A person whose eyes are 1.64 m above the floor stands 2.30 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor. What is the horizontal distance x?

The Quadratic Equation [tex]3x^{2}-13x+6[/tex]  divided by [tex]x-4[/tex] for all the values of the x(except x=4).

Let us consider [tex]3x^{2}-13x+6[/tex] as equation→(1) of a Quadratic Equation assume some values for x which is satisfies the equation and doesn't satisfy equation by "hit and trail method".

x=1 substitute in the equation (1) we get    ⇒  [tex]\frac{4}{3}[/tex]

x=2 we get [tex]3(2)^{2}-13(2)+6[/tex]    [tex]=4[/tex]

x=4 we get[tex]3(4)^{2}-13(4)+6[/tex]    ⇒    [tex]\frac{2}{0}[/tex] which is not defined.

x=6 we get [tex]3(6)^{2}-13(6)+6[/tex]      [tex]= 12[/tex]

x= -2 we get [tex]3(-2)^{2}-13(-2)+6[/tex] ⇒[tex]\frac{22}{-3}[/tex]

And so on for the remaining values of x the equation will satisfy. Except  for the value x= 4 the equation doesn't satisfy because if we substitute x=4 in x-4 we get 4-4 =0 anything divided by zero is not defined.

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Divide [tex]3x^{2}-13x+6 by x-4[/tex]

Fill in the inequality for each problem as follows 32 > -39, 3 < 15, 4  > -6 and -8  > -15

Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

We have different inequality signs as follows:

Greater than (>)

Less than(<)

Less than or equal to (≤)

Greater than or equal to (≥)

Given:

32__-39

3__15

4__-6

-8__-15

For 32__-39:

Since 32 is greater than -39. we can write:

32 > -39

For 3__15:

Since 3 is less than 15. we can write:

3 < 15

For 4__-6:

Since 4 is greater than -6. we can write:

4  > -6

For -8__-15:

Since -8 is greater than -15. we can write:

-8  > -15

Thus, fill in for each problem accordingly

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Complete Question

Fill in >,< or = for each prob

32__-39

3__15

4__-6

-8__-15

Answer:

[tex]\huge\boxed{\sf b = -3}[/tex]

Step-by-step explanation:

-3(3 + 6b) = 36 - 3b

Distribute

-9 - 18b = 36 - 3b

Add 3b to both sides

-18b + 3b - 9 = 36

-15b - 9 = 36

Add 9 to both sides

-15b = 36 + 9

-15b = 45

Divide -15 to both sides

b = 45/(-15)

[tex]\rule[225]{225}{2}[/tex]

Answer:

The value of b is -3.

Step-by-step explanation:

The equation is,

→ -3(3 + 6b) = 36 - 3b

Now the value of b will be,

→ -3(3 + 6b) = 36 - 3b

→ -3(3) - 3(6b) = 36 - 3b

→ -9 - 18b = 36 - 3b

→ -18b + 3b = 36 + 9

→ -15b = 45

→ b = -(45/15)

→ [ b = -3 ]

Hence, the value of b is -3.

The average class size of Newton middle school is 21.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller.

The average class size will be calculated as,

Average class size = 30 x (70%)

Average class size = 30 x 0.7

Average class size = 21

Therefore, the average class size at Newton middle school is 21.

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The difference of given decimal numbers is (12.504, 12.495).

Given that, (13.4-0.896, 8.4+4.095).

Subtracting decimals:

1. Write down the two numbers, one under the other, with the decimal points lined up.

2. Add zeros so the numbers have the same length.

3. Then subtract normally, remembering to put the decimal point in the answer.

Here,

13.4-0.896 =12.504

8.4+4.095 =12.495

So, (13.4-0.896, 8.4+4.095) =(12.504, 12.495)

Hence, the difference of given decimal numbers is (12.504, 12.495).

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The total years taken to double the money according to Compounding will be 12.5  years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $900

Total amount = $1800

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/1200)^12t

T = A[tex](1+r/1200)^{12t}[/tex]

1800 = 900 (1+6/1200)^12t

2 = (1+1/200)^12t

2 = 1.005^12t

taking log on both sides

log 2 = 12t *log 1.005

0.3/0.002 = 12t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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A true proportion of the figure based on the triangle proportionality theorem is: A) i/j = h/k.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

The triangle proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

Since side TU is parallel to side QR, side TU will divide both sides QS and RS proportionally in accordance with the triangle proportionality theorem as follows;

RU/QT = SU/ST ≡ i/j = h/k

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By solving equations, we know that there were 2187 adult partons.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A function is an equation with a single solution for y for each value of x.

Each input of a particular type receives exactly one output when using a function.

Instead of y, a function is frequently named f(x) or g(x).

When x equals 2, we should determine our function's value because f(2) says to do so.

So, the number of adult patrons was:

Let, a be an adult and c be children.

Total tickets:

a + c = 5200

c = (5200-a)

Total amount:

7.50a + 4.50c = 29961

Replace c in the first equation with (5200-a).

7.5a + 4.5(5200-a) = 29961

7.5a + 23400 - 4.5a = 29961

7.5a - 4.5a = 29961 - 23400

3a = 6561

a = 6561/3

a = 2187

Therefore, by solving equations, we know that there were 2187 adult partons.

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It is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.

What is the interior angle?

The inner of the two angles formed where two sides of a polygon come together. any of the four angles formed in the area between a pair of parallel lines when a third line cuts them.

Jasper's claim is not true. The minimum angle of rotation about the center of a regular polygon that carries the polygon onto itself is called the polygon's "order of rotational symmetry." This angle is always less than or equal to 180 degrees, and it is equal to 360 degrees divided by the number of sides in the polygon.

For example, a regular hexagon has an order of rotational symmetry of 60 degrees (360 degrees / 6 sides), and a regular octagon has an order of rotational symmetry of 45 degrees (360 degrees / 8 sides).

Therefore, if the measure of each interior angle of a regular polygon is four times the minimum angle of rotation about its center that carries the polygon onto itself, then the measure of each interior angle would have to be at least 720 degrees. However, the sum of the interior angles of a regular polygon with n sides is 180(n-2) degrees, which is always less than 720 degrees for any value of n greater than 2.

Therefore, it is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.

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In using quarterly time series data, Quarter two  can serve as the base period for interpretation of dummy variables.

What do you mean by interpretation?

The process of interpreting anything involves elaborating, rephrasing, or otherwise demonstrating your own understanding of it.

                           Because they are explaining what someone is saying to someone who doesn't understand, a person who translates one language into another is known as an interpreter.

What are examples and variables?

A trait that is measurable and capable of taking on several values is known as a variable. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling.

                                 The two primary categories of variables are categorical and numeric.

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Answer: The slope is 3

Step-by-step explanation:

Explanation:

The slope of a line in the form

y

=

m

x

+

b

is

m

.

3

x

−

y

=

4

−

y

=

−

3

x

+

4

subtract

3

x

from both sides

y

=

3

x

−

4

multiply both sides by

−

1

The given polygon could be parallelogram , quadrilateral , rectangle.

What is a polygon?

In geometry, a polygonal shape could be a two-dimensional figure that's delineate by a finite range of line segments connected to make a closed two-dimensional figure chain. The delimited plane region, the bounding circuit, or the 2 along, is also referred to as a polygonal shape.

Main body:

As opposite sides of polygon QRST are parallel , it a parallelogram .

A quadrilateral is a polygon with for sides , so it also satisfies the condition.

The opposite sides of rectangle are equal and parallel , which is also satisfied.

Hence ,the given polygon could be parallelogram , quadrilateral , rectangle.

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Answer:

3,11

Step-by-step explanation:

Since y = 2x + 5, if you chose (x,y) (3,11):

11 = 2*3 + 5

11 = 6 + 5

11 = 11

Answer:

(3, 11 ) is a solution

Step-by-step explanation:

substitute the x- coordinate of the points into the equation and if the value of y obtained equals the y- coordinate then the point is a solution.

(5, 20 )

y = 2(5) + 5 = 10 + 5 = 15 ≠ 20 ← not a solution

(6, 12 )

y = 2(6) + 5 = 12 + 5 = 17 ≠ 12 ← not a solution

(3, 11 )

y = 2(3) + 5 = 6 + 5 = 11 ← solution

(4, 14 )

y = 2(4) + 5 = 8 + 5 = 13 ≠ 14 ← not a solution

j(m) = 2ᵐ ⁻ ¹

for functions you will replace the number in the brackets with the letter! so:

j(4) = 2⁴ ⁻ ¹

= 2³

= 8

Answer:

do it yourslef

dont be silly

lol

11111111

Using the Central Limit Theorem, it is found that these conditions are required to avoid the high variability associated with small samples.

[tex]s=\sqrt{p(1-p)/n}[/tex]

[tex]p v=2*p(z < -0.531)=0.595[/tex]

1) Data given and notation

n=500 represent the random sample taken

X=380 represent the number of people with some characteristic

estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

3) Calculate the statistic  

[tex]z=\frac{0.76 - 0.77}{\sqrt{\frac{0.77(1-77)}{500} } =0.531}[/tex]

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha =0.05[/tex]The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]pv=2*p(z < -0.0531)=0.595[/tex]

If we compare the p value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.  

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You may find the answer to this question in the statement of the problem, if the vehicles uses 1 gallon to travel 13 times, then it is traveling at a rate of 13 miles per gallon.

Answer:

  y = -4/9x

Step-by-step explanation:

You want the equation of the line through (0, 0) and (9, -4).

A line through the point (0, 0) represents a proportion. The slope of the line is the constant of proportionality, the ratio of y to x.

  k = y/x = -4/9

The equation of the line is ...

  y = kx

  y = -4/9x

You will always get one triangle. This is because of the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle is always 180°.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The inner angles of every triangle sum up to 180°, 180°, 180°, 180°. Angles in a triangle are the total (sum) of the angles at each of its three vertices.

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Answer:

B. Shape A can be matched to shape B by reflecting about the origin and then shifting –3 on the x-axis and 1 on the y-axis.

Step-by-step explanation:

The trigonometric measures for the triangle in this problem are given as follows:

The six trigonometric measures for a right triangle are given as follows:

From the given right triangle, the sides are given as follows:

a = 9, b = 4.

Then, applying the Pythagorean Theorem, the length of the sqis given as follows:

h² = 9² + 4²

h² = 97

h = square root of 97.

h = 9.85.

The triangle is given by the image shown at the end of the answer.

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Answer:

[tex]P_t=5x+16[/tex]

Step-by-step explanation:

The perimeter of the triangle will be the sum of all the sides,

[tex]P_t=a+b+c[/tex]

For this problem, let a=x, b=3x+12, and c=4+x.  So,

[tex]P_t=(x)+(3x+12)+(4+x)\\P_t=x+3x+12+4+x\\P_t=x+3x+x+12+4\\P_t=5x+16[/tex]

The correct match the following is shown below:

2x + 3 (x - 2) = 6 (x + 1) + x → x = -6

2x + 3 (x - 2) = 6 (x - 1) - x → All real numbers

2x + 3 (x - 2) = 6 (x - 1) + x → x = 0

2x + 3 (x - 1) = 6 (x - 1) - x → No solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

The equation is, 2x + 3 (x - 2) = 6 (x + 1) + x, 2x + 3 (x - 2) = 6 (x - 1) - x, 2x + 3 (x - 2) = 6 (x - 1) + x, and 2x + 3 (x - 1) = 6 (x - 1) - x

Solve the above equations as shown below,

2x + 3 (x - 2) = 6 (x + 1) + x

2x + 3x - 6 = 6x + 6 + x

5x - 6 = 7x + 6

7x - 5x = -6 - 6

x = -6

2x + 3 (x - 2) = 6 (x - 1) - x

2x + 3x - 6 = 6x - 6 - x

5x  - 6 = 5x - 6

Infinity solutions,

2x + 3 (x - 2) = 6 (x - 1) + x

2x + 3x - 6 = 6x - 6 + x

5x - 6 = 7x - 6

x = 0

2x + 3 (x - 1) = 6 (x - 1) - x

2x + 3x - 3 = 6x - 6 - x

5x - 3 = 5x - 6

Parallel line, hence, no solution.

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Answer:

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

For the equation to have infinitely many solutions, the variables and constants should cancel and should end up with 0 = 0. It means for any value of the variable the equation is true, i.e. both sides are equal.

Given equation:

If we solve it for ? we'll get:

Answer:

Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.

Let the measure of one of the supplementary angles be a

.

Measure of the other angle is 2

times a

.

So, measure of the other angle is 2a

.

If the sum of the measures of two angles is 180°

, then the angles are supplementary.

So, a+2a=180°

Simplify.

3a=180°

To isolate a

, divide both sides of the equation by 3

.

3a3=180°3    a=60°

The measure of the second angle is,

2a=2×60°       =120°

So, the measures of the two supplementary angles are 60°

and 120° .

Step-by-step explanation:

Hope this works!....

The letters of "hyperbola" can be combined into 40,320 different nine-letter words by using each letter just once.

Combinations are the procedures used in mathematics to pick k things from n different items without replacement.

The following formula computes the combinations of k items from n:

(n, k) = n! / k!×(n-k)!

There are 8 letters in the word "hyperbola",

So, there are 8 choices for the first letter, 7 choices for the second letter, and so on, down to 1 choice for the last letter.

This means that there are :

⇒ 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

Therefore, 40,320 possible nine-letter words can be formed from the letters of "hyperbola" using each letter once per word.

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The cycle originally cost $120, and he made a $60 profit by selling it for $163 with a $17 helmet.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.

Here,

The cost of bicycle=$163

Cost of helmet=$17

Total cost,

=163+17

=$180

Let the original cost be c,

180=150%*c

180=1.5c

c=$120

He made a profit,

=180-120

=$60

The original cost of cycle was $120 that he sold in $163 with the helmet of $17 making a profit of $60.

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2/6 is the equivalent fraction for the fraction represented on the given number line. So, B is the correct option

What is an equivalent fraction ?

According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.

For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

as 2/6 can further reduced to 1/3 which is represented on to the number line  as 1/3 which is equal to 2/6

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The graph of the proportional relationship is added as an attachment

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

Time = 3 minutes

Supply of water = 12 litres

Using the above parameters, we have the following ordered pairs

(0, 0) and (3, 12)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (3, 12)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (3, 12)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (12 - 0)/(4 - 0)

Evaluate

gradient  = 3

The equation of the line is then calculated as

y = gradient * x

Substitute the known values in the above equation

So, we have the following equation

y = 3 * x

Evaluate the products

y= 3x

Hence, the line equation is y= 3x

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