△ABC has vertices at A(-2, 4), B(-1, 1), and C(2, 2). The slope of AB¯¯¯¯¯¯¯¯ is , the slope of BC¯¯¯¯¯¯¯¯ is , and the slope of AC¯¯¯¯¯¯¯¯ is . △ABC a right triangle because

The number of shirts Samuel can fold in 2 minutes is 12

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

Number of Shirts 3 6 ?

Time (minutes) 0.25 0.50 2

Represent the missing value with x

So, we have the following representation

Number of Shirts 3 6 x

Time (minutes) 0.25 0.50 2

From the above table of values, we have the following equation

6 : x = 0.5 : 2

Multiply the second ratio by 12

So, we have

6 : x = 6 : 12

By comparison, we have

x = 12

Hence, the number of shirts is 12

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The statements which best summarizes the pattern of causality captured by the graph attached are: A change in E causes a shift of the budget constraint; and, the relationship between S and P is not a causal relationship.

Causality means that there is a clear cause-effect relationship between two variables. By using a controlled study is the most effective way of establishing causality among variables. In a controlled study, the sample or population is split in two, with both groups being comparable in almost every way. Then, the two groups receive different treatments, and the outcomes of each group are assessed.

Although part of your question is missing, you might be referring to this full question: Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply. (Graph is attached.)

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The slopes of the linear equations are:

a) -1

b) 0

c) undefined, it is a vertical line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

1) The points are (3, 5) and (2, 6), so the first slope is:

a = (6 - 5)/(2 - 3)  =1/-1 = -1

2) The points are (-3, 2) and (7, 2)

Notice that this is a horizontal line of the form y = 2, so the slope is zero.

3) The points are (6, 8) and (6, -2)

This is a vertical line of the form x = 6, so the slope is undefined.

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                                    [tex]\large\boldsymbol{\rm{Slope}}[/tex]

[tex]\bf{Intro}[/tex]

To find the slope of a line, given that it passes through two points, use the slope formula:

[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{6-5}{2-3}}[/tex]

[tex]\bf{m=\dfrac{1}{-1}}[/tex]

[tex]\bf{m=-1}[/tex]  {slope}

[tex]\rule{250}{1}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{2-2}{7-(-3)}}[/tex]

[tex]\bf{m=\dfrac{0}{7+3}}[/tex]

[tex]\bf{m=\dfrac{0}{10}}[/tex]

[tex]\bf{m=0}[/tex]    {slope}

[tex]\rule{250}{1}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{-2-8}{6-6}}[/tex]

[tex]\bf{m=\dfrac{-10}{0}}[/tex]

[tex]\bf{m=not\:de fined}[/tex]

✦ Therefore, the slopes are: -1, 0, not defined.

Part 1:- The answers are 12, 30, 56, 90

30, 35, 40, 45

2, 3, 4, 5

Part 2:-The correct answer is (D) -23

Part 3:-The surface area for the rectangular prism is 128 square feet.

What is a mathematical expression?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

part 1:-

Solving expression 1:-

for x=2

[tex]4 {x}^{2} - 2x = 4 \times {2}^{2} - 2 \times 2[/tex]

=4×4 - 4

=16 - 4

=12

for x=3

[tex]4 {x}^{2} - 2x = 4 \times {3}^{2} - 2 \times 3[/tex]

= 4 × 9 - 6

= 36 - 6

= 30

for x=4

[tex]4 {x}^{2} - 2x = 4 \times {4}^{2} - 2 \times 4[/tex]

= 4 × 16 - 8

= 64 - 8

= 56

for x=5

[tex]4 {x}^{2} - 2x = 4 \times {5}^{2} - 2 \times 5[/tex]

= 4×25 - 10

= 100 - 10

= 90

solving expression 2:-

for x = 2

[tex]5x + 20 = 5 \times 2 + 20[/tex]

= 10 + 20

= 30

for x = 3

[tex]5x + 20 = 5 \times 3+ 20[/tex]

= 15 + 20

= 35

for x = 4

[tex]5x + 20 = 5 \times 4 + 20[/tex]

= 20 + 20

= 40

for x = 5

[tex]5x + 20 = 5 \times 5 + 20[/tex]

= 25 + 20

= 45

solving expression 3:-

for x=2

[tex] \frac{8x}{2} - 3x = \frac{8 \times 2}{2} - 3 \times 2[/tex]

= 8 - 6

= 2

for x=3

[tex] \frac{8x}{2} - 3x = \frac{8 \times 3}{2} - 3 \times 3[/tex]

= 12 - 9

= 3

for x=4

[tex] \frac{8x}{2} - 3x = \frac{8 \times 4}{2} - 3 \times 4[/tex]

= 16 - 12

= 4

for x= 5

[tex] \frac{8x}{2} - 3x = \frac{8 \times 5}{2} - 3 \times 5[/tex]

= 30 - 15

= 15

Hence the answers are, 12, 30, 56, 90

30 35, 40, 45

2, 3, 4, 5

part 2:-

Given,

4n - 5r;

for n=-2 and r=3

4n - 5r = 4 × (-2) - 5 × 3

= -8 - 15

= -23

Hence the answer is (D) -23

Part 3:-

Given,

The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h

s = 4 feet

h = 6 feet

then,

2 s²+4 s h = 2×4²+4×4×6

= 2×16+96

= 32+96

= 128

Hence the answer is 128 square feet.

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1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :

What is rational coefficients?

A coefficient is a number that is placed in front of a variable. A variable and a rational number are preceded by a rational coefficient, which may be an integer, decimal, or fraction.

(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32

1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisfices the given conditions. The leading coefficient here is 1, we call this a monic polynomial.

2. There may be something missing in the question here

3. We can use the factoring techniques to find the roots :

x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :

(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)

We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :

Y = (x-5)(x²+9)

This is the maximum we can do on R, but on C the set of complex we can still factor again.

x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9

Δ < 0, Δ = - 36

Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i

Y = (x-5)(x-3i)(x+3i)

So the solution is S = {5, 3i, -3i} the three roots of the function.

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The curve for the vector equation r(t) = <t, -t, 2t>, is |r(t)| =  (√6)t.

Find the curve in the attachment

A vector is a physical quantity that has both magnitude and direction

A vector equation is a linear combination of vector quantities

A curve is a path which an object follows.

Since we are given the vector equation r(t) = <t, -t, 2t>, to sketch the curve of the vector equation, we need to know the magnitude of the vector.

The magnitude of a vector r = <a, b, c> is |r| = √(a² + b² + c²)

So, to sketch the vector equation, since r(t) = <t, -t, 2t>, comapring bothnequations,

So, the magnitude of r(t) =  √(a² + b² + c²)

=  √(t² + (-t)² + (2t)²)

= √(t² + t² + 4t²)

= √(6t²)

= (√6)t

Since |r(t)| =  (√6)t, we sketch the curve for this equation

Find the curve in the attachment

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Answer:

#4 is one, and #5 is two.

Step-by-step explanation:

The absolute maximum is 1.29, which occurs at x= 9

What is absolute extrema?

An absolute extremum  of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.

Main body:

Given =

f(x) = [tex](x^{2} -64)^{1/11[/tex]

f' (x) = derivative of function f(x)

f'(x) = 1/11 . 2x[tex](x^{2} -64)^{-10/11[/tex]

   =  2x/11[tex](x^{2} -64)^{-10/11[/tex]

putting f'(x) = 0

2x/11[tex](x^{2} -64)^{-10/11[/tex]  = 0

       [tex](x^{2} -64)^{-10/11[/tex]  = 0

         [tex]x^{2} -64[/tex]            = 0

x² = 64

x = ±8

We are given interval [-8,9].

Hence, calculating f(x) at -8, 8, 9.

f(-8) =  0

f(8) = 0

f(9) = [tex]17^{1/11[/tex]

     = 1.29

Hence, absolute maximum value is 1.29 at x=9.

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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If ∠2=10x+7 and one angle is 67 degrees then value of x is 6.

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

Given that the triangle has two equal sides which makes the triangle as isosceles.

In an isosceles triangle the two sides will be always equal and the angles will be also equal.

One angle of the triangle is 67 degrees

We need to find the ∠2.

As we know that the equal sides make equal angles.

∠2=67 degrees

and from given ∠2=10x+7

Now equation 67 with the 10x+7 to find the value of x.

So 67=10x+7

subtract 7 from both sides

67-7=10x+7-7

60=10x

Divide both sides by 10

x=60/10

x=6

Hence, the value of x is 6.

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Answer:

10(-x + 1)

Step-by-step explanation:

-2x - 8x + 20

-10x + 20

10(-x + 1)

Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.

But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.

So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.

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The equation of the graph in slope intercept form is y = x + 2

The equation of a graph can be represented in slope intercept form as follows:

y = mx + b

where

Hence, let's find the slope using (1, 3) and (2, 4)

Therefore,

slope = 4 - 3 / 2 - 1

slope = 1 / 1

slope = 1

Let's find the y-intercept using (1, 3)

y = x + b

3 = 1 + b

b = 3 - 1

b = 2

Therefore, the equation is y = x + 2

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The set A ∩ (/B ∪ C) is given as { 1, 6 }

From the information given, we have the sets as;

U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A= {1, 2, 4, 6}

B= {3, 7}

C= {1, 3, 6, 7, 8}

Note that;

B∪C = { 1, 3, 6, 7, 8}

A ∩ (/B ∪ C) = { 1, 6 }

Hence, the set is { 1, 6 }

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a) The percentage of $680 which is $490 is 72.06%.

b) When a price is reduced from $680 to $490, the percentage decrease is 27.94%.

The percentage is the ratio of a value to another.

Percentages are depicted as fractional values expressed over 100.

To determine percentages, the smaller value is expressed as the numerator, while the more considerable value is described as the denominator.

The result is then multiplied by 100.

For instance:

$490 of $680 is 72.06% ($490/$680 x 100)

Price reduction from $680 to $490, the percentage decrease is computed as the difference between $680 and $490 divided by $680, multiplied by 100.

Thus, the percentage decrease in price from $680 to $490 is 27.94%, showing that the original price of the good or service has been reduced from 100% to 72.06%.

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In that order. ao(t) is always the function is [tex]$$m_1=A-2 I $$[/tex].

What is function ?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

given: [tex]$\quad d_1=4 \quad$[/tex] and [tex]$A_2=6$[/tex]

[tex]$$m_0=\Sigma=\left[\begin{array}{cc}1 & 0 \\0 & 1\end{array}\right]$$[/tex]

By putzes method

[tex]$$\text { matrix } m_1=A-N_1 p_0=A-d_1 m_0$$[/tex]

here [tex]$r_1=2, m_0=I$[/tex]

[tex]$$m_1=A-2 I $$[/tex]

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The smaller eigenvalue is -4 with multiplicity 2 and larger eigenvalue is 6 has multiplicity 1

If A is a square matrix of order n x n and v is a non-zero column vector of order n x 1 such that Av = λv , then the scalar (real number) λ is called an eigenvalue of the matrix A that corresponds to the eigenvector v.

According to the question,

We have a 3 x 3 matrix that has only two real distinct eigenvalues

Let two distinct eigen values be a and b

Its given that tr(A) = - 2

Det(A) = 96

If we add all the eigen values of a matrix it gives us trace of this and product of eigen values result to the determinant

Therefore , 2a + b = -2 --------(1)

a²b = 96 --------(2)

Using substitution method for solving these equations

=> b = -2 - 2a

Substituting the value of b in equation (2)

=> a²( -2 -2a) = 96

=> -2a² - 2a³ = 96

=> a²(1 + a) + 48 = 0

=> a³ + a² + 48 =0

Solving the cubic equation

a = -4 , 1.5-3i , 1.5+3i (but eigen values are only real)

therefore , a = -4

b = -2 -2(-4)

=> -2+8

=> 6

hence, the eigen values = -4 and 6

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Answer: The variable

Hope this helps :)

Step-by-step explanation:

Answer:124.38

Step-by-step explanation:

103.65*.20=20.73 103.65+20.73=124.38

Answer:

-80x + 28y -56

4(-20x + 7y -14)

Step-by-step explanation:

The first answer is distributing the 8 through the whole expression.  The second answer is when you factor out a 4.

Answer:

(a) 6.33 miles per hour

(b) $4.33 per hour

(c) $0.68 per mile

Step-by-step explanation:

Li drove 6 hours (5pm - 11pm) for a total of 38 miles
[tex]\textrm{(a) Her average speed is determined by the formula}\\\\\dfrac{\textrm{Distance Travelled}}{\textrm{Time taken for travel}}[/tex]

[tex]\textrm{So average speed }=$\dfrac{38}{6} = 6.33$ \;\textrm{miles per hour}}\\\\[/tex]

(b) She paid $26 for 6 hours of usage
[tex]\textrm{So cost per hour } = \dfrac{26}{6} = \$4.33\;\textrm{per hour}\\\\[/tex]

(c) Cost per mile, c, can be computed as follows
[tex]c = \dfrac{\textrm{Total Cost}}{\textrm{Miles Traveled}}[/tex]

[tex]\longrightarrow \dfrac{26}{38} = \$0.68\; \textrm{per mile}[/tex]

The length of the diagonal of the right triangle is 21.2 units.

The game is played on a square court divided into four smaller squares that meet at the centre.

A right triangle QTS is formed, where QTS is 45°. Using trigonometric function, the length of the diagonal can be found as follows:

Therefore,

sin 45 = opposite / hypotenuse

opposite side = 15 feet

hypotenuse side = 15 feet

The hypotenuse side is the diagonal.

Hence,

sin 45° = 15 / h

cross multiply

h = 15 / sin 45

h = 15 / 0.70710678118

h = 21.2132034356

h = 21.2 units

Therefore,

length of diagonal = 21.2 units

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Answer:

-25

Step-by-step explanation:

Answer:

it also decreased by 3 times.

hope this work out.

Thus, 18 weeks are needed for the population of beetles to reach 183. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will take place.

The number of possible outcomes is divided by the total of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event but by probability that it won't.

For instance, how many heads would appear if you throw a coin 100 times? Assuming a probability of 1/2, we can anticipate 50 heads. However, when we actually attempt it, we might just get 48 heads, 55 heads, or anything else, but most of the time it will be close to 50.

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20 is the system's transfer function. A differential equation is a mathematical formula that includes one or more terms

Explanation:

4 +2 + 6 + 8 = 20.

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Answer:

Rhs

Step-by-step explanation:

angle N (R)

pq=mq ( h)

Nq (s)

electricity consumed:28 units

charge upto 20 units : 20 * Rs 3 : Rs 60

charge from (21 to 28) : 8 * Rs 6.50 : 52

total charge including service charge : Rs 60 + Rs 52 + Rs 50 : Rs 162