Find m/G.
F
150°
H
G

Note that the expression when simplified translates to x = -6 (Option 1)

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.

√(x + 14) - √2x + 5) = 1

To solve this, we must square all elements on both sides of the equation. That is:

√(x + 14)² -  √(2x + 5)² = 1²

⇒ x + 14 + 2x + 5 = 1

Collect like terms to arrive at:

3x = -18

x = -18/3

x = -6

Thus the answer to the above expression is x= -6

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Two polynomials simply mean to sum the coefficients of the same powers, if these situations occur. the result of adding two polynomials will always be another polynomial.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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The percent decrease in price for booking early for a spring break vacation package is 16.5%.

This was calculated by taking the amount of money saved ($35) and dividing it by the original price of the package ($209.99). Then, the resulting decimal was multiplied by 100 to convert it into a percentage.

Mathematically, the calculation looks like this:

(35/209.99) ×100 = 16.5%.

The 16.5% decrease in price is a substantial savings and could be used to purchase additional items or activities during the vacation. Booking early is often a great way to save money on vacation packages, since travel agents and companies often lower the prices to incentivize travelers to book in advance.

It is important to remember, however, that the savings may not always be 16.5%. Depending on the travel agent or company, the percentage of savings may vary. Additionally, some packages may not offer any savings at all. Therefore, it is important to do research and compare different packages before booking.

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Answer:

x = 73⁰

Step-by-step explanation:

all values show are measures of exterior angles

the sum of all exterior angles for any polgon is 360 degrees

to find 'x':

50 + 48 + 59 + x + x + 58 + 39 = 360

combine like terms:

2x + 214 = 360

2x = 146

x = 73

The area of given figure is 32 ft².

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given,

the shaded are of shape is 16 ft²

As, twice the area of triangle equals the area of rectangle

⇒ (16 + 16) ft²

⇒ 32 ft²

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Complete Question -

$1200 was invested at a mutual fund of 6% profit while $2000 was invested at a mutual fund of 4% profit

An equation is an expression showing the relationship between numbers and variables.

Let x represented the money at 6% profit and y represent the money at 4% interest. A total of $3200 was invested, hence:

x + y = 3200    (1)

If the investor's total profit was $152, therefore:

0.06x + 0.04y = 152         (2)

From both equations:

x = 1200, y = 2000

$1200 was invested at 6% while $2000 was invested at 4%

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Answer: Linda, Laura, Loraine, and Lila run 2 kilometers altogether.

Step-by-step explanation:

0.5 + 0.5 + 0.5 + 0.5 = 2 km

I hope this helps!

Answer:194.78 cm

Step-by-step explanation:

A 30-60-90 triangle is a special type of right triangle that has angles of 30 degrees, 60 degrees, and 90 degrees. It has the following properties:

The side opposite the 30-degree angle is half the length of the hypotenuse (the side opposite the 90-degree angle).

The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.

To find the sides of a 30-60-90 triangle, you can use these properties.

If you know the length of the hypotenuse (the side opposite the 90-degree angle), you can find the length of the other two sides using the following formulas:

The side opposite the 30-degree angle: hypotenuse / 2

The side opposite the 60-degree angle: (√3) * (hypotenuse / 2)

If you know the length of one of the other two sides, you can use the above formulas to find the length of the hypotenuse and the other side.

For example, if you know the length of the side opposite the 30-degree angle, you can find the length of the hypotenuse by multiplying it by 2 and the length of the side opposite the 60-degree angle by multiplying it by √3

In summary:

The hypotenuse is always twice the length of the shorter leg.

The longer leg is √3 times the length of the shorter leg.

The hypotenuse is always the longest side in a 30-60-90 triangle.

So, 40% of students don't like swimming.

We know that 60% of students like swimming, and 40% of students like dancing. We also know that 20% of students that like swimming also like dancing.

First, we can find the number of students that like swimming and dancing by multiplying the percentage of students that like swimming by the percentage of students that like dancing and also like swimming:

20% * 60% = 12%

This means that 12% of students like both swimming and dancing.

To find the percentage of students who don't like swimming, we can subtract the percentage of students who like swimming from 100%.

100-60 = 40%

So, 40% of students don't like swimming.

It's important to note that if the problem had provided a total number of students this information would have been useful to calculate the exact number of students who don't like swimming.

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You can find the inverse of any function y=f(x) by reflecting it across the line y=x.

Hence, Option A is correct.

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The intensity of the earthquake on the Richter scale of magnitude 5.3 can be calculated for moderate earthquakes, and a strong earthquake can be estimated at magnitude 6.3.

The idea of a logarithmic earthquake magnitude scale was first developed by Charles Richter in the 1930s to measure the magnitude of earthquakes occurring in Southern California using relatively high frequency data from a nearby seismometer station. Developed. The magnitude of an earthquake is expressed on a scale called the Richter scale. The Richter scale is a base 10 logarithmic scale, meaning that each magnitude is ten times stronger than the last. So 2 is 10 times stronger than 1 and 3 is 100 times stronger. On the Richter scale, the increment is the amplitude of the wave. In the Richter scale, magnitude is represented by whole numbers and decimals. More destructive earthquakes are usually between magnitude 5.5 and 8.9. A truly destructive earthquake is an earthquake that exceeds magnitude 7 on the Richter scale.

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The expression is simplified to y⁹/12x². Option A

The index form of a number can be described as that number written as an exponential expression.

It is also seen as a single number that is raised to another number.

Other names for index forms are standard forms and scientific notation.

From the information given, we have that;

3x^⁻⁴y⁵/(2x³y⁻⁷)⁻²

expand the exponential bracket of the denominator by mutiplying the values

3x^⁻⁴y⁵/2x⁶y⁻¹⁴

Now, divide the expression into parts, we have;

3/-4 (x^⁻⁴y⁵/2x⁶y⁻¹⁴)

Since we are finding the quotient, subtract the exponents of the denominator from the numerators, we get;

3× -4(x⁻⁴⁺⁶y⁵⁻¹⁴)

Now, add or subtract the exponential values, we get;

-12(x⁻²y⁻⁹)

y⁹/12x²

Hence, the correct option is y⁹/12x²

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Jacob's speed in kilometers per hour is equal to 8/5 kilometers per hour.

In Science, speed can be defined as the distance covered by a physical object or body per unit of time. This ultimately implies that, speed is a scalar quantity because it has magnitude but no direction.

Mathematically, the speed of a physical object or body can be calculated by using this formula;

Speed = distance/time

Substituting the given points into the speed formula, we have the following;

Speed = 2/5/(1/4)

Speed = 2/5 × 4/1

Speed = 8/5 kilometers per hour.

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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After solving, the solution of the pair of equation is (-1, 0).

In the given question, we have to find the solution of the system of equations y = 4x + 4 and y = -3x - 3.

The given equations are:

y = 4x + 4.....................(1)

y = -3x - 3.....................(2)

Now putting the value of y from equation 1 to the equation 2

4x + 4 = -3x - 3

Subtract 4 on both side, we get

4x = -3x - 7

Add 3x on both side, we get

7x = -7

Divide by 7 on both side, we get

x = -1

Now putting the value of x in equation 1

y = 4(-1) + 4

y = -4 + 4

y = 0

Hence, the solution of the pair of equation is (-1, 0).

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The complete question is:

What is the solution of the system of equations y = 4x + 4 and y = -3x - 3?

Solving the 2 equations will give us the value of x to be -14 and that of y to be 33.

Here we have two equations

2x + y = 5 and 3x - 2y = 4

Now we will use the substitution method to solve the equations

The first equation is

2x + y = 5

or, y = 5 - 2x                                                         [1]

Let 3x - 2y = 4 be equation 2

Substituting the value obtained in equation [1] in [2] we get

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

or, 3x - 10 + 4x = 4

or, x = -14                                                               [3]

Substituting the value of x obtained in equation [3] to equation [1] we get

y = 5 - 2(-14)

or, y = 5 + 28

or, y = 33

Hence, x = -14 and y = 33

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Complete Question

What is the solution of the equations 2x + y = 5 and 3x - 2y = 4?

The required distance between given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.

As given in the question,

Given pair of points in the coordinate plane is represented by the coordinates

( x₁ , y₁ ) = ( 2, 0 )

( x₂ , y₂ ) = ( -2,0 )

Apply the standard formula to calculate the distance between two pair of points in the coordinate plane is :

= √(x₂ - x₁ )² + ( y₂ - y₁ )²  

Substitute the values in the formula and calculate the distance between two pair of points :

= √ ( -2 - 2 )² + ( 0 - 0 )²

= √(-4)² + 0²

= √16

= 4

Therefore, the required distance between the given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.

The above question is incomplete , the complete question is:

What is the distance between the pair of points (2, 0) and (-2, 0) ?

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Answer: The answer is 2

Step-by-step explanation:

Juan's observations are correct, but his incorrect observation is asymptote: x = 0

An exponential function is a mathematical function of the following form: f(x) = aˣ. where x is a variable, and a is a constant called the base of the function.

Given is a graph of an exponential function.

Juan's observations are :-

Initial value: –3

Base: 3

Asymptote: x = 0

Domain: {x | x > 0}

Range: {y | all real numbers}

Studying the graph, we can say his observations are correct but his comment on Asymptote: x = 0 is wrong because, the equation of the horizontal asymptote of the graph of is y = 0, which is the x-axis.

Other than, Asymptote: x = 0, all his comments are true.

Hence, the incorrect observation is asymptote: x = 0

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a. On the 13th day the company sold the same number of each player.

b. 2,451 players were sold on that day.

a. The day on which the company sold the same number of players can be calculated by equating the values of y that we have ;

y = 191x-32 and y = -x² + 200x + 20

Equating both, we have;

191x-32 = -x² + 200x + 20

⇒x² -200x + 191x-20-32 = 0

⇒x²-9x-52 = 0

⇒x²-13x + 4x -52 = 0

⇒x(x-13)+4(x-13) = 0

⇒(x-13)(x+4) = 0

⇒x = 13 or -4

as days cannot be negative, so we choose only x = 13

This means that the company sold equal numbers of players on the 13th day.

b. To get the number of players sold on that day, we select any of the y equations and substitute x = 13

Thus, y = 191x -32; 191(13) - 32 = 2,451 players

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The complete question is:

The equation below models the numbers of two portable music players (y) and days after both players were introduced (x).

Music player A: y=191x-32 and music player B: y=-x^2+200x+20

1. on what day(s) did the company sell the same number of each player?

2. how many players were sold on THAT day (use your answer from #1

The total distance traveled is 46 miles.

Distance Traveled:

Distance traveled is the path covered by a body to get from a starting point to an endpoint in a certain period of time, at a certain velocity. Time and velocity play a major role in measuring the distance traveled. The distance travel formula is: d = v x t

To determine the total distance you have traveled, you will need to add up all the distances you have driven in each direction.

You drove 10 miles north, 14 miles east, 16 miles north, and 2 miles east, 4 miles north.

10 miles north + 14 miles east + 16 miles north + 2 miles east + 4 miles north = 46 miles

So, you have traveled 46 miles.

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Answer:

Step-by-step explanation:

plug in a 0 for y and simplify the equation

because 0*(constant of y)=0, so

x*(constant of x)=something, so

something/(constant of x)=x

ans is (x, 0)

Answer:

Click or copy the link and that is the answer

https://www.leonschools.net/cms/lib/FL01903265/Centricity/Domain/3141/ch%205%20review%20answers.pdf

Step-by-step explanation:

hope it helps :)

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if not try this (copy or paste)

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Answer:MP, NP, MN

Step-by-step explanation:

Rate does Lynn's cost increase for every additional mile she drives will be $0.25

The following is the linear relationship between the two variables:

Eq. 1: C f(d) = m*d + k

where m and k are evaluation-needed constants

Find m: We'll determine the angle of the line connecting the points (480, $380) and (800, $460).

Line slope (m) equals $0.25 per mile

Consider one of the two positions and enter (480,$380) in Eq 1 to find k.

k = 380 - 0.25(480) = $260

The line's equation is C f(d) = 0.25*d + 260.

This equation may be used to plot the graph for section a.

The rate of cost per mile is determined by the graph's slope when the units are scrutinized; as a result, $0.25

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The expression for the width is x (b) The perimeter of the rectangle in terms of x is x +8

You should understand that the perimeter of a rectangle is the distance round the rectangle

The given parameters that will help us to understand and solve the question are

Area = length * width

This implies that 2x +24 =4x

Collecting like terms =4 = 4x-2x

2x = 24

Therefore x = 24/2 = 12

b)  The perimeter is = L+W+L+W

Perimeter = 2L+w

Where W =x

Perimeter = 2(2x+24) +2(x)

The perimeter = 4x+48 +2x

Therefore the perimeter = 6x+48 or x+8

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Answer:

33.56°

Step-by-step explanation:

Base angles of an isosceles triangle are equal.

Base is bisected by a line from top (vertex) of the triangle straight down to form a right angle.  Base, 100 cm, has 2 equal segments, 50 cm each.

Find h, height of the triangle:

h² = 60² - 50²

h = √1100 = 33.17

sin(f) = 33.17/60 = 0.553

m∠f = sin⁻¹(0.553) = 33.56°

To calculate equivalent form of an algebraic expression we can use the following :

1) distributing property

2) factoring.

Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. To represent equivalent form an equality (=) sign is used. 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. To calculate equivalent form by using Distributive Property :

To calculate equivalent form Using Factoring :

This gives you an equivalent form . Again, the equality form, 5xy + 4x = x(5y + 4). Thus, the required equivalent form is determined.

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Answer:

i can not see the question

Step-by-step explanation:

please upload a New photo

There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

Finding the roots of the polynomial will allow you to solve it. P(x) = 0 is obtained by setting each factor to 0 and then calculating x. The polynomial equation can be solved by factoring. For every factor, a value of 0 should be used. 2x4 = 0; (x - 6) = 0; (x + 1) = 0 the answer to x, please.

It's important to note this even if there are only two genuine roots. The final two roots of this equation, which contain the integer I, are not real because I appears in both of them.

There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

The complete question is,

Calculate the overall number of roots for each polynomial function using the factored form. f (x) = (x + 2)(x - 1) (x - 1) (x - 1) [x - (4 + 3i)] [x - (4 - 3i)].

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