Which expression is equivalent to the given expression?

√45

A. 5√9
B. 3√5
C. 9√5
D. 5√3

Answer:

Sum of Interior Angles = (8-2) * 180 = 1080 degrees

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

Step-by-step explanation:

The sum of the interior angles in a polygon can be found using the formula (n-2)*180, where n is the number of sides in the polygon.

In the case of an octagon (8 sides), the sum of the interior angles is (8-2)*180 = 1080 degrees.

The measure of the eighth interior angle can be found by subtracting the sum of the known interior angle measures from the total sum of the interior angles.

So,

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

In short,

Sum of Interior Angles = (8-2) * 180 = 1080 degrees

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

Answer:

g = -19

Step-by-step explanation:

Given equation,

→ -3g = 57

Now the value of g will be,

→ -3g = 57

→ g = 57/-3

→ g = -(57/3)

→ [ g = -19 ]

Hence, the value of g is -19.

Answer:g=-19 I hope this helps

Step-by-step explanation:

-3g=57

Divide both sides of the equation by -3

-3g divide (-3)=57 divide (-3)

Any expression divided by itself equals 1

g=57 divide (-3) then you do

Dividing a positive and a negative equals a negative: (+) divide(-)=(-)

g=-57 divide 3

Next thing you do is

Calculate the quotient which something like this

g=-19

So you’re answer is g=-19

Answer:

25°

Step-by-step explanation:

Please see the attached document for how I set up this problem. I used the law/theorem of alternate interior angles to solve for the missing angle we're looking for, and knowing that a straight line will also have an angle measure of 180 degrees. We can also check the answer we arrive at by adding up all the angles that we have and seeing if they add up to 360 degrees, just as all the angles in a four-sided shape would.

The angle of KLM is 50 degrees. The opposite angle, MJK, is also 50 degrees. JKL and LMJ have the same angle of 130 degrees. When we add this together, we reach 360 degrees, letting us know our answer is correct.

Step-by-step explanation:

for questions about % always find out first what 100% or what 1% are.

everything else can be calculated out of these 2 numbers.

in our case here

100% = 389 ml

1% = 100%/100 = 389/100 = 3.89 ml

18.6% = 18.6×1% = 18.6 × 3.89 = 72.354 ml

so, there are 72.354 ml of acid in the solution.

FYI

as you can see, we can combine both steps into one and do any of the following

18.6% = 18.6 × 100%/100 = 18.6 × 389/100 =

= (18.6/100) × 389 = 0.186 × 389

The perimeter of your new patio is 52.

Given that,

In order to match the shape of your backyard, your family has decided to build a rectangular patio there. The dimensions of your backyard are 20 feet wide by 45 feet long. Your new patio measures 18 feet in length.

To find :  The perimeters of your backyard and of the patio.

The dimensions of the yard are length 45 and width 20.

The patio is going to have the same shape, only smaller.

The length of the patio is 18 feet.

The ratio of the length of the patio to the length of the yard is 18/45.

Since the patio and the yard are to have the same shape, then that same ratio of 18/45, applied to the width of 20, gives you a patio width of 18/45* 20 = 8

Therefore, The perimeter of your new patio is 2 * (18 + 8) = 2 * 26 = 52.

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Adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

Let the fractions be 1/8 and 1/12

8 = 2 × 4

12 = 3 × 4

By using LCM, we get

[tex]$2 \times 3 \times 4=24 \quad\{L C M\}$[/tex]

= 1/8 + 1/12

simplifying the equation, we get

[tex]$=\frac{1 \times 3}{8 \times 3}+\frac{1 \times 2}{12 \times 2}$[/tex]

= 3/24 + 2/24

= 5/24

Therefore, adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.

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The set of potential output values of a function is often referenced by the range () function.

A built-in Python function called range() can be used to produce a series of numbers. The range() function's parameters can be supplied by the user if they want to generate a series of numbers given the starting and ending values.

It can be used to generate a list of numbers or to iterate over a series of numbers in for loops.

For example, range(5) will generate a sequence of numbers from 0 to 4, and range(2, 5) will generate a sequence of numbers from 2 to 4.

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The equation 3x - 5y = 12 could be used to represent the function y = f(x), which is NOT one-to-one.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given that function f(x) is not one-to-one

That means the given equation will have only one solution for the one value of x,

Since Quadratic equations have two values at the one value of x that means option a would not satisfy

option c also makes an exponential graph which means it also has more than one value at x

Since Option (b ) 3x - 5y = 12 has a linear function and linear functions do not have more than one value at a value of x

Therefore, the function y = f(x) is NOT one-to-one, the equation could represent f(x) as 3x - 5y = 12.

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The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.

A. Let "r" be the number of state representatives and "s" be the number of state senators. We know from the problem that:

r + s = 181 (the sum of the number of representatives and senators is 181)

r - s = 119 (the difference of the number of representatives and senators is 119)

So the system of equations is:

r + s = 181

r - s = 119

B. To solve this system of equations, you can use the first equation to solve for one of the variables in terms of the other. Let's solve for "r" in terms of "s":

r = 181 - s

Now we can substitute this expression for "r" into the second equation:

(181 - s) - s = 119

Simplifying, we get:

181 - 2s = 119

2s = 62

s = 31

So there are 31 state senators in the Texas State Legislature. To find the number of representatives, we can use the first equation and substitute in the value of "s" that we just found:

r + 31 = 181

r = 150

So there are 150 state representatives in the Texas State Legislature.

Therefore, The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.

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Correct option is A, The foci of the hyperbola is (0,±√17).

A hyperbola is a plane curve that is produced by a point that is moving so that the difference between the distances from two fixed points is constant. It is created when a double right circular cone intersects with a plane that cuts through both ends of the cone.

The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.

Given the equation of hyperbola is [tex]\frac{y^2}{12} - \frac{x^2}{5} = 1[/tex]

In this equation,

a² = 12

b² = 5

Using the relation c² = a² + b²

c = √(12 + 5)

c = √ 17

As, the hyperbola is vertical,

The value of foci will be (0,±√17)

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The original dimensions of the garden are 12 ft by 16 ft.

Width: x + 4 (not 2 because the width has two ends)

Length: x + 8 (same reason; this is x + 4 + 4)

The area of the garden and the border combined is 320 sq. ft.

The dimensions of the garden with the border around it are (x + 4) and (x + 8).

A (rectangle) = lw

A (garden with border) = lw

320 sq. ft. = (x + 4) (x + 8)

320 sq. ft. = x2 + 12x + 32

Transpose 320 to the right side of the equation.

0 = x2 + 12x + 32 - 320

0 = x2 + 12x - 288

Factor out.

0 = (x + 24) (x - 12)

One or both of the amounts are equal to zero when the product of two values is zero.

Equate the factors to 0.

x + 24 = 0 x - 12 = 0

x = - 24 x = 12

Since we cannit have a negative measure of distance, x = 12.

Find the original dimensions of the garden.

The original dimensions of the garden (without the border) are x and x + 4.

Width = x = 12

Length = x + 4 = 12 + 4 = 16

The original dimensions of the garden are 12 ft by 16 ft.

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The inverse of 8 is 1/8.

The multiplicative inverse of a number for any n is simply 1/n. It is denoted as:

1/x (or) x⁻¹

It is also called the reciprocal of a number and 1 is called the multiplicative identity.

The reciprocal of a number obtained is such that when it is multiplied by the original number, the value equals identity 1.

There are a few steps to find the inverse of a number:

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Answer:

Because the plane is flying due east, it has to turn 90º to face south, before it turns the extra 35.31º to fly towards the airport. 90° + 35.31° = 125.31º It actually turns through the exterior angle of the triangle :

Step-by-step explanation:

hope this helps B)

Answer:

  55°

Step-by-step explanation:

You want to know the additional angle a plane must turn through to be going south after it took off going east, then turned right 35°.

The initial bearing angle was 90° (straight east). After turning right 35°, the airplane now has a heading of (90+35)° = 125°. To be going south (180°), the bearing must increase by ...

  180° -125° = 55°

The airplane will have to turn 55° more to be heading due south.

The height of the rocket 45.161 km.

By adding a and b to h=-b2a, you may determine h, the x-coordinate of the vertex.

Determine k, the vertex's y-coordinate, by calculating k=f(h)=f(b2a).

According to the graph, the velocity first increases for 20 seconds before declining for 120 seconds before changing course.

Thus, it was at its highest peak at t=120 seconds.

Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular = 2 120 * 1000 * 60 km.

The rocket reaches a peak height of 112 feet at a time of 2.48 seconds. The rocket then falls and hits the ground 5.12 seconds after it was launched.

According to the graph, the velocity first increases for 20 seconds before declining for 112 seconds before changing course.

Thus, it was at its highest peak at t = 112  

2.48 seconds.

Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular =  112 * 1000 /2.48 = 45.161 km.

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The number of regular sodas served is 12.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. Percentage is a measure of frequency.

Number of regular sodas served = percentage of regular sodas served x number of sodas served

= 25% x 48

= 25/100 x 48 = 12

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Complex numbers are those whose representation is given by the notation a+ib, where a, b are real numbers and I is a made-up expressions called a "iota." I'm equal to (-1).

If complex numbers are required to answer an equation, it is considered complex. Complex numbers are made up of both imaginary and real parts. This is how it is stated: The letters A and B in the preceding equation both represent numerical values. A complex number is something like 4+3i.

In order to attain vague goals that cannot be met through conventional actions, complex issue solving is a collection of self-regulated psychological processes and activities. It takes a variety of tactics and inventive knowledge combinations.

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Answer: 7 seats in each row.

Step-by-step explanation:

14 / 2 = 7 seats in each row.

The value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

Since ZU and ZV is equal to 8, then QR is equal to ST and the radii ZY and ZW bisect ST and QR respectively.

we shall solve for x in the circle as follows:

QR = ST

4x - 5 = 7

4x = 7 + 5 {add 5 to both sides}

4x = 12

x = 12/4 {divide through by 4}

x = 3

The length VS = 7/2

VS = 3.5

Therefore, the value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

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Answer:

acute and scalene, remember:

Isoceles: An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called legs and the third side is called the base.

Scalene: A scalene triangle is a triangle with all sides of different lengths. None of its angles are congruent.

Equilateral: An equilateral triangle is a triangle with all three sides of equal length. All three angles are congruent and measure 60 degrees.

Answer:

39 miles

Step-by-step explanation:

We can start by using algebra to represent the problem in equation form. Let j be the number of miles Jacob ran.

From the information given, we know that:
Adam ran 21.5 miles less than Jacob.
Adam ran 17.5 miles.

We can use these two pieces of information to set up the following equation:
j = 17.5 + 21.5

Now we can solve for j by adding 21.5 to both sides:
j = 39

So Jacob ran 39 miles.

The measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

here, we have,

It is given that:

The diagram shows two parallel lines cut by a transversal.

As we know from the definition of the vertically opposite angles:

b = 54 degrees

a + c = 54 + b  (a = c)

2a = 54x2

a = 54 degrees

Since a and g are opposite interior angles, they are congruent, so you proceed with the process as you did for the first and check to see if the angles are acute or obtuse to ensure that the angle measurements are accurate.

Similarly:

b = 54

c = 126

d = 54

e = 126

f = 54

g = 126

Thus, the measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

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The number of cans required for John to paint the wall is given by the equation A = 3.375 cans ≈ 4 cans

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the wall be A

Now , the area of wall A = area of rectangle + area of triangle

The side length of the rectangle = 3m

The width of the rectangle = 2 m

The height of the triangle = 1 m

The base of the triangle = 1.5 m

So , the area of the triangle = ( 1/2 ) x 1.5 x 1 = 0.75 m²

Now , the area of the rectangle = length x width

Area of the rectangle = 3 x 2 = 6 m²

So , the area of the figure = 6.75 m²

Now , 11 can of paint covers an area of 22 square meters

So , 1 square meters = 11/22 cans

1 square meters = 1/2 cans

And , the number of cans required for 6.75 m² of area = 6.75 ( 1/2 ) cans

The number of cans required for 6.75 m² of area = 3.375 cans

The number of cans required for 6.75 m² of area = 4 cans

Hence , the number of cans is 4 cans

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Answer:

200.96

Step-by-step explanation:

Pi(8 to the power of 2)

Step 1: The greatest common factor (GCF) in this equation is x^3. So we can factor it out:

y = x^3(x - 343)

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Step 2: We can not take root of a³ and b as there is no square term in the equation.

Step 3:

a= x^3

b= - 343

Step 4: Plugging in a and b into the original equation, we get

y = x^3(x - 343)

This is the simplified form of the equation.

So, the equation is a polynomial equation of degree 4, with the leading coefficient a = x^3 and the constant term b = -343, and it can be written as y = a(x-b) which is y = x^3(x-343)

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Answer:

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side.

Step-by-step explanation:

a)  Pam overtime wage for that week is 110.625

b) Pam works a basic week of 40 hours her basic wage is 150.

c)  Pam gross wage for that week during Christmas 114.375.

What is Basic wages?

An employee may not legally sell their labor for less than the minimum wage, which is the lowest compensation a business may pay their staff. By the turn of the 20th century, minimum wage laws were in place in the majority of nations.

What is Gross wages?

The total of the base salary, overtime compensation, commissions, bonuses, and other regular cash payments is referred to as the monthly gross wage. It does not include employer CPF contributions, bonuses, stock options, other lump sum payments, or payments-in-kind. It is prior to deducting employee CPF contributions and personal income tax.

Given that;

a)Calculation for  Pam overtime wage for that week ;

So, 25% of 3.75 = 0.9375

and add it to 3.75.

then 0.9375 + 3.75 = 4.6875

Since she worked 6 hours at that new wage,

then 6 x 4.6875 = 28.125

Now for 50% of 3.75 =1.875

and add it to 3.75

then  1.875 + 3.75 = 5.625

Since she worked 8 hours at that new wage,

then 8 x 5.625 = 45

She works double time, which means she receives two times her regular pay.

Since she worked five hours at the wage, double her basic wage by two and then by five.

then  2 x 3.75 x 5 = 37.5

So, Pam overtime wage for that week is ;

28.125 + 45 +  37.5 = 110.625

b) Pam works a basic week of 40 hours  her basic wage is ;

    40 x 3.75 = 150

c) Pam gross wage for that week during Christmas is ;

  total wages + overtime wages

⇒110.625 + 3.75 = 114.375

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The probability of forgetting iClicker device in each class = 1/4 = 0.25 = p

The probability of remembering iClicker device in each class = 1-p = 0.75

(a) Given that she is sure she has the iClicker device after leaving the first class.

The probability that she left it in second class = 1(0.25) = 0.25

The probability that she left it in third class = 1(0.75)(0.25) = 0.1875

The probability that she left it in fourth class = 1(0.75)(0.75)(0.25) = 0.1406

The probability that she left it in fifth class = 1(0.75)(0.75)(0.75)(0.25) = 0.1055

The total probability that she left iClicker given that she is sure she has the iClicker device after leaving the first class is:

0.25 + 0.1875 + 0.1406 + 0.1055 = 0.6836

Given that she is sure she has the iClicker device after leaving the first class, the probability that she left it in the 5th class is:

0.1055/0.6836 = 0.154

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Answer: A. 9/19

Step-by-step explanation:

20 + 18(amount of cookies) = 38

there are 18 chocolate chip cookies, so it's an 18/38 chance it's a chocolate chip cookie that broke, but 18/38 can be simplified.

18 divided by 2 is 9 and 38 divided by 2 is 19

so 9/19

The volume and value of x is x>9.

Since x represents the width, it clearly must be greater than zero since a box must have each dimension be positive which makes the lower bound. The question is whether (17-2x) and (4-2x) represent the other 2 dimensions or not.

If so, then (4-2x) must also be greater than zero which makes the possible range of x as 0<x<1.5

If not, then in addition to the above range, values of x such that both 4-2x and 17-2 evaluate to negative still result in a positive volume.

Therefore, additional values of x are x>9.

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