Miguel rode his bike to work which was 15 miles from home. However he was too tired to ride back so he got a ride in a
car from a co-worker. He spent a total of 2 hours traveling. The average speed of traveling by car was 3 times faster
than on his bike. What was Miguel's average speed on his bike and in the car?

The values that are solutions to the inequality -3 < 2x -3 are all real numbers greater than 0.

Given the inequality in the question;

-3 < 2x -3

Solve for x, by making it the subject of the formula.

Subtract 2x from both sides

-3 < 2x -3

-3 - 2x < -3

Add 3 to both sides

-3 + 3 - 2x < -3 + 3

-2x < -3 + 3

-2x < -3 + 3

-2x < 0

Next, divide both sides by -2

-2x/-2 >  0/2

x > 0/2

x > 0

Therefore, the solution to the inequality is x > 0.

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On solving the provided question, we can say that -  here in the function, every element has an unique image

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

every element has an unique image and,

this relation, is not a function, since it is not one-one and onto.

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The science of statistics focuses on creating and researching strategies for gathering, analysing, interpreting, and presenting empirical data.

Research in statistics finds application in almost all scientific domains, and research concerns in the various scientific fields inspire the creation of new statistical methods and theories. Statistics is a very interdisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the theory that supports such methods. Uncertainty and variation are two key concepts in the study of statistics. In science, as well as more generally in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air. Probability is a mathematical language that is used to talk about uncertain events, and it is crucial to statistics. There are numerous causes of variance that can affect any measurement or data collection attempt. By this, we indicate that the result would probably alter if the same measurement was repeated. The goal of statisticians is to comprehend and, whenever feasible, manage the sources of variation.

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Answer:

  DNE

Step-by-step explanation:

You want the value of 'b' so that the system of equations has no solution.

In order for the system of two linear equations to have no solution, the equations must describe parallel lines. That is, the lines must have the same slope.

The slope of the line written in the form px -qy = c is the coefficient of x when the equation is rearranged to "y=" form. Here, that is p/q.

The slope of the first line is 5/2; the slope of the second line is 5/6. These values are different and do not depend on 'b'.

There is no value of 'b' that will make this system have no solution. It does not exist (DNE).

Answer:

Perpendicular line ⇒ 2x + 9y + 42 = 0

midpoint: (-1,1)

Step-by-step explanation:

Let's find the coordinates of midpoint of AB

Here, from figure, A = (-3,-2), B = (1,4)

So midpoint:

[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]

∴ P = (-1, 1)

Now, given straight line is x - 2y = -8(x-8)

⇒x - 2y = -8x+64

⇒9x - 2y - 64 = 0

Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0

Perpendicular line passes though (6,-6)

Putting the values, we get

2(6) + 9(-6) + k = 0

⇒12 - 54 + k = 0

⇒k = 42

∴ Perpendicular line ⇒ 2x + 9y + 42 = 0

Answer:

90 degree

Step-by-step explanation:

since the original angle BAC is 90 degree, no matter the triangle is rotated or translated, the angle remain unchanged

The equation that corresponds to fraction   [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is [tex]\frac{1}{7^{14} }[/tex] . A phrase by itself could contain an action .

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator). A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence.

given

[tex]\frac{7^{-10} }{(7^{4} )(7^{0} )} \\= \frac{1}{7^{4} } *\frac{1}{7^{10} } * 1\\= \frac{1}{7^{14} }[/tex]

The equation that corresponds to fraction   [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is  [tex]\frac{1}{7^{14} }[/tex] .

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Answer:

[tex]a^{12} b^{4}[/tex]

Step-by-step explanation:

To simplify we will have to use the negative exponent rule and the power rule along with some algebra.

Negative Exponent Rule

[tex]a^{-b} =\frac{1}{a^b}[/tex]

Power Rule

[tex](a^b)^{c} =a^{bc}[/tex]

Given

[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]a^{-4}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]b^{-1}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]

Simplify

[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]

Rewrite the base as its reciprocal.

[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]

Cancel the common factor of [tex]c^2[/tex].

[tex]a^8b^2 a^4b^2[/tex]

Apply the power rule.

[tex]a^{12} b^{4}[/tex]

Answer:

[tex]a^{12}\:b^{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]

Simplify:

[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]

Collect like terms:

[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]

Simplify:

[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies a^{12}\:b^{4}(1)[/tex]

[tex]\implies a^{12}\:b^{4}[/tex]

The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).

To correctly model the expression -2/6 + (5/6) on a number line, we can use the following steps:

So to model the expression -2/6 + (5/6) on a number line, we start at 0 and move 1/3 to the left, to represent -2/6, and then move 5/6 to the right to represent 5/6. The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).

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When calculating the surface area of a 3D shape, it is important to remember to include the area of all the components that make up the shape.

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Answer:

The table with (-3, 2), (0, 2), etc.

Every input has exactly one output.

Hope this helps :)

First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.

The line that passes through these two points is y=x-2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here function whose graph contains the points (9, 7) and (4, −8)

Thus using the two point formula for a line we get the equation as              y-7=(x-9)

y=x-2

Hence, The line that passes through these two points is y=x-2

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Answer:

11

Step-by-step explanation:

Based on the given conditions, formulate: 25 - 14

Calculate the sum or difference: 11

get the result: 11

The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=x/(x-9) and g(x)= -8/x.

1) f(g)

Here, f(-8/x)= -8/x ÷ (-8/x -9)

= -8/x ÷ (-8-9x)/x

= -8/x × x/(-8-9x)

= 8/(8+9x)

2) g(f)

Now, -8/x/(x-9)

-8x/(x-9)

3) f(f)

Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)

= x/(x-9) ÷ ((x-9x+81)/(x-9))

= x/(x-9) × (x-9)/(-8x+81)

= x/(-8x+81)

4) g(g)

Now, -8/(-8/x)

= 64/x

Therefore, the function f(g) is 8/(8+9x).

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Answer:

In the quadratic function "y = -x^2q - 2x + 10", the term "-x^2q" is the coefficient of the quadratic term and is represented by the letter "A". The term "-2x" is the coefficient of the linear term and is represented by the letter "B". The constant term "10" is the coefficient of the constant term and is represented by the letter "C".

The axis of symmetry of the graph of this quadratic function is the line that divides the graph into two congruent halves. It can be found by using the formula "x = -B / 2A". In this case, the axis of symmetry is "x = -(-2) / 2(-x^2q) = x^2q / x".

So in the function "y = -x^2q - 2x + 10", the coefficient of the quadratic term is "A = -x^2q", the coefficient of the linear term is "B = -2x", the coefficient of the constant term is "C = 10", and the axis of symmetry is "x = x^2q / x".

The length x is found to be 10 yards and is calculated using Polygon Triangulation.

What is Polygon Triangulation?

The polygonal triangulation is a method in which the area of polygon is divided into triangles to simplify calculation.

From the attached figure, we can find a using Pythagorus Theorem

a = [tex]\sqrt{6^{2} - 4.8^{2} }[/tex] = 3.6

cos θ = [tex]\frac{4.8}{6}[/tex] = 0.8

In ΔXYZ

cos θ = [tex]\frac{8 + 4.8 }{x+ 6} \\\\[/tex]

0.8 =       [tex]\frac{12.8}{x + 6}[/tex]

Solving for x,

x = 10 yards

Therefore the length of x found using polygonal triangulation method is 10 yards.

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The unit rate for meters per second if a car travels 424 meters in 8 seconds is 53 meters per second.

The unit rate meters per second can be determine using this formula

Unit rate meters per second = Number of meters / Numbers of seconds

Where:

Number of meters = 424 meters

Numbers of seconds = 8 seconds

Let plug in the formula

Unit rate meters per second  = 424 meters / 8 seconds

Unit rate meters per second = 53 meters per second

Therefore we can conclude that the Unit rate meters per second  is 53 meters per seconds.

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Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).

An equation is a mathematical representation of two identical variables, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra is the fundamental building block of mathematics.

Here,

[tex](x + 2)^{2}[/tex] / [tex]a^{2}[/tex] +  [tex](y-5)^{2}[/tex] /[tex]b^{2}[/tex] -=1 is (h, k).

the ellipse's nucleus

The major axis is the larger of the two axes, which are 2a and 26.

(H, a, k) and (H, k, b) are the vertices. Vertices are those along the major axis in this case, and covertices are those along the minor axis.

[tex](x + 2)^{2}[/tex]/16 + [tex](y-5)^{2}[/tex] /20 =1

can be written as

[tex](x + 2)^{2}[/tex]/ [tex]4^{2}[/tex]   +       [tex](y-5)^{2}[/tex] /(2√/5)2

hence centre is (-2, 5), maor axis is 2 x 2√√5 = 4√√5 and minor axis

is 2 x 4 = 8

Vertices are ( 2,5 25), or ( 2,5 25) and ( 2,5 + 25), while covertices are ( 2 4, 5) and ( 6,5), respectively.

As a result of the presence of a vertical major axis, eccentricity e and focii are

(h, k ± be). e is given by the relation a2 = b2(1 − e2) i.e.

=> e = [tex]\sqrt{1 - \frac{a^{2} }{b^{2}} }[/tex]

 a2= 16 and b2= 62

=> e = 1/√5

Focii (-2,5 ± (2√5 x 1/√5)

or (-2,5±2) i.e. (-2, 7) and (-2, 3).

Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).

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1) The equation is:

y = -29/x

And when we evaluate in x = 2, we get y = -14.5

2)  The equation is:

y = 88/x

And when we evaluate in x = 2, we get y = 44

We know that the variables x and y vary inversely, then the equation between these variables will be something like:

y = k/x

Where k is a constant.

1) First we know that when x = -1, y = 29, replacing these values we will get:

29 = k/-1

-1*29 = k

-29 = k

Then the equation is:

y = -29/x

If now we evaluate in x = 2, we will get:

y = -29/2

y = -14.5

2) Now we know that x = 8 and y = 11, replacing these we get:

11 = k/8

11*8 = k

88 = k

So the equation is:

y = 88/x

If now we replace x by 2, we will get:

y = 88/2 = 44

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1)Triangle : s = 6cm ; P= 18 cm

2.) Square : s = 7 cm ; P = 28 cm

3.) Rectangle = W = 4cm , L = 8 cm ; P = 24cm

4.) Regular Heptagon : s = 3cm ; P = 21 cm

5.) Circle : r = 12cm ; C = 24∏ cm.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Given that the length of each side of a triangle is 6 cm.

The perimeter of an equilateral triangle is 3a, where a is the length of the side of the equilateral triangle.

The perimeter of the triangle is 3 × 6 = 18 cm

The length of side of a square is 7 cm.

The perimeter of a square is 4a, where a is the length of the side of the square.

The perimeter of the square is 4 × 7 = 28 cm.

The length and breadth of a rectangle is W = 4 cm and L = 8 cm.

The perimeter of a rectangle is 2(L+ W)

The perimeter of the rectangle is = 2(8 + 4) = 2 × 12 =24 cm

The perimeter of Regular Heptagon is 7a, where a is the length of the side of the Regular Heptagon.

The perimeter of a Regular Heptagon is (7  × 3) = 21 cm

The perimeter of a circle with a radius r is 2∏r.

The perimeter of the circle is 2∏ × 12 = 24∏ cm.

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The lines with a slope larger than f(x) are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, you can see that the line crosses the y-axis at y = -4, so the line is something like:

y = a*x - 4

And we can see that it crosses the x-axis at x = 2, then we can write the equation:

0 = a*2 - 4

4 = a*2

4/2 = a

2 = a

So the linear equation on the graph is:

y = 2*x - 4

The slope is 2, the linear equations with a slope larger than that are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

Which can be rewritten as:

y = (5/4)*16x - (5/4)*(1/2)

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Answer: y = 17x - 19

Step-by-step explanation:

17x + y = -19

Subtract 17 on both sides

Y= -19 - 17x

Then put it in y= mx + b

Y= -17x - 19

Answer:

y = -17x -19

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

17x+y = -19

Solve for y

y = -17x -19

The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

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The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.

The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.

The present value is higher when the discount rate is lower, and vice versa.

The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.

In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).

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Answer:

k = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

[tex]\frac{3}{4}[/tex] = k

Answer: 16.10

Step-by-step explanation:

$14 + 15% increase rate = 16.10

15% = 2.10