A right triangle has a hypotenuse
with length 17 and a leg with
length 10. How long is the
triangle's other leg?

In a figure we can see that 0.7 and0.70 are equivalent, we have shade in the figure.

Given that,

To illustrate that 0.7 and 0.70 are equivalent, shade the models.

We have 0.7

We can say 7/10

For example, take a square and divide it by 10 part in column and shade 7 column.

Draw horizontal lines connecting the model's dots using a ruler.

Now divide it into 100 equal pieces.

So,

70/100

Shade the 7 rows and column.

Shaded at 70 or 0.70.

Therefore, in a figure we can see that 0.7 and0.70 are equivalent.

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 55.5000.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation: 8 x = 444

We are given that 8 x = 444            —- 1

x = 444 / 8

= 55.5

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 55.5000.

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The total amount did he earn this month is $3125.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Dave earns his salary by making a 12.5% commission.

sales= $25000 this month.

According to given question we have

The basic formula is

Sales × Commission Percent/100 = Commission

$25000  ×12.5/100= Commission

Commission=$3125

Therefore, the total amount did he earn this month is $3125.

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Step-by-step explanation:

you can ask any questions for clarification

1.

[tex] 2x {}^{2} + 17x + 35 \\ = 2x {}^{2} + 10x + 7x + 35 \\ = 2x(x + 5) + 7(x + 5) \\ = (2x + 7)(x + 5)[/tex]

2.

[tex]2y {}^{2} - 5y - 3 \\ = 2y {}^{2} -6y + y - 3 \\ = 2y(y - 3) + 1(y - 3) \\ = (2y + 1)(y - 3)[/tex]

3.

[tex]3x {}^{2} - 8x + 4 \\ = 3x {}^{2} - 6x - 2x + 4 \\ = 3x(x - 2)( - 2)(x - 2) \\ = (3x - 2)(x - 2)[/tex]

The solution of system of equations is (1,-1).

Given that the system of equations is x+5y=-4, x+6y=-5.

The system of equations can be written in matrix form as

x+5y=-4

x+6y=-5

[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]

Write the matrix on the left as the product of coefficients and variables.

[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]

Firstly, find the inverse of the coefficient matrix.  

The inverse of [tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right][/tex] is

[tex]\begin{aligned}\left[\begin{array}{ll}1& 5\\ 1&6\end{array}\right]&=\frac{1}{6(1)-5(1)}\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right] \\ &=\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right]\end{aligned}[/tex]

Next, multiply each side of the matrix equation by the inverse matrix .  Since matrix multiplication is not commutative, the inverse matrix should be at the left on each side of the matrix equation.

[tex]\begin{aligned}\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{l}-4\\ -5\end{array}\right]\\ \left[\begin{array}{ll}1&0\\ 0&1\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{l}1\\ -1\end{array}\right]\end{aligned}[/tex]

The identity matrix on the left verifies that the inverse matrix was calculated correctly.

[tex]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}1\\ -1\end{array}\right][/tex]

The solution is (1,-1).

Hence, the solution of the system of equtions using matrix is x+5y=-4, x+6y=-5 is (1,-1).

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Yo what up?, Answer:

2/3 yards.

Best Explanation Possible:

Nothing lol just do the math.

1/6 x 4 = 4/6 = 2/3 of a yard per hour

LOL have a good day hope you do good in school kiddo.

Answer:70

Step-by-step explanation:

70 divided by 5 equals 14

1st - 3

2nd-1

3rd-4

5th-2

Answer:

Eighth Grade ( [tex]\frac78[/tex] )

Step-by-step explanation:

The larger the denominator is, the smaller one "piece" of it is.
If we imagine a cake, for instance, then one piece of a cake that is split into 8 pieces would be smaller than a piece of a cake that is split into 7 pieces.

Therefore, if the piece is smaller, the closer the fraction is to being equal to 1, meaning, [tex]\frac78 > \frac67[/tex]

The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.

Let Jackie wants to make x necklace and y bracelets.

Now, Since it take her half an hour to make a necklace and one hour to make a bracelet.

Also since she has fewer than 20 h total to work on the jewelry. So we have

0.5x + 1y < 20

=> 0.5x + y < 20

and she want at least twice as many bracelets as necklace, so we have

y ≥ 2x

also the number of necklace should be greater than 0. So x > 0

So the required inequalities are:

0.5x + 1y < 20

y ≥ 2x

and x > 0

Hence, The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.

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The the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6 is 7x + y + 8 = 0.

A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

The equation of a line parallel to a given line will have the same slope as the given.

The equation of a line having a slope m and passing through the point (x', y') is written as

y - y' = m (x - x').

This is called point - slope equation of a straight line.

In the given equation,

14x+2y=6

⇒ 2y = -14x + 6

⇒ y = -7x + 3

Comparing it with standard equation of a straight line; y = m x + c, the slope m of the given line = -7

Therefore equation of the line parallel to the given line and passing through point (x', y') = (2, -10) would be:

y - (-10) = -7x + 2

⇒ y + 10 = -7x + 2

⇒ 7x + y + 8 = 0

Hence the required equation of line 7x + y + 8 = 0

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Answer:

associative property

Step-by-step explanation:

because the variables match

Reyna will need 0.048 quart of orange juice.

In this question, we have been given a recipe for a punch call for 12 fluid ounces of orange juice.

Reyna needs to make 4 batches of punch for a party.

We need to find number of quarts of orange juice Reyna will need.

From given conditions, we formulate:

= 4 × 12 ÷ 1000

= 12 ÷ 250                  .................(Separate out the common factor)

= 6/125

= 0.048 quart

Therefore, Reyna will need 0.048 quart of orange juice.

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Answer:

12.56 km

Step-by-step explanation:

C = 2πr

= 2 x 3.14 x 2

= 12.56 km

Answer:

12.56km or 12,560m

Step-by-step explanation:

c = 2πr
c = (2)(3.14)(2)
c = (6.28)(2)
c = 12.56

The property with each of Tyrone's steps for solving the equation is;

4x = 2 - 4(2 - 3x)

4x = 2 - 8 + 12x

4x = - 6 + 12x

4x - 12x = -6

-8x = - 6

x = -6 / - 8

x = 3/4

Therefore, the solution to Tyrone's equation for x is 3/4

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Answer:

3 i  √7

Step-by-step explanation:

sqrt (-63)  = sqrt ( -1 * 3 * 7 *3) =  sqrt (-1) * 3 * sqrt 7 =  3 i sqrt 7  

The wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.

We are given that the area of the pond = 22,000 square feet

Area = 22,000 feet²

π r² = 22,000

22 / 7 r² = 22,000

r² = 22000 × 7 / 22

r² = 7000

r = √ 7000

r = 10 √70

r = 83.76 feet

Also, since the wave travels 16 feet per second,

Time taken to cover the entire area = 83.76 / 16 = 5.23 seconds

The diameter of the lake = 83.76 + 83.76

d = 167.52 feet

Therefore, we get that the wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.

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Question 15:

Option B is the correct answer

If the Patriots win their division, then they will go to the playoffs:

- Invalid conclusion was made.

Question 16:

Option D is the correct answer.

Conclusion: Ethan's boy scout dues are free:

- Drawn using the law of detachment.

The Law of Detachment states that we must detach ourselves from the outcome in order to allow what we desire to materialize in the physical universe.

Example:

If p equals q and p is also true. Then q is true.

We have,

- If the Patriots win their next game, then they will win their division.

- If the Patriots win their next game, then they will go to the playoffs.

Each statement's conclusion is drawn using the law of detachment.

Therefore, if the patriots win their division, then they will go to the playoffs is an invalid conclusion made.

Ethan sold $1000 worth of popcorn.

Conclusion: Ethan's boy scout dues are free.

This conclusion was drawn using the law of detachment.

Thus,

Therefore, if the patriots win their division, then they will go to the playoffs: - Invalid conclusion made.

Conclusion: Ethan's boy scout dues are free:

- Drawn using the law of detachment.

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Answer:

Q= (1, -1), R = (7,-1), S = (7,-10), P =. (1,-10)

Step-by-step explanation:

Look at the coordinate grind then look at the coordinates (x) vertically, then look at the coordinates(y) horizontally.

then plot it as (x, y)

Answer:

x=0

Step-by-step explanation:

12 = -4(-6x-3)

12 = 24x+12

-12         -12

0 = 24x

/       /

24   24

0 = x

Check

12 = -4(-6(0)-3)

12 = -4(0-3)

12 = 0 + 12

12 = 12

200+10=210 this is the answer

please like it if it is correct

The estimated value of 197 + 10.3 is 210.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

197 + 10.3

Now, rounding off nearest 10

197---> 200

and, 10.3 ----> 10

So, 197+ 10.3 = 200+ 10 = 210

Hence, the estimated value is 210.

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The value of the expression (4x^6) * 3y^5/6x^3y^3 is 2x^3y^2

The expression is given as

(4x^6) * 3y^5/6x^3y^3

Divide 3 and 6 by 3

So, we have

(4x^6) * 3y^5/6x^3y^3 = (4x^6) * y^5/2x^3y^3

Apply the law of indices to the exponents

(4x^6) * 3y^5/6x^3y^3 = (4x^6) * y^2/2x^3

Remove the bracket

(4x^6) * 3y^5/6x^3y^3 = 4x^6 * y^2/2x^3

Divide 4 and 2 by 2

So, we have

(4x^6) * 3y^5/6x^3y^3 = 2x^6 * y^2/x^3

Apply the law of indices to the exponents

(4x^6) * 3y^5/6x^3y^3 = 2x^3y^2

Hence, the value of the expression (4x^6) * 3y^5/6x^3y^3 is 2x^3y^2

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The answer to the formula are-

Part 1:  7√6 - 4√6

As both the digits have the same value √6. It means they can simply be added with sign to solve.

=  7√6 - 4√6

Take √6 common from both;

= √6(7 - 4)

= 3√6

Thus, the simplification of the expression is 3√6.

Part 2: -0.7√7 + 2.3√7

Here, also the common term is √7.

= √7( -0.7 + 2.3)

Simply add the number with sign.

= 1.6√7.

Thus, the simplification of the number is 1.6√7.

Part 3: √45 + √20

In thus, first write the number in its prime factors;

= √3×3×5 + √2×2×5

Take the root of 3 and 2 from the first and second digits of expression.

= 3√5 + 2√5

Now, both have the same term √5.

= √5(3 + 2)

Do the addition;

= 2√5

Thus, the simplification of given expression is 2√5.

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482 rounded off to nearest 100 is 500 and 482 rounded off to nearest 1000 is zero.

By maintaining a number's value while moving it closer to the next number, rounding off makes the number easier to understand. It is done for entire numbers as well as decimals at different places such as hundreds, tens, and tenths. To maintain the major figures, numbers are rounded off.

At a concert there were 482 people in the audience:

(a) With a number line, 482 was rounded to the nearest hundred.

(b) Since 4 is the hundredth value of 482 and there is no previous thousand to 499. So when 499 is rounded to the nearest thousand, equals 0.

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Shape Y has a volume of 3200 cm3.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

Scale Factor Formula

Scale up (Smaller to larger) =  (lager figure measurement)/(smaller figure measurement)

Scale down (Larger to smaller) = (smaller figure measurement)/(larger figure measurement)

A ratio greater than 1 is the scale factor for scaling up. A ratio of less than 1 is the scale factor for scaling down.

Given data:

The total surface area of shape X is 450 cm².

The total surface area of shape Y is 800 cm².

The volume of shape X is 1350 cm³.

Scale Factor for Area = (Surface area of shape x)/(surface area of shape y)

=450/800

=16/9

Scale factor for Length = [tex]\frac{\sqrt{16}}{\sqrt{9} }[/tex]

= 4/3

Scale factor for volume =4³/3³

= 64/27

Volume of shape y = volume of shape x*scale factor for volume

=1350×(64/27)

=450×(64/9)

=50×64

=3200 cm³.

Therefore, the volume of shape Y is 3200 cm³.

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After solving the given equation 3²x=6561, the value of x=729.

So,

Then,

Therefore, after solving the given equation 3²x=6561, the value of x=729.

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Answer:

0.1 or 1/10

Step-by-step explanation:

-2/5 + 1/2 is also - 4/10 + 5/10 which is 1/10

Step-by-step explanation:

-2x2/5x2+1x5/2x5

-4/10+5/10

1/10