What can you conclude about the triangles? *Hint: What is congruent and how can you prove it?

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.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ12

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.

To learn more about arithmetic sequence refer to :

https://brainly.com/question/6561461

#SPJ1

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 equation that the speed of an object is speed = distance/time

From the question, we have the following parameters that can be used in our computation:

Parameter = Object

Argument = Speed

By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object

Mathematically, this can be represented as

Speed = Distance : Time

Express as fraction

Speed = Distance/Time

Hence, the equation is Speed = Distance/Time

Read more about speed at

https://brainly.com/question/14335655

#SPJ1

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:

three solutions of the equation:

y = -2x - 1

=>

1) (0, -1)

2) (1, -3)

3) ( -1, 1)

Step-by-step explanation:

Answer:

1/2 - 1/7 = 5/14

3/5 - 1/2 = 1/10

Step-by-step explanation:

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

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

Learn more about an equation here:

#SPJ4

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: 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

On solving the provided linear equation question - Jolly = $17.4, Jimmy =2x-30  =4.8 and Johnny = 2x=34.8

A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".

Take Jolly's expenditure as x.

Jimmy would have spent twice as much as Jolly.

Johnny Equals 2x-30 if Johnny spent $30 less than Johnny.

Total amount spent: $57

Therefore,

[tex]x+ (2x-30) + 2x = 57\\ x+ 2x -30 +2x =57.\\ 5x = 57+ 30\\[/tex]

x = 87/5

x= 17.4

Now take is that - X= 17.4.

Jolly is that -  x= $17.4

Jimmy is that - =4.8

Johnny is that = =34.8

To know more about linear equation visit:
https://brainly.com/question/11897796

#SPJ1

Answer:

A

Step-by-step explanation:

because to solve this question the division would change into multiplication and the second fraction would be converted upside down

Check the picture below.

Answer: True

Step-by-step explanation:

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

Answer: Theresa did 18 fewer chin-ups.

Step-by-step explanation:

Melanie 8,16,24,32,40,48

Theresa 5,10,15,20,25,30

48-30=18

Answer: 70% of a discount

Step-by-step explanation:

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.

To learn more about fractions, visit:

https://brainly.com/question/10354322

#SPJ4

The interval where the cosine function is increasing is (π, 2π).

The cosine function for the interval (0, π/2) gives

cos(x) = cos(0) = 1

cos(x) = cos(π/2) = 0

So, the value of the function is decreasing in this interval.

Then, for the interval (0, π), it gives

cos(0) = 1; cos(π) = -1

So, the value of the cosine function is decreasing in this interval.

Then, for the interval (π/2, 3π/2), it gives

cos(π/2) = 0

cos(π) = -1

cos(3π/2) = 0

So, the value of the function decreases up to x = π and then increases up to the same value as before i.e., cos(π/2) = cos(3π/2).

Then, for the interval (π, 2π), the cosine function gives

cos(π) = -1

cos(2π) = 1

Thus, the cosine function in this interval increase from -1 to 1.

Therefore, in the interval (π, 2π), the cosine function is increasing.

This is explained by using a unit circle below:

Learn more about cosine function here:

https://brainly.com/question/17075439

#SPJ4

Answer:

D

Step-by-step explanation:

got it right

Answer:

Step-by-step explanation:

180 because if you add 180 + 180 = 360

Simplifying

2x + 5y = 2

Solving

2x + 5y = 2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5y' to each side of the equation.

2x + 5y + -5y = 2 + -5y

Combine like terms: 5y + -5y = 0

2x + 0 = 2 + -5y

2x = 2 + -5y

Divide each side by '2'.

x = 1 + -2.5y

Simplifying

x = 1 + -2.5y

Simplifying

5X + 10y = 17

Solving

5X + 10y = 17

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-10y' to each side of the equation.

5X + 10y + -10y = 17 + -10y

Combine like terms: 10y + -10y = 0

5X + 0 = 17 + -10y

5X = 17 + -10y

Divide each side by '5'.

X = 3.4 + -2y

Simplifying

X = 3.4 + -2y

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]

To learn more about parabola visit

brainly.com/question/4074088

#SPJ1

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

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

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 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.

To know more about linear equation, visit:

https://brainly.com/question/21835898

#SPJ1

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:

40 people

Step-by-step explanation:

25% = 10

50% = 20

100% = 40

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.

Learn more about the triangles;

https://brainly.com/question/2773823

#SPJ1

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.

To learn more about  algebra

brainly.com/question/850007

#SPJ4