PLEASE HELP
Explain what the unit rate means in the context of the problem.

Answer in at least two complete sentences.

a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).

b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.

c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.

d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.

The quadratic function for this problem is defined as follows:

f(x) = 4x² + 8x - 5.

Hence the coefficients are given as follows:

a = 4, b = 8, c = -5.

The discriminant is given as follows:

D = 8² - 4 x 4 x (-5)

D = 144.

Hence the x-intercepts are given as follows:

Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:

f(x) = 4(x - 0.5)(x + 2.5).

As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.

The y-intercept is given as follows:

f(0) = 4(0)² + 8(0) - 5

f(0) = -5.

The coordinates of the vertex are given as follows:

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On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Month / Brent / Gretel

0/4/ 128

1/ 16 / 256

2 / 64 / 512

3 / 256 / 1024

4 / 1024 / 2048

5 / 4096 / 4096

They will have the same amount of fish in 5 months.

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An inverse does not exist for a parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

An inverse does not exist for a parabola.

One definition of a parabola includes a line and a point (the focus) (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, an inverse does not exist for a parabola.

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Answer:

AC = PF

Step-by-step explanation:

Answer: X^2y + 3xy + 2y -3x^2 -9x -6
explanation

1. Foil (x+2)(x+1)

X^2 +2x + x + 2

2. Simplify

X^2 + 3x + 2

3. Distribute x^2 + 3x +2 (y-3)

X^2y + 3xy + 2y -3x^2 -9x -6

When Python constructs a function, it also generates a temporary variable with the same name, and only the function can access the value of that variable.

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Answer:

They are parallel line.

Using sine and cosine rule, the length of d in the triangle is equal to 4.5cm

The sine rule is a mathematical formula used to calculate the lengths of the sides and angles of any triangle when given two angles and one side or two sides and one angle. It is also known as the law of sines.

To find the length of d, we have to find the length of E.

Using sine rule;

f / sin F = e / sin E

5 / sin 75 = e / sin 79

e = 5sin79 / sin 75

e = 5.7cm

To find the length of d, we have to find the angle D by using the sum of angle theorem.

m∠ E + m∠ F + m∠ D = 180°

79 + 75 + m∠ D = 180

m∠ D = 180 - 154

m∠ D = 26°

Using cosine rule

d² = e² + f² - 2efCosD

d² = 5.7² + 5² - 2(5.7)(5)cos26

d² = 20.615598

d = √20.615598

d = 4.5cm

The length of side d is 4.5cm

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In the spring of 2012, 2300 student athletes participated in a sport.

The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

In 2014, there were 2277 student athletes participating in spring sports.

Suppose there were x contestants in 2013.

The answer was 2277, which was 110 percent more pupils competing in 2014 than in 2013. So,

[tex]$110 \%$ of $\mathrm{x}=2277$$\frac{110}{100} \times \mathrm{x}=2277$$\mathrm{x}=\frac{2277 \times 100}{110}$$\mathrm{x}=2070$[/tex]

2070 pupils therefore competed in 2013.

Let y be the student who will be vying in 2012.

Now, the number of pupils competing in 2070 was 90% that of the year 2012's.

So,

[tex]$90 \%$ of $y=2070$$$\begin{aligned}& \frac{90}{100} \times y=2070 \\& y=\frac{2070 \times 100}{90} \\& y=2300\end{aligned}$$[/tex]

As a result, 2300 students competed in the 2012 competition.

Therefore, the answer is 2300.

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Answer:

the percentage is 62%

Step-by-step explanation:

The equations are n + s = 76 and 2n + 1.50 s = 125.

let n = number of Nachos sold

let s = number of sodas sold

Two equations are presented to us, and we can use them together to solve one variable at a time.

Eq. 1: n + s = 76

Eq. 2: 2n + 1.50 s = 125

So, s = 76 - n

Put (76 - n) for s in the second equation

2n + 1.50 (76 - n) = 125

2n + 114 - 1.50 n = 125

2n - 1.50 n + 114 = 125

0.5n + 114 = 125

0.5n = 125 - 114

0.5n = 11

n = 22

s = 76 - 22

s = 54

22 nachos sold and 54 sodas sold.

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a) The minimum number of dogs that could have a mass of more than 27 kg is 6.

b) The maximum number of dogs that could have a mass of more than 27 kg is 18.

We have a table which shows information about the masses of some dogs.

Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.

But we wants minimum of 12 and 6 is 6 .

so, the minimum number of dogs with mass more than 27 kg is 6.

b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.

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Complete question:

The above table shows information about the masses of some dogs.

a) Work out the minimum number of dogs that could have a mass of more than 27 kg

b) Work out the maximum number of dogs that could have a mass of more than 27 kg

Answer:

by using sine rule and cosine rule.

Answer:

Step-by-step explanation:

3(23-2b) + 3b = 48

1. Use the distributive property and distribute the 3 before the parenthesis

             3(23-2b)   (make sure you read the (-) as part of the 2b so it's -2b

              69 - 6b

2. 69 - 6b +3b = 48   (combine like terms...the bs: -6b + 3b)

    69 -3b=48

3. 69 - 3b = 48         (subtract 69 from both sides)

   -69           -69

4. -3b = -21      (divide both sides by negative three...we want the b to be +

   /-3    /-3

Answer: b = 7

So, C is your answer

[tex]\textit{area of the rectangle}\\\\ A=Lw \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=5\\ w=6 \end{cases}\implies A=(5)(6)\qquad \begin{cases} \textit{tripling the sides}\\[-0.5em] \hrulefill\\ L=3\cdot 5\\ w=3\cdot 6 \end{cases} \\\\\\ A=(3\cdot 5)(3\cdot 6)\implies (3\cdot 3)(5)(6)\implies 9(5)(6)\leftarrow \begin{array}{llll} \textit{new area is 9 times}\\ \textit{the old one}\\ \textit{a ratio of 9 : 1} \end{array}[/tex]

According to the probability, there are 540 arrangements that can the cars stack up so that all three lanes are occupied.

Mathematicians use addition and division as well as counting to calculate probability.

There are three partitions of six using digits 1-3.

(4,1,1), (3,2,1), (2,2,2) (2,2,2)

These could be dispersed between the lanes in order that

(3) Possible solutions to (4,1,1)

There are six possible ways to solve the equation (3,2,1).

There is only one possible solution to the equation (2,2,2).

Cars must now move in the lanes in proper order.

The arrangements for (4,1,1) will be 6C4 * 2C1 = 30. Six cars are chosen, sorted, and placed in the appropriate lanes. then decide on 1 of the 2 surviving vehicles.

then place it in a lane.

The arrangements for (3,2,1) will be 6C3 * 3C2 = 60.

There will be 6C2 * 4C2 = 90 arrangements for (2,2,2).

Consequently, there will be 540 arrangements (3*30 + 6*60 + 1*90 = 90+360 + 90).

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Answer:

17.3 miles / gallon

Step-by-step explanation:

Rates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)

Given information from the question,

2 gallons = 34.6 miles

1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon

Check the picture below.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(4)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{5})(\underset{h}{20})}}\implies 80+50\implies \text{\LARGE 130}~m^2[/tex]

AE is congruent to CE.We can prove by assuming two triangle in the given diagram and by using SAS rule.

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.

Alternate angles are angles that occur on opposite sides of the transversal line. If two parallel lines are cut by a transversal then the alternate angles are equal.The pair of angles formed on the inner side of the parallel lines but on the opposite sides of the transversal are called alternate interior angles.

Now we have

Given a triangle ABC.Where E is the midpoint of AC. We have to prove that AE is congruent to CE.

In ΔAED and ΔCED

ED=ED              (∵Common side are equal)

∠AED=∠CED       (∵Alternate angles)

∠A=∠C        (∵Alternate angles)

By ASA rule, ΔAED≅ΔCED

By Corresponding Parts of Congruent triangles

AE=EC

Hence, AE is conruent to CE.

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The temperature at midnight as required to ve determined in the task content is; 14°C.

According to the task content; the temperature was 11.2°C at 2 : 00am.

However, since the temperature dropped 1.4 °c each hour; we have that;

In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.

On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.

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Answer:

x = - 1 or x = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

3x² + 5x + 2 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × 2 = 6 and sum = + 5

the factors are 3 and 2

use these factors to split the x- term

3x² + 3x + 2x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(x + 1) + 2(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(3x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]

Answer:32 17/18

Step-by-step explanation:

33 + (1/9)(x)

x = -1/2

33 + (1/9)(-1/2) =

33 + -1/18

= 32 17/18

Answer:

Tamicca made 12 monthly payments of $115, for a total payment of 12*$115 = $<<12*115=1380>>1380.

She bought a computer for $1200, so the finance charge that she paid is $1380-$1200 = $<<1380-1200=180>>180.

Therefore, the finance charge that Tamicca paid was $180, rounded to the nearest cent.

Step-by-step explanation:

Answer:

Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.

So (x + 4) + (2x + 4) + (4x + 4) = 61.

7x + 12 = 61 => 7x = 49 => x = 7.

So the answer is

Pat = 7

Mattie = 14

Jon = 28

The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.  

If we take Pat's age as = 'x' years,

so, Mattie's age will be = '2x' years.

and then, Jon would be = 2(2x)

                                        = '4x' years.

Now, the sum of their ages after 4 years =

 => (x+4) + (2x+4) + (4x+4) = 61

 => 7x+12 = 61

 => 7x= 61-12

 => 7x= 49

 => x= 49/7

 => x = 7

Therefore, Pat's age is  = 7 years.

              Mattie's age is = 14 years (2×7).

                  Jon's age is = 28 years (4×7).

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Adding all of the remaining pizzas, and dividing the total pizza into 5 equal fractions, the fraction of pizza that each person gets would be 11/24

A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number. It is different from an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4 is an improper fraction.

To convert a mixed number to an improper fraction, you must first multiply the whole number by the denominator of the fraction. Then add the result to the numerator. Finally, place the sum over the denominator. For example, to convert 3 1/2 to an improper fraction, you would first multiply 3 by 2 (the denominator of the fraction 1/2) to get 6, then add 1 (the numerator of the fraction 1/2) to get 7. So 3 1/2 is equivalent to 7/2 as an improper fraction.

So to find out the fraction of a whole pizza  that each person gets out of the different remaining pizzas, first we need to all the remaining pizzas as shown below,

3/4 of pepperoni + 5/8 of cheese + 11/12 of sausage = 55/24

Now to equally divide this into 5 person, we need to divide this fraction by 5,

i.e 55/(24*5) = 11/24

Therefore, each person gets 11/24 of the whole pizza.

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The equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of the line as -

y = 14x - 4

The given equation of line is -

y = 14x - 4

Slope of the line perpendicular to the given line is -

m{p} = -1/14

The equation of this line will be -

y = -(1/14)x + c

For the point (28, 16), we can write -

16 = -(1/14) x 28 + c

c = 16 + 2

c = 18

So, the equation will be -

y = - (1/14)x + 18

Therefore, the equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

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Answer: 9 2/3

Step-by-step explanation:

you take 29 and divide by 13 to get 2.23076923077 and you then take that times the 4 1/3 to get 9 2/3

Answer:

Step-by-step explanation:

13(X-4 1/3)=29

13X-56.3=29

     +56.3 = +56.3

13X=85.3

X=6.56

if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1)​ IS 1

P(n) :

1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)​

P(1) :

[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]

[tex]1=\frac{6}{6}=1[/tex]

∴ LHS = RHS

Assume P(k) is true

P(k):

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The product of (2x-3y)(2x+3y) is 4x^2-9y^2

Product= (2x-3y)(2x+3y)

Let the product of (2x-3y)(2x+3y) be P

P=2x(2x+3y)-3y(2x+3y)

P= 2x(2x)+2x(3y)-3y(2x)-3y(3y) {using distributive property of multiplication}

This property states that  multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a-b)(a+b) is equal to a^2 - b^2. This result is used as an identity.

P= 4x^2 +6xy - 6xy -9y^2

solving 6xy-6xy=0

P= 4x^2 - 9y^2

4x^2-9y^2 is the product of (2x-3y)(2x+3y).

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Answer:

( - 7, - 1, 1, 4 )

Step-by-step explanation:

( x, y )

where,

x is Domain

y is Range

Hence,

Domain is ( - 7, - 1, 1, 4 )