Solve for x :
5x+8=7x-72​

The number 3.14 is a rational number because it can be written as [tex]\frac{314}{100}[/tex].

p/q of two integers with q 0 can be used to represent a number as a rational number in mathematics. The set of rational numbers also contains all of the integers, which can each be expressed as a quotient with the integer as the numerator and 1 as the denominator. 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. For instance, every integer and 3/7 are rational numbers.

Given that,

3.14 is rational number

Here, 3.14 can be written as [tex]\frac{314}{100}[/tex].

3.14 can be written as fraction, whereas pie cannot be written in fraction form.

Therefore, 3.14 is a rational numbers but pie is not a rational number.

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Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches of box. The volume V(x)=4x³-110x²+750x.

Given that,

Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches and trim the corners to create an open-top box. The open-top box's volume, "V(x)," in cubic inches, depends on the square cuts' side length, "x," in inches.

Length =30 inch

Width=25 inch

The box's size changes when x is taken out of the container.

Length=30-2x

Width=25-2x

Height=x

Because x is eliminated from both ends, we subtract 2x.

The volume is then determined as follows:

V(x)=length×width×height

V(x)=(30-2x)×(25-2x)×x

V(x)=(30-2x)×(25x-2x²)

V(x)=750x-110x²+4x³

V(x)=4x³-110x²+750x

Therefore, the volume V(x)=4x³-110x²+750x.

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The most appropriate choice for linear equation will be given by-

[tex]l = 28 - 0.5d[/tex] is the required expression for the length of the bike

path left to build at any point during the construction.

[tex]l[/tex] is the  length of the bike path left to build at any point during the construction

[tex]d[/tex] is the number of days

What is Linear equation?

A one degree equation is called a linear equation.

Here,

Let the length of the bike path left to build at any point during the construction be [tex]l[/tex] and the number of days be [tex]d[/tex]

In one day, the crew build 0.5 miles of the path

In d days, the crew can build [tex]0.5 \times d[/tex] miles of the path

Length of path left to construct after [tex]d[/tex] days = [tex]28-0.5d[/tex]

By the problem,

                          [tex]l = 28 - 0.5d[/tex]

This is the required expression for the length of the bike

path left to build at any point during the construction.

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Answer:

-49/12

Step-by-step explanation:

The numbers that are greater than 59 1/3 are; C: 59 2/3 and D: 179/3

We want to find the numbers that are greater than 59 ¹/₃.

Now, the given fraction is written in mixed fraction. Looking at the fraction side, we can see that 1/3 can be written as 0.333. Thus;

59 ¹/₃ = 59.333

When we talk about the inequality greater than, we are simply referring to sayin that a figure is more than another figure which could be given or not given.

Looking at the given options, let us rewrite each of the mixed or improper fractions in decimal form to get;

59 ²/₁₀ converted to decimal form gives 59.2

59 ⁴/₁₂ = 59 ¹/₃  converted to decimal form gives 59.333

59 ²/₃  converted to decimal form gives 59.667

179/3 = 59 ²/₃  converted to decimal form gives 59.667

Comparing the options to the given number in the question, we can conclude that 59 2/3 and 179/3 are greater than 59 1/3

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The distance from the base of the ladder to the house is 15 ft.

The length of the ladder is 39 ft.

The ladder is placed to reach a point on the house 36 feet from the ground.

This situation forms a right angle triangle.

The distance from the base of the ladder to the house is as follows:

The distance from the base of the ladder to the house is the other leg of the right angle triangle.

The ladder length is the hypotenuse of the right triangle.

Hence, using Pythagoras theorem,

39² - 36² = b²

b² = 1521 - 1296

b² = 225

b = √225

b = 15 ft

Therefore, the distance is 15 ft.

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No, because it fails vertical line test.

What is vertical line test?

Vertical line test is defined as a method used to find if the given equation or graph represents a function or not. The vertical line test states that a vertical line needs to cuts the graph of a function (equation) at only one point, for it to represent a function.

Hence, in the given graph, the function intercepts the y- axis at two points, therefore, it fails vertical line test.

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Answer:

If B is between A and C, then AB = BC.

x + 5 = 2(x - 3)

x + 5 = 2x - 6

x = 11

The domain of the graph as an inequality is

The range of the graph as an inequality is

The domain of a graph is a term that refers to the input values of the graph. The input values are usually in the x axis and this is why we use x in defining the domain

The extreme of the curve on the left side shows the vertex on the x axis is 0 and the curve ended with an arrow showing it is tending to infinity

The range represents the values in the y axis. The curve started at the point y = -5 with a hollow dot. In inequality, a hollow dot means the number is not included hence we use less than.

The graph continued with an arrow this means it tends to infinity

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Answer:

-8

Step-by-step explanation:

6 + 2 = 8,just make 8 negative

Answer:

We want to imagine where the shading should be, and with that determine which point is a solution for both inequalities. We will see that the solution is the point (7, -8)

Step-by-step explanation:

Interpreting inequalities:

In this case, the inqualities are:

y <  -x + 1

y < (-1/2)*x - 1

You can see that in both cases, y is smaller than the line, thus, for both inequalities, we must shade the part that is below the lines.

With that in mind, the region of solution will be the region that is below both lines at the same time, and that region will be the "triangle" that you can see at the middle below the horizontal axis.

Now that we know the region of solutions, we only need to see which point belongs there, from the given options the only that belongs to that region is the point (7, -8), which means that this point is a solution for both inequalities.

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The distance between in two cities is 360 miles.

Given,

It took a plane 2 hours to fly from Dallas to New York

The headwind and 1.5 hours to return with the tailwind.

and, the speed of the wind was 30 mph.

To find the how far apart are the two cities?

Now, According to the question:

Let speed of be x

Speed of wind be c

Also note D = RT, where

D is distance and R is rate and T is time

For First Leg:

we can write:

(x - c) × 2 = D

2x - 2c = D

For Second Leg:

we can write:

(x+ c) × 1.5 = D

1.5x + 1.5c = D

We can equate and write:

2x - 2c = 1.5x + 1.5c

0.5x = 3.5c

We know Speed of Wind, c, is 30, so we have:

0.5x = 3.5(30)

0.5x = 105

x = 105/0.5 = 210 [speed of airplane]

We know distance is

D = 2x - 2c

D = 2(210) - 2(30)

D = 420 - 60

D = 360 miles

Hence, The distance between in two cities is 360 miles.

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From the given figure, it can be seen that there are two circles with centers A and B respectively.

The circle with the center A is larger in size than the circle with center B. Points P, Q and E lie on the surface of the circle having center A and R, S, C and T points lie on the circle having center B.

Circle A and Circle B's connection

Circle A's size is more significant than Circle B's size.

As a result, circle A's radius exceeds circle B's radius.

The connection between segments

1.

Let M be the location where Segment QT and ER intersect.

Additionally, tangents from an outside point to a circle have identical lengths.

QM = ME———— (1)

MT=MR————(2)

Including (1) and (2)

MR + ME = QM + MT

Q T=ER

2.

Tangents from an exterior point to a circle have identical lengths.

We may write the following segments are equal using this property.

UP=U Q

Z C=ZR

V C=VS

NR=NS

KC=K T

What are Tangents?

A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:

As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):

Utilizing the differentiation principles, determine the gradient function's derivative.

To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate

Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).

Circle's Tangent

A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.

Geometric Tangent

Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.

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John measured two pieces of string. One piece measured \dfrac7{12}\text{ m}127​ mstart fraction, 7, divided by, 12, end fraction, start text, space, m, end text and the other measured \dfrac47\text{ m}74​ mstart fraction, 4, divided by, 7, end fraction, start text, space, m, end text.

The circumference of a circle with diameter of 42 cm is 131.88 cm

The circumference of a circle of diameter 3.5 cm is 11 cm.

The circumference of a circle of diameter 42 cm can be found as follows:

Therefore,

circumference of a circle = 2πr

where

Hence,

diameter = 42 cm

radius = 42 / 2

radius = 21 cm

circumference of a circle = 2 × 3.14 × 21

circumference of a circle = 42 × 3.14

circumference of a circle = 131.88 cm

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The  common reasons for the bank to waive their monthly fee are :  

a. If you open two checking accounts with the same bank they won't charge a monthly fee.

d. If you ask your employer to direct deposit your salary into your bank account the bank will waive the monthly fee

e. If you keep a minimum required balance in the account the bank will waive the monthly fee

Monthly fee can be defined as the fee a bank or financial institution charge their customers for services they rendered to their customers example of this monthly fees is account maintenance fees.

A bank can decide to waived a customer monthly fees or charges when the customer open two checking account with the bank or when a customer make use of a direct deposit as well as when a customer maintain a enough  balance or maintain minimum balance in their bank account.

Therefore the correct options are A, D, C.

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The number of dimes and nickels in her collection are 296 and 108 respectively.

She had collected 540 coins. which were worth $60.

She counted 100 quarters in her saving.

The number of dimes and nickel in her collection can be solved as follows:

Therefore,

let

x = number of dimes

y = number of nickels

number of quarters = 100

Therefore,

x + y + 100 = 504

x + y = 504 - 100

x + y = 404

Hence,

0.1x + 0.05y + 100(0.25) = 60

0.1x + 0.05y  = 60 - 25

0.1x + 0.05y  = 35

combine the equation

x + y = 404

0.1x + 0.05y  = 35

Multiply equation(i) by 0.1

0.1x + 0.1y = 40.4

0.1x + 0.05y  = 35

subtract equation(ii) from equation(i)

0.05y = 5.4

divide both sides by 0.05

y = 5.4 / 0.05

y = 108

x = 404 - 108

x = 296

Therefore,

Number of dimes = 296

Number of nickels = 108

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Answer:

If x= -24

then the equation will be = -24-9

                                          = -24+ -9

                                          = -33

Therefore the value of x-9 when x=-24 is 33

Answer:

i go with the first one cause

Step-by-step explanation:

its the only true one

Answer:

5 1/2 or 5.5

Step-by-step explanation:

First, we can convert these values to improper fractions, where the numerator is larger than the denominator.

Then, we'd get:

3/2 x 11/3

Now, we can multiply the numerators and denominators, and we would get the answer of 33/6

When we convert 33/6 to a mixed number, we get 5 3/6, which can then be further simplified to 5 1/2 OR 5.5 (whichever you prefer)

Answer:

5 1/2

Step-by-step explanation:

1 1/2×3 2/3

[tex](2 \times 1 + 1) \times (3 \times 3 + 2) \\ [/tex]

3/2×11/3

33/6

=5 1/2

Each cow receives seven pounds of cow chow from Bob. Every time he feeds, farmer Bob uses at least 84 pounds of cow chow, which means that each time he feeds, 12 cows in total.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Cow chow fed to each cow by the farmer =7 pounds

Total cow chow used by the farmer to feed the cows every time = 84 pounds

Total cow chow used = no. of cows *cow chow fed to each cow

No. of cows = Total cow chow / cow chow fed to each cow

                    = 84/7

                    =12

No. of cows = 12

Therefore, 84 pounds of cow chow is used to feed 12 cows each time.

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Answer:

20 horseshoes

Step-by-step explanation:

How many horseshoes are needed to fit 5 horses?

5 horses with 4 hooves each:

5 × 4 = 20 horseshoes

Simon had 4 slices of the total pizza.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

There are several fraction examples in daily life, including:

1. If a pizza is split into two equal pieces, each piece represents half of the entire pizza.

2. Each piece of a watermelon slice that is divided into three equal pieces makes up one-third of the whole.

In this question , the ratios given are 5 : 1 : 2

Thus the total is 5 + 1 + 2 = 8

Since Simon's share is 2/8 th of the total

Thus the required fraction is 2 / 8 × 16

On solving further we get;

2 × 2

= 4 slices

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Answer:

they're the same !

Step-by-step explanation:

38*12= 456

456+7=463

hope this helps!!!

3 + 6x = 2x + 27

Move the 2x on the left side with changed sign and the 3 on the right side with changed sign aswell.

6x - 2x = 27 - 3

4x = 24

Now devide 24 by 4.

x = 24 : 6 = 4

Answer:

Step-by-step explanation:

[tex]\bf 3 + 6x = 2x + 27[/tex]

Subtract 3 from both sides:-

[tex]\bf 3+6x-3=2x+27-3[/tex]

Simplify:-

[tex]\bf 6x=2x+24[/tex]

Subtract 2x from both sides:-

[tex]\bf 6x-2x=2x+24-2x[/tex]

Simplify:-

[tex]\bf 4x=24[/tex]

Divide both sides by 4:-

[tex]\bf \cfrac{4x}{4}=\cfrac{24}{4}[/tex]

Simplify:-

[tex]\bf x=6[/tex]

_____________________

∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles, m∠FED + m∠DEW = 90°

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

Complementary Angles defined as angles that sum up to 90 degrees.

Now, we are given that;

∠FED and ∠DEW are complementary.

We want to prove that ∠FEW is a right angle. Thus;

∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles, we can say that;

m∠FED + m∠DEW = 90°

Also,

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

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