Mr. Blair and Ms. Stevenson are teaching their classes how to write in cursive. Mr. Blair has already taught his class 4 letters. The students in Ms. Stevenson's class, who started the unit later, currently know how to write 2 letters. Mr. Blair plans to teach his class 1 new letter per week, and Ms. Stevenson intends to cover 2. new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take?

Answer:

Step-by-step explanation:

To prove that sinA/(1-cosA) = 1/cosA, we will start with the left-hand side and simplify it using trigonometric identities.

sinA/(1-cosA) = sinA/(1-cosA) * (sin^2A + cos^2A) / (sin^2A + cos^2A)

= (sinAsin^2A + sinAcos^2A) / (sin^2A + cos^2A - sin^2AcosA - cos^2AcosA)

= (sinAsinAcosA + sinAcosAcosA) / (sinAcosA - cosAcosA)

= sinA/cosA / (sinA/cosA - 1)

= 1/cosA

Therefore, sinA/(1-cosA) = 1/cosA, which is true.

The equation for a line that passes through the points (-5, 3) and (3, -3) is y=-3/4(x+1)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope of line that passes through the points (-5, 3) and (3, -3)

m=-3-3/3+5

m=-6/8=-3/4

Now let us find y intercept.

3=-3/4(-5)+b

3=15/4+b

b=3-15/4

b=-3/4

So the slope intercept form is y=-3/4x-3/4

Hence, the equation for a line that passes through the points (-5, 3) and (3, -3) is y=-3/4(x+1)

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

The distance between the pair of points (- 5, 7) and (- 1, 3) is 5.7 units.

We know that the distance formula.

The distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given a pair of points (- 5, 7) and (- 1, 3)

Let us assume that  (x₁, y₁) = (-5, 7)

and (x₂, y₂) = (-1, 3)

Using above distance formula,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]} \\\\ d = \sqrt{[(-1 - (-5))^2 + (3 - 7)^2]}\\\\d = \sqrt{[(-1+5)^2 + (-4)^2]}\\\\d = \sqrt{[(4)^2 + (-4)^2]}\\\\d = \sqrt{(16+16)}\\\\d = \sqrt{32}\\\\d = 5.7~ units[/tex]

So, the distance is 5.7 units.

Learn more about the distance formula here:

https://brainly.com/question/12441680

#SPJ4

The complete question is:

What is the distance between the pair of points (- 5, 7) and (- 1, 3)?.

Answer:

No

Step-by-step explanation:

Notice when x increases by 1, y increases by $6?

When x goes from 1.5 to 2.5 gigabytes ( increase by 1 ), y increases from $65 to $71. That's a $6 increase for x increasing by 1 gigabyte.

In addition, when x goes from 2.5 to 3.5 gigabytes ( increase by 1), y increases from $71 to $77. This is also a $6 increase for x increasing by 1 gigabyte.

Yet...

65 / 1.5 doesn't equal 71 / 2.5

65 / 1.5 = 43 1/3

71 / 2.5 = 28.4

43 1/3 [tex]\neq[/tex] 28.4, so there is no proportion

Answer: No.

Step-by-step explanation:

      In a proportion relationship, y = kx. In other words, x times the constant of proportionality will equal y. Without a given constant of proportionality, we can use k =[tex]\frac{y}{x}[/tex]. In all instances, y divided by x should equal the same value (k). We will see if this stands true for all the given values.

      65 / 1.5 = 43.33333

      71 / 2.5 = 28.4

      74 / 3 = 24.66667

      77 / 3.5 = 22

      No. The x and y values do not have a proportional relationship.

Answer:

2 apples

Step-by-step explanation:

It is because she had 1 apple then she added another which made it 2.

To solve complex numbers using steps:

A complicated equation is one that requires the use of complex numbers to solve. A number with both a real element and an imaginary part is referred to as a complex number. It is written as follows: A and B in the previous equation both denote numerical values. A complex number is, as an illustration, <4+3i>.

In order to accomplish vaguely defined goals that cannot be attained through normal behaviors, complex issue solving is a set of self-regulated psychological processes and activities. A wide range of tactics and inventive knowledge combinations are required.

Learn more about complex number Visit: brainly.com/question/5564133

#SPJ4

The relationship of the degree x - [[- b+v(b2 - 4ac)V2a] = 0 describes the relationship between a quadratic equation's factors and its solutions. A quadratic equation's general equation is f(x) = ax*+ bx +. function:

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and respectively.

expression: Terms (constants and variables) are separated by mathematical operators to form a mathematical expression. equation: Two expressions are equated using a mathematical equation. The quadratic equation f(x) = axe + bx + c is given.

The quadratic equation (ax2 + bx + c= 0) can be expressed as a product of its linear factors as (x - k)(x - h), where h, k are the quadratic equation's roots. This process is known as factoring a quadratic equation.

We may write [h] =- b + v(b2 - 4ac)y2a [K]=(-b- V(b2 - 4ac))/2a using the quadratic formula. The link between the elements of a quadratic equation and its solutions can be expressed as - x- [[-b+v(b- 4ac)y2a] =0

X=[(b' - 4AC)y2A] = 0.

To know more about function expression, polynomial visit:

https://brainly.com/question/29959118

#SPJ4

It is called an isosceles right angle triangle.

In a right angle triangle there is one right angle present.

In an isosceles triangle two sides are equal to each other.

But in isosceles right angle triangle both the conditions got fullfield i.e., there is one right angle with other two sides are equal to each other.

Properties of isosceles right angle triangle:

1. The two sides are equal to each other i.e. the base of the triangle is equal to the perpendicular of the triangle.

2. There is only one right angle and other two angles must be equal to each other.

3. The other two angles in isosceles right angle triangle must be 45 degree each.

To Know more about isosceles right angle triangle visit:

brainly.com/question/29789105

#SPJ4

Answer:

Below

Step-by-step explanation:

The point-slope form of a line is:

y - y1 = m(x - x1)

Where m is the slope of the line and (x1, y1) is a point on the line.

Given that the line contains the point (-2, 1) we know that this point is on the line, so we can use it as (x1, y1) in the point-slope form.

By using the point (-2,1) we can write the point-slope form of the line as:

y - 1 = m(x + 2)

This means that the point-slope form of a line with slope that contains the point (-2, 1) is y - 1 = m(x + 2) where m is the slope of the line.

If the number can be expressed in the form of the fraction [tex]\frac{p}{q}[/tex] , then the number is called as Rational Number otherwise it is called as irrational number .

The Rational Numbers are the type of numbers that can be expressed in the form of [tex]\frac{p}{q}[/tex] , where p and q both are integers , and the denominator q should not be equal to 0 .

For Example : the numbers 5 , 2/3 , 6 are rational numbers .

The Irrational Numbers are defined as the type of real numbers which cannot be represented as simple fractions. The Irrational number cannot be expressed as a ratio .

For Example : [tex]\sqrt{2}[/tex] , [tex]\sqrt{5}[/tex] cannot be expressed as a fraction of integers , so they are irrational .

Learn more about Rational Numbers here

https://brainly.com/question/29301201

#SPJ4

5([tex]x^{2}[/tex] + 10/2[tex]x[/tex]) + 2

The number in the brackets is b/2a.

So:

5(x + 10/2(5))^2

5(x + 10/10)^2

5(x + 1)^2

Expand the double brackets for (x + 1)^2:

[tex]x^{2}[/tex] + [tex]x[/tex] + [tex]x[/tex] + 1

This simplifies to:

[tex]x^2[/tex] + 2[tex]x[/tex] + 1

5([tex]x^2[/tex] + 2[tex]x[/tex] + 1)

5x^2 + 10x + 5

2 - 5 = -3

5(x + 1)^2 - 3

Answer:

5(x + 1)^2 - 3

Answer:

x = -3, -1, 1, 3.

Step-by-step explanation:

x^4 - 10x^2 + 9 = 0

Step 1

Let t = x^2

So , we have the quadratic

t^2 - 10t + 9 = 0

Step 2

Factorise:

(t - 1)(t - 9) = 0

Step 3

So, t - 1 = 0 or t - 9 = 0

t = 1, 9.

But t = x^2

So, we have x^2 = 1 or x^2 = 9

So, x = ±1, ±3.

x = -3, -1, 1, 3.

The answer will be 76, using a gradient.

What is the gradient of the slope?

To find the gradient of the given data, horizontal as well as the vertical distance between two points in parallel is necessary to find.

532/7=76

Hence the answer is 76

To learn more about gradient refers to;

https://brainly.com/question/29222498

#SPJ1

Answer:

11,000 or to be more specific $11,000

Step-by-step explanation:

Well there is no equation provided so one has to go by the graph

The y-intercept is where the line intersects the y-axis

Looking at the graph we see this is at y ≅ 11,000

Of course it all depends on your best fit line that you have drawn though it looks OK

Basically the y-intercept for this graph is $11,000 which is the cost of the Prius in 2004

A square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

What is the conversion factor?

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equals 1 foot.

A square yard of carpet is equivalent to 9 square feet because 1 yard = 3 feet and 1 square foot = 1 foot x 1 foot.

So, to find the cost of a square yard of carpet that is selling for $8.95 per square foot, we need to multiply the price per square foot by the conversion factor of 9 square feet per square yard.

$8.95/square foot * 9 square feet/square yard = $80.55/square yard

Hence, a square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

To learn more about conversion factor visit,

https://brainly.com/question/97386

#SPJ1

Carrie average has a head full of 16 curlers, with 4 of them being pink, 8 of them being green, and the remaining 12 being can curlers.

1. There are 16 total curlers on Carrie's head

2. One-fourth of the curlers are pink, so that is 16 ÷ 4 = 4 pink curlers

3. There are twice as many green curlers as pink ones, so that is 4 x 2 = 8 green curlers

4. The remaining 12 curlers are can curlers, so there are 12 can curlers on Carrie's head

Carrie has a head full of 16 curlers in total. One-fourth of the curlers are pink, so we can divide 16 by 4 to get 4 pink curlers. There are twice as many green curlers as pink ones, so we can multiply 4 by 2 to get 8 green curlers. This leaves 12 curlers, which must be can curlers. Therefore, there are 12 can curlers on Carrie's head. We can use basic mathematics to break down the problem into smaller pieces and calculate the number of each type of curler on her head.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

Yes, the square root of 64 is a rational number.

and Square root of 64 is 8

Now, According to the question:

Square numbers are those numbers that are produced by multiplying an integer to itself. If n is an integer, then n2 is the square of n.

What are the examples of square numbers?

The examples for square numbers are:

[tex]6^2[/tex] = 36

[tex]10^2[/tex] = 10 x 10 = 100

[tex]15^2[/tex] = 15 x 15 = 225

[tex]12^2[/tex] = 12 x 12 = 144

Hence, Yes, the square root of 64 is a rational number. As we know that √64 = 8, a rational number.

Learn more about Square Root at:

https://brainly.com/question/3120622

#SPJ4

Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.

What is algebraic equation ?

An algebraic equation is a mathematical statement that uses mathematical symbols (such as numbers, variables and mathematical operations) to express the equality of two expressions. It is used to represent mathematical relationships and to find solutions to problems. The most common operations used in algebraic equations are addition, subtraction, multiplication, and division.

Let x be the number of books that Inola check out

We know that:

Angel checks out 12 books

Inola checks out 1/3 less than Angel

We can set up the equation:

x = 12 - (1/3*12)

x = 12 - 4

x = 8

So, Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.

To learn more about algebraic equation visit : brainly.com/question/953809

#SPJ4

Angel checks out 12 books

Inola checks out 1/3 less than Angel

We can set up the equation:

x = 12 - (1/3*12)

x = 12 - 4

x = 8

The set of values that satisfy a given set of equations or inequalities is known as a solution set in mathematics.

The solution set, for instance, is the subset of a set of polynomials over a ring on which all of the polynomials formal disappear (evaluate to 0).

Plug in each value from the replacement set and evaluate both sides of the equation to determine the solution set from the replacement set. The value is a solution to the equation if the two sides are equal. One example: From the replacement set, choose the set with the solution 11 - 5w = 1.

The set of values that satisfy a given inequality is called a solution set. This indicates that the inequality will be satisfied by every value in the solution set and by no other value. Example: 2x + 3  7, where x is a natural number, is the solution.

To learn more about solution set here:

https://brainly.com/question/4192789

#SPJ4

Answer:30:1

Step-by-step explanation:

60÷2

=30/1

=30:1

Yes, I would like to purchase a ticket for the movie. The discounted sale price would be $8.37 after factoring in the 20percentage student discount and the 5.75% tax rate.

Original Price: $10.90

Student Discount: 20% of 10.90 = 2.18

Subtotal: 10.90 - 2.18 = 8.72

Tax Rate: 5.75% of 8.72 = 0.50

Final Sale Price: 8.72 + 0.50 = 8.37

Yes, I would like to purchase a ticket for the movie. The original price of the ticket is $10.90. As a student, I am eligible for a 20% discount, which when applied to the original price brings it down to $8.72. To calculate the final sale price, I then need to factor in the 5.75% tax rate. This is done by multiplying the subtotal of $8.72 by 0.0575, which gives me a tax amount of $0.50. When this amount is added to the subtotal, the final sale price becomes $8.37.

Learn more about percentage here

https://brainly.com/question/16797504

#SPJ4

The sum of the roots of the equation is

97/9

Generally, The roots of equation 3x^2 + 4x + 12 = 0 can be found by factoring or by using the quadratic formula.

By factoring: 3x^2 + 4x + 12 = 0 \Rightarrow (3x + 4)(x + 3) = 0$

Thus, the roots are

r = [tex]-\frac{4}{3}[/tex][tex]-\frac{4}{3}[/tex]

s = -3.

By using the quadratic formula:

[tex]r,s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\ = \frac{-4 \pm \sqrt{4^2 - 4(3)(12)}}{2(3)} \\\\= \frac{-4 \pm \sqrt{-48}}{6}\\\\ = -\frac{2}{3} \pm \frac{\sqrt{-3}}{3}i[/tex]

The sum of squares of roots is

r^2+s^2 =[tex](-\frac{4}{3})^2 + (-3)^2[/tex]

[tex]= \frac{16}{9} + 9\\\\ = \frac{16+81}{9}[/tex]

= [tex]\boxed{\frac{97}{9}}[/tex]

Read more about the roots of equation

https://brainly.com/question/12029673

#SPJ1

The general form for the absolute value equation to describe a graph is written as f(x) = a|x - h| + k  .

The Absolute Value Function is defined as a function in algebra where the variable is inside the absolute value bars.

The general form for absolute value function is f(x) = a |x - h| + k and  commonly used form of this function is f(x) = |x| .

Plot the graph of  function f(x) = |x| whose formula can also be expressed as f(x) = x, if x ≥ 0 and -x, if x < 0.

Consider different points for x = -1 , y is 1 ,

for x = 1 , y is 1 .

On plotting we get the graph as shown below .

Learn more about Absolute Value here

https://brainly.com/question/30278629

#SPJ4

The value of exponential growth  after 327 minutes is 1870.

Exponential growth is the process by which quantity increases over time. It occurs when a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself.

An exponential function depicts the relationship between an input and an output by using repeated multiplication on an initial value to obtain the output for any given input.

We are aware that

The exponential growth equation is equal to

y = a(1 + r)ˣ

where

an is the starting point.

r denotes the growth rate.

x represents the time in hours.

y is the quantity's value.

We now have

a = 1800

r = 0.7%

 = 0.7/100

 = 0.007

By substituting,

y = 1800(1 + 0.007)ˣ

x = 5.45 hr

y = 1800(1.007)^5.45

y = 1869.748182

y = 1870

To learn more about exponential growth refer to :

https://brainly.com/question/26106075

#SPJ1

The length of the base of the rectangle is B = 11 yards

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

To learn more about area of rectangle click :

https://brainly.com/question/15225905

#SPJ1

Sum in math the sum of the series is computed using the summation formulas.

The sum of the series is computed using the summation formulas. There are many different kinds of sequences, including arithmetic and geometric sequences, and consequently, there are many different kinds of summing formulas for those different kinds of sequences.

There are also summation formulas that determine the sum of natural numbers, sum of natural number squares, sum of natural number cubes, sum of natural number evens, sum of natural number odds, etc. The list of summation formulas is provided here. Each of these formulas will be covered in detail in the section that follows.

a₁ + a₂ + a₃ +.......aₙ = Σ a

Learn more about Summation:

https://brainly.com/question/15973233

#SPJ4

Yes, the function f(x)=2x-3 is a one-to-one function.

The Inverse of a Function:

The inverse of a function can be computed if the function can be proven to be one-to-one. Take the one-to-one function and compute its inverse by interchanging x and y in the expression and solving for y.

Graphically, then, the graphs of the function and its inverse are the reflections of each other about the line y=x.

Use the definition to test the one-to-one of f.

Let x and x be the elements in the domain off and assume f(x₁)=f(x₂)

2x₁-3=2x₂-3

2x₁=2x₂

x₁=x₂

since f(x₁)=f(x₂) implied x the function f is one-to-one.

To know more about one-to-one function:

https://brainly.com/question/28911089

#SPJ4

In mathematics, particularly in algebra, there are mainly two types of solutions for an equation: real and complex solutions.

Real solutions: These are type of solutions that are real numbers, which can be found by solving the equation algebraically. For example, if the equation is x² + 2x - 3 = 0, the real solutions are x = -1 and x = 3.

Complex solutions: These are solutions that are complex numbers, which can be found by solving the equation algebraically. Complex numbers are numbers that have both real and imaginary parts, represented by a + bi, where a and b are real numbers and i is the imaginary unit (i² = -1). For example, if the equation is x² + 1 = 0, the complex solutions are x = i and x = -i.

To know more on solutions

https://brainly.com/question/8307840

#SPJ4

The other equation of the system of linear equation that has no solution is y = 2x - 2.

If a system of linear equations has no solution, it means that the equations are inconsistent, which means that the two lines represented by the equations will not intersect. Therefore, the lines are parallel with each other.

One way to find the equation of the other line that would make the system inconsistent is to find the equation of a line that is parallel to the given equation but has a different y-intercept.

The given equation is in slope-intercept form, y = mx + b, where m is the slope (in this case, m = 2) and b is the y-intercept (in this case, b = -1).

A line that is parallel to the given line will have the same slope (m = 2), but a different y-intercept. For example, a line with y-intercept of -2: y = 2x - 2.

So, one equation that could be the other equation of the system and make it inconsistent is y = 2x - 2.

The problem seems incomplete, it must have been...

"A system of linear equation has no solution. One of the equations of the system is shown. y = 2x − 1 Which equation could be the other equation of the system?"

Learn more about system of linear equations here: https://brainly.com/question/13729904

#SPJ4

Answer:

Step-by-step explanation:

Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks costing a total of $97.50. This will be:

9p + 8d = 97.50

Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. This will be:

5p + 4d = 51.50

where P = popcorn

d = drink

The equations will be:

9p + 8d = 97.50

5p + 4d = 51.50

Multiply equation i by 5

Multiply equation ii by 9

45p + 40d = 487.50

45p + 36d = 463.50

Subtract

4d = 24

Divide.

d = 24/4

d = 6

Since 9p + 8d = 97.50

9p + 8(6) = 97.50

9p + 48 = 97.50

9p = 97.50 - 48

p = $5.50

where P = popcorn and d = drink