Why the ratio of sine of angle of incidence to the sine of angle of refraction is constant?.

Therefore, the real and unequal roots of the quadratic equation. The roots are uneven and real when the discriminant is bigger than zero. The roots are equal and real when discriminant is equal to zero.

When a, b, and c are real integers and the discriminant is bigger than zero (b2 - 4ac > 0), the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal.

In this situation, we say that the roots are hypothetical. Ax2 + bx + c = 0 has real, rational, and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive and perfect square.

D=b \s2 \s −4ac=42 \s −4×2×(−7)=16+56=72>0.

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Full Question = What will be the nature of roots of quadratic equation 2x 2 +4x−7=0?

The system formed by linear equations - 8 · x + 8 · y = 1 and - 32 · x + 32 · y = - 5 has no solution.

In this problem we find a system formed by two linear equations with two variables. There are three kinds of systems of linear equations:

First, write the system of linear equations:

- 8 · x + 8 · y = 1

- 32 · x + 32 · y = - 5

Second, multiply the first equation by 4:

- 32 · x + 32 · y = 4

Third, use transitive property:

4 = - 5 (CRASH!)

The system of linear equations has no solution.

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The letter on the number line that represents the given number is B.

A number line is a straight line which extends from -∞ to -∞, on which the position or location of all directed numbers can be identified.

Directed numbers are numbers which have either a negative or positive sign. Examples include; -4, -1 2/3. 9 etc. Therefore all numbers can be located on a number line.

Considering the given question, to locate the position of 1 85/100. The whole number make us to understand that its position falls between 1 and 2. And the fraction part shows that the number is closer to 2 more than 1.

Therefore, the letter on the number line that represents 1 85/100 is B.

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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The amount of yard that has to be given to Laura is c) 500 m2

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information:

Total of money = 540 000

Laura's money = 300 000

Lets represent the amount of money Laura gave:

Laura's % = (300 000 / 540 000) * 100

Laura's % = 30/54 * 100

Laura's % = 5/9 * 100

Laura's % = 55.56%

The amount of yard should be for Laura is:

Laura's yard = Total yards area * Laura's %

Laura's yard = 900 m^2 * 55.56%

Laura's yard = 500 m^2

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Answer:

The value of the expression when x=3 is:

7^(3/2) + 9x - 3

We can simplify it as:

49 + 9*3 - 3

= 49 + 27 -3

= 73

So the final value of the expression is 73.

Given expression y=7x²+9x-3

Given value of x=3

We want to find the value of y.

Substitute the value of x=3 in y expression

y=7(3²)+9(3)-3

y=7*9+9*3-3

y=63+27-3

y=87

Therefore, the value of given expression is 87

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Complete question

What is the value of the expression below when x=3,

y=7x²+9x-3

it is 21

Step-by-step explanation:

The value of y in equation 2x-3y=-6 is y = (2x+6)/3

Let us proceed to solve the equation 2x - 3y = -6

We take the term 3y to the right-hand side of the equation which gives 2x = -6 + 3y

Now we bring 6 to the left side of the equation 2x + 6 = 3y

And lastly, we bring the 3 also to the other side of the equation thus dividing the term (2x-+6) by 3 which ultimately gives us the value of y.

(2x + 6) /3 = y

Thus, The value of y in equation 2x-3y=-6 is y = (2x+6)/3

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The sum of 11 of the interior angles of a regular dodecagon is 1650°.

The formula (180n-360)/n is used to determine the interior angle of a regular polygon. n=11 for an undecagon.

The interior angle of a regular dodecagon is 150°.The sum of 11 of the interior angles of a regular dodecagon is 150* 11 = 1650°.

The interior angles of a dodecagon are a bit harder. You can use this generic formula to find the sum of the interior angles for an n-sided polygon (regular or irregular).Sum of interior angles = (n-2)\times 180°(n−2)×180°

Sum of interior angles = 10\times 180°=1800°10×180°=1800°

Therefore, the sum of 11 of the interior angles of a regular dodecagon is 150* 11 = 1650°.

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Answer:

26.40

Step-by-step explanation:

r=12

s=4

5r − 8.35s =

5(12) - 8.35(4) = ==> plug in 12 for r and 4 for s

60 - 33.40 =   ==> simplify

60.00 - 33.40 =

60 - 33 + 0.00 - 0.40 =

27 - 0.40 = 26.40

The amount of sales tax is $3,

The total amount the group paid, including tax and tip is $47.79.

A percentage is a figure or ratio that can be stated as a fraction of 100.

If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given The bill, before sales tax and tip,

amount of the bill before sales tax and tip = $37.50

sales tax is 8% on bill

sales tax = 8% of 37.50

sales tax = 37.50*8/100

sales tax = 37.50*0.08

sales tax = $3

amount after sales tax = $37.50 + $3

amount after sales tax = $40.5

the tip is 18% of the amount after the sales tax

tip = 18% of 40.5

tip = 40.5*18/100

tip = 40.5*0.18

tip = $7.29

total bill amount = $37.50 + $3 + $7.29

total bill amount = $47.79

Hence the sales tax is of $3 and the total amount is $47.79.

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Answer:

37.5%

Step-by-step explanation:

We take

12 divided by 32, then times 100% = 37.5%

So, 37.5% of Jayden's rabbits are male

Answer:

5.196152421cm

Step-by-step explanation:

tan= opposite(perpendicular)/adjacent(base)

tan60=9/x

1.732050808=9/x

1.732050808x=9

x=9/1.732050808

x=5.196152421

a) The probability distribution of X

X P(X)

0 022667

1 0.4073511

2 0.27452

3 0.082223

4 0.0093252

b) The most likely value for X is one.

c) The probability that at least two of the four selected have earthquake insurance is 0.3660.

We have, some parts of California are particularly earthquake-prone.Suppose that in one metropolitan area, 31% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random.

Let X denote the number among the four who have earthquake insurance. The probability that the homeowner are insured against earthquake is 0.31. Let S denote a homeowner that has insurance and F denote a homeowner that does not has insurance.

a) For X = 0, {FFFF}

The probability of X = 0

= 0.69x0.69x0.69×0.69

= 0.22667

For X = 1, {SFFF, FSFF, FFSF, FFFS}

P( X = 1) = (0.31 x0.69x0.69×0.69) *4)

= -0.40735116

For X = 2,{SSFF, SFSF, SFFS, FSSF, FSFS, FFSS}

P(X= 2) = (0.31x0.31x0.69×0.69)*6

= -0.27451926

For x = 3,{SSSF, SSFS, SFSS, FSSS}

= (0.31x0.31x0.31x0.69) *4

= -0.08222316

For X = 4, {SSSS}

P(X= 4) = (0.31 <0.31 x0.31x 0.31)

= 0.00923521

Hence, the probability distribution of X

X P(X)

0 022667

1 0.4073511

2 0.27452

3 0.082223

4 0.0093252

(b) The most likely value for X is X = 1, since it has large probability comparing with other values.

(c) We have to calculate the probability that at least two of the four selected have earthquake insurance, P(X ≥2)= P(X=2)+ P(X=3) + P(X=4)

= 0.27452+0.082223+0.0093252

P(X ≥2)=0.3660

Hence, the required probability is 0.3660.

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Answer:

  undefined

Step-by-step explanation:

You want the value of f(-1), given the piecewise defined function f(x).

The function is defined for values of x greater than 1. The value x=-1 is not part of the domain of the function:

  f(-1) = "undefined"

There is a formula to calculate logarithms to base 2 or log base 2 equations. The formula is stated by log₂x = log₁₀x/log₁₀2.

A logarithm is an exponent to which a base must be raised to generate a given number. Expressed mathematically, x is the logarithm of n to the base a if ax = n, in which case one writes x = logₐn.

A logarithm is defined using an exponent.

aˣ = b ⇔ logₐb = x

Here, "log" stands for logarithm. The arrow's right part is read as "Logarithm of b to the base a is equal to x".

Let us take an example of log base 2 equations,

log₂49

Using the change of base formula,

= log₂x = log₁₀x/log₁₀2

= log₂49 = log₁₀49/log₁₀2

= 1.69019608/0.301030

= 5.6147

Therefore, the value of log₂49 is 5.6147.

--The given question is incomplete; the complete question is

"How do you solve log base 2 equations?"--

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An equation that has two variables which the formula Ax + By = C.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1.

So, an equation that has two variables which the formula Ax + By = C.

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Therefore , we can conclude from the answer to the above problem that the equation for a reflection from across y-axis is - (x,y) -> (x,y).

The x-axis and y-axis are the coordinate plane two crucial axes. In contrast to the x-axis, which is a horizontally number line, the y-axis is vertical. Its two orthogonal axes make up a coordinate plane. The ordinate refers to the y-axis, whereas the abscissa refers to the x-axis.

Here,

The Y-axis is the line that runs vertically along the graph from bottom to top. The measurement coordinates are parallel to the this axis.

The numbers on the y-axis are known as y-coordinates.

When expressing following result, the x-coordinate and y-coordinate go in parentheses in that order.

(x, y).

A' ( -1, 1 ) => A"(-1, -1) (-1, -1)

B' (-2, 2) => B"(-2, -2) (-2, -2)

C' (-2, 3) => C"(-2, -3) (-2, -3)

and D' (-1, 4) =>  D " (-1, -4)

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By plotting the points (1, 1) and (4, 4) on the graph and joining the points we get a straight line which is the graph of y = x

Given, the linear equations are y = x and y = -x

We have to draw the graphs of the equations on the same cartesian plane.

Considering the equation y = x

We need a few points to plot on the graph.

For x = 1, y = 1

For x = 4, y = 4

Therefore, the points of the equation are (1, 1) and (4, 4)

By plotting the points (1, 1) and (4, 4) on the graph and joining the points we get a straight line which is the graph of y = x

Considering the equation y = -x

We need a few points to plot on the graph.

For x = 3, y = -3

For x = -4, y = 4

Therefore, the points of the equation are (3, -3) and (-4, 4)

By plotting the points (3, -3) and (-4, 4) on the graph and joining the points we get a straight line which is the graph of y = -x.

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Pyramid A's base is a 20-meter-wide by 10-meter-long rectangle.

Base of Pyramid B has a square shape with 10-meter sides.

The heights are equal.

(L × W × H) / 3 equals the volume of a rectangular pyramid.

Square pyramid volume = a² × h/3

Assume that there are 10 meters above ground.

The rectangular pyramid's V is equal to (10m × 20m × 10m)/3, or 2000/3, or 666.67 m3.

V of  Square pyramid: = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³

Pyramid A's volume is TWICE that of pyramid B's.

In the event when Pyramid B's height doubles that of Pyramid A (from 10m to 20m),

The square pyramid's V is equal to (10m)2 × (10 × 2)/3, 100m² × (20m/3), and 100m2 × 6.67m, or 666.67 m³

The volume of pyramid B has increased to the same level as pyramid A.

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The angle 67.5 degrees is 3 times its complement

Let us assume that the complement of the angle be p degrees.

Given that the measure of the angle is three times its complement.

So, the measure of the angle = 3p

We know that two angles are complementary when their measures add to 90 degrees.

The sum of complementary angles is 90 degrees.

So we get an equation, p + 3p = 90

We solve this equation to find the value of p.

p + 3p = 90

4p = 90

p = 90/4

p = 22.5 degrees

so, the measure of complement of the angle is 22.5 degrees.

And the required angle would be, 3 × 22.5 = 67.5 degrees

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Answer:

the domain is x ≥ -4

Step-by-step explanation:

on the x-axis, the graph does not extend below -4. the point on the graph is filled in, which makes the domain greater than or equal to -4.

hope this helped, good luck!

If the variance is unknown and the sample size is small, then the t-test statistic is appropriate to use.

The t-test is a statistical hypothesis test used to identify whether an unknown population mean is different from a particular value. A t-test is appropriate to use when there is a small random sample collected from some statistical population and the sample is required to be compared with the mean from the sample to another value. Also, the variance of the sample is not known.

Thus, a t-test is appropriate to be used when the population variance or standard deviation is not known, and a sample size is less than 30.

"

Correct question:

If the variance is unknown and the ample size is small, which test statistic is appropriate?

"

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4 less than the product of 1 and x is x - 4.

An algebraic expression is a variable expression described using its terms, and operations on the terms.

In other words, algebraic expression are mathematical expressions where variables and constant are combined using operations such as subtraction, addition, multiplication etc.

Therefore, let's express the word expression in algebraic expression,

Hence, 4 less than the product of 1 and x is represented as follows:

(1 × x) - 4

x - 4

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The degree of the polynomial 2x² 5x³ 7 is 5.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

What is the degree of the polynomial 2x² 5x³ 7?

The investment of $18,500 at 17.6% compounded quarterly for 7.5 years will be worth (a future value of) $67,326.60.

The future value is the present value compounded periodically at an interest rate.

Compounding involves computing interest on interest.

The future value of the investment after the stated period can be determined using an online finance calculator as follows:

N (# of periods) = 30 years

I/Y (Interest per year) = 17.6%

PV (Present Value) = $18,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $67,326.60

Total Interest = $48,826.60

Thus, in 7.5 years' time, the investment will be worth $67,326.60.

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So, the given system of equations has no solutions.

The system of equations 2x + 4y = 10 and 3x + 6y = 12 can be written in matrix form as:

| 2 4 | | x | | 10 |

| 3 6 | | y | = | 12 |

To find the number of solutions, we can use the concept of the determinant of a matrix. The determinant of a matrix is a scalar value that can be calculated from the elements of a square matrix. If the determinant of the matrix is non-zero, the system of equations has a unique solution. If the determinant is zero, the system may have either no solutions or infinitely many solutions.

To find the determinant of the matrix, we can use the formula:

| 2 4 |

| 3 6 | = (26) - (43) = 12 - 12 = 0

Since the determinant of the matrix is zero, the system of equations has either no solutions or infinitely many solutions.

To determine which case applies, we can use the concept of the rank of a matrix. The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of the matrix is less than the number of variables, then the system has no solutions. If the rank of the matrix is equal to the number of variables, then the system has a unique solution.

The rank of the matrix can be found by converting it into the row echelon form or reduced row echelon form.

| 2 4 | | 2 4 |

| 3 6 | = | 0 0 |

The rank is 1, which is less than 2, the number of variables. Therefore, the system of equations has no solutions.

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The pair of the linear equations Kx + 4y + (μ+8) = 0 and 4x + ky + 4 = 0 has infinitely many solutions for k = ± 4.

Given lines are

kx + 4y + (μ+8) = 0

4x + ky + 4= 0

for lines to have infinite solutions

​a₁/a₂ ​​= ​b₁/b₂​ ​= ​c₁/c₂​​        [a₁​x + b₁y + c₁ ​= 0, a₂​x + b₂y + c₂ ​= 0]

∴k/4 ​= 4/k ​= (μ+8)/4​

∴k/4 ​= 4/k ​

⇒k² = 16  

⇒k = ±4    

We have, 4/k ​= (μ+8)/4​

For, k = +4        

⇒4/4 ​= (μ+8)/4​

⇒μ = −4

For, k=−4      

⇒4/-4 ​= (μ+8)/4​            

⇒μ = −12

∴ for k = ±4, the line has infinite solutions.

--The given question is incomplete; the complete question is

"For what value of K, the following pair of the linear equation has infinitely many solutions 

Kx + 4y = (μ+8) = 0

4x + ky + 4 = 0"--

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