Use an outside source to search for a quadratic equation that models something from your daily life. (Be sure to cite the source you use.)
Solve the equation in two ways.
Discuss which method you liked better and why.
In your responses to peers, compare and contrast your preferences for how to solve quadratic equations.

The number of toys is 5 in each container.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Let x be the number of toys in each container.

Weight of one toy car = 6 pounds

Weight of the container in which toy cars shipped = 5 pounds

Weight of x toy cars = 6x

Total weight of the container when toy cars are placed = 6x + 5

Weight of one toy truck = 3 pounds

Container weight = 20 pounds

Weight of x toy trucks = 3x

Total weight of the container when toy trucks are place = 3x + 20

Given that both containers have same weight.

6x + 5 = 3x + 20

6x - 3x = 20 - 5

3x = 15

x = 5

Hence the number of toys in each container is 5.

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The solution to the quadratic equation are x = 1 and -5/2

We have the quadratic function;

2x² + 7x + 5

Using the factorization method of solving quadratic equation. We need to multiply the coefficient of x² and the constant 5.

Then find the pair factors and substitute the values into the function.

Substitute the values, we have;

2x² + 2x + 5x + 5

Factor the expression in pairs

(2x² + 2x) + (5x + 5)

Factor the common terms, we get;

2x(x + 1) + 5( x+ 1)

We have the equations;

2x + 5 = 0

x = -5/2

And

x + 1 = 0

x = -1

Thus, the values are x = -5/2 and -1

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I agree that Freddy ate 1 / 8 of the brownies in the pan because two brownies represents 1 / 8 of the brownies in the pan.

The large pan is said to have been used to make 16 brownies which means that if Freddy ate 2 brownies out of this, the proportion that he would have eaten of the cookies in the pan is:

= Number of brownies Freddy ate / Number of total brownies in the large pan

= 2 / 16

= 1 / 8

This therefore shows that Freddy's friend was right in saying that Freddy ate 1 / 8 of the brownies in the pan.

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Full question is:

A large pan is used to make 16 brownies. Freddy had two of the brownies from a large pan. His friend said he ate 1/8 of the brownies in the pan. Tell why you agree or disagree.

The amount in Ravi account after 6 months will be $410.

The amount in Susan account after 6 months will be $460

From the information, Ravi and Susan each opened a savings account today. Ravi opened his account with a starting amount of $650, and he is going to take out $40 dollars per month. This will be:

650 - 40m

Susan opened her account with a starting amount of $850 dollars, and she is going to take out $65 per month. This will be:

850 - 65m

The amount in Ravi account after 6 months will be;

= 650 - 40(6)

= 410

The amount in Susan account after 6 months will be:

= 850 - 65(6)

= $460

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Answer:

Step-by-step explanation:

1 Wanderer

2 moves on its own orbits the sun

3 Saturn

4 saturn

Answer: d

Step-by-step explanation: -5 is the intercept since x is 0 above it.

using the y2-y1 / x2-x1  we will get 2/4 (1/2 when simplified).

For the polynomial functions f(x) = 3x - 2 and g(x) = x² + 1, then function (f + g)(x) is calculated to be

A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation or the cubic equation.

The equation in the problem has integers as below

f(x) = 3x - 2: integer value here is 1

g(x) = x² + 1 integer value here is 2

In both conditions, the integer values are positive hence both are polynomial functions

(f + g)(x) is addition of the two polynomials

f(x) = 3x - 2 + g(x) = x² + 1

= 3x - 2 + x² + 1

= x² + 3x - 1

hence (f + g)(x) = x² + 3x - 1

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The length of the label is 121 over 28. (option C)

The length of the label is equivalent to the circumference of the cylinder. The circumference of an object is the distance round the object.

The formula for circumference of a cylinder = 2πr

Where:

π = 22/7

r = 2 3/4 = 11/4

2 x 22/7 x (11/4) = 121/28 cm

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Answer: 121/7

Step-by-step explanation: I got it correct :)

26,706.08 nearest to  26,706.14

Purchasing is the set of functions associated with acquiring the goods and services that an organization requires. Purchasing is a small subset of the broader procurement function.

The 6 key steps of the purchasing process are:

Fair secured apr: 5.60% = 0.4666% for 1 month

28,125 x 1.075 = 30,234.38 - 3125 = 27,109.38

27,109.38 x 1.004666 = 27,235.87 - 529.79 = 26,706.08

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According to the trigonometric function,  F(t) = 20 cos (2π/5)t where t represents time, in seconds. representing the pendulum ride of the sea dragon. It will take the pendulum 5 seconds to complete one full cycle.

A period on a graph function is the distance between two repeating points.

The graph repeats itself as it advances along the x-axis, as you can see.

Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.

The equation is F(t) = 20 cos (2π/5)t

The amplitude of the equation is 20 and the graph makes 2π/5 oscillations at every t seconds

the period to complete an oscillation which is 2π

2π/5 * t = 2π

t = 2π * 5/2π  

t = 5 seconds

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Answer: The phrase "5 times a number, divided by 6" can be translated into the algebraic expression:

(5/6)x

This expression represents "5 times a number, divided by 6", where x is the unknown number.

Step-by-step explanation:

61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.

This is a mixture problem that can be solved using algebra. We can set up a system of equations to represent the amount of each solution being used and the final acid concentration.

Let x be the amount of 55% acid solution and y be the amount of 30% acid solution used.

We can set up the following system of equations:

(55/100)x + (30/100)y = (43/100)(x + y) (Equation 1) represents the final acid concentration.

x + y = 100 (Equation 2) represents the total amount of solution mixed

We can solve for one variable in equation (1) by isolating it and substituting it into equation (2).

Solving for x in equation (1) we get: x = (100*43/100 - y30/100)/55/100

Substituting this value into equation (2) we get: (10043/100 - y30/100)/55/100 + y = 100

Solving for y we get: y = (100*100 - 100*43)/30 = 33.33 oz

And then substituting this value back into the equation x = (100*43/100 - y30/100)/55/100 we get x = 61.67 oz

So, 61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.

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Answer:

the slope is -2

Step-by-step explanation:

hope this helps!!

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

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x+10\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 line whose slope is 1/4 and that it passes through (4 , 3)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \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}{3}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-3=\cfrac{1}{4}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x+2 \end{array}}[/tex]

The lines that are true in the following statements are, Parallel lines have the same slope. Parallel lines have equal slopes. Parallel lines have different y-intercepts. Parallel lines have different x-intercepts.

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.

The following key traits and qualities make it simple to recognize parallel lines:

They are usually parallel straight lines that are spaced equally apart.

These lines are coplanar.

No matter how far you extend them in any direction, they never come together.

All the statements mentioned are true.

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19.75 meters is the rocket's height when it has 0.5 seconds after launch

A relation is a function if it has only One y-value for each x-value.

Given that The flight of Jae and Miguel's rocket t seconds after launch is modeled by

h(t) = -5t² + 40t + 1

h(t) is their rocket's height in meters.

we have to find the rocket's height in meters 0.5 seconds after launch

Put t=0.5 in the above function.

h(0.5)=-5(0.5)² + 40(0.5)+ 1

=-5(0.25)+20+1

=-1.25+20+1

=19.75

Hence, 19.75 meters is the rocket's height when it has 0.5 seconds after launch

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The equation for a tangent to the graph of y = arcsin(x/2) at the origin is y = x.

To find the equation for a tangent to a graph at a certain point, we need to find the slope of the tangent at that point. To do this, we can use the derivative of the function. In this case, the function is y = arcsin(x/2). Using the chain rule, we can find the derivative of this function:

y' = d/dx(arcsin(x/2))

= d/dx(sin^-1(x/2))

= 1/√(1 - (x/2)^2)

Now, to find the slope of the tangent at the origin (0,0), we can plug x = 0 into this derivative:

y'(0) = 1/√(1 - (0/2)^2) = 1

So the slope of the tangent at the origin is 1. To find the equation of the tangent, we can use the point-slope form of a line:

y - y1 = m(x - x1) where,

Plugging in the values for the origin and the slope we found above:

y - 0 = 1(x - 0)

or, y = x

So the equation for the tangent is y = x. But the options are incorrect.

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Answer:

  1

Step-by-step explanation:

[tex](\frac{2}{3} )^{0} =1[/tex]

[tex](1)^{-3} =1[/tex]

Hope this helps

Considering the closure under property the polynomials f(x) = a 0 + a 1 x + a 2 x^ 2 ... + a n x^ n; and g(x) = b 0 + b 1 x + b 2 x^ 2 ... + b m x^ m

In mathematics, a set is considered closed if we are able to apply and complete an operation on its components while consistently receiving a component from the same set.

A set therefore either possesses closure for a given mathematical operation or it does not.

Use of real numbers is the closure property of addition. Addition of two real numbers results in areal number

In the given problem, the set considered is polynomial addition and the addition of the two polynomial will give a sum which is a polynomial hence we say it is closed under addition.

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Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

A surface is a measurement of how much overall space an object's surface takes up. Surface area of a three-dimensional shape is determined by the total area of its surroundings. Surface area is the term used to describe a triangular shape's entire surface area. The particular area of each face on a cube with six square faces can be added up to determine the cube's surface area. Alternately, you can get the box's dimensions by using the following formula: Surface (SA) equals twice twice twice twice. A three-dimensional shape's surface area is calculated as the sum of all the space it occupies.

Here,

Given : width : 5/6 yard

and length = 1/4 yard

To find the area = length * width

=> area = 5/6 * 1/4

=> area = 5/24

=> 0.2083 yard square.

Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

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Answer:

Y = 4

Step-by-step explanation:

5x-y=54

50-y=54

circle y and subtract 50 from itself then subtract 50 from 54.

after subtracting you should have y=4

Answer:

280

Step-by-step explanation:

Answer:

8×35=280.

This is the best I can give to you

The complete function table using the defined function rule is as shown below.

We are given the function rule as;

h(x) = 2x - 3

From the function table attached, we will need to find the value of the function h(x) at x = -3, -2, 1, 3, 5

Thus;

Plugging in the value of -3 for x in the given function rule gives us the output as;

h(-3) = 2(-3) - 3

h(-3) = -9

Plugging in the value of -2 for x in the given function rule gives us the output as;

h(-2) = 2(-2) - 3

h(-2) = -7

Plugging in the value of 1 for x in the given function rule gives us the output as;

h(1) = 2(1) - 3

h(1) = -1

Plugging in the value of 3 for x in the given function rule gives us the output as;

h(3) = 2(3) - 3

h(3) = 3

Plugging in the value of 5 for x in the given function rule gives us the output as;

h(5) = 2(5) - 3

h(5) = 7

Thus, the complete function table is;

x        h(x)

-3       -9

-2       -7

1         -1

3         3

5         7

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Note that in the above mathematical scenario involving two similar triangles, the option that MUST  be correct is AC < FH (Option C) This solution is arrived at using the Open Mouth Theorem.

The above-stated Theorem in Geometry asserts that if two sides of two triangles are congruent and the included angle differs, then the greater angle is opposite the longer side.

This theorem is known as the Open Mouth Theorem because it is based on the idea that the two sides of a triangle are "pivoted" at their common vertex.

Please keep in mind that this theorem only works if we know two pairs of sides are congruent like this.

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The features of the cosine function are given as follows:

The equation of the cosine function is given as follows:

y = 1/3cos(2(x - π/3)).

The cosine function is defined as follows:

g(x) = acos(b((x+c))+d.

The coefficients have these following roles:

The function oscillates between -1/3 and 1/3, hence the amplitude is of:

a = 1/3.

The period is of 2π/3 - (-π/3) = π, hence:

2π/B = π.

B = 2.

The horizontal shift is of -π/3, hence the equation is given as follows:

y = 1/3cos(2(x - π/3)).

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The ordered pairs are solutions to the system of equations are (-2,1.6)

In order to determine which ordered pairs are solutions to the system of equations, you need to equate the two equations and solve for x:

y = -0.5x+0.6 and y= x+3 3/5

-0.5x+0.6 = x+3 3/5

-0.5x+0.6 = x+3.6

x+3.6 + 0.5x-0.6 = 0

1.5x + 3 = 0

1.5x = -3

x = -3/1.5

x = -2

y =-0.5x+0.6

y = -0.5(-2) + 0.6

y = 1.6

y = x + 3.6

y = -2 + 3.6

y = 1.6

Thus, the ordered pairs are (-2, 1.6)

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The probability of getting two spades when two cards are drawn from the deck is 1/17.

Probability branch of mathematics the deal with the likewood of an event occouring. It is the measure of how likely it is something will happen or be the case. Probabilities expressed as a number between zero and one 00 indicates impossibility and one indicus certainity. Probability can be used to calculate the chances of certain outcome based on a state condition or data. Probability can also be used to make decision and prediction about the future.

The probability of getting two spades when two cards are drawn from a shuffled deck of cards is 3/52 x 2/51, or 1/17.

This is because there is a 3/52 chance of getting the first spade and a 2/51 chance of getting the second spade (since there is one less card in the deck).

Therefore, the probability of getting two spades when two cards are drawn from the deck is 1/17.

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The discount as a percentage is 13.8%

The price of a picnic basket is marked as $31

The original price is $36

The discount percentage can be calculated as follows

36-31/36 × 100

= 5/36 × 100

= 0.138× 100

= 13.8%

Hence the percentage discount is 13.8%

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The number of rocks in Willy’s collection is 30

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split

In this case, the number of rocks in Willy’s collection can be represented by x and the number of rocks in Billy’s collection is 2 2/3 times the number in Willy’s collection.

The appropriate equation to illustrate this will be:

x + 2 2/3x = 110

3 2/3x = 110

x = 110 ÷ 11/3

x = 110 × 3/11

x = 30

There'll be 30 rocks

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On solving the provided question of arithmetic , we can say that after five years, Offer A will offer a higher total income.

Every subsequent pair of terms in an arithmetic sequence has a constant difference. This resembles linear functions with the formula y=mx+b. There is a fixed ratio between every pair of subsequent terms in a geometric sequence. This would produce a constant multiplier effect.

Given that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:

Offer A = Arithmetic

55000.r1.055 X

70, 195.48 — x

Offer B = Geometric

56000+ (5a•2000) X

56000+ 10000 = x

66,000 = x

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