Katherine has $460 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $362.68.
She buys 3 bicycle reflectors for $10.20 each and a pair of bike gloves for $12.54.
She plans to spend some or all of the money she has left to buy new biking outfits for $27.09 each.

The coordinates of the vertices of the preimage triangle = (4, 1), (6,1) and (6, -6).

Given the figure of the image triangle.

The coordinates of the image triangle are (-4, 1) , (-6,1) and (-6, -6).

We are asked to find the coordinates of the preimage triangle.

The preimage triangle was reflected over the y-axis .

The image triangle is lying on the 2nd and 3rd quadrants.

So the preimage triangle will lie on the 1st and 4th quadrants.

Then the coordinate (-4,1) will be the image of (4,1).

(-6, 1) will be the image of (6,1) and (-6,-6) will be the image of (6,-6).

Hence the coordinates of the vertices of the preimage triangle = (4, 1), (6,1) and (6, -6).

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The 2 graphs are of parabolas .

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola. Also, an important point to note is that the fixed point does not lie on the fixed line. A locus of any point which is equidistant from a given point (focus) and a given line (directrix) is called a parabola. Parabola is an important curve of the conic sections of the coordinate geometry.

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So, 1−x represents the percent of original price being paid as we know that if percentage is given in decimal form, then to get the percent of original.

The decimal number framework has 10 digits which range from 0 to 9 with the base 10 and transformation from paired to decimal can assist us with better figuring out the compound parallel numbers. The decimal numeral framework is the standard framework for meaning number and non-whole number numbers. It is the augmentation to non-whole number quantities of the Hindu-Arabic numeral framework. The approach to meaning numbers in the decimal framework is frequently alluded to as decimal documentation. Numerous numeral frameworks of antiquated civilizations utilize ten and its powers for addressing numbers, perhaps on the grounds that there are ten fingers on all fours began counting by utilizing their fingers. Models are first and foremost the Egyptian numerals, then the Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals.

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Answer:

I don't think this is possible to solve,

Step-by-step explanation:

Answer:

It will not be enough money to pay for the fruit

Step-by-step explanation:

Reason:

3+3.87+2.23+2.37= $11.47

$11.47-10= $1.47

hes missing $1.47

(-4, 2)

This point lies on the second quadrant because this point has negative x-axis value and positive y-axis value

(-1, 0)

This point also lies on the x-axis because the y-axis value is zero.

(-4, -6)

This point also lies on the third quadrant because this point has negative x-axis and y-axis values

On the cartesian plane, four regions are created at the point where the X and Y axes intersect at 90 degrees. These regions are known as quadrants. Each of the four quadrants in each plane is therefore bound by one-half of the axes. Depending on where they are in relation to the axes, each quadrant is identified by a Roman numeral and given the names Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.

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Answer:

c is the answer to it

Step-by-step explanation:

did I help you

The expression can be rewrite as [tex](4\times6)+(5\times6)[/tex] using distributive property.

Use this property of multiplication rather than addition when you need to multiply a number by the sum of two numbers.

Let's use properties to calculate given  expression. The number 6 is divided by two addends. Simply put , multiply each summand by 6 and add the products together.

By using distributive property , we get

[tex](4+5)6=(4\times6)+(5\times6)[/tex]

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Answer:

6x - 14= 5

Step by Step

Let the cost of one milky way be 'x'

Given -

Initial Amount of money= $14

Final Amount of money= $5

Number of Milky Way= 6

Cost of 6 Milky Ways = 6x

Answer-

6x -14= 5

6x = 5+14

6x = 19

x =$3.1

Answer:

6x = 36 is the correct expression.

Answer:

6x=36 so we divide both side by 6, then we will gate the x =6

Step-by-step explanation:

The prices in order from greatest to least unit rate is Price A>Price C>Price B.

Given a table that showing different prices for cans of soup as shown in attached image.

Here, we will calculate the price of 1 quantity of each type of soup.

The Price of 3 quantities of soup price A=$3.87

Now, we will find the price of soup A for the 1 quantity.

The Price of 1 quantity of soup price A=$3.87/3=$1.29

The Price of 2 quantities of soup price B=$2.38

Now, we will find the price of soup B for the 1 quantity.

The Price of 1 quantity of soup price B=$2.38/2=$1.19

The Price of 7 quantities of soup price C=$8.75

Now, we will find the price of soup C for the 1 quantity.

The Price of 1 quantity of soup price C=$8.75/7=$1.25

Hence, the prices in order, from greatest to least unit rate from the given table which is shown in attached image is Price A>Price C>Price B or $1.29>$1.25>$1.19.

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The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

For example:

Find the median of the set {2,5,8,11,16,21,30} .

There are 7 numbers in the set, and they are arranged in ascending order.  The middle number (the 4 th one in the list) is 11.  So, the median is 11.

The center of a data set is also a way of describing the location. The two most widely used measures of the center of the data are the mean (average) and the median. To calculate the mean weight of 50 people, add the 50 weights together and divide by 50. To find the median weight of the 50 people, order the data, and find the number that splits the data into two equal parts. The median is generally a better measure of the center when there are extreme values or outliers because it is not affected by the precise numerical values of the outliers.

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The degree measure for angle B is 28° and angle D is 62°.

We are given that:

∠ C = 90°

∠ B = ( 2 x + 10 )°

∠ D = ( 5 x + 17 )°

Now, using the angle sum property of a triangle, we get that:

∠B + ∠ C + ∠ D  = 180°

Substituting the values:

2 x + 10 + 90 + 5 x + 17 = 180

7 x + 117 = 180

7 x = 63

x = 63 / 7

x = 9

∠ B = ( 2 x + 10 )

∠ B = 2(9) + 10

∠ B = 18 + 10

∠ B = 28°

∠ D = ( 5 x + 17 )

∠ D = 5 (9) + 17

∠ D = 45 + 17

∠ D = 62°

Therefore, the degree measure for angle B is 28° and angle D is 62°.

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Answer:

see explanation

Step-by-step explanation:

the perimeter (P) is the sum of the 4 sides

(a)

P = a + b + c + d

  = x + 7 + 2x + 2 + 8x + x + 10 ← collect like terms

 = 12x + 19

(b)

If x = 4 , then

P = 12x + 19 = 12(4) + 19 = 48 + 19 = 67

(c)

If x = 2 , then

P = 12x + 19 = 12(2) + 19 = 24 + 19 = 43

(d)

P = a + b + c + d

   = x² + 4x + 8 + 2x² + x ← collect like terms

   = 3x² + 5x + 8

tan<0 and csc<0 are in Quadrant II

The slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

According to the question.

A line passes through the two points (-2, 5) and (6, -4).

As we know that, the slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

So, the slope of the line = -4 -5/(6 + 2) = -9/8

And, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4) is given by

y = (-9/8)x + b

Since, the line passes through (-2, 5) and (6, -4). So, both the points must statisfy the above equation.

⇒ 5 = (-9/8)(-2) + b

⇒ 5 = 9/4 + b

⇒ b = 5 - 9/4

⇒ b = (20 - 9)/4

⇒ b = 11/4

Therefore, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

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Answer:

h(x)=-2x²+3

Step-by-step explanation:

Add 5 to -2x²-2.

-2x²-2+5=-2x²+3

h(x)=-2x²+3

Hope this helps!

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1. The equation of the perpendicular line is: y = -x + 4

2. The equation of the parallel line is: y = -x + 4

The equations of two lines that are parallel to each other will have the slope (m), while the equations of two lines that are perpendicular to each other will have slope values that are negative reciprocals of each other.

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

1. The slope (m) of y = x - 4 is 1. The line that is perpendicular to y = x - 4 would have a slope (m) of -1.

Substitute (a, b) = (1, 3) and m = -1 into y - b = m(x - a):

y - 3 = -1(x - 1)

Rewrite in slope-intercept form:

y - 3 = -x + 1

y = -x + 1 + 3

y = -x + 4

2. The slope (m) of y = -x - 4 is -1. The line that is parallel to y = -x - 4 would have a slope (m) of -1.

Substitute (a, b) = (3, 1) and m = -1 into y - b = m(x - a):

y - 1 = -1(x - 3)

Rewrite in slope-intercept form:

y - 1 = -x + 3

y = -x + 3 + 1

y = -x + 4

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Answer:They need 19,000 more

Step-by-step explanation:

The equation to represent the relationship between Distance and Time will be 52y = x, where Speed remains constant

In the given question, it is said that the train runs along a distance of 156 miles, which takes 3 hours to complete.

The equation that represents the relationship between Speed, Distance, and Time is as follows :

=> Speed = Distance/Time

It is also stated that the train runs at the same speed so the Speed will be constant while deriving the relationship between Distance and Time.

First, we have to find the speed of the train with the given Distance & Time by the formula => S = D/T, where Speed = S, Distance = 156 miles, and Time = 3 Hours

=> S = 156/3 => S = 52 miles/hour

As we got our constant speed for the train, We can now find out the Distance Time relation of the train. By taking Distance = x, Time = y, Speed = 52 miles/hour

                     => 52 = x/y      => 52y = x

Hence, we get the relationship between Distance and Time where Speed is constant at 52 miles/hour

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cheap answer, to get the x-intercepts, set x = 0 and solve for "y", to get the y-intercept, set y = 0 and solve for "x".

[tex]y-6=4(x+5) \\\\[-0.35em] ~\dotfill\\\\ y-6=4(\stackrel{x}{0}+5)\implies y-6=20\implies y=26~\hfill \stackrel{y-intercept}{(0~~,~~26)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{y}{0}-6=4(x+5)\implies -6=4x+20\implies -26=4x \\\\\\ \cfrac{-26}{4}=x \implies -\cfrac{13}{2}=x\implies -6\frac{1}{2}=x ~\hfill \stackrel{x-intercept}{\left( -6\frac{1}{2}~~,~~0 \right)}[/tex]

Yes. It is a right-angled triangle.

The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of numbers of equal length (often coordinate vectors) and outputs a single number. The dot product of two vectors' Cartesian coordinates is frequently used in Euclidean geometry. Although other inner products can be defined in Euclidean space, it is frequently referred to as the inner product (or, less frequently, projection product) of Euclidean space (see Inner product space for more).

The sum of the products of the matching entries of the two number sequences is the dot product, according to algebra. B, it is the result of adding the cosine of the angle between the two vectors and the Euclidean magnitudes of the two vectors.

The vectors that make up the triangle must first be located. The vertices are subtracted to achieve this.

QP=(2,0,-4)-(1,-3,-2)=(1,3,-2)

PR=(1,-3,-2)-(6,-2,-5)=(-5,-1,3)

RQ=(6,-2,-5)-(2,0,-4)=(4,-2,-1)

QP.PR = (1, 3, -2).(-5, -1, 3) = -5-3-6= -14

PR.RQ = (-5, -1, 3).(4, -2, -1) = -20+2-3 = -21

RQ.QP = (4, -2, -1).(1, 3, -2) = 4-6+2 = 0

Calculate the dot products to see if these vectors are perpendicular now.

They are perpendicular if the dot product of two vectors equals zero. As you can see, RQ.QP is zero in your triangle, which supports this. Consequently, a right-angled triangle results.

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Check the picture below.

now if the interest rate is 4%, that's in percentage form, we need to use the decimal version of it, namely 4/100 = 0.04, and since we know that x = 1 + r, whilst r = 0.04, that means that x = 1 + 0.04, x = 1.04.

[tex]1000x^3~~ + ~~300x^2~~ + ~~500x\implies 1000(1.04)^3~~ + ~~300(1.04)^2~ + ~500(1.04) \\\\\\ 1124.864~~ + ~~324.48~~ + ~~520 {\LARGE \begin{array}{llll} ~~ \approx ~~ 1969.33 \end{array}}[/tex]

We get the reflection of points T, U and V as T' = (0, 2), U' = (0, 1) and V' = (0, 4) over the x- axis.

We are given some coordinates:

T(0, - 2), U(2, - 1), V(3, - 4)

We have to first plot them on a graph.

Now, we have to reflect them over x - axis.

To reflect over x- axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

For point T:

Additive inverse of - 2 = 2

T' = (0, 2)

For point U:

Additive inverse of - 1 = 1

U' = (0, 1)

For point V:

Additive inverse of - 4 = 4

V' = (0, 4)

Therefore, we get the reflection of points T, U and V as T' = (0, 2), U' = (0, 1) and V' = (0, 4) over the x- axis.

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Answer: 30

Because its thirty

Answer: 8

Step-by-step explanation: Use pemdas

3[9 - (6-3)] – 10 : Complete parentheses (6-3)

3[9 - 3] - 10 : Complete equation in parentheses

3[6] - 10 : Multiply 3 and 6

18 - 10 = 8

Answer:

8

Step-by-step explanation:

3[9 - (6-3)] – 10

3 [9 - (3)] - 10

3 (6) - 10

18 - 10

8

This problem is about "order of operations."  These are the rules we all agree upon that dictate which order we do mathematical operations.  We use the acronym PEMDAS to help remember them:

P - parentheses first, then:

E - exponents (powers, square roots, etc)

MD - multiplication and division (from left-to-right)

AS - addition and subtraction (from left-to-right)

The simplified equation of the given statement = 1.08r.

Even though they also have different operations, adding and subtracting variables follow the same rule: while adding or subtracting terms with the same variables, either add or subtract the coefficients and leave the result with the variable. As an example, consider an addition.

The original cost of the new robotic toy is given as r.

The cost of the new robotic toy after a 8% markup is: c + 0.08r to show that 8% of r was being added to r to increase the price.

Because both numbers in the equation are related to the same variable, they can be added. When r is used alone, it is considered to be 1r.

= r + 0.08r

= 1r + 0.08r

= 1.08r

The simplified equation of the given statement =  1.08r

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I understand that the question you are looking for is:

The cost of a new robotic toy after an 8% markup can be represented by the expression r+0.08r. Simplify the expression.