Roxanne drew an indigo line that was 11 4/5 inches long. Then she drew a white line that was 6 3/5 inches long. How much longer was the indigo line than the white line?

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

The slope-intercept form a line is given by  

where m is the slope of a line and c is the y-intercept.

Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line

Here we have

Slope of line = -4/3

The point of the line

As we know y = mx + c is the line Here m is the slope of the line

From the given data, m = -4/3

=> y = (-4/3)x + c

=> 3y = -4x + 3c

Given that the point on the line is (-6, 2)

=> 3(2) = -4(-6) + 3c

=> 6 = 24 + 3c

=>  3c = 18

=> c = 6

Therefore,

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

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The total amount that Mikaela spent on the paddleboard will be  $449.80.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths.

As per the given,

Original price = $699

The selling price = $699 - 40% of $699

⇒ $699 - 0.40 x $699 = $419.4

The state tax (assuming it applied to the selling price) will be as,

7.25% of $419.4 = (7.25/100) x 419.4 = $30.4065

Final amount = $419.4 + $30.4065 = $449.80

Hence "Mikaela will have spent $449.80 in total on the paddleboard".

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Answer:

f^-1(x) = 2(x-2)^2 + 1

f^-1(x) = (x+3)^3

Step-by-step explanation:

The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.

3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.

The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.

Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.

To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace y with x in the original function to obtain x = ^3√y-3.

3. Solve for y in terms of x to obtain y = (x+3)^3.

The inverse function can then be written as f^-1(x) = (x+3)^3.

Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.

Answer:

[tex]51.4^{\circ}[/tex]

Step-by-step explanation:

Since this is a right triangle, the cosine formula says

[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]

[tex]\longrightarrow cos(x) = 0.6235[/tex]

[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]

Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]

The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units

To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:

length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Substituting the coordinates of P and Q into the formula, we get:

length = √((-1 - 2))²  + (5 - 1))²  + (3 - (-4)))² )

          = √((-3))²  + (4))²  + (7))² )

         = √(9 + 16 + 49)

         = √(74)

        = 8.60 units

Therefore, the length of the line segment is 8.60 units

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yes, z can lie between x and y but z can also lie on another side of x in Number lines.

With an example, define number line?

Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.

                  A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.

What does the math number line mean?

A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.

                               How a number is used—for example, to plot a point—depends on the question that goes with it.

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Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

Answer:

(sqrt3)/2

Step-by-step explanation:

Sin(x)=opposite/hypotenuse

30, 60, 90 right triangle.

ratio of sides are 1, sqrt3, and 2.

Locate the 60 degree angle on the triangle

The opposite side is sqrt3

The hypotenuse is 2

so its (sqrt3)/2

Answer:

√3/2 or 0.866

Step-by-step explanation:

The expression that shows the total number of cans collected by both homerooms is 14n - 4

The expression for more cans collected is 8n - 7 > 6n + 3

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

Homeroom      Cans Collected

Mr. Juarez        8n−7

Ms. Wade         6n+3

The total number of cans collected is calculated as

Cans collected = Mr. Juarez + Ms. Wade

Substitute the known values in the above equation, so, we have the following representation

Cans collected = 8n - 7 + 6n + 3

Evaluate the like terms

Cans collected = 14n - 4

Here, we have

Mr. Juarez's homeroom collected more cans

This means that

Mr. Juarez > Ms. Wade

Substitute the known values in the above equation, so, we have the following representation

8n - 7 > 6n + 3

Hence, the expression is 8n - 7 > 6n + 3

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The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.

What are the Properties of Angles of a Parallelogram?

A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.

The consecutive angles are supplementary then,

5y + 7y - 24 = 180

12y = 180 + 24

12y = 204

y = 204/12

y = 17

The opposite angles of a parallelogram are congruent (equal) then,

5y = 4x + 7

5(17) = 4x + 7

85 = 4x + 7

85 -7 = 4x

4x = 78

x = 78/4 = 19.5

x = 19.5

the consecutive angles are supplementary, then

4x + 7 + 3z = 180

4(19.5) + 7 + 3z = 180

78 + 7 + 3z = 180

85 + 3z = 180

3z = 180 - 88

3z = 92

z = 92/3

z = 30.6

All the angles of a parallelogram add up to 360°, then:

4x + 7 + 3z + 5y +7y - 24 = 360

To check is this a parallelogram? put the values of x, y, and z in the above equation:

4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360

356.8 ≠ 360

hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.

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Answer:

Step-by-step explanation:

Answer:

please tell me if you get the answer. I need it too!

Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.

Figure H

Mapped onto figure I

The required transformation:

reflection along y=x.

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Answer:

Below

Step-by-step explanation:

m = slope = rise / run

m = 5 for this equation

rise /run = 5

15 / run = 5

run = 3

The perimeter of the object is the sum of the lengths of all the sides

which is 302 units.

Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.

In the case of a circle, we call it perimeter circumference it is the distance around the circle.

Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and

HG = 37.

Now the perimeter of this figure is the sum of the lengths of all the sides which is,

= (EF + FD + ED + IG + HG).

= (71 + 80 + 74 + 40 + 37).

= 302 units.

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Sample size  123  is needed to estimate the mean weight to within 135 lbs with a 99% confidence level

What is confidence interval?

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.

Z(α/2) at 99% confidence level = 2.576

λ = 579

margin of error = ( Z(α/2) * λ ) / √n = 135

                        (2.576 * 579) / √n = 135

On simplifying, n ≈ 123

So, sample size  123  is needed to estimate the mean weight to within 135 lbs with a 99% confidence level

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Answer:  BD = 5

Step-by-step explanation:

[tex]a^{2} +12^{2} =13^{2}[/tex]

[tex]a^{2} =13^{2}-12^{2}[/tex]

[tex]a = \sqrt{25}[/tex]

[tex]a = 5[/tex]

Therefore BD = 5

Answer:

find my dad

Step-by-step explanation:

The value of the variable x is -2

An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.

These expressions are also made up of arithmetic or mathematical operations, which includes;

From the information given, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 18

Now, let's find the factors of 18 in 2's and 3's, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2

Collect the common factors, we get;

x+ 3 + x + 4 = 1 + 2

collect like terms

2x = 3 - 7

2x = -4

make 'x' the subject of formula

x = - 2

Hence, the value is -2

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A graph is a collection of points and the connections between some subset of those points that may or may not be empty in mathematical terms.

The given function is f (x ) = [tex]3e^{2x}[/tex]

1. Domain :

2.Range :

3.Continuity:

4.Behaviour that is either increasing or decreasing:

5.Symmetry:

6.Boundedness:

7.Extrema:

8.Asymptotes:

9.End behaviour :

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The length of the other leg of the triangle is 11.7 inches

Now, According to the question:

We have the right triangle

The length of the right triangle is 24 inches

The length of the hypotenuse is 26.7 inches

To find the length of the other leg of the triangle

We know that the Pythagorean theorem.

The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.

Let the length of the other leg of the triangle be 'x'

According to the information:

[tex]24^2 + x^2 = 26.7^2[/tex]

576 + [tex]x^{2}[/tex] = 712.89

[tex]x^{2}[/tex] = 712.89 - 576

[tex]x^{2}[/tex] = 136.89

x = [tex]\sqrt{136.89}[/tex]

x = 11.7

Hence, The length of the other leg of the triangle is 11.7 inches.

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Answer:

The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

The fractions reduced to standard form are -2/5, 1/5, 1/2 and 5/11 for 1), 2), 3), and 4) respectively

To reduce a fraction to standard form, you need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can be evenly divided into both the numerator and the denominator.

Given:

1) -18/45

The GCD of 18 and 45 is 9. Thus:

-18/45 = -2/5

2) -3/-15

The GCD of 3 and 15 is 3. Thus:

-3/-15 = 1/5

3) 28/56

The GCD of 28 and 56 is 28. Thus:

28/56 = 1/2

4) 45/99

The GCD of 45 and 99 is 9. Thus:

45/99 = 5/11

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1)-6/15

2)1/5

3)1/2

4)5/11

1) -18/45

⇒-6/15

2)-3/-15

⇒-1/-5

⇒1/5

3)28/56

⇒4/8

⇒1/2

4)45/99

⇒15/33

⇒5/11

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The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.

To draw the sketch of the graph, we need to consider these three following features:

The function in this problem is defined as follows:

f(x) = x(x - 5)(x - 3).

From the factor theorem, the x-intercepts are taken from the linear factors, as follows:

The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:

f(0) = 0(0 - 5)(0  -3) = 0.

In the problem, we have a cube function, hence:

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The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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Answer:

y = 1/4x - 4

Step-by-step explanation:

4x + y = 3

y = -4x + 3

Perpendicular slope = 1/4

y = 1/4x + b

-3 = 1/4(4) + b

-3 = 1 + b

b = -4

y = 1/4x - 4

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.

Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.

According to the angle bisector theorem;

An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.

a point is equally far from both sides of an angle if it is on the angle's bisector.

According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.

The explanation with diagram is given in the image.

Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

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Answer:

[tex]b = 6\sqrt{2}[/tex]

Step-by-step explanation:

Don't say giving brainiest for work, I will still help you.

Use the Pythagorean Theorem to solve:

[tex]a^2+b^2=c^2[/tex]

A and B refers to the legs, or the shorter sides. C refers to the hypotenuse, or the longest side.

Plug in what you know:

[tex](7)^2+b^2=(11)^2[/tex]

[tex]49 + b^2 = 121[/tex]

Subtract 49 on both sides.

[tex]49 - 49 + b^2 = 121-49[/tex]

[tex]b^2=72[/tex]

Find the square root of both sides.

[tex]\sqrt{b^2} = \sqrt{72}[/tex]

b = [tex]6\sqrt{2}[/tex]

Answer:

1/64

Step-by-step explanation:

1/8 x 1/8 = 1/64