a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe

Using law of logarithm and exponent rules, the value of the unknown is 5

logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.

Logₐ x = n  or   aⁿ = x

Where b is the base of the logarithmic function.

This can be read as “Logarithm of x to the base b is equal to n”.

In this case, we just need to solve for the value of b

4 = logₐ(625)

4 = 1 / log625(a)

multiply both sides by log₆₂₅(x)

log₆₂₅(a) / 4 = 1/4

applying log rules

a = 5

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Answer:

the digit 1 is less than 5, so we round 54.71 down to 54.7.

Step-by-step explanation:

Answer:

1.3,-12,16

Step-by-step explanation:

The equation in slope intercept form of the line that passes through the points (6,1) and (3,3) is y = - 2 / 3 x +5

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, the equation in slope-intercept form of the line that passes through the points (6,1) and (3,3) can be represented as follows;

let's find the slope

m = 3 - 1 / 3 - 6

m =  - 2 / 3

Hence, let's find the y-intercept as follows;

using (3, 3)

y = - 2 / 3 (x) + b

3 = - 2 / 3 (3) + b

3 + 2 = b

b = 5

Therefore, the equation of the line is y = - 2 / 3 x +5

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By the congruence property CD ≅ CX

Congruent examples include what?

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

Which five types of congruence are there?

If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) (RHS).

Given that:

ΔECD ≅ ΔECX

so ED ≅ EX

CD ≅ CX

by the congruence property

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The graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.

What is the graph of the equation?

The graph of an equation is the group of all points on a number line or the coordinate plane that are solutions of an equation (= statement that two amounts are equal).

0 hours- $0

4 hours- $32

8 hours- $64

12 hours- $96

First find the equation of this problem to represent the relationship, which is y = 8x.

Next, you substitute the number of hours into x to get y, which is the amount of money.

Hence, the graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.

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Answer:

C. DIvide both sides by -6 to get 1/9.

Step-by-step explanation:

We want to study the population formula of a given US state according to exponential equation.

a) 23.1 millions.

b) in 2013 - 2014

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main body:

The population state is:

A = 23.1*e^(0.0153*t)

In millions.

Where t represents the number of years after 2000.

a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).

A(0) = 23.1*e^(0.0153*0) = 23.1

The population at year 2000 was 23.1 millions.

b) Now we want to solve:

A(t) = 28.3 = 23.1*e^(0.0153*t)

       28.3/23.1 = e^(0.0153*t)

      1.23 = e^(0.0153*t)

Now we can apply the natural logarithm to both sides:

ln(1.23) = ln( e^(0.0153*t) )

ln(1.23) = 0.0153*t

ln(1.23)/0.0153 = t = 13.5

Hence, 13.5 years after 2000 the population will be 28.3 million.

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Answer:

x = -2

Step-by-step explanation:

hope this will help you

Answer:

137 cheap tickets sold, and 65 best seats sold

Step-by-step explanation:

x+y=202

50x+556y=42900

x=202-y

50(202-y)+556y=42900

10100-50y+556y=42900

10100+506y=42900

506y=32890

y=65

x=202-65

x=137

x= Cheap tickets, y= expensive tickets

Knowing the history of the Earth is of the utmost importance to understand how it got to now and to know where we are going.

The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.

Knowing the history of the Earth is very important because:

¡Hope this helped!

Answer:

The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.

The recursive formula for the arithmetic succession will be written as aₙ = 25 - 5n.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given below.

20, 15, 10, 5, .....

The first term is 20 and the common difference is given as,

d = 15 - 20

d = - 5

Then the recursive formula given the following sequence is given as,

aₙ = a₁ + (n - 1)d

aₙ = 20 + (n - 1) × (-5)

aₙ = 20 - 5n + 5

aₙ = 25 - 5n

The formula for the arithmetic sequence will be written as aₙ = 25 - 5n.

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The Perimeter of the Pentagon in Figure 1 is 40ft

What is Pentagon?

A pentagon is a two-dimensional polygon having five sides and five angles. "Penta" means "five," and "gon" means "angles" in Greek, therefore when we mix the two words "penta + gon," we obtain the term "pentagon."

Solution:

Permieter of Pentagon = 5 * side

In Figure 1, the length of a side is 8 ft,

Then the Perimeter will be 8*5 = 40ft.

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A total of 396 miles and 2.2 hours will pass between the two trains on the Long.

For additional information on how to handle rate-time-distance or motion problems, scroll down the page.

Moving away from one another are the two trains.

85x + 95x = 396

To solve you combine like terms. The like terms are 85x and 95x

85x + 95x = 180x

Right now, you

180x = 396

Now multiply by 180.

180 divided by 396 equals 2.2.

X= 2.2

That's how you do things, in my opinion.

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(a) 2.79 seconds after its release the bag will strike the ground.

(b) At a velocity of 73.28 ft/second it will hit the ground.

What is velocity?

We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.

Assume the acceleration of the object is a(t) = −32 feet per second.

(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;

[tex]s=u t+\frac{1}{2} a t^2[/tex]

Here, s= distance of the balloon above the ground =-80 feet

[tex]$\mathrm{u}=$[/tex] intital velocity =16 feet per second

[tex]$\mathrm{a}=$[/tex]acceleration of the object =-32 feet per second

[tex]$\mathrm{t}=$[/tex] required time

So, [tex]$s=u t+\frac{1}{2} a t^2$[/tex]

[tex]$$\begin{aligned}& -80=(16 \times t)+\left(\frac{1}{2} \times-32 \times t^2\right) \\& -80=16 t-16 t^2 \\& 16 t^2-16 t-80=0 \\& t^2-t-5=0\end{aligned}$$[/tex]

Now, we will use the quadratic D formula for finding the value of t, i.e;

[tex]t=\frac{-b \pm \sqrt{D}}{2 a}[/tex]

Here, a=1, b=-1, and c=-5

Also, [tex]$\mathrm{D}=b^2-4 a c=(-1)^2-(4 \times 1 \times-5)=21$[/tex]

So, [tex]$t=\frac{-(-1) \pm \sqrt{21}}{2(1)}$[/tex]

[tex]t=\frac{1 \pm \sqrt{21}}{2}[/tex]

We will neglect the negative value of t as time can't be negative, so;

[tex]t=\frac{1+\sqrt{21}}{2}=2.79 \approx 3 \text { seconds. }[/tex]

Hence, after 3 seconds of its release, the bag will strike the ground.

(b) For finding the velocity at which it hit the ground, we will use the formula;

v=u+a t

Here, v= final velocity

So,[tex]$v=16+(-32 \times 2.79)$[/tex]

v=16-89.28=-73.28 feet per second.

Hence, the bag will hit the ground at a velocity of [tex]$-73.28 \mathrm{ft} / \mathrm{second}$[/tex].

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Lines with a slope of zero can be thought of as y = 0x + b, which simplifies to just "y = b".

In this case, your equation is y = 16.

If you want to force it explicitly into standard form, you could write it at
   0x + 1y = 16

Answer: Cory can have 6 different schedules

Step-by-step explanation:

Add them all together and divide by fifteen

The required radius of the circle is given as  3.18 m.

Given that,
A circle has a circumference of 20 m. the radius of the circle is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
The perimeter of the circle = 20m
2πr = 20
r = 20/2π
r = 3.18 m

Thus, the required radius of the circle is given as  3.18 m.

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The function in f(t) form that describes the amount of fuel in the plane at time t will be:

f(t) = 112.25t + 31.425.75

What is the Equation of line?

The equation of the line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

we have given that;

After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Now,

Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (32882 - 34902.5) / ((31 - 13)

m = 2020.5 / 18

m = 112.25

Thus, The equation of the line with slope 112.25 is,

⇒ y - 32885 = 112.25 (x - 13)

⇒ y - 32885 = 112.25x - 1459.25

⇒ y = 112.25x - 1459.25 + 32885

⇒ y = 112.25x + 31.425.75

Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be:

f(t) = 112.25t + 31.425.75

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The equation that represents the same relationship is equation 1: x-2y-1=0

We should know that an equation is a mathematical statement that shows the equality of two sides o a statement.

From the given equation:

x-2y-1=0

If we input the various values of x such as -5, 7,31,42 into the equation we are going to obtain the corresponding values of y as indicated in the table

x-2y-1=0

Rewrite the equation

x-1=2y

⇒2y=x-1

=2y=-5-1

y=-3

Also, 2y=7-1

2y=6

y=3

Input the value 31 into the equation or x

2y=31-1

2y=30

y=15

Input the value 45 or x in the equation

2y=45-1

2y=44

y=22

In conclusion, the equation x-2y-1=0 represents the the same relationship  in the table

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Answer: (6,2)

Step-by-step explanation:

(7,5)     (x,2)      m=3     x=?

y=mx+b

y=3x+b   (1)

To find the coefficient b we take the coordinate that belongs to this line (7,5): x=7    y=5

5=3(7)+b

5=21+b

5-21=21+b-21

-16=b

Thus, b=-16

Hence, y=3x-16

To find the x we take the coordinate that belongs to this line (x,2): y=2

2=3x-16

2+16=3x-16+16

18=3x

Divide both parts of the equation by 3:

6=x

Thus, x=6

The quantity of food that would be needed to feed all the cubs for one year is 1825 kg

From the question, we are to determine how much food would be needed to feed all the cubs for one year

From the given information,

"Each cub eats 1.25 kg of food a day"

Assume there are 365 days in a year.

Since there are 4 cubs,

The quantity of food that would feed the cubs for one year = 365 × 4 × 1.25

The quantity of food that would feed the cubs for one year = 1825 kg

Hence, the quantity of food needed is 1825 kg

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The probability of event A and event B of the independent events will be 0.05.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the conditional probability is given as,

P(A and B) = P(A) x P(B)

Event A and event B are independent events. The probability of event A is 0.50 and the probability of event B is 0.10.

Then the probability of event A and event B of the independent events is given as,

P(A and B) = P(A) x P(B)

P(A and B) = 0.50 x 0.10

P(A and B) = 0.05

The probability of event A and event B of the independent events will be 0.05.

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The additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.

What is quadrilateral ?

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Properties include: There are four vertices . There are four sides . 360° is the total of all interior angles. There are two diagonals in them.

Trapezium is one of the five unique quadrilateral shapes. Parallelogram. Rectangle. Rhombus. Square

These bisectors intersect each other at 90 degrees.

And it means that they are perpendicular.

Since they are perpendicular, we find that there 4 congruent triangles, XY is parallel to WZ, and WX is parallel to YZ.

Additionally, opposite angles are equal.

These two latter findings are the characteristics of the parallelogram.  

Hence, the additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.

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1) The legs of △ABC are AB and BC.

2) The name of hypotenuse is AC.

3) The legs of △PQR are PR and RQ.

4) The name of hypotenuse is PQ.

5) The legs of △HLM are LH and ML.

6) The name of hypotenuse is MH.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The right angle of △ABC is ∠ABC. Thus AB and BC meet at right angle. Therefore AB and BC are legs of △ABC.

The opposite side of ∠ABC is AC. Therefore the hypotenuse is AC.

The right angle of △PQR is ∠PRQ. Thus PR and RQ meet at right angle. Therefore PR and RQ are legs of △PQR.

The opposite side of ∠PRQ is PQ. Therefore the hypotenuse is PQ.

The right angle of △HLM is ∠HLM. Thus HL and LM meet at right angle. Therefore HL and LM are legs of △HLM.

The opposite side of ∠HLM is MH. Therefore the hypotenuse is MH.

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Answer:

0.60

Hope this helps, I believe in you!

Answer: The answer is C 0.60

Step-by-step explanation:

Answer:3.71 miles

Step-by-step explanation:

In the given congruent triangle  ΔPHS ≅ ΔCNF,  the values of x, y, and z are 24° , 37/3° , 61/4° respectively

What is a congruent triangle ?

The meaning of congruent in Maths is addressed to those figures and shapes that can be repositioned or flipped to coincide with the other shapes. These shapes can be reflected to coincide with similar shapes.

Two shapes are congruent if they have the same shape and size. We can also say if two shapes are congruent, then the mirror image of one shape is the same as the other.

Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle.

In mathematics, the term "congruent" refers to figures and forms that may be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes. If two forms are similar in size and shape, they are congruent. We may also state that if two forms are congruent, then their mirror images are identical .Triangles that line up. A triangle is a closed polygon with three line segments that intersect at each of its three angles.

When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles may be placed side by side and angle by angle on top of one another.

Since both the triangles are congruent this means the side , angles of both the triangles are equal

therefore,

∠ H = ∠ N

∠ S = ∠ C

∠ P = ∠ F

which means,

6x-29° = 115°

6x=144°

x=24°

∠ S  = 180° - ∠ H - 36°

∠ S = 180°-6x+29°-36°

∠ S = 173°-6x

173°-6x=4z-32°

173°-144°+32° = 4z

61/4° = z

3y-1° = 36°

y= 37/3°

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