Properties of equality can be used to justify steps in solving an equation.

Toads are in the pond is 27.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

"the ratio of men's jobs to women's is 8 to 1".

Given that,

The ratio of toads to frogs was 3: 10.

Let the number of toads = 3x

number of frogs = 10x

9 more frogs then entered the pond and the ratio of toads to frogs became 3:11.

[tex]\frac{3x}{10x+9} =[/tex] [tex]\frac{3}{11}[/tex]

[tex]\frac{x}{10x+9} = \frac{1}{11}[/tex]

11x = 10x+9

x = 9

number of toads = 3x = 3×9 = 27

Hence, Toads are in the pond is 27.

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If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,

Part a

He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery

Part b

He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery

The payment at the grocery store per hour = $20

The payment at the nursery per hour = $21

Part a

Number of hours he works at the grocery store = 13 hours

Number of hours he works at nursery = 9 hours

Total pay = 13×20 + 9×21

= 260 + 189

= $449

Part b

Number of hours he works at the grocery store = g hours

Number of hours he works at nursery = n hours

Total pay = 20g + 21n

Hence, If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,

Part a

He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery

Part b

He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery

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Part of a full number and a means of dividing a number into equal pieces are represented by fractions.The denominator is the total number of parts in the whole, while the numerator is the number of equal portions being counted.

Solve the problem ?

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Answer:

-8 + (-10)

Hope this help!

The first five terms of the given function is:

f(1) = 2.3

f(2) = 5.6

f(3) = 8.9

f(4) = 12.2

f(5) = 15.5

Functions: The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h.

The given function is f(n) = 3.3n-1 for n>= 1

The first 5 terms of this function are as follows:

f(1) = 3.3(1)-1

= 3.3-1 = 2.3

f(2) = 3.3(2)-1

= 6.6-1 = 5.6

f(3) = 3.3(3)-1

= 9.9-1

=8.9

f(4) = 3.3(4)-1

= 13.2-1

=12.2

f(5) = 3.3(5)-1

= 16.5-1

= 15.5

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The coordinates of A are (-5, -5).

How to determine the midpoint of a given segment?
The center point of a straight line can be located using the midpoint formula. We can use this midpoint formula to determine the coordinates of the supplied line's midpoint in order to discover its location on a graph. Assuming that the line's endpoints are (x₁, y₁) and (x₂, y₂), the midpoint (a, b) is determined using the following formula:
(a , b) ≡ (((x₁ + x₂)/2), ((y₁ + y₂)/2))

Given, the line segment under consideration is AB as endpoints.
And, the co-ordinate of B is = (6, 1)
Also, the midpoint of segment AB i.e. M is = (0.5, -2)
Let the co-ordinate of A be = (x, y)
Using the available literature and formula, we get
(0.5, -2) ≡ (((x + 6)/2), ((y + 1)/2))
Equating both parts in the given equation,
0.5*2 = x + 6 ⇒ 1 = x + 6 ⇒ x = -5
and, (-2)*2 = y + 1 ⇒ -4 = y + 1 ⇒ y = -5
Therefore, the co-ordinates of A are (-5, -5).

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Answer: (0,4) and (-1,-1)

Step-by-step explanation:

1) Plug in all of each equation

1a) (0,4)

3(0)-(4)<10

0-4< 10

-4< 10

2(0)+6(4)>=-8

0+24 >= -8

24>= -8

Works!

1b) (2,-1)

3(2)-4(-1)<10

6+4<10

10<10

Nope.

1c) (2,-2)

3(2)-4(-2)<10

6+8<10

14<10

Nope.

1d) (8,2)

3(8) -4(2) < 10

24 - 8 < 10

16<10

Nope.

1f) (-1,-1)

3(-1)-4(-1) < 10

-3 +4 < 10

1 < 10

2(-1)+6(-1)>=-8

-2+-6 >= -8

-8 >= -8

Works.

The break-even points for her graph are given approximately as follows:

C. 15 and 47.

The expenses and the revenue are defined as follows:

The break-even points are the points in which the expenses and the revenue are equal.

In the context of this problem, the functions are given as follows:

The break-even point is given by the intersection of the two curves, which happen around x = 15 and x = 47, hence option C is the correct option.

The problem is given by the image at the end of the answer.

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Answer:

0.4

Step-by-step explanation:

The absolute value is just the number in the line things but positive.

The absolute value is the distance between a number and zero. The distance between − 0.4 and 0 is 0.4

if |-0.4| is all that is in the question it is 0.4

If the amount deposited is a positive integer , so the amount withdrawn is represented by -3748  and the balance amount in the Manvita's account is Rs 1252 .

In the question ,

it is given that

Money deposited by Manvita =  Rs 5000 .

Money withdrawn by Manvita = Rs 3748 .

Since , amount deposited is a positive integer ,

So, the amount withdrawn will be a negative integer

Balance in Manvita's account = Money deposited + Money Withdrawn

Substituting the values , we get

Balance in Manvita's account = 5000 + (-3748)

= 5000 - 3748

= 1252

Therefore , if the amount deposited is a positive integer , so the amount withdrawn is represented by -3748  and the balance amount in the Manvita's account is Rs 1252 .

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It should be noted that the conversion of the measurement of 290 inches will be 0.7366 decameter.

How to illustrate the information?

It should be noted that from the information,.it about equivalents dimensional analysis, to convert the given measurement to the unit indicated.

In this case, we want to convert 290 in. to dam.

It should be noted that we have to divide rye length value by 393.7

Therefore, it should be noted that 290 inches will be:

= 290 / 393.7

= 0.7366 decameter.

Therefore, it should be noted that the conversion of the measurement of 290 inches will be 0.7366 decameter.

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Answer: 45

41.4 is 45 percent of 92

Answer: 45%

Step-by-step explanation:

Solution for 41.4 is what percent of 92:

41.4:92*100 =

(41.4*100):92 =

4140:92 = 45

Now we have: 41.4 is what percent of 92 = 45

Question: 41.4 is what percent of 92?

Percentage solution with steps:

Step 1: We make the assumption that 92 is 100% since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3:  100%=92.

Step 4: In the same vein, x%=41.4.

Step 5: This gives us a pair of simple equations:

$100%=92(1).

$x%=41.4(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

100%/x%= 92/41.4

Step 7: Taking the inverse (or reciprocal) of both sides yields

x%/100% = 41.4/92

-> x=45%

Therefore, 41.4 is 45% of 92.

Answer:

I couldn't do the second question but I did the first and third

1. x=125

3. 11.84

Step-by-step explanation:

2x+6x= 1,000    Set up equation

8x=1,000          Add the like terms-so, 2x and 6x

x=1,000/8         Isolate the x by taking the 8 to the other side to divide

x=125

-2.3x-4.2x=-66.3       Equation

-5.6x= -66.3              Add -2.3 and -4.2 because both r negative

x=-66.3/-5.6              isolate x bu dividing

x= 11.84                        Rounded answer

The value of (-14) 3 when evaluated is -42.

Given,

The expression = (-14) 3

We have to evaluate this and find the value.

Evaluating an expression:

Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.

That is,

(-14) 3 = -14 × 3 = -42

Therefore, the value of (-14) 3 when evaluated is -42

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Examples of permutation matrices are the identity matrices with a permutation in rows. Permutation matrices are invertible and the inverse is a permutation matrix as well.

A permutation matrix is a square matrix which contains exactly one 1 in each row and all other entries 0.

So a permutation matrix can be obtained by rearranging the rows or columns of an identity matrix. Identity matrix is also a permutation matrix with entry 1 exactly once in each row and all other entries 0.

Example of a permutation matrix:

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]

A permutation matrix is invertible because an identity matrix is invertible [since det(I) = 1] and a permutation matrix is just got by exchanging rows or columns which does not change its determinant. So the determinant of a permutation matrix ≠ 0 and hence invertible.

The inverse of a permutation matrix is its transpose itself. The transpose is again a permutation matrix.

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Answer:

Gabriel spent $12 in just Donuts. If fritters are $2 a piece, he could buy 2 fritters at max. Perhaps he bought an extra donut to equal $17.

Step-by-step explanation:

Answer:

7 donuts and 5 fritters

Step-by-step explanation:

The equation x + |y| = y + |x| that contains the absolute values of x and y, is satisfied when the values of x and y are given by the iniquities;

The absolute value or modulus of a real number gives its non negative value irrespective of the sign (positive or negative) of the number.

The given equation is presented as follows;

x + |y| = y + |x|

The possible values of x and y are;

-10 ≤ x ≤ 10 and -10 ≤ y ≤ 10

Collecting the absolute values of the equation on one side gives;

|y| - |x| = y - x, which gives;

+y - +x = y - x

The equation is therefore satisfied when both x and y are larger than zero.

Therefore, x + |y| = y + |x|, gives;

0 ≤ x ≤ 10, and 0 ≤ y ≤ 10

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Answer:

72 doctors recommended the medicine

Step-by-step explanation:

The most appropriate choice for speed will be given by-

Average speed of Trevon is 56 mph

What is speed?

The distance travelled by the body per unit time is called speed of the body.

If d is the distance travelled by the body and t is the time taken, then

speed = [tex]\frac{d}{t}[/tex]

Speed is a scalar quantity as the direction is not taken into account.

Here,

Let the average speed of Trevon be [tex]x[/tex] mph

Average speed of Mike = [tex](x + 14)[/tex] mph

Time for which Trevon driven = [tex](4 + 1)[/tex] h

                                                  = [tex]5[/tex] h

Time for which Mike driven = [tex]4[/tex] h

By the problem,

[tex]5 \times x = 4 \times (x+14)[/tex]

[tex]5x = 4x+56[/tex]

[tex]5x-4x=56[/tex]

[tex]x =56[/tex] mph

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6m/m-3    + m/m+1

Simplify

Identify the common factor

{6m/m-3 + m/m+1

(m+1) . (6-3) /(m+1)  +  (m-3)/ (m+1)

Add fractions with the same denominator together.

terms to put constants on the left and reorder them

Solution

7m^{2}+3m   /  m^2-2m-3

The answered are 7  3  2 3

What does the algebraic expression M mean?

The slope of a line is represented by the letter "m" in algebra. A line's slope defines both its direction and steepness.

The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention. People have discovered over time that adding or multiplying doesn't depend on the order of the numbers

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The expression is equivalent to the given expression  by combining like terms is  -2.2[tex]y[/tex]-1.8 .

An expression is a set of terms combined using the operations +, -, x or ÷

and the variables. Number, symbols and operators are grouped to form an expression . An expression can be simplified by combining like terms.  

Given that,

  1.2y + 4.5 - 3.4y - 6.3

The terms that has same variables are like terms Combine like terms by adding or subtracting the terms.

-1.2[tex]y[/tex]-3.4[tex]y[/tex]+4.5-6.3

-2.2[tex]y[/tex]-1.8

Hence, The expression is equivalent to the given expression  by combining like terms is  -2.2[tex]y[/tex]-1.8 .  

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Answer:

Question 3.

[tex]y = \frac{2}{7} x - 3[/tex]

question 4

[tex]y = - 4x - 1[/tex]

question 5

[tex]y = 5x + 3[/tex]

Step-by-step explanation:

Question 3

1.Write down what is given in equation form

[tex]y = \frac{2}{7} x + c[/tex]

2. Insert the given point to work out c

[tex] - 5 = \frac{2}{7} ( - 7) + c[/tex]

[tex]c = - 3[/tex]

3. answer

[tex]y = \frac{2}{7} x - 3[/tex]

Question 4

1 write what was given in an equation

[tex]y = - 4x + c[/tex]

2. insert given point (-1;3) to work out c

[tex]3 = - 4( - 1) + c[/tex]

[tex]c = - 1[/tex]

3. final answer

[tex]y = - 4x - 1[/tex]

question 5

1.with what was given write it in equation form

[tex]y = 5x + c[/tex]

2. substitute the given point (-2;-7) to work out c

[tex] - 7 = 5( - 2) + c[/tex]

[tex]c = 3[/tex]

3.final answer

[tex]y = 5x + 3[/tex]

The graph of the image of rectangle CDEF after a translation 4 units left and 9 units up is as shown below.

In this question, we have been given the image of rectangle CDEF.

The coordinates of rectangle CDEF are:

C = (-6, -6)D = (-2, -6)E = (-2, 0)F = (-6, 0)

The rectangle CDEF is a translated 4 units left and 9 units up.

When rectangle CDEF is a translated 4 units left then the coordinates of rectangle would be,

C' = (-10, -6)

D' = (-6, -6)

E' = (-6, 0)

F' = (-10, 0)

Then rectangle C'D'E'F' is translated 9 units up  then the coordinates of rectangle would be,

C'' = (-10, 3)D'' = (-6, 3)E'' = (-6, 9)F'' = (-10, 9)

The graph of the image of rectangle CDEF after a translation 4 units left and 9 units up is as shown below.

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Answer:

-18/35

Step-by-step explanation:

the conclusion is that angle AOZ  and XOB is approximately equal

We are given that WOA and AOZ are equal, and since the AB intersects the line WY and XZ, were from the vertical angles theorem, This hypothesis says that when two straight lines meet, they frame two sets of linear sets with congruent angles, then angle WOZ and XOY equal and XOW and YOZ are too, now since the Ab intersects those angle on pint A and by the transitive property If any angles or segments are congruent to the same angle, at that point they are consistent to each other, according to which it was clear that both the angle BOY and XOB are approximately equal, there  vertical angle which are angles WOA and AOZ are equal  to them, So it can be concluded that the angle AOZ and XOB are equal too.

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Answer:

b

Step-by-step explanation:

for edmuntum

The number of members that the club had last year was 85

The number of members that the club has this year is 120.

The number by which it increased is

120 - 85 = 35

Percentage is expressed in terms of 100. Thus, the percentage increase is

35/85 * 100

= 41.2%

The percentage isncrease is 41.2%

Daniel's mother should leave the house at 1:10 P.M. to arrive at the playground at the same time as Daniel.

According to the question,

We have the following information:

Speed of Daniel = 4 miles per hour

So, it means that Daniel covers 4 miles in 1 hour.

1 hour = 4 miles or 4 miles = 1 hour

1 mile = 1/4 hour

1/4 hour means (60/4) minutes or in other words 15 minutes.

Now, Daniel will cover 1 mile in 15 minutes.

So, the time taken by Daniel to cover 2 miles = 15*2 minutes

Time taken by Daniel to cover 2 miles = 30 minutes

So, Daniel will reach the playground at 1:30 P.M.

Now, speed of Daniel's mother = 6 miles per hour

So, we have:

6 miles = 1 hour

6 miles = 60 minutes

1 mile = 60/6 min

1 mile = 10 min

So, to cover 2 miles, Daniel's mother will take (2*10) minutes or 20 minutes.

Now, Daniel will reach the playground at 1:30 P.M.

So, Daniel's mother should start from her house at 1:10 P.M.

Hence, Daniel's mother should start at 1:10 P.M.

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Answer:

See below

Step-by-step explanation:

the two angles add to a total of 360 °

5x - 40    + `150 = 360

x = 50°