Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
A. 8,12,15
B. 10,24,26
C. 12,20,25
D. 15,18,20

Answer:

The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

Step-by-step explanation:

It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.

The scale for drawing is

[tex]Scale=\frac{\text{Length in drawing}}{\text{Actual length}}=\text{Length in drawing}:\text{Actual length}[/tex]

First possible scale for the drawing is

2 inch : 6 feet

It can be written as

1 inch : 3 feet

We know that 1 feet = 12 in

1 inch : 36 inch

We know that 1 feet = 30.48 cm

1 inch : 91.44 cm

Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

Here, we have,

It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.

The scale for drawing is

scale = length in drawn/actual length

scale = length in drawn : actual length

First possible scale for the drawing is

2 inch : 6 feet

It can be written as

1 inch : 3 feet

We know that 1 feet = 12 in

1 inch : 36 inch

We know that 1 feet = 30.48 cm

1 inch : 91.44 cm

Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

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1 foot = 12 inches

 divide 69 by 12

69/12 = 5.75 feet

Final answer:

To solve an algebraic equation, identify knowns, find suitable equations, simplify algebraically, substitute known values, solve for the unknown, and check if the answer is reasonable.

Explanation:

To solve an algebraic equation, follow these systematic steps:

Firstly, identify the knowns and make a list of what is given or can be inferred from the problem.

Then, find the appropriate equation or set of equations that contain the unknown you need to solve for.

Simplify the algebra by eliminating terms wherever possible. This might require algebraic rearrangement such as dividing terms or multiplying both sides of the equation to isolate the unknown.

Substitute the known values into the equation.

Solve for the unknown and make sure to include units where necessary.

Finally, always check your answer to see if it is reasonable and makes sense.

These steps should yield a solution that is both accurate and verifiable.

We know that we are solving for y.

This is a step by step procedure to get the value of y.

First: Move all terms to the left side and set equal to zero.

Second: Then set each factor equal to zero.

The application is:

Given: py+7=6y+q 

-6y -7 -6y -7 = 0

(p-6)y = q-7

divide both sides by p-6
y=(q-7)/(p-6)

Answer is y = (q – 7) / (p – 6) 

The solution of expression for y as,

⇒ y = (q - 7) / (p - 6)

We have to given that,

An expression is,

⇒ py + 7 = 6y + q

Now, We can simplify the expression for y as,

⇒ py + 7 = 6y + q

Subtract 6y both side,

⇒ py - 6y + 7 = 6y + q - 6y

Subtract 7 both side,

⇒ py - 6y = q - 7

⇒ y (p - 6) = (q - 7)

Divide both side by (p - 6);

⇒ y = (q - 7) / (p - 6)

Therefore, The solution of expression for y as,

⇒ y = (q - 7) / (p - 6)

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we know that

If two lines are perpendicular, then the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

In this problem we have

[tex]m1=\frac{2}{3}[/tex]

Substitute in the formula and solve for m2

[tex]\frac{2}{3}*m2=-1[/tex]

[tex]m2=-\frac{3}{2}[/tex]

therefore

the answer is

The slope is equal to [tex]-\frac{3}{2}[/tex]

Two positive integers x and y

x - y = 4

x² + y = 68

x and y

Add the two equations together.

... (x - y) + (x² + y) = (4) + (68)

... x² + x = 72

Rearrange to standard form and factor.

... x² + x - 72 = 0

... (x + 9)(x - 8) = 0

Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.

... x + 9 = 0 ⇒ x = -9

... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution

Then we can find y from

... 8 - y = 4

... y = 4 . . . . . . . add y-4 to the equation

The two positive integers are 8 and 4.

To solve for the two positive integers where their difference is 4 and the sum of the smaller and the square of the larger is 68, we set up a quadratic equation and solve for n to find that the integers are 4 and 8.

The problem given is a classic algebra question where we are asked to determine two positive integers based on their relationship to each other and an additional numeric condition. We know that the difference between these two numbers is 4, and when the smaller integer is added to the square of the larger, the result is 68.

Let's denote the smaller number as n and the larger number as n+4, since there is a difference of 4 between them. Now, according to the second condition given, we can set up the following equation: n + (n+4)2 = 68.

Expanding the squared term and combining like terms, we get a quadratic equation: n2 + 8n + 16 + n = 68. Simplifying, n2 + 9n + 16 = 68. Further simplification leads to n2 + 9n - 52 = 0. Factoring this quadratic equation, we find the integers that satisfy the equation: n = 4 and n = -13. Since we are looking for positive integers, the solution is n = 4 and n+4 = 8.

Therefore, the two positive integers are 4 and 8.

There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.

The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.

To find the number of multiples of 70 in that range, you can use the following steps:

Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.

Answer:

2300

Step-by-step explanation:

Answer:  The required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.

Step-by-step explanation:  Given that the  second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side.

The perimeter of the deck is 68 ​feet.

We are to find the lengths of the three sides of the deck.

Let x feet be the length of the shortest side.

Then, according to the given information,

the length of the second side = (x+6) feet

and

the length of the third side = (2x-6) feet.

Since the perimeter of the deck is 68 feet, so we must have

[tex]x+x+6+2x-6=68\\\\\Rightarrow 4x=68x=\dfrac{68}{4}\\\\\Rightarrow x=17.[/tex]

Therefore the lengths of the three sides are

  17 feet, (17+6) feet and (2×17-6) feet

= 17 feet, 23 feet and 28 feet.

Thus, the required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.

88ft/s

hop this helps