find the circumference

Answer:

The vertex form of the equation is [tex]y = -\frac{1}{3}( x-1)^{2} +1[/tex].

Step-by-step explanation:

You will use the equation [tex]y=a(x-h)^{2} +k[/tex] to solve this parabola. (h, k) is the vertex. So, we plug this into the equation to get [tex]y= a(x - 1)^{2} +1[/tex].

Then, we substitute the point as our x and y to get [tex]-2 = 9a+1[/tex] (a lot of simplifying was done here). Then, add 2 to the right side of the equation and isolate the [tex]9a[/tex] to get [tex]9a = 3[/tex]. Finally, divide by 9 on both sides to get [tex]a=\frac{1}{3}[/tex].

Now, substitute your [tex]a[/tex] back into the equation to get y = [tex]-\frac{1}{3}(x-1)^{2}+1[/tex].

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get [tex]y = -\frac{1}{3} x^{2} +\frac{2}{3} x+\frac{2}{3}[/tex].

Answer:

Its D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The 3 is directly outside the parentheses, meaning you need to distribute the 3 to the x and the 4 because they are inside the parentheses. There is no addition, subtraction, or division involved in this so C is correct.

Answer:

C

Step-by-step explanation:

i took the test

Answer:

x = 2.36603 or 0.633975

Step-by-step explanation:

Here we want to solve the quadratic equation using the completing the square method.

2x^2-6x + 3 = 0

divide through by 2 first;

x^2 -3x + 3/2 = 0

x*2 -3x = -3/2

Half the x term will be -3/2 and squaring it is 9/4

we add this to both sides

x^2-3x/2 + 9/4 = -3/2 + 9/4

(x-3/2)^2 = 3/4

Finding square root of both sides

x-3/2 = √(3/4)

x = 3/2 ± √(3/4)

x = 3/2 + √(3/4) or x = 3/2-√(3/4)

which becomes

x = 2.36603 or 0.633975

Answer:

a = -5

Step-by-step explanation:

negative (5 minus (a + 1)) = 9 minus (5 minus (2a minus 3)) can be expressed mathematically as follows.

- (5 - (a + 1)) = 9 - (5 - (2a - 3))

using the principle of PEMDAS, all the parenthesis values are first solved

- (5 - a - 1) = 9 - (5 - 2a + 3)

-5 + a + 1 = 9 - 5 + 2a - 3

collect like terms

-5 + 1 - 9 + 5 + 3 = 2a - a

-5 = a Therefore,

a = -5

Answer:

-5

Step-by-step explanation:

Answer:

44,886 gallons

Step-by-step explanation:

We need to find the volume

V = l*w*h

V = 30ft*25ft*8ft

V =6000 ft^3

We know that 1 ft^3 = 7.481 gallons

6000 ft^3 * 7.481 gallons/1 ft^3 = 44886 gallons

Answer:

44,883 gallons

Step-by-step explanation:

The amount of water the pool can hold can be found by calculating the volume of the pool.

We know that the pool is rectangular, and it is a three dimensional shape (3 dimensions: length, width and depth). Therefore, we can use the formula for finding the volume of a rectangular prism:

V=l*w*h

We know the length is 30 feet and the width is 25 feet. The height is also the depth, so the height is 8 feet.

l= 30 feet

w=25 feet

h= 8 feet

Substitute these values into the formula.

V= 30 feet * 25 feet * 8 feet

Multiply the numbers together.

V= (30 feet * 25 feet) * 8 feet

V= 750 feet^2 * 8 feet

V=6000 feet^3

Now, let's find how many gallons the pool can hold.

1 ft^3 is equal to 7.4805 gallons. Therefore, we can multiply 6000 ft^3 and 7.4805

6000 ft^3 * 7.4805 gallons/1 ft^3

6000* 7.4805 gallons

44,883 gallons

The pool can hold 44,883 gallons of water.

Answer:

C.  2 1/2

Step-by-step explanation:

Since there is a distance of 6 1/2 units, you have to add and subtract 6 1/2 from the number.

-4 - 6 1/2 = -10 1/2

-4 + 6 1/2 = 2 1/2

Looking at the answer choices, 2 1/2 can represent point Q.

Answer:

The answer is 72

Step-by-step explanation:

You'll do 42 divided by 7 times 2

42/7x2

Hope it helps.

A car travels 72 km on 12 liters of petrol.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

A Car travels 42 km on 7 liters of petrol.

Now,

Since, On 7 liters of petrol a car travel 42 km

Hence, On 1 liter of petrol distance cover by a car = 42 ÷ 7

                                                                             = 6 km

So, On 12 liters of petrol distance cover by a car = 6 × 12

                                                                           = 72 km

Thus, A car travels 72 km on 12 liters of petrol.

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Answer:

Some of the most lucrative jobs are all about math. Most engineering fields are all about sharp math skills, whether it’s civil and mechanical or software engineering. Working in finance also obviously involves a lot of math, and what better way to make money than working in the field that’s all about money? You can also become a statistician or actuary; it’s not easy to find good statisticians, despite the need for them. If you want to earn good money, then you do need good math skills.Then again, you could use math in life anyway.

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-5/3)(-5/3)= 25/9= 2 7/9

Answer:

it’s c i think

Step-by-step explanation:

Answer C

Step-by-step explanation:

Answer:

5.29

Step-by-step explanation:

Answer:

y = -2

Step-by-step explanation:

Plug in 3 for x

y = -2 (3) + 4

y = -6 + 4

y = -2

I hope this helps :))

Answer:

~73.68

Step-by-step explanation:

In the right triangle with one angle = 45 deg

=> Isosceles right triangle

=> a = b = hypotenuse/sqrt(2) = (12sqrt(2))/sqrt(2) = 12

In other right triangle with 3 sides are a, c, and d, we have:

sin (30 deg) = a/d

=> d = a/sin(30 deg) = 12/(1/2) = 12 x 2 = 24

Othwise, cosine (30 deg) = c/d

=> c = d x cos(30 deg) = 24 x sqrt(3)/2 = 12sqrt(3)

=> The perimeter of the biggest triangle is calculated by:

P = 12sqrt(2) + b + c + d = 12sqrt(2) + 12 + 12sqrt(3) + 24 = ~73.68

Hope this helps!

Answer:  [tex]\bold{9)\ \sin \theta=\dfrac{1}{3}\qquad 10)\ \sin \theta = \dfrac{4}{5}\qquad 11)\ \cos \theta = \dfrac{\sqrt{11}}{6}\qquad 12)\ \tan \theta = \dfrac{17\sqrt2}{26}}[/tex]

Step-by-step explanation:

Pythagorean Theorem is: a² + b² = c²   , where "c" is the hypotenuse

[tex]9)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{12}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]

Note: 4² + (8√2)² = hypotenuse²   →   hypotenuse = 12

[tex]10)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{16}{20}\quad \rightarrow \large\boxed{\dfrac{4}{5}}[/tex]

Note: 12² + opposite² = 20²   →   opposite = 16

[tex]11)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{\sqrt{11}}{6}\quad =\large\boxed{\dfrac{\sqrt{11}}{6}}[/tex]

Note: adjacent² + 5² = 6²   →   adjacent = √11

[tex]12)\ \tan \theta=\dfrac{\text{side opposite of}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{17}{13\sqrt2}\quad =\large\boxed{\dfrac{17\sqrt2}{26}}[/tex]

Note: adjacent² + 7² = (13√2)²   →   adjacent = 17

Answer:

18

Step-by-step explanation:

hope it helps!

Answer: D. All interior angles and all sides are congruent.

Step-by-step explanation:

If it is a regular polygon, then all angles and sides have to be congruent.

The interior angles aren’t congruent to the exterior angles.

Not all angles have to be congruent, in regular or irregular.

Since this polygon has 25 sides, opposite pairs aren’t parallel because there are an odd number of sides. That means there are no opposite pairs.

Answer:

D

Step-by-step explanation:

Answer:

x < 6

Step-by-step explanation:

There is an open circle ( no equals) at 6   and the line goes to the left

This means that it is less than 6

x < 6

Answer:

see below

Step-by-step explanation:

Because the area of the square is 36 its side is 6 meaning the circle has a diameter of 6. This means that its radius is 3 so its area is 3² * π = 9π.

Answer:

3, -1

Step-by-step explanation:

the answer is A,B,E

i took the test

Answer:

1

Step-by-step explanation:

Answer:

The answer is A!

Answer:

No, Electric Pole is 40 ft

Step-by-step explanation:

tan 66.8° = [tex]\frac{x}{15}[/tex]

x = 35

but that is from the top of Danny, so you need to add 5 (his height)

Electric Pole is 40 ft

Answer: The total number of ways is wrong. Since there is 12 members, each of them could be the president, vice president, etc.

Step-by-step explanation:

Answer: yes

Step-by-step explanation: A translation is a transformation that slides a figure to a new position.

So in this problem, notice that we can slide the triangle on the top to the position of the triangle on the bottom.

So, this represents a translation.

Answer:

True

Step-by-step explanation:

Apply the distributive property

8a-(8a)- -8

Multiply 8 by -1

8a-8a- -8

Multiply -1 by -8

8a-8a+8

Simplify by adding terms

Subtract 8a from 8a

0+8

Add 0 and 8

8

Hope this helps :)

Answer:

9x^8

Step-by-step explanation:

f(x) is a binomial.  Multiplying a binomial by itself results in a trinomial.  In this problem we need ONLY to specify what the leading coefficient (coefficient of this trinomial product) is.

Here this is obtained by squaring the coefficient −3x^4.  We get"

(-3)^2*(x^4)^2  =  9x^8

Answer:

The value of x is [tex]x=\frac{\log(2)}{\log(6)}[/tex].

Step-by-step explanation:

Solve the equation as follows:

[tex]4\times 6^{x}-7=1[/tex]

     [tex]4\times 6^{x}=7+1[/tex]

           [tex]6^{x}=\frac{8}{4}[/tex]

           [tex]6^{x}=2[/tex]

Take log on both sides.

[tex]\log(6^{x})=\log(2)[/tex]

[tex]x\log (6)=\log(2)[/tex]

        [tex]x=\frac{\log(2)}{\log(6)}[/tex]

Thus, the value of x is [tex]x=\frac{\log(2)}{\log(6)}[/tex].

Answer:

At x = -2 the graph of this polynomial will touch the x-axis.

Step-by-step explanation:

Recall the behavior difference between power functions of even and odd power. Odd powers are associated with the crossing of the x-axis, while even powers are associated with "touching" of the x axis.

in this cases, since they give you the function in factor form, the actual roots (x-values where the function adopts value zero) of the function are evident :

[tex]f(x)=(x-5)^3\, (x+2)^2[/tex]

It has a root at x = 5 [notice that at such x-value the factor (x-5) becomes zero], and this root is of multiplicity "3" (given by the power associated with the binomial factor for this root)

and has another root at x = -2  [notice that at such x-value the factor (x+2) becomes zero], and this root is of multiplicity "2" (given by the power associated with the binomial factor for it)

It is just the second root analyzed the one that shows an even power (2) associated to its binomial factor, and therefore it is at x= -2 that the graph of this function will show as "touching" the x axis.

Answer:

True

parallelogram is a quadrilateral with two pairs of parallel sides. A trapezoid has one pair of parallel sides .

No, All trapezoids are not parallelograms.

We know that,

Trapezoid has only one pair of parallel sides while in a parallelogram there are two pairs of parallel sides.

Having one set of opposing sides that are parallel defines a trapezoid as a quadrilateral. It can have congruent sides (isosceles), right angles (a right trapezoid), although none of those properties is necessary.

Hence, By definition of trapezoids,

All trapezoids are not parallelograms because Trapezoid has only one pair of parallel sides while in a parallelogram there are two pairs of parallel sides.

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