- Solve the system of equations by graphing.
y = x² - 3
x + y = -1

Using the slope concept, the distance from point AA to point BB ≅ 360 feet.

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

We can get, the vertical change is of 144 feet.

At point A, the angle is of 9º, while the horizontal position is of [tex]x_{A}[/tex] ,

Then, we can write,

tan 9º =  [tex]\frac{144}{x_{A} }[/tex]

[tex]x_{A}[/tex] = 144/tan 9º

Hence, tan 9º = 0.15

[tex]x_{A} =[/tex] 144/0.15

[tex]x_{A}[/tex] = 960

At point A, the angle is of 14º, while the horizontal position is of [tex]x_{B}[/tex] ,

Then, we can write,

[tex]x_{B}[/tex] = 144/tan 14º

Hence, tan 14º = 0.24

[tex]x_{B}[/tex] = 144/0.24

[tex]x_{B}[/tex] = 600

So, the distance in feet is of:

d = [tex]x_{A} -x_{B}[/tex]

d = 960 - 600

d = 360

d ≅ 360

Therefore,

A boat is heading towards a lighthouse, then the distance from point AA to point BB ≅ 360 feet.

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Answer:

y = (3/2)x + 3

Step-by-step explanation:

Point 1: (0, 3) Point: (2, 6)

            (x₁, y₁)          (x₂, y₂)

        y₂ - y₁        6 - 3            3

m = ------------ = ------------ = --------

        x₂ - x₁         2 - 0           2

y - y₁ = m(x - x₁)

y - 3 = (3/2)(x - 0)

y - 3 = (3/2)x

  +3               +3

------------------------

y = (3/2)x + 3

I hope this helps!

We must know the following exponent rules to help us solve this question:

[tex]3^p=\dfrac{\sqrt[3]{9}}{3}[/tex]

⇒ Rewrite [tex]\sqrt[3]{9}[/tex] as [tex]9^\frac{1}{3}[/tex]:

[tex]3^p=\dfrac{(3^2)^\frac{1}{3}}{3}[/tex]

⇒ Multiply:

[tex]3^p=\dfrac{3^\frac{2}{3}}{3}[/tex]

⇒ Subtract:

[tex]3^p=3^{\frac{2}{3}-1}[/tex]

[tex]p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}[/tex]

[tex]p=-\dfrac{1}{3}[/tex]

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{13}~~ = ~~\cfrac{11}{x}\implies x^2=(13)(11)\implies x^2=143\implies x=\sqrt{143}[/tex]

the answer is T becouse T is the time which is what you get when distance is divided by 80 mph

Answer:

gradient is 1/2  =  0.5

Step-by-step explanation:

y= 1/2 x−3

Swap sides so that all variable terms are on the left hand side.

1/2 x−3=y

Add 3 to both sides.

1/2 x=y+3

Multiply both sides by 2.

1/2 x = 1/2 y+3

​

Dividing by  1/2 undoes the multiplication by  1/2

x= 1/2 y+3

​

Divide y+3 by  1/2  by multiplying y+3 by the reciprocal of  1/2

​

.

x=2y+6

Notice that the slope of the line is equal to the speed

hence, the speed = 5 miles / hour

Answer:

-31

Step-by-step explanation:

[tex]-38-16-(-23) \\ \\ =-38-16+23 \\ \\ =-54+23 \\ \\ =-31[/tex]

Answer:

y = 4x + - 9

Step-by-step explanation:

(3, 3), (4, 7)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁        7 - 3           4

m = ------------ = ------------ = ------- = 4

        x₂ - x₁         4 - 3           1

y - y₁ = m(x - x₁)

y - 3 = 4(x - 3)

y - 3 = 4x - 12

  +3          +3

----------------------

y = 4x - 9

I hope this helps!

Answer: Eiko

Step-by-step explanation:

Eiko has the shortest time.

Answer:the answer is b

Step-by-step explanation:

The exponent that is understood on the base x in the given expression is; 1

The exponent of a number tells us how many times to use the number in a multiplication. Exponents are also called Powers or Indices. For example in the exponent form ab^(x), we can say that;

The base is a and its' exponent is 1.

Applying the above to our question gives us;

If the exponent form is xy^3, then we can say that;

The base is x.

We can see that there is no exponent attached to x and as such we will use 1 as 1 will still give us the value of x.

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Answer:

Not 100% sure what it's asking but if it's asking what number she used to estimate the 240, she used 100 because it's one-off 99. The actual number would be 237.6

Step-by-step explanation:

THE SUM OF THE INNER ANGLES IS 180°

[tex](x - 7) + (2x - 8) + 90 = 180 \\ x - 7 + 2x - 8 + 90 = 180 \\ x + 2x = 180 + 7 + 8 - 90 \\ 3x = 105 \\ \frac{3x}{3} = \frac{105}{3} \\ x = 35[/tex]

OPTION C IS THE RIGHT ANSWER.

Answer:

He will only afford to rent the car for 4 days, he will spend 160 dolars to just have the car for 4 days. Since he plan to drive 125 miles, the cost for the miles will be 10 dolars. So if we add 160 (4 days with the car) plus 10 (for the miles) it would give 170.

Step-by-step explanation:

Equivalent equations (acceptable moves)

(1)  

4(x+3)=32

       x+3 = 8

(2)

[tex]\frac{(9x+4)}{2} =5\\\\9x+4=10[/tex]

(3)

x- 7+ 3x=25

4x-7=25

Not equivalent (unacceptable moves)

(1)

2(x+5) = 10

2x+5 =  5( 20 is wrong)

(2)

2x+4=22

2x= 22-4= 18 (26 is wrong)

(3)

[tex]\frac{(6x-1)}{3} =27\\\\6x-1=81[/tex] (9 is wrong)

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Rewrite 50% as 1/2

We need a fraction that is equal to 1/2 of 1/6.
-> That fraction equals to 1/2 x 1/6 = 1/12 (or 1/6 : 2)

Answer:

1/12

Step-by-step explanation:

1/6*100/50=1/12.

The probability that a randomly chosen applicant has over 5 years of experience is 0.2768.

It should be noted that probability simply has to do with the likelihood that an event will happen.

From the information, out of 457 applicants for a job, 271 have over 5 years of experience and 75 have over 5 years of experience.

Therefore, the probability that a randomly chosen applicant has over 5 years of experience will be:

= Number of graduate over 5 years / Number of people over 5 years experience

= 75 / 271

= 0.2768

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Answer:

369,962

Step-by-step explanation:

If the rounding digit is 0, 1, 2, 3, or 4, drop all the digits to the right of it

If the rounding digit is 5, 6, 7, 8, or 9, add one to the rounding digit and drop all digits to the right of it

The probability that none of these vehicles requires warranty service is 0.2824

The probability exactly one of these vehicles requires warranty service is

0.3766

The probability that exactly two of these vehicles require warranty service is 0.2301

The mean of this probability distribution is 1.2

Given, n=12, and the probability is 0.1, we use the binomial distribution formula to solve the probabilities:

[tex]P(X=0)=C^{n}_{x} } P^{x} Q^{n-x}[/tex]

The probability that none of these vehicles requires warranty service

[tex]P(X=0)=C^{12}_{0} } (0.1)^{0} (0.9)^{(12-0)}[/tex]

               =0.2824

The probability exactly one of these vehicles requires warranty service

[tex]P(X=1)=C^{12}_{1} } (0.1)^{1} (0.9)^{(12-1)}[/tex]

                =0.3766

The probability that exactly two of these vehicles require warranty service.

[tex]P(X=2)=C^{12}_{2} } (0.1)^{2} (0.9)^{(12-2)}[/tex]

               =0.2301

Compute the mean of this probability distribution

Mean = n*P, where n = 12, P=0.1

          =12*0.1

          =1.2

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[tex]5x - 2y = 4 \\ 5x = 4 + 2y \\ \frac{5x}{5} = \frac{4 + 2y}{5} \\ x = \frac{4 + 2y}{5} ......(3)equation[/tex]

NOTE I AM SOLVING BY SUBSTITUTION

[tex]8( \frac{4 + 2y}{5} ) + 5y = - 10 \\ \frac{32 + 16y}{5 } + 5 y = - 10 \\ \frac{32 + 16y}{5} (5) + 5y(5) = - 10(5) \\ 32 + 16y + 25y = - 50 \\ 41y = - 50 - 32 \\ \\ \\ \\ 41y = - 82 \\ \frac{ - 41y}{41} = \frac{ - 82}{41} \\ y = - 2[/tex]

[tex]x = \frac{4 + 2( - 2)}{5} \\ x = \frac{4 - 4}{5} \\ x = \frac{0}{5} \\ x = 0[/tex]

ATTACHED IS THE SOLUTION

Answer: (0,-2)

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{5x-2y=4\ \ \ \ \ (1)} \atop {8x+5y=-10\ \ (2)}} \right.[/tex]

Multiply equation (1) by 5, and equation (2) by 2:

[tex]\displaystyle\\\left \{ {{25x-10y=20\ \ \ \ (3)} \atop {16x+10y=-20\ \ (4)}} \right.[/tex]

Add equations (3) and (4):

[tex]41x=0[/tex]

Divide both parts of the equation by 41:

[tex]x=0[/tex]

Let's substitute the value of x into equation (2):

[tex]8(0)+5y=-10\\0+5y=-10\\5y=-10[/tex]

Divide both parts of the equation by 5:

[tex]y=-2[/tex]

Thus, (0,-2)

The probability of picking an odd number ball in fraction form is; 6/11

We are told that a bag contains eleven balls labelled 1 through 11. These numbers are;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. This is a total of 11 numbers.

The even numbers are a total of 5 while the odd numbers are a total of 6.

Now, the probability of selecting an odd number will be;

P(selecting odd number) = Number of possible odd numbers/Number of Total Numbers

Plugging in the relevant numbers gives;

P(selecting odd number) =  6/11

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Answer:

8,377.58 [tex]mi^{3}[/tex]

Step-by-step explanation:

To solve for the volume of a right circular cone like the one in the picture, you use [tex]\pi[/tex][tex]r^{2}[/tex][tex]\frac{h}{3}[/tex].

Plug in the radius and height to get [tex]\pi[/tex][tex]20^{2}[/tex][tex]\frac{20}{3}[/tex].

Then solve (and round to the nearest hundredth) and you should get 8,377.58.

Answer:

3/8 barrels / minute.

Step-by-step explanation:

Rate = fraction of barrel filled / time

        = 1/4 / 2/3

        = 1/4 * 3/2

        = 3/8.

Answer:

[tex]\frac{h^6}{h^8}[/tex]

Step-by-step explanation:

1. For now, let's leave the [tex]g^{-6}[/tex] to the side and just worry about the [tex]\frac{h^8}{h^2}[/tex].

2. When you apply the exponent rule you should have learned in class, we know that when you divide two bases with exponents, the exponents subtract. So, you can subtract 8 - 2, and then the greater digit's place in the fraction stays. So, since [tex]h^8\\[/tex] is the greater number (and it's in the numerator), you put the [tex]h^6[/tex] in the numerator as well.

Answer:

x= -11

It only has one solution.

Step-by-step explanation: