which set of ordered pairs represents a function

Answer:

x = -8.75; x = 7.25

Step-by-step explanation:

                                                         2(x + ¾)² - 5 = 123

The graph of your equation is a parabola with x-intercepts at x = -8.75

and x = 7.25.

The list of steps, in order, that will solve the equation is:

The given expression is raised to a power of 2, so we can say that the given expression is a quadratic equation.

A quadratic equation is a form of an algebraic expression in which the variable is usually raised to the power of its second degree.

From the parameters given:

[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 = 123 }[/tex]

[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 +5 = 123+5 }[/tex]

[tex]\mathbf{2(x + \dfrac{3}{4})^2 = 128}[/tex]

[tex]\mathbf{\dfrac{2(x + \dfrac{3}{4})^2 }{2} =\dfrac{ 128}{2}}[/tex]

[tex]\mathbf{(x + \dfrac{3}{4})^2 = 64}[/tex]

[tex]\mathbf{\sqrt{(x + \dfrac{3}{4})^2} =\sqrt{ 64}}[/tex]

[tex]\mathbf{(x + \dfrac{3}{4})} =\pm8}[/tex]

[tex]\mathbf{(x + \dfrac{3}{4} - \dfrac{3}{4}) }\mathbf{= \pm 8-\dfrac{3}{4}}[/tex]

[tex]\mathbf{x= \pm 8-\dfrac{3}{4}}[/tex]

[tex]\mathbf{x= +8-\dfrac{3}{4} \ \ OR \ \ x= -8-\dfrac{3}{4}} [/tex]

[tex]\mathbf{x=7.25 \ \ OR \ \ -8.75} [/tex]

Learn more about quadratic equations here:

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Answer:

[tex]y=250(5)^x[/tex]

Step-by-step explanation:

The growth of a population of bacteria can be represented by exponential growth function,

[tex]y=a(1+r)^x[/tex]

where,

y = the population of the bacteria after x hours,

x = the number of hours,

a = initial population of bacteria,

r = rate of growth,

At the beginning the number bacteria was 250 and the population of bacteria quadruples every hour i.e rate of growth is 400% or 4 per hour.

Putting all the values,

[tex]y=250(1+4)^x[/tex]

[tex]\Rightarrow y=250(5)^x[/tex]

Answer:

Step-by-step explanation:

Given that a storage rack has dimensions as 25x12x5 ft.

Box has dimensions as 15x8x10 inches

Volume of each box = 15(8)(10) = 1200 inches = 1200x12^(-3) feet^3

Volume of 5000 boxes = 5000 (1200x12^(-3) ) = 3472.22 cubic feet

Volume of storage rack = 25(12)(5) = 1500 cubic feet

Volume of 25 storage racks 1500(25) = 37500 cubic feet.

SInce storage racks have sufficient volume it is concluded that enough storage is there.

Answer:

Yes, we have enough storage space.

Step-by-step explanation:

25 storage racks that are:

Length: Lsr = 25 ft = 25 ft (12 in / 1 ft) → Lsr = 300 in

Width: Wsr = 3 ft = 3 ft (12 in / 1 ft) → Wsr = 36 in

Height: Hsr = 12 ft = 12 ft (12 in / 1 ft) → Hsr = 144 in

5000 boxes 15x8x10 in

Length: Lb = 15 in

Width: Wb = 8 in

Height: Hb = 10 in

In the length of each storage rack we can put:

Nl=Lsr/Lb=300 in / 15 in → Nl = 20

In the width of each storage rack we can put:

Nw=Wsr/Wb=36 in / 8 in = 4.5 → Nw = 4

In the height of each storage rack we can put:

Nh=Hsr/Hb=144 in / 10 in = 14.4 → Nh = 14

Then we can put in each storage rack:

N = Nl Nw Nh = (20)(4)(14) → N=1,120 boxes

And we have 25 storage racks, then we can storage in total:

Nt=25N=25(1,120)→Nt=28,000 boxes

And we have 5,000 boxes, then we have enough storage space

Answer:

(x, y) = (4, 5)

Step-by-step explanation:

given the 2 equations

x = 2y - 6 → (1)

y = - 3x + 17 → (2)

Either substitute x = 2y - 6 into (2) or y = - 3x + 17 into (1)

substituting y = - 3x + 17 into (1)

x = 2(- 3x + 17) - 6

x = - 6x + 34 - 6

x = - 6x + 28 ( add 6x to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

substitute x = 4 into (2)

y = - 12 + 17 = 5

solution is (4, 5 )

Answer:

400 divided by 5 is how you get the answer.

Step-by-step explanation:

400 / 5 = 80

80 batches of soup.

Answer:

19 percent

Step-by-step explanation: First we need to convert them all the a similar format. Fractions would be easiest.

.22 = 22/100

1/5 = 20/100

19% = 19/ 100

The one that contains the least is 19/100 or 19%.

[ Answer ]

2 / 3

[ Explanation ]

1 * 8 / 4 * 3

8 / 12

Simplify:

2 / 3

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Answer:

The sum of the interior angles of a triangle is 180 degrees.

d. Scalene

e. Isosceles

f. Isosceles

g. Equilateral

h. Scalene

i. Equilateral

j. Right

l. Acute

m. Obtuse - doesn't add to 180 not a triangle

n. Acute - doesn't add to 180 not a triangle

o. Obtuse

Step-by-step explanation:

The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.

Side lengths: Compare the side lengths and see if any are equal to determine the type.

Angle Measures: Compare the angles measures to 90 degrees.

The greatest number of sets of pens and pencils that can be made, using all of the given 28 pens and 80 pencils in each set, is 4. Each set would contain 7 pens and 20 pencils.

In the problem, we are looking to find the Greatest Common Divisor (GCD), which is the greatest number that can evenly divide both the number of pens (28) and the number of pencils (80). The GCD between 28 and 80 is 4.

Thus, the most sets of pens and pencils you can make would be equal to the GCD, which in this case is 4.

This means you can put together 4 sets with an equal number of pens and pencils in each set. In each of these sets, there would be 7 pens (28 pens ÷ 4 sets) and 20 pencils (80 pencils ÷ 4 sets).

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Final answer:

To maximize the number of sets with 28 pens and 80 pencils, find the greatest common divisor and divide the total by it. You can create 27 sets of 4 pens and 10 pencils each.

Explanation:

To find the greatest number of sets you can make with 28 pens and 80 pencils, you need to determine the highest common factor of the two quantities.

Calculate the greatest common divisor (GCD) of 28 and 80, which is 4.

Divide the total number of pens and pencils by the GCD: (28 + 80) ÷ 4 = 27.

You can make 27 sets, each consisting of 4 pens and 10 pencils.

To determine the number of artists who showed only sculptures or paintings at the art fair, we use the formula for the principle of inclusion-exclusion, resulting in 61 artists.

To find out how many artists showed only sculptures or paintings at the art fair, we apply the principle of inclusion-exclusion. First, we add the number of artists who showed sculptures (25) to those who showed paintings (48), which gives us a total of 73 artists. However, this counts the 12 artists who showed both sculptures and paintings twice, so we subtract 12 from this total to correct for the double counting. Therefore, the number of artists who showed only sculptures or paintings is 73 - 12, which equals 61 artists.

Answer: 4 km/hr and 6 km/hr

Step-by-step explanation:

A runner = 4km/hr

A runner covered distance after 3 hours = 12 km

B runner = 6km/hr

B runnet covered distance after 3 hours = 18 km

Total distance = 12 + 18 = 30km

You would vertically shift the function up a unit, making it clear that the answer should be graph 3.

Use the image below, red is the original function, and blue is the new function.  

Answer:

(x - 2)*(x - 1) is the answer

Step-by-step explanation:

We have to divide the polynomial f(x) = x^{3}-8x^{2}+17x-10 by (x-5).

Now, after dividing f(x) gets simplified into (x-5)*(x^{2}-3x+2).

So, we need to factorize the quadratic equation x^{2}-3x+2.

i.e. x^{2} - 3x + 2 = x^{2} - x - 2x + 2 = x(x-1) - 2(x-1) = (x - 2)*(x - 1)

Therefore, f(x) again gets simplified into (x-5)*(x - 2)*(x - 1)

Now eliminating the common factor (x-5).

We get, [tex]\frac{x^{3}-8x^{2}+17x-10}{x-5}[/tex] = (x - 2)*(x - 1)

Answer:

[tex]x^{2}-3x+2[/tex]

Step-by-step explanation:

Use synthetic division.

5 |  1    -8    17    -10

   +     5    -15    10

      1   -3     2     0

The quotient is [tex]x^{2} -3x+2[/tex].

Answer:

5 pounds

Step-by-step explanation:

:'>

Answer:

She bought 5 pounds of coffee.

Step-by-step explanation:

Answer: -9

Step-by-step explanation: -91/6 ≈ -9.167

21/3 ≈ 2.33333

-17/8 ≈ -1.875

-9.167 + 2.3333 + -1.875 = -8.71

Rounded, the answer is -9.

Answer:

X = apple

y = orange

4x + 4y = 10

6x + 6y = 12

Step-by-step explanation:

Answer:

4a+4r = 10

6a + 6r = 12

No solutions

Step-by-step explanation:

a = cost of the apple

r = cost of the orange

4a+4r = 10

6a + 6r = 12

Divide the first  equation by 2 and the second equation by 6

2a+2r = 5

a +r = 2

Multiply the second equation by -2 so we can eliminate a

-2a -2r = -4

Add the first equation

2a+2r = 5

-2a -2r = -4

---------------------

0 = 1

This system is inconsistent and has no solutions

Answer:

No. It used  1 gallon in 18.41 miles.

Step-by-step explanation:

He travelled 2834 - 2529 = 305 miles.

So his consumption is  305 / 75.2 = 4.056 miles/litre.

This equals 4.056*4.54 = 18.41 miles / gallon.

So this is less than the 1 gallon  every 20 miles stated by the handbook.

Answer: His limo used 1 gallon fuel for 18.4136 miles.

Step-by-step explanation:

Fayez covered distance:

2834 - 2529 = 305 miles.

He used fuel = 75.2 litres

75.2/4.54 = 16.5638 gallons petrol used.

His limo covered distance / total petrol used = 305 miles / 16.5638 gallons petrol = 18.4136 miles per gallon.

That is less than 20 miles per gallon

Answer:

D

Step-by-step explanation:

y>-3x+1                                 Negative slope

y<x+2                                   Positive slope

< or > have dotted line

< or > have a solid line

> or > means solutions are above the line

< or < means solutions are below the line

The one with negative slope has a dotted line and solutions above it.

The one with positive slope has a solid line and solutions below it.

Answer:

Side AB

Step-by-step explanation:

Draw two congruent quadrilaterals.

Label the sides of one A,B,C,and D.

Label the sides of the other E,F,G,and H

Because the sides match up with the order in which they appear in if they are congruent, The first two letters(E and F) should be equivalent to the first two letters of the other shape(A and B).

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies 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-1=3(x-3) \\\\\\ y-1=3x-9\implies y=3x-8[/tex]

40% helping customers + 13% doing paper work = 53% of his time.

This means 100% - 53% = 47% of his time he is doing other tasks.

Answer:

they each get $5.75 for lunch

Step-by-step explanation:

9.25 x 90 students = 832.50

832.50 -315 = 517.50

517.50 / 90 = 5.75

Answer:

remainder = 290

Step-by-step explanation:

[tex]\frac{3x^3-4x^2+2x+8}{x-5}[/tex]

= 3x² + 11x + 57 + [tex]\frac{290}{x-5}[/tex]

quotient = 3x² + 11x + 57 and remainder = 290

Answer:

1 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

​a

​​ x

​b

​​ =x

​a+b

​​  

{a}^{2}+bb=289a

​2

​​ +bb=289

2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

​a

​​ x

​b

​​ =x

​a+b

​​  

{a}^{2}+{b}^{2}=289a

​2

​​ +b

​2

​​ =289

3 Subtract {b}^{2}b

​2

​​  from both sides

{a}^{2}=289-{b}^{2}a

​2

​​ =289−b

​2

​​  

4 Take the square root of both sides

a=\pm \sqrt{289-{b}^{2}}a=±√

​289−b

​2

​​  

​

​​  

5 Rewrite 289-{b}^{2}289−b

​2

​​  in the form {a}^{2}-{b}^{2}a

​2

​​ −b

​2

​​ , where a=17a=17 and b=bb=b

a=\pm \sqrt{{17}^{2}-{b}^{2}}a=±√

​17

​2

​​ −b

​2

​​

6 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

​2

​​ −b

​2

​​ =(a+b)(a−b)

a=\pm \sqrt{(17+b)(17-b)}a=±√

​(17+b)(17−b)

Answer:

A quadratic function can not have a maximum and minimum value. It can only take on one of those. The quadratic only makes one turn, so if the quadratic opens upwards, there is a minimum. If the quadratic opens downwards, there is a maximum.

A quadratic function can have either a maximum value or a minimum value, but not both.

A quadratic function can have either a maximum value or a minimum value, but not both. Whether it has a maximum or minimum value depends on the coefficient of the quadratic term (a) in the function. If a is positive, the graph of the quadratic function opens upwards and has a minimum value. If a is negative, the graph opens downwards and has a maximum value.

For example, the function y = x² has a minimum value of 0 at the vertex of the parabola, while the function y = -x^2 has a maximum value of 0 at the vertex.

Therefore, a quadratic function cannot have both a maximum value and a minimum value.

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