Question 9 (2 points)

Lily threw a ball. The balls equation that demonstrated its height and velocity is:


h(x) = -16x² + 3x + 35


What was the initial height that she threw the ball from?

The price paid by school district for each typewriter after applying 18% quantify discount is equal to  $106.56.

Regular selling price of each typewriter = $129.95

Number of typewriter required by school district  = 50

Total cost of 50 type writers = $129.95 × 50

                                               = $6497.5

Discount percent on whole quantity = 18%

18% of $6497.5

= ( 18 / 100 ) × $6497.5

= $1169.55

Total price paid by school district for 50 typewriters

= $6497.5 - $1169.55

= $5327.95

Price paid by school district for 1 typewriters

= $5327.95 / 50

= $106.559

= $106.56

Therefore, the price paid school district for each typewriter is equal to

$106.56.

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Some of the other types of the separation process are used in every house and company. The process of segregating undesirable particles from necessary components is the essence of the separation method. We will study in-depth information about several physical separation techniques in this particular article. The discussion's conclusion would allow students to recognize various techniques and their importance.

The blind man could use one hand to separate the pills by color, for example by holding one group of pills in one hand and the other group of pills in the other hand. Then, he could reach into one hand and take one pill, and reach into the other hand and take one pill, ensuring that he has taken one red pill and one blue pill. Another way could be to put each color pill in a different pocket, so he can feel the different pockets and take one pill of each color.

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The three (3) true statements about the quadratic function, f(x) = x^2 – 5x + 12 and its graph include the following:

A. The value of f(–10) = 82

B. The graph of the function is a parabola.

D. The graph contains the point (20, –8).

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.

Next, we would determine the other true statements about the graph of this quadratic function:

At data point (-10, 82), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(-10) = -10²/5 – 5(-10) + 12

Quadratic function, f(-10) = 82

At data point (20, -8), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(20) = 20²/5 – 5(20) + 12

Quadratic function, f(20) = -8

In conclusion, the graph of this quadratic function, f(x) = x^2 – 5x + 12 does not contain the data point (0, 0) as shown in the image attached below.

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The terminal side of a 130° angle in standard position lies in the second quadrant. Two angles that are co-terminal to 130° are 490° and -230°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given angle is 130°.

The first quadrant, second quadrant, third quadrant, and fourth quadrant make up the whole graph plane.

Angles in the first quadrant vary from 0° to 90°.

Angles in the second quadrant vary from 90° to 180°.

The angles in the third quadrant can be found between 180° and 270°.

Angles in the fourth quadrant can be found between 270° and 360°.

Therefore, the plot's beginning side is at zero degrees and its terminal side is at 130° in the second quadrant, since the specified angle is 130°.

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Answer: 2nd, -230, 490

Step-by-step explanation:

Edge 2023

Based on the information, it can be concluded Isabella bought  2 paintbrushes and 3 jars of paint.

The average of buying a product is 0.97, which means Isabella can buy a total of 5 items (0.97 x 5 = 4.85)

Based on this different combinations of products are possible, for example, 1 paintbrush and 4 jars or 3 jars and 2 paintbrushes. However, the one that fits the final price is:

2 paintbrushes x 0.95 = $1.9

3 jars of paint x 0.99 = $2.97

$2.97 + 1.9 = $4.87

Note: This question is incomplete, here is the missing information

The paintbrushes cost $0.95 and the jar of paint cost $.099

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Set of all natural numbers which divide 24 in tabular form {1,2,3,4,6,8,12,24} and set-builder form is  {x ∈ ℕ | x ∣ 24} ℕ denotes the set of natural numbers and x ∣ 24 means x divides 24.

Normative Data We utilize the numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 to count or arrange objects in a particular order. Complete numbers are those that fall between the zero and artificial number range. not a decimal or fraction.

Decimal numbers and fractions are not integers. Although all natural whole and numbers are integers (as well as all whole numbers), not all integer are whole or natural numbers. 5 is an integer even though it is not a whole number or a natural number.

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A. We can see that the intersection made by lines C and D classifies ∠7 and ∠8 as vertically opposite angles.

B. The special angles created by intersection of lines C and D can be used to solve for y by equating the expressions, 5y-29 and  3y+19 as they are vertically opposite angles.

C. Solving for y, we have: y = -5

Intersection, in mathematics, refers to the common elements or overlap between two sets. For example, if set A contains the elements 1, 2, and 3, and set B contains the elements 2, 3, and 4, then the intersection of set A and set B would be the set containing the element 2 and 3. In general, intersection is represented by the symbol ∩. Lines can also intersect to form angles.

Vertically opposite angles are actually known to be equal. It then means that:

∠7 = ∠8 (Vertically opposite angles)

Also, 5y-29 = 3y+19 (Vertically opposite angles)

Thus, solving for y, we have:

5y-29 = 3y+19

5y - 29 -29 = 3y + 19 - 29

5y -3y = - 10

2y = -10

y = -10/2 = -5

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The triangle types is impossible to draw is

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

Given:

First, a scalene with right-angled triangle is possible to make.

Now, an isosceles with acute-angled triangle is possible to make such triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement.

Now, an isosceles with obtuse-angled triangle is not possible to make because if two angles are greater than 90 then sum of angles exceed 180.

and, an equilateral with right-angled triangle is not possible to make because in Equilateral triangle are angles are of equal measurement 60.

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The value of the missing angle x of the triangle is; x = 18.67°

The sum of angles on a straight line is 180 degrees. Thus, the supplementary angle to 130 degrees is;

180 - 130 = 50°

Now, the alternate angle to 80 degrees which will be located inside the triangle is 80°.

The sum of angles in a triangle is 180 degrees. Thus;

3x - 6 + 80 + 50 = 180

3x + 124 = 180

3x = 180 - 124

3x = 56

x = 56/3

x = 18.67°

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The process of evaluate the integral by interpreting it in terms of areas is by apply the summation rule on it.

The term called integral is defined as a mathematical object that can be interpreted as an area or a generalization of area.

Here we need to find the way to evaluate the integral by interpreting it in terms of areas.

As we all know that the integration symbol ∫ is an elongated S, suggesting sigma or summation.

Here on a definite integral, we have to use the above and below the summation symbol are the boundaries of the interval, [a, b].

Where the numbers a and b are x-values and are called the limits of integration and it specifically a is the lower limit and b is the upper limit.

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Answer: 50g steel, 30g gold and 70g brass

Step-by-step explanation:

     This means for every 5g of steel there is 3g of gold and 7g of brass. We will find how many g there are total for every 5g of steel.

           5 + 3 + 7 = 15

     Next, we will divide 150g by 15g to see how many times the ratio will "repeat" to create the 150g of alloy.

           150g / 15g = 10g

     Next, we will multiply each amount of metal in one ratio by 10.

5g * 10 = 50g steel

3g * 10 = 30g gold

7g * 10 = 70g brass

Answer:

Step-by-step explanation

                                          to get 50g of steel.

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The pressure on the snow on the boy is P=1379.83 N.

A person weighing 180 pounds stands on snowshoes.

If the total area of the 2 snowshoes is 900 square inches

The mass of person on the snowshoes is given by,

m=180 pounds=180×0.454=81.6455≅81.65 kg

Force acting on a body due to gravity is given by, f = mg

The weight force of the person is given by,

The area of the snowshoes is given by,

⇒A=900 square inches

⇒1inch=0.025 m

Thus, Area in [tex]m^{2}[/tex] given by A=900×[tex]0.0254^{2}[/tex]

=900×0.000645

=0.5805[tex]m^{2}[/tex]

The expression of the pressure in the fluid containing tube is given by FA

; where F is the force exerted by the liquid and A is the area of the tube.

From the expression of pressure, the resulting pressure value is given by FA.

=800.900.5805

=19.82≈19.8pa

The pressure on the snow on the boy is =1379.83 N.

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The ball has both kinetic energy and potential energy.

The values of each type of energy the object has are KE = 37.5 J and GPE = 2205 J

Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.

If a  3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.

Then ball has kinetic energy due to his motion and also has potential energy due to his height.

Thus, M = 3-kg, h = 75 m and V = 5 m/s

KE = 1/2(M)(V)² = 1/2 × 3 × 5² = 37.5 J

GPE = mgh = 3 × 9.8 × 75 = 2205 J

KE + PE = 37.5 + 2205 = 2242.5 J

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Answer: The surface area of a square pyramid with a side length of 2m and slant height of 3m is 12 square meters.

Step-by-step explanation:

The surface area of a square pyramid can be calculated using the formula:

Surface area = Base area + 4 * (Area of one of the lateral faces)

The base area of the pyramid is the area of the square base, which is the side length squared: 2m * 2m = 4m^2

To find the area of one of the lateral faces, we can use the Pythagorean theorem to find the length of the face, which is the hypotenuse of a right triangle with the slant height and half of the side length as the other two sides.

so, (1/2 * 2m)^2 + 3^2 = x^2

x= (1/2 * 2m)^2 + 3^2

x = 2

Therefore, the surface area of the pyramid is:

Surface area = 4m^2 + 4 * 2m^2 = 4m^2 + 8m^2 = 12m^2

So, the surface area of a square pyramid with a side length of 2m and a slant height of 3m is 12 square meters.

Answer:

9

Step-by-step explanation:

9x9=81

Answer:

Step-by-step explanation:

So the rectangle is 9 units wide.

becuase given that the area of the rectangle is 81m'n' square units and the length of the rectangle is 9mn', we can set up the equation as:

81 = 9 x width

To solve for width, we can divide both sides of the equation by 9:

width = 81/9

width = 9

Answer:

3 x (5 + 2)

Step-by-step explanation:

Just use the distributive property, it's very simple.

Answer:

20

Step-by-step explanation:

A, B, C, D, E is a set of 5 letters.

A letter can only be used once.

You have 5 choices for the first letter.

5

Since the letter that was selected to go first cannot be used again, now you have 4 choices for the second letter.

5 × 4

5 × 4 = 20

Answer: 20

The required length of of the third side of isosceles triangle is 9 units.

An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides“.

Let the length of Equal two sides is x.

Third side = 2x - 5

Then, perimeter is 23 cm

x + x + 2x - 5 = 23

4x - 5 = 23

4x = 28

x = 7

Then, third side is 2x - 5

= 2(7) - 5

= 14 - 5

= 9 units

Thus, required length of third side is 9 units.

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Answer: First camera: 5 Pictures per second, Second camera: 6 Pictures per second. Third camera: 7 Pictures per second. The Third camera is the fastest.

Step-by-step explanation: 40/8 = 5, 30/5 = 6, 28/4 = 7

First, we should find the slope of the line we're starting with.

3y = 6x + 5 can be put into slope-intercept form by dividing both sides by 3.

 y = 2x + 5/3

The slope of this line is 2.

A parallel line has to have a slope of 2 as well, so we know we're looking for a line with a slope of 2.

Options A and B have that.  Options C and D do not.

Now if (3,3) is a point on the line, then (3,3) must also be a solution for the equation.

Checking Option A:

    3 = 2(3) - 1  is not true.  3 ≠ 6 - 1

Checking Option B:

    3 = 2(3) - 3 is true.  3 = 6 - 3

Option B is the answer, since it has the right slope and works for the point (3,3).

Answer:

B) y = 2x - 3

Step-by-step explanation:

3y = 6x + 5  To put in the slope intercept form.  Divide all the way through by 3

y = 2x + 5/3

When lines are parallel, they have the same slope.

So the slope will be 2.  We will use the point to find the y intercept

m = 2

x = 3   This is from the point (3,3)

y = 3   this is from the point (3,3)

y = mx + b

3 = 2(3) + b

3 = 6 + b   Subtract 6 from both sides

3-6 = 6- 6 + b

-3 = b

Now that we have the slope (2) and the y intercept (-3) we can write the equation.

y = mx + b

y = 2x -3

AB = BA, the first pair of matrices does not satisfy [tex]AB \neq BA[/tex].

AB = BA in general, even if A and B are both square. We say that A and B commute if AB = BA. We cannot argue that AB = AC provides B = C for a generic matrix A. (However, since A is invertible, we may multiply both sides of the equation AB = AC to the left by A1 to yield B = C.)

For matrices, A and B, the product AB is not necessarily equal to BA. In fact, matrix multiplication is not commutative in general. Therefore, we need to check each pair of matrices to see if their products are equal in order to determine which pair satisfies [tex]$AB \neq BA$[/tex].

[tex]$$\begin{align*}AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 7 + 0 \cdot 3 & 1 \cdot 0 + 0 \cdot 4 \ 3 \cdot 7 - 2 \cdot 3 & 3 \cdot 0 - 2 \cdot 4\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}[/tex]

[tex]$$\begin{align*}BA &= \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \\\&= \left[\begin{array}{cc}7 \cdot 1 + 0 \cdot 3 & 7 \cdot 0 + 0 \cdot (-2) \ 3 \cdot 1 + 4 \cdot 3 & 3 \cdot 0 + 4 \cdot (-2)\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}[/tex]

Since AB = BA, the first pair of matrices does not satisfy [tex]AB \neq BA[/tex]. We can proceed in the same manner to check the other pairs of matrices:

[tex]$$\begin{align*}\\AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}8 & 0 \ 11 & -3\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 8 + 0 \cdot 11 & 1 \cdot 0 + 0 \cdot (-3) \ 3 \cdot 8 - 2 \cdot 11 & 3 \cdot 0 - 2 \cdot (-3)\end{array}\right] \\\&= \left[\begin{array}{cc}8 & 0 \ 2 & 6\end{array}\right]\end{align*}[/tex]

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The length of the hammer is given as follows:

30.36 cm.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The sides in this problem are given as follows:

9 cm and 29 cm.

The length of the hammer is the hypotenuse, hence it is obtained as follows:

l² = 9² + 29²

[tex]l = \sqrt{9^2 + 29^2}[/tex]

l = 30.36 cm.

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Required equation to represent the translation 6 units left and reflected over x-axis is y = - (x + 6 ).

Let us consider the original equation be  y = x.

Translation to the left by k unit is f(x) = f ( x + k )

Now the equation gets translated 6 units to the left represents as

y = ( x + 6 )

Now the reflected over the x-axis is represented by :

Here y -coordinates change the sign.

If ( x, y ) after reflection over x -axis it is  ( x , -y ).

y = - ( x + 6 )

Equation to represents the reflected over x-axis and translated 6 units left of the original function y = x is written as y = - ( x + 6 ).

Therefore, the equation to represent the required translation and reflection is given by y = - ( x + 6 ).

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Answer: To find the number of cars that should be produced to incur minimum cost, we need to find the minimum value of the cost function C(x). Since C(x) is a quadratic function, it will have a minimum value, which is either a relative minimum or an absolute minimum. To find the number of cars that should be produced to incur the minimum cost, we will find the derivative of C(x) and set it equal to zero.

To find the derivative of C(x), we can use the power rule, which states that the derivative of x^n is n*x^(n-1).

The derivative of C(x) = 21000 - 90x + 0.1x^2 is

C'(x) = -90 + 0.2x

To find the minimum cost, we set C'(x) equal to zero and solve for x:

-90 + 0.2x = 0

0.2x = 90

x = 450

So, producing 450 cars will incur the minimum cost.

To verify that this is indeed a minimum, we can find the second derivative of C(x) which is 0.2, since the second derivative is positive, we can confirm that x = 450 is a relative minimum.

Alternatively, we can substitute x = 450 into the cost function and find the minimum value, which is C(450) = 21000 - 90(450) + 0.1(450)^2, which is less than any other value of C(x) for x≠450.

Therefore, to incur the minimum cost, 450 cars should be produced.

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]x-3y=9\implies -3y=-x+9\implies y=\cfrac{-x+9}{-3} \\\\\\ y=\cfrac{-x}{-3}+\cfrac{9}{-3}\implies y=\cfrac{1}{3}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a likne whose slope is 1/3 and it passes through (-10 , 9)

[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-10)}) \implies y -9= \cfrac{1}{3} (x +10) \\\\\\ y-9=\cfrac{1}{3}x+\cfrac{10}{3}\implies y=\cfrac{1}{3}x+\cfrac{10}{3}+9\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{37}{3} \end{array}}[/tex]

The required product of the same 500 consecutive integers whose sum is equal to 250 is zero.

Let us consider consecutive integers represented by x, x+ 1, x+ 2 , ..... so on.

Sum of 500 integers = 250

x + x + 1 + x+ 2 + ....+ x + 499 = 250

⇒ 500x + 1 + 2 + ...+499 = 250

⇒ 500x + ( 500 × 499 )/2 = 250

⇒ 500x + 250 × 499 = 250

⇒ 250 ( 2x + 499 ) = 250

⇒ 2x + 499 = 1

⇒x = -249

Required 500 numbers are :

-249 , -248 , -247 , ......, 0, 1, ....... 250

Here zero is also a part of 500 integers.

Product of 499 number with zero is zero.

⇒( -249 ×-248 ×.....× 250 ) × 0 = 0

Therefore, the product of 500 consecutive integers with sum 250 is equal to zero.

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True -  the statement says that a basic variable corresponds to a pivot column in the coefficient matrix. From the definition of basic variables, basic variables correspond to the columns that have a leading 1's (pivot columns).

A mathematical system model based on the use of a linear operator is known as a "linear system" in systems theory. In contrast to nonlinear cases, linear systems often display considerably simpler traits and attributes.

In linear systems, the variables are really only multiplied with constants and then added together; they are never multiplied by each other. In order to express both static and dynamic relationships between variables, linear systems are used.

Something relating to a line is linear. To build a line, all of the linear equations are used. Any equation that doesn't result in a straight line is considered as non. It has a variable slope value and appears as a curve on a graph.

A linear system is one in which both the superposition and homogeneity principles hold true.

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