Write and solve a system of equations for each situation. Check your answers.A shop has one-pound bags of peanuts for 2 and three-pound bags of peanuts for 5.50 . If you buy 5 bags and spend 17 , how many of each size bag did you buy?

Answer:

-7

Assuming that "It can be any"

The distance between pair of parallel lines with the given equations

x=-2 x=5 is 7 units

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The distance between parallel lines on a graph can be given as x1 - x2 as both are equidistance from y for which y has been cancelled.

here x1 =5 and x2 = -2

So, x1 - x2 = 5 -(-2)

                 = 5 + 2

                 = 7

Learn more about Parallel lines

https://brainly.com/question/4954460

#SPJ4

The common difference d is 6 and the first term a1 is 20.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the two terms of arithmetic sequence,

a3 = 32 and a7 = -8.

now, find the common difference d.

a(n) = a1 + (n - 1)d

Let take a(n) = a7 and a1 = a3.

a7 = a3 + (7 - 3)d

a7 = a3 + 4d

now substitute the values of a6 and a4

-8 = 32 + 4d

-8 + 32 = 4d

d = 24/4

d = 6

so, the common difference d is 6.

then, find the term a1.

take the formula

a(n) = a1 + (n - 1)d

now, substitute a(n) = a3 and d = 6.

32 = a1 + (3-1)d

32 = a1 + 2d

32 = a1 + 2(6)

32 = a1 + 12

a1 = -12+32

a1 = 20.

so, the first term a1 is 20.

Hence, the common difference d is 6 and the first term a1 is 20.

Learn more about Arithmetic progression from here:

https://brainly.com/question/6561461

#SPJ4

Answer:

875

Step-by-step explanation:

215+200+185+170+155+140+125+110+95+80+65+50+35+20+5+(-10)+(-25)+(-40)+(-55)+(-70)+(-85)+(-100)+(-115)+(-130)+(-145) =875

I'm sure there's an easier way to do this, but if you want a correct answer, here you go. Have a good day!

Answer:

875

Step-by-step explanation:

I think hope it right

The  Δ FGH with base FG that is 2a unit long has been drawn below.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Δ FGH is a isosceles triangle.

Now isosceles triangle is a triangle whose two sides are equal.

In the ΔFGH, HF = HG

Hence "The  Δ FGH with base FG that is 2a unit long has been drawn below".

For more about triangles,

https://brainly.com/question/2773823

#SPJ4

Answer:

Step-by-step explanation:

triangles are similar so:

[tex]\frac{10}{10+14} = \frac{x}{36}[/tex]

24x=360

x=15

Answer:

3;m=-6

Step-by-step explanation:

3;m=-6

Answer: c=-0.01

Step-by-step explanation:

The best friend is the faster runner as his speed is 51.28 m/s while my speed is 48.78 m/s.

Speed is defined as the distance travelled by someone or something in unit time. The SI unit of speed is meters per second. The speed is calculated by dividing the distance travelled by the total time taken to travel said distance.  

Given the distance travelled by both of the friends is 400 meters.

Now The first friend travels this distance in 8.2 seconds:

Therefore speed is calculated by distance ÷ time

or, speed = 400 ÷ 8.2

or , speed = 48.7804... m/s

or, speed ≈ 48.78 meters per second

And the best friend travels this distance in 7.8 seconds:

Therefore speed is calculated by distance ÷ time

or, speed = 400 ÷ 7.8

or , speed =51.2820... m/s

or, speed ≈ 51.28 meters per second

Therefore by comparing both the speeds we can conclude that the best friend is the faster runner.

To learn more about speed visit:

https://brainly.com/question/9834403

#SPJ1

Answer:

the answer is great Britain because

Step-by-step explanation:

it is very good for this subject

The magnitude of vector →RS is 3√2

And the direction of vector →RS is given by an angle 315°

Let R(1,0) = (x1, y1) and

S(-2,3) = (x2, y2)

By distance formula, the magnitude of vector is

[tex]|\vec {RS}| = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec {RS}| =\sqrt{(-2-1)^2+(3-0)^2} \\\\|\vec {RS}| =\sqrt{(-3)^2+3^2} \\\\|\vec {RS}| =\sqrt{9+9}\\\\ |\vec {RS}| =3\sqrt{2}[/tex]

To find the direction of the vector RS :

[tex]tan(\theta)=\frac{y_2-y_1}{x_2-x_1} \\\\tan(\theta)=\frac{3-0}{-2-1}\\\\tan(\theta)=\frac{3}{-3}\\\\ tan(\theta)=-1\\\\ \theta=tan^{-1}(-1)\\\\\theta=45^{\circ}[/tex]

However, the angle is in the fourth quadrant, so we add  360°  to obtain a positive angle.

Thus,  −45° + 360° = 315° .

Therefore, the magnitude of vector →RS is 3√2

And the direction of vector →RS is given by an angle 315°

Learn more about the magnitude and direction of vector here:

https://brainly.com/question/10151539

#SPJ4

Answer:

1 is 6 pages, 7 minutes is 24 pages, 14 minutes is 45 pages

Step-by-step explanation:

the unite rate is 3

Using the absolute value function, linear functions and translations, we have that:

9. Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

10. The equation is f(x) = -5x + 100.

11. The correct option is: The slope of f(x) is greater than the slope of g(x).

12. h(-5) = 10.

13. The equation is f(x) = 2x + 5.

14. The graph of y = f(x) will shift right 9 units.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0, and has vertex(turning point) at (0,0). The range is from the y-coordinate of the vertex to positive infinity.

In item 9, from the table, the turning point is at (2,0), hence:

Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

A linear function is modeled by the following rule:

y = mx + b

In which:

For item 10, we have that:

Then:

The equation is f(x) = -5x + 100.

For item 11, the slope is given by change in y divided by change in x, hence:

Hence:

The correct option is: The slope of f(x) is greater than the slope of g(x).

For item 12, we have that:

h(x) = -4x - 10.

Hence, when x = -5:

h(-5) = -4(-5) - 10 = 20 - 10 = 10.

Hence:

h(-5) = 10.

For item 13, we have that when x changes by 4, y changes by 8, hence the slope is:

m = 8/4 = 2.

When x = 1, y = 7, hence, considering the slope, when x = 0, y = 5, and:

The equation is f(x) = 2x + 5.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

For this problem, the rule is given by:

y = f(x - 9).

The translation is x -> x - 9, hence:

The graph of y = f(x) will shift right 9 units.

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

(For number 9) Range {y/0<y<infinity} Vertex (2,0)

Step-by-step explanation:

I took test

I hope I helped for that part of it.

The correct option is F. 25.

The total number of gallons of gas Amanda will use to travel all the distances is 25.

The amount of between two things, or the state of being far apart, is defined as distance. A five-foot distance between two tables is an example of distance. The difference of the two sides of an issue is an example of distance.

Now, as per the given question;

Amanda plans to drive 160 miles, 235 miles, 185 miles, and 220 miles.

Thus, the total distance ravelled by Amanada is;

= 160 miles + 235 miles + 185 miles + 220 miles

= 800 miles

Amanada's car has the average of 32 miles per gallon of gas.

Thus, the car will cover a total of 32 miles for each gallon of gas.

Thus,

The number of gallon of gas requires = Total distance/(distance travelled for one gallon of gas)

The number of gallon of gas requires = 800/32

The number of gallon of gas requires = 25

Therefore, the gas required to travel a total distance of 800 miles is 25 gallons.

To know more about the distance, here

https://brainly.com/question/26046491

#SPJ4

The cost of the meal is 53.

The tip percentage is x.

Percentage is a measure of frequency that is used to describe a number as a fraction out of 100. The sign that is used to represent percentages is %.

The total cost of the meal is the sum of the amount paid for the meal and the amount paid for the tip. The amount that is paid for the tip is a function of the total amount of the meal.

Total cost = cost of the meal + tip paid

Total cost = cost of the meal x (1 + tip)

53( 1 + x)

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

Answer: x<1

Step-by-step explanation:

add 12 to both sides, divide by 2 on both sides.

The range of each amazon box is 1.6035m

According to the question we have been given that

        height of the conveyer belt = 1.4m

        Speed of the belt = 3m/s

We need to find the range of the amazon box, that is we have to find the distance.

Formula for distance is ,  d = speed * time

We have been given the value of speed we need to find the value of time. For that we will use the formula,

                                     h = [tex]\frac{1}{2} g t^{2}[/tex]

where,         h = height

                   g = acceleration due to gravity = 9.8m/s²

                    t = time

Putting the required value for t we get,

        t = [tex]\sqrt{\frac{2h}{g} } \\[/tex]

          = [tex]\sqrt{\frac{2(1.4)}{9.8} } \\[/tex]

          = √0.286

          = 0.5435 s

Putting the value of time in distance formula we get,

                d = 3 * 0.5435 m

                   = 1.6035 m

Hence the range of each amazon box is 1.6035m

Learn more about distance here : https://brainly.com/question/17146782

#SPJ9

The base and height of triangle are 25 and 22 feet.

We are given the relation between base and height of triangle. Let us represent height with h and base with b. The equation relating the two quantities is as follows -

h = b - 3

Now, the area of triangle is given  by the formula -

Area = 1/2 × base × height

Keep the values in formula to find the base of triangle

275 = 1/2 × b × (b-3)

550 = b × (b-3)

b² - 3b - 550 = 0

b² + 22b - 25b - 550 = 0

b (b + 22) -25 (b + 22) = 0

(b + 22) (b - 25) = 0

b = -22 and 25

As the value of base can not be negative, so, the base of triangle is 25 feet.

Calculating height of triangle-

Height = Base - 3

Height = 25 - 3

Height = 22 feet

Hence, the base and height of triangle are 25 and 22 feet.

Learn more about calculations of triangle -brainly.com/question/17335144

#SPJ4

Step-by-step explanation:

Lets understand the situation,

This means Each team can have 3, 4 or 5 people.And 21 people take part.

we have to find How many different possible arrangements of teams are there.

Situation 1.

situation 2.

Situation 3.

situation 4.

The following set of numbers, 8, 15, and 17, can be the measures of the sides of a triangle, specifically a right triangle.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 8, b = 15, and c = 17

a + b > c     8 + 15 > 17     23 > 17     True

a + c > b     8 + 17 > 15      25 > 15     True

b + c > a     15 + 17 > 8     32 > 8     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

8^2 + 15^2 = 289

2. Compare it to the square of the largest side.

17^2 = 289

289 = 289

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 8, 15, and 17 can be the measure of the sides of a right triangle.

To learn more about types of triangle based on side lengths: brainly.com/question/13619935

#SPJ4

Answer:

7 and 27

Step-by-step explanation:

We can make an equation for this, it looks like this:

6+3x+x=34

Simple algebra can be used to solve this (x is the smaller number)

1. 6+3x+x=34

2. 6+4x=34 Combine like terms

3. 4x=28 Simplify

4. x=7 simplify

Now that we have the smaller number we can use a portion of the original equation to solve with x=7.

1. 6+3x

2. 6+3(7)

3. 6+21

4. 27

So the smaller number is 7, and the larger number is 27.

==================================================

Work Shown:

C(x+2) - (x+2)(x-2) = 0

(x+2)(C-(x-2)) = 0

(x+2)(C-x+2) = 0

x+2 = 0 or C-x+2 = 0

x = -2 or x = C+2

If we want one solution only, then we must make C+2 = -2 which solves to C = -4

If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)

According to the given data the m ∠1+m ∠2=m∠6+m∠ 7 proofed by symmetric property:

The symmetric property of equality is significant in mathematics because that tells us that both sides of either an equal sign are equal regardless of which side of the section they are on.

But it wasn't until the nineteenth century that mathematicians like Evariste Galois, an unhappy French genius, uncovered symmetries hidden in mathematical equation solutions.

Given: ∠3 ≅ ∠5

Prove: m ∠1+m ∠2=m∠6+m∠ 7

Now ,

m ∠1+m ∠2=m∠6+m∠ 7..........(1)

m∠6+m∠ 7 = ∠3 + m∠4..............(2)

m ∠1+m ∠2 = ∠3 + m∠4

(subtracting)

m∠4 +m∠3  = m ∠3 + m∠4

symmetric property:

m ∠1+m ∠2=m∠6+m∠ 7

According to the given data the m ∠1+m ∠2=m∠6+m∠ 7 proofed by symmetric property:

To know more about symmetric property visit:

https://brainly.com/question/1527538

#SPJ4

Answer:

3[tex]x^{2}[/tex] + 4x + xy

Step-by-step explanation:

Basically just combining like terms

[tex] \large \bf \implies{ {3x}^{2} + xy + 4x} \\ [/tex]

Step 1) Combine the like terms

Step 2) Add/Subtract the terms

Step 3) We have got the answer

The solutions of the given polynomial equation p⁴+32=12 p² is p = {-2√2, 2√2, -2, 2}.

The given polynomial equation is:

p⁴+32=12 p²

Subtract both sides by 12 p²

p⁴ + 32 -12 p² = 12 p² 12 p²

p⁴ -12 p² + 32 = 0     ...... (1)

Let x = p², then equation (1) becomes

x² -12x + 32 = 0  

This is a quadratic equation.

Factorize:

   x² -12x + 32 = 0  

⇔ (x - 8 ) (x - 4) = 0

Take:

x - 8 = 0

x = 8

p² = 8

p = ±√8 = ±2√2

Take:

x - 4 = 0

x = 4

p² = 4

p = ±√4 = ±2

Hence the solution is p = {-2√2, 2√2, -2, 2}

Learn more about quadratic equation here:

https://brainly.com/question/28038123

#SPJ4

The simplified form of the expression is -29y - 8

Linear equations are equations that has a linear degree of 1. For instance the expression y =mx + b has a linear degree of 1.

Given the linear equation below:
-7 (3y)+2(-4y+-4)

When solving linear equation, first we will need to expand the expression first.

-7 (3y)+2(-4y+-4)

-21y + 2(-4y) + 2(-4)

Simplify the resulting expression

-21y -8y. - 8

-29y - 8

Hence the simplified form of the expression is -29y - 8

Learn more on linear function here: https://brainly.com/question/15602982

#SPJ1

Answer:

?

Step-by-step explanation:

The arithmetic series 1+5+9+. . . . . +41+45 can be expressed in summation notation as [tex]\sum\limits^{12}_{n=1} {(4n-3)}[/tex]

The given arithmetic series:

    1+5+9+. . . . . +41+45

To write the series in summation notation:

Find the common difference (d) of the series.

d = 5 - 1 = 4

Recall the formula for the nth term in an arithmetic sequence:

a(n) = a(1) + (n-1) . d

Substitute a(1) = 1 and d = 4:

a(n) = 1 + (n-1) . 4

a(n) = 4n - 3

Find n that leads to a(n) = 45

a(n) = 4n - 3

45 = 4n - 3

4n = 48

n = 12

Thus, the lower limit of the summation is n =1, and the upper limit is n = 12

Now write in summation notation as:

[tex]\sum\limits^{12}_{n=1} {a(n)}= \sum\limits^{12}_{n=1} {(4n-3)}[/tex]

This summation notation can be further simplified using the properties of summation operator:

[tex]\sum\limits^{12}_{n=1} {(4n-3)}=\sum\limits^{12}_{n=1} {4n}-\sum\limits^{12}_{n=1} {3}[/tex]

[tex]=\sum\limits^{12}_{n=1} {4n}-12\times3[/tex]

[tex]=\sum\limits^{12}_{n=1} {4n}-36[/tex]

Learn more about summation notation here:

https://brainly.com/question/542712

#SPJ4