7. a. Use the distributive property to rewrite the equation.
Enter the new equation as your answer.
2 (x - 1) - 3 = 5
Enter your answer
8.b. Combine any like terms to rewrite the equation that you entered as an answer in part a.
Enter the new equation as your answer.
Enter your answer
9.c Use addition or subtraction to rewrite the equation that you entered as an answer in part b.
Enter the new equation as your answer.
Enter your answer
10.d. Use multiplication or division to rewrite the equation that you entered as an answer in part c.
Enter the new equation as your answer."

the 4th one is a relationship that is a fuction I think

Answer:

4th image

Step-by-step explanation:

the others cannot be functions since one domain cannot be in two ranges

Answer:

M=3

Step-by-step explanation:

Hope this helps:)

Answer:

The Set of Natural Numbers: {1, 2, 3, 4, 5, . . .}

The Set of Whole Numbers: {0, 1, 2, 3, 4, 5, . . .}

The Set of Integers: {. . . , −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, . . .}

Step-by-step explanation:

The matrices C, D, F, and G are symmetric while matrix H is skew-symmetric and matrix E is non-symmetric.

A matrix is an array of elements(numbers) in a peculiar order. A matrix with m rows and n columns is said to be of order m × n.

As it is known that [tex](A + B)^t = A^t + B^t[/tex] and [tex](AB)^t = B^t A^t[/tex] for any n × n matrices A and B.

Also, if matrices A and B are symmetric, then

[tex]A^t = A[/tex] and [tex]B^t = B[/tex].

a) Given that

C = A + B

Take the transpose of matrix C,

[tex]C^t = (A + B)^t[/tex]

    [tex]= A^t + B^t \\= A + B = C[/tex].

Hence, matrix C is symmetric.

b) Given that

D = A²

Take the transpose of matrix D,

[tex]D = (A^2)^t[/tex]

   [tex]= (AA)^t \\= A^t A^t \\= AA \\= A^2 = D[/tex].

Hence, matrix D is symmetric.

c) Given that

E = AB

Let's take an example,

A = [tex]\left[\begin{array}{cc}1&2&2&1\end{array}\right][/tex] and

B = [tex]\left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right][/tex]

So,

E = AB

  [tex]=\left[\begin{array}{cc}1&2&2&1\end{array}\right] \times \left[\begin{array}{cc}1 &-1 &-1&2\end{array}\right]\\= \left[\begin{array}{cc}-1&3&1&0\end{array}\right][/tex]

Clearly, matrix E is non-symmetric.

d) Given that

F = ABA

Take the transpose of matrix F,

[tex]F^t = (ABA)^t[/tex]

    [tex]= A^t B^t A^t\\ = ABA = F[/tex].

Hence, matrix F is symmetric.

e) Given that

G = AB + BA

Take the transpose of matrix G,

[tex]G^t = (AB + BA)^t[/tex]

    [tex]= (AB)^t + (BA)^t \\= B^t A^t + A^t B^t \\= BA + AB = G[/tex].

Hence, matrix G is symmetric.

f) Given that

H = AB-BA

Take the transpose of matrix H,

[tex]H^t = (AB - BA)^t[/tex]

     [tex]= (AB)^t - (BA)^t \\= B^t A^t - A^t B^t \\= BA - AB = -H[/tex].

Hence, matrix H is skew-symmetric.

Thus, the matrices C, D, F, and G are symmetric while the rest are not.

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Answer:

10

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Given:

Total

Ratio of squares to total shapes:

Answer:

1:6

Step-by-step explanation:

There are 20 triangles and four squares, so we know the first part of the ratio is 4. The total number of shapes is 24, so we get 4:24, and if we simplify, we then get 1:6.

Hope this helps!

Answer:

$216

Step-by-step explanation:

We know that the cost of an outfit for one team member is 10 + 26 + 18 = $54, therefore, the cost of outfits for all 4 team members will be 54 * 4 = $216.

Answer:

13:9

Step-by-step explanation:

The ratio of the number of apples to the number of fruits in the fruit salad is given by the equation A = 9 : 22

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the ratio of number of apples to the number of fruits be A

Now , the proportion will be

The number of pears = 13 pears

The number of apples = 9 apples

Now , the number of fruits = number of pears + number of apples

Substituting the values in the equation , we get

The number of fruits = 13 + 9 = 22

Now , the proportion of apples to fruits A is

Ratio of the number of apples to the number of fruits in the fruit salad A = number of apples : number of fruits

Substituting the values in the equation , we get

Ratio of the number of apples to the number of fruits in the fruit salad

A = 9 / 22

A = 9 : 22

Therefore , the value of A is 9 : 22

Hence , the proportion is 9 : 22

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Answer: 1 million

Step-by-step explanation:

Answer:

1,000,000

Step-by-step explanation:

Step 1:

400,000 + 600,000 = 1,000,000

Answer:

1,000,000

Hope This Helps :)

Answer:

Step-by-step explanation:

Average cost = Total cost to produce / number of items produced

Fixed cost per year = $240,000

Variable cost = $3.50s

Where s = number of shoes produced

Total cost= fixed cost + variable cost

Total cost = $240,000 + $3.50s

When average cost = $7.50

Average cost = Total cost to produce / number of items produced

7.50 = $240,000 + $3.50s / s

Cross product

7.50s = $240,000 + $3.50s

Collect like terms

7.50s - 3.50s = 240,000

4s = 240,000

divide both sides by 4

s = 240,000 / 4

= 80,000

s = 80,000

Answer:

In bold below.

Step-by-step explanation:

p^2 - 4 = (p - 2)(p + 2)

Note that 8 = 2^3 so

p^3 + 8 = ( p + 2)(p^2 + 4 - 2p)

So The HCF is p + 2.

The LCM =  (p + 2)(p - 2)(p^2 + 4 - 2p)

Answer:

306 min

Step-by-step explanation:

Answer:

1.4/0.21= 140/21= 20/3

Step-by-step explanation:

Answer:

20:3

Step-by-step explanation:

decimal points can't be ratios so we have to convert to whole numbers:

so 1.4:0.21 becomes:

140:21

after simplifying fully( i divided both sides by 7) we come to 20:3.

Answer:

26/36

Step-by-step explanation:

The probability of something = the amount of favourable outcomes/total possible outcomes.

The total number of dice combinations is 36 (6x6).

In this case there are more outcomes more than 5 than less than 5 so for the sake of simplicity we are going to find the number of outcomes less than 5 and then find the inverse.

There are only 10 possible dice combos which add to totals 5 or under:

1,1 1,2 2,1 1,3 3,1 1,4 4,1 2,2 2,3 and 3,2

That means there is a 10/36 probability of getting a total score less than 5 so to get the probability of getting more than 5, we just do 36/36 - 10/36 (because all probabilities add to 1)

Therefore there is a 26/36 probability that the toatals will add to greater than 5.

Alternatively you could also draw up a possibilities table and count the favourable outcomes.

Hope this helped!

Answer:

13/18.

Step-by-step explanation:

The favourable outcomes are (1,5) (1,6) (2,4) (2,5) (2,6) (3,3) (3,4) (3,5) (3,6) (4,2)(4,3) (4,4) 4,5) (4,6) 5,1) (5,2) 5,3) (5,4) (5,5) (5,6 )(6,1) to (6,6).

= total of 26.

As the total of all possible outcomes is 36 the answer is 26/36

= 13/18.

Answer:

$4000

Step-by-step explanation:

Assuming a = money invested at 9%

Assuming b = money invested at 8%

then we can form am equation from the question given

1) a + b = $10000, also

0.09a + 0.08b = $860 -> multiply by 100

2) 9a + 8b = $86000

Next we try to solve both equations simultaneously. We multiply both the left hand side and the right hand side of the first equation by 8. We have

3) 8a + 8b = $80000, now we subtract 3 from 2

9a + 8b = $86000

-8a - 8b = -$80000

a = $6000.

Then, we plug this in any of the first 2 equations, to get b

9 * $6000 + 8b = $86000

$54000 + 8b = $86000

8b = $86000 - $54000

8b = $32000

b = $32000/8

b = $4000.

Therefore, he invested $4000 at 8%

Answer: m+3

Step-by-step explanation:

Since the jump from each number increases by 3, you would write m+3, since m is indicated in the pattern.

Answer:

96

Step-by-step explanation:

The value of AZ will be 40.

A is a point between Y and Z and YA = 14x , AZ = 10x and YZ = 12x + 48.

We have to calculate the value of AZ.

What is the value of MP , if N is the midpoint of M and P ?

The value of MP will be equal to the summation of NM and NP i.e., MP = NP + NM .

As per the question ;

A is the midpoint of Y and Z.

⇒ AZ + YA = YZ

⇒ 10x + 14x = 12x + 48

⇒ 24x = 12 x + 48

⇒ 12x = 48

⇒ x = 4

So ,

The value of AZ will be ;

AZ = 10 × 4

AZ = 40

Thus , the value of AZ will be 40.

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Answer:

All the numbers ranging from 14,500 to 15444 would be rounded to 15000

Step-by-step explanation:

All the numbers ranging from 14,500 to 15444 would be rounded to 15000.

How this is possible.

1) all the numbers from 0-4 are not counted as the next number when rounded off.

2) all the numbers from 5-9 are counted as the next number when rounded off.

Example Suppose we have numbers from 15- 19.

These numbers can be rounded off to 20

But numbers from 10-14 would never be rounded off to 20 instead they are rounded as 10.

Same happens in the hundreds case.

If we have numbers from 450 - 499 they can be rounded as 500

And numbers from 400 - 444 cannot be rounded as 500  but the number 445 may be rounded as 450 . When we carry  5 from units place and replace it as 450 then again 450 can be rounded to 500.

Same happens with 15000  but when are rounding nearest hundred not ten.

Thus all the numbers ranging from 14,500 to 15444 would be rounded to 15000.

Answer:

the number of families needed for the survey is 2,157

Step-by-step explanation:

The computation of the number of families needed for the survey is shown below:

Given that

The Standard deviation is $900

Service level = 99%

z value at 99% = 2.58

Expenditures = $50

Based on the above information

The number of families needed for the survey is

[tex]n = (\frac{zs}{E})^2\\\\= (\frac{2.58\times 900}{50})^2[/tex]

= 2,157

Hence, the number of families needed for the survey is 2,157

Answer:

100 girls

Step-by-step explanation:

The ratio of boys : girls is 2 : 5.

In other words, boys are 2 parts of the school while girls are 5 parts of the school.

Since there are 40 boys, 2 parts of the school is 40. Thus:

[tex]2p = 40\\p = 20[/tex]

1 part is 20.

Since there are 5 parts girls, there are

[tex]5p = 5*20 = 100[/tex]

100 girls.

Answer: 100 girls

The total number of students in school is 140 and number of girls at the school is equal to 100.

What do you mean by ratio ?

Ratio is the quantitative relationship between two values indicating how frequently one value contains or is contained within the other.

It is given that the ratio of boys to girls at the school is 2:5.

Let's assume the total number of students in school is x.

We now need to find the number of girls in the school but before that we must try to find the total number of students in the school.

Sum of ratios = 2 + 5 = 7

It is given that there are 40 boys in students.

2/7 of the total number of students are boys.

i.e., the expression can be written as :

2x / 7 = 40

2x = 40 × 7

2x = 280

x = 140

The total number of students in school is 140.

So , the number of girls in school is :

= 140 - 40

= 100

There are 100 girls in the school.

Therefore , the total number of students in school is 140 and number of girls at the school is equal to 100.

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Answer:

$10,000

Step-by-step explanation:

-12,000+23,200-1,200= 10,000

The profit of the restaurant during it's first 3 years is 9800 dollars.

When the amount of money we get is more than what we have invested is more we have profit and when the amount of money we get is less than what we have invested we have loss.

Let us assume Alice start with a net profit or or of 0 dollars.

During its first year in business, Alice's restaurant shows a loss of 12,000 dollars.

∴ He is in loss of (0 - 12000) dollars which is

= - 12000 dollars.
During its second year, the restaurant makes a profit of 23200 dollars.

∴ His net profit is

= ( -12000 + 23000 ) dollars.

= 11000 dollars.

During its third year, the restaurant shows a loss of 1200 dollars so his ne profit is

= ( 11000 - 1200 ) dollars

= 9800 dollars.

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Answer:

C ON EDGE 2020

The function f(x) = [tex]\sqrt{1/x}[/tex] if, F[g(x)] = [tex]\sqrt{(1/x^2 - 3)}[/tex], g(x) = x² - 3, so option C is correct.

The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).

Given:

F[g(x)] = [tex]\sqrt{(1/x^2 - 3)}[/tex]

g(x) = x² - 3

Put the value of g(x) in all the options and check whether it is equal to F[g(x)]  as shown below,

Put it in option 3,

f{g(x)} = [tex]\sqrt{(1/x^2-3)}[/tex]

Thus, f(x) = [tex]\sqrt{1/x}[/tex]

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Answer:

c.

Step-by-step explanation:

Answer:

x =-16

Step-by-step explanation:

[tex]-2(2x + 5) - 3 = -3(x -1)[/tex]

Expand

[tex]\mathrm{Expand\:}-2\left(2x+5\right)-3:\quad -4x-13\\\\\mathrm{Expand\:}-3\left(x-1\right):\quad -3x+3\\\\-4x-13=-3x+3[/tex]

Collect like terms and simplify

[tex]-4x+3x =3+13\\-x =16\\[/tex]

Divide both side by -1

[tex]\frac{-x}{-1}=\frac{16}{-1}\\\\x =-16[/tex]

Answer:

The graph is in the image

Step-by-step explanation:

[tex]y = \frac{3}{5} x -3\\\\2x -y =-4\\\\y=-6,\:x=-5\\[/tex]

Answer:

Step-by-step explanation:

The question lacks the appropriate diagram. Find the diagram attached.

The triangle is a right angled triangle that is made of of three sides namely the opposite, the adjacent and the hypotenuse (the longest side). According to the diagram, the longest side is the side with length x. To get the side length x, we will use the Pythagoras theorem as shown;

hyp² = opp²+adj²

hyp² = 33²+56²

x² = 1089+3136

x² = 4225

take the square root of both sides

√x² = √4225

x = 65

Hence the unknown side length x is 65