D. W

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The best statement that describes the strategy for estimating the perimeter of the figure (please see the attached diagram) is the option;

Ad the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

An estimate is an approximation of a true value, which is a value that is close to the actual value of the measured quantity.

Please find attached a diagram of the possible figure created with MS Word

The length of the side of the sides of the possible figure in the figure, obtained from a similar question on the internet are;

Base length = 5 units

Height = 4 units

The figure has a diagonal side which is 4 units wide and 2 units tall.

The length of the slant side, found using Pythagorean theorem can be obtained as follows; Length = √(4² + 2²) = 2·√5 ≈ 5

The correct option is therefore to add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

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The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).

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Answer:

1820

Step-by-step explanation:

13 x 14 x 10 = 1820

Please mark brainliest

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(2^{60} =2^{2 \times 30} =(2^{2} )^{30}=4^{30}\)

Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.

Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.

You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.

Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.

Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.

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The minimum volume of the box =  11220 cubic centimeters

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

One notebook:

length, l= 29 cm

width = 21.5 cm

height = 1.5 cm

Volume of 1 notebook =  l*w*h

                                     =  29*21.5*1.5

                                     =  935.25

                                     ≈  935 cubic centimeters ( nearest whole number )

Volume of 12 notebooks = 935 * 12 = 11220 cubic centimeters

So, the minimum volume of the box =  11220 cubic centimeters

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Answer:

11,223

Step-by-step explanation:

Answer:

1st equation: 3(12) - 12 = 24

2nd equation: 36 - 12 = 24

Answer:

3(12) - 12 = 24

Step-by-step explanation:

The equation of this circle in standard form is (x - 3)² + (y - 5)² = 3².

A sketch of the equation of this circle is shown below.

In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Since the center of the circle lies on the line x = 3, and it is tangent to the y-axis at (0, 5), we can logically deduce that its center would be located at  (3, 5) and the radius would be 3 units.

Based on the information provided in above, we have the following parameters for the equation of this circle:

Center (h, k) = (3, 5)

Radius (r) = 3 units.

By substituting the given parameters into the equation of a circle, we have:

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 5)² = 3²

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The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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Answer:

The  t-statistic is \(t = 0.6956\)

Step-by-step explanation:

From the question we are told that

     The population mean is  \(\mu = 22 \ minutes\)

       The standard deviation is  \(s = 7.043\)

       The  given data is  23, 35, 17, 30, 20, and 19.

Generally the sample mean is mathematically evaluated as

      \(\= x = \frac{23+ 35+17+ 30+ 20+ 19 }{6}\)

     \(\= x =24\)

The t-statistic is mathematically evaluated as

       \(t = \frac{ \= x - \mu }{\frac{s}{ \sqrt{n} } }\)

=>   \(t = \frac{ 24 - 22 }{\frac{ 7.043}{ \sqrt{6} } }\)

=>   \(t = 0.6956\)

Answer: 0.70

Step-by-step explanation:

Using expression 3 x 14, The rate chart will be

Number of Scoops of Coffee Grounds 18 24 30 36 42.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a mathematical phrase or idea. Expressions can be simple or complex and may involve functions, trigonometric functions, logarithms, and other mathematical operations.

Now,

To find the number of scoops of coffee grounds needed for 14 pots of coffee, we can use proportional reasoning and set up a proportion:

Number of scoops of coffee grounds / Number of pots of coffee = 18 / 6

Simplifying the fraction on the right side of the equation gives us:

Number of scoops of coffee grounds / Number of pots of coffee = 3

To solve for the number of scoops of coffee grounds needed for 14 pots of coffee, we can multiply both sides of the equation by 14:

Number of scoops of coffee grounds / Number of pots of coffee = 3

Number of scoops of coffee grounds / 14 = 3

Number of scoops of coffee grounds = 3 x 14

Number of scoops of coffee grounds = 42

So the completed rate chart is:

Number of Pots of Coffee 6 8 10 12 14

Number of Scoops of Coffee Grounds 18 24 30 36 42.

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The angles 5 and 6 which are given in the diagram above are typical example of an adjacent angle.

An adjacent angle is defined as the type of angle that has a common sides which is shared by the two angles that are being compared.

A vertical angle is the type of angle that is usually opposite and they constructed by the intersection of two lines.

Therefore since a common sides exists between angle 5 and 6.

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Answer:

D

Step-by-step explanation:

1/2 is not equal to 1/2.5 is not equal to 0.5/2.25.

The perimeter of PQRS would depend on the lengths of the tangent segments and the lengths of the intercepted arcs. Without specific measurements, we cannot determine the precise perimeter.

To determine the perimeter of quadrilateral PQRS, we need more information about the lengths of the sides or the relationship between the sides and angles. Without specific measurements or additional details, we cannot calculate the exact perimeter of the quadrilateral.

However, we can provide some general information.Since PQ¯ is tangent to circle R at point Q, it is perpendicular to the radius drawn from the center of the circle to point Q. Similarly, PS¯ is tangent to circle R at point S, so it is perpendicular to the radius drawn to point S.

The quadrilateral PQRS is formed by the tangents PQ¯ and PS¯ along with the two arcs intercepted by these tangents on the circle R.

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Using conditional probability, it is found that there is a 0.4235 = 42.35% probability that the patient  really is HIV positive.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

The percentages involving a positive test are:

Hence:

\(P(A) = 0.95(0.03) + 0.04(0.97) = 0.0673\)

The probability of both having a positive test and being HIV positive is:

\(P(A \cap B) = 0.95(0.03)\)

Then, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.03)}{0.0673} = 0.4235\)

0.4235 = 42.35% probability that the patient  really is HIV positive.

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Answer:

The answer to the questions is

a)1

b)60°

Step-by-step explanation:

tan 45°=1

sin‐¹(√3/2)=60°

The values of the given trigonometric expression are:

(a) tan 45° = 1

(b) \(\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ\)

Use the concept of trigonometric identity defined as:

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

(a) The given trigonometric ratio is,

tan 45°

Since we know that,

In the trigonometric ratio table for the measure 45°,

The value of tangent is 1.

Hence,

tan 45° = 1

For the given trigonometric exprssion,

\(\text{sin}^{-1}(\frac{\sqrt{3}}{2})\)

Since we know that,

Sin 60° = √3/2

Therefore,

\(\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = \text{sin}^{-1}(\text{sin }60^\circ)\\\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ\)

Hence,

The value of the given expression is 60°.

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Answer:-87

Step-by-step explanation:

Answer:

-87

Step-by-step explanation:

-28-47-12= -75-12=-87

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

\(20\pi\) m

OR

62.8318531 m

Step-by-step explanation:

This is actually pretty simple

The distance the tip travels is the arc length and the length of the pendulum is the radius of a circle

The formula for arc length is Angle in Radians x Radius

So pi/12 * 4 = pi/3 m

We know this is how much it travels every second so it is going at pi/3 m/s

One minute is 60 seconds

pi/3 * 60 = 20pi m

Answer:

\(\dfrac{(a+2\sqrt{b})^2 }{a^2-4b}\)

Step-by-step explanation:

To rationalise the denominator, multiply by the expression by \(\dfrac{a+\sqrt{4b} }{a+\sqrt{4b} }\):

\(=\dfrac{a+\sqrt{4b} }{a-\sqrt{4b} }\times\dfrac{a+\sqrt{4b} }{a+\sqrt{4b} }\)

\(=\dfrac{(a+\sqrt{4b}) (a+\sqrt{4b})}{(a-\sqrt{4b}) (a+\sqrt{4b})}\)

\(=\dfrac{(a+\sqrt{4b})^2 }{a^2-4b}\)

\(=\dfrac{(a+2\sqrt{b})^2 }{a^2-4b}\)

\(\\ \rm\hookrightarrow \dfrac{a+\sqrt{4b}}{a-\sqrt{4b}}\)

\(\\ \rm\hookrightarrow \dfrac{a+x}{a-x}\)

\(\\ \rm\hookrightarrow \dfrac{(a+x)^2}{a^2-x^2}\)

\(\\ \rm\hookrightarrow \dfrac{a^2+2ax+x^2}{a^2-x^2}\)

\(\\ \rm\hookrightarrow \dfrac{a^2+2a\sqrt{4b}+4b}{a^2-4b}\)

Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

Answer:

1

Step-by-step explanation:

61.26=61

59.593=60

61-60=1

Answer:

1

Step-by-step explanation:

61.26 rounded to the nearest whole number = 61

59.593 rounded to the nearest whole number = 60

61 - 60 = x

61 - 60 = 1

x = 1

Answer:

1/6

Step-by-step explanation:

A (6,1)

B (12,2)

slope = (2-1)/(12-6)

1/6

The most reasonable temperature for a snowy day is given as follows:

C. -6°C

Considering that it snows, the temperature is either negative or very low positive, as snow only happens on temperatures close to freezing (like 2º C) or negative.

17ºC and 26ºC are far from cold enough to generate snow, hence the most reasonable temperature for a snowy day is given as follows:

C. -6°C

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