[
1
Solve the equation.
y + 3 = y + 9
f
O y= 1
O y = 3
O y = 6
O y = 9

Answer:

(-7.5, 3.5)

Step-by-step explanation:

\(midpoint \: = ( \frac{x1 + x2}{2} \: , \: \frac{y1 + y2}{2} )\)

\( = ( \frac{ ( - 5) + ( - 10)}{2} , \frac{(5) + (2)}{2} )\)

\( = ( \frac{ - 15}{2} , \frac{7}{2} )\)

\( = ( - 7.5,3.5)\)

Answer:

x = 55° (nearest degree)

Step-by-step explanation:

Trig ratios:

\(sin(\theta)=\dfrac{O}{H} \ \ \ cos(\theta)=\dfrac{A}{H} \ \ \ tan(\theta)=\dfrac{O}{A} \ \ \\)

where \(\theta\) is the angle, O is the side opposite the angle, A is the side adjacent to the angle, and H is the hypotenuse of a right triangle

Given:

\(\implies cos(x)=\dfrac{3.3}{5.7}\)

\(\implies x=\arccos \dfrac{3.3}{5.7}=54.623459...\)

⇒ x = 55° (nearest degree)

Answer:

54.6° OR 55° rounded up.

Step-by-step explanation:

So it is a fact that 3.3 is adjacent to x. And 5.7 is the hypotenuse.

Now, let's think of SOHCAHTOA: *Always remember that*

SOH: Sin = Opp/Hyp

CAH: Cos = Adj/Hyp

TOA: Tan = Opp/Adj

We will be using CAH since we have the adjacent and the hypotenuse.

Now, you need to plug in the numbers to the correct placement, in this case, it will look like this:

Cos(x) = 3.3/5.7

*If I were you, I'd use a Cosine calculator online or just your handy-dandy standard calculator because you can't just plug in 3.3/5.7 like that and expect to get the answer.*

*In order to find the cosine on a regular calculator, you must press the inverse button, followed by the cos button. Or just use the "arccos" button if it's on there*

REMEMBER SOHCAHTOA FOR THE FUTURE

Answer:

y=x-12x (times -12x or -12x)

Step-by-step explanation:

you can notice that if you do -1 x -12 you get 12

0 x -12 is 0

1 x -12 is 12 and so on

Answer:

4th one

Step-by-step explanation:

18/6=3      3 units on the y-axis / vertical

That's the only one with (-4,-2)

Answer:

Irrational number

Step-by-step explanation:

It's an Irrational number

Answer:

-0.5

Step-by-step explanation:

Answer:

-0.5

Step-by-step explanation:

I think this is the answer again im very sorry if it isnt

The perimeter of DREPFQ is 1

In an equilateral triangle, the intersection is the centroid

From the information given, we have that;

AB =√3

Then, we can say that;

AG = BG = CG = √3/3

Also, we have that D, E, and F are the midpoints of the sides of triangle Then, DE = EF = FD = √3/2.

AP = BP = CP = √3/6.

To find the perimeter of DREPFQ, we need to add up the lengths of the line segments DQ, QE, ER, RF, FP, and PD.

The perimeter of DREPFQ is √3/6 × √3/2)

Multiply the value, we get;

√3× √3/ 6 × 2

Then, we get;

3/18

divide the values, we have;

= 0.167

Multiply this by six sides;

= 1

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The complete question:

G is the centroid of equilateral Triangle ABC. D,E, and F are midpointsof the sides as shown. P,Q, and R are the midpoints of line AG,line BG and line CG, respectively. If AB= sqrt 3, what is the perimeter of DREPFQ

Answer:

1)110m^2

2)1.75m

3)96.25m^2

Step-by-step explanation:

Rate of painting= The cost to paint it /

inner curved surface area of the vessel

20m^2=(Rs 2200 /inner curved surface area of the vessel)

If we make inner curved surface area of the vessel subject of the formula,

inner curved surface area of the vessel= =(Rs 2200/20)

= 110m^2

2)cost surface area of a cylinder can be calculated using expression below

(2πrh,) then the values was calculated in question 1 as 110m^2

Then from (2πrh=110) we can make "r" subject of the formula

r= 110/(2πh). h=10m deep

r=110/(2×3.14×10)

r= 1.75m

3)(iii)capacity of the vessel (in litres

The capacity of the vessel can be regarded as the volume which equals to πr^2h

From question 2 r=1.75m, and h=10m

Then

πr^2h= 3.142×(1.75)^2 ×10

=96.25m^2

Hence the capacity is 96.25m^2

Answer:

x intercept=12,0

y intercept= 0,2700

Step-by-step explanation:

It takes the second marathoner 4 hours and 40 minutes to complete the marathon.

Let's assume the distance of the marathon is "d" miles.

The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:

speed = distance / time = d / 4

The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:

speed = 4(d / 4) = d

For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:

d / 2 = (3/4)(d / 4)(t)

Simplifying this equation, we get:

t = (2/3) hours

So the total time it takes the second marathoner to finish the race is:

4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.

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Answer:

the answer is 0.55

density=mass/volume

density=396/720(8*1*90)

Answer:

The number is 8

Step-by-step explanation:

Lets say the number is x

1: Create equation

x+4=12

2: Subtract 4 from both sides

x+4-4=12-4

x+0=8

x=8

The number is 8

Answer:

x=4

Step-by-step explanation:

The y axis is a line where the value of x does not change ( x=0)

It is a vertical line

The only line where the value of x does not change is x=4

It is a vertical line at x=4

1177.5 cubic cm is the volume of the cylinder.

The formula to calculate the volume of a cylinder is V = πr²h, where V represents the volume, r is the radius of the base, and h is the height of the cylinder.

In this case, the radius (r) is 5 cm and the height (h) is 15 cm. Let's calculate the volume:

V = π * (5 cm)² * 15 cm

V ≈ 3.14159 * 25 cm² * 15 cm

V ≈ 1177.5 cm³

Therefore, the volume of the cylinder is approximately 1177.5 cubic cm (rounded to the nearest tenths place).

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Answer:

210 gallons

Step-by-step explanation:

120 x 1 = 120

120 / 4 = 30 x 3 = 90

120 + 90 = 210

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer: I cant see the problem

Step-by-step explanation:

Answer:

Where is the question?

Step-by-step explanation:

Answer:

x=50

Step-by-step explanation:

If 2*x=100

Then x is :

x=100:2

x=50

Step-by-step explanation:

2x=100

x=100/2

x=50.

keep learning sis !

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

16

Step-by-step explanation:

the quadratic equation –3 = –x2 + 2x can be changed into :

x²-2x-3= 0

a=1, b= -2 , and c = -3

so, the discriminant = (-2)²-4(1)(-3)

= 4 + 12 = 16

so, she has three boards, 36, 39 and 42 inches, hmmm but she wants the length or longer side to be 3.25 ft, hmmm 36 ÷ 12 is just 3, so that won't do, 42 ÷ 12 is 3.5 ft, nope not that one, 39 ÷ 12 is 3.25, well, that's our board.

so the width has to be smaller than the length, and it has to be a full board, so since we used the 39 incher already, smaller than 39 is 36, so we'll use the 36 incher for the width, that is, the 3 feet one.

From the 3rd board, Mia is going to have to make it match with the 36 incher, that means she needs to saw it off by 6 inches, 42 - 6 = 36, and 6 inches is just 6 ÷ 12 = 0.5 feet.

Check the picture below.

the answer for the following question is 7

Answer:

A. $296.06

Step-by-step explanation:

$399-30%= $399*0.7= $279.30

$279.30+6%= $279.30*1.06= $296.06

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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mode is 4 and the median is also 4

mode is the number that appears the most which is 4 and median is the number that is in the middle when you line up all the numbers in order  (0,2,2,3,3,4,4,4,4,5,5,5,6,6,10)

The probability of a) is (80 * 79 * 78 * ... * 2 * 1) / (40^80), b) is  (C(80, 3) * C(77, 3)) / (40^80) and c) is  (number of ways for case 1 + number of ways for case 2 + ... + number of ways for case n) / (40^80).

Let us know how we arrived at the answers:

a) To find the probability that both the first and second boxes are empty, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes.

First, let's calculate the number of ways the first box can be empty. Out of 80 balls, there are 80 options to choose from for the first ball, and 79 options for the second ball, and so on. This gives us 80 * 79 * 78 * ... * 2 * 1 ways to arrange the balls in the first box. Similarly, the second box can be empty in the same number of ways.

Since each ball has 40 options for which box it goes into, there are 40^80 ways to distribute the balls into the boxes.

Therefore, the probability that both the first and second boxes are empty is (80 * 79 * 78 * ... * 2 * 1) / (40^80).

b) To find the probability that both the first and second boxes have 3 balls each, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes.

The number of ways to choose 3 balls out of 80 is given by the combination formula: C(80, 3) = (80 * 79 * 78) / (3 * 2 * 1).

Once we have selected the 3 balls for the first box, we need to choose 3 balls out of the remaining 77 balls for the second box. Again, using the combination formula, we have C(77, 3) = (77 * 76 * 75) / (3 * 2 * 1).

Since each ball has 40 options for which box it goes into, there are 40^80 ways to distribute the balls into the boxes.

Therefore, the probability that both the first and second boxes have 3 balls each is (C(80, 3) * C(77, 3)) / (40^80).

c) To find the probability that the first box has more balls than the second box, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes.

First, let's consider the cases where the first box has more balls than the second box. We can have 1 ball in the second box and any number of balls from 2 to 80 in the first box, 2 balls in the second box and any number of balls from 3 to 80 in the first box, and so on.

For each case, we need to calculate the number of ways to arrange the balls in the first and second boxes.

The total number of ways to distribute the balls into the boxes is 40^80.

Therefore, the probability that the first box has more balls than the second box is the sum of the probabilities of each case: (number of ways for case 1 + number of ways for case 2 + ... + number of ways for case n) / (40^80).

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Your answer is False

Answer: \(x=10\)

Step-by-step explanation:

\(3(4x-12)=84\\\\4x-12=28\\\\4x=40\\\\x=10\)