what is the rate of change in y= 2x+3

Answer:

37°

Step-by-step explanation:

angle B = angle D (alternate angle)

2X = 74°

X = 37°

Answer:

29

Step-by-step explanation:

right in acellus

Step-by-step explanation:

add 88 and 57, then subtract it from 180

Answer:

its answer is 31 hope it helps

Answer:

17,576,000 different combinations possible.

Step-by-step explanation:

Based on the trends displayed in the given line graph, the answer choice that represents a likely situation for 2010 is Option B: There will be over 6 million construction employees in 2010, and the average hourly earnings will be less than twenty dollars.

Analyzing the line graph, we observe that the average hourly earnings of production workers in the construction industry gradually increase over the years. Starting at 17.2 in January 2000, it slowly rises to 19.7 by January 2006. Then, there is a steeper increase to 20.5 in January 2007, followed by a further increase to 22.4 in January 2009.

Considering this trend, it is reasonable to expect that the average hourly earnings in 2010 would be less than twenty dollars. Option B states that there will be over 6 million construction employees in 2010, aligning with the increasing trend in employment. Additionally, it mentions that the average hourly earnings will be less than twenty dollars, which is consistent with the graph's pattern of a gradual increase rather than a sudden jump.

Therefore, based on the trends displayed in the graph, Option B is the most likely situation for 2010, indicating over 6 million construction employees and average hourly earnings less than twenty dollars.

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a) cos  φ= -4/13`

b) cos φ  -2√13/13`c)

c) inverse tangent function will not give us the angle we are looking for because our angle is in the third quadrant

d) tanφ=32​ => φ ≈ -57.99°

e) coterminal angles to -57.99° in radians is:`(-319.93 + 360n)π/180`, where `n` is an integer.

a) The formula for the tangent of an angle in the third quadrant is, `tan(π + φ) = tan φ` and, hence, we have:`tan(π + φ) = 3/2`Using the fundamental identity for the tangent, we get:`tan(π + φ) = -tan φ``tan φ = -3/2`Then, using the Pythagorean identity `sin^2 φ + cos^2 φ = 1` to solve for `cos φ` in the third quadrant where `cos φ < 0`, we get:`cos φ = -√(1 - sin^2 φ) = -√(1 - (tan^2 φ)/(1 + tan^2 φ)) = -√(1 - (9/13)) = -4/13`b) Since `tan φ = 3/2`, we can construct a right triangle with legs of length `3` and `2` and hypotenuse of length `√(3^2 + 2^2) = √13`.Since the angle is in the third quadrant, the cosine of the angle is negative. Thus:`cos φ = -2/√13 = (-2/√13) * (√13/√13) = -2√13/13`c) The inverse tangent function is only able to give you the value of the angle in the first or fourth quadrant. Therefore, using the inverse tangent function will not give us the angle we are looking for because our angle is in the third quadrant.d) `tanφ=32​ => φ ≈ -57.99°`e) All coterminal angles to -57.99° in radians are given by:`θ = -57.99° + 360n, n ∈ ℤ`Thus, we can convert to radians using the formula `π/180°`:`θ = (-57.99° + 360n)π/180°`Simplifying:`θ = (-319.93 + 360n)π/180`Therefore, the expression for all coterminal angles to -57.99° in radians is:`(-319.93 + 360n)π/180`, where `n` is an integer.

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Answer: 1,-1,-7

Step-by-step explanation:

-3-2(-2)= -3+4= 1

-3-2(-1)= -3+2= -1

-3-2(2)= -3-4= -7

The probability of flipping at least two heads in a row when a fair coin is flipped three times can be calculated by determining the favorable outcomes and dividing it by the total number of possible outcomes. The probability is 1/8 or 0.125.

To calculate the probability, we need to determine the favorable outcomes and the total number of possible outcomes.

In this case, the favorable outcomes are when we have at least two consecutive heads. There are three possible scenarios: (1) HHH, (2) THH, and (3) HHT.

The total number of possible outcomes when flipping a fair coin three times is 2^3 = 8, since each flip has two possible outcomes (head or tail), and we multiply them together for three flips.

Therefore, the probability of flipping at least two heads in a row is 3 favorable outcomes out of 8 total possible outcomes. This can be expressed as 3/8 or 0.125.

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The value of df for a test with four categories and a sample of any size is 3.

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as (number of categories - 1) since one category can be determined from the frequencies of the other categories.

In this case, there are four categories, so the degrees of freedom would be (4 - 1) = 3.

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There are 72 different bracelets with 4 identical red beads, 4 identical orange beads, and 2 yellow beads, after flipping a bracelet.

To find the number of different bracelets, we can use the concept of permutations.

First, let's consider the red beads.

Since there are 4 identical red beads, the number of ways to arrange them in a line is 4! (4 factorial).

However, since rotating the bracelet does not change it, we need to divide by 4 to account for the different rotations of the same arrangement.

So, the number of arrangements of the red beads is 4!/4 = 6.

Next, let's consider the orange beads.

Similarly, there are 4!/(4 * 2) = 12 different arrangements of the orange beads.

Again, we divide by 4 to account for the different rotations.

Lastly, we have the yellow beads. Since there are 2 identical yellow beads, there is only 1 arrangement for them.

To find the total number of different bracelets, we multiply the number of arrangements for each type of bead:

6 * 12 * 1 = 72.

Therefore, there are 72 different bracelets with 4 identical red beads, 4 identical orange beads, and 2 yellow beads, if rotating or flipping a bracelet does not change it.

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Answer:

w = 8

Step-by-step explanation:

2(3w - 7) = 34 ( divide both sides by 2 )

3w - 7 = 17 ( add 7 to both sides )

3w = 24 ( divide both sides by 3 )

w = 8

Answer:

speed of Jim's train = 35 mi/h

speed of Sarah's train = 35 +20 mi/h = 55 mi/hour

Step-by-step explanation:

Let the speed of Jim's train be x mi/h

Given, Sarah and Jim leave a train station at the same time traveling 20mi/h faster that Jim’s train.

speed of Sarah's train = x + 20 mi/h

we know distance = speed * time

time = 3 hours

distance traveled by Sarah's train = 3*(x+20) = 3x+60 miles

distance traveled by Jim's train = 3*x =  3x miles

It is not given that if trains are moving in same or opposite direction.

__________________________________

if they are travelling in same direction

Then, then distance between them = total distance traveled by

faster train -  total distance traveled by

slower train = 3x +60 -3x = 60 miles

which is wrong as the two trains are 270 miles apart

hence, they are travelling in opposite direction

In this case

distance between them = total distance traveled by

faster train +  total distance traveled by

slower train = 3x +60 + 3x = 6x + 60 miles

given that the trains are 270 miles apart

6x + 60 miles = 270 miles

6x = 270 - 60 = 210

x = 210/6 = 35

Thus, speed of Jim's train = 35 mi/h

speed of Sarah's train = 35 +20 mi/h = 55 mi/hour

Answer:

I’m pretty sure you have to multiply the 4 because that’s how many points you get per Galo and multiply by 7 because it was the seventh game so 28.

Step-by-step explanation:

The value of the fraction is 3/-2

A fraction can simply be described as the part of a whole variable, a whole number or a whole element.

The different types of fractions in mathematics are;

From the information given, we have that;

4/-2 - 3/-6

find the lowest common factor

12 - 3/-6

subtract the value, we get;

9/-6

Divide the values into simpler forms

3/-2

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the answer would be 104

How you would get this answer if by dividing 156 ÷3 =52

then you would take the 52 and multiply it by 2 and get 104

I have also provided the work on how to write it out!

Hope this helps and have a good day!

Proofs and Fundamentals: A First Course in Abstract Mathematics" is a textbook that provides an introduction to the fundamental concepts and techniques of abstract mathematics, with a focus on proof writing and logical reasoning.

Unfortunately, as an AI language model, I do not have access to specific solutions or resources like textbooks. However, the book is designed to guide students through various topics such as logic, sets, functions, relations, and basic proof techniques.

It aims to develop students' ability to think critically and construct rigorous mathematical arguments. It is recommended for individuals seeking to enhance their understanding of abstract mathematics and develop foundational skills in proof writing and problem-solving.

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The speed of the current of the river will be 4.47 km per hour.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.

Let 'y' be the speed of the current of the river. Then the equation is given as,

T = T₁ + T₂

17.5 = [110 / (14 + y)] + [110 / (14 - y)]

17.5 / 110 = (14 - y + 14 + y) / (196 - y²)

196 - y² = 176

y² = 20

y = 4.47 km per hour

Then the speed of the current of the river will be 4.47 km per hour.

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The eccentricity of an infinitely long ellipse will be less than 1.

The ratio of the focus's distance from the ellipse's center and the ellipse's distance from one of its ends.

It is easy to comprehend how circular an ellipse is in relation to a circle when we consider its eccentricity. It also measures the ovalness of the ellipse and eccentricity close to one refers to the high degree of ovalness.

The eccentricity of an ellipse is always less than 1 i.e e < 1. The formula for the eccentricity of an ellipse is given by

Which can be written as

Where

e = Eccentricity of the ellipse

c = Distance of the focus from the center of the ellipse

a = Distance of the end of the ellipse from the center

As we know the eccentricity of an ellipse is always less than 1, So we can conclude that the eccentricity of an infinitely long ellipse is less than 1.

Therefore,

The eccentricity of an infinitely long ellipse will be less than 1.

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Answer:

h=3

Step-by-step explanation:

I divided -3.6 on both sides to get h by itself, and now I have h=-3.6/-10.8. combine like terms (-3.6/-10.8) and I got 3. My final answer would be h=3

Step-by-step explanation:

The volume of a cube is the edge³, so to find the edge, you need to calculate the cubic root of it:

\( \sqrt[3]{ \frac{1}{8} } = \frac{1}{2 } \)

Answer:

Step-by-step explanation:

first plug in -21 as X

-21-3=-24

-24/4=-6

(a) f(x) = -x² - 6x - 5:

Roots: x = -5 and x = -1

Y-intercept: -5

Vertex: (-3, 4)

(b) g(x) = 2(x - 1)(x - 3):

Roots: x = 1 and x = 3

Y-intercept: 6

Vertex: (2, -2)

(c) h(x) = 3x² + 12x + 9:

Roots: x = -1 and x = -3

Y-intercept: 9

Vertex: (-2, -3)

Let's find the roots, y-intercept, and vertex for each of the given quadratic function:

(a) f(x) = -x² - 6x - 5:

To find the roots, we set f(x) = 0 and solve for x:

-x² - 6x - 5 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a = -1, b = -6, and c = -5.

x = (-(-6) ± √((-6)² - 4(-1)(-5))) / (2(-1))

x = (6 ± √(36 - 20)) / (-2)

x = (6 ± √16) / (-2)

x = (6 ± 4) / (-2)

So, the roots are:

x = (6 + 4) / (-2) = 10 / (-2) = -5

x = (6 - 4) / (-2) = 2 / (-2) = -1

The roots of f(x) are x = -5 and x = -1.

To find the y-intercept, we set x = 0:

f(0) = -(0)² - 6(0) - 5 = -5

So, the y-intercept of f(x) is -5.

To find the vertex, we use the formula: x = -b / (2a).

x = -(-6) / (2(-1))

x = 6 / (-2)

x = -3

To find the corresponding y-coordinate of the vertex, substitute x = -3 into f(x):

f(-3) = -(-3)² - 6(-3) - 5

f(-3) = -9 + 18 - 5

f(-3) = 4

So, the vertex of f(x) is (-3, 4).

(b) g(x) = 2(x - 1)(x - 3):

To find the roots, we set g(x) = 0 and solve for x:

2(x - 1)(x - 3) = 0

Setting each factor equal to zero:

x - 1 = 0   -->   x = 1

x - 3 = 0   -->   x = 3

The roots of g(x) are x = 1 and x = 3.

To find the y-intercept, we set x = 0:

g(0) = 2(0 - 1)(0 - 3) = 6

So, the y-intercept of g(x) is 6.

To find the vertex, we need to expand the equation:

g(x) = 2(x² - 3x - x + 3)

g(x) = 2(x² - 4x + 3)

g(x) = 2x² - 8x + 6

The vertex of a quadratic function in the form f(x) = ax² + bx + c is given by (-b/(2a), f(-b/(2a))).

Using this formula, we find:

x = -(-8) / (2(2))

x = 8 / 4

x = 2

To find the corresponding y-coordinate of the vertex, substitute x = 2 into g(x):

g(2) = 2(2)² - 8(2) + 6

g(2) = 8 - 16 + 6

g(2) = -2

So, the vertex of g(x) is (2, -2).

(c) h(x) = 3x² + 12x + 9:

To find the roots, we set h(x) = 0 and solve for x:

3x² + 12x + 9 = 0

Divide the equation by 3 to simplify:

x² + 4x + 3 = 0

Factoring the quadratic equation:

(x + 1)(x + 3) = 0

Setting each factor equal to zero:

x + 1 = 0   -->   x = -1

x + 3 = 0   -->   x = -3

The roots of h(x) are x = -1 and x = -3.

To find the y-intercept, we set x = 0:

h(0) = 3(0)² + 12(0) + 9 = 9

So, the y-intercept of h(x) is 9.

To find the vertex, we use the formula: x = -b / (2a).

x = -12 / (2(3))

x = -12 / 6

x = -2

To find the corresponding y-coordinate of the vertex, substitute x = -2 into h(x):

h(-2) = 3(-2)² + 12(-2) + 9

h(-2) = 3(4) - 24 + 9

h(-2) = 12 - 24 + 9

h(-2) = -3

So, the vertex of h(x) is (-2, -3).

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Answer:

1/4

Step-by-step explanation:

I think that you forgot the addition or the subtraction sign between -4x  and 5.  I will assume that it was an addition sign

3(-4x+5) = 12  Multiply everything in the parentheses by 3

-12x + 15 = 12  Subtract 15 from both sides

-12x = -3  Divide both sides by -12

x = -3/-12 = 3/12 =1/4

Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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Answer:

The answer is $105

Step-by-step explanation:

Solution: 4x = 12

Answer:

$46.00

Step-by-step explanation:

$46.00 - $20 + $5 = $21

Answer:

\( \: x = 10\)

Step-by-step explanation:

prefer the attachment

according to the question

\( \displaystyle \: \frac{6}{17.5-x} = \frac{8 + 6}{17.5} \)

simplify addition:

\( \displaystyle \: \frac{6}{17.5-x} = \frac{14}{17.5 } \)

simplify fraction;

\( \displaystyle \: \frac{6}{17.5 - x} = 0.8\)

cross multiplication:

\(\displaystyle 6 = 14 - 0.8x\)

cancel 14 from both sides:

\( \displaystyle - 8= - 0.8x\)

divide both sides by -0.8:

\( \therefore \: x = 10\)

Functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

a) L(A) = 1 - 1: This function is not a linear operator because it does not preserve scalar multiplication. Multiplying A by a scalar c would yield L(cA) = c - c, which is not equal to cL(A) = c(1 - 1) = 0.

b) L(A) = 1 + 17: Similar to the previous case, this function is not linear since it fails to preserve scalar multiplication. Multiplying A by a scalar c would result in L(cA) = c + 17, which is not equal to cL(A) = c(1 + 17) = c + 17c.

c) L(1) = C1 + AC: This function is a linear operator since it satisfies both the preservation of addition and scalar multiplication properties. Adding matrices A and B and multiplying the result by scalar c will yield L(A + B) = C(1) + AC + C(1) + BC = L(A) + L(B), and L(cA) = C(1) + cAC = cL(A).

d) L(1) = C°1: This function is a linear operator since it satisfies the properties of linearity. Addition and scalar multiplication are preserved, and L(cA) = C(0)1 = c(C(0)1) = cL(A).

e) L(1) = 1?C: This function is not a linear operator as it does not preserve scalar multiplication. Multiplying A by a scalar c would give L(cA) = 1?(cC), which is not equal to cL(A) = c(1?C).

In summary, functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

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Answer:

(a)  5/12

Step-by-step explanation:

to solve this problem you can make all fractions equivalent with 12 as the denominator

a) 5/12

b) 2/3 = 8/12      Multiply top and bottom by 4

c) 5/6 = 10/12     Multiply top and bottom by 2

d) 3/4 = 9/12       Multiply top and bottom by 3

if you compare numerators, the smallest one is the closest to zero, which would be (a) 5/12

Answer:

A 5/12

Step-by-step explanation:

first you need to round these all to /12 so a is 5/12

12/3 is 4 so multiply 4 by two which means b is 8/12

12/6 is 2 so multiply 5 by two which gives us c = 10/12

12/4 is 3 and multiply 3 x 3 which is 9 so d is 9/12

5 is the lowest decimal/fraction which makes it the closest to 0

Step-by-step explanation:

\( \tt{1. \: {a}^{6} \times {a}^{8} = {a}^{6 + 8} = \boxed{ \tt{{a}^{14}} }}\)

\( \tt{2. \: \: {x}^{5} \times {x}^{3} = {x}^{5 + 3} = \boxed{ \tt{{x}^{8} }}}\)

{ To multiply two terms with same base , their indices are added and the same base is taken }

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By solving the equation we know that 15 players can be brought to the tournament.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, we know that:

Softball players raised $1186.50 to attend a tournament.

They allocated $21.50 for meals per player and paid $842.50 for the bus rental.

We must apply the following calculation to determine the total number of players they are permitted to bring:

Formula: Total amount of money= fixed cost + unitary variable cost × number of players

1186.50 = 842.50 + 21.50 × number of players

1186.50 - 842.50 = 21.50 × number of players

344/21.50 = number of players

15 = Number of players

Therefore, by solving the equation we know that 15 players can be brought to the tournament.

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