Jim began a 167​-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 4 miles per hour and rides at 30 miles per​ hour, find the amount of time he spent on the bicycle.

The GCF of 10 and 4x is 2.

The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into each of them. Factoring a number means breaking it down into its prime factors. That is;

10 = 2 * 5 , we can see that 2 and 5 are the prime factors of 10.

4x = 4 * x, we can see that 4 and x are the prime factors of 4x.

Since 2 is the only common factor between 10 and 4x, we can conclude that 2 is the GCF of 10 and 4x.

It means that 2 is the greatest number that divides into both 10 and 4x with a remainder.

Therefore, the GCF of 10 and 4x is 2.

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The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter.

given

This equation can be used to represent the value of the computer: price of the computer one year ago x (1 - rate of decline)

The computer's current market value 0 = $800

Computer value at time 1 is $800 multiplied by 3/14 by 1 to get $600.

The computer's current market value 2 = $600 x 3/4 = $450

Computer value at time 3: $450 multiplied by 3/4, or $337.50

The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.

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You get a quadratic equation when the square of the expression that comes after b plus b times that same expression not squared plus c equals 0.

Any equation in algebra that can be written in standard form as

ax^2+bx+c=0,

where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.

The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.

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Answer:

Step-by-step explanation:

y = (a-3)x+5

Answer:    

y=3x+5

Step-by-step explanation:

The expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the expression as -

(−4)⁸(−4)⁻⁵(-4)⁰

The given expression is -

(−4)⁸(−4)⁻⁵(-4)⁰

(- 4)⁸ ⁻ ⁵ ⁺ ⁰

(- 4)³

Therefore, the expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.

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Answer:

-1050 = -800 = 25 = 80

Step-by-step explanation:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

1) look at the your numbers and find the negatives. they always are the SMALLEST.

2) as you can see on the line above, there's the middle and from there negative numbers go to the left and positive numbers go to the right.

3) the bigger negative numbers are the smaller they are, super confusing ik

The measure of the angle ∠G of the isosceles triangle will be 51°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

In triangles △GHI, IG ≅ HI, and the measure of the angle ∠H = 51°. Then the measure of the angle ∠G will be given as,

The two sides of the triangle △GHI will be congruent. Then the triangle is known as an isosceles triangle.

If IG ≅ HI, then the measure of the angle ∠G ≅ ∠H.

The measure of the angle ∠G of the isosceles triangle will be 51°.

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Answer: r= 1/5 and s = 2/5

Step-by-step explanation:

trust me

Answer:

Step-by-step explanation:

As 9: 16.2

Then 6: EF   Lets take EF as side x

9:16.2 as

6:x    CROSS MULTIPLY ( 9×x and 16.2×6)

Cross multiplying gives you: 9x and 97.2

Then divide both answers by 9 ( 97.2÷9 and 9x÷9)

This gives you x=10.8 which is side EF

To find side AB ADD 9 and 6 to get 15 and subtract this from 36 and you get 21.

Using the same method to find EF find DE and you will get 37.8

Therefore, perimeter becomes:

16.2 + 37.8 + 10.8 = 64.8

HOPE THIS HELPS

Answer:

P△DEF=64,8

Step-by-step explanation:

P△ABC=36, AC=9, BC=6 → AB=21

AB/DE=BC/EF=AC/DF

AC/DF=9/16,2; AB/DE=21/DE ⇒ DE=(21*16,2)/9=37,8

AC/DF=9/16,2; BC/EF=6/EF ⇒ EF=(6*16,2)/9=10,8

P△DEF=16,2+37,8+10,8=64,8

The number of months that it would take for Linda to replenish the amount she took out is 4 months.

The number of months it would take Linda to make back the $ 100 that she took from her savings account will depend on the amount that she saves every month.

This amount is $ 25 per month.

The number of months it would take for Linda to replenish the $ 25 would therefore be:

= Amount taken out of account / Amount saved per month

= 100 / 25

= 4 months

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Rest of the qyestion is:

How many months will it take Linda to replenish the amount she took out of her savings account ?

Answer:

First question(unnumbered):
 [tex]\mathrm{Choice \; (B) : \;\;\dfrac{1}{2}}[/tex]

Question 48

[tex]\mathrm{Choice \;(C)\;\; (x, y) = \left(-1, \dfrac{3}{2}\right)}[/tex]

Question 49
[tex]\mathrm{Choice \; (D)\;\;-1}[/tex]

Step-by-step explanation:

The imaginary variable i is [tex]\sqrt{-1}[/tex] and [tex]i^2 = -1[/tex]

For the unnumbered first question we have

the equation
[tex]\dfrac{1}{1-i}[/tex]

Multiply numerator and denominator by [tex]i + 1[/tex]

[tex]\rightarrow \dfrac{1\cdot \left(1+i\right)}{\left(1-i\right)\left(1+i\right)}\\\\\\= \dfrac{1 + i}{1 - i^2} \;\;\;\;\;\;\;since \;(a +b)(a-b) = a^2 - b^2\\\\\textrm{Since $i^2 = -1$, the denominator becomes:}\\\\1-i^2 = 1 -(-1) = 2\\\\\\[/tex]

Therefore ,

[tex]\dfrac{1}{1-i} = \dfrac{1 + i}{2}\\\\= \dfrac{1}{2} + \dfrac{i}{2}\\\\[/tex]

The real part is [tex]\dfrac{1}{2}[/tex]   and the imaginary part is [tex]\dfrac{i}{2}[/tex]

Answer to first question is: ) [tex]\dfrac{1}{2}[/tex]
-------------------------------------------------------------------------

#48

Solve [tex](x, y)[/tex]  for [tex]2y\:+\:xi\:=\:4+x-i[/tex] for  [tex]$x,y\in\mathbb{R}$[/tex]

For the equation

[tex]2y\:+\:xi\:=\:4+x-i[/tex]

Move the the x and i terms from the right to left side:

[tex]2y + xi - x + i = 4\\\\2y - x +xi + i =4\\\\[/tex]

Since this works out to a real number, the imaginary part is 0

So

[tex]xi + i = 0\\\\xi = -i\\\\x = \dfrac{-i}{i}\\\\x = -1[/tex]

and the real part

[tex]2y - x = 4[/tex]

Substitute for x = -1 in the above to get
[tex]2y -(-1) = 4\\\\2y + 1 = 4\\\\2y = 4-1\\\\2y = 3\\\\y = \dfrac{3}{2}\\\\[/tex]

[tex](x, y) = \left(-1, \dfrac{3}{2}\right)[/tex]
which is choice (C)

------------------------------------------------------------------------

#49

For [tex]$a,b\in\mathb{R}$[/tex]

[tex]a+ib\:=\:\left(2-i\right)^2 \\\\[/tex]

Expand [tex]x(2-i)^2[/tex]

[tex]= 2^2 - 2.2.i +i^2\\\\[/tex]

Since i² = -1 this works out to:
[tex]4 - 4i -1[/tex]

[tex]3 - 4i[/tex]

Therefore
[tex]a + ib = 3 - 4i\\\\[/tex]

Equation real part on left to the real part on the right :
[tex]a = 3[/tex]

Equation imaginary part on left to the imaginary part on the right :
[tex]ib = 4i[/tex]

[tex]b = -4[/tex]

[tex](a + b) = (3 +(-4))\\\\= 3 - 4 \\\\= -1\\\\[/tex]

This would be option (D)

A ratio remains the same if both antecedent and consequent are multiplied or divided by the same non-zero number.

Step by step explanation:

i.e., a/b = pa/pb = q a/q b ,p ,q ≠0

From the given table we can see that:

For the second column

Since, 6*0.5=3

So, multiply 10 by same number

10*0.5=5

For third column:

since 24=10*5

So, multiply 6 by same number

5*6=30

Hence, the missing values are 30,5

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The number 9 is a numerical digit used in many numeral systems. It is the highest single-digit number and has no specific meaning in and of itself.

The meaning of 9 may vary depending on the context in which it is used. For example, in mathematics, 9 is a composite number, meaning it can be divided by numbers other than itself and 1. In numerology, the number 9 is considered to be a powerful, spiritual number and is often associated with universal love, selflessness, and completion. In other cultures, 9 may hold different meanings or symbolism.

If we check the single digit series we will find the 9 is the 10[tex]th[/tex] and last digit in single digit series.

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Complete question is: What is the meaning of 9?

Answer:

25x+125< 500 15 fewer seats

Step-by-step explanation

this is number 1

Answer:

  j = 1.5

Step-by-step explanation:

You want to solve the equation 0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 for the value of j.

It usually works well to simplify such an equation as the first step. That means eliminating parentheses and combining like terms.

  0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 . . . . . . given

  0.3j -0.1j +3 +0.1 = 2j +0.2 +0.2 . . . . . . eliminate parentheses

  0.2j +3.1 = 2j +0.4 . . . . . . . . . . . . collect terms

  2.7 = 1.8j . . . . . . . . . . . subtract (0.2j +0.4)

  1.5 = j . . . . . . . . . divide by 1.8

The solution is j = 1.5.

__

Additional comment

You are often taught to solve this kind of 3-step equation by subtracting the unwanted variable term and the unwanted constant term in two steps. (The third step is dividing by the coefficient of the variable.) Here, we show those subtractions being done both at once.

The variable term we choose to subtract is the one with the smallest coefficient. That way, the result of the subtraction (1.8j) leaves the coefficient of the variable as a positive number.

Sometimes the variable term on the right is subtracted, so you end up with a "j = " equation. In that case, the equation you would be solving as the last step is ...

  -1.8j = -2.7

which requires arithmetic with negative numbers. Negative numbers tend to be associated with more mistakes, so we choose not to go there.

The solution to the simplification of each of the fractions are;

1) ³/₄ * ¹¹/₅

2) 1 ³/₅ miles

3) 1¹/₈ yards

1) We are told that;

Caleb has 2¹/₅ yards of rope

Quantity of rope used by Caleb = ³/₄

Thus;

³/₄ of 2¹/₅ simply means that we will multiply both.

2¹/₅ can also be expressed as 11/5. Thus, we now have;

³/₄ * ¹¹/₅

2) Number of miles mary hiked = 6²/₅ miles = 32/5 miles

He stopped at 1/4 of the way.

Thus;

Number of miles before stopping = 1/4 * 32/5 = 8/5

= 1 ³/₅ miles

3) The area is gotten by;

A = length * width

A = 1¹/₂ * ³/₄

= 3/2 * 3/4

= 9/8

= 1¹/₈ yards

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Answer:11

Step-by-step explanation:

77 divided by 7 is 11.

The volume of the pyramid is 3.5 cubic centimeters.

The volume of a pyramid can be calculated using the formula:

V = (1/3) * Base area * Height

Where Base area is the area of the base of the pyramid, and Height is the distance from the base to the apex of the pyramid.

Given that the area of the base of the pyramid is 4.6 cm^2 and the height of the pyramid is 2.3 cm, we can substitute these values into the formula and solve for the volume:

V = (1/3) * 4.6 cm^2 * 2.3 cm = 3.53 cm^3

So the volume of the pyramid is 3.53 cubic centimeters. Rounded to the nearest tenth of a cubic centimeter, the volume is 3.5 cm^3.

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................ ................................ 

The money market account earns 8/4 = 2% interest per quarter.

In one year, there are 4 quarters.

so, the formula to calculate the balance after 8 years is:

A = P (1 + r/n)^(nt)

where A is the final balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested for.

Substituting in the given values,

A = 1000 (1 + .02)^(4*8)

A = 1000 (1.02)^32

A = 1000 (1.8587)

A = 1858.7

So after 8 years, Ed will have earned $1858.7.

The proportional equation that is on the graph can be written as:

y = 0.83*x

Remember that a general proportional equation is written as:

y = k*x

Where k is the constant of proportionality.

To find the value of the constant of proportionality, we need to identify one point that lies on its graph. For example, we could use the point (0.6, 0.5)

Where x = 0.6

y = 0.5

Replacing that in the general proportional equation we will get:

0.5 = k*0.6

0.5/0.6 = k

0.83 = k

Then the proportional equation is:

y = 0.83*x

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Therefore , the solution of the given problem of expression comes out to be  0.8x is the required expression.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

Let x be the original price

To find the expression after 20 % discount :

=> x * 20/100 = 0.2x

So,

New price:

=> x - 0.2x

or

=> 0.8x

Therefore , the solution of the given problem of expression comes out to be  0.8x is the required expression.

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The Implicit Differentiation of 5x^2-xy-4y^2=0 is Dy/Dx= (5x-y)/(-4y)

Using implicit differentiation, Dy/Dx can be found by taking the derivative of both sides with respect to x.

On the left side, the derivative with respect to x of 5x2 is 10x and the derivative with respect to x of -xy is -y.

On the right side, the derivative of 4y2 with respect to x is 0.

Therefore, the equation becomes 10x - y = 0.

Solving for y gives y = 10x.

Substituting this into the original equation, we get 5x2 - 10x2 - 4(10x)2 = 0, which simplifies to -5x2 - 40x2 = 0.

Finally, we can solve for Dy/Dx:

Dy/Dx= (5x-10x)/(-4(10x))

Dy/Dx= (5x-y)/(-4y)

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Answer:

y = 13

Step-by-step explanation:

given (7, 33 ) is a solution of the top equation, then

x = 7, y = 33 satisfies the equation , that is

33 = 7a + 5 ( subtract 5 from both sides )

28 = 7a ( divide both sides by 4 )

4 = a

then

y = 4x + 5 ← top equation

substitute y = 4x + 5 into the other equation

9x + 2(4x + 5) = 44

9x + 8x + 10 = 44

17x + 10 = 44 ( subtract 10 from both sides )

17x = 34 ( divide both sides by 17 )

x = 2

substitute x = 2 into the top equation for value of y

y = 4x + 5 = 4(2) + 5 = 8 + 5 = 13

Answer:

This is just a basic mathematical function in which 18.00$ is the starting cost of Happy Paws service and they charge 4.50$ an hour, and we can represent this with [tex]18.00$ + 4.50h = C[/tex].

C is the total cost and h represents the number of hours that took place.

Now looking at Woof Watchers, the starting cost is 12.00$ and they charge 5.75$ an hour, we can also represent this with the equation [tex]12.00 +5.75h=C[/tex].

Now we can figure out the answer the long way or the short way.

The short way is a lot more simple, so I will use that.

The short way is plugging these equations into a graphing calculator.

After that, the number of hours they both babysit to have equal total costs is 4.8 hours or 4 hours and 48 minutes, and the total cost for both services after 4.8 hours will be approximately 40$ or to be exact, 39.60$

Answer: he could've gotten a 60

Step-by-step explanation:

if you follow the line up from 50 on paper 1, it fits onto a 60 for paper 2

The value of x is that will ensure that quadrilateral VWXY is parallelogram is 0.25.

•A polygon called a quadrilateral has four sides, four angles, and four vertices. Parallelograms, Squares, Rectangles, and Rhombuses are the different types of quadrilaterals. Parallelograms also include squares, rectangles, and rhombi.

• All quadrilaterals have a few characteristics. Parallelograms characteristics are each of them has four vertices, each side has four sides, 360 degrees is the sum of all interior angles and two diagonals are present.

•There are regular and irregular quadrilaterals. An ordinary quadrilateral must have four equal sides, four equal angles, and diagonals that cross one another. Only the square can fulfill each of these requirements of a quadrilateral.

As we know that the opposite angles of a parallelogram are equal

hence 10x + 27 = 2x + 29

8x = 2

x = 0.25

Hence, the angles are 29.5

Let the value of angle v and x be a

Now using angle sum property of a parallelogram

29.5 +29.5 + a + a = 360

2a = 301

a = 150.5

hence angle V is 150.5

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