Juan and Houa are reading the same book. At the beginning of the month, Juan was on page 45 and Houa was on page 9. Juan will read 15 pages per day and Houa will read 18 pages per day. Let J represent the page of the book that Juan is on at the end of t days into the month, and let H represent the page of the book that Houa is on at the end of t days into the month. Write an equation for each situation, in terms of t, and determine what page Juan and Houa will be on on the day they are both on the same page.

Using linear functions, it is found that:

a) The cheaper costs are given as follows:

b) Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the cost functions are given as follows:

The costs are equal when:

A(x) = B(x)

3.75 + 4x = 2.5 + 4.5x

0.5x = 1.25

x = 1.25/0.5

x = 2.5.

Hence the cheaper costs are given as follows:

Alley B has the lower initial cost due to the lower cost for the pair of shoes.

For item b, if we increase the cost per game by $0.50 for alley A, we have that:

A(x) = 4.5x + 3.75.

Hence:

Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

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Answer:With what?

Step-by-step explanation:there is no page

Answer:

I helped you on your first question, I wasn't too sure about the others because their answer options are mostly inaccurate from what I know.

Function composition exists a mathematical procedure where two functions, f and g, are taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)).

If the function be f(x) = 10x - 10 then the value of (f ⁰ f⁻¹)(d) is 99.

Function composition exists a mathematical procedure where two functions, f and g, exists taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)). The function g is used in this operation on the outcome of applying the function f to x.

Let the function be f(x) = 10x -10

We want to find (f ⁰ f⁻¹)(d)

To differentiate with respect to X, then we get

[tex]F^{-1}[/tex](x) = 10

To find the value of (f ⁰ f⁻¹)(d)

F([tex]f^{-1}[/tex](x)) = F(10)

F([tex]f^{-1}[/tex](x)) = 10x - 10

substituting the values in the above equation, then

F([tex]f^{-1}[/tex](x)) = 10(10) - 10

simplifying the above equation, we get

F([tex]f^{-1}[/tex](x)) = 100 -10

F([tex]f^{-1}[/tex](x)) = 99

Therefore, the value of (f ⁰ f⁻¹)(d) = 99

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The factored form of the given expression is (3x+2)(9x²-6x+4).

Given the expression is 27x³+8.

In order to be factor out any polynomial expression, we want to identify firstly the method of factoring to be used in the given expression. We also need to simplify the factors.

We are given the expression 27x³+8.

We want to factor out the given expression.

Applying the sum of two cubes formula x³+y³=(x+y)(x²-xy+y²), we have:

27x³+8=(3x)³+(2)³

27x³+8=(3x+2)(3²x²-3x·2+2²)

27x³+8=(3x+2)(9x²-6x+4)

Hence, the factored form of the given expression 27x³+8 is (3x+2)(9x²-6x+4).

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The correct option is (A) The y-coordinate is -5. If point D(-1, 5) is reflected across the x-axis then the coordinates of D’ are (-1, -5).

Geometry. The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).

Determine the location of the mirror line before reflecting an object on a coordinate plane. Simply multiply the coordinate of the point by -1 to reflect over the axis. Use the symbols. Simply multiply the coordinate of the point by -1 to reflect over the axis.

Given coordinates of D= (-1, 5)

While reflecting any points across the x-axis with coordinates as (x, y) becomes, (x, -y). i.e sign of y-coordinate changes.

The rule is: (x, y) arrow (x, -y)

Applying so, after reflecting point D, its reflection D' will have coordinates as (-1, -5)

Therefore, the y-coordinate is -5.

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According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.

Therefore, the given expression is [tex]3 ln x+2 ln y = ln5[/tex]

The values get multiplied in addition. Therefore, the above expression can be written as: [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]

Expression = [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]

Using logarithmic definition, we can write:

[tex]ln(x^{3} )+ln(y^{2} )+ln5\\ln(5x^{3} y^{2} )[/tex]

The solution for the given expression is [tex]ln(5x^{3}y^{2} )[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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The difference of the amounts after practice and before practice is 18 full.

The difference as a fraction in simplest form will be 9/28.

The sports drink bottle is 56 full and after practice, the bottle is 38 full, the difference of the amounts after practice and before practice will be:

= 56 - 38

= 18

The difference as a fraction in simplest form will be:

= Difference / Original value

= 18 / 56

= 9 / 28

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The midpoint of AB is M(-4, -3). If the coordinates of A are (−1,−2), then B has coordinates of (-2, -7/3)

Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.

Line AB has a midpoint, M.

A is (-1, -2)

B is unknown, M is(−4,−3)

Let's assume straight line of the form y=mx+b, where m is the slope.

Rise = (-3-(-2))= -1

Run = (-4-(-1)) =  -3

Slope = (Rise/Run) = (1/3)

The line becomes y=(1/3)x+b

Calculate b, the y-intercept (the value of y when x is 0)

y=(1/3)x+b

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

b = -2 + (1/3)

b = -5/3

The equation becomes:

y=(1/3)x - -5/3

Find the value of y for x=-2:

y=(1/3)x - -5/3

y=(1/3)(-2) - 5/3

y= -7/3

B has coordinates of (-2, -7/3)

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Answer:

1/4

Step-by-step explanation:

Get x by itself by dividing both sides by 8

x = 2/8

Reduce

1/4

Answer:

8x=2

/8   /8

Step-by-step explanation:

it is 0.25

8x=2

/8   /8

x=0.25

Answer:

-3.78= (-1.2y)+(-4.2y)

y= 0.7

Step-by-step explanation:

-3.78= (-1.2y)+(-4.2y)

-3.78= -5.4y

/-5.4    /-5.4

y=0.7

The length of each rope is 1.35 meters

Lola went to the hardware store and bought 6 yellow ropes

The total length of the rope was 8.1 meters

Therefore the length of each rope can be calculated as follows

= 8.1/6

= 1.35

Hence the length of each rope at the hardware store is 1.35 meters

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Step-by-step explanation:

first : the sum of all angles in a triangle is always 180°.

second : the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides, A, B, C are the the corresponding opposite angles.

therefore,

angle J = 180 - 71 - 46 = 63°

j/sin(J) = k/sin(K)

11/sin(63) = k/sin(46)

k = 11×sin(46)/sin(63) = 8.880673249... m

The match is

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

Given:

10 + 14

=2(5 +7)

25 + 10

=5(5 +2)

32 + 12

=4(8 + 3)

6+9

=3(2 +3)

So, the matching is

10 + 14 -------> 2(5 +7)

25 + 10 --------> 5(5 +2)

32 + 12 --------->4(8 + 3)

6 + 9-----------> 3(2 +3)

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Check the picture below.

Tristian and Barry both are correct as 9,32 is a rational and terminating decimal.

A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.

A terminating decimal is a decimal number with a finite number of digits after the decimal point. The repeating decimal 5.6500000000... can be used to represent a terminating decimal like 5.65, however, when it is zero, the value is typically referred to as terminating.

A decimal number having a limited number of digits following the decimal point is referred to as a terminating decimal. Therefore, all decimal numbers that terminate are rational numbers.

Hence both are correct.

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The solution for the expression ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴

Given expression is ( -8x³) ⁻ ⁴/₃

= ( -8x³) ⁻ ⁴/₃

It can be written as

We know that 8 = 2³ then

= ((-2x)³) ⁻ ⁴/₃

= ((-2x)³* ⁻ ⁴/₃

On the exponents '3' will be canceled then we get

= (-2x) ⁻ ⁴

We know that x ⁻ ¹ can be written as 1/x, then

= 1/(-2x)⁴

= 1 / 16x⁴

∴  ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴

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If Jodi wants to visit her extended family in Barbados next summer, and the flight costs $450, then she needs to save 50$ each month if she wants to buy the flight in exactly 9 months.

If the flight costs $450, then the amount of money Jodi needs to save each month can be determined by using division.

Division is one of the four basic operations of arithmetic and involves the separation into equal parts.

By dividing the cost of the flight by the number of months, the money Jodi needs to save each month can be calculated.

Considering x to be money Jodi needs to save each month,

x = flight cost / number of months

x = 450 / 9

x = 50

Hence, the money Jodi needs to save each month if she wants to buy the flight in 9 months is calculated to 50$.

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Answer: 1:15

Step-by-step explanation:

we know that the total number of eggs is the same as the number of eggs in 30 boxes. Hence the ratio will be 2 : 30, and then divide both sides by 2 to get 1 : 15 as the ratio in its simplest terms.

The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.

We have,

To find the ratio of the number of eggs in three boxes to the total number of eggs, first, let's calculate the number of eggs in three boxes:

Number of eggs in three boxes

= 3 boxes * 6 eggs per box

= 18 eggs

Now, the ratio of the number of eggs in three boxes to the total number of eggs is:

18 eggs : 30 boxes x 6 eggs per box

18 eggs : 180 eggs

Cancel out the common factors.

1 egg : 10 eggs

So, the simplified ratio is:

1 egg : 10 boxes

Therefore,

The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.

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[Mathematical Problem]

[tex](2x)^2y; x=4,y=8[/tex]

Solution:

Substitute the value of the variable into the expression, then simplify.

[tex](2(4))^2[/tex] × [tex]8[/tex]

↓

[tex](8)^2[/tex]

↓

[tex](8)^2[/tex] × [tex]8[/tex]

↓

[tex]64[/tex]

↓

[tex]64[/tex] × [tex]8[/tex] = 512

Hence, our solution is 512.

Hope this helps! It's been a while since I've done this, but this should be correct. Lmk if it helps! Thanks and good luck!

Motorcycle A  has a greater top speed.

A unit conversion expresses the same property as a different unit of measurement.

given:

Motorcycle A can reach a top speed of 140 miles per hour.

Motorcycle B can reach a top speed of 200 feet per second

Now,

1 miles/h = 1.46667 feet/sec

140 miles/h = 140*

                    = 205.333 feet/sec

So, Motorcycle A can reach a top speed of 205.333 feet/sec.

Hence, Motorcycle A  has a greater top speed

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The negative exponent of 1/16 is   2⁻^{4}.

A statement is considered to be an expression if it has a minimum of two numbers or variables as well as at least one mathematical action.

The multiplicative inverse of the base raised to the power opposite to the provided power is the definition of a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. For instance, (2/3)-2 may be represented as (3/2)2.

1/16 = 16⁻¹  

1/16 = 16⁻¹  = 4⁻²

1/16 = 16⁻¹  = 4⁻² =  (2^2)⁻²  =  2⁻^{4} .

1/16 =   2⁻^{4} .

Hence, the negative exponent of 1/16 is   2⁻^{4}.

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Answer:

5. 18%

6. 5.25% o 5.3 o 5

7. 33.33%

8. 2005-2010

The total number of seats in row g is 224.

Number of seats in a row a = 10

Number of seats in row b = 16

Number of seats in row c = 22

The common difference is d.

d = (22-16) = 6

The first term is a.

a = 10

The total number of rows is n.

n = 7

[tex]a _{n} = a + (n - 1)d[/tex]

[tex]a _{n} = 10 + (7 - 1)6[/tex]

= 46

The total number of seats in row g is,

[tex]S _{n} = \frac{n}{2} (a + a _{n})[/tex]

[tex]S _{n} = \frac{8}{2} (10 + 46)[/tex]

= 224

Therefore, the total number of seats in row g is 224.

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The solutions of the equation [tex]4(3x-3)^{\frac{2}{3} } = 36[/tex] are x = 10 and x = - 8.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

[tex]4(3x-3)^{\frac{2}{3} } = 36[/tex]

Now, divide each side of the equation by 4.

[tex]\frac{4(3x-3)^{\frac{2}{3} }}{4}=\frac{36}{4}[/tex]

[tex](3x-3)^{\frac{2}{3} } = 9[/tex]

Cubing the above equation.

[tex]((3x-3)^{\frac{2}{3} })^{3}=(9)^{3}[/tex]

( 3x - 3 )² = 729

3x - 3 = ( √729 )

3x - 3 = ± 27

Now,

3x - 3 = 27

3x = 30

x = 10

and;

3x - 3 = - 27

3x = - 24

x = - 8

Checking for extraneous solutions,

x = 10

[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(10)-3)^{\frac{2}{3} }=36\\4(27)^{\frac{2}{3} }=36\\27^{\frac{2}{3} }=9\\(3^{3})^{\frac{2}{3} } = 9\\3^{2}=9\\9=9[/tex]

When x = - 8,

[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(-8)-3)^{\frac{2}{3}}=36\\(-27)^{\frac{2}{3}}=9\\(-27)^{2}=(9)^{3}\\729=729[/tex]

The solutions for the equation are x = 10 and x = - 8.

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Answer:

k=4

Step-by-step explanation:

−4k+6−2k=−3(4k−10)

−4k+6−2k=−3(4k−10)

−4k+6+−2k=(−3)(4k)+(−3)(−10)

−4k+6+−2k=−12k+30

(−4k+−2k)+(6)=−12k+30

−6k+6=−12k+30

−6k+6=−12k+30

−6k+6+12k=−12k+30+12k

6k+6=30

6k+6−6=30−6

6k=24

6k/6=24/6

k=4

(sorry if this was confusing)

Answer:

-3.5

Step-by-step explanation:

-4k+ 6 - 2k= -3(-6k)

-4k+ 4k= 18k

-4k = 18k-4k

-4k = 14

-4k/-4 = 14/-4

K= -3.5