Given the equation 5 + x - 12 = x - 7.
Part A. Solve the equation 5 + x - 12 = x - 7. In your final answer, be sure to state the solution and include all of your work.

Part B. Use the values x = -4, 0, 5 to prove your solution to the equation 5 + x - 12 = x - 7. In your final answer, include all of your calculations.

The solution (x, y) to a system of equations is the point where both equations intersect, meaning the coordinates (x, y) satisfy both equations simultaneously.

In mathematics, specifically in algebra, the solution (x, y) to a system of equations is the point where they intersect. This means that the coordinates (x, y) satisfy both equations simultaneously.

For example, if you have the system of equations y = 2x + 1 and y = 4x - 3, their solution would be the point (x, y) that would make both equations true when substituted into these equations. This is an important concept in algebra and serves as the foundation for many subsequent topics.

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The solution to a system of equations is the point where their graphs intersect, representing values that satisfy both equations. This method is practical for two-variable systems.

The solution to a system of equations is the point where the graphs of the equations intersect. This point represents the values of x and y that satisfy both equations simultaneously.

For example, consider the system of equations:

Equation 1: 2x + y = 5
Equation 2: -x + 3y = 4

Graphing these equations, the point where the lines cross is the solution. If the lines intersect at (x, y) = (1, 3), then (1, 3) is the solution to the system. This graphical method is useful for two-variable systems but becomes impractical for systems with more variables.

Answer:

x = - 1

Step-by-step explanation:

Given

15x - 7 = 4x - 18 ( subtract 4x from both sides )

11x - 7 = - 18 ( add 7 to both sides )

11x = - 11 ( divide both sides by 11 )

x = - 1

Answer:

85 ft

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let h be the hypotenuse, then

h² = 40² + 75² = 1600 + 5625 = 7225 ( take the square root of both sides )

h = [tex]\sqrt{7225}[/tex] = 85

Answer:

85

Step-by-step explanation:

The most obvious way to solve this is by using the Pythogream therom which I strongly reccomend learning.

[tex]a^{2} + b^{2} = c^{2}[/tex]

Answer:

Explanation:

Any multiple of 3 and 4 shall blow clouds of smoke through its nostrils and breathe fire. Those are:

Hence, that is 8 dragons that shall have both characteristics.

Any multiple of 6 shall have glowing eyes. The common multiples of 6 and 3 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.

Then, that adds:

Hence, add 8 more dragons.

And the common multiples of 6 and 4 are: 12, 24, 36, 48, 60, 72, 84, and 96, all of which are already included.

Any multiple of 8 shall have a tail with spikes on it. Then, you must find the common multiples of 8 and 3, 8 and 4, and 8 and 6.

Common multiples of 8 and 3 are: 24, 48, 72, and 96, which are already included.

Common multiples of 8 and 4 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96. Then, you must add:

Those are other 8 dragons.

At the end the number of dragons that shall have more than one of these characteristics is:

Final answer:

By calculating the least common multiples (LCMs) of the intervals for the dragon's characteristics and considering the first 100 dragons, we find that there will be 12 dragons with overlapping features.

Explanation:

Sir Dwayne at the King's Toy Factory is tasked with creating dragons with characteristics that occur at different intervals. Specifically, every 3rd dragon billows smoke, every 4th breathes fire, every 6th has glowing eyes, and every 8th has a spiked tail. We are asked to calculate how many of the 100 dragons will have more than one of these features.

To solve this problem, we need to consider the least common multiples (LCMs) between the provided intervals: 3, 4, 6, and 8. The LCM of any two numbers is the smallest number that is a multiple of both numbers. We'll find the number of dragons that have characteristics occurring at multiple intervals (overlapping features).

We must not forget to find the LCM for all three and four characteristics together, if any, to see if there is any dragon with three or all four features:

Since the highest LCM (which covers all the characteristics) is 24, and we are making 100 dragons, we can divide 100 by 24 to find how many dragons would have all four characteristics. This results in 4 dragons with some remaining. Now, we'll consider all unique multiples of our LCMs up to 100 and sum them up, taking care not to double-count any dragons:

Note that every multiple of 24 is also a multiple of 12, which means these have already been counted. So, we only count the additional multiples of 12 that are not multiples of 24.

Counting all the unique multiples, we have: 8 (from LCM 12) + 4 (from LCM 24) = 12 dragons. Thus, Sir Dwayne will make 12 dragons having more than one of these characteristics.

A Quick Guide to the 30-60-90 Degree Triangle

The 30-60-90 degree triangle is in the shape of half an equilateral triangle, cut straight down the middle along its altitude. It has angles of 30°, 60°, and 90°. In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, you can find the long leg by multiplying the short leg by the square root of 3.

Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. The long leg is the leg opposite the 60-degree angle.

Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles. All 30-60-90 triangles, have sides with the same basic ratio. If you look at the 30–60–90-degree triangle in radians, it translates to the following:

30, 60, and 90 degrees expressed in radians.

The figure illustrates the ratio of the sides for the 30-60-90-degree triangle.

A 30-60-90-degree right triangle.

A 30-60-90-degree right triangle.

If you know one side of a 30-60-90 triangle, you can find the other two by using shortcuts. Here are the three situations you come across when doing these calculations:

Type 1: You know the short leg (the side across from the 30-degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.

Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.

Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.

Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.

Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.

In the triangle TRI in this figure, the hypotenuse is 14 inches long; how long are the other sides?

Because you have the hypotenuse TR = 14, you can divide by 2 to get the short side: RI = 7. Now you multiply this length by the square root of 3 to get the long side:

The long side of a 30-60-90-degree triangle.

To find the other endpoint of the diameter of a circle, you can use the midpoint formula in reverse with the given center and one endpoint. In this case, the coordinates of the other endpoint of the diameter are (5, 7).

The coordinates of the other endpoint of a diameter of a circle given that one endpoint and the center of the circle are known. We know the center of the circle, O, is at (2, 3) and one endpoint of the diameter is at (-1, -1). The diameter of a circle is a straight line through the center connecting two points on the circle. If you have one endpoint (x₁, y₁) and the center (x₂, y₂), the coordinates of the other endpoint (x₃, y₃) can be calculated using the midpoint formula in reverse:

x₃ = 2 × x₂ - x₁

y₃ = 2 × y₂ - y₁

For this circle:

x₃ = 2 × 2 - (-1) = 4 + 1 = 5

y₃ = 2 × 3 - (-1) = 6 + 1 = 7

So, the coordinates of the other endpoint of the diameter are (5, 7).

D is the correct answer.

Answer:

5sqrt(2)

Step-by-step explanation:

Z - Y

-i+5j+3k - (-6i+2j-k)

-i + 6i + 5j - 2j + 3k + k

5i + 3j + 4k

Magnitude:

sqrt(5² + 3² + 4²)

sqrt(50)

5sqrt(2)

Answer is

B = 5sqrt(2)

Answer:

(-5,-2)

Step-by-step explanation:

g is on those coordinates.

Answer:

(-5,-2)

Step-by-step explanation:

Answer:

(C) A'(4, 1)

Step-by-step explanation:

When a point is reflected across the x-axis, the following happens

Given the Point A(4, –1)

When it is reflected, following the rules above

The coordinates of A' will therefore be: A'(4,1)

Answer:

c

Step-by-step explanation:

just did it on ed 2020

Answer:

C. 7mm

Step-by-step explanation:

the prism is rectangular so the answer is c

Answer:

f/3=6

18 total fish

Step-by-step explanation:

Answer:

Okay so,

Step-by-step explanation:

the first one is

1.25 or 1 [tex]\frac{1}{4}[/tex]

second one is

0.5 or [tex]\frac{1}{2}[/tex]

the third one is

i'm not sure what the question is

the fourth one is

i'm not sure what the question is. Are you dividing?

the fifth one is

153.18

the sixth one is

1010.25

the seventh one is

4.066362

the eight one is

i'm not sure what the question is

Can you make me brainliest please

Answer: Option D.

Step-by-step explanation: I did this.

Answer:

Option D

Step-by-step explanation:

BECAUSE I KNOW!!!

Answer:

C

Step-by-step explanation:

Euler's formula for polyhedra states that

F + V - E = 2 ( F is faces, V vertices and E edges ), thus

F + 8 - 12 = 2, that is

F - 4 = 2 ( add 4 to both sides )

F = 6

The number of faces is 6

Answer: I believe it’s c

Answer:

2

Step-by-step explanation:

Answer:

√49 = 7

Step-by-step explanation:

√49 = 7 is the only given number that is rational.

Answer:

171

Step-by-step explanation:

180 - (5% × 180)

180 - 5% × 180

(1 - 5%) × 180

(100% - 5%) × 180

95% × 180

95 ÷ 100 × 180

95 × 180 ÷ 100

17,100 ÷ 100 = 171.

Answer:

-13x+8

Step-by-step explanation:

add the x's including negatives

Answer:

-13x + 8

Step-by-step explanation:

Add the x's including the negatives

Answer:

60,000 I think.

Step-by-step explanation:

the value (100,000) minus the damage (40,000) would equal 60,00

Answer:

C) 223.6m³

Step-by-step explanation:

Area of the trapezium = sum of parralel sides / 2 = 6.5m × 4.3 (perpendicular height) = 27.95m²

× 8 = 223.6m³

Answer:

the answer is -8

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The average rate of change over the interval [tex][a,b][/tex] for a function [tex]f[/tex] is [tex]\frac{f(b)-f(a)}{b-a}[/tex].

So the average rate of change for [tex]f(x)=2^x[/tex] on [tex][2,4][/tex] is:

[tex]\frac{2^4-2^2}{4-2}=\frac{16-4}{2}=\frac{12}{2}=6[/tex].

Answer:

2/3x+5

Step-by-step explanation:

when x=0 your y-int is that y-coord.

the rest is just rise over run

The word describing 3y is "term". The correct option is (D).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given algebraic expression is as below,

5x + 3y + 9

Since an algebraic expression consists of different terms separated by each other by a plus or minus sign.

The given expression has three terms as  5x, 3y and 9.

Hence, the word that describes 3y for the given expression is "term".

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Final answer:

In the expression 5x + 3y + 9, the term '3y' is one of the three terms present, with '3' serving as the coefficient, making '3y' correctly identified as a term.

Explanation:

In the given expression 5x + 3y + 9, the term "3y" is described as a term. In algebra, a term is a single mathematical expression that may form a part of a larger expression, which can include numbers, variables (like x or y), or the product of numbers and variables. Here, "3y" is one of the three terms in the expression, with "5x" and "9" being the others. The number 3 in "3y" is called the coefficient, which is the numeric part of the term that multiplies the variable y. Therefore, the correct answer to the question is D) term.

Answer:

0.123601

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x < - 4

divide both sides by 2

[tex]\frac{2x}{2}<\frac{-4}{2}[/tex]

x < -2

x= {.........-5, -4 , - 3}

All values less than -2

Answer:

thats an error??

Step-by-step explanation:

Answer:

3.273391e+150

Step-by-step explanation:

Use a calculator