The length of each side of an equilateral triangle having an area of 9√3 cm² is

Answer:

50

Step-by-step explanation:

x + 30 = 180 - 2x   [vertically opposite angles]

x = 180 - 30 - 2x

x = 150 - 2x

x + 2x = 150

3x = 150

x = 150/3

x = 50

A general linear equation is given by:

[tex]y = a*x + b[/tex]

Where a is the slope and b is the y-intercept.

Here we will find that the linear equation that represents the situation is

[tex]y = 0.033*x + 1.269[/tex]

And we can expect that the median salary in 2048 is $2.853 million

If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we know that:

in 2007 (x = 7) the median player salary was y = $1.5 million

in 2013 (x = 13) the median player salary was y = $1.7 million.

Then we have two points that we can write as:

(7, 1.5)

(13, 1.7)

Note that the y-value is in millions.

Then the slope of the linear equation will be:

[tex]a = \frac{1.7 - 1.5}{13 - 7} = 0.033[/tex]

So the linear equation is something like:

[tex]y = 0.033*x + b[/tex]

To find the value of b, remember the point (7, 1.5), this means that when we have x = 7, we also have y = 1.5, then we can replace these in the above equation:

[tex]1.5 = 0.033*7 + b\\\\1.5 - 0.033*7 = b = 1.269[/tex]

Then the linear equation is:

[tex]y = 0.033*x + 1.269[/tex]

b) Now we want to predict the median salary in 2048. For 2048 the x-value is x = 48

So we just need to evaluate this in the linear equation:

[tex]y = 0.033*48 + 1.269 = 2.853[/tex]

Then the median salary in 2048 will be $2.853 million

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Step-by-step explanation:

if I understand the typed information here, we have

(-4 + 8x) + 3 > -4

so, I am looking at that :

-4 + 8x + 3 > -4

let's first add 4 on both sides

8x + 3 > 0

then subtract -3 on both sides

8x > -3

and finally divide both sides by 8

x > -3/8

since we never multiplied or divided by a negative number, the inequality sign stays the same.

so, this inequality is true for all x > -3/8

Answer:

im pretty sure your answer is correct :)

Step-by-step explanation:

Answer:

line [tex]l[/tex]

The length of JM is 9.

Step-by-step explanation:

Since JM ≅ MK then we can form the following:

[tex]JM=MK\\JM=3x+15\\MK=8x+25\\\\3x+15=8x+25\\15=5x+25\\-10=5x\\-2=x\\x=-2\\\\JM=3x+15\\JM=3(-2)+15\\JM=-6+15\\JM=9[/tex]

x=5

Step-by-step explanation:

x-2=3(x-4)

x-2=3x-12

12-2=3x-x

10=2x

x=10/2

x=5

Answer:

x = 5

Step-by-step explanation:

x - 2 = 3(x - 4)

x - 2 = 3x - 12

-2x - 2 = -12

-2x = -10

x = 5

Answer:

Hope it helped

Step-by-step explanation:

The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

An inverse function or an anti function is defined as a function, which can reverse into another function.

Now the given quadtratic function is,

f(x) = x² + 2

Now vertex of the given quadratic function is (0,2)

Thus the range of the function is [2,∞)

If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.

Now the inverse function is given as,

y = x² + 2

Upon interchanging x and y, we get:

x = y² + 2

⇒ y² = x - 2

or, y = ±[tex]\sqrt{x-2}[/tex]

Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

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Answer:

Step-by-step explanation:

The probabilities for each point:

Required probability:

Correct choice is D

Your answer is in the attachment .

Note: I have only done upto q.n d because you haven't clearly uploaded question of no. e. stay blessed !!!!!!

Answer:

C

Step-by-step explanation:

y and 67 are alternate exterior angles and are congruent , then

y = 67° → C

Answer:

Step-by-step explanation:

lkj

Answer:

Step-by-step explanation:

Answer:

[tex] \sqrt{24} = 4.9[/tex]

[tex] \sqrt{102} = 10.1[/tex]

positive integers = x

4.9 < x < 10.1

x = 5, 6, 7, 8, 9, 10

sum = 5 + 6 + 7 + 8 + 9 + 10

= 45

Answer:

705.92

Step-by-step explanation:

hope it's help

#MASTER GROUP

# FIRST MASTER

# PHILIPPINES

Answer:

There’s not

Step-by-step explanation:

It’s 618

Answer:

[tex]commutative \: property \: of \: addition \\ thank \: you[/tex]

Answer:

x = -7

Step-by-step explanation:

Please view the detailed answer in the image attached

Answer:

[tex]2x - 9 = 5x + 12 \\ - 3x = 21 \\ x = - 7[/tex]

Step-by-step explanation:

x = -7

Answer:

[tex]f'(x)=1+\ln x[/tex]

Step-by-step explanation:

[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

Therefore, we have:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]

Simplify:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]

The derivative is:

[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]

[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]

[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]

Answer:

12 miles in a day.

Step-by-step explanation:

Variable x = number of miles

Company A: 120 + 0.20x

Company B: 60 + 0.40x

Set up an equation:

120 + 0.20x = 60 + 0.40x

60 + 0.20x = 0.40x

60 = 0.20x

12 = x

Answer:

Option 3

Step-by-step explanation:

If he burned off 400 calories from 1500 consumed calories, he has 1100 consumed calories.  1900 - 1100 = 800 calories left to consume.

While option 2 also says no, it's not the right reason.  

The calories left to consume for the day is 800 calories.

No, 1,100 will cause him to exceed 1,900.

Given,

Jace has consumed 1,500 calories so far today.

He has also burned off 400 calories at the gym.

He would like to keep his daily calorie total to 1,900 calories per day.

We need to find how many calories he has left to consume for the day.

And see which option is the best choice.

We have,

Calories consumed in a day = 1500

Burned calories = 400

Calories to keep in a day = 1900

Find the Calories left

= 1500 - 400

= 1100

Find how many calories need to be consumed to keep 1900 calories.

= Calories needed to keep in a day - calories remaining after burned

= 1900 - 1100

= 800

We see that the calories left to consume is 800 calories.

So 1100 is not a viable solution. It will cause him to exceed 1,900.

Thus,

The calories left to consume for the day is 800 calories.

No, 1,100 will cause him to exceed 1,900.

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Answer:

4.43

Step-by-step explanation:

4 3/7

~Turn into an improper fraction

31/7

~Divide

4.42885714286...

~Round

4.43

Best of Luck!

The point of intersection of the line 2x+3y+2=0 with the curve 2xy = -1 will be (1/2, - 1) and (1/6, 1/3).

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The equation of lines are,

⇒ 2x + 3y + 2 = 0

⇒ 2xy = - 1

Now,

Since, The equation of lines are,

⇒ 2x + 3y + 2 = 0  ..(i)

⇒ 2xy = - 1   ..(ii)

From (ii);

⇒ 2xy = - 1

⇒ x = - 1/2y

Put above value in (i), we get;

⇒ 2 × - 1/2y + 3y + 2 = 0

⇒ - 1/y + 3y + 2 = 0

⇒ - 1 + 3y² + 2y = 0

⇒ 3y² + 2y - 1 = 0

⇒ 3y² + 3y - y - 1 = 0

⇒ 3y (y + 1) - 1 (y + 1) = 0

⇒ (3y - 1) (y + 1) = 0

⇒ y = 1/3

And, y = - 1

So, The value of x is,

⇒ x = - 1/2y

⇒ x = - 1/2 × - 1

⇒ x = 1/2

And, x = - 1/2 × 1/3

⇒ x = 1/6

Thus, The intersection point on the lines = (1/2, - 1) and (1/6, 1/3)

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Answer:

400

Step-by-step explanation:

[tex] {20}^{2} = 20 \times 20[/tex]

that is equal to 400

Answer: 400

Step by step explanation:

20*20= (2*2)*(10*10)= 4*100=400

Answer:

It’s 48 just do 8*6=48 I don’t know how I got that answer but Ik it’s right lol

Answer:

Step-by-step explanation:

1) 7/10 × 2/21

1/15

2) 9/16 × 10/21

90/336

15/56

3) 11/12 × 26/55

13/30

4) 2/6 × 18/12 × 2/3

72/216

1/3

5) ⅚ × 9/10

45/60

3/4

Answer:

x > 2

Step-by-step explanation:

Distribute and cross-simplify 1/2 with parenthesis

4x + x + 2 > 12

Solve left side

5x + 2 > 12

Subtract 2 from both sides

5x > 10

Divide both sides by 5

x > 2

Answer:

A

Step-by-step explanation:

-2x-4>8

-2x>12

-x>6

x<-6

Answer:

[tex]x < - 6[/tex] (first option)

Step-by-step explanation:

[tex] - 2x - 4 > 8[/tex]

[tex] - 2x > 8 + 4[/tex]

[tex] - 2x > 12[/tex]

[tex] = x < - 6[/tex]

Answer:

Ada is correct.

Step-by-step explanation:

Problems with Naman:

Naman is supposed to follow PEMDAS, which is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Division

Addition

Subtraction

~

The mistake: Naman moved +6 to the left and added it to the 2 located on the left side of the expression. You cannot do that, as it breaks the law of PEMDAS. On the other hand, Ada did the correct thing, which was to distribute 2 to all terms within the parenthesis (as one term in the parenthesis has a variable, and the other is a constant, meaning that they cannot be combined). This leads to Naman not doing the rest of the question correct.

Next, Ada correctly combined the two constants, which resulted in 0. 0 means nothing, therefore the placeholder is not needed. Therefore, 8x is the final answer.