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Triangle OPQ, with vertices O(3,4), P(8,3), and Q(4,8), is drawn inside a rectangle, as
shown below.

What is the area, in square units, of triangle OPQ?

D. y-2 cos(2x) + 4 is not a solution to the differential equation y" + 4y = 0.

The differential equation y" + 4y = 0 is a second-order, homogeneous linear differential equation with constant coefficients. The general solution to this type of differential equation is of the form y = e^(rt) where r is a root of the characteristic equation r² + 4 = 0. The roots of this equation are r = +/- √(4) = +/- 2i, which are both imaginary. Therefore, the general solution to the differential equation is y = c1cos(2x) + c2*sin(2x), where c1 and c2 are arbitrary constants.

Option D. y - 2 cos(2x) + 4 is not a solution to this differential equation because it doesn't have the same form as the general solution. It is a combination of a constant term, cosine and sine function but the general solution only contains sine and cosine function.

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To simplify a radical expression, you can use a few different techniques. One common technique is to factor the expression under the radical sign (the radicand) as much as possible.

Another technique you can use is to use the properties of radicals. For example, you can use the product property of radicals to combine like terms under the radical sign

You can also use the quotient property of radicals to divide out a factor under the radical sign. Finally, some radicals are unsimplifiable by these methods. You can approximate a value of radical or try to get it in a form of fraction with radical.

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The value of x from the given quadrilateral is 3.

A rhombus is a closed two-dimensional plane figure. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. A rhombus is also called an equilateral quadrilateral since all of its sides are equal in length.

Given that, rhombus (6x + 32)º and (17x - 1)º for what value of x is the figure given the special parallelogram.

A rhombus has two diagonals that bisect each other at right angles and diagonal bisects angles.

Now, (6x + 32)º=(17x - 1)º

17x-6x=32+1

11x=33

x=3

Therefore, the value of x is 3.

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There are four main datatypes: String, Integer, Float, and Boolean.

String: A string data type is used to store textual data. Strings are usually enclosed in quotation marks, and are used to represent words or phrases.

Integer: An integer data type is used to store numeric values that are whole numbers. Integers are usually used to represent counts or quantities.

Float: A float data type is used to store numeric values that have decimal points. Floats are usually used to represent real numbers, such as money amounts, measurements, and scientific values.

Boolean: A boolean data type is used to store values that can only be either true or false. Booleans are usually used to represent logical values, such as whether a certain condition is met or not.

Datatype is a classification of data which tells the computer how the programmer wants to use the data. It is used to store different types of values such as strings, integers, floats, and booleans. Each data type has its own specific purpose and can be used to store different types of information.

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Answer:

g(3) = 11

Step-by-step explanation:

g(n) = n^2 +2

g(3) = 3^2 +2

g(3) = 9 + 2

g(3) = 11

The rocket will reach its maximum height after 7.438 seconds.

An equation shows the relationship between numbers and variables in an expression.

Let y represent the height of the rocket x seconds after its launch.

Given that:

y = -16x² + 238x + 81

The height of the rocket is maximum when the rate of change is zero. Hence:

The rocket reaches it maximum at dy/dx = 0

dy/dx = -32x + 238

-32x + 238 = 0

32x = 238

x = 7.438

The rocket height would be maximum at 7.438 seconds.

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By solving a system of equations we will see that she has 9 quarters and 15 dimes.

Let's define the variables.

We know that Moolah has 24 coins, then:

d + q = 24

And the total value is $3.75, then:

q*0.25 + d*0.10 = 3.75

Then we can write the system of equations:

d + q = 24

q*0.25 + d*0.10 = 3.75

We can isolate d on the first equation to get:

d = 24 - q

Replacing that in the other equation we will get:

q*0.25 + (24 - q)*0.10 = 3.75

q*0.15 + 2.4 = 3.75

q*0.15 = 3.75 - 2.4

q*0.15 = 1.35

q = 1.35/0.15 = 9

So Moolah has 9 quarters and 15 dimes.

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Identify two points for each line and connect to graph lines.

Consider that x = 1 is the critical point, which gives us one included point (1, 0) marked as closed circle and one excluded point (1, 3) marked as open circle.

The second point for the first line is selected at x = - 3, which is (-3, 4) and for the second line is selected at x = 3, which is (3, 7).

See the lines attached.

number of minibuses required = 7

Division is the process of dividing some object into a number of parts. It is opposite to the multiplication process. In mathematics, the number that is divided by other number is called dividend and the other number is called divisor.

given, number of tourists = 169

each minibus can accommodate 26 passengers.

number of minibuses required for the total 169 tourists.

will be 169/26 = 6.5 = 7

they need to hire total 7 minibuses for a tour around Tokyo.

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The fourth ordered pair using the two

sequences is ( 7/3 ,106) .

The first sequence is constructed by first multiplying the terms by 2 and then adding one-third starting from zero. So, sequence starts from 0.

First term of first sequence, a₁ = 0

a₂ = (2x0) + 1/3 = 1/3

a₃ = (2x1/3) + 1/3 = 2/3 + 1/3 = 1

a₄ = (2x1) + 1/3 = 2 + 1/3 = 7/3

Hence, the sequence is 0, 1/3, 1, 7/3, ...

The second sequence is constructed by first adding one half in terms and then multiplying by 4. The sequence starts from 1 ,

a₁ = 1

a₂ = (1 +1/2) × 4 = (3/2)4 = 6

a₃ = (6+1/2) x 4 = 13/2 x 4 = 26

a₄ = (26 + 1/2)× 4 = 53/2 x 4 = 106

Hence, the sequence is 1, 6, 26, se106, ...

Therefore, the fourth terms of the two sequences are the following, 7/3 and 106.

So, required ordered pairs is ( 7/3, 106).

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Given the figure below, the value of x is  1.4 and z is 5.85 according to vertical angles rule.

Vertical angles, also known as vertically opposite angles, are formed when two lines intersect. Angles that are vertically opposite to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles; that is, they add up to 180 degrees.

For instance, if two lines intersect and form an angle, say X=45°, then its opposite angle is also 45°. And the angle next to angle X will be 180 - 45 = 135°. As we know vertical angles of intersection are equal:

63 = (15x + 42)

15x = 21

x = 1.4

For 20z, we know that opposite angle is 20z too

and all angles add upto 360°

So,

63 + 63 + 20z + 20z = 360

126 + 40z = 360

40z = 234

z = 5.85

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If a researcher finds that the probability of a word recognition program correctly interpreting a hand-written word is 9/10 . The number of  words that  the researcher expect the program to interpret correctly out of 40 words is 36 words.

Using this formula to find the number of words

Number of words = Probability of correctly interpreting a hand-written word × Expected words

Let plug in  the formula

Number of words = 9/10 × 40

Number of words = 36 words

Therefore we can conclude that the number of words is 36 words.

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The percentage of students in eighth grade who have music is 60%

Total number of eighth grade students = 75

Number of students who goes to music class = 45

Number of students who have art = Total number of eighth grade students - Number of students who goes to music class

= 75 - 45

= 30

Percentage of students who have art = Number of students who have art / Total number of eighth grade students × 100

= 30/75 × 100

= 0.4 × 100

= 40%

Percentage of students who have music = Number of students who have music / Total number of eighth grade students × 100

= 45/75 × 100

= 0.6 × 100

= 60%

Hence, 60% of the eighth grade students have music.

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The y-coordinate of the point (-3, p) is p = 0.

A line can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:

y = (-3)x + b

We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:

3 = (-3)(-4) + b

3 = 12 + b

-9 = b

Therefore, the equation for the line is y = -3x - 9.

To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:

y = (-3)(-3) - 9

y = 9 - 9

y = 0

Therefore, the y-coordinate of the point (-3, p) is p = 0.

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The y-coordinate of the point (-3, p) is p = 0.

Now, According to the question:

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line. The slope or gradient of a line describes how steep a line is. It can have either a positive or a negative value. When a standard form of a linear equation is of the form Ax + By  = C, where 'x' and 'y'  and 'C' are variables and 'A', 'B' are constants, the slope-intercept form is the most preferred way of expressing a straight line due to its simplicity, as it is very easy to find the slope and the 'y intercept' from the given equation.

In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:

y = (-3)x + b

We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:

3 = (-3)(-4) + b

3 = 12 + b

-9 = b

Therefore, the equation for the line is y = -3x - 9.

To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:

y = (-3)(-3) - 9

y = 9 - 9

y = 0

Therefore, the y-coordinate of the point (-3, p) is p = 0.

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Answer:

  y ≤ -3/2x -2

Step-by-step explanation:

You want the inequality shown on the graph that has a solid line through points (0, -2) and (2, -5).

The slope of the solid boundary line can be found from the slope equation:

  m = (y2 -y1)/(x2 -x1)

  m = (-5 -(-2))/(2 -0) = -3/2

The y-intercept is the point marked on the y-axis: (0, -2).

The boundary line has the slope-intercept equation ...

  y = mx +b . . . . . . . . where m is the slope and b is the y-intercept

  y = -3/2x -2

The shading is to the left and below the boundary line, so y-values in the shaded area are less than those on the line. The inequality reflects this:

  y ≤ -3/2x -2

__

Additional comment

The solid boundary line is included in the solution set, so we use the ≤ symbol, instead of the < symbol that excludes the line. When the < symbol is used, the boundary line is dashed.

We use the term "y-intercept" to refer to both the ordered pair that describes the point on the y-axis, (0, -2), and the y-value in that ordered pair, -2. We understand the x-value of any point on the y-axis is 0.

The results generated in the map phase are combined in the _reduce_ phase.

In maps, the "reduced phase" refers to a technique used to remove the phase ambiguity present in interferometric synthetic aperture radar (InSAR) data. InSAR uses radar to measure the distance between a satellite or aircraft and the ground and can be used to create detailed maps of changes in the surface of the earth over time.

However, because InSAR data is collected using radar waves, which are sensitive to the phase of the signal, the data can be affected by phase ambiguities. The reduced phase technique is used to remove these ambiguities and create more accurate maps.

Therefore, The results generated in the map phase are combined in the _reduce_ phase.

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The graph of the system of inequality is plotted and attached

In mathematics,  the term inequality refers to a relationship between two expressions or values that is not equal to each other.

Therefore, inequality emerges from a lack of balance.

The graph of the inequality is represented by two horizontal lines one is a dashed line and the other is a solid line

y < 8

This is a dashed line at point y = 8, the dashed line is because the inequality does not have the "equal to".

Also the shading is below the line since it is less than

y ≥ 3

This is a solid line at point y = 3, the solid line is because the inequality have the "equal to". as in greater than or equal to.

Also the shading is above the line since it is greater than symbol.

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The given expression of an [tex]{ }^{44} P_2[/tex] is 1892.

The given expression is [tex]{ }^{44} P_2 & =[/tex]0

[tex]{ }^{n} P_r[/tex]:-

 [tex]{ }^{n} P_r=[/tex][tex]\frac{n !}{(n-r) !} \\[/tex]

where

In the nPr formula, the letter "P" stands for "permutation," which is another word for "arrangement." The nPr formula calculates the number of possible combinations for choosing and arranging r items from the given n items.

Let's imagine that r various objects should be chosen and organised among n different objects. Let's explore some options for how to accomplish this.

Since there are n total objects, there are n methods to select the first one.

The number of options for selecting the second thing is limited because the first object has already been selected (n - 1).

Similar to how there are numerous ways to select the third item (n - 2).

While choosing the [tex]r^{th}[/tex] object, there are only (n - r + 1) objects are left and hence it can be chosen in (n - r + 1) ways.

[tex]{ }^{44} P_2 & =? \\\\P(n, r) & =\frac{n !}{(n-r) !} \\\\44 P_2 & =\frac{44 !}{(44-2) !} \\\\& =\frac{44 \times 43 \times 421}{421} \\[/tex]

=44×43

=1892

[tex]{ }^{44} P_2=[/tex]1892

Therefore, the value of [tex]{ }^{44} P_2[/tex]=1892.

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The value of the vertex(central) angle EJF formed by the given polygon is; 30°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, we are told that the sum of the central vertex angles sums up to 180 degrees. Now, by careful observation, we can tell that the number of isosceles triangles that will be formed in the semi circle are 6. Thus;

Number of polygon sides of the semi circle = 6 sides

Thus;

Central angle = 180/6

Central angle = 30°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠E = ∠F = [180 - 30]/2

∠E = ∠F = 75°

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The equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -

(y - b) = (dy/dx) (x - a)

Given is the curve y = f(x) = x⁴ + 6x² − x.

The given curve is -

y = x⁴ + 6x² − x

f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx

f'(x) = dy/dx = 4x³ + 12x + 1

Now -

f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1

f'(x){1, 6} = 17

We can write the equation as -

(y - 6) = 17(x - 1)

Therefore, the equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

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The number 96 into simplest radical form is 4√6.

In the given question we have to simplify the number into simplest radical form.

The given number is 96.

To simplify and obtain the radical form of square roots, we will first identify every element below the square root.

The square factor for 96 is 16.

Now we can factor 96 as 16 * 6.

The radicals are not in their least complicated form, as should be evident.

When we pay close attention now and subtract the square root of 16 * 6.

As √16 = 4 is the starting point, which leads to 4√6.

Currently, all radicals have been upgraded.

Never again will the extreme have any square factors.

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The complete question is:

Simplify the number into simplest radical form. Use the factor tree to help determine the factors 96.

Use the factor tree, the simplest radical form of 64 is 8.

Lets Simplify the number 64 into the simplest radical form.

To solve this, we can use a factor tree.

First, we will start with the number 64. We can break this down into two groups of two numbers, one being 4 and the other being 16.

Next, we can break down the 4 into two groups of two numbers, one being 2 and the other being 2.

Finally, we can break down the 16 into two groups of two numbers, one being 4 and the other being 4.

Now we have our factors, 2, 2, 4, and 4. We can use these factors to simplify the number 64 into its simplest radical form.

The formula for the radical form of a number is √(a × b × c × d).

In this case, our a, b, c, and d values are 2, 2, 4, and 4 respectively.

Therefore, our simplified radical form of 64 is √(2 × 2 × 4 × 4) = √64 = 8.

This means that the simplest radical form of 64 is 8.

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The first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3. (Option C)

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like ^n for a nonnegative integer n. For a binomial series, the formula for the expansion of any terms is given by

(1+x)^m=1+mx+  m(m-1)/2! x^2+  m(m-1)(m-2)/3! x^3+⋯.

For the given function (1+ x/4)^(-2)

m = -2

x = x/4

Hence, using the above expansion formula

The first term = 1

The second term = mx = (-2)(x/4) = -x/2

The third term =m(m-1)/2! (x/4)^2=  (-2(-2-1))/(2*1*16) x^2=3/16 x^2

The fourth term = m(m-1)(m-2)/3! (x/4)^3=(-2(-2-1)(-2-2))/(3*2*1*64) x^3=-1/16 x^3

Hence, the first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3.

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Answer:

excluded values

y=0

Simplify the expression

3xy−5/y

​

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

i got 100

Answer:

c.-a²-a-35

Step-by-step explanation:

a(4-a)-5(a+7)

=4a-a²-5a-35

=a²-a-35

Answer: Simple 75 peanuts for $3.50

Step-by-step explanation:

The inequality that describes Mr. Clarke's problem is x < 450/3.

This means that the cost of each camera must be less than $450/3, or $150.  This inequality means that Mr. Clarke can spend up to $450 on the cameras, but the amount he spends on each camera must be less than $450 divided by 3, or $150. To calculate this, we take the total budget of $450 and divide it by the number of cameras, which is 3. To solve this, we can use the formula x < 450/3. We can calculate the maximum amount Mr. Clarke can spend on each camera by multiplying 450 by 1/3, resulting in $150. Therefore, Mr. Clarke can spend a maximum of $150 on each camera in order to stay within his budget of $450.

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Answer:

Madison

Step-by-step explanation:

Madison is the better free throw shooter. We can tell this because her free throw percentage of 78% is higher than Lara's free throw ratio of 24, which is the number of successful free throws out of 100 attempted shots. Hope this helps!

For the given regular polygon with the angle sum of 10x + 4, the value of x = 143.6

They are referred to as regular polygons if the interior angles and sides are all equal. Equilateral triangles, squares, and other shapes are examples of regular polygons. Along with the sides being congruent, regular polygons also have congruent angles. They are equiangular, according to that.

We know that sum of interior angles of a regular polygon is

( n − 2 ) × 180°, where n is sides

For the given question

( 10 − 2 ) × 180°

= 8 × 180°

= 1440°

Given that

10x + 4 = 1440°

10x = 1436

x =  1436/10

x =  143.6

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Answer:

2 & 4 :)

Step-by-step explanation: