Find the midpoint of the line segment joining points A and B.
A(6-7); B(4,3)

Cheese proof:

We can just prove that it is divisible by 3, which means that it is composite. We can use modular exponentiation, where if [tex]a \equiv b \pmod{n}[/tex] then [tex]a^x \equiv b^x \pmod{n}[/tex]. In this case, [tex]{-1}^{8^{2014}} \equiv 20^{8^{2014}} \pmod{3}[/tex]. This is much easier to calculate! Since [tex]8^{2014}[/tex] is even, [tex]-1^{8^{2014}}=1[/tex], meaning that now we only need to prove that [tex]0\equiv(1+113) \pmod{3}[/tex], which is obviously true.

Answer:

length = 14 cm; width = 6.4 cm

Step-by-step explanation:

We can use proportions to find the length and width.

Thus, for length, l, we have:

[tex]\frac{1}{25}=\frac{l}{350} \\25l=350\\l=14[/tex]

For width, w, we have:

[tex]\frac{1}{25}=\frac{w}{160}\\ 25w=160\\ w=6.4[/tex]

Answer:

70/29 or 2 12/29

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

We can multiply both the whole equation by [tex]c^2-7c-18[/tex]. This is the LCM of all of the denominators. Notice that when [tex]c^2-7c-18[/tex] is factored, we obtain [tex](c - 9)(c+2)[/tex].

[tex]\frac{5}{c-9}\times(c^2-7c-18)=\frac{5}{c-9}\times(c-9)(c+2)=5(c+2)=5(c)+5(2)=5c+10[/tex]

An easier approach is to multiply each individual fraction like so:

[tex]\frac{5c-2}{c^2-7c-18}\times(c^2-7c-18)=5c-2[/tex]

[tex]\frac{3}{c+2}\times(c^2-7c-18)=\frac{3}{c+2}\times(c-9)(c+2)=3(c-9)=3c-27[/tex]

Then, we add them:

[tex]5c-2+(3c-27)=5c-2+3c-27=8c-29[/tex]

Therefore the whole equation is now:

[tex]5c+10=8c-29[/tex]

Subtract 5c from both sides:

[tex]10=3c-29[/tex]

Add 29 to both sides:

[tex]39=3c[/tex]

Divide both sides by 3

[tex]c=13[/tex]

[tex]\frac{5}{13-9}=\frac{5(13)-2}{169-91-14}+\frac{3}{13+2}\\\\\frac{5}{4}=\frac{63}{60}+\frac{3}{15}\\\\\frac{5}{4}=\frac{21}{20}+\frac{1}{5}\\\\\frac{5}{4}=\frac{21}{20}+\frac{1}{5}\\\\\frac{5}{4}=\frac{21}{20}+\frac{4}{20}\\\\\frac{5}{4}=\frac{25}{20}\\\\\frac{5}{4}=\frac{5}{4}\Rightarrow Correct![/tex]

Therefore,

c = 13

Answer:

20 cm

Step-by-step explanation:

When two triangles are similar, they're just dilated by a certain scale factor. In other words, each side is multiplied by the same value to create the similar triangle.

So to find this scale factor, we can use the two sides: 6 and 12, since we're going from the triangle with a 6 cm side to a 12 cm side, we divide 12 cm, by 6 cm to get a scale factor of 2

This means that the bottom side in the top triangle, which is 10 cm, is multiplied by a scale factor of 2, to get the new bottom side of x. So to find x, we simply multiply 10 cm by 2 to get 20 cm

Answer:

parallel

Step-by-step explanation:

//

Answer: these lines are parallel.

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{6x-2y=-2} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x-2y+2=0} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x+2=2y\ |:2} \atop {x=2}} \right. \\\\\left \{ {{3x+1=y} \atop {y=3x+12}} \right.\\ \\\left \{ {{y=3x+1} \atop {y=3x+12}} \right. \\So,\ these\ lines\ are\ parallel.[/tex]

Answer:

Step-by-step explanation:

Answer:

  62.5 feet

Step-by-step explanation:

The markings on the angles in the figure tell you the triangles are similar. Similar triangles have proportional corresponding sides. This is used to write and solve an equation for x.

The angles in each triangle are marked with the following symbols:

The purpose of the marks is to signify that angles with the same mark are congruent. When the angles of one triangle are congruent to the angles of another triangle, the two triangles are similar.

Similar triangles have another feature: corresponding sides are proportional. That is, their ratios are identical.

This can be taken a couple of different ways:

In the given triangles, we can identify the corresponding sides as ...

  smaller triangle : larger triangle

  between right angle and double arc angle — 36 ft : 50 ft

  hypotenuse — 45 ft : x ft

Our description of similarity tells us we can write the statements of proportionality as either of ...

For proportions written in this way, the "outer" and "inner" products are the same. This is sometimes expressed by saying "the product of the means is equal to the product of the extremes."

  a : b = c : d   ⇒   ad = bc

When the ratios are written as fractions, this result is what you get from "cross multiplication":

  a/b = c/d   ⇒   ad = bc . . . . . the result of multiplying both sides by bd

Once the proportion is written in this product form, the value of any of the variables can be found by dividing both sides of the equation by the coefficient of that variable.

Using either of the proportions we wrote above, the product form is ...

  36x = 45·50

  x = (45·50)/36 . . . . . . divide by the coefficient of x

  x ≈ 62.5 . . . . feet

The distance from the playground to the swimming pool is 62.5 feet.

Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

The definition of the piecewise function is given by:

Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.

The lateral limits are:

The numeric value is:

f(2) = 1.5 x 2 = 3.

Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

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Answer:

6x^4-5x^3-8x^2+3x

Step-by-step explanation:

-factor it using FOIL (first outside inside last)

Step-by-step explanation:

that is a huge gas tank. that car is practically a tank.

the volume of the gas tank is

4×3×3 = 36 m³

I assume you use liters for liquid mass.

remember

1 meter (m) = 100 centimeter (cm)

10 cm = 1/10 m = 1 decimeter (dm)

1 liter = 10×10×10 cm³ = 1000cm³ = 1 dm³

1 m³ = 10×10×10 dm³ = 1000 dm³ = 1000 liters

so, his gas tank contained 36,000 liters.

he used the 36,000 liters in 45 hours.

his corresponding rate of gas consumption was

36,000 liters / 45 hours = 800 liters / hour

Answer:

20 lorries are needed to transport.

Mark brainliest

Answer:

14day

Step-by-step explanation:

lorries trip per day. crates

3. 5 2500

? 6 10000

(6×3×10000)÷(5×2500)=14days

Answer:

D

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards.

this is angle D in the diagram

Total value of all coins together is $2.7

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

1 Nickel = $0.05 and 1 quarter = $0.25.

Let number of nickels and number of quarter be x.

According to the situation

x.(0.25) = $1.80 + x.($0.05)

x(0.25 - 0.05) = $1.80

x (0.2) = $1.80

x = $1.80/0.2

x = 9 coins

Therefore total value of the currency is 9(0.05 + $0.25) = 9 (0.3) = $2.7

Thus total value of all coins together is $2.7.

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Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:

Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

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Answer:

3,500 people

Step-by-step explanation:

10% of 35,000 is the same as .10 × 35,000, or 3,500.

Answer:

£13.75

Step-by-step explanation:

→ Call the charge x

x

→ Multiply by 16

16x

→ Equate to total

16x = 220

→ Divide both sides by 16

x = £13.75

Using a linear function, it is found that Company D would have given you the best deal for 7 hours of moving.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we consider:

Hence the costs for x hours of moving from each company are given as follows:

For 7 hours, the costs are given as follows:

Due to the lower cost, Company D would have given you the best deal for 7 hours of moving.

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The simplest form of the given expression ( x⁴ )⁸ exists x³².

Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.

The given expression will be simplified as:-

( x⁴ )⁸ = x ⁴ ⁽⁸⁾

( x⁴ )⁸ = x ³²

Therefore the simplest form of the given expression exists as x³².

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Answer:

b/a

Step-by-step explanation:

Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).

In the equation

ax + by = c,

the slope of the line is

-a/b

If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.

by = -ax +c

y = -a/b x + c/b

The slope is -a/b

So a perpendicular line would be opposite sign and flipped, b/a

Answer:

Step-by-step explanation:

1/3 + 1/3 x 1/3 / 1/3 - 1/3

= 1/3 + 1/3 x 1/1 -1/3

= 1/3 + 1/3 - 1/3

= 2/3 - 1/3

= 1/3

Answer:

5/9.

Step-by-step explanation:

1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3

= 1/3 + 1/3 * 1 - 1/3 * 1/3

= 1/3 + 1/3 - 1/3 * 1/3

= 2/3 - 1/9

= 5/9.

Answer:

15 mister of cloths are needed to make 15 m if 1 puchu is 1 miter

Answer:15 meters

step by step explanation

Answer:

A. because 5 < 6. 1-(-4)=5. and 4-(-2) =6

Answer: B

Step-by-step explanation:

We can rearrange the equation to get [tex]x^2=-\frac{2}{3}[/tex], which clearly has complex roots.

The domain of f(x) is all set of real values while, the domain of g(x) is x ≤ -1 or x ≥ 2 and both functions have the same range

The functions are given as:

f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4

g(x) = √(x^2 - x - 2)

Domain

The polynomial function f(x) has no restriction on its input.

So, the domain of f(x) is all set of real values

Set the radical of g(x) = √(x^2 - x - 2) greater than 0

x^2 - x - 2 ≥ 0

Factorize

(x + 1)(x - 2) ≥ 0

Solve for x

x ≥ -1 and x ≥ 2

Combine both inequalities

x ≤ -1 and x ≥ 2

So, the domain of g(x) is x ≤ -1 or x ≥ 2

Range

Using a graphical calculator, we have:

Hence, both functions have the same range

We have:

h(x) = (-x^2 + x)/(x^2 - x - 2)

Set the denominator to 0

x^2 - x - 2 = 0

The above represents the radical of the function f(x)

This means that the breaks in the domain of h(x) and the zeros of f(x) are the same

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Complete question

Let f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4, g(x) = √(x^2 - x - 2) and h(x) = (-x^2 + x)/(x^2 - x - 2)

Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points)

Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)

Using the arrangements formula, the number of orders is given as follows:

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are no restrictions, the number of ways is:

[tex]A_{11} = 11! = 39,916,800[/tex]

When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:

[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]

When the first and last are cats, we have that:

Hence:

20 x 9! = 7,257,600.

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Así, concluimos que la liebre da un total de 38 saltos.

Notar que solo se nos pregunta cuantos saltos da la Liebre, no importa en que dirección son dichos saltos.

Entonces solo debemos sumar todos los números de saltos que se nos dan, esto es:

18 saltos + 5 saltos + 9 saltos + 6 saltos = 38 saltos.

Así, concluimos que la liebre da un total de 38 saltos.

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Answer:

40 + 5r

usually you put the one with the variable infront

so 5r+40

Step-by-step explanation:

5(8+r)

5*8 + 5*r

40 + 5r

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:(b - 2) \sdot(b - 7)[/tex]

[tex] \qquad❖ \: \sf \:(b \sdot b) + (b \sdot - 7) - (2 \sdot b) - (2 \sdot - 7)[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 7b - 2b + 14[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \sf \:(b - 2) \sdot(b - 7) = {b}^{2} - 9b + 14[/tex]

Answer:

b² - 9b + 14

Step-by-step explanation:

(b - 2) × (b - 7)

= b×b - 7b - 2b + 2×7  (Expand)

= b² - (7b + 2b) + 14  (gather like terms)

= b² - 9b + 14

Answer:

associative

combining

commutative

Step-by-step explanation:

1. associative property of addition since the grouping is changed

2. combining like terms since it's the addition of 4 and 6

3. commutative property of addition since it's a change of order