PLS HELP I HAVE QUESTIONS

The length of side X in simple radical form with a rational denominator is 10/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 2 × 5/√3

Hypotenuse, x = 10/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

A Type I error occurs when the null hypothesis is rejected, even though it is true.

In this case, the null hypothesis states that a whole foods diet would not have any impact on general health.

Therefore, a Type I error would occur if Megan's results show significant improvements in health associated with a whole foods diet.

This means that Megan would reject the null hypothesis and conclude that a whole foods diet does have an impact on general health, even though it is not true.

So, the statement that would indicate a Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

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The equation of a parabola with center (h, k) and focus (h + p, k) can be written in standard form as:

What exactly is a parabola?

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.

(x - h)²  + (y - k)²  = 4p² (y - k)

Plugging in the values from the given information:

h = 6, k = -4, p = 2√6

The equation is:

(x - 6)²  + (y + 4)² = 4(2√6)² (y + 4)

Expanding and simplifying:

(x - 6)² + (y + 4)²  = 144(y + 4)

Expanding the right side further:

(x - 6)²  + (y + 4)²  = 144y + 576

Rearranging the equation:

(x - 6)²  = 144y + 576 - (y + 4)²

Distributing and completing the square on the right side:

(x - 6)²  = 144y + 576 - y²  - 8y - 16

(x - 6)²  = 144y - y²  - 8y + 560

Expanding the square on the left side:

x²  - 12x + 36 + y² - 144y + 8y²  = 560

Combining like terms:

x²  - 12x + y²  - 156y + 8y²  + 36 = 560

Rearranging to standard form:

8y²  - 156y + x² - 12x + 36 = 560

Subtracting 560 from both sides:

8y²  - 156y + x² - 12x - 524 = 0

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Answer:

yes it is true it is not an empty set

Answer:using the graph of a function you can find the value of f (x), all you need to do is locate on the x axis, the value, in this case 3, and we will find f (3), locate the number (3 ) on the x-axis and see what is the value of y that the function takes at that point, that will be the value f (3)

Step-by-step explanation:it’s a

b. The function f(x)=g(x)/h(x) will have a horizontal asymptote only if the degree of g is less than or equal to the degree of h.

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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The  ways the batting order can be chosen if the coach wants no more than 2 juniors to be in the lineup

1.66053888* 10^{10}

Generally, There are a total of 6 + 3 + 7 + 4 = 20 players and 4 of them are freshmen.

Therefore, there are 13 non juniors and 7 juniors

No more than 7 juniors to be in the lineup means either 0 or 1 or 2 freshmen are selected.

After selecting all 9 players, we can arrange them in 9! ways.

Number of ways to select 9 players with 0 freshman = 13C9 * 7C0 = 715* 1 = 715

Number of ways to select 9 players with 1 freshman = 13C8 * 7C1 =9009

Number of ways to select 9 players with 2 freshmen = 13C7 * 7C2 = 36036

A total number of ways the batting order can be chosen if the coach wants no more than 2 freshmen to be in the lineup is:

9! * (715+ 9009+ 36036) =1.66053888* 10^{10}

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The height of the hexagonal-based pyramid is approximately 101.61 inches.

To find the height of the hexagonal-based pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) × Base Area × Height

In this case, the base of the pyramid is a regular hexagon, and we have the side length (s) and apothem (a) given.

The base area of a regular hexagon can be calculated using the formula:

Base Area = (3√3/2) × s²

Let's calculate the base area first:

Base Area = (3√3/2) × (6 in)²

Base Area = (3√3/2) × 36 in²

Base Area ≈ 93.53 in²

Now, we can rearrange the volume formula to solve for the height:

Height = Volume / ((1/3) × Base Area)

Height = 3168 in³ / ((1/3) × 93.53 in²)

Height = 3168 in³ / (31.177 in²)

Height ≈ 101.61 in

Therefore, the height of the hexagonal-based pyramid is approximately 101.61 inches.

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the coordinates of the point that represents the number of snowballs needed to make 2 snowmen should be option C. which is (2,6)

Answer:

\(\dfrac{11}{16}\\\\\)
Option C

Step-by-step explanation:

We have the following information:

AB = 2DH

DH = 2BE or BE = DH/2

The area of square ABCD = (2DH)² = 4DH²

The area of square BEFG = BE² = (DH/2)² = DH²/4

The area of square DHFJ = DH²

Area of the unshaded region

= area of square BEFG  + area or square DHFJ

= DH²/4 + DH² = DH²/4 + 4DH²/4 = 5DH²/4

Area of shaded region

= area of square ABCD - area of unshaded region

\(= AB^2 - \dfrac{5}{4}DH^2\\\\= 4DH^2 - \dfrac{5}{4} DH^2\\\\= \dfrac{4DH^2 \cdot 4}{4} - \dfrac{5}{4} \cdot DH^2\)

\(= \dfrac{16DH^2 - 5DH^2}{4}= \dfrac{11DH^2}{4}\)

\(\textrm{Probability of a point falling in the shaded region} =\dfrac{\textrm{Area of shaded region}}{\textrm{Total area of both regions}}\\\\= \dfrac{11DH^2/4}{4DH^2} = \dfrac{11}{16}\\\\\)

Answer:

1) ∫₀¹ 2π x (x − x²) dx

4) ∫₀¹ π ((√y)² − y²) dy

Step-by-step explanation:

The solid formed is a hollow, upside down cone.  We can either use washer method or shell method to find the volume.

If we use washer method, the thickness of the washers is dy.  The outside radius is R = x₂ = √y, and the inside radius is r = x₁ = y.

Therefore, the volume of each washer is:

dV = π (R² − r²) t

dV = π ((√y)² − y²) dy

The total volume is the sum of all washers from y=0 to y=1.

V = ∫ dV

V = ∫₀¹ π ((√y)² − y²) dy

If we use shell method, the thickness of each shell is dx.  The radius of each shell is r = x.  The height of each shell is h = y₂ − y₁ = x − x².

Therefore, the volume of each shell is:

dV = 2π r h t

dV = 2π x (x − x²) dx

The total volume is the sum of all shells from x=0 to x=1.

V = ∫ dV

V = ∫₀¹ 2π x (x − x²) dx

Answer: 600 cm³

Step-by-step explanation:

Volume of square pyramid = (1/3) · b² · h

Therefore, the volume can be calculated as

\(\frac{1}{3} *10^{2}*18=\frac{1}{3}*100*18=\frac{1}{3}*1800=\frac{1800}{3}=600\)

Answer

900

Step-by-step explanation:

it is pyramid and finding its volume we use the 3 components that is length, with and the height

1/2 base x width x height

5 x 18 x 10 = 900cm³

Answer:

Step-by-step explanation:

Cost of 3 oranges = cost of 54 oranges / 18

The profit made in week 1 is 0.69 and week 2 is 0.71.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

A takeaway sells 10-inch pizzas and 12-inch pizzas.

From the table

For week 1:

Proportion= 509/ 736 = 0.69

and, week 2:

Proportion= 765/ 1076 = 0.71

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The correct statement which does not describe the data set is,

⇒  It has a range of 19.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

A data set has these values:

⇒ 10, 12, 12, 14, 14, 14, 14, 16, 16, 18

Hence, We get;

Range = 18 - 10 = 9

Median = 10/2 + 1 term

            = 5 + 1 term

            = 6th term

           = 14

Thus, The correct statement which does not describe the data set is,

⇒  It has a range of 19.

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Answer: 1/ 3 ^9

Step-by-step explanation:

Answer:

1/39

Step-by-step explanation:

3-9=1/39

The answer is 0ne over three exponent nine

Answer:

8 yards wide

Step-by-step explanation:

if you divide 40 yards by 5 feet you get 8

Answer:

19

Step-by-step explanation:

10 + 9 = 19. If you look at how many students are above the "30 mark", you will count 10 on the first bar and 9 on the second.

Answer:

0

Step-by-step explanation:

\(f(x)=\cos[\ln(x^5)]\implies \stackrel{chain~rule}{\cfrac{df}{dx}=-\sin[\ln(x^5)]\cdot \cfrac{1}{x^5}\cdot 5x^4} \\\\\\ \left. \cfrac{df}{dx}=-\cfrac{5\sin[\ln(x^5)]}{x} \right|_{x=1}\implies -\cfrac{5\sin[\ln(1^5)]}{1}\implies -\cfrac{5\sin(0)}{1}\implies 0\)

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Answer:

The cube root of 27 is expressed as ∛27 in radical form and as (27)⅓ or (27)0.33 in the exponent form.

Have a good day!

Answer:

i think its 3 im not sure

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30/30

→ [ x = -1 ]

Hence, the value of x is -1.

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Answer:

A

Step-by-step explanation:

Equation

2x + 3x + 8 + 7x - 2 = 90        

Solution

Combine like terms on the left

12x + 6 = 90                    Subtract 6 on both sides

12x = 90 - 6

12x = 84                         Divide by 12

x = 84/12

x = 7

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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