Which of the following is equivalent to the quotient below?
√135/√3
A. 5√3
B. √45/3
C. 3√5
D. 3√15

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.

Learn more about Linear equations here :

https://brainly.com/question/11897796

#SPJ1

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

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.

More can be learned about the arrangements formula at https://brainly.com/question/24648661

#SPJ1

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.

Answer:

look at attached image for the step-by-step proof. thanks for reposting this lol

The equation of parabola is given by  

                                         (X-h)^2 = 4p(Y-k)^2

2p = 30 - 0

p = 15

4p = 4 × 15

    = 60

In this case h = 0

So, we have (h,p) = (0,15)

So we get  

We have equation: x^2 = 60(y-15)

y = x^2 / 60 + 15

To learn more about parabola from the given link

https://brainly.com/question/4061870

#SPJ4

Answer:

120

Step-by-step explanation:

Lets find the numbers multiples of 6 that are in the range from 104-140:

108, 114, 120, 126, 132, 138

Now out of these lets find which is divisible by 15

[tex]\frac{108}{15}=7.2\\\\\frac{114}{15}=7.6\\\\\frac{120}{15}=8\\\\\frac{126}{15}=8.4\\\\\frac{132}{15}=8.8\\\\\frac{138}{15}=9.2[/tex]

120 Is the only solution in this set which is also equally divisible by 15, making it the answer.

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.

To learn more about expression refer to:

brainly.com/question/723406

#SPJ4

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:

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

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.

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

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]

The altitude of the trapezoid, based on the given parameters is 5 units

From the question, we have the following parameters about the trapezoid

Base length 1 of the trapezoid = 6

Base length 2 of the trapezoid = 10

Area of the trapezoid = 40

Altitude of the trapezoid = h

The area of the trapezoid is calculated using

Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid

Substitute the given parameters in the above formula

40 = 0.5 * (6 + 10) * h

Evaluate the sum of 6 ad 10 (do not approximate)

40 = 0.5 * (16) * h

Evaluate the product of 0.5 and 16 (do not approximate)

40 = 8 * h

Divide both sides by 8 (do not approximate)

h = 5

Hence, the altitude of the trapezoid, based on the given parameters is 5 units

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

Answer:

5 units

Step-by-step explanation:

Answer:

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

Answer:

Yes

Step-by-step explanation:

First we need to determine how much money Allen has

2 dollars = 2.00

5 quarters = 5 * .25 = 1.25

2 dimes = 2 * .10 = .20

7 pennies = 7 * .01 = .07

Add this together

2.00 + 1.25+.20+.07 =3.52

3.52 > 3.50

This is more than 3.50 so he has enough money to buy the pencils

The probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.

According to thr question.

We have to find the probability of selecting none of the correct six integers from the positive integers not exceeding 48.  

Let E be the event of selecting 6 numbers from 40 and S be the sample space of all integers not exceeding 48.

Now,

The total number of ways of selecting 6 numbers from 48

[tex]= ^{48} C_{6}[/tex]

[tex]= \frac{48!}{6!\times 42!}[/tex]

[tex]= \frac{48\times 47\times46\times45\times44\times43\times42!}{6!\times\ 42!}[/tex]

= 8835488640/6!

And, the total number of ways of selecting 6 incorrect numbers from 42

= [tex]^{42} C_{6}[/tex]

[tex]= \frac{42\times41\times40\times39\times38\times37\times36!}{6!\times36!}[/tex]

= 3776965920/6!

Therefore, the probability of selecting none of the correct six integers, when the order in which they are selected does not matter is given by

[tex]= \frac{^{42C_{6} } }{^{48} C_{6} }[/tex]

[tex]= \frac{\frac{3776965920}{6!} }{\frac{8835488640}{6!} }[/tex]

= 3776965920/8835488640

= 0.427

≈ 0.43

Hence, the probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.

Find out more information about probability here:

https://brainly.com/question/17083464

#SPJ4

Using the algebraic equation, (2x + 6)/5 = 4x - 3, it has been proved that x = 7/6

Algebraic Proof for the Given Algebraic Equation

The given algebraic equation is,

(2x + 6)/5 = 4x - 3

2x + 6 = 5(4x - 3)

2x + 6 = 20x - 15

20x - 15 = 2x + 6

This algebraic equation can be written as,

20x - 2x - 15 = 6

18x = 15 + 6

18x = 21

x = 21/18

x = 7/6

Hence, using the given algebraic equation, it has been proved that the value of x is 7/6.

Learn more about algebraic equation here:

https://brainly.com/question/953809

#SPJ1

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.

Know more about LCM here:

https://brainly.com/question/233244

#SPJ4

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

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

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.

By applying the theorem of intersecting secants, the measure of angle XYZ is equal to: A. 35°.

By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the theorem of intersecting secants.

The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, angle XYZ will be given by this formula:

<XYZ = ½ × (m<WZ - m<XZ)

Substituting the given parameters into the formula, we have;

<XYZ = ½ × (175 - 105)

<XYZ = ½ × 70

<XYZ = 35°.

By applying the theorem of intersecting secants, we can infer and logically deduce that the measure of angle XYZ is equal to 35°.

Read more on intersecting secants here: https://brainly.com/question/1626547

#SPJ1

Answer: 35

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

-factor it using FOIL (first outside inside last)

The y-intercept of the equation  g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation  g(x) = 3^x - 5 is y = -5

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The y-intercept is a point on the graph where the value of x is 0

This is represented by x= 0 or (0, y)

This means that we substitute 0 for x in the above equation

So, we have:

g(0) = 3^0 - 5

Evaluate the exponent 3^0

g(0) = 1 - 5

Evaluate the difference of 1 and 5

g(0)  = -4

Rewrite this point as

(0, -4)

This means that the y-intercept of the equation  g(x) = 3^x - 5 is (0, -4)

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The asymptote is a point on the graph where that is parallel to the graph

In the above equation, we have:

g(x) = 3^x - 5

Express the radical as 0

y = 0 - 5

Evaluate the difference of 0 and 5

y  = -5

This means that the asymptote of the equation  g(x) = 3^x - 5 is y = -5

Read more about asymptote at:

https://brainly.com/question/1851758

#SPJ1

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:

1413.86 ft^2.

Step-by-step explanation:

The diameter of the circle = 50 - 2(18)

= 50-36

=  14 ft.

So its radius is 7 ft.

The total area of the blue shape

= 2(35 * 18) + 3.14*7^2

= 1413.86 ft^2.

Answer:

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

Answer:15 meters

step by step explanation

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

Read more about domain and range at:

https://brainly.com/question/2264373

#SPJ1

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)

Answer:

x=10

Step-by-step explanation:

x-3(+3)=7+3

We need to add 3 to both sides to isolate x.

x=10

Answer:

Step-by-step explanation:

x - 3 = 7

x = 7 + 3

x = 10