1. Find the length of each leg.
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Q
30⁰
4
60%
P

In mathematical notation, you can use the following format to write "9 more than a number":

total + 9

This indicates that you are adding 9 to the original number.

For instance, you can write "9 more than 5" as 5 + 9 = 14 if the integer is 5.

Another option is to use the format: 9 + number.

The outcome is the same as this.

If a variable, such as x, is used to denote the number, you can express "9 more than x" as x + 9 or 9 + x.

This way, you can use the same expression for any number.

  In general, when you want to find out a value which is 'x' more than a number 'a', you can use the following mathematical notation:

a + x

This is read as "a plus x".

So ,this  indicates that you are adding 9 to the original number.

  Therefore, the adding 9 to original number is the answer of this question.

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Answer:

hard one goof luck

Step-by-step explanation:

This kind of evidence is an example of a claim. Hence, the correct answer is option 1.

A claim is a statement or assertion that is made about a particular topic or issue. In this case, the statement is being made by "doctors" and is being presented as evidence of a causal relationship between lack of sleep and negative health outcomes. The statement is not an argument, which would include reasoning or logic to support the claim, nor is it a testimony or excerpt, which would be a statement or quote from a specific person or source.

Option 2, "an argument," is incorrect because it suggests that reasoning or logic is being provided to support the claim. However, in the sentence provided, there is no indication that any reasoning or logic is being presented to support the claim that many people who do not get enough sleep each night suffer from illness and stress. Usually, an argument has a claim and evidence or reasoning to back up that claim.

Option 3, "a testimony or an excerpt," is incorrect because it suggests that a statement or quote is being provided from a specific person or source. However, in the sentence provided, there is no indication of a specific person or source providing the statement. Instead, the statement is being attributed to "doctors" in general rather than any specific individual. A testimony would typically include a statement or quote from a specific person or source, given under oath or affirmation in a formal legal setting.

This question should be provided as:

Use the sentence to answer the question. Most doctors say many people who don't get enough sleep every night struggle with illness and stress. Which kind of evidence is this an example of? Responses:

 The correct answer is option 1.

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Parabola is called as a curve that is formed by the locus of a point whose distance from a fixed point and from a fixed line is the similar.

This set point is called focus, while the fixed line is known as the directrix of parabola.

Parabola does not have any inverse. Let a parabola having equation y = x^2,

it is graph looks like a U-Shaped curve opening up.

Here does not have an inverse as it fails the horizontal line test.

The inverse equation y=√x, only has the positive input values from the domain of parabola.

If we are constrain the domain to be greater than zero, then only it is possible for the function to pass the horizontal line test.

Therefore, Parabola does not have an inverse.

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The longest and the shortest distances are 1 mile and 5 miles

The greatest number of miles left is 4.5 miles

From the question, we have the following distances that can be used in our computation:

Luke = 3 miles

Logan = 2 miles

This means that

Shortest = 3 - 2 = 1 mile

Longest = 3 + 2 = 5 miles

Represent the distance with x

So, we have

3 - 2 < x < 3 + 2

Evaluate

1 < x < 5

The number line is | 1 | 2 | 3 | 4 | 5 |

In (a), we have

Longest = 5 miles

So, we have

Greatest = 5 - 0.5

Greatest = 4,5 miles

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The angle of incline, of the target θ = 14.036.

The angle of elevation or depression can be calculated using the following formula: t a n = O A, where A is the horizontal distance between the observer and the point and O is the length of the side opposite the angle of elevation or depression, or the object's perpendicular distance from the horizontal line.

To calculate the slope percentage, multiply the result by 100 after dividing the height difference between two points by their separation. The rise is the height difference between two locations. The distance between the locations is known as the run. The result is that (rise / run) x 100 is equal to the percent slope.

Given,

the height of triangle = 12in

base of triangle = 48 in

tan θ = perpendicular / base

tanθ = 12/48

θ = tan ⁻¹( 12/48)

θ = 14.036

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Complete question -

4/9 of the spectators in a football match are males. If 200 of them are females, then the total number of spectators is 360.

What is the proportion?

A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.

Given that 4/9 of the fans in a football match are men and 200 are women. We must determine the total number of spectators at the football game.

If 4/9 of the total spectators are men, the remaining 5/9 are women.

Let x be the total number of spectators.

Mathematically,

5/9 of x = 200

5/9 × x = 200

5x = 1800

X = 360

As a result, the total number of spectators is 360.

The number of male spectators may also be calculated.

Males + Females = Total number of spectators

360 = Males + 200

Males = 160

Therefore, 4/9 of the spectators in a football match are males. If 200 of them are females, then the total number of spectators is 360.

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Answer:

  1.6 L or 1600 mL

Step-by-step explanation:

You want to know the total volume of one 0.9 L box and two 350 mL boxes.

The units are related by ...

  1 L = 1000 mL

Then the volumes of the given boxes are ...

  0.9 L = 900 mL

  350 mL = 0.35 L

You can add the volumes in either of the like units:

  900 mL + 2 × (350 mL) = 1600 mL

  0.9 L + 2 × (0.35 L) = 1.6 L

The total volume of the juice boxes is 1.6 L or 1600 mL.

__

Additional comment

You can convert the units a couple of ways.

Because the fraction has equal measures in the numerator and denominator, it does not change the size of the volume. It only changes the units of the volume.

Answer:7032

Step-by-step explanation:

The population of the town in 2016 will be 7032

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

Given that, A small town had a population of 12,000 people in 2001. The population has been decreasing at a rate of 3.5% each year.

We know that, Decrease rate =

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = rate

n = years or time

Therefore,

A = 12000(1-0.035)¹⁵

A = 12000(0.965)¹⁵

A = 7032.19

A ≈ 7032

Hence, the population of the town in 2016 will be 7032

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Answer:

slope = -4/5x

y - int = 7/5

Step-by-step explanation:

4x + 5y = 7

-4x on each side

5y = -4x + 7

divide by 5 on each side

y = -4/5 x + 7/5

Answer: 10/7x + 8/7

Step-by-step explanation:

Slope intercept form : y = mx + b

10x - 7y = -8

-7y = -10x - 8

7y = 10x + 8

y = 10/7x + 8/7

Answer:

35

Step-by-step explanation:

35

Answer: 25

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

67 minus 33 leaves 34 red bikes but divided that by half gives you 17

Answer:160%

Step-by-step explanation:

100%...........50                     80:0.5=160

1%..............0.5                       50:100=0.5

?.............80

160%...............80

Amount of water necessary to water all the plants in the house is 10/3.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Amount of water needed to water 2/5 of plants = 4/3

Equation representing the amount of water needed to water 5/5 of plants = (4/3) / (2/5)

          = (4/3) × (5/2)

          = 10/3

Hence 10/3 of water is needed to water all the plants in the house.

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Domain of any function is all the input value of the function for which condition of the function exist.

Therefore, the domain of the function is its input value for which there exist a successful output value.

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The equation Y = -2x + 3 is a linear equation in slope-intercept form.

This equation represents a straight line with a slope of -2 and a y-intercept of 3.

The slope -2 tells us that for every unit increase in x, the value of y will decrease by 2. The y-intercept 3 tells us that the line passes through the point (0,3) on the coordinate plane.

It's a line that goes down as the slope is negative and the line can be represented by a graph, that can be easily plotted using the slope and the y-intercept. This equation can be used to model real-world situations like linear regression and many other fields.

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The proportion when to make 4 cups of rice, Iain needs 5 cups of water and make 16 cups of rice, he needs 20 cups of water is 4/5 = 16/20.

Proportion in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, to make 4 cups of rice, Iain needs 5 cups of water and make 16 cups of rice, he needs 20 cups of water. The proportion will be:

4/5 = 16/20

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The 3 types of line graphs are Simple line graph, Multiple line graph and Compound line graph.

Simple line graph - On the graph, there is only one line drawn.

Multiple line graph - On the same set of axes, many lines are plotted. An excellent way to compare similar objects over the same time period is via a multiple line graph.

Compound line graph - if data can be separated into two or more different categories. Compound line graphs are the name given to this kind of line graph. To represent the component portion of a total, lines are drawn. Part of the total is shown on the line below the top line, which displays the total. The size of each component is indicated by the space between every two lines.

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A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.

No, a triangle is not always 90 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.

This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).

Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.

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equation of a line : y=mx+b

Answer : y= -1x+2

Answer:

-28

Step-by-step explanation:

f(-4) = 5(-4) - 2³ = -20 - 8 = -28

The given equations do not represent a par of coincident lines. As the equations do not satisfy the conditions.

It is given that the pair of equations are,

4x + 3y - 1 = 5 and 12x + 9y = 15

To determine if the equations represent a pair of coincident lines.

Here we get, a₁ = 4, b₁ = 3, c₁ = -1

a₂ = 12, b₂ = 9, c₂ = -15

So, a₁/a₂ = 4/12 = 3

b₁/b₂ = 3/9 = 3

c₁/c₂ = -1/-15 = 1/15

Therefore,

[tex] \frac{a1}{a2} = \frac{b1}{b2}≠ \frac{c1}{c2} [/tex]

Thus, the given equations do not represent a pair of coincident lines

Now, if you put these equations in any graphing software or here I have used Desmos then you will get the graph (attached image), which further shows that the lines do not coincide.

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Answer:

Step-by-step explanation:

To solve the system of equations using substitution, we first need to isolate one of the variables in one of the equations. We can start by solving the first equation for y:

x - 5y = -6

y = (x + 6) / 5

Now we can substitute this expression for y into the second equation:

7x - 3y = 42

7x - 3((x + 6) / 5) = 42

Simplifying and solving for x:

(35/5)x - (3/5)x - 18/5 = 42

32x = 210+18

x=57/8

Now we can substitute this value of x back into the first equation to find the value of y:

y = ((57/8) + 6) / 5

y = 21/8

So the solution of the system is (x, y) = (57/8, 21/8).

Different properties, significance of those properties and their applications in mathematics.

Associative property : Associative law states that the order of grouping the numbers does not matter. This law holds for addition and multiplication but it doesn’t hold for subtraction and division. This can be observed from the following examples.

Addition:

a+ (b+c) = (a+b) + c

Subtraction:

a-(b-c) ≠ (a-b) – c.

Multiplication:

a x (b x c) = (axb) x c

Division:

a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

Distributive property : This property is used to eliminate the brackets in an expression. The distributive property states that each term inside the bracket should be multiplied with the term outside. This property is very useful while simplifying the expressions and solving the complicated equations.

Addition:

a(b+c) = ab + ac

Subtraction :

a(b-c) = ab – ac

Commutative property : This property states that there is no change in result though the numbers in an expression are interchanged. Commutative property holds for addition and multiplication but not for subtraction and division.

Addition:

a+b = b+a.

Subtraction:

a-b ≠ b-a.

Multiplication:

a x b = b x a

Division:

a ÷ b ≠ b ÷ a.

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Answer:

true

because 22+8=30,

and 30 is greater than 16.

Answer:

Linear equations

Step-by-step explanation:

hope this helps

Addition is commutative because the order in which two numbers are added does not affect the result.

Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers.

Addition is commutative because the order in which two numbers are added does not affect the result. For example, 1 + 2 = 2 + 1 = 3. In contrast, subtraction is not commutative because the order in which two numbers are subtracted does affect the result. For example, 1 - 2 = -1, but 2 - 1 = 1. The operation is different when the order of the numbers are changed.

so, addition is commutative because the order in which two numbers are added does not affect the result.

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