square corners, 5 units on a side, are removed from a 20 unit by 30 unit rectangular sheet of cardboard. the sides are then folded to form an open box. the surface area, in square units, of the interior of the box is

Step-by-step explanation:

x² - y² = (x + y)(x - y)

3x - 3y = 3(x - y)

(x + y)(x - y) / (3(x - y)) = (x + y)/3

Answer:

x^2 - y^2

_______

3x - 3y

(x+y) (x-y)

_______ { (x-y) (x-y) cancels out}

3(x-y)

(x+y)

____

3

Hope this will help you...!!!!

The expression of the side length is 6y - 5

The complete question is added as an attachment

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

Perimeter = 48y - 40

Number of sides = 8

The side length s can be calculated as

s =(48y - 40)/8

Evaluate the quotient

s = 6y - 5

Hence, the side length expression is 6y - 5

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Answer: yes

Step-by-step explanation:

It's right angled if and only if A^2 + B^2 = C^2

- a^2 = (11-3^2 + 11-5^2) = (64 + 36) = 100

- b^2 = (6-3^2 + 1-5^2) = (9 + 16) = 25

a^2 + b^2 = 125 = sqrt(125)^2

Answer: 7

Step-by-step explanation:

Patricia has  6 cans of almonds that each contain eight 1/3 cup servings, meaning that Patricia has a total of

6 cans x 8 servings x 1/3 cup = 16 cups of almonds

If she needs 2.25 cups of almonds, that would be equal to

16/2.25 = around 7.1

since you can't have a fraction of a snack bag, Patricia just has 7 snack bags.

The numbers that correctly complete the two-way table are 100,70, 170, 80, 130, 210, 180,200, and 380 as shown in the attached chart.

Total of sweatshirts= 380

Total with no hood= 210

Green sweatshirts= 180

Purple sweatshirts with no hood= 70

Based on this information we can conclude:

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The measure of the side length n is equal to 14 for the right triangle.

Considering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent m and hypotenuse 28+7= 35;

cosθ = m/35

for the smaller right triangle with adjacent 7 and hypotenuse m

cosθ = 7/m

m/35 = 7/m

m² = 245 {cross multiplication}

m = √245 = 7√5 {take square root of both sides}

(√245)² = 7² + n² {by Pythagoras rule for the smaller right triangle}

245 = 49 + n²

n² = 245 - 49 {collect like terms}

n² = 196

n = √196 {take square root of both sides}

n = 14

Therefore, the measure of the side length n is equal to 14 for the right triangle

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Since function f andg are continuous and u g subseteq u f, Theorem 2.1.13 states that f circ g is continuous on u g.

In accordance with Theorem 2.1.13, if two functions,f andg, are continuous on open domains [tex]$u f$[/tex]and [tex]$u g$[/tex] respectively, and $g(u g)subseteq u f, then $ circ g is continuous on u g. This is the case since the domain of f, which is u g is a subset of the domain of f, which is u g, and the composition of continuous functions is continuous. The composition of these two functions will be continuous onu g because both of these functions are continuous and u g subseteq u f.

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Yes, these numbers meet the triangular inequalities, then these can be the measures of the sides of a triangle.

Remember that if A, B, and C are the sides of a triangle, then the triangle inequality says that:

A + B > C

A + C > B

C + B > A

As long as 3 values are solutions of the inequalities, then these can be the sides of a triangle.

if we use:

A = 7

B = 10

C = 10

Then we get:

7 + 10 > 10 ---> 17 > 10

7 + 10 > 10 ---> 17 > 10

10 + 10 > 7 ---> 20 > 7

All the ienqualities are true, thus, these can be the measures of the sides of a triangle.

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Answer:

47.21

Step-by-step explanation:

Subistitute:-47.4-0.19

Calculate the sum or difference:-47.21

The two expressions are written as :

3f+4s+2f this expression that we have here is a mathematical expression that we can  combine by making use of the commutative addition.

We would have the first expression when we write the equation as:

3f+4s+2f = 3f + 2f + 4s

We would have the second expression when we write the equation as

5f + 4s

This is the solution of the expression.

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two expressions that are equivalent to 3f+4s+2f ?

The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π

When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.

Thus, since we want to find the radian measure of 170 degrees, it means that;

If 180° = π radians,

then; 170° = (170 * π)/180

= ¹⁷/₁₈π

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The solution to the simultaneous equations is; 5 comma one half

The simultaneous equations are;

y = -¹/₂x + 3    -------(1)

y = ¹/₂x - 2    -------(2)

Substitute ¹/₂x - 2 for y in eq 1 to get;

¹/₂x - 2 = -¹/₂x + 3

Add -¹/₂x to both sides using addition property of equality to get;

¹/₂x + ¹/₂x - 2 = 3

Add 2 to both sides using addition property of equality to get;

x = 3 + 2

x = 5

Thus;

y = ¹/₂(5) - 2

y = ¹/₂

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Answer:

Solve the system of linear equations by graphing.

y equals negative one half times x plus 3

y equals one half times x minus 2

Step-by-step explanation:

Answer:

( y + z - z )

given, y= 6 z=5

(6 + 5 - 5 )

Use DMAS rule

D=division M= multiplication A= addition S=subtraction

(11-5)

6 (ans)

The artist charges $25 for a small painting and $65 for a large painting.

How to substitute two equations?

To substitute one equation into another, you can replace one of the variables in the second equation with the expression from the first equation.

Let K be the price of small painting and L be the price of large painting.

From the information given, we know that:

Last month:

6K + 8L = $670 (1)

This month:

12K + 10L = $950 (2)

We have two equations and two unknowns, so we can use a system of equations to find the values of K and L.

Solving the system of equations:

From (1) equation, we have:

6K + 8L = $670

From (2) equation, we have:

12K + 10L = $950

Now we can solve for K (small painting) by multiplying equation (1) by 2 and equation (2) by -1 and adding the two equations together:

12K + 16L = $1340

-12K - 10L = -$950

0K + 6L = $390

Therefore, L = $390 / 6 = $65

Now we can substitute this value of L back into the first equation (1) and solve for K:

6K + 8($65) = $670

6K = $670 - 8($65) = $670 - $520 = $150

K = $150 / 6 = $25

So, the artist charges $25 for a small painting and $65 for a large painting.

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Answer:

see attached

Step-by-step explanation:

The linear equation y = - 4 · x + 1 includes point (x, y) = (2, - 7).

In this problem we need to plot a linear equation on Cartesian plane, linear equations are first polynomials of the form:

y = m · x + b

Where:

If we know that b = 1 and (x, y) = (2, - 7), then the equation of the line is:

- 7 = 2 · k + 1

- 8 = 2 · k

k = - 4

y = - 4 · x + 1

Now we proceed to graph the line. First, find two points of the line:

x = 0

y = - 4 · 0 + 1

y = 1

x = 1

y = - 4 · 1 + 1

y = - 3

Second, plot the points on Cartesian plane.

Third, construct the line that passes through the two points.

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The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.

The unit tactic is a strategy for addressing issues that entails first figuring out the value of a particular unit, then increasing that value to figure out the needed value. Simply put, the unit method is employed to obtain a minimum unit value from a multiple that is supplied. For example, 40 pens may cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its homologue and reciprocal are equal in terms of mathematics, algebra, linear algebra, applied mathematics, or mathematics for matrices or operators.

given

1 pound = 16 ounces

for 2 packages

2 pounds 10 ounces + 4 pounds 12 ounces

6 pounds and 22 ounces

= 7 pounds 10 pounces

The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.

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The critical values for a one-sample t test given the following conditions are  +1.796, -1.796 2. -2.60 3. +2.576, -2.576 4. +1.729.

Value is a term used in many different contexts to refer to the worth or importance of something. It is used to describe the worth of an item or service in terms of its utility, its ability to satisfy a need or desire, or its usefulness in exchange. Value can also refer to the worth of an individual or group in terms of their contribution to society or their inherent worth. Value is subjective and can vary greatly from one person or group to another.

1. +1.796, -1.796
2. -2.60
3. +2.576, -2.576
4. +1.729

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A, C, B, and D make up the list of ABCD's angles, from largest to smallest, with 90°, 54°, 24°, and 12°, respectively.

The sides of a triangle, or angle, are two rays that make up the figure. The Law of Cosines can be used to find Angle A. We can solve for the angle A by using the formula

                               c² = a² + b² - 2abcos(C).

Since we know the lengths of all sides, we can substitute in the values.                                    

                        c² = 122 + 102 - 2(12)(10)cos(A)

                          Cos(A) = (144 + 100 - 120)/240

                       = 24/240

                       = 0.1

In the end, we use the inverse cosine to determine the angle A, which is roughly 74 degrees.

The same formula can be used to determine Angle D.

                                c² = 62 + 102 - 2(6)(10)cos(D)

                              Cos(D) = (36 + 100 - 60)/120

                                       = 76/120

                                               = 0.63 .

When we take the inverse cosine, we get the angle D, which is about 27.3 degrees.

The same formula can be used to determine Angle C.

                                 c² = 122 + 62 - 2(12)(6)cos(C)

                                      Cos(C) = (144 + 36 - 72)/144

                                                 = 108/144

                                       = 0.75

When we take the inverse cosine, we get the angle C, which is about 36.9 degrees.

The same formula can be used to determine Angle B.

                              c² = 122 + 102 - 2(12)(10)cos(B) .

                               Cos(B) = (144 + 100 - 120)/240

                                                 = 24/240

                                                = 0.1

We obtain the angle B, which is roughly 74 degrees, by applying the inverse cosine.

Therefore, ABCD's angles, from largest to smallest, are as follows: angle C (36.9°), angle B (74°), and angle D (27.3°)

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A two variable linear equation means an equation having two variables. It is usually represented as ax+by =c. We can solve a two variable linear equation in many ways.

If the linear equation is only given, to solve it we have to calculate the x-intercept and y-intercept. It is one way of solving a two variable linear equation. Lets look into an example.

 2x+5y = 19

The x intercept is when y=0,

then, 2x+ (5×0) = 20

          2x = 20, x=10

y intercept is when x=0, then

2×0 + 5y = 20

   5y = 20,  y= 20/5 =4

So, by solving the equation, we get x=10 at x intercept and y=4 at y intercept.

If one the values are given , we can substitute it in the equation to calculate the other variable.

In the equation, 2x+3y= 12, if y=2, we can calculate by substituting.

    2x + (3×2) = 12

     2x = 12-6

     2x = 6

      x =3

So when y=2 then x=3.

Constraints are the restrictions on the domain of a linear equation, like a number of days or students should be a positive integer.

So, we can solve a two variable linear equation through different ways.

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Answer:

your question is 6=1/v+2

Step-by-step explanation:

6-2=1/v

4v=1

v=1/4

The average velocity (in m/s) over the given time intervals is [1,2]

Part A.

Keep in mind that the formula for average velocity is

(Y2 - Y1)/V avg = displacement/time interval (t2 - t1)

Given that the rock's position at time t is determined by:

y = 16t - 1.86*t^2

Part 1

for the time period [1, 2]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*2 - 1.86*22 = 24.56 m when t2 = 2 sec.

So

average Velocity = (24.56 - 14.14)/(2 - 1) (2 - 1) = 10.42 m/s V avg

Part 2.

for the time period [1, 2]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.5 - 1.86*1.52 = 19.815 m when t2 = 1.5 sec.

So,

average Velocity  = (19.815 - 14.14)/(1.5 - 1) (1.5 - 1) = 11.35 m/s V avg

Part 3.

During the period [1, 1] .1]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.1 - 1.86*1.12 = 15.3494 m when t2 = 1.1 sec.

So,

average Velocity  = (15.3494 - 14.14)/(1.1 - 1) (1.1 - 1)

average Velocity = 12.094 m/s and equals 12.09 m/s (In two decimal places)

Part 4.

During the period [1, 1] .01]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.01 - 1.86*1.012 = 14.262614 m when t2 = 1.01 sec.

So,

average Velocity = (14.262614 - 14.14)/(1.01 - 1) (1.01 - 1)

12.26 m/s and V avg = 12.2614 m/s (In two decimal places)

Part 5.

During the period [1, 1] .001]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.001 - 1.86*1.0012 = 14.15227814 m when t2 = 1.001 sec.

So,

average Velocity = (14.15227814 - 14.14)/(1.001 - 1) (1.001 - 1)

12.28 m/s V avg = 12.27814 m/s (In two decimal places)

Part B.

Rock's immediate velocity will be determined by:

d[16t - 1.86t2]/dt = V= dy/dt

Velocity = 16*1 - 2*1.86*t

time = 1 second,

Velocity = 16 - 2*1.86*1

average velocity at time t is equal to V = 12.28 m/s.

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Out of the given vectors is in the span of the other vectors,  b. One of the vectors is in the span of the other vector. Since u and v have the same last component, they are linearly dependent, so u is in the span of v and w.

If a set of vectors is linearly dependent, then one of the vectors can be expressed as a linear combination of the other vectors. This means that one vector is in the span of the other vectors. In this case, u can be expressed as a linear combination of v and w, so u is in the span of the other vectors.  

To check for linear dependence, we can first check for a zero row in the matrix formed by the vectors. If there is a zero row, then the vectors are linearly dependent. In this case, the last row of the matrix formed by the vectors is [3,3,0], which is a zero row, so the vectors are linearly dependent.  We can also check for linear dependence by computing the determinant of the matrix formed by the vectors.

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The market share of the vape machine market had sales of $1.4M is given as 63.57%.

To calculate the brand's market share, you would need to divide the brand's sales by the total sales of the market and then multiply by 100 to get the percentage.

In this case, the brand's sales are 10000 units x $89/unit = $890,000.

So the market share would be:

$890,000 / $1,400,000 x 100 = 63.57%.

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Method 2 is the best option for estimating the average yearly income of the class of 2005.

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For the given equation, the binomial factor is (5x² + 3).

In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y

Factors in polynomial equations with exactly two terms are called binomial factors. Because binomials are simple to solve and their roots are the same as the polynomial's roots, binomial factors are fascinating. Finding a polynomial's roots begins with factoring it.

5x³ - 25x² + 3x - 15

Taking 5x² and 3 as common factors -

⇒ 5x² (x - 5) + 3 (x - 5)

GCF of 1 step is 5x²

⇒ (5x² + 3) (x - 5)

GCF of 2 step is 5x² + 3

Common binomial factor is (5x² + 3)

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A line that is parallel to y = -4x + 11 and goes through the point (2, 1) in point slope form is: A. y - 1 = -4(x - 2).

Mathematically, the point-slope form of a line is modeled by this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the given linear equation y = -4x + 11, the slope is given by:

y = -4x + 11

m₁ = -4

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ (m represents the slope.)

At point (2, 1), an equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -4(x - 2)

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Answer: EF = 12 is the correct answer.

Step-by-step explanation: EF = GP - FP = 16 - 4 = 12Given that GH=10, GP=16, and FP=4. We have to find the value of EF. We can use this formula to find it:EF = GP - FP = 16 - 4 = 12So the value of EF is 12. In the given figure, ABCD is a rectangle and GP and GH are the diagonals. EF is the length of the rectangle.Therefore, EF = 12 is the correct answer.

Answer:Well i think EF would be 10 since it looks like the same length as GH

Step-by-step explanation:

A man who is 1.853m tall would have a z-score of  1.297.

Generally, To find the z-score for a man who is 1.853m tall, we need to use the formula for a z-score:

= (x - mean) / standard deviation.

In this case, the mean height for men is 1.757m and the standard deviation is 0.074m, so the z-score for a man who is 1.853m tall would be:

(1.853 - 1.757) / 0.074 = 1.297297297

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