A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?

Answer:

Step-by-step explanation:

I am assuming you want to factor these functions

G= -x^2 - 2xy - y^2

  =  -(x^2 + 2xy + y^2)

We need 2 terms whose product is y^2 and whose sum is +2xy

- they are  + x and + y

  = - (x + y)(x + y)

  = -(x + y)^2

The other functions are worked out in the same way:

K =  x^2 + 4y^2 + 4xy

  = (x  + 2y)(x + 2y)

  = (x + 2y)^2

H = 4x^2 - 12xy + 9y^2

   = (2x - 3y)^2

L= 25 - 10 + y^2

 = (5 - y)^2

M =  10y^4 + 25x^6 +y^8

    - this is prime  (no factors)

The approximate number of text messages sent in 2011 is 2 x 10^1.

Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

118, 000, 000, 000 in scientific notation is 1,18 x 10^11

2,357, 000, 000, 000 in scientific notation is 2.357 x 10^12

Difference in messages sent in 2011 compared to 2005 : (2.357 / 1.18) x 10^(12 - 11)

2 x 10^1

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The area of quadrilateral ABCD exists equivalent to the area of triangle ABD plus the area of triangle ADC

Heron's Formula exists a technique for estimating the area of a triangle when you know the lengths of all three sides.

Therefore, the total area of  quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].

Let a, b, and 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 exists half the perimeter

[tex]$p = \frac{a+b+c}{2}[/tex]

To estimate the area of triangle ABD

we have

a = AB = 2.89 units

b = BD = 8.59 units

c = DA = 8.6 units

To estimate the perimeter

[tex]$p = \frac{2.89+8.59+8.6}{2}[/tex]

= 10.4 units

To estimate the area

[tex]$A = \sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]

[tex]$A = \sqrt{10.04(7.15)(1.45)(1.44)}[/tex]

[tex]$A = \sqrt{149.89}[/tex]

A = 12.24 [tex]$$units^2[/tex]

To estimate the area of the triangle ADC

we have

a = AC = 4.3 units

b = AD = 8.6 units

c = DC = 7.58 units

To estimate the half perimeter p

[tex]$p = \frac{4.3+8.6+7.58}{2}[/tex]

= 10.24 units

To estimate the area

[tex]$A = \sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]

[tex]$A = \sqrt{10.24(5.94)(1.64)(2.66)}[/tex]

[tex]$A = \sqrt{265.35}[/tex]

A = 16.29 [tex]$$units^2[/tex]

To estimate the total area

A = 12.24+16.29 = 28.53 [tex]$$units^2[/tex].

Therefore, the total area of  quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].

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Answer:

A is the answer

[tex]x = \frac{1}{48} [/tex]

Point E is where the statue should be placed.

At what point should the statue be:

The intersection of the doors to the arena, the spirit store, and the parking lot forms a triangle, with Point E in its center. The radius of the circumscribed circle will therefore equal the distance from the statue to each vertex, placing it at the same distance from all three landmarks.

Point E is where the statue should be placed.

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The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

According to the given question.

The total number of elements, n = 3

The number of elements to be selected at a time when repetition is  allowed, r = 5

Since, we know that " the number of ways or permutations of n things taken r all at a time, when repetition of things are allowed, is [tex]n^{r}[/tex].

Therefore,

The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed

= [tex]3^{5}[/tex]

= 243

Hence, the number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

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The length of HI in the similar triangles is: (4) 24.

The corresponding sides of triangles that are similar to each other have ratios that are equal to each other, thus, they are proportional.

Triangle EFI and triangle GHI are similar to each other. Therefore, their corresponding sides have ratios that are equal. Thus, we will have the following:

HI/FI = HG/EF

Given:

EF = 5,

HG = 12,

FI = 1.4x + 3

HI = 6.1x - 6.5

Plug in the values

6.1x - 6.5/1.4x + 3 = 12/5

Cross multiply

5(6.1x - 6.5) = 12(1.4x + 3)

Open the bracket

30.5x - 32.5 = 16.8x + 36

30.5x - 16.8x = 32.5  + 36

13.7x = 68.5

Divide both sides by 13/7

13.7x/13.7 = 68.5/13.7

x = 5

HI = 6.1x - 6.5

Plug in the value of x

HI = 6.1(5) - 6.5

HI = 30.5 - 6.5

HI = 24

The length of HI in the similar triangles is: (4) 24.

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Answer:

C

Step-by-step explanation:

Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1  and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5

Answer:

C

Step-by-step explanation:

　　＿＿＿　 AA

*～/■　■　⊂ P

　 |　■　■.（＿）

　 U U￣￣U U

Answer:

   [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

mean: (22+12+14+14+13+9)=14

|22-14| + |12-14| + ... + |9-14| =16

MAD = 16/6 = [tex]\frac{8}{3}[/tex]

Look at the attached image above ☝️for explanation

Hope it helps! and if it's not pls tell me on the comment.

Answer:

182000

Step-by-step explanation:

4.82 x 10^5

1.

10^5 is equal to 10 being multiplied 5 times. So this can be expressed as:

10 x 10 x 10 x 10 x 10.

When you multiply 10s, you just add the number of zeros next to one.

==> 100000 (5 zeros total)

2.

We multiply 100000 to 4.82.

100000 x 4.82 = 182000

So our final answer will be 182000.

Answer:

482,000.

Step-by-step explanation:

The 5 tells us this number is 6 digits long.

The answer is

482,000

Step-by-step explanation:

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

The number of combinations of n objects taken r at a time is determined by the following formula:.

nCr = n! / (n-r)! r!

n = total number of objects in the set

r = number of choosing objects from the set

so here , Jane has 8 toys and first she wants to take 2 toys ....

so , 8C2 = 8! / 6! 2! = 28 ways

so , she selected 2 toys ,,, After she wants to take 2 toys among 6 toys ....

so , 6C2 = 6! / 4! 2! = 15

next , picking 2 toys out of 4

So , 4C2 = 4! / 2! 2! = 6

next , 2C2 = 2! / 0! 2! = 1

total ways to pick toys = 28 × 15 × 6 × 1

= 2520 different ways ..

request :- Sorry if there are some mistakes in my English.

The front of the base is 1.25 ft and the total base is 14.05 ft.

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

The sides CD and BD can be found using similar triangle principle.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, the following proportion can be established as follows;

[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]

Hence,

[tex]\frac{12.8}{4}=\frac{4}{CD}[/tex]

cross multiply

4 × 4 = 12.8 CD

16 = 12.8CD

divide both sides by 12.8

CD = 16 / 12.8

CD = 1.25 ft

BD = 1.25 + 12.8 = 14.05 ft

Therefore, the front of the base is 1.25 ft and the total base is 14.05 ft.

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The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)

When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.

Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;

(10x^(0.5) - 8)(5x^(0.5) + 4)

The output will retain the same thing.

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The total surface area is 1308 meters square

From the question, we have the following dimensions

Length = 19 m

Width = 16 m

Height = 10 m

The total surface area is then calculated as:

Total surface area = 2 * (Length * Width + Width * Height + Length * Height)

Substitute the known values in the above equation

Total surface area = 2 * (19 * 16 + 16 * 10 + 19 * 10)

Evaluate the expression

Total surface area = 1308

Hence, the total surface area is 1308 meters square

The question is incomplete, and the resources cannot be found online.

So, I used the attached figure to answer the question

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Answer:1,238yd squared

Step-by-step explanation:

Step-by-step explanation:

Arranging fractions in descending order means arranging the fractions starting from the highest to the lowest.

Finding the LCM of 3, 16, 12, 24,

[tex] \frac{2}{3} \: \frac{5}{16} \frac{7}{12} \frac{11}{24} \\ \\ \frac{32 + 15 + 28 + 22}{48} \\ \\ Arranging \: the \: fractions \: in \: descending \: order \\ \frac{2}{3} \frac{7}{12} \frac{11} {24} \frac{5}{16} [/tex]

Answer:

is 54, 45, 36, 27, 18

Step-by-step explanation:

Recursive formulas give us two pieces of information:

1. The first term of the sequence

2. The pattern rule to get any term from the term that comes before it

In the formula given,

n is any term number

f(n) is the nth term

This means

f(1) is the first term

f(f-1) is the term before the nth term

To find the first five numbers in this arithmetic sequence, we know the formula has given us these two pieces of information:

1. The first term is 54

2. The rule to get any term from its previous term is -9

So, we know the sequence for this formula is 54, 45, 36, 27, 18 because starting off with 54, then minus 9 from every sum gives us the following equations

54-9=45

45-9=36

36-9=27

27-9=18

The coordinates of point F are (15/4 , -5/2)

From the image attached:

AB divided into 4 similar parts, hence

Note that the rule of the mid-point states that:

When M (x , y) is the mid-point of the segment of AB, where A (x1 , y1)  and B (x2 , y2), Then  x = (x1 + x2)/2 and that of  y = (y1 + y2)/2

Then lets solve for points E, F, D

Since A (-3 , -1) and B (6 , -3),

E is the mid-point of AB

Then  E =[(-3 + 6)/2, (-1 + -3)/2]

         = (3/2 , -2)

Since  F is the mid-point of EB,

         E (3/2 , -2) , B (6 , -3)

Then F = [(3/2 + 6)/2 , (-2 + -3)/2]

       = (15/4 , -5/2)

Since D is the mid-point of AE, A (-3 , -1), E (3/2 , -2)

Then  D = [(-3 + 3/2)/2 , (-1 + -2)/2]

           = (-3/4 , -3/2)

Note also that:

 BC is said to be an  horizontal segment due to the fact that B and C have similar y - coordinate and G can be found on BC.

Since the y-coordinate of G is similar to y-coordinate of B and C

Then  y-coordinate of G is =  -3

Since DG ⊥ BC

Then DG =  vertical segment

So  G has similar x-coordinate of D

Then  The x-coordinate of G = -3/4

The  G = (-3/4 , -3)

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The domain of the function shown in the graph is x < 7

The complete question is added as an attachment

The domain is the set of x values the function can take

From the graph, we have the following x values

This means that the domain of x in the graph is  x < 7

Hence, the domain of the function shown in the graph is x < 7

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(a) (x-12)(x+11)

(b) x³-4x=x(x²-4)=x(x-2)(x+2)

The value of n from the given expression is 5.5

Fractions are expression written as a ratio of two integers. The linear equation on the other hand has a leading degree of 1.

Given the equation below;

n/11 = 3.5/7

Simplify to have

n/11 = 1/2

Cross multiply the given result to have:

11 = 2n

Swap

2n = 11

Divide both sides by 2 to have;

2n/2 = 11/2

n = 5.5

Hence the value of n from the given expression is 5.5

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Answer:

y-intecept: (0,14), x-intercept: (-8,0)

Step-by-step explanation:

Let us first solve for the y-intercept, solve the equation for y to set it to slope-intercept form.

[tex]-7x+4y=56\\4y=56+7x\\y=14+\frac{7}{4}x\\y=\frac{7}{4}x+14\\[/tex]

Now we have our y-intercept, 14

To solve for the x-intercept, all we have to do is set y to 0 and solve for x:

[tex]0=\frac{7}{4}x+14\\-14=\frac{7}{4}x\\-56=7x\\-8=x[/tex]

Therefore our x-intercept is -8.

To find the vector (x and y value) of the x intercept, we set the y value equal to 0, such as the vector of the x-intercept is equal to (-8,0).

For the y-intercept we follow a similar approach setting the x-value equal to 0, making it (0,14)

The simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x  - 4x³√10x

The complete question is added as an attachment

From the attached figure, the product expression is:

2√8x³(3√10x⁴ - x√5x²)

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) =  2 *2x√2x(3x²√10 - x²√5)

Evaluate the products

2√8x³(3√10x⁴ - x√5x²) =  4x√2x(3x²√10 - x²√5)

Open the bracket

2√8x³(3√10x⁴ - x√5x²) =  12x³√20x  - 4x³√10x

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) = 24x³√5x  - 4x³√10x

Hence, the simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x  - 4x³√10x

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Answer:

Second option

Step-by-step explanation:

edge

Based on the logarithms given, the requirement to use one digit, and the figures to be produced, the right numbers are:

The log of a number gives 1 which is an integer so we can find numbers that when multiplied, produce a number that can be taken a log of. Those numbers are 2 and 4:

= 2 x 4

= 8

Log₈ = 1

Taking the log of a number to a decimal form leads to an irrational number. So, find numbers that when divided, will give a decimal:

= 6/5

= 1.2

Take a log of 7:
log₇ (1.2) will give an irrational number.

The remaining numbers ae 9, 3, and 1.

With the numbers 9,3 and 1, the log to produce a rational number is:
log₉3¹ = log₉9¹/² = 1/2

1/2 is a rational number.

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Answer:

The solution is x < 3. To represent that on a number line, you'd have an open (not filled in) circle on 3 and shading to the left.

Step-by-step explanation:

You would only have a closed (solid/filled in) circle if the inequality had a ≤

Sariah has just begun training for a half-marathon, which is latex: 13.1 13 . 1 miles. since she was on vacation, she started the training program later than the rest of her running club. there are latex: 6 6 weeks of training runs remaining before the race. in her first week of training, sariah ran latex: 3 3 miles. she ran latex: 4.5 4 . 5 miles the second week and latex: 6 6 miles the third week. if she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance? describe how you would solve this problem using polya's four-step problem-solving method. complete each task as part of your response. be sure to number your answers task 1–task 4 so that your instructor can tell which part you are answering. otherwise, you may not receive credit. Understand the problem.

Task 1: Read the problem and restate in y0ur own words what the question asks.

2. Formulat3 a plan.

Task 2: Identify the model y0u would use to represent the problem and explain why y0u chose that model.

3. Implement th3 plan.

Task 3: Solve the problem and state y0ur answer.

4. Review th3 results.

Task 4: Explain the problem-solving process and how y0u know y0ur answer is correct.

Half of a marathon's distance, or 21.0975 kilometers (13 miles 192.5 yards), is covered during a half marathon. Using nearly the same course with a later start, an earlier finish, or shortcuts, a half marathon event is sometimes held alongside a marathon or a 5K race. If finisher medals are given out, they might not look exactly like the ones given out for the full marathon. Although these measurements are rounded and not officially correct, the half marathon is frequently referred to as a 21K, 21.1K, or 13.1 miles.

The International Association of Athletics Federations recognizes a half marathon world record.

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Answer:

not sure but I think it is this