A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!

The first step to find the value of 'x' in this expression is to calculate the product with the parenthesis term:

Then, we need to isolate in one side of the equation the terms with the variable 'x', and in the other side the terms without the variable 'x'. Then, we can calculate the value of x:

So the value of x in this expression is -7

1220 km apart

rates

320 km/ hr

290 km/hr

___________________________________

x= t* rate

t = time in hours

x = distance in km

__________________

total distance = t1 * 320 Km/h + t2* 290 km/h

because they started at the same time

Total distance = 1220 km = t * 320 Km/h + t* 290 km/h

1220 = (320 + 290 ) t

1220 = 610 t

t = 1200/ 610

t = 2 hours

_______________________--

Answer

2 hours

Answer:

y=8x+8

Step-by-step explanation:

Slope Intercept form: y=mx+b

m=slope

b=y-intercept.

so if you put them together using what we have, you get y=8x+8

The constant of proportionality for the equation y = 2x is k = 2.

The number of pieces of fruit the monkey can eat is two times the amount of time the monkey takes.

The equation y = 2x can be used to represent a monkey eating 24 pieces of fruit in 12 hours.

The constant of proportionality, which is a fixed value that represents the rate at which two or more ratios rise or decrease, is used to compare them. The result of dividing the denominator by the numerator when a ratio is expressed as a fraction is the constant of proportionality.

When a ratio is expressed as a fraction, the constant of proportionality is found by dividing the denominator by the numerator. The constant of proportionality, k, can be calculated from the equation if x is the ratio's numerator and y is its denominator.

k = y/x

Therefore, the constant of proportionality in this case is:

y = 2x

k = y/x = 2

The constant of proportionality in this case represents that the number of pieces of fruit a monkey eats is two times the amount of time the monkey takes.

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After solving the equations we can conclude that the two numbers are 265 and 137.

So, let the first number be 'x' and the second is 'y'.

Now, the two equations can be formed as:

Merge equations as follows:

So x will be:

Therefore, after solving the equations the two numbers are 265 and 137.

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Answer:5in

Step-by-step explanation:

1. Identify the triangle

you are given a right triangle with the hypotonus missing and are given the side lengths 3 and 4 you know the hypotonus is 5 by the 3,4,5 Pythagorean tripe, if you do not notice this it can be solved with the Pythagorean theorem a^2+b^2=c^2

2. solve (if not done with 3,4,5 triple)

3^2+4^2=c^2

9+16=c^2

25=c^2

5=c | square root both sides to cancel the square

The total number of terms in the given expression 2x + 7 is equal to two.

As given in the question,

Expression is given by:

2x + 7

Number of terms in the given expression 2x + 7  are as follow:

7 is the constant term of the given expression 2x + 7

x is the variable which is multiply by two written as 2x in the given expression 2x + 7.

Both the terms 7 and 2x in the given expression are related with the operation addition'+'

Therefore, the total number of terms in the given expression 2x + 7 is equal to two.

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The elements in the set A'∩B is { z } .

Set theory is a branch of mathematical logic that studies sets, which are essentially collections of objects.

Given universal set U = {q, r, s, t, u, v, w, x, y, z}

set A = {q, s, u, w, y}

∴A' = {r, t, v, x, z}

set B =  {q, s, y, z}

Now A'∩B = { z }

Hence the elements in the set A'∩B is { z } .

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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.

For these items, the word equal is frequently used in place of congruent. If two line segments are the same length, they are said to be congruent. If two angles have the same measure, they are said to be congruent. If two circles have the same diameter, they are congruent.

While equality deals with numbers, congruence deals with shapes (also known as objects). Neither "two shapes are equal" nor "two numbers are congruent" are statements that you make. If one shape can be perfectly superimposed on the other, then two shapes are said to be congruent. While equality deals with numbers, congruence deals with shapes (also known as objects).

Gestures are logical and consistent with what is being spoken. Despite not being the same, both ideas are entirely consistent. We play a game, say things we don't mean, and act contrary to our ideals. The choice is more challenging if the hip appears to be in congruence even with the

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The comparison of 364, 879; 463, 000; 436, 765 using scientific notation ,number has the least value is 3.64879 x 10⁵ .

As given in the question,

Converting 364, 879 using scientific notation, 364, 879 = 3.64879 x 10⁵

Converting 463, 000 using scientific notation, 463, 000 = 4.63 x 10⁵

Converting 436, 765 using scientific notation, 436, 765 = 4.36765 x 10⁵.

Hence when ordered in ascending terms, using scientific notations, the given numbers can be arranged as follows:

3.64879 x 10⁵ <  4.63 x 10⁵ < 4.36765 x 10⁵.

First term 364, 879 has the least value, since it is the smallest number.

Therefore,  comparison of 364, 879; 463, 000; 436, 765 using scientific notation ,number has the least value is 3.64879 x 10⁵.

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Answer:

[tex]y=-6+\frac{2x}{5}[/tex]

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

property value = $496300

tax rate = 1.825%

Step 02:

percentage:

property tax:

= 1.825 / 100 = 0.01825

property tax = property value * tax rate

$496300 * 0.01825 = 9057.475$

The answer is:

property tax =

The required numbers are [tex]2\frac{2}{5}[/tex] and [tex]2\frac{5}{8}[/tex] .

In this question , given is [tex]2\frac{2}{5}[/tex] , [tex]2\frac{2}{7}[/tex] , [tex]1\frac{7}{8}[/tex] , [tex]2\frac{1}{10}[/tex] , [tex]2\frac{5}{8}[/tex]

So when we solve it we get;  [tex]\frac{12}{5} , \frac{16}{7} , \frac{15}{8} , \frac{21}{10} , \frac{21}{8}[/tex]

We need two numbers whose sum should be greater than 5

first adding the numbers which have the same denominator we get:

[tex]\frac{15}{8} + \frac{21}{8}[/tex]

[tex]\frac{36}{8}[/tex]

which on dividing will give us 4.5 < 5

Lets take numbers [tex]\frac{12}{5} , \frac{16}{7}[/tex]

On taking LCM we get ;

[tex]\frac{84+ 80}{35}[/tex] = [tex]\frac{164}{35}[/tex] = 4.6 < 5

Lets now take [tex]\frac{16}{7} + \frac{15}{8}[/tex] = [tex]\frac{128+ 105 }{56}[/tex] = [tex]\frac{233}{56}[/tex] = 4.16 < 5

Lets take [tex]\frac{12}{5} + \frac{21}{8}[/tex] = [tex]\frac{96+ 105}{40}[/tex] = 5.025 > 5

Thus the required numbers are : [tex]\frac{12}{5} and \frac{21}{8}[/tex].

So in these type of questions we are supposed to take two or the numbers which have been given in the question and then we should add or subtract them as per the question .

Likewise in this question we had to find two numbers and after so many trials we were able to get the two required numbers.

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From geogebra

Answer Letter A

we have the equation

i will assume

a=2

b=5

c=3

d=5

solve for x

substitute the given values

subtract 3 both sides

Divide by 2 both sides

squared both sides

the values of x are

x=-4 and x=-6

Verify each solution

For x=-4

x=-4 ------> is a solution

Verify x=-6

Is not true

therefore

x=-6 --------> is an extraneous solution

On 300 call the station first give away all three prizes to one caller.

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory. The LCM method is used to determine the least multiple of two or more numbers. Least Common Multiple is referred to as LCM. The LCM of two numbers can be divided by both of them. The LCM of 6 and 8 is 24, for instance. 24 can be divided by both 6 and 8.

Given Data

A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller.

To find When will the station first give away all three prizes to one caller, we will take LCM

5      15 , 25, 100

5       3, 5 , 20

3     3, 1 , 4

4       1, 1 , 4

LCM = 5² × 3× 4

LCM = 300

On 300 call the station first give away all three prizes to one caller.

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The mapping diagram above does not represent a function since

for each number in Set A (the input) where there are multiple mappings

from Set B (the output).

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).

Based on the mapping diagram shown above, we can reasonably infer and logically deduce that Set A with inputs (-4, 8), (1, 8) and (1, -3) are ordered pairs which does not represent a function because they indicate multiple mappings in Set B (the output).

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Jimmy would've jogged 32.02m if he ran through a straight line by Pythagorean theorem.

What is Pythagorean theorem?

We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.

Mathematically, the theorem can be expressed as

              x² = y²  +  z²

Let's substitute the values into the equation and solve

     x² = 20²  + 25²

      x = 32.02m

Jimmy would've jogged 32.02m if he ran through a straight line.

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An example of two fraction whose product is an integer due to common factors is [tex]\frac{6}{3}[/tex].

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

What is a common factor?

The largest positive integer that divides each of the integers is known as the greatest common divisor of two or more non-zero integers. The greatest common divisor of two integers x and y is indicated by the display style "gcd"

Given that,

Two fraction whose product is an integer due to common factor.

The fraction is

[tex]\frac{6}{3}[/tex].

Since,

2 x 3 = 6

1 x 3 = 3

Here, 3 is the common factor.

[tex]\frac{6}{3}[/tex] = 2

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The combination of two shirts and six hats will maximize the amount of money the shopper can spend.

An inequality results from the comparison of two or more algebraic expressions using the symbols <, > ≤, or ≥. They are mathematical expressions with unequal sides.

Let's assume x is the number of shirts and y is the number of hats brought then,

Total amount spend = 21x + 16y

It is given that the total amount the shopper can spend is $140.

So, 21x + 16y ≤ 140,

As x and y are the number of shirts and the number of hats so x and y will assume positive integral values only, to find out the values of x and y plot the region 21x + 16y ≤ 140 with x ≥ 0, y ≥ 0 as shown in the graph.

From the graph, it is clear that the highest integer value which is close to the boundary of 21x + 16y ≤ 140 is x = 2 and y = 6.

The amount spend when x = 2 and y = 6 is 21(2) + 16(6) = 138

Hence, two shirts and six hats will maximize the amount of money the shopper can spend.

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Answer:

the anwser is 100x69 yes

Hence, the derivative of [tex]g(x)=8x^5+x^4-5x^2+6[/tex] is [tex]g`(-4)=10536[/tex].

What is the derivative?

The derivative is a way to show instantaneous rate of change: that is, the amount by which a function is changing at one given point.

Here given function is

[tex]g(x)=8x^5+x^4-5x^2+6[/tex]

So,

[tex]g`(x)=5(8x^4)+4x^3-2(5x)\\\\g`(x)=40x^4+4x^3-10x\\\\x=-4\\\\g`(-4)=40(-4)^4+4(-4)^3-10(-4)\\\\g`(-4)=40(256)+4(64)+40\\\\g`(-4)=10240+256+40\\\\g`(-4)=10536[/tex]

Hence, the derivative of [tex]g(x)=8x^5+x^4-5x^2+6[/tex] is [tex]g`(-4)=10536[/tex].

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Explanation

we have a linear function, to graph a linear function you need 2 points

Step 1

find 2 coordinates of the line

a) when x= 0

then

b)when x=2

Step 2

now, draw a line that passes through the points

I hope this helps you

Answer:

x = 15

Step-by-step explanation:

[tex]4 + \frac{x}{3} = 9[/tex]

[tex] \frac{x}{3} = 5[/tex]

[tex]x = 15[/tex]

Answer:

x = 15

Step-by-step explanation:

Subtract 3 from each side: 12 + x = 27

Subtract 12 from both sides: x =27 − 12

Subtract 12 from 27 to get 15: x = 15

The non-real solutions of the polynomial expression are x = (2 + i√26)/3 and  x = (2 - i√26)/3

The equation of the polynomial expression is given as:

3x^3 + 14x^2 - 14x + 60 = 0

From the question, we have

Real solution = -6

Rewrite the above equation as

x = -6

Add 6 to both sides of the equation

So, we have

x + 6 = 0

The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0

This is represented as

3x^3 + 14x^2 - 14x + 60/x + 6

Using a graphing calculator, we have

3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10

Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3

So, we have

x = (4 ± √-104)/6

This gives

x = (4 ± 2√-26)/6

Divide

x = (2 ± √-26)/3

Rewrite as

x = (2 ± i√26)/3

Split

x = (2 + i√26)/3 and  x = (2 - i√26)/3

So, the conclusion is that

Using the polynomial expression, the non-real solutions are x = (2 + i√26)/3 and  x = (2 - i√26)/3

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define a quadratic equation that does not passes through the x-axis

When a quadratic function never crosses the x-axis, then it has no real roots or solutions. Hence, the discriminant must be negative. meaning the solutions are imaginary/complex.

Hence, the answer will be:

The function has two imaginary roots

Given:

f(X) will be differentiated by chain rule.