Admission for a state fair is $10, and each ride ticket is $2.50.Write an expression to represent the situation.

Answer: see below

Step-by-step explanation:

30 - 60 - 90 triangles have angles in the triangle measuring 30, 60, and 90 degrees. A 30 - 60 - 90 triangle also has special side ratios according to a side's location in the triangle.

The side across from the 30 degree angle is represented by x.

The side across from the 60 degree angle is represented by x[tex]\sqrt{3}[/tex].

The side across from the 90 degree angle is represented by 2x.

45 - 45 - 90 triangles have angles in the triangle measuring 45, 45, and 90 degrees. A 45 - 45 - 90 triangle has special side ratios similar to the 30 - 60 - 90 triangle.

The side across from either of the 45 degree angles is represented by x.

The side across from the 90 degree angle is represented by x[tex]\sqrt{2}[/tex].

These ratios can be used to find missing sides. If you know that a triangle is one of these special triangles and you also know one of its side lengths, you can plug the known length in for x in the proper place.

EX: you have a 30 - 60 - 90 triangle with a side length of 2 across from the 30 degree angle. You then know that the side across from 60 is 2[tex]\sqrt{3}[/tex] and the side across from 90 is 4.

Answer:

[tex]\large\boxed{a=4\sqrt3}[/tex]

Step-by-step explanation:

We have the triangle 30° - 60° - 90°.  In that triangle sides are in proportion

1 : √3 : 2 (look at the picture).

We have

[tex]a\sqrt3=12[/tex]         multiply both sides by √3   (use √a · √a = a)

[tex]3a=12\sqrt3[/tex]       divide both sides by 3

[tex]a=4\sqrt3[/tex]

[tex]b=2a\to b=2(4\sqrt3)=8\sqrt3[/tex]

Answer:

Part 2) [tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex] or [tex]P=22.36\ units[/tex]

Part 4) [tex]P=[19+\sqrt{17}]\ units[/tex] or [tex]P=23.12\ units[/tex]

Part 6) [tex]A=36\ units^{2}[/tex]

Part 8) [tex]A=16\ units^{2}[/tex]

Part 10) [tex]A=6.05\ units^{2}[/tex]  

Step-by-step explanation:

we know that

The formula to calculate the distance between two points is equal to  

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]  

Part 2) we have the rectangle ABCD

[tex]A(-4,-4),B(-2,0),C(4,-3),D(2,-7)[/tex]

Remember that in a rectangle opposite sides are congruent

step 1

Find the distance AB

[tex]A(-4,-4),B(-2,0)[/tex]

substitute in the formula

[tex]AB=\sqrt{(0+4)^{2}+(-2+4)^{2}}[/tex]  

[tex]AB=\sqrt{(4)^{2}+(2)^{2}}[/tex]  

[tex]AB=\sqrt{20}\ units[/tex]  

step 2

Find the distance BC

[tex]B(-2,0),C(4,-3)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-3-0)^{2}+(4+2)^{2}}[/tex]  

[tex]BC=\sqrt{(-3)^{2}+(6)^{2}}[/tex]  

[tex]BC=\sqrt{45}\ units[/tex]  

step 3

Find the perimeter

The perimeter is equal to

[tex]P=2[AB+BC][/tex]

substitute

[tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex]

or

[tex]P=22.36\ units[/tex]

Part 4) we have the quadrilateral ABCD

[tex]A(-2,-3),B(1,1),C(7,1),D(6,-3)[/tex]

step 1

Find the distance AB

[tex]A(-2,-3),B(1,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1+3)^{2}+(1+2)^{2}}[/tex]  

[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]  

[tex]AB=5\ units[/tex]  

step 2

Find the distance BC

[tex]B(1,1),C(7,1)[/tex]

substitute in the formula

[tex]BC=\sqrt{(1-1)^{2}+(7-1)^{2}}[/tex]  

[tex]BC=\sqrt{(0)^{2}+(6)^{2}}[/tex]  

[tex]BC=6\ units[/tex]  

step 3

Find the distance CD

[tex]C(7,1),D(6,-3)[/tex]

substitute in the formula

[tex]CD=\sqrt{(-3-1)^{2}+(6-7)^{2}}[/tex]  

[tex]CD=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]  

[tex]CD=\sqrt{17}\ units[/tex]  

step 4

Find the distance AD

[tex]A(-2,-3),D(6,-3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(-3+3)^{2}+(6+2)^{2}}[/tex]  

[tex]AD=\sqrt{(0)^{2}+(8)^{2}}[/tex]  

[tex]AD=8\ units[/tex]  

step 5

Find the perimeter

The perimeter is equal to

[tex]P=AB+BC+CD+AD[/tex]

substitute

[tex]P=[5+6+\sqrt{17}+8]\ units[/tex]

[tex]P=[19+\sqrt{17}]\ units[/tex]

or

[tex]P=23.12\ units[/tex]

Part 6) Calculate the area of rectangle ABCD

[tex]A(-1,5),B(3,5),C(3,-4),D(-1,-4)[/tex]

Remember that in a rectangle opposite sides are congruent

step 1

Find the distance AB

[tex]A(-1,5),B(3,5)[/tex]

substitute in the formula

[tex]AB=\sqrt{(5-5)^{2}+(3+1)^{2}}[/tex]  

[tex]AB=\sqrt{(0)^{2}+(4)^{2}}[/tex]  

[tex]AB=4\ units[/tex]  

step 2

Find the distance BC

[tex]B(3,5),C(3,-4)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-4-5)^{2}+(3-3)^{2}}[/tex]  

[tex]BC=\sqrt{(-9)^{2}+(0)^{2}}[/tex]  

[tex]BC=9\ units[/tex]  

step 3

Find the area

The area is equal to

[tex]A=[AB*BC][/tex]

substitute

[tex]A=[4*9]=36\ units^{2}[/tex]

Part 8) Calculate the area of right triangle ABC

[tex]A(-3,3),B(-3,-1),C(5,-1)[/tex]

step 1

Find the distance AB

[tex]A(-3,3),B(-3,-1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(-1-3)^{2}+(-3+3)^{2}}[/tex]  

[tex]AB=\sqrt{(-4)^{2}+(0)^{2}}[/tex]  

[tex]AB=4\ units[/tex]  

step 2

Find the distance BC

[tex]B(-3,-1),C(5,-1)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-1+1)^{2}+(5+3)^{2}}[/tex]  

[tex]BC=\sqrt{(0)^{2}+(8)^{2}}[/tex]  

[tex]BC=8\ units[/tex]  

step 3

Find the distance AC

[tex]A(-3,3),C(5,-1)[/tex]

substitute in the formula

[tex]AC=\sqrt{(-1-3)^{2}+(5+3)^{2}}[/tex]  

[tex]AC=\sqrt{(-4)^{2}+(8)^{2}}[/tex]  

[tex]AC=\sqrt{80}\ units[/tex] -----> is the hypotenuse

step 4

Find the area

The area is equal to

[tex]A=(1/2)AB*BC[/tex]

substitute

[tex]A=(1/2)(4*8)=16\ units^{2}[/tex]

Part 10) Calculate the area of triangle ABC

[tex]A(3,0),B(1,8),C(2,10)[/tex]

step 1

Find the distance AB

[tex]A(3,0),B(1,8)[/tex]

substitute in the formula

[tex]AB=\sqrt{(8-0)^{2}+(1-3)^{2}}[/tex]  

[tex]AB=\sqrt{(8)^{2}+(-2)^{2}}[/tex]  

[tex]AB=\sqrt{68}\ units[/tex]  

step 2

Find the distance BC

[tex]B(1,8),C(2,10)[/tex]

substitute in the formula

[tex]BC=\sqrt{(10-8)^{2}+(2-1)^{2}}[/tex]  

[tex]BC=\sqrt{(2)^{2}+(1)^{2}}[/tex]  

[tex]BC=\sqrt{5}\ units[/tex]  

step 3

Find the distance AC

[tex]A(3,0),C(2,10)[/tex]

substitute in the formula

[tex]AC=\sqrt{(10-0)^{2}+(2-3)^{2}}[/tex]  

[tex]AC=\sqrt{(10)^{2}+(-1)^{2}}[/tex]  

[tex]AC=\sqrt{101}\ units[/tex]  

step 4

we know that  

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  

a,b,c be the lengths of the sides of a triangle.  

The area is given by:  

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]  

where  

p is half the perimeter  

p=[tex]\frac{a+b+c}{2}[/tex]  

we have  

[tex]a=AB=\sqrt{68}=8.25\ units[/tex]  

[tex]b=BC=\sqrt{5}=2.24\ units[/tex]  

[tex]c=AC=\sqrt{101}=10.05\ units[/tex]  

p=[tex]\frac{8.25+2.24+10.05}{2}=10.27\ units[/tex]  

Find the area

[tex]A=\sqrt{10.27*(10.27-8.25)(10.27-2.24)(10.27-10.05)}[/tex]  

[tex]A=\sqrt{10.27*(2.02)(8.03)(0.22)}[/tex]  

[tex]A=6.05\ units^{2}[/tex]  

Answer:

The answer is AB.

Choice D.

Step-by-step explanation:

We are given four blood types and the number of females and males having each of the blood type. We are to determine the blood type that is independent of the gender.

It is evident that the disparity in the number of males and females in the blood types A, B and O is large.

Only in the blood type AB, the difference is very small. The number of males and females having AB blood type is more or less same. So, we can conclude that blood type AB is independent of gender.

Answer:

* Domain: all reals except multiples of 2π

* Range: (-∞ , -2] ∪ [2 , ∞)

Step-by-step explanation:

* Lets revise the period, the domain and the range of csc(x)

- The period of csc(x) is 2π

- To find the period of csc(x) use 2π / coefficient of x

- The domain of csc(x) is all x ≠ nπ

- The range is y ≤ -1 , y ≥ 1

* Lets revise the vertical and the horizontal stretch and compress

- A vertical stretching is the stretching of the graph away from

the x-axis

• if k > 1, the graph of y = k•f(x) is the graph of f(x) vertically

 stretched by multiplying each of its y-coordinates by k.

- A vertical compression is the squeezing of the graph toward

 the x-axis.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

  by multiplying each of its y-coordinates by k.

- A horizontal stretching is the stretching of the graph away from

 the y-axis

• if 0 < k < 1 (a fraction), the graph is f (x) horizontally stretched by

 dividing each of its x-coordinates by k.

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

• if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally

 compressed by dividing each of its x-coordinates by k

∵ f(x) = 2csc(x/2)

- The coefficient of x is 1/2

∵ The period of x = 2π

∴ The period of x/2 = 2π/1/2 = 4π

∵ The domain of csc(x) is all x ≠ nπ

∴ The domain of csc(x/2) is all x ≠ n2π

∵ f(x) = 2csc(x/2)

∵ csc(x/2) multiplying by 2

- That means every y-coefficient multiplying by 2

∵ The range of csc(x/2) is y ≤ -1 and y ≥ 1

∴ The rang of f(x) = 2csc(x/2) is y ≤ -1(2) and y ≥ 1(2)

∴ The rang of f(x) = 2csc(x/2) is y ≤ -2 and y ≥ 2

* Domain: all reals except multiples of 2π

* Range: (-∞ , -2] ∪ [2 , ∞)

* Look to the graph attached

- The red is y = csc(x)

- The blue is f(x) = 2csc(x/2)

Answer:

increasing the radius makes the circle larger.  (Answer B)

Step-by-step explanation:

The formula for the area of a circle is A = πr².  Hence, Area of a Circle depends solely on the variable r and the constant of proportionality π.

Thus, increasing the radius makes the circle larger.

Answer:

H(t)= -16t^2+40t+1.2

Step-by-step explanation:

H(t) = -16t^2 + vt + s

I hope this is what you were looking for.

Answer:

Events C and D are  mutually exclusive.

P(C ∩ D) = 0

Step-by-step explanation:

We notice that event C is even numbers and Event D is odd number.  We cannot roll a die and have both events occur at the same time.  That means they are mutually exclusive.  Either one event occurs or the other occurs.

P(C ∩ D) = 0  This means the events do not intersect (overlap).  Or are mutually exclusive.

Answer:

The radius of the cylinder is [tex]11.5\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]V=2,908.33\ in^{3}[/tex]

[tex]h=7\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values and solve for r

[tex]2,908.33=(3.14)r^{2}(7)[/tex]

[tex]r^{2}=2,908.33/[(3.14)(7)][/tex]

[tex]r=11.5\ in[/tex]

Answer:

  B) [tex]\left[\begin{array}{cc}1&0\\0&-1\end{array}\right][/tex]

Step-by-step explanation:

When the coordinates are represented by a column vector, the vertical reflection transformation (x, y) ⇒ (x, -y) looks like the matrix of answer choice B.

Answer:

Option B

[tex]g(x) = -6x^2[/tex]

Step-by-step explanation:

If the graph of the function [tex]g(x)=cf(x)[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

In this problem we have the function [tex]f(x)=x^2[/tex]  

We now that this function  is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis

Then  [tex]|c| =6 >0[/tex]  and [tex]c=-6<0[/tex]

Therefore the graph of [tex]g(x)[/tex] is [tex]g(x) = -6f(x)[/tex]

[tex]g(x) = -6x^2[/tex]

Answer:

10 cm

Step-by-step explanation:

Answer:

10 cm

Step-by-step explanation:

Since, the volume of a cuboid is,

V = l × w × h,

Where,

l = length,

w = width,

h = height,

∵ The shape of the aquarium must be cuboid,

We have, l = 20 cm, w = 12 cm, V = 2400 cm³,

By substituting the values,

2400 = 20 × 12 × h

2400 = 240h

[tex]\implies h = \frac{2400}{240}=10[/tex]

Hence, the height of the water in Nemo's aquarium would be 10 cm.

Answer:

[tex]36\ liters\ of\ soil[/tex]

Step-by-step explanation:

we know that

The ratio of soil, manure and leaf mould is [tex]3:1:2[/tex]

That means

For every 6 liters of the compost, he use 3 liters of soil

so by proportion

Find how many liters of soil does he use for 72 liters of compost

[tex]\frac{3}{6}=\frac{x}{72}\\ \\x=3*72/6\\ \\x=36\ liters\ of\ soil[/tex]

Answer:

Shift to the right 3 units.

Answer:

Shift to the right 3 units

Step-by-step explanation:

Translations are a type of rigid transformation of functions, in which the position of the graph of a function is modified. The general form of the graph of a function moves up, down, left, or right.

Vertical translations:

Let:

[tex]a >0[/tex]

[tex]y=f(x)+a[/tex]  shifts the graph [tex]a[/tex] units up

[tex]y=f(x)-a[/tex] shifts the graph [tex]a[/tex] units down

Horizontal translations:

Let:

[tex]b>0[/tex]

[tex]y=f(x+a)[/tex] shifts the graph [tex]b[/tex] units to the left.

[tex]y=f(x-a)[/tex] shifts the graph [tex]b[/tex] units to the right.

Using the previous information we can conclude that the function:

[tex]f(x-3)[/tex]

Is a Horizontal translation in which the graph was shifted [tex]b=3[/tex] units to the right.

[tex]f(x-3)=(x-3)^3[/tex]

I leave you the graphs, so you can corroborate the answer easily.

Answer:

around %114.98

C because it would be the best amount

Answer:

d

Step-by-step explanation:

Answer:

We apply the chain rule, along with the quotient rule, to find d ... 3. (4 pts) A particle moves on a line so that its coordinate at time t is y ... (10 pts) A cylindrical tank with radius 5 m is being filled with water at a rate of ... h/(t) = V /(t)/25π m2. ... cup has the shape of a cone with height 10 cm and radius 3 cm (at.

Step-by-step explanation:

Answer:

V = 392.7 m3

Step-by-step explanation:

To find the volume of the cone, first calculate the hieght and the radius.

To find the length of the radius, equate the given area to the formula for the area of a circle and solve for r.

πr2=25π

Divide both sides by π.

r2=25

Take the positive square root of both sides.

r=5 m

It is given that the height of the cone equal to three times the radius. So, use the radius to find the height.

h=3r

Substitute 5 for r.

h=3⋅5

Simplify.

h=15 m

To find the volume of the cone, use the formula for the volume of a cone.

V=13πr2h

Substitute 5 for r and 15 for h.

V=13⋅π⋅52⋅15

Simplify.

V=125π

Use a calculator to approximate.

V≈392.7 m3

Therefore, the volume of the cone is about 392.7 m3.

Answer:

Step-by-step explanation:

Given are some properties of triangles and we have to check whether they are correct

i) Only two of three angle bisectors of the internal angles of a triangle are concurrent.

This is incorrect since all three angle bisectors concur at incentre

ii) The circumcenter of a triangle is the point where the perpendicular bisectors of the sides meet.

-- correct because the meeting point is equidistant from all three vertices

iii) Given any three non-collinear points, there exists exactly one circle that passes through the points.

-- correct because any three points determine a circle

iv) Given any three non-collinear points, there exists exactly one circle that passes through the points.

-- Correct

v) The incenter of a triangle is the point where the angle bisectors meet.

-- Correct and the centre is equidistant from the sides of the triangle

Statements 2, 3, and 5 are correct.

Analyze each statement to determine which are correct:

Answer:

Left ends is +ve infinity and Right end is -ve infinity. however both tends to be infinity.

Step-by-step explanation:

Let us under stand the basics of determining the end behavior of a graph , by just analyzing the degrees and coefficient of a polynomial.Please refer to the image we have shared with this for a better understanding also.

The rule is bifurcated in two broad category and and two sub category in them.

Category .

The nature of degree (Even / Odd )

Subcategory .

The coefficient of term containing degree ( Negative/Positive )

Rule 1 :

Degree : Even

If coefficient is

Rule 1(a) : Positive ⇒Both ends are towards +ve infinity

Rule 1(b) : Negative⇒Both ends are towards -ve infinity

Rule 2 :

Degree : Odd

If coefficient is

Rule 2(a) : Positive ⇒ Left ends is -ve infinity and Right end is +ve infinity

Rule 2(b) : Negative ⇒ Left ends is +ve infinity and Right end is -ve infinity

Let us see our function f(x) = [tex]-2x^3 + 3x[/tex] now

Here

Degree is 3 which is Odd

Its coefficient is (-2) which is negative

Hence we go to rule 2(b)

That is the Left ends is +ve infinity and Right end is -ve infinity. however both tends to be infinity.

Answer:

The water bill increases by about $19 for every additional resident in the home

Step-by-step explanation:

This is because times x shows that it is to each and every person and it is increasing.

Answer:

The answer is C. The water bill increases by about $19 for every additional resident in the home.

Step-by-step explanation:

The equation above consists of y as the dependent variable, x as the independent variable, 19.485 as the slope, and 86.912 as the constant. The constant represent the fixed water bill. The x variable represents the additional water usage.

I believe it’s the second option 2^2x+6=2^6

Answer:

[tex]\large\boxed{2^{2x+6}=2^6}[/tex]

Step-by-step explanation:

[tex]4^{x+3}=64\\\\4^{x+3}=4^3\\\\(2^2)^{x+3}=(2^2)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+3)}=2^{(2)(3)}\\\\2^{2x+6}=2^6[/tex]

Answer:

The last choice is your answer

Step-by-step explanation:

Plot your point in an x/y coordinate plane.  We are in QII where x is negative and y is positive.  From that point, if you drop an altitude to the negative x axis, you have a right triangle with a base measure of -2, a height of 5 and a hypotenuse that is unknown as of right now.  We will find it using Pythagorean's Theorem.  [tex]5^2+(-2)^2=c^2[/tex]

The length of the hypotenuse is √29.  That means that the cosine of that angle is the side adjacent over the hypotenuse.  Rationalizing the denominator gives us [tex]-\frac{2\sqrt{29} }{29}[/tex]

Answer:

$6.54 per pound

Step-by-step explanation:

we know that

To find the unit price divide the total cost by the total pounds

so

[tex]\frac{4.36}{(2/3)}=\frac{4.36*3}{2}=\$6.54\ per\ pound[/tex]

Answer:

leading coefficient is 1

degree is 9

Leading coefficient: 1

Degree: 9

Answer:

x = 13.7

Step-by-step explanation:

Sin = Opp./Hypo.

so

Sin (17) = x / 47

x = sin (17) * 47

x = 0.2924 * 47

x = 13.7

Let point Q = (4,y)

√[ (4-0)^2 + (y-0)^2 ] = √[ (6-0)^2 + (0-0)^2 ]

Square both side

(4-0)^2 + (y-0)^2 = (6-0)^2 + (0-0)^2

4^2 + y^2 = 6^2

16 + y^2 = 36

y^2 = 36-16

y^2 = 20

y= √20

y= 2√5

Answer:

2√5

Step-by-step explanation:

On the graphic, you see point Q is roughly between 4 and 4.5 units on the Y-axis.

So, all we have to do is find a value similar to that in the answer choices.  So, let's look at the values:

2√5:  2 * 2.23 = 4.46... that's pretty much what we're looking for.

4√2: 4 * 1.41 = 6.4.  Way too big.

2√13: 2 * 3.6 = 7.2, way too big.

8√2: We know that will necessary be way bigger than 4.5, so let's not even evaluate it.

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The arcsine ([tex]\sin^{-1}[/tex]) function of x is defined as the inverse sine function of x when -1≤x≤1.

So, when

[tex]-4\le x\le 4,[/tex]

we have that

[tex]-1\le \dfrac{1}{4}x\le 1.[/tex]

This gives us the domain [tex]-4\le x\le 4[/tex] of the function [tex]y=\sin^{-1}\left(\dfrac{1}{4}x\right).[/tex]

The range of the function [tex]y=\sin^{-1}x[/tex] is [tex]-\dfrac{\pi }{2}\le x\le \dfrac{\pi }{2},[/tex] so the range of the function [tex]y=\sin^{-1}\left(\dfrac{1}{4}x\right)[/tex] is the same (options A and C are false).

When x=-4,

[tex]y=\sin^{-1}\left(\dfrac{1}{4}\cdot (-4)\right)=\sin^{-1}(-1)=-\dfrac{\pi}{2}.[/tex]

So, option B is false and option D is true.

Answer:

Well there are 6 toppings. For one person to select sausage, it is  \frac{1}{6} . For two people, multiply them together and the probability is  \frac{1}{36}

Answer:

[tex]72\pi\ in^{3}[/tex]

Step-by-step explanation:

step 1

Calculate the volume of the cylinder (flower vase)

The volume is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=6/2=3\ in[/tex] -----> the radius is half the diameter

[tex]h=12\ in[/tex]

substitute the values

[tex]V=\pi (3)^{2}(12)=108\pi\ in^{3}[/tex] ------> exact value

step 2

Calculate  2/3 of the volume

[tex]V=(2/3)108\pi=72\pi\ in^{3}[/tex]