The longest leg of a right triangle is 12 inches. The hypotenuse is 3 inches longer then twice the shortest leg. How long is the shortest leg and the hypotenuse of the triangle.

the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

We know that odd consecutive numbers means the difference between the numbers will be 2

So, let the first odd number be x

Second number will be = x + 2

Third number will be = x + 2 + 2 = x + 4

Now, we are given that, the sum of these odd integers is 153

So, we get the equation as:

x + x + 2 + x + 4 = 153

3 x + 6 = 153

3 x = 153 - 6

3 x = 147

x = 147 / 3

x = 49

Largest integer = x + 4 = 49 + 4 = 53

Therefore, we get that, the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

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Answer:

(x-3)^2 - 8, so a is 3 and b is 8

Step-by-step explanation:

use completing the square

hope this works :)

Answer:

2 units

Step-by-step explanation:

radius = diameter/2 -> r = 4/2 = 2 units

The value of JK is 12

From the diagram shown, we can see that;

But line JL is the line with JK and KL as the line segments and K the midpoint between J and K

This can be represented as;

JK + KL = JL

substitute the values into the equation, we have;

3x + 8 = 5x

collect like terms

3x - 5x = -8

subtract like terms

-2x = -8

makes 'x' the subject of formula

x = -8/-2

x = 4

But JK = 3x = 3(4) = 12

Thus, the value of JK is 12

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The multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.

At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another.

Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend.

Division has two parts dividend and divisor.

Division is not commutative, meaning that a / b is not always equal to b / a.

Division is also not, in general, associative.

Division is traditionally considered as left-associative.

Division is right-distributive over addition and subtraction.

Division is shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a fraction bar, between them. For example, "a divided by b" can written as:

a/b

Now it is given that,

5 divided by 1/3

This can be expressed as,

5 divided by 1/3 = 5 ÷ 1/3

Since to convert the division of fraction into multiplication, we reciprocate the fraction

So, applying division we get,

5 ÷ 1/3 = 5 x 3

So, the multiplication equation is,

5 x 3

Now multiplying 5 and 3 we get,

5 x 3 = 15

this is the required multiplication equation of 5 divided by 1/3.

Thus, the multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.

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Answer:

b = ± 5

Step-by-step explanation:

8b² = 200 ( divide both sides by 8 )

b² = 25 ( take square root of both sides )

b = ± [tex]\sqrt{25}[/tex] = ± 5

b = - 5 , x = 5

Answer:

The scale factor is 3.

Step-by-step explanation:

9÷3=6÷2

3=3

this makes the scale factor be 3.

If all agree that the fair outcome would be the one where each person gets four slices, then could be improved at the expense of each person equally.

In mathematics, it deals with numbers of operations according to the statements.

Here,

If all agree, that each of one should get an equal number of slices, then it can be concluded that each of them should pay an equal amount for the 4 pizzas.

Thus, if all agree that the fair outcome would be the one where each person gets four slices, then could be improved at the expense of each person equally.

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Answer:

0.89 g/cm³

Step-by-step explanation:

used the formula d=M/V

M is mass which is = 80g

V is volume which is = 90cm³

d = 80/90

d = 0.89 g/cm³

Answer:

x = -2

Step-by-step explanation:

Solve for x:

-5 x - 10 = -(x + 4) + 2

-(x + 4) = -x - 4:

-5 x - 10 = (-x - 4) + 2

Grouping like terms, -x - 4 + 2 = -x + (2 - 4):

-5 x - 10 = (-x + (2 - 4))

2 - 4 = -2:

-5 x - 10 = -x + -2

Add x to both sides:

x - 5 x - 10 = (x - x) - 2

x - x = 0:

x - 5 x - 10 = -2

Grouping like terms, x - 5 x - 10 = (-5 x + x) - 10:

((-5 x + x) - 10) = -2

x - 5 x = -4 x:

-4 x - 10 = -2

Add 10 to both sides:

(10 - 10) - 4 x = 10 - 2

10 - 10 = 0:

-4 x = 10 - 2

10 - 2 = 8:

-4 x = 8

Divide both sides of -4 x = 8 by -4:

(-4 x)/(-4) = 8/(-4)

(-4)/(-4) = 1:

x = 8/(-4)

The gcd of 8 and -4 is 4, so 8/(-4) = (4×2)/(4 (-1)) = 4/4×2/(-1) = 2/(-1):

x = 2/(-1)

Multiply numerator and denominator of 2/(-1) by -1:

Answer: x = -2

Answer:

Step-by-step explanation:

Distribute:

-5x - 10 = 2 - (x + 4)

-5x-10=2-x-4

x = -2

1.2 because you take 2 congruent sides of each shape and divide the larger one by the small one. in this example you could do

8.4÷7

36.6÷30.5

19.2÷16

they all give you 1.2

Step-by-step explanation:

-282.02 its korrect now

Using a system of equations, the amounts of each ticket sold are given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The theater sold 250 tickets, hence:

x + y + z = 250.

The theater brought in $2,825, hence, considering the value of each ticket:

15x + 10y + 8z = 2825.

The number of student tickets sold is twice the number of adult tickets sold, hence:

y = 2x.

Replacing in the first two equations:

Multiplying the first equation by -8 and adding with the second, we have that:

11x = 825

x = 825/11

x = 75.

Then:

The amounts of each ticket sold are given as follows:

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Answer:

Step-by-step explanation:

following the clarification in the comment

3x+2=2x+13 all divided by 3  (both side)

(3x + 2)/3 = (2x + 13)/3

3x + 2 = 2x + 13

x = 13 - 2

x = 11

--------------------

check

(3 * 11 + 2)/3 = 2 * 11 + 13)/3

3 * 11 + 2 = 2 * 11 + 13

35 = 35

the answer is good

Answer:

x = 2

y = 5

Step-by-step explanation:

-x - 3y = -17

2x - 6y = -26

--------------------

(-x - 3y = -17) × 2

-2x - 6y = -34

-------------------------

-2x - 6y = -34

2x - 6y = -26

-------------------------

       -12y = -60

       ÷-12      ÷-12

-------------------------------

               y = 5

-x - 3y = -17

-x - 3(5) = -17

-x - 15 = -17

    +15 + 15

--------------------

-x = -2

÷-1  ÷-1

-----------

x = 2

I hope this helps!

Answer:

5.5%

Step-by-step explanation:

answer:

7.65, 7.321, 7.3, 7.065

explanation:

on a number line, these numbers would be in order as shown above from right to left (decreasing value)

Answer:The order for the given decimal numbers, from the greatest to the least, is: D. 7.65, 7.321, 7.3, 7.065.

Step-by-step explanation:

Order the following numbers from greatest to least: 7.321, 7.3, 7.065, 7.65

7.065, 7.3, 7.321, 7.65

7.3, 7.321, 7.065, 7.65

7.321, 7.3, 7.65, 7.065

this is correct--> 7.65, 7.321, 7.3, 7.065

Answer: -48

Step-by-step explanation:

k/3 + 16

find the roots by factoring

which leads to -48

k/3 + 16

To add or subtract expressions, expand them so their denominators are the same. Multiply 16 by 3/3.

                   k/3 + 16 × 3/3

Since k/3 and 16 × 3/3 have the same denominator, we join their numerators to add them.

                          k + 16 × 3/3

We perform the multiplications in k+16×3.

                                         k + 48/3

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In a condition where Sophia needs to earn at least $1800 as a part of her living expenses, she will need to sell goods worth at least $16,745 if she earns 10.75% commission on everything she sells.

What is the significance of living expenses?

Living expenses of an individual can be referred to or considered as the amount of expenditure made by a person for living for a predefined period of time. The living expenses also include the spending towards the necessities of an individual.

In the condition given above, the provided information can be used in order to find out about the living expenses as,

Living Expenses = Sales x Commission

1800 = Sales x 10.75%

Sales = 1800 / 10.75%

Sales = $16,744.12

Therefore, the significance regarding the living expenses has been aforementioned.

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Answer:

-8/3 < -2 1/2 < 9/2 < 4 3/4

Step-by-step explanation:

-2.667 < -2.5 < 4.5 < 4.75

5 IS THE DERIVATIVE OF k(x)= 5x at x=10

The rate at which a function alters in relation to a variable is known as a derivative in mathematics. Problems involving calculus and differential equations need the use of derivatives.

f(x)=5x

∴f'(10)=f(10+h)−f(10)h

=5(10+h)−5(10)

= h→0/h

=[tex]\lim_{h\to 0}[/tex]5h/h

=[tex]\lim_{h\to 0}[/tex]5

=5.

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Answer:

If it is M x N then it is 161.

If it is 63 x M x N then it is 10,143.

Answer:

multiples of 14

Step-by-step explanation:

we multiply 7×2

Answer:

60

Step-by-step explanation:

divide 39 by 65%,

you will get
39 / ( 65/ 100)
= 39 * (100/65)
= 39 * (20 /13)
= 3*20
= 60

Answer:a

Step-by-step explanation:its a

Answer:

2, 20, 200, 2,000, 20,000, 200,000

Answer: 0.2, 0.02 0.002

Answer:

-143/12  or -11 11/12

Step-by-step explanation:

Convert each to improper fraction and multiply straight across (numerator times numerator, denominator times denominator)

-1 5/6 x 6 1/2

= -11/6  x  13/2

= -143/12

Answer:

-143/12 as a fraction and 11.916666666... (six repeating) as a decimal

Step-by-step explanation:

Turn into improper fractions.

(-6/6 + -5/6) = -11/6

2/2 + 2/2 +2/2 + 2/2 +2/2 + 2/2 + 1/2 = 13/2

-11/6 times 13/2

-11 times 13 = -143

6 times 2 = 12

-143/12 = 11.916666666... (six repeating)

Answer:

the answer is 70,007

Step-by-step explanation:

again the answer is 102,002

Answer:

Step-by-step explanation:

70007

The area of the six-sided polygon = 220.5 square ft.

Given that the six-sided polygon consists of two isosceles triangles and a rectangle. So the total area to be cut will be equal to the sum of areas of the triangles and the rectangle.

First triangle has base = 15 ft and height = 15 ft

Area of a 1st triangle = 1/2 x base x height

                             = 1/2 x 15 x 15

                             = 112.5 square feet

Second triangle has base = 4 ft and height = 4 ft

Area of the 2nd triangle = 1/2 x base x height

                                        = 1/2 x 4 x 4

                                        = 8 square ft

The rectangle has length = 25 ft and width = 4 ft

Area of the rectangle = length x width

                                    = 25 x 4

                                    = 100 square ft

So the total area of the six-sided polygon = 112.5 + 8 + 100

                                                                      = 220.5 square ft.

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