Is a number closer to 0 greater or less than a number more away from 0? (negatives and positives)

As per the linear function, the destination after 57 minutes of driving is 1055 miles.

Linear function:

The linear equation is defined as an algebraic equation of the form

y = mx + b.

involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given,

Trey is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes).

Trey has 49 miles to his destination after 37 minutes of driving, and he has 37.8 miles to his destination after 51 minutes of driving.

Here we need to find his destination after 57 minutes of driving.

In this one, first we have to find the linear equation for the situation.

For that, we need the slope and the intercept.

So, here we consider the distance as y axis and the corresponding time as x axis. then we get the points as,

(x1. y1) => (37, 49)

(x2, y2) => (51,37.8)

Then the slope of the line is calculated as,

m = (37.8 - 49) / (51 - 37)

m = -11.2/14

Now, the intercept is calculated using the point (37,49) and the slope m = -11.2/14 is,

49 = -11.2/14(37) + b

686 = -414.4 + b

b = 1100.4

So, the linear equation of the function is

y = -11.2/14x + 1100.4

Here we need to find the distance when the time is 57 minutes,

For that, we have to apply the value of x as 57, to get the value of y,

Therefore,

y = -11.2/14 (57) + 1100.4

y = -45.6 + 1100.4

y = 1055

Therefore, the destination after 57 minutes of driving is 1055 miles.

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The volume of remaining solid is 7 in³.

The whole three-dimensional area occupied by a cube is its volume.

A cube is a solid 3-D object with six square faces and equal-length sides.

The cube is one of the five platonic solid shapes and is also referred to as a regular hexahedron.

The cubic units are used to represent the cube's volume.

Imagine performing each cut individually.

A box 2*2*3 is eliminated in the initial cut. Two boxes with dimensions of 2*2*0.5 are removed during the second cut, and the third cut eliminates the same number of boxes on the final two faces.

Therefore, the sum of all cuts is 12 + 4 + 4 = 20.

∴Volume of rest of cube = 3³-20

                                         = 7 in³

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Answer:

y=2x+4

Step-by-step explanation:

get x is get two point let’s say (-2,0) and (0,4)

The 4-0/0-(-2)=4/2=2 so 2 is x and (0,4) is where it hit the y axis so 4 is b plug in

Y=2x+2

The number of mathematics assignments are 69.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

Given : Brianna has 113 assignments in history, science and art.

Let x be the number of assignments that are in math section. There are 182 assignments in total.

The equation to represent this is

113 + x = 182

x = 182 - 113 = 69.

So the number of math assignments are 69.

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Answer:

-87

Step-by-step explanation:

-4x^2 + 3x - 11

-4(-4)^2 + 3(-4) - 11

-4 * 16 + 3(-4) - 11

-4 * 16 - 12 - 11

-64 - 12 - 11

-76 - 11

-87

Hope this helps! :)

Expressing [tex]\frac{x-1}{2x+1}[/tex]  in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]

Given that:

[tex]x=\frac{2a+3}{3a-2}[/tex]

[tex]\frac{x-1}{2x+1}[/tex]

The Knowledge required here is substitution, the value of x is given. Substitute [tex]x=\frac{2a+3}{3a-2}[/tex] in any place x is seen in the numerator and the denominator.

The numerator

x - 1

substituting the value of x

[tex]\frac{2a+3}{3a-2}-1[/tex]

[tex]\frac{(2a+3)-(3a-2)}{3a-2}[/tex]

[tex]\frac{2a+3-3a+2}{3a-2}[/tex]

[tex]\frac{5-a}{3a-2}[/tex]

The denominator

2x + 1

substituting the value of x

[tex]2*\frac{2a+3}{3a-2} +1[/tex]

[tex]\frac{4a+6}{3a-2} +1[/tex]

[tex]\frac{(4a+6)+(3a-2)}{3a-2}[/tex]

[tex]\frac{7a+4}{3a-2}[/tex]

combining the fraction

Here the numerator and the denominator is brought together and division of fraction is used to solve

[tex]\frac{\frac{5-a}{3a-2}}{\frac{7a+4}{3a-2}}[/tex]

[tex]\frac{5-a}{3a-2}}*\frac{3a-2}{7a+4}[/tex]

[tex]\frac{5-a}{7a+4}[/tex]

Using substitution as required, then expressing the equation in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]

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Suppose the function f(x) = 3x+10 and g(x) = 17x+4, then the value of (f+g)(x) is 20x+14

The function is an expression the show the relationship between one variable and another variable. If one variable is dependent variable another variable will be independent variable.  We can also says that the function shows the relationship between set of inputs and set  of out puts

The function f(x) = 3x+10

g(x) = 17x+4

We have to find the value of (f+g)(x)

We know,

(f+g)(x) = f(x) + g(x)

Substitute the values in the equation

(f+g)(x) = 3x+10 + 17x+4

Add the like terms

(f+g)(x)  = 20x+14

Hence, suppose the function f(x) = 3x+10 and g(x) = 17x+4, then the value of (f+g)(x) is 20x+14

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Answer:

3:7

Step-by-step explanation:

AR has 3 spaces while AB has 7 means its 3:7

The slope of the line will be equal to 30.

Slope of a line may be defined as the steepness of a curve. Slope of line can be positive, negative or zero. Slope of a line is used to determine the equation of the line which is given as y = mx + b where m is the slope, b is y intercept and x and y are independent and dependent variables respectively. The slope of a line on points (x₁, y₁) and (x₂, y₂) is given by the formula, m = y₂ - y₁/x₂ - x₁.

According to the question the value of points is (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 60).

Now, the slope can be calculated as

m = (60 - 0)/(2 - 0)

=> m = 60/2

=> m = 30 which is the required slope.

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The answer is b(x)=f(x)-7, which is option B.

The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The parent linear function is given below.

f(x) = x

The function is shifted downward direction by 7 units. Then the function b(x) will be given as,

b(x) = f(x) - 7

The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.

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Answer:

x-3+4 = x+1

Step-by-step explanation:

x-3+4 = x+1.

Answer:

2

Step-by-step explanation:

7y-14=0

7y=14

7y/7=14/7

y=2

The line segment AB with endpoints (-10,0) and (6,8). The equation of the line segment is x-2y+10=0.

Given that,

The line segment AB with endpoints (-10,0) and (6,8).

We have to find the equation of the line segment.

The equation of the line formula is y-y₁=m(x-x₁).

Here we don't know the m value that is nothing but slope of the line.

First we have to find the slope of the line segment.

Slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=(8-0)/(6+10)

m=8/16

m=1/2

Now,

We know the equation of line is y-y₁=m(x-x₁)

y-0=1/2(x+10)

2y=x+10

x-2y+10=0

Therefore, The equation of the line segment is x-2y+10=0.

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The value of the equation d = 4n - 2 for n is (d + 2) ÷ 4.

Given data, d = 4n - 2

For finding the value of n first add 2 to both the side,

d + 2 = 4n - 2 + 2

d + 2 = 4n

Now, divide 4 into both sides of the equation:

(d + 2) ÷ 4 = 4n ÷ 4

(d + 2) ÷ 4 = n

∴ The value of n after solving the equation d = 4n - 2 is (d + 2) ÷ 4.

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answer: associative property

Step-by-step explanation:

NOTE -3 MUST MULTIPLY EVERYTHING IN THE BRACKETS.

[tex] = - 3(v) - 3(2) - 2v \\ = - 3v - 6 - 2v \\ = - 3v - 2v - 6 \\ = - 5v - 6[/tex]

GOODLUCK.

Answer:

I believe you typed that wrong.

The third term should be -15X

And the 3 answers are 3 -6 -1

Step-by-step explanation:

Answer: x=-1   x=-6   x=3

Step-by-step explanation:

[tex]f(x)=x^3+4x^2-15x-18[/tex]

Let's isolate the multiplier (x+1) from the expression  x³+4x²-15x-18  :

[tex]x^3+4x^2-15x-18=\\\\x^3+x^2+3x^2-15x-18=\\\\x^2(x+1)+3(x^2-5x-6)=\\\\x^2(x+1)+3(x^2+x-6x-6)=\\\\x^2(x+1)+3(x(x+1)-6(x+1))=\\\\x^2(x+1)+3(x+1)(x-6)=\\\\(x+1)(x^2+3(x-6))=\\\\(x+1)(x^2+3x-18)[/tex]

Decompose the polynomial х²+3х-18 into factors:

[tex]x^2+3x-18=\\\\x^2+6x-3x-18=\\\\x(x+6)-3(x+6)=\\\\(x+6)(x-3)[/tex]

[tex]Thus,\\\\x^3+4x^2-15x-18=(x+1)(x+6)(x-3)\\\\[/tex]

[tex](x+1)(x+6)(x-3)=0\\\\x+1=0\\x+1-1=0-1\\x=-1\\\\x+6=0\\x+6-6=0-6\\x=-6\\\\x-3=0\\x-3+3=0+3\\x=3[/tex]

Answer:

Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1).

The answer will be .25 and .25 for both set of question. using probablity.

What is Probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.

Total number of students =1-juniors+chemistry+neither+both

(a) For both a junior and chemistry major =1/4 =. 25

(b) probability that she is also a chemistry major will be 1/4 =. 25

Hence The answer for the above two set of qustion will be .25 and .25.

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Equation is 4x-1 =27. that means the correct answer is 27

The equals sign is used in mathematical formulas to show that two expressions are equal. In contrast to English, where an equation is defined as any well-formed formula that consists of two expressions joined by the equals sign, French defines an equation as containing one or more variables. The first stage in resolving a variable equation is determining the values of the variables that lead to equality.

Here, 4x-1 =27
We know that x=7
4x=27+1
4x= 28
Therefore x = 28÷4 = 7.
Hence, 4x-1 =27

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Answer: 20 x 1 x 0.1 + 8 + 1

              2 + 8 = 10

Answer: The 9th term is 41990400

Step-by-step explanation:

As we can see here 25, 150, 900 to find the common ratio i'll divide 150 by 25 which gives me 6

to 25 times 6 is 150

150 times 6 is 900

T=Term

1t=25 2t=150 3t=900 4t=5400 5t=32400 6t=194400 7t=1166400 8t=6998400 9t= 41990400

900*6= 5400

5400*6=32400

32400*6= 194400

194400*6= 1166400

1166400*6= 6998400

6998400*6=41990400

Answer:

3/2

Step-by-step explanation:

XY/Z

-2×-3/4

6/4

3/2

Answer: CAELYNN YOU WWELCOME

Step-by-step explanation:

7 +7+7+7+7+7

Answer:

[tex]x \leq -1[/tex]

Step-by-step explanation:

divide both sides by -4

-2 >= x - 1

(FLIP THE INEQUALITY!!!)

now add 1 to both sides

-1 >= x

flip the equation

x <= -1

that is your answer

Some examples of ratios are:

There are 20 passengers on each bus

There are 2 red and 3 black balls in each box.

Some examples of unit rates are:

The man can run 10 miles in one hour.

I can type 100 words in 30 minutes.

A unit rate means a rate for one of something.

We write this as a ratio with a denominator of one. 

The ratio is the comparison of two quantities of the same units.

We have,

Ratio:

For every 1 car, there are 4 tires.

We can have some examples of ratios as:

1 - There are 20 passengers on each bus

2 - There are 2 red and 3 black balls in each box.

Unit rate:

Car driving 60 miles per hour.

We can have some examples of unit rates:

1 - The man can run 10 miles in one hour.

2 - I can type 100 words in 30 minutes.

Thus,

Some examples of ratios are:

There are 20 passengers on each bus

There are 2 red and 3 black balls in each box.

Some examples of unit rates are:

The man can run 10 miles in one hour.

I can type 100 words in 30 minutes.

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Answer:

Step-by-step explanation:

An equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .What is the Point-slope form?The equation of the straight line has its slope and given point.If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equationy-y₁ = m(x-x₁)Which is the required equation of a line in a point-slope form.WE havex + y = 6y = - x + 6Slope= -1Now, Use the same slope since the two lines are parallel to each other.Point-slope formula:y - 8 = -1 (x - - 4)y - 8 = -1 (x + 4)y - 8 + 8 = -x - 4 + 8y = - x + 4 (Slope-intercept form)Hence, an equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .Learn more about slope here: brainly.com/question/2503591#SPJ2

⇒Parallel lines have equal gradients . It means that to obtain the gradient of the new equation we should first find the gradient of the given equation by writing the given equation in the form y=mx+c

[tex]x-y=6\\y=x-6[/tex]

⇒The gradient of the given equation is 1 as we know that the gradient of the equation is the coefficient of the variable x

This means the equation of the new equation is also going to be 1 since I explained above why.   to find the value of c in the new equation we will substitute the known values in the general equation including the point.

[tex]5=1(-1)+c\\6=-1+c\\c=5+1\\c=6[/tex]

This means that the new equation is going to be:

[tex]y=x+6[/tex]

There are 12,565,671,261 ways to assign scores to the problems in discrete mathematics exam.

In this case, we must employ the combination as well as repetition formula.

C(n + r-1, r) = (n + r -1)!/ r! (n - 1) !

n = 10 is provided (The number of questions)

Every question is worth a minimum of 5 points.

For 10 question = 10×5 = 50 points.

The total are 100 (sum of the scores)

r = 100 - 50

r = 50

Applying the formula.

C(10 + 50 - 1 , 50) = (10 + 50 - 1)!/ 501 (10 - 1)!

C(59, 50) = 59!/50!9!

We get by clarifying the above factorial.

C(59, 50) = 12,565,671,261

Thus, there are 12,565,671,261 ways to assign scores to the problems in discrete mathematics exam.

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