A tangent line is a line that insersecta a circle at exactly two points.
true or false

Answer:

240

Step-by-step explanation:

Multiply everything together. 6*4*5 is 240.

Answer:

y = -1/3x -3

Step-by-step explanation:

-2x - 6y = 18

We want to solve for y since the slope intercept form is y =mx+b where m is the slope and b is the y intercept

Add 2x to each side

-2x-6y +2x = 2x+18

-6y = 2x+18

Divide each side by -6

-6y/-6 = 2x/-6 + 18/-6

y = -1/3x -3

This is in slope intercept form with the slope -1/3 and the y intercept -3

Answer:

[tex]y = - \frac{x }{ 3} - 3[/tex]

Step-by-step explanation:

-2x - y = 18

Add 2x to both sides.

-6y = 2x + 18

divide both sides by -6.

[tex]y = \frac{2x + 18}{ - 6} [/tex]

divide 2x + 18 by 6

[tex]y = - \frac{x }{ 3} - 3[/tex]

Answer: 13.7

Step-by-step explanation:

The total distance Carlo travelled form his house to Kelvin's house to the game store and back to his house is 13.7 km.

Using the distance formula, we can caulate the distance he rode from his house to Kelvin's house and then to the video game store.

Therefore,

d = √(y₂ - y₁)²+(x₂- x₁)²

Hence,

(0, 0)(2.5, 6)

Distance from his house to Kelvin's house = √(6- 0)²+(2.5 - 0)²

Distance from his house to Kelvin's house = √36 + 6.25 = 6.5 km

Therefore,

(2.5, 6)(2.5, 2)

Distance from Kelvin's house to game store =  √(2- 6)²+(2-5 - 2.5)²

Distance from Kelvin's house to game store = √16  = 4 km

Hence,

Total distance travelled = 6.5 + 4 + 3.2 = 13.7 km

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Start with y: [tex]y[/tex]

Subtract 4: [tex]y-4[/tex]

Multiply by 9: [tex]9(y-4)=9y-36[/tex]

Answer:

[tex]9(y - 4) \\ = 9y - 36[/tex]

Step-by-step explanation:

[tex]start \: \: \: \: \: \: \: \: \: \: = y \\ subtract \: = y - 4 \\ times \: \: 9 \: \: \: = 9(y - 4) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 9y - 36[/tex]

Answer: 12 cupcakes will get chocolate frosting

Step-by-step explanation: John started with 30 cupcakes and spresd mint icing on 1/5 of these. That means he did the following

Mint icing = 30 x 1/5

Mint icing = 6

That leaves him with a total of 30 minus 6 cupcakes which equals 24 cupcakes.

Next he spreads chocolate icing on half of the remaining, that is half of 24. That means he did the following;

Chocolate icing = 24 x 1/2

Chocolate icing = 12

Therefore 12 cupcakes will get chocolate frosting

Answer:

The diffrence written in simple expression form is 40/63

Step-by-step explanation:

To solve for the difference normally you have to subtract your own subscription from that of your friends,

Let's perform this operation step wise

Now your subscription is

(7w = 6)

w=6/7

Your friends own is

( 9w = 2)

w=2/9

So the difference in simple form is

6/7-2/9

The LCM is 63 I.E 9*7=63

=54-14/63

=40/63

Answer:

3 1/5 ft

Step-by-step explanation:

We can set up a proportion:

[tex]\frac{1}{2\frac{2}{7} } =\frac{1\frac{2}{5} }{x}[/tex] , where x is how long the pants are in real life

Cross multiply:

x = (2 2/7) * (1 2/5)

It's easier if we have improper fractions, so convert the mixed numbers into improper fractions:

2 2/7 = 16/7

1 2/5 = 7/5

Now, put these back in:

x = (16/7) * (7/5) = 16/5 = 3 1/5

Thus, in real life, the pants would be 3 1/5 ft long.

Hope this helps!

Answer:

3⅕ ft

Step-by-step explanation:

1 in --> 2 2/7 ft

2 2/7 = 16/7

1 2/5 in = 7/5 in

7/5 × 16/7 = 16/5 ft

3 1/5 ft

The Euclid's mug holds the most root beer.

Step-by-step explanation:

Euclid's mug :

Height = 8 inches

Radius = 3 inches

Volume = π(r x r) h

= (3.14) (9) 8

= 226.08 cubic inches

Aristotle's mug:

Height = 18 inches

Diameter = 4 inches

Radius = 2 inches

Volume = (1/3) π(r x r) h

= (1/3) (3.14) (4) 18

= 37.68 cubic inches

The Euclid's mug holds the most root beer.

Step-by-step explanation:

[tex]1+1=2 \\

2+2=4 \\

57-2+5=60 \\

7000+3+67+90=7160[/tex]

Answer:

7160

Step-by-step explanation:

1+1=2

2+2=4

5x7-2+5=5x7+3

7000+3+67+90+7160

Answer:

Step-by-step explanation:

For right triangles, we can use the Pythagorean theorem. This means that a2+b2 = c2. In this problem, a and b are the given side lengths of the triangle. This means that a=b=13. To solve this problem, we plug in 13 to the equation above and solve for c.  

132 + 132 = c2

169+169 = c2

338 = c2

square root(338) = c

c = 18.38

Answer:18.38

Step-by-step

13^2 +13^2=338

square root 338

=18.38

Answer:

0.0545454545455

Step-by-step explanation:

Answer:

Step-by-step explanation:

you would find the slope by doing the change in y over the change in x. in your case, the change in y is 11 and the change in x is -11.

Answer:

Slope formula is y2-y1 over x2-x1

Once you find the slope you are going to need to put it into point slope form which is y-y1=m(x-x1)

Step-by-step explanation:

9-(-2) divided by -3-8 is 11 over -11 which your slope is -1 m=-1

Then you use the point slope formula

y-(-2)=-1(x-8)

Then solve algebraically

Y+2=-1x+8

-2. -2

Y=-1x+6 , that is in slope-intercept form your m which is your slope is -1 and your b which is your y intercept is 6

So basically your answer is slope(m) which is -1.. hope this helps!!

Answer: Y-intercept: When the car doesn’t move...

Relative max or min: The most efficient...

Increasing or decreasing interval: As the car accelerates...

Step-by-step explanation:

The parameters are matched and shown below..

The [y] - intercept of a graph is the point where the graph cuts the [y] axis.

We have a curve that models the fuel efficiency of a certain car as a function of the car's speed.

The [y] - intercept of the graph would be at y = 0. This point represents the situation when the car does not have any fuel to move.

The increasing or decreasing value represents as car accelerates towards 55 Km/hr, it gets more efficient.

The relative maximum value represents that the most efficient the car can get is 20 Km/litre.

Therefore, the parameters are matched and shown above.

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Answer:

[tex]V(x) = 4x^3 - 54x^2 + 180x[/tex]  

Step-by-step explanation:

We are given the following in the question:

A rectangular piece of cardboard of side 15 inches by 12 inches is cut in such that a square is cut from each corner.

Let x be the side of this square cut. When it was folded to make the box.

The height of box =

[tex]x\text{ inches}[/tex]

The length becomes

[tex](15-2x)\text{ inches}[/tex]

The width becomes

[tex](12-2x)\text{ inches}[/tex]

Volume of box =

[tex]V =l\times w\times h[/tex]

Putting values, we get

[tex]V(x) = (15-2x)(12-2x)x\\V(x) = (180-30x-24x+4x^2)(x)\\V(x) = (4x^2 - 54x + 180)(x)\\V(x) = 4x^3 - 54x^2 + 180x[/tex]

is the required polynomial for volume of box formed.

Answer:

a = -1  b = -9   c = -20

x1 = [--9 +- (sq root -9^2 - 4 * -1 * -20)] / 2 * -1

x1 = 9 +sq root (81 - 80) / -2

x1 = [9 + 1 ] / -2

x1 = -5

x2 = 9 -sq root (81 - 80) / -2

x2 = 8 / -2

x2 = -4

Step-by-step explanation:

9514 1404 393

Answer:

  43.1

Step-by-step explanation:

The perimeter is the sum of the lengths of the two straight edges, each of which is 9 units long, and the circumference of the full circle of diameter 8 units. The circumference is pi times the diameter.

  P = 2(9) +8π = 18 +25.13

  P ≈ 43.1 . . . units

The perimeter of the combination of a rectangle and two semicircles is found by adding the straight sides of the rectangle and the circumference of the resulting full circle formed by the semicircles. In this case, it's 43.1 units.

To find the perimeter of the combined shape consisting of a rectangle and two semicircles, we need to consider the lengths of the straight parts as well as the circumference of the circles. The perimeter is the sum of the lengths of the straight sides of the rectangle, each of which is 9 units long, and the circumference of the full circle with a diameter of 8 units.

Using the formula for the circumference of a circle (C = πd) where d is the diameter, the circumference of the full circle would be 8π. So, the total perimeter of the shape is:

P = 2*(9) + 8π

That gives us:

P = 18 + 25.13 approximately

So, P ≈ 43.1. . . units

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Answer:

the domain is anything with the x-axis and range the y-axis

Answer:

Domain- is the set of all possible x-values or "input" for the function that gets you to the "output" or y-values. Range- is the difference between the highest and the lowest values.

Step-by-step explanation:

Answer:

2 pounds of turkey?

Step-by-step explanation:

Margot will therefore need 3 pounds of turkey to make 4 liters of her turkey chili.

To find out how many pounds of turkey Margot will need to make 4 times her turkey chili recipe for 1 liter, we first identify the amount needed for 1 liter based on the given ratio, and then multiply that amount by 4.

Margot uses 1/2 pounds of turkey for 2/3 liters of turkey chili. If we need to find out the amount for 1 liter, we can set up a proportion:

1/2 pounds turkey / (2/3 liters) = x pounds turkey / 1 liter

We cross multiply to solve for x:

(1/2) * 1 = x * (2/3)

Now we solve for x:

x = (1/2) * (3/2)

x = 3/4 pounds of turkey for 1 liter of chili

For 4 liters of chili (4 times the recipe), we would multiply:

4 * (3/4 pounds) = 3 pounds of turkey

Answer:

39.6x +26.4

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 13.2 * (3x+2)

Distribute

    39.6x +26.4

Answer:

6.5 units

Step-by-step explanation:

In circle with center O, AB is diameter.

[tex] \therefore m\angle ACB = 90°\\[/tex]

(Angle inscribed in a semicircle)

[tex] \therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\[/tex]

By Pythagorean theorem:

[tex]AB = \sqrt{ {12}^{2} + {5}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ AB \: = 13 \\ r = \frac{13}{2} = 6.5 \: units[/tex]

Answer:

(x,y)=(2,-3)

Step-by-step explanation:

6x+2y=6

7x+3y=5

Multiply both sides by 3

18x+6y=18

7x+3y=5

Multiply both sides by -2

18x+6y=18

-14x-6y=-10

Eliminate one variable by adding the equations

4x=8

x=2

Substitute the value of x to get y

6(2)+2y=6

y=-3

x=2

y=-3

The solution to the system of equations 6x+2y=6 and 7x+3y=5 is x = 2 and y = -3.

The solution to the system of equations 6x+2y=6 and 7x+3y=5 involves finding the values of x and y that satisfy both equations simultaneously.

First, let's multiply:

3(6x + 2y) = 3(6)
=> 18x + 6y = 18

2(7x + 3y) = 2(5)
=> 14x + 6y = 10

Next, we subtract the second equation from the first:

18x + 6y - (14x + 6y) = 18 - 10

4x = 8

x = 2

Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. For instance, substituting x into the first original equation:

6(2) + 2y = 6

12 + 2y = 6

2y = 6 - 12

2y = -6

y = -3

The solution to the system of equations is x = 2 and y = -3.

Answer: A

Step-by-step explanation:

Answer:

[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]

Step-by-step explanation:

Given the expression:

[TeX] x^2+17x=-5 [/TeX]

To complete the square,

First Step: Identify the Coefficient of x.

Coefficient of x=17

Second Step: Divide the coefficient of x by 2.

Third Step: Square your result from the second step.

This gives:

[TeX] (\frac{17}{2})^{2}[/TeX]

Fourth Step: Add your result to both sides if the equation.

[TeX] x^2+17x+(\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]

Fifth Step:Express the left hand side as a square

[TeX] (x+\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]

Sixth Step:Simplify the Right Hand Side

[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]

These are the values that make an equivalent number sentence.

Answer:

The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

Step-by-step explanation:

Let the width of rectangular solid be x

We are given that the length of the container must be one meter longer than the width

So, Length of solid = x+1

We are also given that height must be one meter greater than twice the width

So, Height of solid = 2x+1

So, Volume of solid = [tex]Length \times Width \times height[/tex]

Volume of solid = [tex](x+1) \times x \times (2x+1)[/tex]

Volume of solid =[tex](x^2+x)(2x+1)[/tex]

Volume of solid =[tex]2x^3+x^2+2x^2+x=2x^3+3x^2+x[/tex]

We are given that  a rectangular solid must have a volume of 84 cubic meters

So, [tex]2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\[/tex]

On equating

x-3=0

x=3

So, Length of solid = x+1=3+1 = 4 feet

Height of solid = 2x+1 =2(3)+1=7 feet

Width of solid = 3 feet

Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

The volume of a rectangular solid shipping container = 84 cubic meters

The width of the container = 3m

The length of the container = (x + 1) = (3+1) = 4m

The height of the container = (2x + 1) = (2 x 3 + 1) = 7m

Given:

The volume of a rectangular solid shipping container = 84 cubic meters

Let: The width of the container be x

The length of the container must be one meter longer than the width.

So, The length of the container be (x + 1)

The height must be one meter greater than twice the width.

So, The height of the container be (2x + 1)

To find the dimensions of the container

The Volume of the container = Length x Width x Height

[tex]84=x(x+1)(2x+1)[/tex]

[tex]84=(x^{2} +x)(2x+1)[/tex]

[tex]84=2x^{3} +3x^{2} +x[/tex]

[tex]2x^{3} +3x^{2} +x-84=0\\(x-3)(2x^{2} +9x+28)=0\\x-3=0\\x=3[/tex]

So, The width of the container = 3m

The length of the container = (x + 1) = (3+1) = 4m

The height of the container = (2x + 1) = (2 x 3 + 1) = 7m

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Answer:

3/9 or 33.33%

Step-by-step explanation:

there are 9 total cans and 3 pink cans. So, that'd be 3/9 or 33.33%

hope this helps!

Answer:

1/3

Step-by-step explanation:

Answer: (x+3)2 + (y+5)2 =36

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Probability thay the next page she turns to will have an advert = 0.4042

Step-by-step explanation:

In the last 12 issues of the magazine, 384 out of 950 pages contain an advertisement.

We now need to find the probability that the next page has an advertisement.

Probability of an event

= n(of that event) ÷ n(total sample spaces)

n(of the event of an advert) = number of pages with adverts in those issues = 384

n(total sample spaces) = total number of pages = 950

Probability that the next page or any page at all will have an advert = (384/950) = 0.4042

Hope this Helps!!!

Answer:

[tex]log(10a)[/tex]

Step-by-step explanation:

[tex]log(a\sqrt{44})+log(a \sqrt275)-log(11a)[/tex]

We can simplify this using these log laws:

[tex]log(a)+log(b)=log(ab)\\log(a)-log(b)=log(\frac{a}{b})[/tex]

[tex]log(\frac{a^2\sqrt{44} \sqrt{275}}{11a})[/tex]

We also have laws to simplify square roots

[tex]\sqrt{a}*\sqrt{b} = \sqrt{ab}[/tex]

So this becomes

[tex]log(\frac{a^2\sqrt{12100}}{11a})[/tex]

[tex]\sqrt{12100} = 110[/tex]

so this becomes

[tex]log(\frac{110a^2}{11a})=log(10a)[/tex]