A school ordered 3 large boxes of markers. After giving 15 markers to each of 3 teachers, there were 90 markers left in the box. Draw a diagram and write an equation to represent this situation.

Each fraction must first be transformed into its simplest form.Hence, The  problem can be solved in this way.

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The required maximum and minimum x-values are 4 and 1 respectively and maximum and minimum y-values are 4 and 0 respectively.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
Graph of the inequalities 4x - 2y ≤8, x ≥ 1 and 0 ≤ y ≤ 4 has been shown, the red dotted quadrilateral shows the solutions of the given inequalities, From the graph maximum and minimum x-values are 4 and 1 respectively and maximum and minimum y-values are 4 and 0 respectively.

Thus, the required maximum and minimum of the given inequalities exist.

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The governments are possible 90 different student body if there are 6 seniors, 5 juniors and 3 sophomores.

We need to fill three positions. There are six options for the senior position. There are five options for the junior position.There are three options for the sophomore position.

Whoever is elected senior president has no bearing on who is elected junior or sophomore president, and vice versa, i.e. the three events are completely separate.

The number of possibilities for separate events is simply the product of the individual number of possibilities, i.e.                    

As a result, the total number of ways to assign the student body is
(ways to choose senior president) * (ways to choose junior president) * (ways to choose sophomore president) = 6*5*3= 90          

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The value of x is = -0.5, for the equation [tex]$$ e^x \times e^{x+1}[/tex], after converting it to logarithm form.

The inverse function to exponentiation in mathematics is called the logarithm. In other words, to produce a number x, b must be raised to an exponent equal to the logarithm of x to the base b. Assuming that 1000 = 10³, for instance, the logarithm of 1000 in base 10 is 3, or log10 (1000) = 3.

When there is no possibility of confusion or when the base is irrelevant, such as in big O notation, the logarithm of x to base b is written as logb (x), logb x, or even without the explicit base, log x.

When multiplying two powers of the same base, the exponents are added.

= [tex]$$ e^x \times e^{x+1}[/tex]

= [tex]$$ e^{x + x+1}[/tex]

= [tex]$ \text e^{2x+1}[/tex]

=  [tex]$ \text e^{2x+1}[/tex] = 1

Convert to logarithm form

[tex]\log_e(1) = 2x+1[/tex]

Solve the equation

Isolate the variable by dividing each side by factors that don't contain the variable.

[tex]$\text x = -\frac{1}{2}[/tex]

x = -0.5

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A system of linear equations that represents this situation include the following:

y = 0.5x + 2.5

y = 0.5x + 5.5

In order to write the required system of linear equations, we would have to determine the slope for your friend and cousin respectively as follows;

y - y₁ = m(x - x₁)

Where:

Substituting the given parameters into the point-slope formula, the equation for your friend's hair is given by;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (6.5 - 4)/(8 - 3)(x - 3)

y - 4 = 2.5/5(x - 3)

y - 4 = 0.5x - 1.5

y = 0.5x - 1.5 + 4

y = 0.5x + 2.5

Also, the equation for your cousin's hair is given by;

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 7 = (9 - 7)/(8 - 3)(x - 3)

y - 7 = 2/5(x - 3)

y - 7 = 0.5x - 1.5

y = 0.5x - 1.5 + 7

y = 0.5x + 5.5

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Answer:

the length of MR is 53 units bro

The total number of ants and spiders can be represented using the expression 6a+8s.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

1) Given a is for total number of ants and s is for total number of spiders.

If  for one ant, number of legs is 6 legs, then for a number of ants,

total number of legs = 6×a = 6a

Similarly for s number of spiders, total numbers of legs = 8 × s = 8s

Therefore ,Total number of legs of all ants and spiders in terrarium = 6a + 8s

2) The term 6a represent the total number of legs of all ants in terrarium.

    The term 8s represent the total number of legs of all spiders in terrarium.

Hence the expression 6a+8s.

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The equation of the linear graph is y = x-2

A linear equation is an algebraic equation of the form y=mx+c. involving only a constant and a first-order (linear) term, where m is the slope and c is the y-intercept. Linear equation can also be defined as an equation with the highest power of the variable to be 1.

on the graph, the y intercept is the point where the graph line crosses the y axis. Therefore the y intercept is -2

The slope of the line = 0-(-2)/2-0

slope = 2/2 = 1

therefore the equation of the graph is ;

y = mx+c

y = x+(-2)

y = x-2

therefore the equation of the linear graph = y = x-2

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Answer: the slant height of the cone is 7ft

Step-by-step explanation:

Population A and B are in geometric sequence.

A geometric sequence is one where each phrase is obtained by multiplying the term before it by the same number.

Formula to find nth term of geometric sequence is aₙ = a₁ rⁿ⁻¹. The common ratio is expressed as the value r.

In the given table,

The population A of the table changing with respect to time,

0 hours =  12 millions

1 hour = 6 millions

2 hours = 3 millions

3 hours = 1.5 millions

The population B of the table changing with respect to time,

0 hours =  64 millions

1 hour = 48 millions

2 hours = 36 millions

3 hours = 27 millions

Since, the population A changes in geometric sequence.

And the common factor is 1/2.

Also, population B changes in geometric sequence.

and the common factor is 3/4.

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In triangle ADC and CD = 10 in triangle ABC, this means that the length of DB in triangle ABC is 10 - 4 = 6. Therefore, DB = 6.

In right triangle ABC, if CD is an altitude drawn to the hypotenuse and AD is also an altitude drawn to the hypotenuse, then triangles ADC and BDC are both right triangles. This means that triangles ADC and BDC are similar to triangle ABC.

We can use this similarity to find the length of DB. If AD = 4 and CD = 10, then we know that the ratio of AD to CD in triangle ABC is 4/10. This means that the ratio of AD to CD in triangle ADC is also 4/10. Since AD = 4 in triangle ADC, this means that CD = 10 * (AD/CD) = 10 * (4/10) = 4 in triangle ADC.

Since CD = 4 in triangle ADC and CD = 10 in triangle ABC, this means that the length of DB in triangle ABC is 10 - 4 = 6. Therefore, DB = 6.

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In right triangle ABC, where altitude CD is drawn to the hypotenuse AB with CD = 10 and AD = 4, then DB equals 25.

Therefore the answer is 25.

By Pythagoras theorem in ΔACD right angled at ∠CDA

AC² = CD² + AD², that is

[tex]AC^{2} = CD^{2} + AD^{2}[/tex]

AC² = 10² + 4²

AC² = 116

By Pythagoras theorem in ΔBCD right angled at ∠CDB

BC² = CD² + DB², that is

[tex]BC^{2} = CD^{2} + DB^{2}[/tex]

BC² = 10² + DB²

BC² = 100 + DB²

By Pythagoras theorem in ΔABC right angled at ∠BCA

BC² + AC ² = AB², that is

[tex]BC^{2} + AC^{2} = AB^{2}[/tex]

As AB = AD + DB

BC² + AC ² = (AD + DB)²

BC² + AC ² = AD² + 2×AD×DB + DB²

Substituting for AD, BC² and AC²

100 + DB² + 116 = 4² + 2×4×DB + DB²

8DB = 216 - 4²

DB = 200/ 8

DB = 25

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It will takes 3 seconds for the bullet to return to the ground.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given the function that models the height of a ball

s(t) = -16t² + 48t

At maximum height, the velocity is zero ie. ds/dt  = 0

ds/dt = -16t² + 48t

0 = 48 - 16t

48 = 16t

t = 3 secs

Get the maximum height

s(t) = -16t² + 48t

s(t) = -16(3)² + 48(3)

s(t) = 0

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An expression for the total number of fish in the store is 22n.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. Since the pet store has n tanks of fish. Each tank has 22 fish. Using n, an expression for the total number of fish in the store will be

= 22 × n

= 22n

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The triangle is isosecles. AB=BC=√53 units, AC=√106 units

Given the coordinates of ABC: A(-2,5), B(-4,-2), and C(3,-4).

To find the length of each side of the triangle, we use the distance formula:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Length of AB:

[tex]\begin{gathered} AB=\sqrt[]{(-2-5)^2+(-4+ 2)^2} \\ =\sqrt[]{(-7)^2+(-2)^2} \\ =\sqrt[]{49+4} \\ =\sqrt[]{53}\text{ units} \end{gathered}[/tex]

Length of BC:

[tex]\begin{gathered} BC=\sqrt[]{(-4 + 2)^2+(3 + 4)^2} \\ =\sqrt[]{(-2)^2+(7)^2} \\ =\sqrt[]{49+4} \\ =\sqrt[]{53}\text{ units} \end{gathered}[/tex]

Length of AC:

[tex]\begin{gathered} AC=\sqrt[]{(-4 - 5)^2+(3 + 2)^2} \\ =\sqrt[]{(-9)^2+(5)^2} \\ =\sqrt[]{81+25} \\ =\sqrt[]{106}\text{ units} \end{gathered}[/tex]

The lengths of the side of the triangle are;

AB=BC=√53 units, AC=√106 units

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y = −2x+3 is Neither parallel nor perpendicular to line a.

y = −2x+5 is Parallel to line a.

y = (1/2)x+7 is  Perpendicular to line a

The slope-intercept form of the equation a straight line is:

y = mx + c,

where m is the slope and c is the y-intercept

When two lines are perpendicular, the product of their slope is -1 i.e.

m₁ × m₂ = -1

where m₁ and m₂ represent the slope of the lines

But when two lines are parallel, they have the same slope i.e.

m₁ = m₂

Let's examine the equations:

Line a, y = −2x+3

y = 2x-1

y = −2x+5

y = (1/2)x+7

For Line a and  y = 2x-1:

Comparing their slopes. So y = −2x+3 is Neither parallel nor perpendicular to line a

For Line a and y = −2x+5:

They have the same slope (-2). So y = −2x+5 is Parallel to line a

For Line a and y = (1/2)x+7:

(1/2) × −2 = -1.  The product of their slope is -1 (i.e. 1/2 × −2 = -1 ). So  y = (1/2)x+7 is  Perpendicular to line a

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x > 1200 and x < 1600; Patrice needs to consume more than 1200 calories, but less than 1600 calories.

The 1st option is the answer

Given that: Patrice is trying a low-calorie diet. She would like to keep her calories consumed between the levels shown in the following compound inequality: 2450 < 2x + 50 and 2x + 50 < 3250.

Solve the two inequalities separately:

2450 < 2x + 50

2450 - 50 < 2x

2400 < 2x

1200 < x

x > 1200

2x + 50 < 3250

2x < 3250 - 50

2x < 3200

x < 1600

Therefore, Patrice needs to consume more than 1200 calories (i.e. x > 1200), but less than 1600 calories  (i.e. x < 1600).

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The measure of missing angle is 65°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

From the given triangle 68°, 47° and the missing angle is x.

By angle sum property of triangle, we get

68°+47°+x=180°

115°+x=180°

x=65°

Therefore, the measure of missing angle is 65°.

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The question for the rational expressions 5x/2x+3 divided by x+1/3x is "What is the result of 5x/2x+3 divided by x+1/3x?"

So, the degree measure of one angle of a 30-sided regular polygon is 5,040°.

The degree measure of an angle is a measure of the size of the angle, in degrees. Angles are typically measured in degrees, with a full circle being 360°. The degree measure of an angle can range from 0° to 360°, with smaller angles having a degree measure between 0° and 90°, right angles having a degree measure of 90°, and larger angles having a degree measure between 90° and 360°.

To find the degree measure of one angle of a 30-sided regular polygon, we can use the formula:

angle measure = (n-2) * 180° / n

where n is the number of sides in the polygon. Plugging in n = 30, we get:

angle measure = (30-2) * 180° / 30 = 28 * 180° / 30 = 5,040°

Therefore, the degree measure of one angle of a 30-sided regular polygon is 5,040°. The correct answer is therefore 5,040°.

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The degree measure of One angle of a 30 sided regular polygon is 168°

​

Now, According to the question:

We know that:

Sum of Angles of a Polygon:-

A regular polygon has all its sides of equal length. All the interior angles of a regular polygon are also equal. The sum of interior angles of a n sided polygon is given as:

                     (n - 2) × 180°

Let the number of sides of the given polygon be n

but, Value of n = 30 (given)

We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is

(Side - 2) × 180°

(30 - 2) × 180°

= 5040°

Measure of each angle of 30-gon

= 5040°/30

= 168°​

Hence,  the degree measure of One angle of a 30 sided regular polygon is 168°​

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The value of the annual premium is $2609.9

From the question, we have the following parameters that can be used in our computation:

Policy value = $89,657

Plan = 20-Payment Life insurance policy

From the given table:

The annual premium for a 20-Payment Life insurance policy for a 26-year-old male is $29.11

This means that

Total cost = 20 * $29.11

Total cost = $582.2

The annual premium is then calculated as

Annual premium = Total cost * 4.4829

This gives

Annual premium = $582.2 * 4.4829

Evaluate

Annual premium = $2609.9

Hence, the annual premium is $2609.9

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The day in which this company sold the same number of each player is on the 13th day.

The number of players on the 13th day is 2,451 players.

In order to determine the days in which this company sold the same number of each player, we would have to equate the linear equation representing Music player A to the quadratic function representing Music player B and then solve for the value of x.

By equating equation 1 and equation 2, we have the following:

y = 191x - 32             .........equation 1.

y = -x² + 200x + 20     ......equation 2.

191x - 32 = -x² + 200x + 20

x² - 200x - 20 + 191x - 32 = 0

x² - 9x - 52 = 0

Next, we would solve the above quadratic equation by using the factorization method;

x² - 13x + 4x - 52 = 0

x(x - 13) + 4(x - 13) = 0

(x + 4)(x - 13) = 0

x = -4 or 13 days.

Therefore, the company sold the same number of each player on the 13th day.

For the number of players, we have:

y = 191x - 32

y = 191(13) - 32

y = 2,483 - 32

y = 2,451 players.

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The dashed lines b,c,d and e do not create a symmetric figure when the figure is folded on.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

when the figure is folded on the dashed line "a", it will create a symmetric figure.

When the figure is folded on other dashed lines, they will not create a symmetric figure.

The dashed lines b,c,d and e do not create a symmetric figure when the figure is folded on.

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The required trasformation vector is given as,
[tex]\vec z = z\hat i + z\hat j\\\vec u = u \hat i + u\hat j\\\vec x = x\hat i + x\hat j\\\vec y = y\hat i+ y\hat j[/tex]

Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.  

Here,
From the figure,
A component for of trasformation vector is given as,
[tex]\vec V= v\hat i + v\hat j[/tex]

where v is the magnitude of the vector and [tex]\hat i[/tex], [tex]\hat j\\[/tex] is the unit vector which shows the direction of the vector.
So vector trasformation equation is given as,
[tex]\vec z = z\hat i + z\hat j\\\vec u = u \hat i + u\hat j\\\vec x = x\hat i + x\hat j\\\vec y = y\hat i+ y\hat j[/tex]

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The Fourier series is a summation of sine waves with different amplitudes and frequencies that, when combined, approximate the original function. The coefficients of the sine waves are determined by the values of the function at certain points.

The Fourier series for the given function f(x) can be derived as follows:

Step 1: Calculate the average value of f(x) over one period.

Average value = (1 + 0)/2 = 0.5

Step 2: Calculate the Fourier coefficients for the given function.

Fourier coefficients =[tex](1/2L) + (1/π)∑_(n=1)^∞▒(sin(nπx/L) - sin(nπx/2L))/n[/tex]

Step 3: Construct the Fourier series by combining the Fourier coefficients and the sine waves of different frequencies.

Fourier series = [tex]0.5 + (1/π)∑_(n=1)^∞▒(sin(nπx/L) - sin(nπx/2L))/n[/tex]

The Fourier series is a way of expressing a function as a sum of sine and cosine waves, each of which has a specific amplitude and frequency. This can be used to approximate the original function. To find the Fourier series of a given function, the average value of the function over one period must first be determined. Then, the Fourier coefficients of the function can be calculated, which are determined by the values of the function at certain points. Finally, the Fourier series can be constructed by combining the Fourier coefficients and the sine waves of different frequencies.

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Side AC is computed s by applying similar triangles to give 12

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

From the description, pair of equivalent sides are

AB and BD, AC and CE

The solution is worked out using sides AB and BD, AC and CE

AB / BD = AC / CE

where

AB = 8

BD = 10

CE = 15

AC = ?

8 / 10 = AC / 15

cross multiplying

8 * 15 = 10 * AC

AC = 8 * 15 / 10

AC = 12

hence  AC is 12

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0.2% of 3500 is equal to 7

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, 7 is what percent of 3500

Let 7 be the x% of 3500,

Therefore,

x% of 3500 = 7

x/100 × 3500 = 7

x = 1/5

1/5 = 0.2

Hence, 7 is 0.2% of 3500

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Descartes' number is 30.453 while mine is 45.3 times higher than 3,000 when multiplied by 100.

When m and p are coprime numbers and 2n = (m) (p + 1), where p is regarded as a "spoof" prime, the result is an odd number, which is known as a Descartes number. The provided example is the sole one that is currently known. A number that comes very near to becoming the ideal number is known as a Descartes number in mathematics. They are called after René Descartes, who noted that the number D, which is 32, 72, 112, 132, 22021 (which equals 198585576189), would be an odd perfect number if only 22021 were a prime number, because the sum-of-divisors function for D is satisfied.

given

n = (3000+45.3)/100

=     n = 3045.3/100

=     n = 30.453

Descartes' number is 30.453 while mine is 45.3 times higher than 3,000 when multiplied by 100.

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D) The value of x is 12 units in the triangle shown below:

The value of the base of a right angled triangle, given the length of the hypotenuse is 13 units and the length of the perpendicular is 5 units, is 12 units.

This can be determined by using the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right angled triangle is equal to the sum of the squares of the lengths of the other two sides (a^2 + b^2 = c^2). In this case, the hypotenuse is 13 units long, and the perpendicular is 5 units long,

so the equation would be: a^2 + 5^2 = 13^2, which can be simplified to: a^2 = 169-25 = 144. Therefore, a = √144 = 12.

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Complete question :

Find the value of x in the triangle shown below. .

Choose 1 answer:

A = 80

B = 48

C = 132

D = 12