Sonia will paint a large triangular sign with a base of 14 ft and a height of 8 ft. What is the area of the sign?

Answer:

Step-by-step explanation:

Similarly one knows that the set of polynomials is much like the set of integers because both sets are closed under addition, multiplication, negation, and subtraction, but are not closed under division. Particularly interesting examples of closure are the positive and negative numbers.

Compute the characteristic polynomial of [tex]A[/tex].

[tex]p(\lambda) = \det(A - \lambda I) \\\\ ~~~~~~~~ = \begin{vmatrix} \beta - \lambda & 0 & 1 \\ 2 & 1 - \lambda & -2 \\ 3 & 1 & -2-\lambda \end{vmatrix} \\\\ ~~~~~~~~ = (\beta-\lambda)\begin{vmatrix}1-\lambda&-2\\1&-2-\lambda\end{vmatrix} + \begin{vmatrix}2&1-\lambda \\ 3 & 1 \end{vmatrix} \\\\ ~~~~~~~~ = -\lambda^3 + (\beta-1) \lambda^2 + (\beta + 3) \lambda - 1[/tex]

By the Cayley-Hamilton theorem,

[tex]p(A) = -A^3 + (\beta - 1) A^2 + (\beta + 3) A - I = 0[/tex]

Note that

[tex]A^7 - (\beta - 1) A^6 - \beta A^5 \\\\ ~~~~~~~~ = -(-A^3 + (\beta - 1) A^2 + \beta A) A^4 \\\\ ~~~~~~~~ = -(\underbrace{-A^3 + (\beta - 1) A^2 + (\beta + 3) A - I}_{p(A)=0} - 3A + I) A^4 \\\\ ~~~~~~~~ = (3A - I) A^4[/tex]

Recall that [tex]\det(AB) = \det(A) \det(B)[/tex]. Note that [tex]A[/tex] is not singular, and hence [tex]A^n[/tex] is not singular for any natural [tex]n[/tex].

[tex]\det(A) = \begin{vmatrix} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{vmatrix} \\\\ ~~~~~~~~ = \beta \begin{vmatrix}1&-2\\1&-2\end{vmatrix} + \begin{vmatrix}2&1\\3&1\end{vmatrix} \\\\ ~~~~~~~~ = -1 \neq 0[/tex]

Then [tex]3A-I[/tex] must be singular. So

[tex]\det(3A-I) = \begin{vmatrix} 3\beta - 1 & 0 & 3 \\ 6 & 2 & -6 \\ 9 & 3 & -7 \end{vmatrix} \\\\ ~~~~~~~~ = (3\beta-1) \begin{vmatrix}2&-6\\3&-7\end{vmatrix} + 3 \begin{vmatrix}6&2\\9&3\end{vmatrix} \\\\ ~~~~~~~~ = 4 (3\beta-1)[/tex]

[tex]4(3\beta-1) = 0 \implies \beta = \dfrac13 \implies 9\beta = \boxed{3}[/tex]

The probability of P(A and B) based on the information given will be E. None of the above.

It should be noted that probability is used to illustrate the likelihood that something will occur.

In this case, P(A) = 0.1 and P(B) = 0.4. Therefore, the probability of P(A and B) will be

= P(A) + P(B)

= 0.1 + 0.4

= 0.5

Sine the value of 0.5 isn't given, the correct option is E.

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The half-life of carbon-14 is 5,730 years. Assuming you start with 100% of carbon-14, what is the expression for the percent, P(t), of carbon-14 that remains in an organism that is t years old and what is the percent of carbon-14 remaining (rounded to the nearest whole percent) in an organism estimated to be 20,000 years old

Carbon-14, C-14, 14

C or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues (1949) to date archaeological, geological and hydrogeological samples. Carbon-14 was discovered on February 27, 1940, by Martin Kamen and Sam Ruben at the University of California Radiation Laboratory in Berkeley, California. Its existence had been suggested by Franz Kurie in 1934.[2]

There are also trace amounts of the unstable radioisotope carbon-14 (14C) on Earth. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbfon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.

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Answer:

x, y =8 -3

Step-by-step explanation:

System of Linear Equations entered :

  [1]    x - 4y = 20

  [2]    2x + 5y = 1

Graphic Representation of the Equations :

   -4y + x = 20        5y + 2x = 1  

Solve by Substitution :

// Solve equation [1] for the variable  x

 [1]    x = 4y + 20

// Plug this in for variable  x  in equation [2]

  [2]    2•(4y+20) + 5y = 1

  [2]    13y = -39

// Solve equation [2] for the variable  y

  [2]    13y = - 39

  [2]    y = - 3

// By now we know this much :

   x = 4y+20

   y = -3

// Use the  y  value to solve for  x

   x = 4(-3)+20 = 8

Solution :

{x,y} = {8,-3}

The mathematical statement given as 0.09 is 1/10 as much as 0.90 is true

The mathematical statement is given as:

0.09 is 1/10 as much as 0.90

To determine if the above statement is true, we start by representing the statement as an equation

So, we have

0.09 = 1/10 * 0.90

Express 1/10 as decimal

So, we have

0.09 = 0.10 * 0.90

Evaluate the product

So, we have

0.09 = 0.09

The above equation is true

Hence, the mathematical statement given as 0.09 is 1/10 as much as 0.90 is true

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Possible question

Determine if the following statement is true or false

Answer:

First, Outer, Inner, Last: Usually referred to as FOIL for simplicity is a rule for expanding polynomials. It is quite straight forward. You can do as follows for any binomial expression multiplied by a secondary binomial as you have provided.

(3x+1)(2x-1).

Step 1 of FOIL is to multiply the first 2 expressions in your binomials.

(3x)(2x) = 6x^2

Step 2 is to multiply the first by the last

(3x)(-1) = -3x

Step 3 is to do the last by the first

(1)(2x) = 2x

Step 4 is to do the last by the last

(-1)(1) = -1

You are left with the following:

6x^2 -3x + 2x -1

ADD LIKE TERMS!!

6x^2 -x -1

Remember, -x and -1x are the same!

Hope that helps!

To find the probability of an outcome the steps are as follows:

Urn -some objects of real interest are represented as colored balls .

Given data

space Ω = {a, b, c}

p(a )= 1/7,

p(b) = 2/7 and

p(c) = 4/7.

p(E) = p(a) + p(b) +p(c).

where p(E) = random experiment i. e. union

p(E) = 1/7 + 2/7 + 4/7

p(E) = 7/7

p(E) =1

An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set. Here are some examples of random experiments and their sample spaces:

Random experiment: toss a coin; sample space: S={heads,tails} or as we usually write it, {H,T}.

Random experiment: roll a die; sample space: S={1,2,3,4,5,6}.

Random experiment: observe the number of iPhones sold by an Apple store in Boston in 2015; sample space: S={0,1,2,3,⋯}.

Random experiment: observe the number of goals in a soccer match; sample space: S={0,1,2,3,⋯}.

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The measure of the angles 1,2 and 3 are 75, 42 and 138 respectively.

The value of ∠1 = 180- 105             [supplementary angles]

∠1 = 75°

∠1 + ∠2 + 63° = 180                          [angle - sum property]

75 + ∠2 + 63 = 180

∠2 = 180 - (75 + 63)

∠2 = 42°

∠2 + ∠3 = 180                                       [supplementary angles]

42 + ∠3 = 180

∠3 = 180 - 42

∠3 = 138°

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Answer:

[tex](x^2y^5)5 = 5x^2y^5[/tex]

Step-by-step explanation:

Remove the parentheses to factor.

[tex]= x^2y^5 \times 5[/tex]

Flip the expression, creating a leading term and simplifying the equation.

[tex]= 5x^2y^5[/tex]

Using the concept of absolute and relative change, it is found that:

a) The absolute change in the monthly cost of cable TV is of $4.15.

b) The relative change in the monthly cost of cable TV is of 5.53%.

c) The absolute change in the monthly cost of eggs is of $0.67.

d) The relative change in the monthly cost of eggs is of 39.41%.

e) Due to the higher relative change, the cost of the eggs increased the most.

Hence the absolute changes are given as follows:

The relative changes are given as follows:

Hence, for item e:

Due to the higher relative change, the cost of the eggs increased the most.

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Answer:

x(down 1)=-11/5, x(down 2) =3

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

6 times 6 = 36, so 6 is the answer

Hope this helps. Please mark me brainliest!

The answer to the question 36/12=3

It will cost 13.85 million to build the school

The school district paid a construction business 1.5 million to build a school

They still need to pay 12.35 million for the total amount of work

Therefore the cost of building the school can be calculated as follows

= 1.5 million + 12.35 million

= 13.85 million

Hence it will cost 13.85 million to build the school

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Answer:

36 min

Step-by-step explanation:

rate b = 1 / 90

rate m = 1/60

now add the rates together for 1 lawn

1 lawn / (1/60 + 1/90) = 36 min

The estimate of the number of pretzel rolls sold in March will be 890.

The following can be deduced based on the information that given:

March 8-14. 304

March 15-21 271

March 22-28. 316

Therefore, it should be noted that 304 to the nearest ten is 300.

271 to the nearest ten will be 270

316 to the nearest ten will be 320

Therefore, the total number sold in March will be:

= 300 + 270 + 320

= 890

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Another point on function assuming it as direct and linear proportion with the independent variable will be (1,5/2).

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let,s suppose the given graph is a direct relationship and linear as well.

Now,

y ∝ x

By removing proportion,

y = kx

Since (4,10) lies on the graph thus it must satisfy the equation.

So,

y = kx

10 =k (4)

k = 10/4 = 5/2

So the equation is y = (5/2)x

Now corresponding to x = 1 ⇒ y = 5/2

So point (1,5/2) lies on the graph.

Hence "Another point on function assuming it as direct and linear proportion with the independent variable will be (1,5/2)".

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a solution to the system of inequalities will be a point within the intersection region, namely the region overlapped by both, Check the picture below.

The equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up.

The parent function is:

f(x) = ∛x

Horizontally stretched by a factor of 4:

g(x) = ∛[(1/4)x]

Translated 5 units right:

G(x) = ∛[(1/4)x - 5]

Translated 3 units up:

h(x) = ∛[(1/4)x - 5] + 3

Thus, the equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.

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Answer:

D

Step-by-step explanation:

[tex]h(x)=2x^5+(a+s)x^4+(b+t)x^3[/tex]

For the polynomial to be divisible by x⁴, the coefficient od the x³ term must be 0, and thus the answer is D.

When five and five hundred sixty -two thousandths is written in expanded form, the result is 5 + (5 x 0.1) + (6 x 0.01) + (2 x 0.001).

When writing in expanded form, you should multiply each figure by the power of 10 that corresponds with their position.

Tens will be multiplied by 10

Tenths will be multiplied by 0.1

Hundredths will be multiplied by 0.01

Thousandths will be multiplied by 0.001

These numbers are then added to each other.

Five and Five hundred sixty -two thousandths is 5.562 so when written in expanded form it becomes:

5 + (5 x 0.1) + (6 x 0.01) + (2 x 0.001)

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Answer:

x + 7

Step-by-step explanation:

5(2x + 2) - 3(3x -1)

10x + 10 - 9x - 3

x + 7

Solving a system of equations we can see that the two numbers are 727 and 4

Let's define x as the 3-digit number and y as the one-digit number.

Then we know that the sum is equal to 731:

x + y = 731

And the product is equal to 2,908, then:

x*y = 2,908

So we have a system of equations:

x + y = 731

x*y = 2,908

Isolating x on the first equation gives:

x = 731 - y

Now we can replace that in the other equation to get:

(731 - y)*y = 2,908

Now we can solve this quadratic equation to find the value of y.

731*y - y^2 = 2,908

-y^2 + 731*y - 2,908 = 0

The solutions are:

y = (-731 ± √( 731^2 - 4*(-2,908)*(-1))/(-2)

y = (-731 ± 723)/-2

Now, y is an one digit number, then:

y = (-731 + 723)/-2 = 4

And x will be the 3 digit number:

x = 731 - x = 731 - 4 = 727

So the two numbers are 727 and 4

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If my allotted budget for a week in $500, and considering I spend $400 dollars as my complete expenses up till the end of the week, (since no information about my expenses is the question statement), the amount that I will be able save from my budget is $100, calculated using basic subtraction.

As per the question statement, my allotted budget for a week in $500 and there is no further information about my expenses for the week. Hence, Let us consider that I had to spend $400 dollars as my complete expenses for the week.

We are required to calculate the amount that I will be able save from my budget.

To solve this question, we simply have to subtract my total week's expenses from my weekly budget, i.e., [tex][(500-400)=100][/tex].

Hence, I will be able to save upto $100 from my weekly budget.

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Step-by-step explanation:

Mathematically the statement can be written as

SUPPLEMENTARY Angles add up to 180°

x+y=180°....(1)

let y be the larger angle and x be the smaller angle.

y=x+88°....(2)

plug in the (2) in the first equation

[tex]x + (x + 88) = 180 \\ 2x + 88 = 180 \\ 2x = 180 - 88 \\ 2x = 92 \\ \frac{2x}{2} = \frac{92}{2} \\ x = 46[/tex]

the measure of the larger angle is y=x+88°

[tex]y = 46 + 88 \\ y = 134[/tex]

The bigger angle is equal to 134°

HOPE THIS HELPS!!!!

Answer: 134°

here's your answer

Answer:

∠ 2 = 122°

Step-by-step explanation:

given ∠ 2 = 2 ∠ 1 + 6

a linear pair of angles sum to 180° , then

∠ 1 + ∠ 2 = 180° , that is

∠ 1 + 2∠ 1 + 6 = 180° ( subtract 6 from both sides )

3∠ 1 = 174° ( divide both sides by 3 )

∠ 1 = 58° , then

∠ 2 = 180° - 58° = 122°

Answer:

Step-by-step explanation: 3x^2-4x+15

1. (5x^2+3)-(2x^2+4x-12)

2. (5x^2+3)-1(2x^2+4x-12)

3. 5x^2+3-2x^2-4x+12

4. 3x^2-4x+15

Answer:

-6 = 1

-4 = 2

0 = 4

2 = 5

8 = 8