In the morning, the temperature in Westfield City was
–
2°F. By afternoon, a north wind caused the temperature to drop another 8°F. What was the afternoon temperature in Westfield City?
To solve the problem, Martin subtracted
–
2–(
–
8) and came up with an answer of 6°F. Is Martin correct? Why or why not?

The answer to the given word problem is as follows. From the calculations: Johanna purchased

A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation.

The calculations is given as follows:

Step 1 -  First, let's define the variables to represent the unknowns.

Let p = number of pens

Let n = number of notebooks

Let h = number of highlighters

p + n + h = 17 ......................... 1  (purchased 17 items)

.5p + 4n + 1.5h = 41.5 ...................2 (total cost $41.50)

n = h+3  ................................3 (3 more notebooks than highlighters)

Step 2...............Solve for P in equation 1

P = 17 - n - h..................4

Recall that in equation 3,

n = h + 2

If we make n the subject of the expression, we have:

n = h+ 3

Substituting that into equation 4, we have

p = 17 - (h+3) - h
p = 17 -2h - 3 ..................5

Going back to equation 2, let's substitute n with h+3 and replace p with 17 -2h - 3

.5(17 -2h - 3) + 4 (h+3) + 1.5h = 41.5

To remove all decimals, we can multiply all with 10 to get:

5(170-20h -30) + 40(10h +30) + 15h = 415

Expand all brackets and we have:

850 - 100h - 150 + 400h + 1200 + 15h = 415

Collect like terms

-100h + 400h + 15h = 415-850+150-1200

315h = -1485

h = -1485/315

h = -4.71

Since a physical item cannot be negative, we utilize the absolute value which is:

h = 4.71

h [tex]\approx[/tex] 5 highlighter

Recall that

n = h + 3

Hence

n = 5 +3 = 8 notebooks

Recall that

p + n + h = 17

Hence we have

p + 8 + 5 = 17

p = 17 -8 - 5

p = 17 - 13
P = 4 pens.

Hence Johanna purchased

4 pens, 8 notebooks and 5 highlighters.

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Based on the trend found in the data set, the x-coordinate that would yield a y-coordinate of 30 is 28

Pick two points from the data set:

(26, 31) and (64, 13)

The slope is:

= Change in y / Change in x

= ( 13 - 31) / (64 - 26)

= -18 / 38

= -9/19

The y-intercept is:

y = mx + b

13 = -9/19(64) + b

b = 43.3

The x-coordinate that gives a y-coordinate of 30 is:

30 = -9/19x + 43.3

x = 28

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Answer:

1. perpendicular

2. parallel

3. neither

Step-by-step explanation:

The first set of lines are perpendicular because they intersect each other at a right angle.

The second set of lines are parallel because they never cross.

The first pair forms a 90° angle therefore the lines are perpendicular.

The second lines are straight that it's obviously clear they will never meet meaning they are parallel

the third lines are neither perpendicular nor parallel.

The representation of the expression is 4 < x + 7

The mathematical statement is given as

"4 less than the sum of a number and 7"

Sum means Plus

So, we have the following representation

"4 less than the sum of a number and 7" ⇒  4 less than a number + 7"

Let the number be x

So, we have

"4 less than the sum of a number and 7" ⇒  4 less than x + 7"

Less than as used here means <

So, we have

"4 less than the sum of a number and 7" ⇒  4 < x + 7"

Hence, the expression represented by "4 less than the sum of a number and 7" is  4 < x + 7

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Answer: 5.18 x 10^-3

Step-by-step explanation:

0.00518

**Move the decimal 3 spaces to the right**

5.18

**Since it goes like 0.00, you want to make sure the exponent is negative**

5.18 x 10^-3

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{7}~~ = ~~\cfrac{10}{x}\implies x^2=70\implies x=\sqrt{70}[/tex]

Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Equation of line is y = 2/3x + 2

Step-by-step explanation:

I hope this will be helpful for you.

[tex]2x(x+3)-(12x-4)\\=2x^{2} +6x-12x+4\\=2x^{2} -6x+4[/tex]

I hope this helps.

Answer:

y=x/4

Step-by-step explanation:

if the line is perpendicular (m2)=-1/(m1)

m2=1/4

y=x/4+c

sub in 8,2

2=8/4+c

c=0

equation is therefore y=x/4

Answer:

A.) 30 degrees

Step-by-step explanation:

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If the family’s monthly income is $3,286, Wren family budgets for entertainment each month is $328.60.

Income, which is typically stated in the monetary terms, is the spending and saving opportunity acquired by an entity within a given duration. Conceptually, income is hard to define, and different fields may have the distinct definitions. For instance, a person's income may differ from their income as defined by law and in an economic sense.

Haig-Simons income, which defines income as Consumption + Change in Net Worth and is commonly applied in economics, is a very significant definition of income.

Income is a total that includes any wages, salaries, profits, interest payments, rent, or other forms of earnings received in a calendar year for families and individuals in the United States, as defined by tax law. Gross income less taxes and other deductions (such as required pension payments) is a common definition of discretionary income and is frequently used as a benchmark to assess the wellbeing of taxpayers.

The idea may include the accumulation of both monetary and non-monetary consumption capacity, with the former (monetary) serving as a stand-in for total income in the field of public economics.

Gross income for a business is the total revenue less the cost of items sold. Costs are subtracted from revenue by cost of goods sold, expenses, depreciation, interest, and taxes to arrive at net income.

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If a case of 24 pairs of the same kind of switches cost a little more than $800. $28 per pair with tax included is not  good estimate of the price  but  $33.33 is the good estimate for the price .

Assuming that the  cost per pair is the amount of $28. Hence, cost of 24 pairs is calculated as:

Cost= $28x24

Cost  = $672.

Based on the above calculation for the cost of 25 pairs we can see that that the  24 pairs of the same kind of switches does not cost more than $800 which implies that $28 is not good estimate for the price.

Now let determine the best estimate of the price with tax included :

Cost = $800/24

Cost = $33.33

Therefore the good estimate for the price with the tax included is $33.33.

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4y = x + 6 is the equation of the line using the slope value.

The steepness of a line segment is explained by the slope of the line. It is a ratio of the vertical x-axis coordinates and the y-axis coordinates. The classification of whether two lines are parallel or perpendicular depends on the slope value.

The parameters for the line segment are as follows, in accordance with the question:

The coordinate points (6, 3) and the slope of a line (1/4) are as follows: (x = 6; y = 3)

Using the line segment's standard equation now: y = mx + c

If (x, y) are coordinates, "m" is the slope, "c" is the y-intercept,

The following results are obtained by replacing the slope and y-intercept values in the formula:

y = mx + c

⇒ 3 = (1/4)(6) + c

⇒ c = 3 - 3/2 = 3/2

Consequently, c = (3/2) is the y-value. intercept's

by changing the slope value and y-intercept value in the line's equation:

y = (1/4)x + (3/2) = 4y = x +6

Consequently, 4y = x + 6 is the equation of the line using the slope value.

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If a space rover has a mass of 3900 kg, then its weight on Earth N will be 38220 N.

Weight can be described as the body's relative mass  which can be regarded as the quantity of matter that can be found in the particles of the object and the unit can be written as Newton.

To calculate the weight of a particular particles, we can use the formular (mg) which is that product of the mass of the object to that of the gravity.

from the question, the gravity is been given as  g-9.81m/s

Then the weight = (3900 kg* 9.8) = 38220 N

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The number of volunteers needed for each case is given as follows:

a. 0.4 miles: 5.

b. 2/7 miles: 7.

c. 0.125 miles: 16.

d. 6/45 miles: 15.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates of the context of the problem along with basic arithmetic operations, especially multiplication and division.

In this problem, a two mile section will be cleaned, hence the number of volunteers needed is calculated as follows:

n = 2/s.

In which s is the section cleaned by each volunteer.

In item a, the section is of 0.4 miles, hence the number of volunteers is given as follows:

n = 2/0.4 = 5 volunteers.

In item b, the section is of 2/7 miles, hence the number of volunteers is given as follows:

n = 2/(2/7) = 2 x 7/2 = 7 volunteers.

In item c, the section is of 0.125 miles, hence the number of volunteers is given as follows:

n = 2/0.125 = 2/(1/8) = 2 x 8 = 16 volunteers.

In item d, the section is of 6/45 miles, hence the number of volunteers is given as follows:

n = 2/(6/45) = 2 x 45/6 = 90/6 = 15 volunteers.

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Answer: 145

Step-by-step explanation:

To find the total of the three numbers: 115 x 3 = 345

So the 3rd number must be 345 - 110 -90 = 145

Check the answer= 110 + 90 +145

                                         3

= 115

The illness is spreading at a rate of 10% per hour -> it is spreading 1.1x faster per hour as 10% more people are infected each time.

Therefore, we can write the amount of people infected as 3 x [tex]1.1^{n}[/tex], where n is the hour. So, if n equals 1, the amount of people infected is 3 x 1.1 = 3.3 (so when this mark surpasses the 1200 limit, we round up to the nearest whole number)

It will take 1200 : 3 : 1.1 = 363.636364.. (hours)

If it's only 363 hours, the number of people infected will not have reached 1200, as we have .636364 hours left. So, it will take 364 hours.

The inequality that describes the domain is 0 ≤ x ≤ 5

The given parameters are

Size of tank = 3 gallons

Rate = 0.6 gallons per hour

The highest number of time is calculated as

Time = Size of tank/Rate

Substitute the known values in the above equation

So, we have the following equation

Time = 3/0.6

Evaluate

Time = 5

The domain is then represented as

0  ≤ x ≤ Time

This gives

0 ≤ x ≤ 5

Hence, the domain of the situation is 0  ≤ x ≤ 5

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Answer:

Plane EFGH

Step-by-step explanation:

we can see that plane ABCD is on the bottom

and that plane EFGH is on the top

so if the go left and right, they will never touch that is what parallel is

any other plane will intersect or touch eventually

Answer:

8/9 cups is the correct answer

The correct equation that is balanced using the given numbers once is;

5(-1 + (-3)) = (7 * -4) + 8

There are different properties of Algebra such as;

Commutative Property of Addition or multiplication

Associative Property of Addition or multiplication

Distributive Property

Now, from the given numbers, it will be best to use only a positive digit outside the bracket on the left hand side to make it easy to balance on the right hand side. Thus, for the left hand side we will try;

5(-1 + (-3))

When that is solved we will get -20

Now, to balance that on the right hand side , we will have;

(7 * -4) + 8

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Answer:0.6

Step-by-step explanation:

20/3 is 6

The simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18

The given the expression is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)

To solve this problem first we have to use the distributive property

The distributive property states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together

The distributive property of addition

A(B+C) = AB + AC

The distributive property of subtraction

A(B-C) = AB - AC

The given equation is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)

Apply distributive property

4(4y-[tex]7y^{2}[/tex])-9(5y+2) = 16y -28[tex]y^{2}[/tex]-45y-18

Rearrange the terms

-28[tex]y^{2}[/tex]-45y+16y-18 = -28[tex]y^{2}[/tex]-29y-18

Hence, the simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18

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Based on the number of bushels that the farmer has to sell, the equation that represents the total change in the number of bushels after seven days is 220 - 15⁵/₈(7).

The farmer has a total of 220 bushels of wheat to sell and then sells about 15⁵/₈ every day.

After 7 days, the total change in the number of bushels would be:

= Total bushels to be sold - Bushels of wheat already sold

= Total bushels to be sold - (Number of bushels sold per day x Number of days)
= 220 - 15⁵/₈(7)

= 110 bushels of wheat

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Answer:

the length is 99m

Step-by-step explanation:

you have to add 86 to 86 to get 172, subtract 172 from 370 then you have 198 then divide to have  99m the length.

Answer:

9h=p

9 times the number of hours worked equals the total pay.

Step-by-step explanation:

when we put gasoline in a car that will depend on how much it will cost us, also for example if we are going to buy popcorn depending on how many we buy will be the price

Answer:

1

Step-by-step explanation:

The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.