For each system, choose the method of solving that seems easier to use. Explain why you made each choice. Solve each system.
6x - 3y = 3 , 5x - 5y = 10

Answer:

b=100 c=80

Step-by-step explanation:

Software to rotate △ABC 75°, I can see that this image coincides with △A″B″C″.

What is a math conjecture?

A rotation of 75° (because 30 + 45 = 75) should map  △ABC to △A″B″C″. By using the

software to rotate △ABC 75°, I can see that this image coincides with △A″B″C″.

Learn more about conjecture

brainly.com/question/24881803

#SPJ4

Answer:

-3x+y=14

Step-by-step explanation:

add the x and -4x which gives you -3x

add the -y and 2y which is y

then -14 and 28 add up to 14

The table derive from the area formula of a triangle is summarized below:

     h (cm)                        A (cm²)

        6                                 24

        7                                 28

        8                                 32

        9                                 36

The area formula of a triangle (A), in square centimeters, is equal to the half of a product of the base (b), in centimeters, and the height (h), in centimeters. In this question we have the following triangle formula:

A = (1 / 2) · (8) · h

A = 4 · h

Where h is the height of the triangle.

Now we proceed to make a table with the given heights:

     h (cm)                        A (cm²)

        6                                 24

        7                                 28

        8                                 32

        9                                 36

To learn more on area formulas: https://brainly.com/question/3134284

#SPJ1    

Step-by-step explanation:

A) x(2x-4)

=2x^2-4x

B) 2y^2(3x+4y)

=6xy^2+8y^3

C) (x-3)(x+8)

=x^2+8x-24

Answer:

c. y = -1/2x - 4

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c (m is the slope and c the y- intercept )

y = 2x + 8 ← is in slope- intercept form

with slope m = 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (8, - 8 ) into the partial equation

- 8 = - 4 + c ⇒ c = - 8 + 4 = - 4

y = - [tex]\frac{1}{2}[/tex] x - 4 ← equation of perpendicular line

The range of the function is represented by y ∈ [- 0.5, 3].

Functions are relations between an input set named domain and an output set named range such that each element of the domain is related only to one element of the range. Graphically speaking, the range of the function is represented by the vertical axis of the Cartesian plane.

The picture shows that the range of the function is between - 0.5 and 3. Then, the range of the function is represented by y ∈ [- 0.5, 3].

To learn more on functions: https://brainly.com/question/12431044

#SPJ1

The 10th term of an arithmetic sequence is found to be a₁₀ = 115.

In Arithmetic Progression, the difference between two mathematical orders is a constant quantity (AP). Arithmetic Sequence is another name for it.

We'd come across a few specific terms in AP that had been labeled as:

As shown below, the AP can also be viewed in analysed in terms of common differences.

Now, as per the given question;

Let the 9th term be 'a₉' = 132.

The 11th term be 'a₁₁' = 98.

The 10th term be 'a₁₀'.

The AP must have contain equal common difference. So,

d = a₁₀ - a₉

d = a₁₀ - 132

And, also

d = a₁₁ - a₁₀

d = 98 - a₁₀

Since, a₁₀ - a₉ = a₁₁ - a₁₀ for forming an AP.

Equate the common difference.

a₁₀ - 132 = 98 - a₁₀

Bring the variable part on single side.

2a₁₀ = 98 + 132

2a₁₀ = 230

a₁₀ = 115.

Therefore, the value of the 10 th term is estimated as a₁₀ = 115.

To know more about the arithmetic progression, here

brainly.com/question/16954227

#SPJ4

The solution of the given system of equations is (4,0)

We can use 3 methods to solve a system of equations:

- graphical method

- elimination method

- substitution method.

The given system of equation is:

-2x + 8y = -8  ....... (1)

5x - 8y = 20  ........(2)

Notice that in the both equations the coefficients of y are -8 and 8, hence if we add those coefficients, they will be cancelled out.

Therefore, we will choose elimination method.

Add equation (1) and equation (2)

-2x + 8y = -8

5x - 8y = 20   +

3x        = 12

 x        = 12/3 = 4

Substitute x = 4 into equation (1):

-2x + 8y = -8

-2.(4) + 8y = -8

-8 + 8y = -8

Add 8 to both sides:

-8 + 8y +8 = -8 + 8

8y = 0

y = 0

Thus, the solution is (4,0)

Learn more on how to solve system of equations here:

https://brainly.com/question/25976025

#SPJ4

The expression that is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b − 6.9

The expression is given as:

3(−4.5b − 2.1) − (6b + 0.6)

Open the brackets

3(−4.5b − 2.1) − (6b + 0.6) = -13.5b − 6.3 − 6b - 0.6

Collect the like terms

3(−4.5b − 2.1) − (6b + 0.6) = -13.5b  − 6b − 6.3 - 0.6

Evaluate the like terms

3(−4.5b − 2.1) − (6b + 0.6) = -19.5b − 6.9

Hence, the expression that is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b − 6.9

Read more about equivalent expression at

https://brainly.com/question/2972832

#SPJ1

Answer:

C: -19.5b-6.9

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

9 seeds in 3 packets is a 3:1 ratio which means that there are 3 seeds per packet. With 5 packets you simply multiply 5 by 3

Answer: b = 11/3 (or) 3.67

Step-by-step explanation:

Five less than the product of 3 and a number 6 equals .

five less = - 5

product of 3 and a number =  (multiply) 3 x b

equals 6 = = 6

3b - 5 = 6

3b = 6 + 5

3b = 11

b = 11/3

b = 3.67 ( rounded )

Answer:

Step-by-step explanation:

I think you meant

-0.4 - x = -6(x - 3.1) + 6x

-0.4 - x = -6x + 6x + 18.6

-0.4 - x = 18.6

       -x = 18.6 + 0.4

       -x/-1 = 19/-1

           x = -19

check

-0.4 - (-19) = -6(-19 - 3.1) + 6(-19)

           18.6 = -6(-22.1) + (-114)

           18.6 = 132.6 - 114

           18.6 = 18.6

Answer:

18

Step-by-step explanation:

Answer:

Terms: 17xy, 4, 3x

Coefficients: 17, 3

Variables: x, y

Constants 4, 3

Answer:

3

Step-by-step explanation:

1.5/1*2

 The ratio of the height of the larger prism to the smaller prism is a/b = 5.

 To solve this problem we must know what a scale factor is.

  The scale factor is a dimensionless number that allows us to relate dimensions in figures, it is also known as numerical ratio or proportion.

  If we have as reference the volumes of two hexagonal prisms, with the values of:

  If the reason or scale for the volume is given by

 Let's go for the reason of the length, for this we apply the cubic root.

a³/b³ ⇒ ∛(a³/b³)

∛250/2

a/b = 5

Learn more about scale factor in:

https://brainly.com/question/28562468

#SPJ4

Using function concepts, it is found that:

3. Two ordered pairs are: (0, 0) and (130,260). The slope is of 2.

4. The equation of the line is of y = 2x.

5. The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.

6. a)

For Hill 1, we have that:

For Hill 2, we have that:

6. b) The rate of change down Hill 1 is of -5, while it is of -2 for Hill 2.

6. c) Due to the higher rate of change, Hill 1 is steeper.

7) The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.

Two ordered pairs are: (0, 0) and (130,260).

The slope is given by change in y divided by change in x, hence:

m = (260 - 0)/(130 - 0) = 2.

Considering the slope and the intercept(which is of 0, as when x = 0, y = 0), we have that:

The equation of the line is of y = 2x.

Hence:

The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.

For Hill 1, we have that:

For Hill 2, we have that:

The rates of change(change in height divided by change in length) are given as follows:

Due to the higher rate of change, Hill 1 is steeper.

A graph is a function if it has no vertically aligned points, that is, each value of the input is mapped to only one value of the output.

Hence:

The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.

More can be learned about function concepts at https://brainly.com/question/10891721

#SPJ1

2.5x4=10(Bert's walking distance)

22-10=12(Brenda's walking distance)

12/4=3

3km/h is Brenda's walking distance.

The International System of Units (SI) defines the kilometer, sometimes known as the kilometer in American English, as one thousand meters (kilo- being the SI prefix for 1000). The United States and the United Kingdom are significant outliers, where the statute mile is the unit of measurement used to express distances between geographical locations on land.

1 mile is equivalent to 1.609 kilometers. Both the mile and the kilometer are units of measurement. A mile is longer than a kilometer, nevertheless. A larger unit is a "mile."

1000 meters make up one kilometer. We use kilometers to calculate distance when traveling between two points.

To learn more about Kilometer from the given link:

brainly.com/question/13987481

#SPJ4

Here no enough information to determine if the triangles are congruent.

Option C is true.

What is Congruent triangle?

Congruent triangle have both the same shape and the same size.

Given that;

Two sides of triangles are 6 and 13.

Now,

Since, Congruent triangles are triangles that have equal corresponding angles and sides.

From the images of the triangles (see attachment),

We can see that the two triangles have 6cm and 13cm as the lengths of their sides.

However, The side lengths of both triangles are not corresponding, and the angle measures are not given.

Hence, There is no enough information to determine if the triangles are congruent.

Option C is true.

Learn more about congruent triangles visit:

https://brainly.com/question/28397291

#SPJ1

The elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet.

Here, we are given two elevation levels from the surface of the ocean.

One elevation is of -10 feet and another one is of -8 feet.

An elevation of -10 feet implies that the distance from the surface level is 10 feet.

On the other hand an elevation of of -8 feet implies that the distance from surface level is 8 feet.

Thus, by comparing the distances, we can see that elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet. To be more precise, it is 2(10-2) feet farther than an elevation of -8 feet.

Learn more about surface level elevation here-https://brainly.com/question/27894219

#SPJ9

Common difference = 3 , 32nd term = 100

The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms.

The given series is

7, 10, 13, 16....

common difference = 10-7 = 13- 10= 16-13 = 3

Therefore there is a common difference between the two consecutive number.

In this series the common difference is 3.

Hence we get to know that the given series is an arithmetic series.

To identify the 32nd term we have a formula:

[tex]t_{n}[/tex] = a +(n-1)d

Here a = first number of the series

        n = number of series

        d = common difference

[tex]t_{32}[/tex] = 7 + (32-1)3

    = 7 + 31×3

    = 7 + 93

    = 100

Hence the 32nd term is 100.

To know more about the arithmetic series refer to the link given below:

https://brainly.com/question/22972770

#SPJ4

The soluton of the given linear equation in one variable 4 + x = -52  is x = -56.

According to the given question.

We have a linear equation in one variable 4 + x = -52.

Since, we have to solve the above equation for x.

As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofore, the solution of the above equation 4 + x = -52 is given by

4 + x = -52

⇒ x = -52 - 4    ( subtract 4 both the sides)

⇒ x = -56

Hence, the soluton of the given linear equation in one variable 4 + x = -52  is x = -56.

Find out more information about equation here:

https://brainly.com/question/15265517

#SPJ4

The Measurement of  ∠6 i.e. m∠6 is 120°

The measurement of angle if the degree of that angle or we can also say that the angles are always measured in degrees. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.

As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360.  

In the question

as  ∠7 is an alternate angle to 60 degree,

thus ∠7 = 60°

According to sum of angle property :

∠7 +  ∠6 = 180

60 +  ∠6 = 180

∠6 = 180-60 = 120

Thus  m∠6 = 120°

To know more about measurement of angle, visit :

https://brainly.com/question/27243531

#SPJ4

The complete question is :

Find measure m∠6

Answer:

yes, it’s proportional

Step-by-step explanation:

The given series is an arithmetic series. The sum of its first 8 terms is 156.

To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic series, then:

    a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric series, then:

    a(n) = a(n-1) . r

where d is the common ratio.

The given series is:

       2+7+12+ . . . .

and the number of terms is 8.

In the given series:

a(1) = 2

a(2) = 7

a(3) = 12

Notice that the difference is constant,

 d = a(3) - a(2) = a(2) - a(1)

    = 7 - 2 = 5

Sum formula for the first n term of an arithmetic series is:

S(n) = n/2 . [2a(1) + (n - 1) . d]

Substitute n = 8, a(1) = 2, and d = 5

S(8) = 8/2 ( 2.(2) + (8 -1) .5)

S(8) = 4. 39 = 156

Learn more about series here:

https://brainly.com/question/8919590

#SPJ4