In a history class, 30 students were asked about other courses that they were enrolled in: 20 said they were taking math, 22 were taking English and 26 students were in either math or English. a) How many students are taking both math and English b) How many are in neither c) What percent of the students are taking math but not English

Answer:

  -1 ≤ x ≤ 2

Step-by-step explanation:

The given equation can be rewritten as a piecewise function and solved in pieces.

The term |x+1| changes definition at x=-1. For x-values less than that, it is defined as -(x+1). Similarly, the term |x-2| changes definition at x=2. For x-values less than that, its definition is -(x-2). In the following, we consider the three pieces of the function.

__

In this domain, the absolute value functions both have negative arguments, so the equation is effectively ...

  -(x +1) -(x -2) = 3

  -2x +1 = 3 . . . . . . . simplify

  -2x = 2 . . . . . . subtract 1

  x = -1 . . . . divide by -2

This value of x is not in the domain we have defined, so there is no solution in this domain.

__

In this domain, the function |x+1| has a non-negative argument, but the function |x-2| has a non-positive argument. The equation is effectively ...

  (x +1) -(x -2) = 3

  x -x +1 +2 = 3 . . . . . eliminate parentheses, group like terms

  3 = 3 . . . . . . . . . true for the entire domain

The solution here is -1 ≤ x ≤ 2.

__

Both absolute value terms have positive arguments in this domain, so the equation is effectlvely ...

  (x +1) +(x -2) = 3

  2x -1 = 3 . . . . . simplify

  2x = 4 . . . .  add 1

  x = 2 . . . . divide by 2

This value of x is not in the domain we have defined, so there is no solution in this domain.

__

The solution to the given equation is -1 ≤ x ≤ 2.

Answer:

120 square feet     ( 13.333 square yards)

Step-by-step explanation:

8 ft   x   15 feet   = 120  ft^2    

Answer:

choice for your help today 12 m is not answering me, sorry I think 25m

Answer:

[tex]x=-7,-3[/tex]

Step-by-step explanation:

Completing the square means you are changing the polynomial so that it is a perfect square trinomial. Since the middle term is 10, we need the last term to be 25 since 5+5=10, thus, 5*5=25:

[tex]x^2+10x+21=0\\x^2+10x+21+4=0+4\\x^2+10x+25=4\\(x+5)^2=4\\x+5=\pm2\\x=-7,-3[/tex]

As you can see, because we change [tex]x^2+10x+21[/tex] to [tex]x^2+10x+25[/tex] by adding 4 to both sides, we were able to reduce it to [tex](x+5)^2[/tex], a perfect square, and solve the rest of the problem.

Answer:

[tex]5x^{3} y^3 \sqrt{15y}[/tex] is the right answer and other are wrong

Answer:

B

Step-by-step explanation:

i took the test and got a 100% so ys that the answer.

Answer:

B

Step-by-step explanation:

"lateral" means "belonging to the side".

so, the lateral area of a square pyramid (or any kind of pyramid or other 3-D structure, really) is the sum of the areas of its side faces.

so, in essence we have to calculate the area of one of the side triangles, and then multiply it by 4, as the other 3 are equal (due to the fact that the base is a square, and we are clearly dealing with a regular, symmetric pyramid).

each of the side triangles is an isoceles triangle (both legs are equal long, therefore both side angles are equal too).

that means both side angles are 60° each.

and because we know that the sum of all angles in a tingle is always 180°, the angle at the top is

180 - 60 - 60 = 60°

hey, all 3 angles are the same !

that means the triangle is not only isoceles but equilateral (all 3 sides are equally long).

and that means all sides are 18 cm long.

the area of a triangle can be calculated for our scenario in 2 major ways :

1. baseline × height / 2

2. Heron's formula (since we know all 3 sides) :

A = sqrt(s(s-a)(s-b)(s-c)), s = (a+b+c)/2

I don't know which one your teacher wants you to use.

so,

1.

the height we get via Pythagoras

leg² = (baseline/2)² + height²

18² = (18/2)² + height²

324 = 81 + height²

81×4 = 81 + height²

81×3 = height²

height = sqrt(81×3) = 9×sqrt(3)

the area of the triangle is

18 × 9 × sqrt(3) / 2 = 9 × 9 × sqrt(3) = 81×sqrt(3) cm²

2.

s = (18+18+18)/2 = 54/2 = 27

A = sqrt(27(27-18)(27-18)(27-18)) =

= sqrt(9×3×9×9×9) = 3×3×3×3×sqrt(3) = 81×sqrt(3) cm²

the total lateral area is then

4×81×sqrt(3) = 324×sqrt(3) = 561.1844617... cm²

oh, I see, i think you did not include the square root in the answer options. that is confusing.

but as you can see, option B must be correct.

Step-by-step explanation:

First find out the value of X and second find the value of Y and where is figure

A vertical line going through any given point would pass through the x-coordinate.

In this case, the x-coordinate is 3. Therefore, the vertical line that would pass through the point (3, 5) is x = 3.

Hope this helps!

The plane HGD contains at least three points

The three points on the plane are H, G and D

Coplanar points are at least three points that are in the same plane

The name of the plane is given as:

Plane = HGD

The above means that points H, G and D are on the plane HGD

Hence, the three points on the plane are H, G and D

Read more about coplanar points at:

https://brainly.com/question/1593959

Answer:

b 64

Step-by-step explanation:

because p is just a mirror of o ,and o =64

side length 2 km and slant height 2 km.

the surface area of the pyramid.

area of 4 triangle= 1/2 × 2 × 2 × 4

= 8km

area of rectangle= 2×2

= 4km

area= 4+8

= 12km

so, the surface area of the pyramid is 12km.

Answer:

0.25

Step-by-step explanation:

Every number has equal probability here

Answer:

D&E, A&B

Step-by-step explanation:

It's pretty confusing but I know any of the answers with "c" in it is incorrect. The other options seem correct.

Answer:

30%

Step-by-step explanation:

The sign means that x can be equal to or LESS than -3. The only ones are -3 and -5. 0.17+0.13=0.30

Answer:

C. 4 × 10 × 2

Step-by-step explanation:

There are four walls that are ten feet on each side.

You would take 4 (number of walls) × 10 (number of feet in length), and because there are 2 sides of the walls, you would take that × 2.

Therefore, your answer is 4 × 10 ×2

Answer:

95

Step-by-step explanation:

9025 is a perfect square of 95. hence the number of rows is 95.

[tex]☞︎︎︎ \: x \: \times \: x = 9025[/tex]

[tex]☞︎︎︎ \: {x}^{2} = (5 \times 5) \: \times \: (19 \times 19)[/tex]

[tex]☞︎︎︎ \: {x}^{2} = {95}^{2} [/tex]

[tex]☞︎︎︎ \: x \: = \sqrt{ {95}^{2} } [/tex]

[tex]☞︎︎︎ \: x = 95[/tex]

Answer:

from my side it's blurry

Margin of error = 0.8226401

Confidence interval = (9.17736,10.82264)

We have given data for one week recorded for 6 plants.

With a sample standard deviation of 1 inch and a sample mean of 10 inches.

For this sample, it is given that,

Sample size = n = 6

Sample SD = s = 1

Sample mean = x = 10

At a 0.10 significance level, the critical point is with t-distribution (n-1)df=5 df,

t*  =2.015048

Margin of error = E=2.015048*s/ √n = 0.8226401

Confidence interval

= (9.17736,10.82264)

Learn more about Margin of error here: https://brainly.com/question/10218601

#SPJ4

The equation that can be used to determine the number of bean bags in the instuctor's box is b = 17 x 4.

The number of bean bags in the instructor's box is 68.

Multplication is a mathematcial operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

To learn more about multiplication, please check: https://brainly.com/question/13814687

17.29162

[tex]\sqrt{18^2-5^2}[/tex]

__________________________________________

[tex]17.29162[/tex]

I hope this helps you

:)

Answer:

42 Pages

Step-by-step explanation:

7x5=35

7+35=42

Answer:

28.26 ft squared

Step-by-step explanation:

Area is pi*r^2

3.14*(3)^2

3.14*9

28.26

Answer:

9

Step-by-step explanation:

2 is in the ones place

4 is in the tens

1 is in the hundreds

6 is in the thousands

9 is in the ten thousands

Answer:

The number that is in the ten thousands is 9, whose value is 90,000.

---

Thank you so much for participate in the community of Brainly.com

I hope help you :)

Kind regards, Antonio.

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Recall that the projection of a vector [tex]u[/tex] onto [tex]v[/tex] is [tex]\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v[/tex].

Identify the vectors:

[tex]u=\langle-10,-7\rangle[/tex]

[tex]v=\langle-8,4\rangle[/tex]

Compute the dot product:

[tex]u\cdot v=(-10*-8)+(-7*4)=80+(-28)=52[/tex]

Find the square of the magnitude of vector v:

[tex]||v||^2=\sqrt{(-8)^2+(4)^2}^2=64+16=80[/tex]

Find the projection of vector u onto v:

[tex]\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v\\\\proj_vu=\biggr(\frac{52}{80}\biggr)\langle-8,4\rangle\\\\proj_vu=\biggr\langle\frac{-416}{80} ,\frac{208}{80}\biggr\rangle\\\\proj_vu=\biggr\langle\frac{-26}{5} ,\frac{13}{5}\biggr\rangle\\\\proj_vu=\langle-5.2,2.6\rangle[/tex]

Thus, B is the correct answer

Problem 2

Treat the football and wind as vectors:

Football: [tex]u=\langle42\cos172^\circ,42\sin172^\circ\rangle[/tex]

Wind: [tex]v=\langle13\cos345^\circ,13\sin345^\circ\rangle[/tex]

Add the vectors: [tex]u+v=\langle42\cos172^\circ+13\cos345^\circ,42\sin172^\circ+13\sin345^\circ\rangle\approx\langle-29.034,2.481\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v||=\sqrt{(-29.034)^2+(2.481)^2}\approx29.14[/tex]

Find the direction of the resultant vector:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{2.841}{-29.034}\biggr)\approx -5^\circ[/tex]

Because our resultant vector is in Quadrant II, the true direction angle is 6° clockwise from the negative axis. This means that our true direction angle is [tex]180^\circ-5^\circ=175^\circ[/tex]

Thus, C is the correct answer

Problem 3

We identify the initial point to be [tex]R(-2,12)[/tex] and the terminal point to be [tex]S(-7,6)[/tex]. The vector in component form can be found by subtracting the initial point from the terminal point:

[tex]v=\langle-7-(-2),6-12\rangle=\langle-7+2,-6\rangle=\langle-5,-6\rangle[/tex]

Next, we find the magnitude of the vector:

[tex]||v||=\sqrt{(-5)^2+(-6)^2}=\sqrt{25+36}=\sqrt{61}\approx7.81[/tex]

And finally, we find the direction of the vector:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{6}{5}\biggr)\approx50.194^\circ[/tex]

Keep in mind that since our vector is in Quadrant III, our direction angle also needs to be in Quadrant III, so the true direction angle is [tex]180^\circ+50.194^\circ=230.194^\circ[/tex].

Thus, A is the correct answer

Problem 4

Add the vectors:

[tex]v_1+v_2=\langle-60,3\rangle+\langle4,14\rangle=\langle-60+4,3+14\rangle=\langle-56,17\rangle[/tex]

Determine the magnitude of the vector:

[tex]||v_1+v_2||=\sqrt{(-56)^2+(17)^2}=\sqrt{3136+289}=\sqrt{3425}\approx58.524[/tex]

Find the direction of the vector:

[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{17}{-56} \biggr)\approx-17^\circ[/tex]

Because our vector is in Quadrant II, then the direction angle we found is a reference angle, telling us the true direction angle is 17° clockwise from the negative x-axis, so the true direction angle is [tex]180^\circ-17^\circ=163^\circ[/tex]

Thus, A is the correct answer

Problem 5

A vector in trigonometric form is represented as [tex]w=||w||(\cos\theta i+\sin\theta i)[/tex] where [tex]||w||[/tex] is the magnitude of vector [tex]w[/tex] and [tex]\theta[/tex] is the direction of vector [tex]w[/tex].

Magnitude: [tex]||w||=\sqrt{(-16)^2+(-63)^2}=\sqrt{256+3969}=\sqrt{4225}=65[/tex]

Direction: [tex]\displaystyle \theta=tan^{-1}\biggr(\frac{-63}{-16}\biggr)\approx75.75^\circ[/tex]

As our vector is in Quadrant III, our true direction angle will be 75.75° counterclockwise from the negative x-axis, so our true direction angle will be [tex]180^\circ+75.75^\circ=255.75^\circ[/tex].

This means that our vector in trigonometric form is [tex]w=65(\cos255.75^\circ i+\sin255.75^\circ j)[/tex]

Thus, C is the correct answer

Problem 6

Write the vectors in trigonometric form:

[tex]u=\langle40\cos30^\circ,40\sin30^\circ\rangle\\v=\langle50\cos140^\circ,50\sin140^\circ\rangle[/tex]

Add the vectors:

[tex]u+v=\langle40\cos30^\circ+50\cos140^\circ,40\sin30^\circ+50\sin140^\circ\rangle\approx\langle-3.661,52.139\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v||=\sqrt{3.661^2+52.139^2}\approx52.268[/tex]

Find the direction of the resultant vector:

[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{52.139}{-3.661} \biggr)\approx-86^\circ[/tex]

Because our resultant vector is in Quadrant II, then our true direction angle will be 86° clockwise from the negative x-axis. So, our true direction angle is [tex]180^\circ-86^\circ=94^\circ[/tex].

Thus, B is the correct answer

Answer:

A. evaluate progress

Step-by-step explanation:

common sense

Answer:

4 hours

Step-by-step explanation:

the rate of people coming in it 700 per hour

so for a height of 869 feet the time will be 21.725s

[tex]1s = 40ft \\ x = 869ft \\ x= \frac{869}{40} \\ x = 21.725ft[/tex]

Step-by-step explanation:

You must set up a proportion, it is called finding the geometric mean.

[tex] \frac{x}{4} = \frac{36}{x} [/tex]

Then, you must cross multiply to get:

[tex] {x}^{2} = 144[/tex]

Then, take the square root

[tex] \sqrt{ {x}^{2} } = \sqrt{144} [/tex]

[tex]x = 12[/tex]

If this answer helped you, I would greatly appreciate the brainliest :D

Step-by-step explanation:

[tex]see \: if \: 10 \: are \: left \: then \: we \: hve \: spent \\ 250 - 10 = 240 \: dollars \\ [/tex]

hence

[tex]six \: flasks \: cost \: 240 \: dollars \\ so \: if \: we \: divide \: 240 \: by \: 6 \: we \: get \: 40 \: \\ [/tex]

so one flask costs 40$