What is an equation of the line that passes through the point (6,1)(6,1) and is parallel to the line x+3y=15

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:

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:

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:

Answer:

A) 2nd graph

Explanation:

The 1st graph shows a radical expression, where:

to find the inverse, replace f(x) with y, switch the x and the y, then solve for y. The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)

Answer: (6, -5)

Step-by-step explanation:

       The slope 2/3 means that there is a positive change of 2 in the y-value ( + 2) and a positive change in the x-value of 3 (+ 3) for every new point. To find another point on the line, we can add 2 to the y-value and 3 to the x-value.

    ➜ Slope is written as y over x

    ➜ Coordinate points are written as (x, y)

       (3, -7)

       (3 + 3, -7 + 2)

       (6, -5)

       We can also find a point on the line by graphing. See attached.

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]

[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 variables a and b have a possible value of 7 and 11

The given parameters are

GCF(a, b)• LCM (a, b) = 77

As a general rule, the product of two numbers equals the product of the greatest common factor and the least common multiple of the numbers

This implies that

a * b = GCF(a, b)• LCM (a, b)

So, we have

a * b = 77

Express 77 as 7 * 11

a * b = 7 * 11

By comparison, we have

a = 7 and b = 11

Hence, the possible values are a = 7 and b = 11

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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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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:

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!

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:

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

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.

Answer:the answer is b

Step-by-step explanation:

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.

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

hence, the speed = 5 miles / hour

Base on the given ratio of quantity of sugar to number of cakes, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar

Ratio refers to a number representing a comparison between two named things or quantities. The ratio of sugar and cake is the comparison between the quantity of sugar used to make cake.

Find the ratio of quantity of sugar to number of cakes

Quantity of sugar : Number of cakes

71.1 g : 9 cakes = x : 4 cakes

71.1 / 9 = x / 4

71.1 × 4 = 9 × x

284.4 = 9x

x = 284.4 / 9

x = 31.6g of sugar

In conclusion, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar

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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:

[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.

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]

∠K , ∠1 and ∠JKL  are the three names of the angle 1 indicated by red color in the figure given in the question.

We need to select three names of the angle 1 indicated by red color in the figure given in the question . We are provided with the following options ∠JLK , ∠K , ∠LJK , ∠1 , ∠JKL and ∠J .  

∠JLK is not similar to ∠1 .  ∠K and  ∠1  are same angle. ∠LJK is not similar to ∠1 . ∠JKL and  ∠1  are same angle.  ∠J and ∠1 are different angles. So, we can finally conclude that the three names of the angle 1 indicated by red color in the figure given in the question are ∠K , ∠1 and ∠JKL .

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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: Eiko

Step-by-step explanation:

Eiko has the shortest time.

We found the length of the other leg by using Pythagoras’ theorem y is equal to 21.0 centimeters when the length of one of its legs is 20.0 centimeters.

In this question we have to make an equation by using the right triangle's value which is given in the question,

by putting these values in the Pythagoras’ theorem.

As given, the hypotenuse of a right triangle = 29.0 centimeters.

The length of one of its leg = 20.0 centimeters

Now, by using Pythagoras’ theorem we will find the length of the other leg:

hypotenuse^2 = base^2 + perpendicular^2,

We put the value according as given in question:

29^2 = 20^2 + y^2

After finding the square of number of both side:

841 = 400 + y^2

Now we will rearrange this equation:

y^2 = 841 - 400  

y = 21 centimeters is the length of the other leg.

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

Answer:

x= -11

It only has one solution.

Step-by-step explanation: