let (-3,-2) be a point on the terminal side of 0. find the exact values of cos0 csc0 and tan0

Step 3 of the argument could be that the translation preserves the size of circle A.

Step 3 of the argument could be: 3. The translation preserves the size of circle A.

Explanation: In step 2, it is stated that there exists a translation that can be performed on circle A so that it will have the same center as circle B.

In order for this translation to be possible, the size of circle A must be preserved. This means that the radius of this circle A remains the same even after the translation is applied.

Therefore, step 3 could be that the translation preserves the size of the given circle A.

Answer:

Solution is x= 0 , x = \frac{1}{14}  , x = \frac{-1}{12}

Step-by-step explanation:

Given, equation is  \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} →→→ (1)

Now, by cubing the equation on both sides, we get

( \sqrt[3]{15x-1} + \sqrt[3]{13x+1} )³ = (4\sqrt[3]{x})³

⇒ (15x-1) + (13x+1) + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} +  \sqrt[3]{13x+1}) = 64 x.

(since (a+b)³ = a³ + b³ + 3ab(a+b) ).

⇒ 28x + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} +  \sqrt[3]{13x+1})  = 64x.        

(since from (1), \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} )

⇒ 12×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1}×\sqrt[3]{x}= 36x.

⇒ 3x = [tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex] .

Now, once again cubing on both sides, we get

(3x)³ = ([tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex])³.

⇒ 27x³ = (15x-1)(13x+1)(x).

⇒ 27x³ = 195x³ + 2x² - x

⇒ 168x³ + 2x² - x = 0

⇒ x(168x² + 2x -1) = 0

⇒ by, solving the equation we get ,

x = 0 ; x = \frac{1}{14}   ; x = \frac{-1}{12}

therefore, solution is x= 0 , x = \frac{1}{14}   ,  x = \frac{-1}{12}

Answer:

[tex]4\times \sqrt{11}\div \(11)[/tex]

Step-by-step explanation:

[tex]\sqrt{16}\div \sqrt{11}[/tex]

[tex]\sqrt{16}\times \sqrt{11}\div \sqrt{11}\times \sqrt{11}[/tex]

[tex]4\times \sqrt{11}\div \(11)[/tex]  answer

answer: 828$

Step-by-step explanation:

step 1

Find out the total cost of the land

Multiply the total area in acres by $1,863 per acre

step 2

we know that

To determine the selling price of each lot to reach break even, divide the total cost by the number of lots.

To solve for the number of adults going to the exhibition, you can set up a system of linear equations based on the given information about ticket costs and quantities, leading to the conclusion that there were 2 adults attending.

The problem is a classic example of a system of linear equations which can be solved using substitution or elimination.

Step-by-step Solution:

Let's denote the number of adults going to the exhibition as A and the number of children as C.

Therefore, there were 2 adults going to the exhibition.

Answer:

y=1/3x+2

Step-by-step explanation:

y=3x-6

x=3y-6

3y=x+6

y=1/3x+6/3

y=1/3x+2

Answer:

m∠1 = 30°

m∠2 = 60°

Step-by-step explanation:

There are two 30-60-90 triangles. For each, the angles have to add up to 180°

Answer:

m∠1 = 30°

m∠2 = 60°

Step-by-step explanation:

Divide total miles by miles per gallon:

364 miles / 20 miles per gallon = 18.2 gallons

The Original length of each side of square was 14.25 inches.

Step-by-step explanation:

Perimeter of a square is given by:

Perimeter = 4 * side

Let x be the original length of each side of square

So

decreasing 2 inch will mean

[tex]x-2[/tex]

Perimeter of square after reducing 2 inches from each side

[tex]4(x-2) = 49\\4x-8 = 49\\4x = 49+8\\4x = 57\\\frac{4x}{4} = \frac{57}{4}\\x = 14.25[/tex]

So,

The Original length of each side of square was 14.25 inches.

Keywords: Perimeter, square

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Answer:

Mike = 3

Robert = 9

Step-by-step explanation:

R = Robert

M = Mike

Mike is 6 years younger than Robert

R = M + 6

Add 3 years to both sides

R + (3) = 2M + (3)

Represent that Robert is now twice as old as Mike

2M + 3 = M + 3 + 6

Solve + Subtract the 3 years

2M + 3 = M + 9

M = 6 - 3 = 3

R = 12 - 3 = 9

Hope this helps :)

The volume of the solid generated by rotating triangle ABC around AB is 24π cubic units.

To find the volume of the solid generated by rotating triangle ABC around side AB, you can use the method of cylindrical shells. The volume of the solid generated by rotating a region bounded by a curve around an axis is given by the formula:

[tex]\[ V = \int_{a}^{b} 2\pi x \cdot h(x) \, dx \][/tex]

Where:

[tex]\( a \) and \( b \) are the limits of integration along the x-axis (in this case, from 0 to the length of side AB),[/tex]

[tex]\( h(x) \) is the height of the curve at the position x, and[/tex]

[tex]\( 2\pi x \) represents the circumference of the cylindrical shell with radius x and height \( h(x) \).[/tex]

In this case, triangle ABC is a right triangle, so rotating it around AB will generate a cone with height AB and base radius AC.

Given that AB = 2 and AC = 6, the radius of the base of the cone formed by rotating the triangle will be [tex]\( r = AC = 6 \)[/tex]. The height of the cone will be the same as the length of side AB, so [tex]\( h = AB = 2 \).[/tex]

Now, we can calculate the volume:

[tex]\[ V = \int_{0}^{2} 2\pi x \cdot 6 \, dx \][/tex]

[tex]\[ = 12\pi \int_{0}^{2} x \, dx \][/tex]

[tex]\[ = 12\pi \left[\frac{x^2}{2}\right]_{0}^{2} \][/tex]

[tex]\[ = 12\pi \left(\frac{2^2}{2} - \frac{0^2}{2}\right) \][/tex]

[tex]\[ = 12\pi \left(\frac{4}{2}\right) \][/tex]

[tex]\[ = 12\pi \cdot 2 \][/tex]

[tex]\[ = 24\pi \][/tex]

So, the volume of the solid generated by rotating triangle ABC around side AB is [tex]\( 24\pi \)[/tex] cubic units.

The solid formed by rotating triangle ABC around side AB is a cone. The volume of this cone is calculated using the formula V = (1/3)πr^2h where r is the radius of the base and h is the height, resulting in approximately 57.91 cubic units.

The question asks for the volume of the solid generated by rotating a triangle around one of its sides. In this case, rotating triangle ABC with AB = 2, BC = 5, and AC = 6 around side AB will generate a conical surface. Since side AB will be the axis of rotation, the other two sides will act as generating lines of the cone, where side AC becomes the slant height (l) and side BC becomes the base's radius (r).

To calculate the volume of the cone, we use the formula V = (1/3)\u03c0r^2h, where r is the radius of the base, and h is the height of the cone. Here the height (h) of the cone is not directly provided, but with the Pythagorean theorem, we can find it since we know the slant height and radius: h = \\/(l^2 - r^2) = \\/(6^2 - 5^2) = \\/(36 - 25) = \\/11. Finally, the volume can be calculated: V = (1/3)\\(3.1415)\(5)^2\\/11\approx 57.91 cubic units.

The theorem of Pappus is a useful approach to solving this problem, but it requires knowing the centroid's distance from the axis of rotation, which is not provided, so we are not using that method here.

Answer:

slower 50mph faster 60mph

Step-by-step explanation:

Distance=s⋅t

Distance

=

(

+

10

)

⋅

(

−

0.5

)

Distance=(s+10)⋅(t−0.5)

Equate the distances:

⋅

=

(

+

10

)

⋅

(

−

0.5

)

s⋅t=(s+10)⋅(t−0.5)

Expand and simplify:

⋅

=

⋅

−

0.5

+

10

−

5

s⋅t=s⋅t−0.5s+10t−5

0

=

−

0.5

+

10

−

5

0=−0.5s+10t−5

Rearrange to find

t:

0.5

=

10

−

5

0.5s=10t−5

10

=

0.5

+

5

10t=0.5s+5

=

0.5

+

5

10

t=

10

0.5s+5

​

Substitute

t back into the distance equation:

⋅

0.5

+

5

10

=

(

+

10

)

⋅

(

0.5

+

5

10

−

0.5

)

s⋅

10

0.5s+5

​

=(s+10)⋅(

10

0.5s+5

​

−0.5)

Simplify and solve for

s:

After solving, you will find that the average speeds are approximately:

Slower car: 50 mph

Faster car: 60 mph

Answer:

192

Step-by-step explanation:

Your sequence of numbers is

131 517 … 123

Space them as a two-digit sequence

13 15 17 19 21 23

Now, regroup then as a three-digit sequence

131 517 192 123

The missing number is 192.

Answer:

0.3 lbs. of meat per hamburger

The equation D is the equation that best fits the data.

Why?

We can find the best option by substituting the easiest values into the given options.

Let's substitute f(0), f(1) and f(4) for each equation:

A.

[tex]f(0)=3.02(3.67)^{0}=3.02[/tex]

[tex]f(1)=3.02(3.67)^{1}=11.08[/tex]

[tex]f(4)=3.02(3.67)^{4}=547.86[/tex]

We can see that the values are too far from the given values, so the equation A is discarded.

B.

[tex]f(0)=2.27(2.09)^{0}=2.27[/tex]

[tex]f(1)=2.27(2.09)^{1}=4.74[/tex]

[tex]f(4)=2.27(2.09)^{1}=43.31[/tex]

We can see that the values are too far from the given values, so the equation B is discarded.

C.

[tex]f(0)=8.04(0.98)^{0}=8.04[/tex]

[tex]f(1)=8.04(0.98)^{1}=7.87[/tex]

[tex]f(4)=8.04(0.98)^{4}=7.41[/tex]

We can see that the values are too far from the given values, so the equation B is discarded.

D.

[tex]f(0)=6.61(1.55)^{0}=6.61[/tex]

[tex]f(1)=6.61(1.55)^{0}=10.26[/tex]

[tex]f(4)=6.61(1.55)^{0}=38.15[/tex]

We can see that the values are the closest values from the given values, so the equation D is the equation that best fits the data.

Have a nice day!

The basketball player's mass is approximately 46.2857 kilograms.

To solve for the player's mass, we can rearrange the equation to isolate the mass variable. The equation can be rewritten as m = 36S/h.

Plugging in the given values, we get m = 36 * 2.7 / 2.1.

Solving this expression gives us a mass of approximately 46.2857 kilograms.

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Answer: OPTION C.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

In order to verify which fucntion is not linear, you can solve for "y" from each function. Then:

[tex]A.\ y+1= x\\\\y=x-1[/tex]

This is a Linear function.

[tex]B.\ x=2y-3\\\\x+3=2y\\\\y=\frac{1}{2}x+\frac{3}{2}[/tex]

This is a Linear function.

[tex]C.\ xy=2\\\\y=\frac{2}{x}[/tex]

This is NOT a Linear function.

[tex]D.\ x+1=\frac{3}{4}y\\\\4x+4=3y\\\\y=\frac{4}{3}x+\frac{4}{3}[/tex]

This is a Linear function.

Final answer:

Option C) xy = 2 does not represent a linear function because it cannot be rewritten in the form y = mx + b, which is characteristic of linear equations. Instead, it represents a hyperbola.

Explanation:

The question asks: "Which does NOT represent a linear function?" with the options being A) y+1= x, B) x=2y-3, C) xy=2, and D) x+1=3/4y. To determine which equation does not represent a linear function, we must recall that linear functions can always be written in the form y = mx + b, where m is the slope and b is the y-intercept.

A) y+1 = x can be rewritten as y = x - 1, which is linear.

B) x = 2y - 3 can be rewritten as y = 1/2x + 3/2, which is linear.

C) xy = 2 cannot be rewritten in the form y = mx + b because it involves both x and y being multiplied together, which is characteristic of a hyperbola, not a linear equation.

D) x + 1 = 3/4y can be rearranged to y = 4/3x + 4/3, which is linear.

Therefore, the equation that does NOT represent a linear function is C) xy = 2.

Answer:

The time after which only 40 mg of medicine left inside body is 9.8 hours

Step-by-step explanation:

Given as :

The initial quantity of medicine ingest in body = i=200 mg

The final quantity of medicine in body = f= 40 mg

The rate at which body remove medicine = r = 15%

Let The time taken to remove = t hours

According to question

The final quantity of medicine in body after t hours = The initial quantity of medicine ingest in body × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

I.e f = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, 40 mg = 200 mg × [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]

Or, [tex]\dfrac{40}{200}[/tex] = [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]

Or , 0.2 = [tex](\frac{100 - 15}{100})^{t}[/tex]

Or,  [tex](\frac{85}{100})^{t}[/tex] = 0.2

Taking Log both side

So, [tex]Log_{10}[/tex] [tex](\frac{85}{100})^{t}[/tex] = [tex]Log_{10}[/tex]0.2

Or, t ×  [tex]Log_{10}[/tex]0.85 =  [tex]Log_{10}[/tex]0.2

Or, t (-0.07) = - 0.69

∴  t = [tex]\dfrac{.69}{.07}[/tex]

I.e t = 9.8 hours

So, The time after which only 40 mg left inside body = t = 9.8 hours

Hence,The time after which only 40 mg of medicine left inside body is 9.8 hours .Answer

Answer:

Benny's:

2.00 / 4 = $0.50 per sandwich

ABC:

1.50 / 2 = $0.75 per sandwich

Sandwich Hut:

2.00 / 2 = $1.00 per sandwich

Benny's has the best deal

Answer:

The answer for this question would be $3.00 for sandwiches

Step-by-step explanation:

Answer:

Second option: [tex]3 + 4 x\leq 2 (1 + 2x)[/tex]

Step-by-step explanation:

Let's solve for "x" from each inequality:

[tex]a.\ 6 (x + 2)>x-3\\\\6x+12>x-3\\\\6x-x>-3-12\\\\5x>-15\\\\x>\frac{-15}{5}\\\\x>-3[/tex]

[tex]b.\ 3 + 4 x\leq 2 (1 + 2x)\\\\3+4x\leq 2+4x\\\\3-2\leq 4x-4x\\\\1\leq 0\  (FALSE.\ IT\ HAS\ NO\ SOLUTION)[/tex]

[tex]c.\ -2 (x + 6)<x-20\\\\-2x-12<x-20\\\\-12+20<x+2x\\\\8<3x\\\\x>\frac{8}{3}[/tex]

[tex]d.\ x-9<3(x-3)\\\\x-9<3x-9\\\\x-3x<-9+9\\\\-2x<0\\\\x>0[/tex]

The inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).

The correct option is 2nd.

Given are inequalities, we need to check which of them has no solution.

Let's solve each inequality to determine if it has a solution:

1) 6(x + 2) > x - 3

First, distribute the 6:

6x + 12 > x - 3

Now, let's isolate the variable x on one side:

6x - x > -3 - 12

5x > -15

Finally, divide by 5 to solve for x:

x > -3

This inequality does have a solution, and x can take any value greater than -3.

2) 3 + 4x ≤ 2(1 + 2x)

First, distribute the 2 on the right side:

3 + 4x ≤ 2 + 4x

Now, subtract 4x from both sides:

3 ≤ 2

This is not true, and there is no value of x that satisfies this inequality.

So, this inequality has no solution.

3) -2(x + 6) < x - 20

First, distribute the -2:

-2x - 12 < x - 20

Now, let's isolate the variable x on one side:

-2x - x < -20 + 12

-3x < -8

Finally, divide by -3 to solve for x (note the sign change when dividing by a negative number):

x > 8/3 or x > 2.67

This inequality has a solution, and x can take any value greater than 2.67.

4) x - 9 < 3(x - 3)

First, distribute the 3 on the right side:

x - 9 < 3x - 9

Now, move the variables to one side:

x - 3x < 9 - 9

-2x < 0

Finally, divide by -2 to solve for x (note the sign change when dividing by a negative number):

x > 0

This inequality has a solution, and x can take any value greater than 0.

Hence, the inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).

The correct option is 2nd.

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Answer:

Option A) x=4,12 is correct.

The solution of the given quadratic equation is x=4,12

Step-by-step explanation:

Given equation is in quadratic form

Given quadratic equation is

[tex]0=4x^2-64x+192[/tex]

Rewriting the above equation

[tex]4x^2-64x+192=0[/tex]

Now dividing the equation by 4 we get

[tex]\frac{1}{4}(4x^2-64x+192)=\frac{0}{4}[/tex]

[tex]x^2-16x+48=0[/tex]

For quadratic equation [tex]ax^2+bx+c=0[/tex]

solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

where a and b are coefficients of [tex]x^2[/tex] and x respectively, c is a constant

Here a=1, b=-16, c=48

[tex]x=-\frac{(-16)\pm\sqrt{(-16)^2-4(1)(48)}}{2(1)}[/tex]

[tex]=\frac{16\pm\sqrt{16^2-192}}{2}[/tex]

[tex]=\frac{16\pm\sqrt{256-192}}{2}[/tex]

[tex]=\frac{16\pm\sqrt{64}}{2}[/tex]

[tex]x=\frac{16\pm 8}{2}[/tex]

Therefore

[tex]x=\frac{16+8}{2}[/tex] and [tex]x=\frac{16-8}{2}[/tex]

[tex]x=\frac{24}{2}[/tex] and [tex]x=\frac{8}{2}[/tex]

[tex]x=12[/tex] and [tex]x=4[/tex]

Therefore the solution of the given quadratic equation is x=4,12

Option A) x=4,12 is correct.

Answer: -7/-3.

Step-by-step explanation: In this problem we're asked to find the slope of the line that passes through the points (4,3) and (1,-4).

Using our slope formula, we take the second y minus the first y which in this case is -4 - 3 over our second x minus our first x which in this case is 1 - 4.

-4 - 3 is -7 and 1 - 4 is -3.

So the slope of this line is -7/-3.

Answer:

-7/-3

Step-by-step explanation:

Slope is represented as m

m = Rise/Run =( Y2 - Y1) / (X2 - X1)

m =  (-4  -3) / (1 - 4)

m = -7 / -3

The negative sign (minus) will cancel out

Therefore,

m = 7 / 3

m = 2 whole number, 1/3

Answer:

C - 19.43

Step-by-step explanation:

first you need to find how much 1 pound of jelly beans costs. to find that you do 14.74 ÷ 5.5 to get 2.68. Then you times that by 7.25 to get the answer, 19.43

The cost of the 7.25 pounds of the jelly bean will be $19.92. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jacob bought 5.5 pounds of jelly beans for $14.74.

The cost of the 7.25 pounds of the jelly bans will be calculated as,

5.5 pounds ⇒ $14.74

1 pound ⇒ $(14.74/5.5)

7.25 pounds ⇒ (14.74x7.25)/5.5

7.25 pounds = $19.43

Therefore, the cost of the 7.25 pounds of the jelly bean will be $19.92. The correct option is B.

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Answer:

Problem 1: 5x-3y=-7 has One Solution

Problem 2: 10x-6y=-14 has One Solution

If bills new porch is rectangular with an area of 50 square feet if the length of the porch is two times the width. Then 30 feet is the perimeter of the porch

The area of Rectangle is length times of width.

Given,

bills new porch is rectangular with an area of 50 square feet

Area=50  square feet

Length of the porch is two times the width

Length=2Width

Area=Length×Width

50=2W×W

Divide both sides by 2

25=W²

Take square root on both sides

W=5ft

Hence width of bills new is 5 feet.

The perimeter of rectangle=2(Length+width)

=2(2W+W)

=2(2(5)+5)

=2(10+5)

=2(15)

=30

So perimeter of rectangle is 30 feet.

Hence 30 feet is the perimeter of the porch.

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Answer:

NO, It is non terminating / recurring decimal

Step-by-step explanation:

3/9= 0.33333333......

remainder= 3

Let X = the number of weeks.

Jeanette will pass 3 per week, so 3x, and she already passed 8, so Jeanette would be 3x +8

Paul would be 4x + 3

Set them to equal to solve for x ( the number of weeks.)

3x +8 = 4x +3

Subtract 3x from both sides:

8 = x +3

Subtract 3 from both sides:

X = 5

So it will take 5 weeks to be the same.

Replace X with 5 to find the number of scales.

3x + 8 = 3(5) + 8 = 15 +8 = 23

They would have 23 scales.

Answer:

$200,000

Step-by-step explanation:

Base Salary = 40,000

Total Salary = 70,000

So, the rest, Allison earns from commissions. How much??

70,000 - 40,000 = 30,000

So, 15% of total sales is equal to 30,000

Let total sales be "t", so we can write an equation as:

15% * t = 30,000

15% in decimal is:

15/100 = 0.15

So, equation to solve is:

0.15t = 30,000

Finding t:

t = 30,000/0.15 = 200,000

Allison's total sales were $200,000

Answer:

155/2

Step-by-step explanation:

7/7=1

1*1/2=1/2

61-1/2+17

122/2-1/2+17

121/2+17=155/2

Answer:

The given numbers from smallest to largest is

[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

Step-by-step explanation:

Given numbers are

[tex]\frac{652}{900}, 0.012,\frac{7}{10}, 32\%,\frac{1}{10}, 0.721, 65\%[/tex]

We have to arrange the given numbers from smallest to largest

That is to write in ascending order.

Rewritting the given numbers are

[tex]\frac{652}{900}, 0.012,\frac{7}{10}, \frac{32}{100},\frac{1}{10}, 0.721, \frac{65}{100}[/tex]

[tex]\frac{652}{900}, 0.012,0.7, 0.32, 0.1, 0.721, 0.65[/tex]

[tex]0.724, 0.012, 0.7, 0.32, 0.1, 0.721, 0.65[/tex]

Now arranging the above numbers from smallest to largest

[tex]0.012, 0.1, 0.32, 0.65, 0.7, 0.721, 0.724[/tex]

ie, 0.12, [tex]\frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

The given numbers in ascending order is

[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]