Find the equation of the line that contains the points (-4, -3) and is parallel to the line 4x + 5y= 9. Write the equation in slope-intercept form, if possible.

Answer:

31 7/8

16+8=24

4+2=6

2/4+1/4=3/4+1/8=7/8

Answer:

y = 2x-3

Step-by-step explanation:

y – 1 = 2(x – 2)

Distribute

y-1 =2x-4

Add 1 to each side

y-1+1 = 2x-4+1

y = 2x-3

Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

For such more question on package

https://brainly.com/question/12251427

#SPJ8

Answer:

75 should be the answer

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

Answer:

Explanation:

Here, we want to get the properties listed for the plot shown

a) Amplitude:

b) Period

The period is simply the distance from max to max or min to min

We have that as:

c) Midline:

Answer:

92

Step-by-step explanation:

92 appears the most

Answer:

92 is the mode because is the most occurring number. 92 appear 4times

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Responder:

Parte A: 32 yardas cuadradas por galón

Parte B: 13 pies cuadrados por galón de diferencia

Explicación paso a paso:

Parte A:

Para saber cuántas yardas cuadradas cubre cada galón, tienes que dividir 42 2/3 entre 1 1/3, lo que equivale a 32. Eso significa que cada galón de pintura cubre 32 yardas cuadradas.

Parte B:

Primero, tienes que convertir cuánto cubrió Ángela en yardas cuadradas a pies cuadrados. Como una yarda cuadrada equivale a 9 pies cuadrados, tenemos que multiplicar 32 por 9, lo que equivale a 288. Para encontrar la diferencia, debes restar 288 - 275, lo que equivale a 13.

mORE DETAILS : brainly.com/question/22904243

#SPJ9

Answer:

For the first city, the 95% confidence interval would be:

28,900 +/- 2300 x 3 = 28,900 +/-6900$

For the second city, the 95% confidence interval would be:

30,300 +/- 2100 x 3 = 30,300 +/- 6300$

Answer:

7/2

or

\(\frac{7}{2}\)

Step-by-step explanation:

To get an improper fraction is very simple.

You multiply the whole number by the denominator

And then you add the product to the numerator

3 x 2 = 6 + 1 = 7

You always keep the denominator

so you get 7/2

These are the steps you will ALWAYS use when you have a fraction with a whole and you are turning it into an improper fraction.

(Hope this helps!)

Using it's concept, it is found that the coefficient of the mathematical expression 7m² + 2(19) is of 7.

The leading coefficient of a polynomial is the term that multiplies the highest exponent.

In this problem, the expression is given by:

7m² + 19.

The highest exponent is of 2, in m², hence the leading coefficient is of 7.

More can be learned about the coefficient of a mathematical expression at https://brainly.com/question/24380382

#SPJ1

The fractions in ascending order are:  2÷7, 3÷14, 1÷2

What is a fraction ?

A fraction is a number that represents a part of a whole or a ratio of two quantities. It is written as two numbers separated by a horizontal or diagonal line, with the number above the line called the numerator and the number below the line called the denominator.

To write the fractions 2÷7, 1÷2, and 3÷14 in ascending order, we need to find a common denominator and then compare the numerators. Here's how we can do it:

Find the least common multiple (LCM) of the denominators:

7, 2, and 14 have a common multiple of 14, but it's not the least common multiple.

The prime factorization of 7 is 7,

The prime factorization of 2 is 2,

The prime factorization of 14 is 2 x 7.

Therefore, the LCM of 7, 2, and 14 is 2 x 7 = 14.

Convert each fraction to an equivalent fraction with the common denominator of 14:

2÷7 = (2÷7) x (2÷2) = 4÷14

1÷2 = (1÷2) x (7÷7) = 7÷14

3÷14 = 3 ÷ 14

Compare the numerators and write the fractions in ascending order:

4 ÷ 14 < 7 ÷ 14 < 3 ÷14

Therefore, the fractions in ascending order are: 2÷7, 3÷14, 1÷2

To learn more about Fraction from given link.

https://brainly.com/question/10354322

#SPJ1

Answer:

4

Step-by-step explanation:

Answer:

The coordinate is (5,4)

the x=5

the y=4

4 and 5

Step-by-step explanation:

on y axis it is 4

while on x axis it is 5

based on the point

Answer:

the axis of symmetry would be: b. x=2

The equation of the axis of symmetry of the parabola will be x = 2. Then the correct option is B.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = 3x² - 12x + 11

Convert the equation into a vertex form. Then we have

y = 3x² - 12x + 11

y = 3x² - 12x + 12 - 1

y = 3(x² - 4x + 4) - 1

y = 3(x - 2)² - 1

The equation of the axis of symmetry of the parabola is given as,

x - 2 = 0

x = 2

The equation of the axis of symmetry of the parabola will be x = 2. Then the correct option is B.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

#SPJ2

Answer:

5x^2 + x + 7.

Step-by-step explanation:

6x^2 + 7 + x - x^2

= (6x^2 - x^2) + (x + 7) // Rearranging the terms

= 5x^2 + x + 7

So, 6x^2 + 7 + x - x^2 simplifies to 5x^2 + x + 7.

Answer: the answer is c

Step-by-step explanation:brainlist \(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\)

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Answer:

1. (a)  [-1, ∞)

   (b)  (-∞, -1) ∪ (1, ∞)

2. (a)  (1, 3)

    (b)  (-∞, 1) ∪ (3, ∞)

3. (a)  9.6 m and 0.4 m

   (b)  03:08 and 15:42

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Part (a)

When x < 0, the function is f(x) = x².

Since the square of any non-zero real number is always positive, the range of the function f(x) for x < 0 is (0, ∞).

When x ≥ 0, the function is f(x) = sin(x).

The minimum value of the sine function is -1 and the maximum value of the sine function is 1.  As the sine function is periodic, the function oscillates between these values.  Therefore, the range of function f(x) for x ≥ 0 is [-1, 1].

The range of function f(x) is the union of the ranges of the two separate parts of the function.  Therefore, the range of f(x) is [-1, ∞).

Part (b)

The domain of the function g(x) = ln(x² - 1) is the set of all real numbers x for which (x² - 1) is positive, since the natural logarithm function (ln) is only defined for positive input values.

Find the values of x:

\(\implies x^2-1 > 0\)

\(\implies x^2 > 1\)

\(\implies x < -1, \;\;x > 1\)

Therefore, the domain of function g(x) is (-∞, -1) ∪ (1, ∞).

Part (a)

To determine the interval where f(x) < 0, we need to find the values of x for which the quadratic is less than zero.

First, set the function equal to zero and solve for x:

\(\begin{aligned} x^2-4x+3&=0\\x^2-3x-x+3&=0\\x(x-3)-1(x-3)&=0\\(x-1)(x-3)&=0\\ \implies x&=1,\;3\end{aligned}\)

Therefore, the function is equal to zero at x = 1 and x = 3 and so the parabola crosses the x-axis at x = 1 and x = 3.

As the leading coefficient of the quadratic is positive, the parabola opens upwards. Therefore, the values of x that make the function negative are between the zeros.  So the interval where f(x) < 0 is 1 < x < 3 = (1, 3).

Part (b)
Since the square root of a negative number cannot be taken, and dividing a number by zero is undefined, function f(x) has to be positive and not equal to zero:  f(x) > 0.

As the parabola opens upwards, the values of x that make the function positive are less than the zero at x = 1 and more than the zero at x = 3.

Therefore the domain of g(x) is (-∞, 1) ∪ (3, ∞).

Part (a)

The range of a sine function is [-1, 1]. Therefore, to calculate the maximal and minimal possible water depths of the bay, substitute the maximum and minimum values of sin(t/2) into the equation:

\(\textsf{Maximum}: \quad 5+4.6(1)=9.6\; \sf m\)

\(\textsf{Maximum}: \quad 5+4.6(-1)=0.4\; \sf m\)

Part (b)

To find the times when the depth is maximal, set sin(t/2) to 1 and solve for t:

\(\implies \sin \left(\dfrac{t}{2}\right)=1\)

\(\implies \dfrac{t}{2}=\dfrac{\pi}{2}+2\pi n\)

\(\implies t=\pi+4\pi n\)

Therefore, the values of t in the interval 0 ≤ t ≤ 24 are:

Convert these values to times:

9514 1404 393

Answer:

  { }, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}, {a,b,c,d}

Step-by-step explanation:

The number of subsets of a set with n elements is 2^n, including the empty set and the full set. Your subsets are ...

  { }, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}, {a,b,c,d}

Answer:

3 times 5 = 15 and 5 times 5 = 25. 15 plus 25 = 40

Step-by-step explanation:

Answer:

22.22% probability of getting a total that is a factor of 6

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have these possible outcomes:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes.

Cases in which the total are factor of 6:

The factors of 6 are the number for which 6 is divisible by, so 1,2,3 and 6.

The cases that have these totals are:

(1,1), (1,2), (1,5) (2,1), (2,4), (3,3), (4,2), (5,1)

8 outcomes, out of 36

8/36 = 0.2222

22.22% probability of getting a total that is a factor of 6

Answer:

24 square yards

Step-by-step explanation:

Find the diagram attached.

The area of the diagram = Area of rectangle + Area of triangle

Area of rectangle = 3 * 4

Area of rectangle = 12 square yards

Area of triangle = 1/2 * base * height

Area of triangle = 1/2 * 6 * 4

Area of triangle = 12 square yards

Area of the diagram = 12 + 12

Area of diagram =  24 square yards

Hence 24 square yards of carpeting is needed

When value of x is given as 3 then according to the said proportional relationship y will be  13.15.

We are given that y and x have a proportional relationship, and y = 9 when x = 2. This means that there is a constant of proportionality, k, such that y = kx.

We can use the information given to find the value of k:

y = kx

9 = k(2)

k = 9/2

Now that we know the value of k, we can use it to find the value of y when x = 3:

y = kx

y = (9/2) * 3

y = 13.5

So the value of y when x = 3 is 13.5

A ratio is a way of comparing two or more values or quantities. It is a mathematical expression that shows the relationship between different values, typically by using the symbol ":" to separate the values. For example, if we have three apples and two oranges, we can express the relationship between the apples and oranges as a ratio 3:2. Ratios can also be written as fractions, in this case the ratio 3:2 can be written as 3/2.

Learn more about Percentages here.

https://brainly.com/question/29116686

#SPJ1

Based on the information, we can infer that the theoretical probability of these colors would be 33.33%. However, the table reflects different data.

To calculate the theoretical probability of each color we must perform the following mathematical operation.

Bearing in mind that 300 is 100% of the people, we must divide 300 by 3 to know how many people should choose a specific color. In this case, every 100 people should choose a different color.

Additionally, these 100% would represent 33.33% of the total population.

100 * 100 / 300 = 33.33%

Learn more about probability in: https://brainly.com/question/30034780

#SPJ1

Help Center to Water Slide #1: Level line, y = 3. Toddler area to Concessions: Negative incline, y = (-1/3)x - 7. Gift Shop to Restrooms: Level line, y = -9. Security desk to Water Slide #2: Even line, y = 4. Lazy river to large Whirlpool: Positive incline, y = (2/5)x + 61/5.

To calculate the slope between attractions and discover the midpoints, we'll utilize the given requested sets for each fascination. Here are the calculations:

Help Center to Water Slide #1:

Slope = ((y2 - y1) / (x2 - x1)) = ((3 - 3) / (-6 - 2)) = / -8 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((2 + (-6)) / 2), ((3 + 3) / 2)) = (-2, 3)

Toddler area to Concessions:

Slope = ((y2 - y1) / (x2 - x1)) = ((-6 - (-3)) / (6 - (-3)) = (-3 / 9) = -1/3

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((-3 + 6) / 2), ((-9 + (-6)) / 2)) = (1.5, -7.5)

Gift Shop to Restrooms:

Slope = ((y2 - y1) / (x2 - x1)) = ((-9 - (-9)) / (8 - 2)) = / 6 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((8 + 2) / 2), ((-9 + (-9)) / 2) = (5, -9)

Security desk to Water Slide #2:

Slope = ((y2 - y1) / (x2 - x1)) = ((4 - 4) / (16 - 5)) = / 11 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((5 + 16) / 2), ((4 + 4) / 2) = (10.5, 4)

Lazy River to Large Whirlpool:

Slope = ((y2 - y1) / (x2 - x1)) = ((10 - 14) / (-7 - 3)) = (-4 / -10) = 2/5

Midpoint = ((x1 + x2) / 2)), ((y1 + y2) / 2)) = ((-7 + 3) / 2), ((10 + 14) / 2)) = (-2, 12)

Presently, let's calculate the linear equations for each case:

Help Center to Water Slide #1:

The Slope is 0, and the y-coordinate is consistent, so the equation is y = 3.

Toddler area to Concessions:

The Slope is -1/3, and the y-intercept can be calculated utilizing the midpoint facilitates:

-7.5 = (-1/3)(1.5) + b

-7.5 = -0.5 + b

b = -7

Gift Shop to Restrooms:

The Slope is 0, and the y-coordinate is steady, so the equation is y = -9.

Security desk to Water Slide #2:

The Slope is 0, and the y-coordinate is steady, so the equation is y = 4.

Lazy River to Large Whirlpool:

The Slope is 2/5, and the y-intercept can be calculated utilizing the midpoint arranges:

12 = (2/5)(-2) + b

12 = -4/5 + b

b = 61/5

The Linear equations for each case are as follows:

Help Center to Water Slide #1: y = 3

Toddler area to Concessions: y = (-1/3)x - 7

Gift Shop to Restrooms: y = -9

Security desk to Water Slide #2: y = 4

Lazy River to Large Whirlpool: y = (2/5)x + 61/5

Learn more about slope here:

https://brainly.com/question/29044610

#SPJ1

Step-by-step explanation:

1/4×48

=12

So if 12people are out of state

48-12=36,is the number of people living in the state