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Express the answer as [tex]a^n[/tex].
[tex](3^2)^6 * (4^2)^4[/tex]

Answer:

Year = 1995 and population = 315

Year = 2015 and population = 715

Step-by-step explanation:

It is given that the population of two different villages is modeled by the given equations:

[tex]y=x^2-30x+540[/tex]

[tex]y=20x+15[/tex]

The population of both villages are same after x years after 1980 if

[tex]x^2-30x+540=20x+15[/tex]

[tex]x^2-30x+540-20x-15=0[/tex]

[tex]x^2-50x+525=0[/tex]

Splitting the middle term, we get

[tex]x^2-15x-35x+525=0[/tex]

[tex]x(x-15)-35(x-15)=0[/tex]

[tex](x-15)(x-35)=0[/tex]

[tex]x=15,35[/tex]

It means, after 15 or 35 years, the population will same.

For x=15, years is [tex]1980+15=1995[/tex] and population is  

[tex]y=20(15)+15=315[/tex]

For x=35, years is [tex]1980+35=2015[/tex] and population is  

[tex]y=20(35)+15=715[/tex].

Therefore, population are equation in Year = 1995 and population = 315 or Year = 2015 and population = 715.

Year = 1995 and population = 315

Year = 2015 and population = 715

The equation is

[tex]y = x^2 - 30x + 540\\\\y = 20x + 15[/tex]

Now

[tex]x^2 - 30x + 540 = 20x + 15\\x^2 - 30x + 540 - 20x - 15=0\\\\x^2 - 50x + 525 = 0\\\\x^2 - 35x - 15x + 525=0\\\\x(x - 15) -35(x-15) = 0\\\\(x-15) (x-35) = 0[/tex]

x = 15,35

so,

When x is 15 , the population is = 20(15 )  +15 = 300 + 15 = 315

And, x is 35 , the population is = 20(35 )  +15 = 700 + 15 = 715

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Answer:

Step-by-step explanation:

Zeros mean basically the values of x which make y = 0.

(x + 4)(x - 1) = y

x^2 + 3x - 4 would be a quadratic function whose zeros are -4 and 1

Answer: (-6,10)

Step-by-step explanation:

Since you are reflecting over the y-axis, the x value becomes the negative

The coordinates for R' the reflected point are (-6,10).

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.

If you study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

Thus, if you're reflecting a point (x,y) along x axis, then its

f=x

abscissa will stay same but

f=y

ordinates will negate. Thus (x,y) turns to (x, -y)

Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)

We are given that;

The point R(6, 10)

Now,

When reflecting a point over the y-axis, we simply negate the x-coordinate while keeping the y-coordinate the same.

So, to reflect point R(6,10) over the y-axis, we flip its x-coordinate to get R'(-6,10).

Therefore, by reflection answer will be (-6,10).

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Answer:

x = 3 or x = -1

Step-by-step explanation:

     25^x = 5^(x^2 - 3)

<=> (5^2)^x = 5^(x^2 - 3)

<=> 5^(2x) = 5^(x^2 - 3)

<=> 2x = x^2 - 3

<=> x^2 - 2x - 3 = 0

<=> x^2 + x - 3x - 3 = 0

<=> x(x + 1) - 3(x + 1) = 0

<=> (x - 3)(x + 1) = 0

<=> x = 3 or x = -1

I hope this helps!

Answer:

I think the correct answer is

A. (-2)

Step-by-step explanation:

This answer seems the most reasonable compared to the others

Hope this helps!

Answer: (-2)

Step-by-step explanation: The international standard symbol for inch is in (see ISO 31-1, Annex A) but traditionally the distance is denoted by a double prime, which is often approximated by double quotes, and the foot by a prime, which is often approximated by an apostrophe. For example, three feet two inches can be written as 3′ 2″. Symbol: in or ″ (the double prime)

HOPE IT HELPS!

Angle a = 1/2 of the given central angle.

Angle a = 130/2= 65

The answer is 65

Answer:

B.

Step-by-step explanation:

Using Pythagoras theorem

c² = a²+b²

Where c = hypotenuse, a = base and b = perpendicular

So putting the givens

c² = (2√5)² + (6)²

c² = 20+36

c² = 56

Taking square root on both sides, we get

c = √2×2×14

c = 2√14

Answer: m∠3 = 30° and  m∠8=  150°  .

Step-by-step explanation:

From the given figure it can be seen that a and b are two parallel lines, where t is transversal intersecting them.

Also, m∠3=x,  m∠8=5x

To find : m∠3, m∠8

Since ∠3=∠5 [Interior alternate angles]

So, m∠5 =m∠3= x

Also, ∠5+∠8=180°  [Linear pair]

⇒ x + 5x = 180°   [Substituted the value of ∠5 and ∠8 in terms of x ]

⇒ 6x = 180°

⇒ x = 30° [Divide both sides by 6]

That means,

m∠3 = 30°

and m∠8= 5(30° ) = 150°

Hence, m∠3 = 30° and  m∠8=  150°  .

Answer:

Connie, Josie, Patrick, Mimi, Emma

I took the test, I hope this helps! Its okay, but I tried the answer above, and it wasn't correct

Connie, Josie, Patrick, Mimi, and Emma are the farmers that had more cows than other farmers.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

We know that the number of cows is shown on the graph on the y-axis.

The number of pigs is shown on the x-axis of the graph.

we can conclude from the graph that Connie, Josie, Patrick, Mimi, and Emma had more cows than the other farmers.

If we add all of them that would become greater than others.

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Answer:

Central angle of θ

[tex]\dfrac{A}{\pi r^2} =\dfrac{\theta}{2\pi}[/tex]

[tex]A=\dfrac{\theta r^2}{2}, (\theta$ in radians)[/tex]

Step-by-step explanation:

Suppose a sector of a circle with radius r has a central angle of θ.

Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the central angle of θ to the measure of a full rotation of the circle.

A full rotation of a circle is 2π radians.

This proportion can be written as:  [tex]\dfrac{A}{\pi r^2} =\dfrac{\theta}{2\pi}[/tex]

Multiply both sides by [tex]\pi r^2[/tex]

[tex]\dfrac{A}{\pi r^2} *\pi r^2=\dfrac{\theta}{2\pi}*\pi r^2[/tex]

Simplify to get:

[tex]A=\dfrac{\theta r^2}{2}[/tex]

Where θ is the measure of the central angle of the sector and r is the radius of the circle.

Answer:

Suppose a sector of a circle with radius r has a central angle of θ. Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the CENTRAL ANGLE to the measure of a full rotation of the circle. A full rotation of a circle is 2π radians. This proportion can be written as A/πr^2 =θ2π. Multiply both sides by πr2 and simplify to get A= θ/2 r^2 , where θ is the measure of the central angle of the sector and r is the radius of the circle.

Step-by-step explanation:

i hope this helps a bit

Answer:

250

Step-by-step explanation:

1000 divided by 4 is 250

Answer:

See explaination

Step-by-step explanation:

All these questions can be solved remembering that the area of a triangle is the base*height/2

1) 9.8*3.6/2 = 17.64

2) 14*35/2  = 245

3) 8.4*6.9/2 = 28.98

4) For this one, it is important to realize that if a triangle contains 2 perpendicular lines, it is a right triangle, and therefore, those two lines must be the base and the height. So the answer is just 1.8*2.5/2 = 2.25

5)3.2*9.6/2 = 15.36

Answer:

first is 17.64cm second is 245m third is 28.98cm fourth is 15.36

Answer:

52

Step-by-step explanation:

Answer:

x= 12

Step-by-step explanation:

Please see attached picture for full solution.

Feel free to ask if you have any queries :)

Answer:

42°

Step-by-step explanation:

all triangles have 180 degrees, you are given 48. the symbol above 48 tells you it is 90 degrees. ther fore you can use 180- 90 - 48= 42

Answer:

[tex]a_{n}[/tex] = 100n - 112

Step-by-step explanation:

Given the recursive formula

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 100 with a₁ = - 12

This tells us that any term is found by adding 100 to the previous term

That is common difference d = 100 and a₁ = - 12

The explicit formula for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d , thus

[tex]a_{n}[/tex] = - 12 + 100(n - 1) = - 12 + 100n - 100 = 100n - 112

Answer:

100 = 100n - 112

Step-by-step explanation:

Answer:

2(20-64)

Step-by-step explanation:

4*10-64*2

40-128

2(20-64)

Answer:

$0.17

Step-by-step explanation:

2.04/12=0.17

Please mark as Brainliest! :)

Have a nice day.

Answer: 0.17 for 1 pencil

Step-by-step explanation:

Attached the work.

Answer:

I think its I,II,III

because first r+q = 90 as we'll as z= 90

second s and z are vertically opposite angles and so are equal

third x+s+r= 180 degrees because they are on a straight line

Answer:

A. 6

E. -4

Step-by-step explanation:

x² - 2x - 24 = 0

x            - 6

x              4

(x - 6)(x + 4) = 0

Set each parenthesis equal to 0:

(x - 6) = 0

Isolate the variable, x. Add 6 to both sides;

x - 6 (+6) = 0 (+6)

x = 0 + 6

x = 6

(x + 4) = 0

Isolate the variable, x. Subtract 4 from both sides:

x + 4 (-4) = 0 (-4)

x = 0 - 4

x = -4

x = -4, 6 are your solutions, or A. &  E.

~

Answer:

[tex] \boxed{A. \: 6 \: \: \: and \: \: \: E. \: -4} [/tex]

Step-by-step explanation:

[tex] = > {x}^{2} - 2x - 24 = 0 \\ \\ = > {x}^{2} - (6 - 4)x - 24 = 0 \\ \\ = > {x}^{2} - 6x + 4x - 24 = 0 \\ \\ = > x(x - 6) + 4(x - 6) = 0 \\ \\ = > (x - 6)(x + 4) = 0 \\ \\ = > x - 6 = 0 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: x + 4 = 0 \\ \\ = > x = 6 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: x = - 4[/tex]

Answer:

(3y - 11z)2

Step-by-step explanation:

hahaha hello again

Step-by-step explanation:

(3y - 11z)(3y - 11z)

9y^2: 3y 3y

121z^2: 11z 11z

(3y - 11z)(3y - 11z)

9y^2 - 33yz - 33yz + 121z^2

9y^2 - 66yz + 121z^2

Answer:

It is d

Step-by-step explanation:

I did the test

Answer:

d

Step-by-step explanation:

An Irrational Number is a real number that cannot be written as a simple fraction.

one of the examples is [tex]\pi[/tex]

Answer:

The correct option is;

BC = 4 cm and DE = 4 cm

Step-by-step explanation:

The given sides parameters are;

In ΔABC

AB = 3 cm

AC = 5 cm

In ΔDEF

CD = 3 cm

CE = 5 cm

We note that the point F on ΔDEF is the same as point C on ΔABC

For the two triangles to be congruent, the third side must be equal hence e have;

Where ∠B = ∠D = 90°

Hence, AC² = AB² + BC²

∴ BC = √(5² - 3²) = 4

Similarly,

CE² = CD² + DE²

∴ DE = √(5² - 3²) = 4

Hence the additional information needed to prove that ΔABC ≅ ΔDEF is BC = 4 cm and DE = 4 cm.

Answer:

The answer would be, 81cm.

Step-by-step explanation:

36÷4=9

9×9=81

Answer:

490.1

Step-by-step explanation:

A=2πrh+2πr2=2·π·6·7+2·π·62≈490.08845

Answer: Lis saved $1166.4 .

Step-by-step explanation:

Given , Ellen saved $2000 and she spent 10% of it to buy a bike.

Then, Ellen's left saving = saved amount - 10% of  (saved amount)

= $2000 - 0.10 x $2000 [We convert perecntage to decimal by diving it by 100]

= $2000 - $200

= $1800

So, Ellen's left saving= $1800

Also, Kim saved 8% more than that of Ellen's left savings.

Kim's Saving = Ellen's left saving + 8% of (Ellen's left saving)

= $1800  + (0.08) x ($1800) [We convert perecntage to decimal by diving it by 100]

= $1800 +  $144

i.e. Kim's Saving= $1944

If Lisa saved 60% as much as Kim, then Lisa's saving  = 60% of (Kim's Saving)

= (0.60) x ($1944) [We convert perecntage to decimal by diving it by 100]

i.e. Lisa's saving = $1166.4

Answer:

1166.40

Step-by-step explanation:

i got it right on my test.

Answer:

1.33 or 133/100

Step-by-step explanation:

formula=area of base x height x 1/3

A=2 x 2 x 1/3 or

A=2 x 2 / 3

A=4 / 3

A=1.33 or 133/100

Answer:

The answer is 4/3 ft^3

Step-by-step explanation:

The formula to find a pyramid is length times width times height divided by 3

Answer:

25 minutes.

Step-by-step explanation:

We can set up an equation: 3/30=2.5/n. This situation is directly proportional, since the number of minutes increases as the runner runs more miles.

We can cross multiply: 3n=30*2.5

3n=75

n=25

Answer:if the answer your looking for is the area, then it’s 16.15

Step-by-step explanation: