I'm doing topic about classifying numbers can you please help me with these problems?

Enrollment in finite mathematics plus enrollment in calculus is less than 300.

The first step in solving a word problem is identifying the variables. The variables in any algebraic expression is the unknown value, and to solve it we usually assign a letter to represent it (x and y being the most commonly used).

In the question above, we already know that the number of student enrollees is less than 300 and not equal to 300 (might as well be just 20, we do not know) but we do know that it is NOT EQUAL TO 300, but less than.

Also we do not know the number of those enrolled for finite mathematics, so we shall call that f. Those that enrolled for calculus we shall call c. Since both categories are less than 300, the two variables f and c can now be written as an inequality which reads,

f plus c is less than 300

That is;

f + c ⊂ 300

Simplifying,

Answer:

In slope-intercept form:

[tex]y = - 2x - 11[/tex]

First, notice that the two sides of the right triangle are equal, then, using the pythagorean theorem,we get:

therefore, x = 3*sqrt(2)

We were told that the farmer's land is separated in sections of size 2 1/7 acres. Converting 2 1/7 to improper fraction, we multiply 2 by 7 and add 1. The denominator remains 7. it becomes 15/2

There are 4 3/8 such sections. Converting 4 3/8 to improper fraction, it becomes 35/8

Therefore, the number of acres of land that the farmer owns is

15/2 * 35/8 = 525/16

Converting to improper fraction, it becomes

32 13/16 acres

Answer:

32 13/16 acres

Step-by-step explanation:

You have to graph the following function

This is a linear function with slope m=1, this means that each time x increases one unit, y also increases one unit.

To sketch this function you have to choose at least two values of x and determine the corresponding value of y.

Then plot the points and draw the line.

I will make a table with 5 points of the line:

Now what's left is to plot all points and link them with a line:

Answer:

x=11

Step-by-step explanation:

The inside(interior) angles of a triangle must add up to 180 degrees. A line is 180 degrees, so the angle GFH (the measure of the acute angle at point F) would be 180-(11x+1)

Now we have information on all 3 angles of the triangle; they must sum up to 180, so add all of these equations together

180-(11x+1) = 179-11x

Add this to 3x+19 and 70 gives 268-8x=180

Solving this equation for x we get -8x=180-268

-8x=-88

x=11

Hoped this helped and I hope you feel better!

Answer:

11°

Step-by-step explanation:

Here,

∠FGH=3x+19
∠GHF=70°

∠QFG=11x+1
Now,

11x+1+∠GFH=180[Sum of a straight line is 180°]
∴∠GFH=179-11x

Again,
∠GFH+∠GHF+∠FGH=180[Sum of all angles of a triangle is 180]

179-11x+70+3x+19=180

-11x+3x=180-179-70-19

-8x=-88

∴x=11°

Graphing the set of data in a dot plot, we have:

Since this set has 18 elements, the median is the average between the 9th and 10th elements using the set in the crescent order.

Looking at the dot plot, the 9th element is 7 and the 10th element is 8, so the median is (7 + 8)/2, that is, the median is 7.5.

One is traveling at a constant pace of 30 mph and is 5 miles south of the intersection. The distance d between the cars changes with time t as [tex]\sqrt{26-320t+1000t ^{2}}[/tex].

Given that,

An intersection is being approached by two cars. One is traveling at a constant pace of 30 mph and is 5 miles south of the intersection. At the same time, the second vehicle is traveling at a constant speed of 10 mph and is located one mile to the east of the intersection.

We have to describe how the distance d between the cars changes with time t.

The distance is d=[tex]\sqrt{(t_{1}) ^{2} +(t_{2}) ^{2}}[/tex]

t₁=1-10t

t₂=5-30t

d=[tex]\sqrt{(1-10t) ^{2} +(5-30t) ^{2}}[/tex]

d=[tex]\sqrt{1-20t+100t^{2}+25-300t+900t ^{2}}[/tex]

d=[tex]\sqrt{26-320t+1000t ^{2}}[/tex]

Therefore, We got the distance d between the cars changes with time t as [tex]\sqrt{26-320t+1000t ^{2}}[/tex].

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Answer:

(5, 2)

Explanation:

If point P with coordinates (x, y) is rotated 90 degrees counterclockwise about the origin, the image will have (-y, x) as coordinates of the image, P'.

So if triangle RST was rotated 90 degrees counterclockwise about the origin, we'll have the below as coordinates of the image of vertex T;

Theorem is a statement that can be proved or that is proven to be true.

Option A is a theorem because it is proven that the area of two congruent figures are equal.

Option B is a theorem because the area of a square is the square of the length of its side.

Option C is a theorem because the area of a rectangle is the product of its base and height.

Thus, A, B and C are CORRECT

Abel walks 2.6 miles each day of the week.

The week has 7 days.

So, to calculate how many miles he walks in one week we simply have to multiply the number of miles that he walks per day (2.6) by the number of days in a week (7).

2.6 miles per day x 7 days = 2.6 x 7 = 18.2 miles a week.

Answer:

The two types of the sequence include

1) Arithmetic sequence

2) Geometric sequence

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression.

The Nth term of an arithmetic sequence is given below as

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

The Nth term of a geometric sequence is given below as

Real life illustrations of the types of sequence

Sequences are useful in our daily lives as well as in higher mathematics. For example, the interest portion of monthly payments made to pay off an automobile or home loan, and the list of maximum daily temperatures in one area for a month are sequences.

Example: arithmetic sequence

A boy building a tower with blocks uses 15 for the bottom row. Each row has 2 fewer blocks than the previous row. Suppose that there are 6 rows in the tower. Find a for n = 6

The number of blocks in each row forms an arithmetic sequence with a₁ = 15 and d= −2. The formula to be used is an = a₁ + (n − 1)d.

Hence,

On the sixth row, he will have 5 blocks left

Example: geometric sequence

A country's population is growing in such a way that each new generation is 1.5 times as large as the previous generation. Suppose there are 100 insects in the first generation. How many will there be in the fifth generation?

Here,the common ratio r=1.5

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

The line that passes through the point (1,-1) and is parallel to another line whose slope is 1 will be y = x-2.

A straight line is a combination of endless points joined on both sides of the point.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that line that passes through the point  (1,-1) and is parallel to another line whose slope is 1.

The standard from the equation is,

y = mx + c

The equation with slope 1 is,

y = x +c

For the y-intercept, the value of y is -1.

-1 = 1(1) + c

-1 = 1+c

c = -2

Substitute the value of the slope, m as -1 and c as -2 we get,

y = 1x-2

y = x-2

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The given expression is - 7(2x - 3)

The first step is to open the bracket by multiplying each term inside the bracket by the term outside. Then we would add or subtract where necessary.

It becomes

- 7 * 2x + - 7 * - 3

Recall, - * - = +

The simplified expression would be

- 14x + 21

The correct option is A

We have the next points

H(-4,1)

I(-2,2)

J(-1,-2)

K(-4,-4)

The rule to rotate 180° counterclockwise

with rule, we can find the points

H'=(-(-4),-1)=(4,-1)

I'=(-(-2),-2)=(2,-2)

J'=(-(-1),-(-2))=(1,2)

K'=(-(-4),-(-4))=(4,4)

so the answer is

H'=(4,-1)

I'=(2,-2)

J'=(1,2)

K'=(4,4)

we can graph them they are the points in red

Let's draw the figure to better understand the scenario:

To be able to get the measure of ∠WXY, we will be using the relationship of the interior angles of a triangle.

The sum of all interior angles of a triangle is 180°. Therefore we can say,

The formula or measure of ∠XYW isn't given. However, we observed that ∠XYW and ∠XYZ are pairs of Supplementary Angles. This means that the sum of two angles is equal to 180°.

We get,

Therefore,

We will use this to complete the formula of the sum interior angles, substituting ∠XYW = 180° - ∠XYZ.

Substituting the given formulas of each angle, let's find x.

Let's substitute x = 5 to ∠WXY = 3x - 2 to find its measure.

Therefore, the measure of ∠WXY = 13°.

The number of associates is 9 and the number of partners is 10.

Given, The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1300.

The law firm assigned a total of 19 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services.

we need  to determine the number of associates assigned to the case and the number of partners assigned to the case.

Suppose the number of associates is x and the number of partners be y.

Then the required equations are formed:

x+y=19 ..eq(1)

700x+1300y=19300 ...eq(2)

from eq(1) we get:

y=19-x .. eq(3)

Plug eq(3) into eq(2)

700x+1300(19-x)=19300

700x+24700-1300x=19300

700x-1300x=19300-24700

-600x=-5400

x=9

Thus, y=19-9

y=10

Thus the number of associates are 9 and the number of partners are 10.

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Answer: 12.00705

Step-by-step explanation:

Simplify the equation to obtain the value of k.

So value of k is 4.

ANSWER

A. 300 seconds

EXPLANATION

Half a minute is 30 seconds. If Jing answers 1 question in 30 seconds, then he will answer 10 questions in:

300 seconds.

Answer:

300

Step-by-step explanation:

30 (seconds) x 10 (minutes) = 300 (seconds) hope this helps!

                                                    o((>ω< ))o

Step 1:

What is an isosceles triangle?

What is Isosceles Triangle? A triangle with two sides of equal length is an isosceles triangle.

Step 2: What is an acute angle?

An acute angle is an angle that measures between 90° and 0°.

Step 3:

The figure is an acute isosceles.

Final answer

Acute Isosceles

The amount of rubber flooring will be the area of the floor.

We can calculate the area as the sum of two rectangles:

Then, the area is:

We can convert this area into square yards as:

As we have to purchase a whole number of square yards, we will buy the next integer greater than 11.44, that is 12 sq yd.

Answer:

The floor area is 103 square feet.

This is equivalent to 11.44 square yards.

He has to purchase 12 square yards of rubber floor.

Answer:

Add the 20%, 0.40 and the 40/100 chart

Add the 1/10, the 0.10, and the 80/100 chart

And finally, add the 6%, the 4/100 chart, and the 90/100

First, you can know how many minutes are 8 hours using the rule of three like this

Now, using the rule of three again, you can find out how many gifts Dracula would wrap in 8 hours if she wrapped 3 gifts every 20 minutes

Therefore, Dracula would wrap 72 gifts in 8 hours if he wrapped 3 gifts in 20 minutes

Given:

Explanation:

a) To draw: The Graph

Let us find the intercepts.

When x = 0, we get

Therefore, the y-intercept is (0, 4).

The x-intercepts are,

Let us find the vertex.

The given function can be written as,

So, the vertex is,

The graph becomes,

b) The equation of symmetry is,

This line divides the parabola into two equal parts.

c) The coordinates of the vertex is,

d) Intercepts:

The x-intercepts are,

The y-intercept is (0, 4).

We have that the formula for the area of the sector of a circle is:

In this case, we have to find the area of the sector of a circle with radius r= 21 and then the area in the case of the r=21-14=7, and then find the difference.

Given the information, we have the following: