20 point question! Please help!

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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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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1(a) The value of f(2) in the fuction f(x) = x³+7x²-36 0, 1 (b) The factors of the function f(x) =  (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

(a) To calculate the f(2), we substitute 2 into the function below.

(b) To factor f(x), we need to look for the zeros of f(x). The zeros of f(x) are

Putting them in polynomial form

(2) To calculate the amount he would invest initially to have the neccessary amount in 4 years, we use the formula below.

Formula:

Where:

Make P the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Hence, 1(a) The value of f(2) = 0, 1 (b) The factors of f(x) =  (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.

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One of the interior angles of the triangle, angle y is equal to 67° and the exterior angle x is equal to 113°.

The interior angles of a triangle have a total sum of 180°.

Considering the triangle with interior angles: y, 51°, and 62° we have that;

y + 51° + 62° = 180°

y + 113° = 180°

y + 113° - 113° = 180° - 113° {subtract 113° from both sides}

y = 67°

the exterior angle x and the angle y lie on a straight line, so they sum up to 180°.

x + 67° = 180°

x + 67° - 67° = 180° - 67° {subtract 67° from both sides}

x = 113°

Therefore, the interior angle y = 67° and the exterior angle x = 113°.

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Answer: There is a 54% chance that you will not choose one of those cards.

Step-by-step explanation: There are 4 of ever card in a deck.

3, 4, 5, 6, 7, and 8 are 6 different types of cards

6 x 4 = 24

24 divided by 52 ( the total cards ) = .46

So there is a 54% chance that you will not choose one of those cards.

Answer:124.38

Step-by-step explanation:

103.65*.20=20.73 103.65+20.73=124.38

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 required unit rate for the dollars per class is 16 dollars per class,

Given that,
The "constant of proportionality" between to cost and the number of classes is 16. The unit rate for dollars per class is to be determined.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Let, y be the dollars is directly proportional to the x classes,
According to the question,
y = kx
k = 16
y = 16x
Now,
y/x = 16 dollars per class

Thus, the required unit rate for the dollars per class is 16 dollars per class,

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Answer: The variable

Hope this helps :)

Step-by-step explanation:

The length of side DE of the rectangle ABCD is 11/5 units .

What is rectangle?

In euclidean plane geometry, a rectangle may be a quadrilateral with four right angles. It also can be outlined as: an angular quadrilateral, since angular means all of its angles square measure equal; or a tetragon containing a right angle.

Main body:

given:

AE = 4x+8       -----------(1)

CE = 7x - 3      -----------(2)

as we know diagonal of rectangle bisect each other , which means AE = CE

using the property , we get

4x+ 8 = 7x -3

taking like terms to one side,

7x - 4x = 8+3

3x = 11

x = 11/3

put the value of x in any equation,

AE = 4(11/3) +8

AE = 44/3 +24/3

AE = 68/3

as AE = DE

Hence the value of DE is 68/3 units.

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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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Good now whats the question?

1. We can prove these triangles are congruent through J. SSS.

2. A triangle with 3 congruent angles is called an equilateral triangle.

If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned.

SSS rule states that two triangles are congruent if all three sides of one triangle are equivalent to the corresponding three sides of the other triangle.

An equilateral triangle has all three sides and angles equal.

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When the truck cost 60,000 it depreciate in value 4000 per year, the model is 60000 - 4000x

Equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

In this case, the truck cost 60,000 it depreciate in value 4000 per year.

Let the number of years be x.

The linear model in the representation will be:

60000 - 4000(x)

= 60000 - 4000x

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Answer:

third option

Step-by-step explanation:

sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]

tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]

The number 490 is 72% of the number 680.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that 490 is some percentage of the number 680.

The percentage of 490 to the number 680 will be calculated as,

680 x (x / 100) = 490

x = (490 x 100)/680

x = 72%

Therefore, the number 490 is 72% of the number 680.

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Answer:

18 jumps

Step-by-step explanation:

5*10 = 50cm

50/100 = 0.5m (metre conversion)

9/0.5 = 18

Step-by-step explanation:

since AD is an altitude (height) of ABC, the angle at D must be 90° (that is the definition of an altitude or height).

so,

90 = x² + 6x + 18

72 = x² + 6x

0 = x² + 6x - 72

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-6 ± sqrt(6² - 4×1×-72))/(2×1) =

= (-6 ± sqrt(36 + 288))/2 = (-6 ± sqrt(324))/2 =

= (-6 ± 18)/2 = -3 ± 9

x1 = -3 + 9 = 6

x2 = -3 - 9 = -12

so, the 2 solutions are

x = 6

x = -12

Therefore, the probability of the first case : 94.5% and second case:9.7%

the likelihood that an event will take place. The proportion of feasible outcomes to outcomes in an exhaustive set of equally likely outcomes that result in a particular event. a field of mathematics that focuses on the investigation of probability.

Here,

Thus, the probabilities of following cases comes out to be:

1) The odds that either the pedestrian or the driver weren't are

=>(246+603+83)*100/986

=>(932/986)*100 =94.5%

2) The likelihood that both incidents involved inebriated pedestrians is equal to

=>(305/978)*(304/977)*100 = 9.7%

Therefore, the probability of the first case : 94.5% and second case:9.7%

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In linear equation ,The correct order from least time to greatest time is: Andy, Beth, Cindy.

Describe a linear equation using an example.

An equation with only one variable is referred to as a linear equation in one variable.

                   It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

Consider the provided information,

Andy walked [tex]2\frac{3}{4}[/tex]  mi at a constant speed of [tex]2\frac{1}{2}[/tex] mi/h.

As we know

       Time = distance/speed

           = [tex]\frac{2\frac{3}{4} }{2\frac{1}{2} }[/tex]

            =  [tex]\frac{11/4}{5/2}[/tex]

           = 11/40

Therefore, Andy takes 1.1 hours.

Beth walked 1 1/2 mi at a constant speed of 1 1/8 mi/h .

  time = [tex]\frac{1 1/2}{ 1 1/8}[/tex]

           = 3/2/ 9/8

           = 4/3

Therefore, Beth takes 1.33 hours.

Cindy walked for 1 h and 24 min at a constant speed of 1[tex]\frac{1}{4}[/tex] mi/h.

   1  hour 24 min   =  1 + 24/60   = 1.4 hours

    Therefore Cindy takes 1.4 hours.

Andy spent least time i.e 1.1 hours and Cindy spent greatest time i.e 1.4 hours.

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Answer:

D

Step-by-step explanation:

x=9 and y=4 is given in the graph, this makes the answer between B and D

Since y=-⅔x+10 and y=x-5, 4=-⅔(9)+10 and 4=9-5

So the answer is D

Answer:

it also decreased by 3 times.

hope this work out.

Answer:

A circle is formed.

Step-by-step explanation:

When a plane, parallel to the base of a cone, slices a cone, a circle is formed

and for proof:

Answer:

34 in base 2 = 10011

Step-by-step explanation:

34 written in base 2 or in binary form is 10011 . 34 written in base 10 or decimal form is 19 .

Given, Convert 34 in base 5 to base 2

Firstly convert base 5 to base 10 .

34(base 5) = [tex]3\times 5 ^1 + 4\times 5^0[/tex]

34(base 5) = 19(base 10)

Convert base 10 to base 2 .

To convert 19 to binary, divide it by 2 repeatedly and note the remainders:

19 ÷ 2 = 9, remainder 1

9 ÷ 2 = 4, remainder 1

4 ÷ 2 = 2, remainder 0

2 ÷ 2 = 1, remainder 0

Reading the remainders from bottom to top including the last 1.

10011.

So, 19 in binary is 10011.

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The two column proof is written as follows

Statement                                                           Reason

line UT ≅ line GH                                     given

line UV ≅ line GH                                     given

< U ≅ < G                                                  given

Δ TUV  ≅  Δ BEC                                     Congruent triangles by SAS

< F ≅ < V                                                  CPCTC theorem

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent

The SAS have it that the two sides of the triangles being compared should be equal and the included angles are equal

The given sides and the included angle are

line UT ≅ line GH    Side

< U ≅ < G                  included angel

line UV ≅ line GH    Side

< F ≅ < V                  CPCTC theorem

According to the CPCTC theorem, whenever two triangles are congruent, then each of their corresponding parts are also congruent. In other words, if two or more triangles are congruent, then their corresponding sides and angles are also congruent or equivalent in size.

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Answer: 28055

Step-by-step explanation:

We are told that 6 is two-fifths of the brownies. So we can figure it out as such:

[tex]\frac{6}{x} = \frac{2}{5}[/tex]

Cross multiply

6 * 5 = x * 2

30 = 2x

Divide both sides of the equal sign by 2 to get x by itself

[tex]\frac{30}{2} =\frac{2x}{2}[/tex]

15 = x

15/5 = 3. Every third piece is 1/5 of the pan.

The equally likely events are

The probability that all three children are male

0.875.

the probability that at least one child is female.

0.875.

(a) The equally likely events for the gender of the three children, from oldest to youngest, are:

(b) The probability that all three children are male is (0.5)^3 = 0.125.

The probability that at least one child is female is the complement of the event "all three children are male," which means it is 1 - 0.125 = 0.875.

In conclusion, The probability that at least one child is female is 1 - (0.5)^3 = 0.875.

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Total amount payable including sales tax and tip =  $68.12

A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.

Given:

Bill at dinner was before tax and tip = $58.24

Sales tax = 6%

Tip = 18%

As per the question:

first, we will calculate the amount payable after adding tax.

The amount payable after adding sales tax = bill + 6% sales tax of the bill

The amount payable after adding sales tax = 58.24 + [tex]\frac{6}{100} 58.24[/tex]

Amount payable after adding sales tax = A = $57.73

Now we will calculate the total amount payable after adding the tip.

Total amount payable = A + 18% of A

Total amount payable = $57.73 + 18% of $57.73

Total amount payable =  57.73 + 10.40

Total amount payable including sales tax and tip =  $68.12

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Total amount payable including sales tax and tip =  $68.12

A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.

Given:

Bill at dinner was before tax and tip = $58.24

Sales tax = 6%

Tip = 18%

As per the question:

first, we will calculate the amount payable after adding tax.

The amount payable after adding sales tax = bill + 6% sales tax of the bill

The amount payable after adding sales tax = 58.24 +

Amount payable after adding sales tax = A = $57.73

Now we will calculate the total amount payable after adding the tip.

Total amount payable = A + 18% of A

Total amount payable = $57.73 + 18% of $57.73

Total amount payable =  57.73 + 10.40

Total amount payable including sales tax and tip =  $68.12

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