The population of Arlington High School can be modeled using the equation P(t)=3,500(1.027)^t , where t represents the number of years since 2010. Is the population of Arlington High increasing or decreasing? Explain how you can tell using the equation. What would the population be after 29 years?

Answer:

x = 14

Step-by-step explanation:

Add 10 to both sides.

x− 10 + 10 = 4 + 10

x=14

Answer:

62

Step-by-step explanation:

Khan Academy. I got this correct, so trust me :)

The measurement of the angle A for the considered triangle is found being of 62° approximately.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

For the considered triangle, we can use sine rule.

In triangle ABC, we're given that:

The side opposite to angle A is BC and the side opposite to angle B is AC. Thus, by sine law, we get:

[tex]\dfrac{\sin(m\angle A)}{|BC|} = \dfrac{sin(m\angle B)}{|AC|}\\\\\dfrac{\sin(m\angle A)}{15} = \dfrac{\sin(28^\circ)}{8}\\\\\sin(m\angle A ) \approx \dfrac{15 \times 0.46947}{8} \approx 0.88026\\\\m\angle A \approx \sin^{-1}(0.88026)\\\\m\angle A \approx 61.67^\circ, 118.32^\circ[/tex]

But since angle A is acute(angle with measure of less than 90 degrees), thus, m∠A ≈ 61.67° ≈ 62°

Thus, the measurement of the angle A for the considered triangle is found being of 62° approximately.

Learn more about law of sines here:
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Answer:

it's area is 1/2 b×h

1/2×7×3.8

13.3

Answer:

13.3 ft^2

Step-by-step explanation:

area = base x h / 2

A = 7 x 3.8 / 2

A = 26.6 / 2

A = 13.3 ft^2

Answer:

0.51 and 11.24 seconds.

Step-by-step explanation:

The height h of a rocket with an initial upward velocity of 188 feet per second after t seconds is modeled by the function:

[tex]h(t)=188t-16t^2[/tex]

And we want to find all values of t for which the rocket's height is 92.

So, we can set h(t) = 92 and solve for t:

[tex]92=188t-16t^2[/tex]

We can divide everything by four:

[tex]23=47t-4t^2[/tex]

Rearrange the equation:

[tex]4t^2-47t+23=0[/tex]

We can use the quadratic formula:

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

In this case, a = 4, b = -47, and c = 23. Substitute:

[tex]\displaystyle x=\frac{-(-47)\pm\sqrt{(-47)^2-4(4)(23)}}{2(4)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{47\pm\sqrt{1841}}{8}[/tex]

Hence, our two solutions are:

[tex]\displaystyle x=\frac{47+\sqrt{1841}}{8}\approx 11.24\text{ or } x=\frac{47-\sqrt{1841}}{8}\approx0.51[/tex]

So, the rocket reaches a height of 92 feet after 0.51 seconds and again after 11.24 seconds.

Answer:

y = 3/4x - 5

Step-by-step explanation:

An equation of a line can be written in slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

Let's plug in what we know.

The slope is 3/4.

y = 3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the point (4, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/4(4) + b

To find b, multiply the slope and the input of x(4)

-2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-5 = b

Plug this into your standard equation.

y = 3/4x - 5

This is your equation. It has a slope of 3/4, and passes through (4, -2)

Hope this helps!

Answer:

$1.42

Step-by-step explanation:

Ava buys a book for $8.58

She pays with a $10 bill

Hence her change would be

= 10-8.58

= 1.42

Ava change is $1.42

Answer:

[tex]k = 1[/tex]

Step-by-step explanation:

Given

[tex]3y = 5x + k[/tex]

Opposite points: [tex](1,-2)[/tex] and [tex](-2,1)[/tex]

Required

Find k

First, calculate the midpoint of the opposite points.

[tex](x,y) = 0.5(x_1 + x_2,y_1 + y_2)[/tex]

This gives:

[tex](x,y) = 0.5(1 -2,-2 + 1)[/tex]

[tex](x,y) = 0.5(-1,-1)[/tex]

Open bracket

[tex](x,y) = (-0.5,-0.5)[/tex]

The equation [tex]3y = 5x + k[/tex] becomes:

[tex]3 * -0.5 = 5 * -0.5 + k[/tex]

[tex]-1.5 = -2.5 + k[/tex]

Solve for k

[tex]k = 2.5-1.5[/tex]

[tex]k = 1[/tex]

Answer: Most views  mayber black panther

Step-by-step explanation:

Answer:

556.5 cm²

Step-by-step explanation:

Area of trapezium :

Area = 1/2 (a + b)h

a = base length 1

b = base length 2

h = height

From the information given :

Distance between MN and PQ = Height, h = 21 cm

Base MN, a = 28 cm

Base PQ, b = 25 cm

Hence,

Area = 1/2 (28 + 25) * 21

Area = 1/2 (53) * 21

Area = 556.5 cm²

Answer:

1100 Inches Squared

Step-by-step explanation:

Let the triangle on the top right be - (i)

Let the triangle on the top left be - (ii)

Let the bottom rectangle be - (iii)

1) The base of the triangle (i) = 10 + (20/2) (It is the base of the rectangle halfed + the given amount of half base of the triangle)

=> 10 + 10

=> 20 in

Base = 20 in

Height = 30 in

Area = 1/2 * 20 * 30

=> 10 * 30

=> 300 in

Triangle (i) = (ii)

So, the area of triangle (ii)

=> 300 in

Area of rectangle,

Length * Breadth

=> 20 * 30

=> 500 in

Total arrow's area = 300 + 300 + 500 (i + ii + iii)

=> 1100

Therefore the total area of the shape = 1100 in squared.

Hope it helps :)

Answer:

3.75

Step-by-step explanation:

Answer:

The area of each figure is:

Step-by-step explanation:

To find the area of that figure, first, we're gonna find the area of the rectangle and next the area of the triangle, to make this we need to identify the measurement of each one, the rectangle has 2 units wide and 5 units high, then, we use the next formula:

Now, we identify the measurements of the triangle (base = 4 units, height = 5 units) and we use the formula:

And we obtain the area of the whole figure when we add the two areas:

As you can see, the area of the picture is 20 square units.

Answer:

22=2x+6

Step-by-step explanation:

you subtract 6 from both sides

that leaves u with 16=2x

then divide 2 by 16 and that equals

8

so 8=x

each game costs $8

you put the 2 in front of the x in the beginning due to Toni playing 2 games while the shoes are a one time fee.

Answer:

28 degrees

Step-by-step explanation:

147 - 119 = 28

Answer:

Step-by-step explanation:

Since we already know that PQR is 147 degrees, we just need to subtract PQR to QR, and you will get, (147 - 119), PQ as 28 degrees!

Answer:

A and B

Step-by-step explanation:

96% of 25

= [tex]\frac{96}{100}[/tex] × 25 ( per cent means out of 100 ) → A

= 0.96 × 25 ( divide 96 by 100 ) → B

Answer:

56 inches squared

Step-by-step explanation:

(4x6) ÷ 2 = 12

12 x 4 = 48

4 x 4 = 16

48 + 16 = 56

Answer:

f^-1(-32)=6

Step-by-step explanation:

Find the inverse of the function f(x)=4-6x:

f(x)=4-6x

y=4-6x

x=4-6y

x-4=-6y

(x-4)/-6=y

-1/6x+2/3=y

y=-1/6x+2/3

f^-1(x)=-1/6x+2/3

Plug in f^-1(-32) for f^-1(x) and simplify:

f^-1(-32)=-1/6(-32)+2/3

f^-1(-32)=16/3+2/3

f^-1(-32)=18/3

f^-1(-32)=6

Answer:

The modes are 0 and 2. There are two because there are the same number of numbers. (four 0s and four 2s)

Answer:

B. 5/16

Step-by-step explanation:

Multiply each side by the reciprocal of 2/5 to solve for x

(2/5)(1/8)=x

2/16=x

Answer:

Polynomial

[tex]x^4 +3x^3 -5x^2 -7x +20\\\\x^3 -2x^2 +x -12\\\\x^2 + 3x^5 -6x +12x^3[/tex]

not a polynomial

[tex]4\sqrt[3]{x} -\sqrt{x} -20\\\\x^{-3}-x}^{-2}-6x^{-1}+8\\\\\frac{5}{x^3} -\frac{1}{x^2} +\frac{8}{x} -40\\\\[/tex]

Answer:

18

Step-by-step explanation:

Answer:

778.5

Step-by-step explanation:

Area of any regular polygon = ( apothem * side length * number of sides ) divided by 2

Given information:

Apothem = 15

Side length = 17.3

Polygon Type = Hexagon ( its important to note that a hexagon has 6 sides )

* Plug in the given values into the formula *

Area = [tex]\frac{15*17.3*6}{2}[/tex]

15 * 17 = 259.5

259.5*6=1557

[tex]\frac{1557}{2} =778.5[/tex]

Hence, area = 778.5 square units

Answer:

778.5

Step-by-step explanation:

Answer:

55 tickets for adults

Step-by-step explanation:

Start by setting up two equations. One equation will be the total amount of money spent and the other is the total amount of tickets sold. a is the # of adult tickets and c is the # of children tickets sold.

7a+4c=469

a+c=76

Now solve for c in the second equation. Then use that to substitute for c in the first equation.

c=76-a

7a+4(76-a)=469

7a+ 304-4a =469

7a+4a=165

3a=165

a=165/3

a=55

Answer: 12

Step-by-step explanation:

Answer:

33.8

Step-by-step explanation:

a²+b²=c²

15²+b²=37²

225+b²=1369

-225     -225

b²=1144

√1144

b=33.8

The distance from the bottom of the ladder to the bottom of the building would be 33.8 foot.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

If you place a 37-foot ladder against the top of a 15-foot building.

Let BC be the distance from the bottom of the ladder to the bottom of the building.

[tex]|AC|^2 = |AB|^2 + |BC|^2 \\15^2+BC^2=37^2\\225 + BC^2=1369\\BC^2 = 1369 - 225\\\\BC^2 = 1144\\\\BC = 33.8[/tex]

Learn more about Pythagoras' theorem here:

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Answer:

184.96

Step-by-step explanation:

V = (base × height) ÷ 3

base = pi × radius^2

2 × pi × radius = circumference

2×pi×r = 29.516

÷2 ÷2

pi×r = 14.758

÷3.14 ÷3.14

r=4.7

base= 3.14 × 4.7^2

= 69.36

V = (69.36 × 8) ÷ 3 = 184.96

Answer:

50

Step-by-step explanation:

x= the number of pounds of the tropical taffy that should be used

You need to take the value of the Tropical Taffy + the value of the Passion Fruit taffy to = the value of Tropical Passion

value- price per pound times the number of pounds

Your equation is going to look like this-->

5.50x+6.25(100)=6(x+100)

5.50x+625=6x+600

-5.50x        -5.50x

625=0.5x+600

-600         -600

25=0.5x

50=x

Hope this helps!

Answer:

Here.

Step-by-step explanation:

Step-by-step explanation:

BC is tangent to the circle at point B.

Therefore, by tangent-radius theorem:

Step-by-step explanation:

BC is tangent to the circle at point B.

Therefore, by tangent-radius theorem:

Answer:

16 tiles

Because there are 4 parts in 4/4 and the  if you have 4 of the four parts that is 16.