For what value of k are the roots of the quadratic equation 3x² 2kx 27?.

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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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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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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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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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

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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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"

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!

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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Grams per cubic centimeter to kilograms per cubic meter is 1000.

1 g/cm³ = 1000 1 kg/m³

The conversion value:

Find the conversion from grams per cubic centimeter to kilograms per cubic meter!

Multiply the number with the each conversion value!

See that the cubic centimeter is as a denominator. So, we reverse the fractional value.

1 g/cm³

= 1 × 1/1000 × 1000000/1 kg/m³

= 1000 kg/m³

Hence, the conversion value from grams per cubic centimeter to kilograms per cubic meter is 1000.

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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 polynomial function is obtained to be h(x) = -2 (x - 4)(x - 1)²(x + 2), with the values a = -2, b = -4, c = -1 and d = 2.

What is a polynomial?

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

The characteristics of the polynomial are -

The zeros are located at 4, 1 (multiplicity of 2) and-2

The end behavior is as follows -

As x reaches negative infinity, f(x) reaches negative infinity.

As x reaches infinity, f(x) reaches negative infinity.

The y-intercept of the function is (0, 16)

The equation of h(x) can be written as -

h(x) = a(x+b)(x+c)²(x+d)

The zeroes of the polynomial can be written as -

x = 4 ⇒ (x - 4)

x = 1 ⇒ (x - 1)

x = 1 ⇒ (x - 1)....Since the multiplicity is 2 so write it two times.

x = -2 ⇒ (x + 2)

So, the equation will be -

y = a (x - 4)(x - 1)(x - 1)(x + 2)

The y-intercept is given as (0,16).

So, substitute the values of x and y with 0 and 16 respectively.

y = a (x - 4)(x - 1)(x - 1)(x + 2)

16 = a (0 - 4)(0 - 1)(0 - 1)(0 + 2)

16 = 2a(-4)(-1)(-1)

16 = 2a × -4

16 = -8a

a = -2

Hence, the equation becomes y = -2 (x - 4)(x - 1)(x - 1)(x + 2).

On graphing the equation it can be seen that -

As x → -∞, f(x) x → -∞

As x x → ∞, f(x) x → -∞

Therefore, the polynomial equation is h(x) = -2 (x - 4)(x - 1)²(x + 2).

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To determine the amount of work done by the person in the wheelchair going up the ramp, you can use the formula for work:

work = force x distance x cos(theta)

where force is the force exerted by the person (25 N), distance is the distance traveled (10 m), and theta is the angle between the force and the displacement.

The angle between the force and the displacement is 90 degrees because the force is perpendicular to the displacement.

The force exerted by the person is to overcome the force of gravity on the person and wheelchair weight (60 N).

work = force x distance x cos(90)

work = (25 N + 60 N) x 10 m x cos(90)

work = 85 N x 10 m x 0

work = 0 J

It's impossible to do work when the angle between the force and the displacement is 90 degrees because the force and the displacement are perpendicular to each other.

The height of the ramp (3 m) is not used in this calculation, as it is not related to the force or distance.

The work done by the person in the wheelchair is 0 J because the force exerted by the person is perpendicular to the displacement. However, the person will be expending energy to overcome the force of gravity and move the wheelchair up the ramp.

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Three points can define the two distinct vectors AB and AC (A, B, and C). The two vectors' cross product, which they both lie on, may be utilized as the plane's normal.

It is logical to assume that this is the case since a plane contains precisely two linearly independent vectors since it has a dimension of two. If the three points were collinear, there wouldn't be two linearly independent vectors; instead, the origin and tips of the two vectors are the three points.

The three points that make up a plane in a three-dimensional space can be used to define it as long as they are not on the same line. On a plane, there exist at least three non-collinear points. A line that connects any two locations in a plane is also considered to be a part of the plane. A line is created at the place of intersection when two planes clash.

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First, solve the equation for one of the variables in the pair of equations to be solved using substitution method x = 2/13, y = 52

The substitution method is one algebraic approach to solving a linear system. By substituting one y-value for another, the substitution method works. We will illustrate this with an example. Since y = y, we can use y in the first equation instead of the second one.

                                      4x+2y=10⋅2x=26+2y

Take the first equation, for example. For a result of 20, multiply 10 by 2.

                                     4x+2y=20x

20 x both sides should be subtracted.

                                    4x+2y−20x=0

Get 16x by combining 4x and 20x.

                                  −16x+2y=0

The second equation is an example. For a result of 20, multiply 10 by 2.

                                      20x=26+2y

From both sides, subtract 2y.

                                          20x−2y=26

First, solve the equation for one of the variables in the pair of equations to be solved using substitution. Replacing that variable in the other equation with the result follows.

                                       −16x+2y=0,   20x−2y=26

By placing x on the left side of the equal sign, isolate x from one of the equations and solve it for x.

                                                −16x+2y=0

In the equation, deduct 2y from both sides.

                                     −16x=−2y

Subtract 16 from both sides.

                                          x= − 16/ 1(−2)y

16 divided by 2y is the answer.

                                         x= 8  / 1 y

The second equation, 20x2y=26, should now read 8 y instead of x.

                                  20×( 8 /1  )y−2y=26

multiply 20 times 8 y.

                          2  / 5 ​ y−2y=26

Boost 2y by 2.5 years.

                                 2 /1  y=26

2 times both sides will give you y=52.

In the formula x = 81y, change y to 52. You can solve for x directly because the resulting equation only has one variable.

                                        x= 8 /1  ×52

52 x 8 /1 is the multiplication.

                                   x= 2 /13

The system has now been resolved substitution equation are

x = 2/13, y=52

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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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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(4.6cm + 6.8cm) =10.2cm

11.4cm = 10.2cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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No, All 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles.

No, not all right triangles are 30-60-90 triangles. A right triangle is a type of triangle that has one right angle (90 degrees) and two acute angles. The other two angles in a right triangle can have any measurement, they don't have to be 30-60-90 degrees.

A 30-60-90 triangle is a special type of right triangle that has specific angle measurements: one angle is 90 degrees (the right angle), one angle is 30 degrees, and one angle is 60 degrees. The ratio of the sides in a 30-60-90 triangle is also fixed, the longest side is opposite the 90-degree angle and it is always twice the length of the shortest side and the medium side is opposite the angle of 60 degrees and it's always the square root of 3 times the length of the shortest side.

For example, if a right triangle has angles of 45 degrees, 45 degrees, and 90 degrees, it is not a 30-60-90 triangle. The angles do not fit the pattern of 30-60-90 degrees.

Therefore, In short, all 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles. A 30-60-90 triangle is a special type of right triangle with specific angle measurements and side ratios.

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The nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.

The nature of the roots of a quadratic equation is determined by its discriminant (b2 – 4ac). The discriminant of the given equation 9x2 12x + 4 is (12)2 – 4(9)(4) = 144 – 144 = 0.

Since the discriminant is equal to zero, the equation has two equal (or identical) roots. This indicates that the equation has one root since its roots are equal. We may apply the quadratic formula to get the equation's root.

The quadratic formula states that the roots of a quadratic equation can be found by solving the equation:

x = (-b ± √(b2 – 4ac))/2a

When we apply the formula to the given equation, we get:

x= (-12 ± √(0))/2(9)

Since the discriminant is equal to zero, the equation has one root. The root of the equation is x = -4.

Therefore, the nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.

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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 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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it is 21

Step-by-step explanation:

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 odd one out is the furthest to the right. the Nickels.

The first square is 25 cents. The second square is 25 cents. The third square is 15 cents.

I hope this helps you :D

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

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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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 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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