9. Construct Arguments Al made a tree house last summer. He started by
making a model. The model included a window with a height of inch
and a width of inch. The actual window had a height of yard and a
width of yard. Was Al's model an accurate representation? Explain.

The best estimate of the cost of renting a car if you plan to drive 268 miles is 234.72 or round off to 235 dollars.

There must be an equal sign (=) in an equation. You can imagine an equation as having a left side and a right side since there will be a mathematical expression on either side of it. Unknowns are a necessary part of algebraic equations. A symbol, such as x, y, or z, is used to symbolize this.

According to the given values in the question,

y = 0.54x + 90

Where y represents the cost of renting the car and x represents the number of miles.

The plan is to drive 268 miles, so the cost according to that will be :

y = 0.54(268) + 90

y = 234.72 or,

y = 235.

Hence, the round-off cost will be 235 dollars.

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The value of cos I as a fraction in simplest terms is 4/5.

This is a problem based on trigonometry. Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles. The length of the hypotenuse is 25. The length of the perpendicular is 15. The length of the base is unknown. We know that the angle ∠IJK = 90°.

We need to find the value of Cos(I). But we don't know the value of the length of the base of the triangle. So, we will first find Sin(I).

Sin(I) = 15/25

Sin(I) = 3/5

We know the trigonometric identity that Sin²θ + Cos²θ = 1.

Sin²I + Cos²I = 1

Cos²I = 1 - Sin²I

Cos²I = 1 - (3/5)²

Cos²I = 1 - (9/25)

Cos²I = (25 - 9)/25

Cos²I = 16/25

Cos(I) = √(16/25)

Cos(I) = 4/5

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Answer:

pretty sure it's -7/4, hope this helps

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x).Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

What are a relationship's domain and range?

Each given relation's scope and domain are as follows:

1. Range: 0.0, 0.5, 1.0,1.5,2.0 Domain: -10,-5,o,5,10

As a result, each relation's domain and range are as follows:

Domain  -10,-5,o,5,10

Range  0.0, 0.5, 1.0,1.5,2.0

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Answer:

Step-by-step explanation:

Given conditional:

→ If a number is a natural number, then is it also a whole number.

If P then Q.

P= "a number is a natural number"-hypothesis

Q="is it also a whole number"-conclusion

Inverse negates both the hypothesis P and the conclusion Q.

If not P then not Q.

→ If a number is not a natural number, then is it also not a whole number.

Converse interchanges hypothesis P for the conclusion Q.

If Q then P.

→ If a number is a whole number, then is it also a natural number.

Contrapositive interchanges hypothesis for the conclusion of the inverse

or negates both the hypothesis and conclusion of converse.

If not Q then not P.

→ If a number is not a whole number, then is it also not a natural number.

Biconditional

P if and only if Q

→ A number is a natural number if and only if is it also a whole number.

Step-by-step explanation:

I assume this actually is

revenue : R(x) = 12x

cost : C(x) = 5x + 20

profit : P(x) = R(x) - C(x) = 12x - 5x - 20 = 7x - 20

Answer:

x³ + 8x² + 11x - 20

Step-by-step explanation:

(x + 5)(x² + 3x - 4) =

= (x + 5)[x² + 3x + (-4)] =

= (x + 5)(x²) + (x + 5)(3x) + (x + 5)(-4)

= x³ + 5x² + 3x² + 15x + (-4x) + (-20)

= x³ + 8x² + 11x - 20

If the tringle of the grid translated by using the rule ( x, y) = (x+5, y-2)  the coordinate of b'  is (0,-2).

we know that

the coordinates of point B ( -5,0)

the translation has the following rule

(x,y)--------> (x+5, y-2)

so

(-5,0)-----> (-5+5,0-2)-----> (0,-2)

coordinates is defined as a pair of numbers that describes the exact location of a point on a rectangular plane using horizontal and vertical lines called coordinates. In general, (x, y) represents the x and y value of a point on a graph. Each point or ordered pair contains two coordinates.

the x-coordinate is called the abscissa and the y-coordinate is called the order. Both coordinates (x, y) represent a point on the plane.  

Three coordinate systems are commonly used:

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If Fred and Bob share sweets in the ratio 3:7, Bob gets 48 sweets more than Fred. There are 120 sweets in total.

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

By given

Fred and Bob share sweets in the ratio 3:7 ,Bob gets 48 sweets more than Fred.

Let x be the sweets with Fred.

Let us form a equation by the given data

3/7=x/(x+48)

Apply cross multiplication

3(x+48)=7x

Apply distributive property on left side.

3x+144=7x

Subtract 3x from both sides.

144=7x-3x

144=4x

Divide both sides by 4.4

x=36

Fred has 36 sweets and Bob has 36+48=84 sweets.

The total number of sweets is 36+84

120

Hence there are 120 sweets in total.

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Answer:

200

Step-by-step explanation:

1000/5
Cancel the common factor of 1000 and 5.

Answer:

The width is 72

Step-by-step explanation:

Answer: 20.51%

Step-by-step explanation: This question uses the binomial distribution.

210/1024=105/512≈0.2051

The greatest common factor of 24,40 and 72 is 8, which is correctly found by Brenden.

Given the numbers for which the GCF is to be found are:

24,40 and 72.

first take out the least common factors of the numbers:

24 = 2×2×2×3

40 = 2×2×2×5

72 = 2×2×2×3×3

When two or more numbers are supplied, the GCF (Greatest Common Factor) is the sum of all the common factors, which is the largest number. The greatest integer that can divide both x and y evenly and leave no leftover is the GCF of two natural numbers, x and y. Division, multiplication, and prime factorization are the three common methods used to determine GCF.

so the GCF is 2×2×2 = 8

we should choose Brendon.

Hence the correct GCF is 8, computed by Brendan.

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Answer: Brendan

Step-by-step explanation: I took the quick check trust me

In order to find the quotient and remainder of the division, let's divide the polynomials doing the following steps:

x³ divided by x: x².

x² times (x + 2): x³ + 2x²

x³ + 6x² + 17x + 11 minus (x³ + 2x²): 4x² + 17x + 11

4x² divided by x: 4x

4x times (x + 2): 4x² + 8x

4x² + 17x + 11 minus (4x² + 8x): 9x + 11

9x divided by x: 9

9 times (x + 2): 9x + 18

9x + 11 minus (9x + 18): -7

Therefore the quotient is x² + 4x + 9 and the remainder is -7

Correct option: first one.

Answer:

15/20-8/20

Step-by-step explanation:

3/4-2/5=0.35

15/20-8/20=0.35

It is equivalent.

Taking out the equation of line in the given questions

What is Slope-Intercept?

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis)

9) slope = 2/3 and points (-1, 2)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

2 = (2/3)(-1) + b

2 = (-2/3) + b

2 + 2/3 = b

(6 + 2)/3 = b

4/3 = b

so slope intercept form is y = (2/3)x + 4/3

10) slope = 5/4 and points (12,15)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

15 = (5/4)(12) + b

15 = (5)(3) + b

15 = 15 + b

15 - 15 = b

b = 0

so slope intercept form is y = (5/4)x + 0

11) slope = 4 points (0, -1)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

-1 = 4(0) + b

-1 = 0 + b

-1 = b

so slope intercept form is y = 4x - 1

12) slope = -1/4 and (1,-1)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

-1 = (-1/4)(1) + b

-1 = -1/4 + b

1/4 - 1 = b

(1 - 4)/4 = b

-3/4 = b

so slope intercept form is y = (-1/4)x - 3/4

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Answer:

The answeris -35/10

Step-by-step explanation:

Answer:54.98783

Step-by-step explanation:

1 times a number is just the number itself.

Nadeem plans to ride her bike between 12 mi and 15 mi. The hours Nadeem will be riding.

12mi ≤ x ≤ 15mi

Thus, the inequality is:

Inequalities are connections between non-equal expressions. Inequalities utilize <, >, and. reads "7 is bigger than" (or "is less than 7," right to left).

If we define x as the number of miles she can bike, the minimum is 12 miles, hence x may be more than 12 miles.

12 mi ≤ x

Since her maximum ride is 15 miles, x might be less than or equal to 15 miles:

x ≤ 15 mi

We get:

12mi by 15mi

In conclusion, we know her riding range.

12mi ≤ x ≤ 15mi

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So if you let x and y be the two numbers...

the sum of the two means you add them together... so you get:

x+y=56: the difference means you subtract them.. so

x-y = 16

now you have two equations and two unknowns... which you can solve with various methods... you can use elimination, substitution, or trial and error.

x+y=56

x-y = 16

I will use the elimination method: Because there is a plus y and a negative you cancel that out and add the 2x's. Therefore:

2x=72

x=36

Now, you can plug 36 into one of your original equations:

36+y=56

y=20

Those are your two numbers!

Answer:

If its asking what kind of slope it would be an undefined slope  

Step-by-step explanation:

The probability least 1 zodiac sign match astrological signs is just the product of (12/12)(11/12 … (8/12).

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated.

The probability that in a group of five friends, at least two share the same astrological sign

= 1 - the probability that all five friends have different astrological signs

= 1 - (12/12)(11/12)(10/12)(9/12)(8/12)

= 1 - 12P5/125

= 1 - 0.381944

= 0.618056

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The rectangle's area varies by 4%.

What is the area?

The area of a rectangle in such a two-dimensional plane is the area that it occupies.

It has length and breadth.

A quadrilateral, a form of a two-dimensional object with four sides plus four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees.

Length will be 20% longer with an increase, or 120%, or 1.2.

The breadth will indeed be 80% = 0.8 after being reduced by 20%.

Rectangle's area is equal to 1.2 x 0.8, or 0.96, or 96%.

% of the original area

As a result, the rectangle's area varies by 4%.

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In the quadratic equation f(x) = a(x - h)² + k , then the graph is given on the right

f(x) = [tex]-2 (x- 3)^{2} + 8[/tex]

According to the question, given that

the quadratic equation f(x) = a(x - h)² + k

Axis of symmetry : x = h = 3

The coordinates of the highest point is (3,8)  {it is the ordinate of the    highest point of the image}

so, k = 8

f(x) =  [tex]a (x- 3)^{2} + 8[/tex]

plug in (0,- 10)

       - 10 = 9a + 8

          a  = - 2

f(x) = [tex]-2 (x- 3)^{2} + 8[/tex]

Therefore, f(x) = a(x - h)² + k quadratic equation we get the value of f(x),

f(x) = [tex]-2 (x- 3)^{2} + 8[/tex]

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

The parent quadratic function connects the locations whose coordinates have the type f(x) = x2 and is of the kind (number, number2). This function, which normally has the form f(x) = a (x - h)2 + k, is capable of being transformed. It can also be changed to take the form f(x) = ax2 + bx + c.

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The height of the antenna is 0.54m.

Let the height of the antenna be represented by x, and the distance from Cai's eyes to the top of building A by y. And let z = x + y, so that:

Tan 24,

y = Tan 24 x 21

y = 0.4452 x 21

y = 9.3492

y = 0.93 m

Also, Tan 35,

z = Tan 35 x 21

z = 0.7002 x 21

z = 14.7042

z = 1.47 m

Therefore,

x = z - y

x = 1.47 - 0.93

x = 0.54

x = 0.54 m

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The system of equation are

y=-x²+2x-9

y=-6x+6

The solution of the system of equation is (5,-24) and (3,-12). Option-A is correct.

Given that,

The system of equation are

y=-x²+2x-9

y=-6x+6

We must identify the equation system's solutions.

A system of equations is a collection of equations with one or more variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.

Take the equation.

y=-x²+2x-9

y=-6x+6

We can write as

-x²+2x-9=-6x+6

-x²+2x-9+6x-6=0

-x²+8x-15=0

x²-8x+15

By solving the factorization we get the x values.

x²-5x-3x+15=0

x(x-5)-3(x-5)=0

(x-5)(x-3)=0

Take,

x-5=0    (or)    x-3=0

x=5        (or)    x=3

Take x=5 and substitute in the equation.

y=-6x+6=-6(5)+6=-30+6=-24

Take x=3 and substitute in the equation.

y=-6x+6=-6(3)+6=-18+6=-12

Therefore, The solution of system of equation is (5,-24) and (3,-12). Option-A is correct.

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Considering the measure of each "small square" 1 x 1:

Each side of the complete square (a) measure 3 units.

Thus, since the area (A) is A = a², the area is:

Answer: 9 sq units.

Answer:

15 ft

Step-by-step explanation:

3 ft / 2 in    *  10 in = 15 feet tall