Chapter 4: Explain how you can
calculate the x- and y-intercepts for
the graph of the equation given. It
is not necessary to calculate the
intercepts. y = x² + 6x - 7

Answer:

10

Step-by-step explanation:

48-20=28

28-18=10

that is how I see it at least

The proprtions are  25/10 = 5/2 and 3/4 = 15/20

Proportion is an equation that defines that the two given ratios are equivalent to each other e.g. 1/3 = 3/9

25/10 and 5/2  are proportions:

25/10 = (5×5)/(5×2)      (Divide both the numerator and denominator by 5)

25/10 = 5/2

3/4/10 and 15/20  are proportions:

3/4 = (3×5)/(5×4)      (Multiply both the numerator and denominator by 5)

3/4 = 15/20

Therefore, 25/10 = 5/2 and 3/4 = 15/20 are proprtions

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Answer:

\(x^{\frac{3}{2} } p^{6}\)

Step-by-step explanation:

Answer: i think b

Step-by-step explanation:

The combined area of dark pieces is 253.5 in².

First, Area of 5 light pieces

= length x width

= 3 3/4 x 39

= 15/4 x 39

= 146.25 in²

Now, Area of board

= L x W

= 29 x 39

= 1131 in²

Thus, the combined area of dark pieces

= 1131 - 146.25 x 6

= 253.5 in²

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We conclude that he used 89/76 feet of rope to make the swing.

We know that he bought a total of 15/12 feet of rope, and then he used some length X, such that at the end he has 3/38 feet of rope left.

To find the amount that he used, X, we need to calculate the difference between the initial amount and the length of rope left, then we can write the difference of fractions:

X = 15/12 ft - 3/38 ft

We need to find a common denominator for the two fractions, we know that:

38*6 = 228

12*19 = 228

Then we can rewrite the fractions as:

X = (19*15)/228 ft - (6*3)/228 ft

X = 267/228 ft = 89/76 ft

We conclude that he used 89/76 feet of rope to make the swing.

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The clinic should hire at least 7 doctors in order to serve 122 patients per day.

To determine how many doctors the clinic should hire in order to serve 122 patients per day, we need to calculate the number of patients each doctor can see within their working hours.

Let's start by calculating the total number of minutes each doctor works per day. Since each doctor works 8 hours per day and there are 60 minutes in an hour, the total minutes worked by a doctor per day would be 8 hours × 60 minutes = 480 minutes.

Next, we need to find out how many patients a doctor can see within their working hours. Given that each patient requires an average of 27 minutes with a doctor, the number of patients a doctor can see per day would be 480 minutes ÷ 27 minutes per patient = 17.7778 patients.

Since we can't have a fractional number of patients, we need to round this number up to the nearest whole number to ensure that each patient gets the required attention. Therefore, each doctor can see approximately 18 patients per day.

To serve 122 patients per day, we divide the total number of patients by the number of patients each doctor can see per day: 122 patients ÷ 18 patients per doctor = 6.7778 doctors.

Again, we can't have a fractional number of doctors, so we need to round this number up to the nearest whole number. Therefore, the clinic should hire at least 7 doctors to serve 122 patients per day.

In summary, the clinic should hire at least 7 doctors in order to serve 122 patients per day.

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The x-values at which the function\(\( f(x) \)\)is not continuous are \(\( x = 7 \) and \( x = -6 \).\) At these points, the denominator of the function is equal to zero, leading to a division by zero, which results in a discontinuity in the function.

To determine the x-values at which the function \(\( f(x) = \frac{x + 6}{x^2 - x - 42} \)\) is not continuous, we need to identify any potential points of discontinuity. These occur when the denominator of the function is equal to zero, as division by zero is undefined.

To find the x-values that make the denominator zero, we solve the equation\(\( x^2 - x - 42 = 0 \) for \( x \).\)

Factoring the quadratic equation, we have:

\(\( (x - 7)(x + 6) = 0 \)\)

Setting each factor equal to zero, we get:

\(\( x - 7 = 0 \) or \( x + 6 = 0 \)\)

Solving these equations, we find:

\(\( x = 7 \) or \( x = -6 \)\)

Therefore, the x-values at which the function\(\( f(x) \)\)is not continuous are \(\( x = 7 \) and \( x = -6 \).\) At these points, the denominator of the function is equal to zero, leading to a division by zero, which results in a discontinuity in the function.

The complete question is:

Find the x-values (if any) at which f is not continuous. Which of the discontinous \(\[ f(x)=\frac{x+6}{x^{2}-x-42} \]\)

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Answer:

The coordinate r is the length of the line segment from the point (x,y) to the origin and the coordinate θ is the angle between the line segment and the positive x-axis.

Step-by-step explanation:

=>

Answer:

5000

Step-by-step explanation:

in order to find how many revolutions, you need to find the circumference of the circle which is  2pi r.

thus, you will get this working out:

circum= 2 times 22/7 times 14

= 88cm

4.4 km = 440000cm

Then, 440000cm divide 88 cm =5000.

Thus, 5000 revolutions.

Step-by-step explanation:

Hey there!

Given;

The triangle is a right angled triangle, whose one side is 26 and another side is X. It has also one angle that is 41°.

Now, taking reference angle as angle 41°. We get;

Perpendicular= 26

Base = X

and Reference angle = 41°.

We know that the ratio of tan is p/b. So, let's use this ratio.

\( \tan(41°) = \frac{26}{x} \)

\(0.869 \times x = 26\)

\(x = \frac{26}{0.869} \)

Therefore, The value of x is 29.90.

Hope it helps...

The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.

This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.

According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.

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200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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Answer:

10.59%

Step-by-step explanation:

percentage of change is given by

{(old number - new number)/old number} * 100

_________________________

given

no. of student  went to the first school dance = 340

no. of student  went to the last school dance = 306

Percentage of change between two dance

= ((no. of student  went to the first school dance - no. of student  went to the last school dance)/ no. of student  went to the fist school dance)*100

= (340 - 306)/340 *100

= (36/340 )*100 = 10.59%

The percent of change between the two dances 10.59%.

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

y-intercept is 3 and x-intercept is -3/7

Step-by-step explanation:

to find the y-intercept let x = 0 and solve for y.

y=7(0) +3

y=0+3

y=3

to find the x-intercept let y = 0 and solve for x

0 = 7x + 3

-3 = 7x

-3/7 =x

The rate of 50 deaths per 1,000 births is known as the infant mortality rate.

What is infant mortality rate?

Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age. Infant mortality rate is an essential demographic statistic for assessing population health status and identifying health disparities among different groups of the population.

IMR reflects the underlying mortality rate of infants in a society, which can be influenced by several factors, including maternal health, access to healthcare, nutrition, and socio-economic factors.Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age.

The rate of 50 deaths per 1,000 births is known as the infant mortality rate. The infant mortality rate is considered one of the most critical indicators of a country's health status and is often used to compare the health status of different populations.

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a) The bird would fly approximately 4.17 km in a straight line from the starting point to the final point. b) The bird would fly at an angle of approximately 47.46 degrees counterclockwise from the east.

To find the distance and angle that a bird would fly in a straight line from the starting point to the final point, we can use the concept of vector addition.

(a) Distance:

The person's total displacement can be represented as a vector sum of their individual movements: 2.8 km north + 2.9 km west - 5.8 km south.

To simplify this, we can break it down into horizontal (x-axis) and vertical (y-axis) components:

Horizontal displacement = -2.9 km (west)

Vertical displacement = 2.8 km (north) - 5.8 km (south) = -3 km (south)

Now, we can calculate the straight-line distance using the Pythagorean theorem:

Distance = √(Horizontal displacement² + Vertical displacement²)

= √((-2.9 km)² + (-3 km)²)

= √(8.41 km² + 9 km²)

= √(17.41 km²)

≈ 4.17 km

Therefore, the bird would fly approximately 4.17 km in a straight line from the starting point to the final point.

(b) Angle:

To determine the angle counterclockwise from the east, we can use trigonometry. The angle can be found using the inverse tangent function:

Angle = arctan(Vertical displacement / Horizontal displacement)

= arctan((-3 km) / (-2.9 km))

= arctan(1.034)

≈ 47.46 degrees

Therefore, the bird would fly at an angle of approximately 47.46 degrees counterclockwise from the east.

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The complex exponential Fourier series of a signal can be determined by computing the coefficients A₀ and Aₙ.

For (i), the complex exponential Fourier series is given by:

X(ω) = A₀ + ∑[Ancos(nωt + φn) ], where

A₀ = 1/2

Aₙ = (1/2)[cos(2nπ/8) + cos(2nπ/8 + π/2)]

For (ii), the complex exponential Fourier series is given by:

X(ω) = A₀ + ∑[Ancos(nωt + φn) ], where

A₀ = 1

Aₙ = (2/2)[sin(nπ/3) + 3cos(nπ/3 + π/3)]

In conclusion, the complex exponential Fourier series of a signal can be determined by computing the coefficients A₀ and Aₙ. This technique can be used to analyze any periodic signal or system and is invaluable in signal processing, communications, and control engineering.

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The trend projection for time period 18 is 197.6. The correct option is B

A mathematical equation used to represent the trend or pattern seen in a time series of data is called a linear trend expression, sometimes referred to as a linear trend model.

To find the trend projection for time period 18 using the given linear trend expression, we substitute t = 18 into the equation:

Yt = 129.2 + 3.8t

Y18 = 129.2 + 3.8 * 18

Y18 = 129.2 + 68.4

Y18 = 197.6

Therefore, the trend projection for time period 18 is 197.6.

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The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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There are 76 oatmeal cookies:

4 + 11 = 15

285/15 = 19

19 × 4 = 76

Answer:

16 degrees, I believe

Step-by-step explanation:

You would use an inverse sine, if I'm not mistaken. You have the O (opposite) and the H (hypotenuse). With that you can do SOH - or sine. But since you want the angle, you do an inverse. So you do the inverse sine of O over H, or the inverse sine of 5/18. It gives you 16.128 degrees or so.

The distance between the opposite sides of the trampoline can be found to be 14. 42 yards

To find the distance between the opposite sides of the trampoline, we are essentially finding the diagonal length. We can use the Pythagorean theorem to do this by dividing the trampoline into two right triangles.

The distance between the opposite sides would then be:

c ² = a ² + b ²

c ² = 8 ² + 12 ²

c ² = 64 + 144

c ² = 208

c = √ 208

c = 14. 42 yards

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Answer:

Step-by-step explanation:

Answer:

Check out Tiger algebra

it gave me

Slope=-2.000/2.000=-1.000

x - intercept = 3/1 = 3.00000

y - intercept = 3/2 = 1.50000

and

Slope=1.000/2.000=0.500

x - intercept = 10/1 = 10.00000

y - intercept  = 10/2 = 5

It requires nothing.

Answer:

75 in^2

Step-by-step explanation:

Given data

From the figure

We can see a rectangle and a triangle

The area of the rectangle is

Area= L*W

Area= 13*5

Area= 65 in^2

Area of the triangle

Area= 1/2b*h

Area= 1/2*4*5

Area= 2*5

Area= 10 in^2

Hence the area of the composite figure is

Area= 65+10

Area= 75 in^2

The solution is Option C and Option D.

The exponential function is given by f ( x ) = 2 ( 3 )ˣ

The exponential function is given by f ( x ) = 800 / 4ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 7 , 19 , 31 , 43 }

The equation of line is y = 12x + 7

This is a linear equation

b)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 5 , 10 , 15 , 30 }

The equation is a quadratic equation

c)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 2 , 6 , 18 , 54 }

The equation is y = 2 ( 3 )ˣ

This is an exponential function

d)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 800 , 200 , 50 , 12.5 }

The equation is f ( x ) = ( 800 / 4ˣ )

This is an exponential function

Hence , the exponential equations are solved

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