Determine if each answer choice represents a proportional or not proportional linear relationship. drag each answer choices to the correct column. The order does not matter.

The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application",

The equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .

It is given to us that -

The vertex of the parabola = (-8,5)

The directrix of the parabola is y = -3

We have to find the equation of the parabola with the given vertex and directrix.

We know that any point on a given parabola represented as () is equidistant from the directrix and the focus.

So, the equation for the point can be represented as

[tex][y-(-3)]=\sqrt{([x-(-8} ]^{2} +(y-5)^{2}[/tex]

[tex](y+3)^2} =(x+8)^{2} +(y-5)^{2} \\=y^{2}+9+2*y*3=(x+8)^{2} +y^{2}+25-2*y*(-5)=6y-10y=(x+8)^{2} +16=-4y=(xx+8)^{2} +16=y=\frac{-1}{4} (x+8)^{2}+4[/tex]

Thus, the equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .[tex]=y=\frac{-1}{4} (x+8)^{2} +4[/tex]

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The minimum value of the function y = 2(x - 3)² - 4 is -4. Domain of the function is set of all real numbers and the range is all real numbers ≥ -4.

Domain of a function y = f(x) is the set of all the values of x where the function is defined.

The range of the function is the set of all values of the function on the defined domain.

The given function is,

y = 2(x - 3)² - 4

y = 2(x² - 6x +9) - 4

y = 2x² - 12x + 14

This is a quadratic function and the graph of the function will be a parabola.

The parabola is directed upwards if the coefficient of x² in a quadratic equation is positive and so will be having a minimum value.

The parabola is directed downwards if the coefficient of x² is negative and so will be having the maximum value for the function.

Here, coefficient of x² = 2, is positive.

So there will be a minimum value.

The value of [tex]\frac{-b}{2a}[/tex] in the quadratic equation ax² + bx + c, is the x value of the vertex of the parabola.

x = - (-12) / (2 × 2) = 3

∴ Minimum value, y = 2 (3 - 3)² - 4 = -4

Domain of the function will be the set of all real numbers because the function is defined for all real numbers.

The range will be all real numbers ≥ -4, because any values of x in the function does not make the value of the function less than -4.

Hence the minimum value of the function is -4 and the domain and the range of the function is set of all real numbers and all real numbers ≥ -4 respectively.

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Answer:

74

Step-by-step explanation:

if a is 122 b is 58

b is congruent to g to g=58

58+48=106

180-106=f

180-106=74

Answer: 12.5%

Step-by-step explanation:

5/40

0.125 x 100

12.5%

Answer:

2 children I believe so

Step-by-step explanation:

because you take 40%×5 and u will get 2

Answer:

three solutions of the equation:

y = -2x - 1

=>

1) (0, -1)

2) (1, -3)

3) ( -1, 1)

Step-by-step explanation:

The measure of angles form an scalene triangle.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

An angle requires two straight line, such that they're connected on one of their endpoints. The point of their joint is called vertex of that angle.

We are given that the angles of a triangle are 44 degrees, 110 degrees, and 26 degrees.

Since we know that angle sum property of a triangle;

44 + 110 + 26

180

Therefore, the measure of angles form an scalene triangle.

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The equation to find how many loads of bricks that Roger move will be 44x=243.

A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.

This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."

In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.

Given,

Total amount of bricks load carried by Roger=40 1/2pounds

=81/2 pounds

Per each load --- 7 1/3pounds

1 load --------- 22/3 pounds

x   -----81/2 pounds

(81/2)(3/22)=x

243=44x

44x=243

Therefore, the equation to find how many loads of bricks that Roger move will be 44x=243.

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Answer: b=13

Step-by-step explanation:

This equation is in point-intercept form:  y = mx + b

slope = m = 4/3

y-intercept = b = 13

Answer:

Step-by-step explanation:

180 because if you add 180 + 180 = 360

Answer: 5x+3 is a linear expression

Step-by-step explanation:

The linear expression is y=mx+b

5x +3 has a slope and y-intercept, so it is a linear expression!

8xy is not because it is just a variable

3x^2 is not because it has ^2

The number of sets to be printed to ascertain at least 4 identical subset is there on the list when a computer is printing out subsets of a 5 element set is 97.

The total number of subset for a n element set is 2^{n}. Therefore, for a 5 element set is 2^{5} = 32.

Thus to ensure there are at least 4 identical subset, the computer should print 3 times the total number of subsets possible plus 1 additional subset, i.e. 3×32 + 1 = 97.

-- The question is incomplete, the correct question is as follows --

"A computer is printing out subsets of a 5 element set (possibly including the empty set). a. at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?"

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Answer: x= -1  y= 1

Step-by-step explanation: Times  -3 to get the same x

-3x - 15y = -12

3x - 7y = -10

      -22y = -22

            y= 1

Then put 1 back in for letter y and you get x= - 1

Answer:2p

Step-by-step explanation:

Check the picture below.

If you start with 1/4, you can create an entire class of fractions equivalent to 1/4 by multiplying 1/4 by different forms of the number 1.

The connection between two numbers, known as the numerator and the denominator, is expressed mathematically as fractions. The number of pieces is represented by the numerator, while the total number of components is represented by the denominator. For instance, if a pizza is cut into 8 slices and someone eats 3 of them, the fraction corresponding to the quantity consumed would be 3/8.

Diverse mathematical ideas, including division, ratios, and proportions, can be represented using fractions. They can also be used to represent decimal and percentage values, with the decimal point placed to the right of the numerator and the number of decimal places represented by the denominator.

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Answer: True

Step-by-step explanation:

The rate of change or the slope is the changes to another quantity with a constant.

The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

We have,

To find the three consecutive prime numbers with a sum that is a multiple of 5 and each less than 100, start by listing the prime numbers less than 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Check each combination:

(2, 3, 5): Sum = 2 + 3 + 5 = 10 (which is a multiple of 5)

(3, 5, 7): Sum = 3 + 5 + 7 = 15 (which is a multiple of 5)

(5, 7, 11): Sum = 5 + 7 + 11 = 23 (not a multiple of 5)

(7, 11, 13): Sum = 7 + 11 + 13 = 31 (not a multiple of 5)

(11, 13, 17): Sum = 11 + 13 + 17 = 41 (not a multiple of 5)

(13, 17, 19): Sum = 13 + 17 + 19 = 49 (which is not a multiple of 5)

(17, 19, 23): Sum = 17 + 19 + 23 = 59 (not a multiple of 5)

(19, 23, 29): Sum = 19 + 23 + 29 = 71 (not a multiple of 5)

(23, 29, 31): Sum = 23 + 29 + 31 = 83 (not a multiple of 5)

(29, 31, 37): Sum = 29 + 31 + 37 = 97 (not a multiple of 5)

(31, 37, 41): Sum = 31 + 37 + 41 = 109 (which is not a multiple of 5)

(37, 41, 43): Sum = 37 + 41 + 43 = 121 (which is not a multiple of 5)

(41, 43, 47): Sum = 41 + 43 + 47 = 131 (not a multiple of 5)

(43, 47, 53): Sum = 43 + 47 + 53 = 143 (which is not a multiple of 5)

(47, 53, 59): Sum = 47 + 53 + 59 = 159 (which is not a multiple of 5)

(53, 59, 61): Sum = 53 + 59 + 61 = 173 (not a multiple of 5)

(59, 61, 67): Sum = 59 + 61 + 67 = 187 (not a multiple of 5)

(61, 67, 71): Sum = 61 + 67 + 71 = 199 (not a multiple of 5)

(67, 71, 73): Sum = 67 + 71 + 73 = 211 (not a multiple of 5)

(71, 73, 79): Sum = 71 + 73 + 79 = 223 (not a multiple of 5)

(73, 79, 83): Sum = 73 + 79 + 83 = 235 (which is a multiple of 5)

(79, 83, 89): Sum = 79 + 83 + 89 = 251 (not a multiple of 5)

(83, 89, 97): Sum = 83 + 89 + 97 = 269 (not a multiple of 5)

Thus,

The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

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Answer:

1/2 - 1/7 = 5/14

3/5 - 1/2 = 1/10

Step-by-step explanation:

The compound interest formula [tex]A = P(1 + r/n) ^nt[/tex] Monthly compounding is a common strategy used by interest-bearing CDs to boost returns. The annual interest rate is divided by twelve in this scenario.

After 4 years, you should have $763 in your account.After four years of saving $4 every month, your funds may reach $762.90. This includes a $500.00 initial balance and a 2.85% yearly rate of return.

Invest $500 in a 4-year certificate of deposit (CD) earning 2.85% interest compounded monthly.utilizing the compound interest formula [tex]A = P ( 1 + r / n ) ^{nt}[/tex]

The formula for calculating simple interest is S.I. = P R T, where P stands for principal, R for the annual percentage rate of interest, and T for time, which is typically expressed as the number of years. The interest rate is expressed as a percentage, or r%, and should be represented as r/100.

Many interest-bearing CDs use monthly compounding to increase returns. This model divides the annual interest rate by twelve.

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2 toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.

Let x be the number of toppings to be added to each pizza and y be the total cost of pizza.

A large pizza at Palanxio's Pizzeria cot $6. 80 plu $. 90 for each topping.

So, we get an equation,

y = 6.80 + 0.90x

The cot of a large pizza at Guido's Pizza i $7. 30 plu $. 65 for eachtopping.

So, we get an equation,

y = 7.30 + 0.65x

 We need to find the number of toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax.

Now let's equate the costs of both pizzas and solve for x.

6.80 + 0.90x = 7.30 + 0.65x

0.25x = 0.50

x = 2

Therefore, 2 toppings to be added to each pizza

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Answer:

Washer = $849

Dryer = $283

Step-by-step explanation:

Dryer = x

Washer = 3x

3x + x = 1132

Simplify:

4x = 1132

Divide both sides by 4:

x = 283

The dryer costs $283, and since the washer is three times the cost of the dryer, the washer is:

283x3 = 849

The value of x that makes the perimeters of the figures equal is; x = 3.

To find the perimeter of a figure, add all its side together. That is, the sum of all its sides will give you the perimeter.

Perimeter of the triangle = (x + 6) + 5x + (3x + 3)

Open the bracket and simplify

x + 6 + 5x + 3x + 3

Combine like terms

= 9x + 9

Perimeter of the square = 4(x + 6)

= 4(x) + 4(6)

= 4x + 24

Make both equation equal to each other and find x:

9x + 9 = 4x + 24

9x - 4x = -9 + 24

5x = 15

x = 3

The value of x is 3.

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The sum in simplest terms is 1/(p-6)

What is LCM?

Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Utilizing the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.

(16-p)/[ (p+4)(p-6) ] + 2/ (p+4)

Take LCM = (p+4)(p-6)

= [ 16-p + 2(p-6) ] / [  (p+4)(p-6)  ]

=  [ 16-p + 2p-12) ] / [  (p+4)(p-6)  ]

= ( p +4 ) / [  (p+4)(p-6)  ]

= 1/(p-6)

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The solution for the system of equations is the point (3, 5), and the difference x - y gives:

x - y = -2

Here we have the following system of equations:

5x + 3y = 30

-5x - 2y = -25

Notice that in the two equations we have the "5x", but in one case is positive and in the other negative, then we can just add them so we get:

(5x + 3y) + (-5x - 2y) = 30 - 25

(5x - 5x) + (3y - 2y) = 5

0 + y = 5

y = 5

So we found the value of y, by evaluating the second linear equation in y = 5 we will get:

-5*x - 2*5 = - 25

-5x = -25 + 2*5

-5x = -25 + 10

-5x = -15

x = -15/-5 = 3

So y = 5 and x = 3, the difference x - y gives:

3 - 5 = -2

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Answer: 70% of a discount

Step-by-step explanation:

Answer: By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.

In order to score 90 average in algebra her quiz average should be  82%.

It involves calculating the result of multiplying a number of quantities by their sum, then dividing the result by the total number of quantities.

Given,

She has a test grade of 55%, a quiz grade of 30%, and a homework grade of 15%.

If she achieved a score of 92% on the test

Make x the number of tests,

x = (90 - (0.55(92) + 0.15(100)))/0.30

x = 82

To receive a 90 in math, Olivia needs to have a quiz average of 82.

One of the oldest subfields of mathematics, algebra covers number theory, geometry, and analysis. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.

Algebra covers a wide range of topics, from the study of abstractions to the solution of simple equations.

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Answer:

The number is 15

Answer:

15

Step-by-step explanation:

The number is between 10 and 20.

10 11 12 13 14 15 16 17 18 19 20

The number is composite or have more than 2 factors.

10 12 14 15 16 18 20

The number is odd.

15

Answer:

117.94 Ropani

Step-by-step explanation:

Area Of Rhombus=½×d1×d2

=½×480×250

=60,000m²

1Ropani=508.72 {As Given}

60,000m²=(60,000÷508.72)Ropani

=117.94 Ropani

Answer:

60000 m^2

117.943 ropani

Step-by-step explanation:

the area of rhombus = 250 × 480 ÷2=60000 m^2

60000 m^2 = 117.943 ropani



The rule for the nth term of arithmetic sequence is a + (n - 1)d.

Here also,

We use the definition for the nth term of an arithmetic sequence:

an = a1 + (n - 1) d

Here first term (a1) = 51

common difference (d) = a2 - a1

                                      = 48 - 51

                                      = -3

We have to find 20th term,

a[20] = a1 + (20 - 1) d

         = 51 + 19 x -3

         = 51 - 57

         = - 6

Therefore 20th term of the sequence 51,48,45,42,... is -6.

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