150 students
110 studied mathematies
95 studied physics
question 1
-The students took mathematics and physics.​

Answer: Choice D. [tex]\angle A \cong \angle E[/tex]

Explanation: Since AB is parallel to ED, this means the alternate interior angles A and E are congruent as marked below.

Angle A is congruent to angle E by alternate interior angle theorem. Therefore, option D is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle CAB is similar to triangle CED and AB is parallel to ED.

From the given figure, AB=7 miles, DC=16 ft, EC=12 ft and DE=21 ft.

Here, in figure,

∠A ≅ ∠E  (Alternate interior angles)

∠B ≅ ∠D  (Alternate interior angles)

∠ACB ≅ ∠DCE  (Vertically opposite angles are congruent)

Therefore, option D is the correct answer.

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The conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved  without the l'hopital's rule,

The limit expression is given as:

[tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex]

The limit of the expression cannot be solved without l'hopital's rule, because a direct substitution of ∞ for x would result in the following expression ∞/∞

i.e.

[tex]\lim_{x \to \infty} \frac{6 (2^{\infty}) - 1}{5(\infty)^2+ 10} = \frac{\infty}{\infty}[/tex]

So, the best way is to apply the l'hopital's rule.

This is done as follows:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}[/tex]

When the numerator and the denominator are differentiated, we have:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln(2)\cdot 2^{x + 1}}{10x}[/tex]

Further, differentiate

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{x + 1}}{10}[/tex]

Now, we can substitute [tex]\infty[/tex] for x

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{\infty + 1}}{10}[/tex]

Evaluate the numerator

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{\infty}{10}[/tex]

Evaluate the quotient

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty[/tex]

Hence, the conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved  without the l'hopital's rule

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Answer:

(B) 3

Step-by-step explanation:

Remember that a parallel lines always have the same slope!

Answer:

d = 2* sqrt(a^2 + b^2)

Step-by-step explanation:

Interesting question. You should begin by noting that 0 is not the answer although it looks like it should be.

P = (a,b)

Q= (-a,-b)

x1 = a

x2 = - a

y1 = b

y2 = - b

d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

d = sqrt( (-a - a)^2 + (-b - b)^2  )

d = sqrt ( -2a)^2 + - (2b)^2 )

d = sqrt(4a^2 + 4b^3)

d = 2* sqrt(a^2 + b^2)

Answer:

2c+5

Step-by-step explanation:

Answer:

7c

Step-by-step explanation:

You do PEMDAS.

6-3c is 3c.

so itd be 8c + 2(3c) - 7

then id multiply 3c with 2 so its be6c.

then id add 6c with 8c, and its be 14c. then i subtract it with 7 and get 7c.

Answer:

A. Yes

Step-by-step explanation:

it is always yes because no os negative

Answer

a

Step-by-step explanation:

it does represent a function

Answer:

n-32

Step-by-step explanation:

edmentum

Answer I think the answer is 9 if you round off to the nearest ones,in this case you are rounding off to 9 which will still be 9 because 4 is less than 5.

I hope this helps

Answer:

-1

Step-by-step explanation:

im pretty sure its right

sry if it not good luck!!

Answer:

√122

Step-by-step explanation:

To find the distance/length between two points

Use this formula: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]\sqrt{(1 - 2)^2 + (3 + 8)^2}[/tex]

[tex]\sqrt{(-1)^2 + (11)^2}[/tex]

[tex]\sqrt{1 + 121}[/tex]

[tex]\sqrt{122}[/tex]

Answer:

0.92

Step-by-step explanation:

cosine = adjacent/ hypotenuse

cosine of t = 12/ 13

cos t= 0.92308

Answer:

The horizontal distance of the ball from Noli when it reached maximum height is approximately 4.1 feet

Step-by-step explanation:

The horizontal distance from the hoop at which Noli threw the ball, y₀ = 7 feet

The height of the hoop = 10 feet

The height from which the ball was thrown = 6 feet

The height to which the ball is thrown = 2 × The initial horizontal distance from the hoop

∴ The height to which the ball is thrown, [tex]y_{max}[/tex] = 2 × 7 feet = 14 feet

The coordinates of points on the path of the ball are;

(0, 6), (7, 10), (x, 14)

The projectile in vertex form is y = a·(x - h)² + k

Where;

(h, k) = The x, and y-coordinate of the maximum height

The y-coordinate of the maximum height reached = k = 14 feet

The x-coordinate of the maximum height = h = The horizontal distance of the ball from Noli when it reached maximum height

At y = 6, x = 0, therefore, we get;

6 = a·(0 - h)² + 14 = a·h² + 14

6 = a·h² + 14

a = -8/h²

At y = 10, x = 7, we get;

10 = a·(7 - h)² + 14 = (-8/h²)·(7 - h)² + 14

10·h² = -8·(7 - h)² + 14·h²

-4·h² =  -8·(7 - h)²

4·h² - 8·(7 - h)² = 0

-4·h² + 112·h - 392 = 0

h = (-112 ± √(112² - 4 × (-4) × (-392)))/(2 × -4)

h ≈ 4.1, or h ≈ 23.9

We reject the value, h ≈ 23.9 feet given that the distance between the where the Noli threw the ball and the hoop = 7 feet

Therefore, the horizontal distance of the ball from Noli at which the ball reached its maximum height, h ≈ 4.1 feet

The required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

The formula for calculating the volume of the conical lid's is expressed as

[tex]V = \frac{1}{3} \pi r^2h[/tex] where:

r is the radius

h is the height

v is the volume

Given the following

r = x

If the conical lid’s height is 2 centimeters less than the radius, x, then;

h = x - 2

V = 25π cm³

Substitute the given values into the formula as shown:

[tex]25 \pi = \frac{1}{3} \pi x^2 (x-2)\\3(25) = x^2(x-2)\\Expand\\75=x^3-2x^2\\Swap\\x^3-2x^2 = 75\\Equate \ to \ zero\\x^3-2x^2 - 75 = 0[/tex]

Hence the required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

Answer:

y = -2x + 5

[tex]\frac{risex}{run} = slope =[/tex]Δy/Δx = -8/4 = -2

Step-by-step explanation:

Answer:

(y/7)x(4+9)

Step-by-step explanation:

statement one y/7

statement two 4+9

(y/7)x(4+7)

Answer:

I believe the answer would be 48.6 milliliters

Step-by-step explanation:

54 * 0.9 = 48.6

Trả lời:

86 và 91

Giải thích từng bước:

Cho hai số là x và y. Nếu tổng của chúng là 177, thì;

x + y = 177 ... 1

Nếu 17 bị trừ đi số đầu tiên, nó được biểu thị là x - 17

Nếu 25 được thêm vào số thứ hai l, nó được biểu thị bằng y + 25

Nếu số thứ nhất bây giờ bằng 2/3 số thứ hai, thì:

x-17 = 2/3 (y + 25) .... 2

Từ 1, x = 177-y ... 3

Thay thế 3 thành 2

177-y-17 = 2/3 (y + 25)

160-y = 2/3 (y + 25)

3 (160-y) = 2 (y + 25)

480-3y = 2y + 50

-3y-2y = 50-480

-5y = -430

y = 430/5

y = 86

Vì x = 177-y

x = 177-86

x = 91

Do đó hai số là 86 và 91

Answer:

56

Step-by-step explanation:

Answer:

56 hours

Step-by-step explanation:

I divided 384 dollars by 3w hours and then was Sue made 12 an hour. Then I tried mukyiplong different times until I discovered 12×56=672. So, 56 hours

Answer:

D

Step-by-step explanation:

Doubling the height will guarantee that the volume gets twice since V=(1/3)*B*h

If Bob wants to create a pyramid of volume 28 then he needs to double the height of the pyramid.

Design or construction with a base that is a polygon and sides that are three or more triangles that come together at the top.

A pyramid is a 3D shape where 3 triangle comes and meet in such a way that the base side creates a triangle.

The volume of a pyramid is given by

Volume = (1/3)base²×height.

Let say

Base width is = w

Height is = h

Volume V = w²h/3

Given

14 = w²h/3

For volume to be 28

28 = w²(2h)/3

So it is clear that he needs to double the height.

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Answer:

3.465 %

Step-by-step explanation:

10000 = 5000 [tex]e^{20r}[/tex]

2= [tex]e^{20r}[/tex]

ln(2) = 20r ln(e)

r = ln(2)/20

r = 0.03465

Answer:

∠ T = 82°

Step-by-step explanation:

In a Isosceles trapezoid, any lower base angle is supplementary to any upper base angle , so

∠ T + ∠ P = 180°

∠ T + 98° = 180° ( subtract 98° from both sides )

∠ T = 82°

Answer:

It's rational because it's not a decimal numbet

Step-by-step explanation:

First, a half plane can be defined as one side of a line, e.g. x < y-3.

1: True. A solution to two half planes is where the two half planes intersect. If they never intersect, then there literally cannot be a solution.

2: False. Take, for example, y=x and y=x+1. These two lines are parallel because in the equation y=mx+b, m represents the slope, and in these two lines, x is multiplied by 1, so both lines have the same slope and are therefore parallel. Then, take two boundary planes -- y > x and y>x+1. If we graph this out (see picture), the planes clearly intersect when y>x+1. The solution is where the planes intersect, so there is a solution area

Answer:

B

Step-by-step explanation:

2 units to the right -> -2 in the brackets next to x

4 units down -> -4 as a constant at the end of the equation

Answer:

Step-by-step explanation:

draw a parallel line to x at a distance of 23 cutting the quadrilateral in two points.

A right angle is formrd at the bottom.

Hypotenuse=59

one side=45-23=22

x= other side=√(59²-22²)=√(59-22)(59+22)=√((37)(81))=9√(37)≈54.74

Answer:

These are the entervals of the people who are atleast adults and are mature enough to take the surevy seriosly and answer correctly

Step-by-step explanation: