Debra and Sue went to a clearance
sale at a clothing store. All blouses were
selling for the same price and all skirts
were selling for the same price. Debra
bought 4 blouses and 3 skirts for a total
of $68. Sue bought 6 blouses and 3
skirts for a total of $84. What was the
cost of each blouse and each skirt?

Please show work and the bottom question

Kevin's solution is incorrect. He found the area of the triangle as [tex]bh[/tex], not [tex]\frac{1}{2}bh[/tex].

The correct area of the triangle is [tex]\frac{1}{2}(8)(5)=20 \text{ in}^2[/tex].

The cost of 1 hot dog is $2.25

Proportion is a mathematical comparison between two numbers.

Given that, the cost of 4 hot dogs are $9, we need to find the cost of 1 hot dog,

Let the cost of 1 hot dog be x, therefore, setting the proportion,

4 / 9 = 1 / x

x = 9/4

x = 2.25

Hence, the cost of 1 hot dog is $2.25

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Line AB and CD are two parallel lines

The slope of a line is defined as the change in y- the coordinate with respect to the x-coordinate and the formula is given by    

Note:

Here we have  

AB formed by (-4, 7) and (-2, 6)

Slope of AB = (6 - 7)/(-2 + 4) = -1/2

CD formed by (2, -2) and (-8, 3)

Slope of CD = (3 + 2)/(-8 - 2) = 5/-10 = -1/2

Here Slope of AB = Slope of CD  

As we know the slope of parallel lines is equal

Therefore,

Line AB and CD are two parallel lines

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Answer:

f'(2)=64

Step-by-step explanation:

After plugging in 2 for x our equation would look like

log(2^2+(3×2))×2^(3x2)

Now just follow PEMDAS, starting with the left.

1: 2^2=4, 3×2=6, 4+6= 10

2: 3×2=6, 2^6=64

3: log(10)=1

4: 1×64=64

5: f'(2)=64

The set of pairs for which x and y vary inversely is given as follows:

{(-1, -2/7), (4, 1/14), (6, 1/21)}.

(third set).

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse relation, the relation is modeled as follows:

y = k/x.

Meaning that when x increases, y decreases at a constant rate.

The constant is then obtained as follows:

k = yx.

Hence the third relation is then the relation for which x and y vary inversely, as:

k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.

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The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.

1. The product of the numbers are:

a. √2 (√8) = √16 = 4

b. √49 (∛ 8) = 14

c. √3 (2/ √3) = 2

d. √2(4)

Option d is the correct answer.

Similarly, taking the product:

2. Option a is correct.

3. Option d is correct.

4. Option b is correct.

Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

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The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.

If two variables of two quantities, x and y, are represented on a graph to show their relationship, they are proportional quantities if for every ratio of y to x, the value we get is the same, which means they have a constant of proportionality, k.

Using the points on the graph in the image attached below, the table can be completed as follows:

Part A:

Number of T-shirts (x): 1   2   3   4

Time in minutes (y):     5  10  15 20

Part B: Find the ratio of y to x for each of the points on the graph.

5/1 = 5

10/2 = 5

15/3 = 5

20/4 = 5

The table derived from the graph is:

Number of T-shirts (x): 1   2   3   4

Time in minutes (y):     5  10  15 20

B. The quantities are proportional.

The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.

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"Your question is incomplete, probably the complete question/missing part is:"

The missing information are in the attachment below.

The required graph of the equation is given by y=x/2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: A graph proportional to the line that passes through the point.

Now one of the graph has the equation y= x/2

we can treat this line as some proportional equation with 1/2 as the constant.

And it also passes through the point (2,1)

Hence, The required graph of the equation is given by y=x/2

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The options containing the graph are attached

Answer:

The base is 8 and the height is 3. Multiply.

8 * 3 = 24

You will then multiply your product by 1/2.

24 * 1/2 = 12

The area is 12 inches squared.

Step-by-step explanation:

Hope it helps! =D

Answer:

[tex] {12cm}^{2} [/tex]

Step-by-step explanation:

Given

[tex]a = \frac{1}{2} bh[/tex]

b= 8in

h= 3in

8x3 = 24

24 ÷ 2 (Same as multiplying by half)

Factorization of  6ax - 15x is 3x.(2a - 5)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression,

6ax - 15x

It can be written as

3×2 . a . x - 3×5 . x

Factoring out common factor

3x.(2a - 5)

Hence, 3x.(2a - 5) is the factorization of 6ax - 15x.

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The exponential function from the table is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

Option D is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The exponential function is given as,

f(x) = m[tex]a^x[/tex]

Now,

From the table,

2 = m[tex]a^0[/tex]

m = 2

1 = m[tex]a^1[/tex]

m = 1/a ____(1)

0.5 = m[tex]a^2[/tex]

m = 0.5/[tex]a^2[/tex] _____(2)

Now,

From (1) and (2).

1/a = 0.5/[tex]a^2[/tex]

a = 0.5

Now,

f(x) = 2 [tex](0.5)^x[/tex]

Thus,

The exponential function is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

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answer is 2 because if we expand the bracket we get 2x–8y+3y which is 2x–5y but if it was 2(x+4y) it would be equal to 2x+8y+3y therefore being 2x+11y

The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12%  and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)

Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)

Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470

Now

y = 1470 + 350
y = $1820

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The angles  on the quadrilaterals she drew are 47 in number.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles

As there are four rectangles, The total number of angles in a rectangle are 4 × 4 = 16 angles.

The number of triangles is 3, the total number of angles is 3 × 3 = 9 angles.

Number of pentagons are 2,  the total number of angles is 2 × 5 = 10 angles.

The number of trapezoids are 3, the total number of angles is 3 × 4 = 12 angles.

Total number of angles on the quadrilaterals she drew is 16 + 9 + 10 + 12 = 47 angles.

Hence, the angles  on the quadrilaterals she drew 47.

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Answer:

<YTZ

Step-by-step explanation:

Vertical angles are congruent.

<VTW measures 40°.

<YTZ is vertical to angle VTW.

m<YTZ = m<VTW

m<YTZ = 40°

Answer: <YTZ

The solution of the expression is, 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ h (9) = 2x - 3

Now, Substitute x = 9, we get;

⇒ h (9) = 2 × 9 - 3

⇒ h (9) = 18 - 3

⇒ h (9) = 15

Thus, The solution of the expression is,

⇒ h (9) = 15

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Answer:

The length of 5 inches should be counted 1 time.

Step-by-step explanation:

The 5 inches between the triangle and rectangle is inside the shape. So, it doesn't count as perimeter.

The horizontal distance which the car must have travelled is equal to 450 meters.

Mathematically, the gradient (slope) of a geometric figure or line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the given image, we have the following distances and gradient (slope):

Rising vertical distance = 60

Horizontal distance (Run) = x

Gradient (slope) = 2/15

Substituting the given parameters into the formula, we have;

2/15 = 60/x

2x = 900

x = 450

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The area for this figure is given as follows:

38.13 cm².

The composite area of the figure is obtained by the sum of the areas of each component of the figure.

The figure is composed as follows:

The area of the rectangle is given by the multiplication of the dimensions, hence:

Ar = 6 x 4 = 24 cm².

The area of the semicircle is given by half the multiplication of π = 3.14 by the radius square, hence:

As = 0.5 x 3.14 x 3² = 14.13 cm².

Hence the total area is given as follows:

A = Ar + As

A = 24 + 14.13

A = 38.13 cm².

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The surface area of the pyramid, given the height and base of the triangles, and the area of the hexagonal base, is 439. 8 square inches

Let's determine the area of the six isosceles triangles using the formula;

= 6 x 1 /2 x base x height

= 6 x 1 / 2 x 10 x 6

= 180 square inches

The surface area of the pyramid is therefore;

= Area of triangles + Area of hexagonal base

= 180square inches + 259.8 square inches.

Add the values, we get;

= 439. 8 square inches

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Answer: 439.8

Step-by-step explanation:

The length of CE in the triangle is 20.

A triangle is a three-sided polygon that consists of three edges and three vertices.

From the given triangle ABC

BC=CD which are congruent sides

x-5=14

x=19

AB=DE

2x+3=6

2x=3

x=3/2

Now DE 2x+3=2(3/2)+3=6

CE=CD+DE

=14+6

=20

Hence, the length of CE in the triangle is 20.

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Answer:

Step-by-step explanation:

The reflection of point A will be at (3, -4) - that is 2 units directly below the red X.

The potential energy increases as the charges or the poles get further apart.

Static charges does not build up by polarization.

A field force is a force that acts on a particle without physical contact. It arises from the presence of a field, such as an electric field, magnetic field, or gravitational field.

The field exerts a force on a particle based on its charge, mass, or other property, and the strength of the force is determined by the field intensity and the properties of the particle. For example, an electric field exerts a force on a charged particle, while a gravitational field exerts a force on a mass.

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Answer:

Step-by-step explanation

Sort the data: 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97

Find the median (Q2): 53

Split the data set into two parts: Q1 (25th percentile) and Q3 (75th percentile)

Q1: 41, 41, 43, 43, 45, 50, 52, 53

Q3: 54, 62, 63, 63, 67, 75, 97

Find the median (Q1) of Q1 and the median (Q3) of Q3:

Q1 = 45

Q3 = 63

Finally, calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 63 - 45 = 18

So, the interquartile range of the given data set is 18. This means that 50% of the data falls within a range of 45 + 18 = 63 and 45 - 18 = 27.  

Answer:

3734.24100725

Step-by-step explanation:

This is related for all problems like this, not just this one:

When you see the key words below, this is what it means, and you can craft an equation from it:

Per = division

Of = multiplication

Using this above, we can replace the words with an equation:

The question is asking the amount of money per person.

Remember above, per means division:

Money/person

We know the amount of money and the number of people, so let's plug it in:

1,130,000,000/302,605

After division:

3734.24100725, final answer.

Hope this helps :D

Answer:

50to70

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

You are given distance (30 km)  and time  ( 3/4 hr) and want km/hr

soooo    30 km / ( 3/4 hr) = 40 km/hr

AB vector is a vector whereas AB bar is a line segment.

What is a vector ?

The vectors are described as an object containing both significance and course. Vector describes the motion of an item from one point to any other. Vector math may be geometrically picturised via the directed line segment.

The duration of the phase of the directed line is known as the value of a vector and the angle at which the vector is inclined shows the path of the vector. The start line of a vector is referred to as “Tail” and the finishing factor (having an arrow) is referred to as “Head.”

The difference is in their names itself.

AB vector is a vector whereas AB bar is a line segment.

A vector has a direction and a magnitude while a line segment ( scalar ) has only magnitude.

Therefore, AB vector is a vector whereas AB bar is a line segment.

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Answer:

"of -1 and 2."

Step-by-step explanation:

The quadratic function has a maximum value between the two input values of -1 and 2, with a maximum output of 9.