Use the substitution method to solve the system of equations. choose the correct ordered pair.
3x- y=3
Y=2x +2

A. (2,6)
B. (5,12)
C. (4,10)
D.(3,8)

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

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:

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:

10 1/2

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]

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]

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

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                                                        

➷ 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 ^-^

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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.

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.

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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:

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

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

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 :

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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.

Answer:

look in picture below :)

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.

Answer:

the mean (average) will change

Step-by-step explanation:

Answer:

the rangue

Step-by-step explanation:

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.

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:

➷ 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:

  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:

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:

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:

A. quadrilateral, parallelogram, rhombus

Step-by-step explanation:

Parallel sides are equal

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:

380

Step-by-step explanation:

11^2 x 3.14 = 380

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:

C

Step-by-step explanation:

We will graph [tex]3^{-x}[/tex]  and  [tex]6^{-x}[/tex]  and find WHERE in the x-axis,  [tex]3^{-x}[/tex]  is greater than  [tex]6^{-x}[/tex].

Attached is the graph of both the functions. RED color graph is of  [tex]3^{-x}[/tex]  and BLUE color graph is of  [tex]6^{-x}[/tex].

So, WHICH WHERE IN X-AXIS IS THE RED GRAPH "ABOVE" THE BLUE GRAPH?

We can clearly see that this occurs when x > 0.

Hence, C is the correct answer.

Answer:

C edge

Step-by-step explanation:

Final answer:

To compare Plan A's increase of 200 homes per year and Plan B's 10% increase per year for a town's housing development, Plan A adds homes linearly, while Plan B's growth is exponential, potentially leading to a larger increase and more significant infrastructure needs over time.

Explanation:

To compare the two growth plans for the town's development—which are Plan A, an increase of 200 homes per year, and Plan B, a 10% increase each year—we need to analyze the two scenarios mathematically.

Under Plan A, the town will add a fixed number of homes each year, that is, 200 homes. After one year, the total will be 1200 homes, after two years 1400 homes, and this pattern will continue linearly.

Plan B's 10% annual increase results in exponential growth. Starting with 1000 homes, in the first year, there will be 1000 + (10% of 1000) = 1100 homes. The second year, the growth will be based on the new total, so it will be 1100 + (10% of 1100) = 1210 homes, and this pattern will continue to result in an increasingly larger number of homes added each year.

In terms of the community's development, Plan A adds homes predictably and steadily, while Plan B accelerates growth over time. This could lead to a boom in construction and investment depending on the current needs and infrastructure of the town.

Plan B's compound growth could lead to a much larger number of homes in the long run, but might require more significant investment in infrastructure and services as the growth compounds.