How do you find the coordinates of two points given an equation?

The equations that can be set up correctly to find the length of the unknown side using the Pythagorean theorem are:

6² + x² = 17²

x² + 6² = 17²

The Pythagorean Theorem is a statement in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The theorem can be written as an equation:

c² = a² + b², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Using the Pythagorean theorem, the equations that can be set up correctly to find the value of x are:

6² + x² = 17²

x² + 6² = 17²

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The formula of commutative property is α + β = β + α or α × β = β × α.

The commutative property is the property that deals with the arithmetic operations of addition and multiplication. So mathematically, if we change the order of the operand and it does not change the result of the arithmetic operation then that particular arithmetic operation is commutative.

If two numbers α and β are given, then the formula of the commutative property of numbers is given as,

α + β = β + α

α × β = β × α

α - β ≠ β - α

α ÷ β ≠ β ÷ α

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There are 80 dogs and 20 cats in the animal shelter.

The ratio of dogs to cats is 4:3. This means for every 4 dogs, there are 3 cats. We know that there are 40 more dogs than cats.

To calculate the number of each animal, we can set up the equation 40 = 4x - 3x, where x represents the number of cats.

After solving the equation, we get x = 20. This means that there are 20 cats in the animal shelter. To find the number of dogs, we can use the ratio. We know that for every 4 dogs, there are 3 cats. So, for 20 cats, there must be 4 × 20 = 80 dogs.

Therefore, there are 80 dogs and 20 cats in the animal shelter.

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The value of G(2) of the given sequence formula is; -42

The general formula for the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

We have the following parameters;

G(1) = 50

G(n) = 8 - g (n-1)

Thus;

G(2) = 8 - g(2-1)

G(2) = 8 - g(1)

Since (g(1) = 50 ), then we have;

G(2)= 8 - 50

G(2) = -42

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Answer:

y = 1425 * (1 + 0.05)^x

Step-by-step explanation:

An exponential function of the form y = a * b^x can be used to model exponential growth or decay, where a is the initial value, b is the base (growth or decay factor), and x is the time period. In this case, the initial value is 1,425 and the rate of increase is 5%. We can write this as an exponential function as follows:

y = 1425 * (1 + 0.05)^x

where y is the final value after x time periods, and x is the number of time periods (in years, for example). To find the value of the function after x time periods, you can substitute the value of x into the equation.

Trucks will be able to pass through tunnel B while tunnel A is destroyed.In light of this, the equations for tunnels A and B are x2 + y2 + 30x + 56 = 0 and x2 - 30x + 16y - 95 = 0, respectively.

A parabola's general equation is either y = a(x-h)2 + k or x = a(y-k)2 + h, where (h, k) stands for the vertex.

y2==4ax is the typical equation for a normal parabola.

Section A: x2+y2+30x+56=0

On both sides of an equation, add 152.

This is,

x²+30x+15²+y²=-56+15²

⇒ (x+15)²+y²=169⇒ (x+15)²+y²=13²

On both sides of the equation, divide 132.

⇒ (x+15)²/13² + y²/13² =1

Part B:x²-30x+16y-95=0

x2-30x+16y=95 now,

On both sides of an equation, add 152.

In other words, x2-30x+152+16y=95+152

⇒ (x-15)²=320-16y

⇒ (x-15)²=16(20-y) (20-y)

Part C:greatest height:A: 13 feet

B: 20 feet ,8 feet wide

A: x+15=8/2=4 y=12.37<13.5

B: x-15=8/2=4 y=19>13.5

In turn, tunnel A will sustain damage while the truck can travel via tunnel B.

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Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression  XYZ  is 1.

By substituting each variable with a number and conducting mathematical functions, an algebraic formula must be checked. The solution variable in the previous example is identical to 6 since 79 + 8 = 87. To evaluate the expression, we can replace the variables values with ones we are familiar with.

Here,

Given :

XYZ

To find the coefficient of given expression ,

Thus,

From observing we can see XYZ

can be written as

=>1*XYZ

Where 1 is coefficient.

Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression  XYZ  is 1.

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The value of h(-2)+g(4) by substitution is 6

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

For instance if h(x)=3x+1 . This means h(-2) means we are going to substitute -2 for variable x

Therefore h(-2) = 3(-2)+1

= -6+1 = -5

Similarly g(x)=x²-5. This means g(4) means we are going to substitute 4 for x in the equation.

Therefore g(4) = 4²-5

= 16-5 = 11

Therefore h(-2)+g(4) = -5+11

= 6

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Answer:The slope of the given line is -4

Step-by-step explanation:

The side opposite the 30-degree angle is called the shorter leg in a 30 − 60 − 90 triangle

A right triangle is any triangle that has a 90-degree angle.

A 30-60-90 triangle is a special type of right triangle that has a 30-degree angle and a 60-degree angle in addition to the right angle.

The side opposite the 30-degree angle is called the shorter leg.

The side opposite the 60-degree angle is called the longer leg.

The side opposite the right angle of 90 degrees is called the hypotenuse.

The hypotenuse is twice the shorter leg.

The longer leg is √3 times the shorter side.

if the length of the shorter leg is given, then these properties are used to find the longer side and the hypotenuse.

However, the 30-60-90 properties hold no matter which side is provided.

If the length of the hypotenuse is given, divide it by 2 for the shorter leg. Then multiply that result by √3 to get the length of the longer leg.

If the length of the longer leg is given, divide it by √3 to get the shorter leg. Then, multiply that result by two to get the length of the hypotenuse.

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Therefore , the solution to the given problem of perimeter model of the sports stadium has a 12 inch height. The right response is option C.

The perimeter of a shape is sometimes refers to as its entire length in geometry. The perimeter of something like a form can be calculated by summing the distances of all of its sides and edges. The lenght of all a form's sides can be added up to find its perimeter. A rectangle that is 24 yards long and 15 yards broad, for instance, will have a perimeter of 78 yards.

Here,

A man can cover 6 miles on foot in 2 hours.

A man will cover 3 miles on foot in one hour.

10 potatoes can be sliced by a machine in 5 minutes.

2 potatoes can be cut by a machine in a minute.

Those are

2 inches per thirty feet

By 30 multiply both sides.

1 foot Equals 2/30 inches.

Now,

1 foot Equals 2/30 inches.

180 times on both sides.

180 feet = 180 x 2/30 inch

180 feet equals 6 by 2 inches.

120 feet equals 12 inches.

Thus,

Considering that a foot equals two inches, a sports arena's height would be 180 feet.

The scale model of both the sports stadium has a 12 inch height.1 foot Equals 2/30 inches.

Now,

1 foot Equals 2/30 inches.

180 times on both sides.

180 feet = 180 x 2/30 inch

180 feet equals 6 by 2 inches.

120 feet equals 12 inches.

Thus,

Considering that a foot equals two inches, a sports arena's height would be 180 feet. The scale model of both the sports stadium has a 12 inch height.

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Answer:

[tex]\huge\boxed{\sf H=18.4\ cm}[/tex]

Step-by-step explanation:

Base = 7 cm

Perpendicular = 17 cm

Hypotenuse = H

[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2\\\\(H)^2=(7)^2+(17)^2\\\\(H)^2=49+289\\\\(H)^2=338\\\\Take \ square\ root \ on \ both\ sides\\\\\sqrt{(H)^2} =\sqrt{338} \\\\H=18.4\ cm\\\\\rule[225]{225}{2}[/tex]

Any set of ordered pair cannot be called as a function , the ordered pairs that in which no two different ordered pairs have the same x coordinate is called as a Function .

What is a Function ?

The set of ordered pair (x,y) is called a function, in which no two different ordered pairs have the same x coordinate. and the equation that produces such a set of ordered pairs can be called as function.

For Example : Let us Consider ordered pairs , F = [tex][(1,5) , (3,6)][/tex] ;

we see that ,  the element 1 has the image as 5 , and the element 3 has the image as 6 .

So , we can conclude  that , the each value of x has exactly only one corresponding value of y .

Therefore , the ordered pair can be called as a function .

The given question  is incomplete , the complete question  is

Is any set of ordered pair is called a Function ?

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when x is 0.5 then y value is 3, x is 1.5 then y is 9 and x is 4.5 then y is 27.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other

In the given table the value of x is 0.5 and value of y is 3

y/x=3/0.5=6

In the second row the value of x is 1.5 we need to find value of y.

3/0.5=y/1.5

4.5=0.5y

Divide both sides by 0.5

y=9

In third row the value of x is 4.5 and y is 27

Hence, when x is 0.5 then y is 3, x is 1.5 then y value is 9 and x is 4.5 then y is 27.

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The expression equivalent to - 8.2 - 5 is - 8.2 + (-5)

What is an expression?

A mathematical expression is a phrase that includes at least two numbers or variables, and at least one arithmetic operation. The mathematical operations used can be addition, subtraction, multiplication or division.

Note ,

         - × - = +

         - × + = -

         + × + = +

For the expression - 8.2 - 5

In the above expression, we are subtracting positive integer 5 from -8.2

  So we get the answer as

                 -8.2-5 = = -13.2

Now this is the solution we should get while solving the given options.

  a) 5 - ( -8.2)  = 5 + 8.2 = 13.2

  b) -8.2 + 5 = - 3.2

  c) -8.2 -5 [tex]\neq[/tex] 8.25 (as seen above)

   d) - 8.2 + ( -5) = -8.2 - 5 = -13.2

Comparing the solutions, we get that option(d) matches with the required answer.

Therefore option(d) is the correct expression that gives the same answer.

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The equation which gives infinite solutions, x-10+x = 8+2x-18.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

For the infinite solution the both side of equation must contain equal quantity.

For example,

x-10+x = 8+2x-18

now, solving for x

x-10+x = 8+2x-18

2x-10 = 2x-10

-2x = -2x

-10 = -10

As, both sides are equal  which shows the system of equation.

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The value of 27 5/3 in simplest radical form will be 86 / 3.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Here the value of 27 5/3 in simplest radical form will be the calculated thus:

(27 × 3) + 5 / 3

= (81 + 5) / 3

= 86 / 3

The value in radical form will be 86 / 3.

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The final solution of the given integral ∫ ([tex]x^3[/tex] - 2) dx is ([tex]x^4[/tex])/4 - 2x + C.

To integrate ∫ (x^3 - 2) dx, we use the power rule of integration, which states that ∫[tex]x^n[/tex] dx = ([tex]x^{(n+1)}[/tex])/(n+1) + C, where C is the constant of integration.

In this case, we have [tex]x^3[/tex] as the inside function, so we apply the power rule by raising the exponent by 1 and dividing by the new exponent. This gives us ([tex]x^4[/tex])/4 + C as the antiderivative.

However, we also have the constant term -2. To integrate a constant term, we add it as a separate term to the antiderivative. So the final solution is ([tex]x^4[/tex])/4 - 2x + C.

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Answer:

To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area......

Step-by-step explanation:

If Amy walked 25 seconds, she travelled 150 feet.

The definition of direct proportion states that "When the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease, then the two quantities are said to be in a direct proportion". which means the ratio of two quantities is constant.

Given, In table

Relationship between distance and time of Amy travel is given

Feet   Second

 18           3

48           8

 c           25

From the above table ratio between distance and time = Distance/ Time

= 18/3 = 48/8 = c/25

= 6/1 = 6/1 = c/25

⇒ c/25 = 6/1

⇒ c = 6 × 25 = 150

So, In 25 seconds distance will be 150 feet.

Hence, in 25 seconds Amy will travel 150 feet.

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The three steps of factoring include taking the common component out of the polynomial then simplifying the polynomial such that the most simple values are left and finally rearrangement.

If we are provided with the polynomial that is very complex in nature then first thing we have to do in order to solve the problem related to that polynomial is to factorise the polynomial.

The factory of that particular polynomial can be done by taking out the most common component out of the polynomial in a multiplication.

After this we have to simplify the polynomial such that only the simplest values are left in the polynomial and finally we have to rearrange the polynomial because after such operations on that polynomial the polynomial will not be easy to understand in the first look of it.

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The jazz band has 15 seventh graders playing according to the ratio.

A ratio, which is a number, is a way to represent one quantity as a portion of another. A ratio can only be compared when the two numbers in it have the same unit. To compare two objects, ratios are utilized.

Given One fifth of the 75 seventh graders at Charles School participate in the jazz band.

Presented as a ratio

75 pupils, or 1/5 of them, participate in the jazz band.

75 pupils out of the total play in the jazz band.

15 kids in total participate in the jazz band.

15 seventh graders are therefore playing in the jazz band in accordance with the ratio.

Hence, The jazz band has 15 seventh graders playing according to the ratio.

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Answer:

P=Ix100/RT

therefore P is made the subject formula

The missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.

What is the missing number?

Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them.

let's take a look at pebbles along each part of the path, there is 1 number of addition to each pebble number to go on next pebble.

i.e. 12, 13, 14, 15, 16, 17

so, the missing numbers are 14 and 17.

now, as given Hansel and Gretel used a pebble to mark every 10 steps as they walked along the path. How many steps have they taken when they get to the last pebble on this part of the path?

so, to go on next pebble there are 10 steps to walk.

therefore, from starting pebble  number 12 to last pebble number 17, there are 50 steps ( difference between two pebbles is 10 steps).

hence, the missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.

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Answer:

  30%

Step-by-step explanation:

You want the percentage reduction each year that will result in a reduction of 51% over two years.

The growth factor is 1 added to the growth rate. If the desired growth rate over 2 years is -51%, then the growth factor for that period is ...

  1 -51% = 0.49

If the growth factor is the same for each of two years will be ...

  (1 +r)² = 0.49 . . . . . . . where r is the growth rate each year

Solving for r gives ...

  1 +r = √(0.49) = 0.7

  r = 0.7 -1 = -0.3 = -30%

The required growth rate each year is -30%.

The pollution must be reduced by 30% each year for 2 years.

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Answer:

7) B.

8) D.

Step-by-step explanation:

The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the function. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.

What is a function?

A mathematical phrase, rule, or rule that establishes the link between explanatory variables or a dependent variable  In mathematics, curves exist everywhere, and they are crucial for constructing physical links in the sciences.

A Method can be defined by a module, an object, or another function. An internal feature of a class is called a method. Methods are listed inside a base class to make the connections between it class and thus the method clear. A method can be called or invoked using different syntax. We can convert a type into an object before being able to access its methods.

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Answer: 30,000

Step-by-step explanation:

150,000 x 0.2 = 30,000

The expression  [tex]$1\frac{2}{7}x -1=26[/tex]  gives {x} value as equivalent to 21.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the expression as -

[tex]$1\frac{2}{7}x -1=26[/tex]

We can write the expression as -

(9/7)x - 1 = 26

(9/7)x = 27

x = (27 x 7)/9

x = 3 x 7

x = 21

Therefore, the expression  [tex]$1\frac{2}{7}x -1=26[/tex]  gives {x} value as equivalent to 21.

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