3. Find the quotient of 5/31 divided by 15/23. Reduce your answer to the lowest fraction.

Answer:

A) w + w

Step-by-step explanation:

Combine like terms

A)w+w   = 2w

B)2w+w   = 3w

C)2w-w  = w

D) w+2 = w + 2

So answer is A) w + w

Answer:

w+w

Step-by-step explanation:

Answer:

Part B. see the procedure

Part C. see the procedure

Step-by-step explanation:

we have

[tex]f(x)=x^{2}+2x+1[/tex] -----> equation A

[tex]g(x)=3-x-x^{2}[/tex] -----> equation B  

Part B. Solve the system algebraically

equate the equation A and the equation B

[tex]x^{2}+2x+1=3-x-x^{2}[/tex]

[tex]2x^{2}+3x-2=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2}+3x-2=0[/tex]

so

[tex]a=2\\b=3\\c=-2[/tex]

substitute in the formula

[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4a(2)(-2)}} {2(2)}[/tex]

[tex]x=\frac{-3(+/-)\sqrt{25}} {4}[/tex]

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

[tex]x1=\frac{-3(+)5} {4}=0.5[/tex]

[tex]x2=\frac{-3(-)5} {4}=-2[/tex]

Find the values of y

For x=0.5

[tex]f(0.5)=0.5^{2}+2(0.5)+1=2.25[/tex]

For x=-2

[tex]f(-2)=(-2)^{2}+2(-2)+1=1[/tex]

the solutions are the points

(0.5,2.25) and (-2,1)

Part C. Solve the system by graph

using a graphing tool

we know that

The solution of the non linear system is the intersection point both graphs

The intersection points are (0.5,2.25) and (-2,1)

therefore

The solutions are the points (0.5,2.25) and (-2,1)

see the attached figure

Answer:

Step-by-step explanation:

3y + 19 = 6y + 1

6y + 1 = 3y + 19

6y - 3y = 19 - 1

3y = 18

y = 6

6y + 1

6.6 + 1

37

The first one

I hope I helped you.

Answer:

Option A. 37

Step-by-step explanation:

We will understand first what is a regular hexagon?

Hexagon is a structure in which number of all the sides are 6 and since its a regular hexagon all the sides will be equal.

Since all the sides are equal and given two sides are (3y + 19) and (6y + 1)

Therefore, by the definition of regular hexagon

3y + 19 = 6y + 1

19 = 6y - 3y + 1

19 - 1 = 6y - 3y

18 = 3y

y = [tex]\frac{18}{3}=6[/tex]

Now we have to calculate the length of both the sides given.

Side ST = 6y + 1 = 6×6 + 1 = 36 + 1 = 37

and QR = 3y + 19 = 3×6 + 19 = 18 + 19 = 37

Therefore, option A. 37 is the correct answer.

Parallel lines are lines that do not intersect each other at any point.

The correct definition of parallel lines is option A: 'Parallel lines are lines that do not intersect.' Parallel lines are two lines in a plane that do not intersect each other at any point, no matter how far they are extended.

https://brainly.com/question/7966281

#SPJ12

Answer:1/3

Step-by-step explanation:

2/3*1/2=1/3

The area of a parking lot measuring 2/3 km long and 1/2 km wide is 1/3 km². This is found by multiplying the length by the width.

The question is asking for the area of a rectangular parking lot that measures 2/3 km long and 1/2 km wide. The formula for the area of a rectangle is length times width. Applying this formula, we multiply 2/3 km by 1/2 km.

It's important to remember that when multiplying fractions, you just multiply the numerators (top numbers) and the denominators (bottom numbers) separately. So, (2/3) x (1/2) = 2/6 km², which simplifies to 1/3 km².

So, the area of the parking lot is 1/3 km².

https://brainly.com/question/15218510

#SPJ3

Answer:

  an = 2(−4)^(n − 1); all integers where n ≥ 1

Step-by-step explanation:

The equation has the form ...

  an = a1(r)^(n-1) . . . . . where a1 is the first term and r is the common ratio.

The first term is given as 2, and the ratio will be the ratio of the first two terms:

  r = (-8)/(2) = -4

Terms are numbered starting with n=1, so the formula is ...

  an = 2(-4)^(n-1) for n≥1

Answer:

4/9

Step-by-step explanation:

Given rate is 1/3 acre per 3/4 hours.

To calculate the rate per hour, we have to divide total acres by the fraction of hour

=> [tex]\frac{\frac{1}{3} }{\frac{3}{4} }[/tex]

=> [tex]\frac{4}{3*3}[/tex]

=> 4/9

Here is your answer

[tex]<b>always</b>[/tex]

REASON :

Integers are all natural numbers their negative including 0.

Rational numbers are the numbers of the form p/q where p and q are integers and q is not equal to 0.

So, the definition itself defines that every integer is a rational number.

Exa- Integers

1, -2 , 3, 90, -6

These are rational numbers as

1=1/1 (p/q form)

-2=-2/1 (p/q form)

3= 3/1 (p/q form)

90= 90/1 (p/q form)

-6= -6/1 (p/q form)

HOPE IT IS USEFUL

the answer is always :)))))

Answer:

1056.25π square units

Step-by-step explanation:

A few formulas an definitions which will help us:

(1) [tex]\pi=\frac{c}{d}[/tex], where c is the circumference of a circle and d is its diameter

(2) [tex]A=\pi r^2[/tex], where A is the area of a circle with radius r. To put it in terms of d, remember that a circle's diameter is simply twice its radius, or mathematically, (3) [tex]d=2r \rightarrow r=\frac{d}{2}[/tex].

We can rearrange equation (1) to put d in terms of π and c, giving us (4) [tex]d = \frac{c}{\pi}[/tex], and we can make a few substitutions in (2) using (3) and (4) to get use the area in terms of the circumference and π:

[tex]A=\pi r^2\\=\pi\left(\frac{d}{2}\right)^2\\=\pi\left(\frac{d^2}{4}\right)\\=\pi\left(\frac{(c/\pi)^2}{4}\right)\\=\pi\left(\frac{c^2/\pi^2}{4}\right)\\=\pi\left(\frac{c^2}{4\pi^2}\right)\\\\=\frac{\pi c^2}{4\pi^2}\\ =\frac{c^2}{4\pi}[/tex]

We can now substitute c for our circumference, 65, to get our answer in terms of π:

[tex]A=\dfrac{65^2}{4\pi}=\dfrac{4225}{4\pi}=1056.25\pi[/tex]

Answer:

Area = 2112.5 / pi

Step-by-step explanation:

They are asking you not to use 3.14 for pi. Just leave it as a symbol.

C = 2*pi*r

C = 65

65 = 2*pi*r

65/(2*pi) = r

The area of a circle is 2*pi * r^2

Area = 2 * pi * (65/2pi)^2

Area = 2 * pi * 65^2/(4*pi^2)           Cancel out one of the pi-s in the denominator

Area = 2 * 65^2 / (4 * Pi)                  Expand the numerator

Area = 8450/(4*pi)                           Divide by 4

Area = 2112.5 / pi

Answer:

380

Step-by-step explanation:

11^2 x 3.14 = 380

Answer:

6

Step-by-step explanation:

***If choosing one of each, this is the answer*** This wasn't clearly asked for in the question though

When counting the number of arrangements of multiple choices, multiply the number of choices of each item together.

(3)(2)(1) = 6

Here is them listed..

Green ball 1, red ball 1, white ball

Green ball 1, red ball 2, white ball

Green ball 2, red ball 1, white ball

Green ball 2, red ball 2, white ball

Green ball 3, red ball 1, white ball

Green ball 3, red ball 2, white ball

Answer:

b.  (√15)/4

Step-by-step explanation:

Since Sin Ф = (opposite side)/Hypotenuse, we have 2 sides of a right triangle.  

Use Pythagorean theorem to solve for the missing leg (the adjacent side)

 1² + b² = 4²

    1 + b² = 16

            b² = 15

                 b = √15

So the adjacent side is √15, so Cos Ф = (√15)/4

Answer:

b. [tex]\frac{\sqrt{15}}{4}[/tex]

Step-by-step explanation:

Given that [tex]\sin(\theta)=\frac{1}{4}[/tex] where [tex]0\:<\: \theta \:<\:\frac{\pi}{2}[/tex].

Recall and use the Pythagorean Identity;

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

This implies that;

[tex](\frac{1}{4})^2+\cos^2(\theta)=1[/tex]

[tex]\frac{1}{16}+\cos^2(\theta)=1[/tex]

[tex]\cos^2(\theta)=1-\frac{1}{16}[/tex]

[tex]\cos^2(\theta)=\frac{15}{16}[/tex]

Take the square root of both sides;

[tex]\cos(\theta)=\pm \sqrt{\frac{15}{16}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{15}}{4}[/tex]

Since we are in the first quadrant;

[tex]\cos(\theta)=\frac{\sqrt{15}}{4}[/tex]

Option: C is the correct answer.

    C.   [tex]f(1)=4\\\\f(n)=5\cdot f(n-1)\ ;\ n\geq 2[/tex]  

Recursive Formula--

It is the formula which is used to represent the nth term of a sequence in terms of (n-1)th term of the sequence.

Here we are given a table of values by:

            n            f(n)

            1              4

            2             20

            3             100  

i.e. when n=1 we have:

[tex]f(1)=4[/tex]

Also,

[tex]f(2)=20\\\\i.e.\\\\f(2)=5\cdot 4\\\\i.e.\\\\f(2)=5\cdot f(1)[/tex]

Also,

[tex]f(3)=100\\\\i.e.\\\\f(3)=5\cdot 20\\\\i.e.\\\\f(3)=5\cdot f(2)[/tex]

Hence, the recursive formula is:

[tex]f(n)=5\cdot f(n-1)\ for\ n\geq 2[/tex]

Answer:

for plato family

f(1)=4

f(n)=5. f(n-1) ,for n [tex]\geq[/tex] 2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

To find the best equation, we simply substitute the values of a, b, and c into the given equations.

a = 21

b = 5

c = 36

[tex]a=\dfrac{7}{10}b\sqrt{c}[/tex]

[tex]21=\dfrac{7}{10}5\sqrt{36}[/tex]

[tex]21=\dfrac{7}{10}5(6)[/tex]

[tex]21=\dfrac{7}{10}30[/tex]

[tex]21=(0.7)30[/tex]

[tex]21=21[/tex]

The lateral area is the area not including the base.

You have 2 sides that are 6 x 8 = 48 x 2 = 96 square feet.

One side of 4 x 8 = 32 square feet

And the top triangle = 1/2 x 4 x 6 = 12 square feet.

For lateral area you would not include the triangle at the bottom ( base).

Total Lateral area = 96 + 32 + 12 = 140 square feet.

Answer:

10 1/2

Step-by-step explanation:

Carol's total earnings can be calculated by adding up her net salary plus her taxes paid.                                              

So, Total earnings of Carol = 642.20 + 115.34 + 62.75 = $820.29

So, her hourly wage = [tex]\frac{820.29}{37} =22.17[/tex]

Hence, Carol's hourly wage is = $22.17                                                        

In a system of equations, if the variable x is found to be equal to 2 and y is found to be equal to 4, the value of x - y is -2.

To solve for the values of x and y in this pair of linear equations, we can use a method known as substitution or elimination. However, the question asks for the value of x-y, not for the individual values of x and y.

First, let's multiply the first equation by 2 and the second equation by 3:

4x - 6y = -28 (equation 1)

9x - 6y = -18  (equation 2)

If we subtract Equation 2 from Equation 1, we get -5x = -10. Solving for x, we find that x = 2.

Substituting the value of x into the first equation, we get:

2(2) - 3y = -14

Solving for y, we find that y = 4.

Therefore, x - y = 2 - 4 = -2.

https://brainly.com/question/21620502

#SPJ6

➷ You have to subtract the values:

38,428 - 21,728 = 16,700

He should have $16,700 (you can change the currency symbol if required)

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

the the third graph

Step-by-step explanation:

this is because the third graph shows a correlation of the time and when the rainfall in a proporational relesho=inshop

Answer:

the third graph :)

Step-by-step explanation:

each hour the rain is increasing by 2 drops.

Answer:

A. quadrilateral, parallelogram, rhombus

Step-by-step explanation:

Parallel sides are equal

➷ There is only one '3' on the cube

Therefore, it would be B. 1/6

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

i think its 5x-15 OR -1x-15

Answer:

Step-by-step explanation:

Use the cosine law:

[tex]BC^2=AB^2+AC^2-2(AB)(AC)\cos(\angle A)[/tex]

We have:

[tex]BC=a\\\\AB=4\\\\AC=3\\\\m\angle A=32^o\to\cos32^o\approx0.848[/tex]

Substitute:

[tex]a^2=4^2+3^2-2(4)(3)(0.848)\\\\a^2=16+9-20.352\\\\a^2=4.648\to a=\sqrt{4.648}\\\\a\approx2.2[/tex]

Answer:

The answer is ellipse; 30° ⇒ answer (d)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 13x² + 6√3xy + 7y² - 16 = 0

∵ A = 13 , B = 6√3 , C = 7

∴ B² - 4 AC = (6√3)² - 4(13)(7) = -256

∴ B² - 4AC < 0

∴ The graph is ellipse or circle

* If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

* If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs with different values

∴ It is an ellipse

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 13 , B = 6√3 , C = 7

∴ cot(2Ф) = (13 - 7)/6√3 = 6/6√3 = 1/√3

∵ tan(2Ф) = 1/cot(2Ф)

∴ tan(2Ф) = √3 ⇒ 2Ф = [tex]tan^{-1}\sqrt{3}=60[/tex]

∴ 2Ф = 60°

∴ Ф = 30°

* The answer is ellipse; with angle of rotation = 30°

Answer:

The answer is ellipse; 30° ⇒ answer (d)

Step-by-step explanation:

For the last part, you have to find where [tex]f'(t)[/tex] attains its maximum over [tex]0\le t\le8[/tex]. We have

[tex]f'(t)=-6\sin3t+6\cos2t[/tex]

so that

[tex]f''(t)=-18\cos3t-12\sin2t[/tex]

with critical points at [tex]t[/tex] such that

[tex]-18\cos3t-12\sin2t=0[/tex]

[tex]3\cos3t+2\sin2t=0[/tex]

[tex]3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0[/tex]

[tex]\cos t(3\cos^2t-9\sin^2t+4\sin t)=0[/tex]

[tex]\cos t(12\sin^2t-4\sin t-3)=0[/tex]

So either

[tex]\cos t=0\implies t=\dfrac{(2n+1)\pi}2[/tex]

or

[tex]12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi[/tex]

where [tex]n[/tex] is any integer. We get 8 solutions over the given interval with [tex]n=0,1,2[/tex] from the first set of solutions, [tex]n=0,1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1+\sqrt{10}}6[/tex], and [tex]n=1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1-\sqrt{10}}6[/tex]. They are approximately

[tex]\dfrac\pi2\approx2[/tex]

[tex]\dfrac{3\pi}2\approx5[/tex]

[tex]\dfrac{5\pi}2\approx8[/tex]

[tex]\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1[/tex]

[tex]2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7[/tex]

[tex]2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6[/tex]

The correct answer for part (d) is: The particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]5[/tex] units per time period.

To find when the particle is moving the fastest, we need to determine the time at which the velocity of the particle is maximized. The velocity of the particle is given by the derivative of the position function with respect to time. The position function is [tex]\( f(t) = 2 \cos(3t) + 3 \sin(2t) \)[/tex]. Differentiating this with respect to [tex]\( t \)[/tex] gives the velocity function:

[tex]\[ v(t) = \frac{d}{dt}(2 \cos(3t) + 3 \sin(2t)) = -6 \sin(3t) + 6 \cos(2t) \][/tex]

To find the maximum velocity, we need to find the critical points of the velocity function by setting its derivative equal to zero:

[tex]\[ \frac{d}{dt}(-6 \sin(3t) + 6 \cos(2t)) = -18 \cos(3t) - 12 \sin(2t) = 0 \][/tex]

Solving for [tex]\( t \)[/tex] in the interval [tex]\( 0 \leq t \leq 8 \)[/tex] will give us the times at which the velocity is maximized or minimized. Let's solve for [tex]\( t \)[/tex]:

[tex]\[ -18 \cos(3t) = 12 \sin(2t) \][/tex]

This is a transcendental equation and cannot be solved algebraically. We would typically use numerical methods or graphing to find the solutions. However, since we are given that the time when the particle is moving the fastest is [tex]\( t = 4.7 \)[/tex], we can assume that this is the time at which the velocity function reaches its maximum value.

Now, to find the speed at which the particle is moving the fastest, we evaluate the velocity function at [tex]\( t = 4.7 \)[/tex]:

[tex]\[ v(4.7) = -6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7) \][/tex]

Calculating the sine and cosine values and then substituting them into the equation will give us the maximum velocity. Since we are looking for the speed, which is the absolute value of the velocity, we take the absolute value of the result.

The speed is given by the magnitude of the velocity vector, so we have:

[tex]\[ |v(4.7)| = |-6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7)| \][/tex]

Evaluating this expression will give us the speed at which the particle is moving the fastest. The correct answer, rounded to the nearest integer, is [tex]\( 5 \)[/tex] units per time period, not [tex]\( -5 \).[/tex] The negative sign in the velocity does not affect the speed, as speed is a scalar quantity and is always positive.

Therefore, the particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]\( 5 \)[/tex] units per time period.

Answer:

158 square feet

Step-by-step explanation:

The surface area of a prism is found using the following formula: SA = 2(lh+lb+bh). This formula takes the area of each face (6 in total( and adds them together to find a total sum. Substitute l = 8, b = 3 and h = 5 to solve for the surface area.

SA = 2(lh+lb+bh)

SA = 2(8*5+8*3+3*5)

SA = 2(40 + 24 + 15)

SA = 2(79)

SA = 158

The y coordinate of the point which lies on the circle is y = 2√5

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r = 6 units

The point on the circle is P ( x , y )

where the x coordinate is x = 4

So , the point is P ( 4 , y )

And , the equation of circle is given as

x² + y² = r²

On simplifying , we get

x² + y² = ( 6 )²

The point will lies on the circle , so

when x = 4

( 4 )² + y² = ( 6 )²

Subtracting ( 4 )² on both sides , we get

y² = 36 - 16

y² = 20

Taking square roots on both sides , we get

y = ±2√5

The point P lies in the first quadrant , so

y = 2√5

Hence , the y coordinate of the circle is y = 2√5

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ7

Final answer:

Without a specific circle equation, it's impossible to definitively determine the correct y-coordinate for point Q on the circle with an x-coordinate of 4. Additional information such as the circle's center and radius is needed.

Explanation:

The question asks us to identify a possible y-coordinate value for a point Q that lies on a circle with an x-coordinate of 4. Using the information on parametric equations, Pythagorean theorem, and circle equations provided, we can infer that the circle equation might typically be in the form of (x - h)² + (y - k)² = r², where h and k are the coordinates of the center of the circle and r is the radius. However, without a specific equation for the circle in question, we cannot conclusively determine the y-coordinate that corresponds to an x-coordinate of 4 on this circle. Therefore, additional information is required to answer this question correctly.

You're answer to the following question: "Which Point Must be the Centre of the Circle?" Is C

Answer:

D

Step-by-step explanation:

maximum at 12am which is time, t = 0 and 12pm which is time, t = 12

so we’ll use a cosine function since no phase shift is given.

period, T: 1 cycle = 2π and time taken to complete one cycle is 12hrs

T = 2π/(12) = ⅙π

med-line = ½(1 + 2.2) = 1.6

and thus amplitude = 1.6 - 1 = 0.6 or 2.2 - 1.6 = 0.6

h(t) = 0.6 cos(⅙πt ) + 1.6

ANS: D  Can I get brainliest on this please because I only need two more until virtuoso

The function h(t) = 0.6 cos (πt/6) + 1.6 models the height of the tide at Dolphin Beach.

1. To model the height of the tide at Dolphin Beach, we need to consider the given tide heights and times. High tide occurs at 12 a.m. and 12 p.m. with a height of 2.2 meters, and low tide occurs at 6 a.m. and 6 p.m. with a height of 1 meter. This suggests a periodic function with a 12-hour period.

2. The general form for such a function can be a sine or cosine function. Based on the information, we can match the function's characteristics with the function options provided:

3. The cosine function, which starts at its maximum value, would be appropriate, and since the low tide occurs 6 hours later, the function should resemble a cosine function shifted by 6 hours:

Among the options provided h(t) = 0.6 cos (πt/6) + 1.6, perfectly alligns :

Thus, the function h(t) = 0.6 cos (πt/6) + 1.6 models the height of the tide at Dolphin Beach.