5: 2.1 Modeling with Expressions rpreting Parts of an Expression 1. In the given expression 12x + 13y - 4z + 2, identify the following: . Terms: . Coefficients: 3. Sally identified the terms of the expressions 9a + 4b - 18 as 9a, 4b and 18. Explain her error. . What is the coefficient of b + 10. rpreting Algebraic Expressions in Conte: Its 1​

Answer:

B.

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The formula for E is given as   E = L/250M

According to the question we have been given that the level of monsters is measured by as follows

                  L = 250M E      (1)

 where , M = number of monsters

              E = experience of monsters.

Now we need to find the formula for E. For that we will solve equation (1) for E .

                  L = 250M E

Dividing both the sides by 250M we get

                  L/250M = E

          or,    E = L/250M

Thus above is the equation or the formula for E.

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The equation expressed in terms of x is x = √47/ 2

A line segment can be defined as the part of a line that connects two points which are considered to be its endpoints.

From the information given, we have that LN is a line with segments LM, MN and LN and M is the midpoint between L and N

Now, the equation is expressed as;

LM + MN = LN

Where;

Substitute the values

x² + x² + 9x = 56

collect like terms

2x² = 56 - 9

2x² =  47

To make 'x' the subject of formula

x² = 47/ 2

Find the square root of both sides

x = √47/ 2

Thus, the equation expressed in terms of x is x = √47/ 2

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Answer:

y = 112 and z = 30

Step-by-step explanation:

Since the y angle and the 68 angle are same side exterior angles, they add up to 180

68+y = 180

y = 112

If we take (5z -82) angle's alternate interior angle, we get:

5z-82+112 = 180

5z = 150

z = 30

3:15=3/15

The numerator and the denominator can both be divided by 3.

so, it is 1/5 which is equal to 1:5.

The simplest ratio of triangles to total shapes is 1 : 6.

Given that, there are 3 triangles and 15 circles.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, total number of shapes

= 3+15

= 18

Now, ratio of triangles to total shapes is 3 : 18

So, the simplest form = 1 : 6

Hence, the simplest ratio of triangles to total shapes is 1 : 6.

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Using proportions, it is found that Elena's group hiked 6.3 km each day.

A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For this problem, we have that Priya's group hiked 19 kilometers in 5 days, hence the daily amount is found applying the proportion as follows:

19/5 = 3.8 km a day.

Elena's group hiked 2.5 km a day more, hence:

3.8 + 2.5 = 6.3 km a day.

Elena's group hiked 6.3 km each day.

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Answer:

[tex] \sf \: r = \sqrt{V/2πh³} [/tex]

Step-by-step explanation:

V=2πr²h³

Divide both sides by 2πh³

V/2πh³= 2πr²h³/2πh³

V/2πh³ = r²

Flip equation

r² = V/2πh³

Take square root of both sides

√r² = √V/2πh³

∴ r = √V/2πh³

The number of kilometers represented by 8cm is 80km.

According tot he question we have been the proportion of scaling on the map which is as follows:

                             1 cm : 10 km   or it is also written as   1cm/10km

We need to find the number of kilometers represented by 8 cm

Let the number of kilometers that we need to find be x km. Mathematically the proportion can be written as

                              8 cm : x km     or it is written as    8cm / x km

Also both the proportion will be equivalent. Therefore, the proportion is equal to

                              1/10 = 8/x

we will solve this for x, we get

                                x = 8*10

                                x = 80 km

Hence the number of kilometers represented by 8cm is 80 km

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The values of the given summation of units are;

The values of the given expressions are;

1. 40 mm + 50 mm = 90 mm

2. 68 mg + 57 g is found as follows;

1000 mg = 1 g

68 mg = 0.068 g

Therefore;

68 mg + 57 g = 0.068 g + 57 g = 57.068 g

3. 45 L + 34 mL is found as follows;

1,000 mL = 1 L

Therefore;

34 mL = 0.034 L

45 L + 34 mL = 45 L + 0.034 L = 45.034 L

4. 78 km + 33 m is found as follows;

1000 m = 1 km

Therefore;

33 m = 0.033 km

78 km + 33 m = 78 km + 0.033 km = 78.033 km

5. 67 cg + 23 g is found as follows;

100 cg = 1g

Therefore;

67 cg = 0.67 g

67 cg + 23 g = 0.67 g + 23 g = 23.67 g

6. 34 km + 89 m

34 km + 89 m = 34 km + 0.089 km = 34.089 km

7. 72 cm + 88 mm

10 mm = 1 cm

88 mm = 8.8 cm

72 cm + 88 mm = 72 cm + 8.8 cm = 80.8 cm

8. 121 L + 42 cL

100 cL = 1 L

Therefore;

121 L + 42 cL = 121 L + 0.042 L = 121.042L

9. 156 cg + 38 mg

10 mg = 1 cg

156 cg + 38 mg = 156 cg + 3.8 cg = 158.8 cg

10. 56 kg + 333 mg

56 kg + 333 mg = 56 kg + 0.333 kg = 56.333 kg

11. 31 km 1/3 m + 82 km 1/6 m = 113 km 1/2 m

12. 48 m 50 cm + 17 m 281 1/2 cm = 65 m 331 m 1/2 cm

13. 97 L 3/4 m/L + 44 L 2/3 m/L = 141 L 17/12 m/L

14. 26 km 5/9 mm + 64 km 1/5 mm = 90 km 34/45 mm

15. 27 kg 1/4 g + 67 kg 1/3 g = 94 kg 7/12 g

16. 30 kL 1/3 mL + 3 kL 1 mL = 33 kL 4/3 mL

17. 87 kg 1024 mg + 23 kg 237 mg = 110 kg 1261 mg

18. 83 L 1/3 cL + 22 L 1/6 cL = 105 L 1/2 cL

19. 93 kg 1/5 g + 29 kg 1/3 g = 122 kg 8/15 g

20. 32 m 572 mm + 78 m 2/7 mm = 110 m 572 2/7 mm

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The present age of the father is 36 and the present age of the son is 12 years.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that a father is three times as old as his son. After 4 years, his age will be 4 times his son's age 2 years ago.

Let the present age will be "F" and "S". The equations will be solved as:-

F = 3S

F + 4 = 4 ( S - 2 )

F + 4 = 4S - 8

3S + 4 = 4S - 8

S = 12 years

F = 3S

F = 3 x 12 = 36 years

Therefore, the present age of the father is 36 and the present age of the son is 12 years.

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1. Least Common Denominator ⇒ The LCM of two or more denominators.

2.Greatest Common Factor ⇒ It is the largest number that divides

                                               exactly into two or more numbers.

3. Integer ⇒ All the numbers within the whole number set {0,1,2,3,…} as

                   well as all of the opposites.

4. Simplifying Fractions ⇒  Also called reducing means to make the

                                         fraction as simple as possible.

5. Dimensional Analysis ⇒ A procedure of multiplying be conversion factors to divide out common units and convert between different measurements.

6. Factor ⇒ A number that is multiplied by another number.

What is Greatest Common Factor ?

The highest number that divide exactly into two or more numbers is called Greatest Common Factor.

Now, We can match each by the definitions as;

Since, Least Common Denominator is the LCM of two or more denominators.

1. Hence, Least Common Denominator ⇒ The LCM of two or more denominators.

Since, Greatest Common Factor is the largest number that divides exactly into two or more numbers.

Hence, Greatest Common Factor ⇒ It is the largest number that divides exactly into two or more numbers.

Since, All the numbers within the whole number set {0,1,2,3,…} as well as all of the opposites.

Hence,  Integer ⇒ All the numbers within the whole number set {0,1,2,3,…} as well as all of the opposites.

Since, Simplifying Fractions also called reducing means to make the fraction as simple as possible.

Hence, Simplifying Fractions ⇒  Also called reducing means to make the fraction as simple as possible.

Since,  A procedure of multiplying be conversion factors to divide out common units and convert between different measurements is called

Dimensional Analysis.

Hence, Dimensional Analysis ⇒ A procedure of multiplying be conversion factors to divide out common units and convert between different measurements.

Since, When a number is multiplied by another number then it is called a factors of that number.

So, Factor ⇒ A number that is multiplied by another number.

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Speed is 0.01 miles per minute.

we know speed is = distance/ time

since we need speed in miles per minute we need to convert km into miles.

and hours in minute.

distance= 5km

1km= 0.621371 miles

5km= 50.621371 miles = 3.10686 miles= 3.12 miles

1hour= 60 minutes

4.5 hour = 4.5×60 minutes=270 minutes

speed= distance in km/time in minutes=3.12 miles/270 minutes

speed = 0.012 miles per minute

speed is 0.01 miles per second.

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The cost of 32 Christmas trees when Noel orders the trees is $2560.

Based on the information, it should be noted that

Noel runs a shop that sells christmas trees and that her supplier Connie for charges $80 for each Christmas tree.

Therefore, the cost of 32 Christmas trees will be:

= Price of one Christmas tree × Number ordered

= $80 × 32.

= $2560

Therefore, the cost of 32 Christmas trees when Noel orders the trees is $2560.

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Noel runs a shop that sells christmas trees. Her supplier Connie for charges $80 for each Christmas tree. What is the cost of 32 Christmas trees?

Answer:

Y = -X + 5

Step-by-step explanation:

I want this equation in the form

y = mx = b

2x + 2y = 10  Subtract 2x from both sides of the equations

2y = -2x + 10  Now divide everything by 2

y = -1x + 5

or

y = -x + 5

We need to know about

linear equation

to solve this problem. (a) The equation that will allow Robel to calculate what his total cost will be is 52+94n (b) Robal's total cost if he decides to stay 3 nights is $334

A

linear equation

is one that has

one or two variables

in it, the variables in a linear equation are linearly related to each other which means that the graph of such an equation is a straight line.

In part (a) it is said that Robel is charged $52 as a one time fee and the

cost per night

is $94, let us consider the

total cost to be t

and the

number of nights he stays be n,

then the equation for the total cost will be

t=52+94n

In part (b) we have to find out the total cost if he stays 3 nights, which means n=3,

substituting the value of n

in the equation for total cost

t=52+94x3=334

Therefore we found out that the

equation for Robel's total cost

is 52+94n and the total cost if he stays for 3 nights is $334.

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The per cent of students who have college careers lasting between 2 and 9 years is 95%.

Given that, the normally distributed with a mean length of 5.5 years and a standard deviation of 1.75 years.

The normal distribution is a continuous probability distribution that is symmetrical around its mean with most values near the central peak.

Let x be the length of student's college careers.

\mu = 5.5 years

\sigma = 1.75 years

A percentage of students have college careers lasting between 2 and 9  years.

P(2<=x<=9)=P (2-5.5<=x-5.5<=9-5.5)

P(2<=x<=9)=P (-3.5<=x-5.5<=3.5)

=P (-3.5/1.75<=(x-5.5)/1.75<=3.5/1.75)

We know if x =-=N (4.6^2)

Then x-\mu/\sigma =-= Z (0.1)

=P(-2<=Z<=2)

=0.95

Percentage = P(-2<=Z<=2)*100

=95%

Therefore, the per cent of students who have college careers lasting between 2 and 9 years is 95%.

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Using a linear function and the work integral, it is found that the work that was done lifting the sand this far is of 944 ft-lb.

A linear function is modeled by the following rule:

y = mx + b

In which:

For the weight of the bag of sand in this problem, we have that:

Hence the weight of the bag after being lifted x feet is given by:

W(x) = 144 - 4x.

The work realized for a function f(x) in an interval [a,b] is given by the following integral:

[tex]W = \int_{a}^{b} f(x) dx[/tex]

For this problem, the function and the bounds of the interval are given as follows:

Hence the work is given by:

[tex]W = \int_{a}^{b} (144 - 4x) dx[/tex]

W = 144x - 2x², from x = 0 to x = 18.

Applying the Fundamental Theorem of Calculus:

W = 144(18) - 2(18)² - 144(0) + 2(0)² = 1944 ft-lb.

The work that was done lifting the sand this far is of 944 ft-lb.

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The value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

Divide 4 and 5 over 6 ÷ negative 2 and 1 over 7.

Rewrite the above expression properly as follows:

Divide 4 5/6 ÷ -2 1/7

Using LaTeX, the above expression can be further represented as

[tex]4 \frac{5}{6} \div - 2\frac 17[/tex]

Rewrite the above fractions and express it as improper fractions

[tex]\frac{29}6 \div -\frac{15}7[/tex]

Rewrite the above fractions and express it as products

[tex]\frac{29}6 \times -\frac7{15}[/tex]

Evaluate the product in the above expression

[tex]-\frac{203}{90}[/tex]

Rewrite the above expression as a mixed fraction

[tex]-2\frac{23}{90}[/tex]

Hence, the value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]

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The complete table is

x         y

-5      49

-1        9

0       -1

1        -11

From the question, we are to fill in the table for the given values of x

Using the given equation,

y = -10x - 1

Determine the value of y when x = -5

y = -10x - 1

y = -10(-5) - 1

y = 50 - 1

y = 49

Determine the value of y when x = -1

y = -10x - 1

y = -10(-1) - 1

y = 10 - 1

y = 9

Determine the value of y when x = 0

y = -10x - 1

y = -10(0) - 1

y = 0 - 1

y = -1

Determine the value of y when x = 1

y = -10x - 1

y = -10(1) - 1

y = -10 - 1

y = -11

Hence, the complete table is

x         y

-5      49

-1        9

0       -1

1        -11

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Answer: 560

Step-by-step explanation: i had this exact question on OW

Answer:

a₅₃ = 560

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 12 and d = a₂ - a₁ = - 1 - (- 12) = - 1 + 12 = 11 , then

a₅₃ = - 12 + (52 × 11) = - 12 + 572 = 560

When Sue wrote a double fact. It has a sum less than 10 and greater than 4. The addends are each less than 5, the numbers that she wrote include 4+4 and 3+3.

It is given that the sum is greater than 4 and smaller than 10.

If the sum is less than 10 and greater than 4 that limits you to 5,6,7,8,9

It should be noted that 5+5 is 10, and the sum has to be lower then 10.

The addends are less than 5 so it could be 4+4, 4+3, 4+2, 4+1

This shows that Sue might have written 5,6,7, or 8.

Therefore, the numbers are 3+3 and 4+4.

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Answer:

199 miles

Step-by-step explanation:

if you multiply 33 in 6 places it gives 198 then you plus 1 to get $25.00

GOOD RIGHT please rate

The Equation representing the charge to be to paid to mechanic is -

c = 150h + 257.

Equation modelling is defined as a method for deriving a mathematical relation from a mathematical statement taking into consideration the variables defined and the relations between them.

Given is a mechanic who charges $150 per hour. He also charge the cost of parts to fix the car.

Assume that the mechanic worked for 'h' hours and 'c' represents the total cost of repair. Extra cost of parts is $257.

If the mechanic works for 'h' hours, then the money received by the mechanic will be → $150 x h.

The equation representing the above situation can be written as -

c = $150 x h + Extra parts charge.

c = 150h + 257

Therefore, equation representing the charge to be to paid to mechanic is -   c = 150h + 257.

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Answer: The following expression: (-5)(-3)(4) = 60

Step-by-step explanation:

Given that,

The following expression is : (-5)(-3)(4)

Let us assume,

These values represented by X1, X2, X3    

Let us assume,       X1 = -5

                                X2 = -3

                                X3 = 4

So, the following expression is: (X1)(X2)(X3)    

                                                    (-5)(-3)(4)

This values using by multiplication,

So, we can write,

                                  = (X1)(X2)

                                  = (-5)(-3)                    [sign (-) (-) = (+)]

                                  = 15

Therefore, X1X2 values = 15

We can solve X3 value,

                                = (X1)(X2)(X3)

                                = 15 (X3)

 Replace X3 value,

                                = 15(X3)

                                = 15 (4)

                                 = 60

Therefore, (X1)(X2)(X3) = 60

The following expression: (-5)(-3)(4) = 60

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Answer:120

Step-by-step explanation:

so if its a 10x12 plane that would be 10 12 times so 10+10+10+10+10+10+10+10+10+10+10+10

or 12+12+12+12+12+12+12+12+12+12

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\hspace{10em} \underset{gradient}{\stackrel{slope}{m}} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y - 2 = \cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x[/tex]

Answer:

B

Step-by-step explanation:

a c and d are unessecary answers

Answer:

[tex]\left \{ {{-x+2=0} \atop {x+2y=7}} \right.[/tex]

-x + 2 = 0 --> -x = -2

x + 2y = 7 --> x + 2y = 7              

                    ________  

                    2y = 7-2 = 5 --> y = 5/2

x = -2y + 7 --> x = -5 + 7 --> x = 2

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Have a nice day!

Answer:5

Step-by-step explanation:look on my page