The perimeter of parallelogram ABCD is 96 cm. AD is 3 cm more than twice AB. Find the lengths of all four sides of ABCD

Standard form of a function is

So by comparing the given equation to the standard form, we get

a=1, b=pi/6, c=pi, d=3

amplitude can be written as mod a or

So the amplitude is 1

Now for the period, we use generalization as

So the period is 12

Here, c is the phase shift, so c=pi

Hence phase shift is pi

Midline is the line that runs between maximum and minimum values

Since, the amplitude is 1 and the phase shift is -pi, the minimum and maximum values are

Midline will be the centre of region (1+pi, 1-pi)

So the midline will be

Answer:

A: 2 Feet

Step-by-step explanation:

Got it right

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer: 0.09

Step-by-step explanation:

Given: The probability that a surprise quiz on any given day is 0.30.

Since quizzes are given independently of the day

Then, the probability there will be a surprise quiz on the next two consecutive days  = 0.30 x 0.30  [When events are independent then the probability of them both occurring is the product of the probabilities of each occurring. ]

= 0.09

Hence, the probability there will be a surprise quiz on the next two consecutive days =0.09

Answer:

If your asking what t is it’s 35

Step-by-step explanation:

Answer:

5inches in all angles 2 right 2 obtuse 1 acute

Step-by-step explanation:

Answer:

(4,-4)

Step-by-step explanation:

let the coordinates of B be (x,y)

midpoint formula = (x1 +y1/2, x2 +y2\2)

(3,0) = (2+x\2),(4+y\2)

comparing we get

3=( 2+x\2), 0=( 4+y/2)

6= 2+ x 0=4+y

x= 4 y=-4

hints: that divide sign is both for 2 and x

The time when the ball hits the ground is 8. 09 seconds

A function can be defined as an expression, theorem, law, or rule that elaborates, explains or holds true for the relationship between two variables.

These variables are namely;

From the information given, we have that;

f(x) = 1048 - 16x²

Where;

To determine the time, we have;

collect like terms

- 16x² = - 1048

Divide both sides by the coefficient of x²

-16x²/-16 = -1048/-16

x² = 65.5

Find the square root of both sides, we have;

x = √65.5

x = 8. 09 seconds

Hence, the value is  8. 09 seconds

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Answer:

180cm cubed (the tiny three symbol)

Step-by-step explanation:

4 x 5 x 9

(4 x 5) x9

20 x 9

=180cm cubed

For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).

The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:

Perimeter = 2(length + width)

Substituting the expressions for the length and width, we get:

280cm = 2(4x + 3x)

Simplifying the right-hand side, we get:

280cm = 14x

Dividing both sides by 14, we get:

x = 20

Therefore, the length of the rectangle is 4x = 4(20) = 80 cm

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The Taylor expansion of the given function is:

3z^4 - 6z^7 + 3z^10

To find the Taylor expansion of the given function, we can use the binomial theorem. The binomial theorem states that for any real number a and b, and a positive integer n, the expansion of (a + b)^n can be written as:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + C(n, 2)a^(n-2) b^2 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n

where C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k!(n-k)!)

Now let's apply the binomial theorem to the given function:

3z^4 (1 - z^3)^2

Expanding (1 - z^3)^2:

(1 - z^3)^2 = 1^2 - 2(1)(z^3) + (z^3)^2

= 1 - 2z^3 + z^6

Multiplying by 3z^4:

3z^4 (1 - z^3)^2 = 3z^4 (1 - 2z^3 + z^6)

= 3z^4 - 6z^7 + 3z^10

Therefore, the Taylor expansion of the given function is:

3z^4 - 6z^7 + 3z^10

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The sum of the particular and homogeneous solutions will give the general solution of the given differential equation.

The given differential equation is,3y'' + 2y'

= x² cos (3x) e^(-2x)

We know that the particular solution can be found by using the method of undetermined coefficients.

Let us consider the given equation and find the corresponding homogeneous equation.

3y'' + 2y' = 0On solving this, we get the characteristic equation as3m² + 2m

= 0=> m (3m + 2)

= 0=> m₁

= 0, m₂ = -2/3

The general solution of the homogeneous equation is given as y_ h = c₁ + c₂ e^(-2x/3)

To find the particular solution, Here, the given function isx² cos (3x) e^(-2x).

In this function can be expressed as:

Ax² Bx C sin(3x) D cos(3x) e^(-2x)

On differentiating this twice, we get,

3A sin(3x) + 3C cos(3x) - 20A x e^(-2x)

- 4B x e^(-2x) - 4C sin(3x) e^(-2x)

- 12D cos(3x) e^(-2x) + 4D sin(3x) e^(-2x)

- 2Ax² e^(-2x) - 8B x e^(-2x) + 16Ax e^(-2x)

- 4C cos(3x) e^(-2x) + Dx² cos(3x) e^(-2x)

+ 6Dx sin(3x) e^(-2x)

- 9D cos(3x) e^(-2x)

Using the above equation, we can find the values of the coefficients A, B, C and D.

Substitute the coefficients in the general expression of the particular solution. Add the general solution of the homogeneous equation to the particular solution.

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Step-by-step explanation:

Perpendicular : means two lines meet at 90°

1) angle B = 90° - 50°

= 40°

2) Angle D = 90° - 30°

= 70°

Answer:

5

Step-by-step explanation:

Work Shown:

L = (0,1)

N = (6,1)

m = slope of LN

m = (y2-y1)/(x2-x1) is the slope formula

m = (1-1)/(6-0)

m = 0/6

m = 0

Points L and N are on the same horizontal level, so line LN is horizontal and completely flat. We can see this by noting the y coordinates are both the same. All horizontal lines have a slope of 0 to indicate no change in y value (ie, no change in rise; no increase nor decrease)

Answer:

14 smoothies

Step-by-step explanation:

trust me

Answer:

\( \huge{ \fbox{ \sf{ \: ( \: 3 \: ,  \: - 1 \: )}}}\)

Step-by-step explanation:

\( \star{ \sf { \: Let \: the \: points \:be \: A \: and \: B}}\)

\( \star{ \sf{ \: Let \: \: A (8,6) \: be \: (x1 \:, y1) and \: B(-2,-8) \: be \: (x2 \:, y2)}}\)

\( \underline{ \sf{Finding \: the \: midpoint}}\)

\( \boxed{ \rm{Midpoint \: = \: ( \frac{x1 + x2}{2} \: ,  \: \frac{y1 + y2}{2} )}}\)

\( \mapsto{ \sf{Midpoint = ( \frac{8 + ( - 2)}{2} \: ,  \: \frac{6 + ( - 8)}{2} )}}\)

\( \mapsto { \sf{Midpoint = ( \frac{8 - 2}{2} \: ,  \: \frac{6 - 8}{2} }})\)

\( \mapsto{ \sf{Midpoint = ( \frac{6}{2} \: ,  \: \frac{ - 2}{2}) }}\)

\( \mapsto{ \sf{Midpoint = (3 \: \: ,  - 1)}}\)

Hope I helped!

Best wishes!! :D

~\( \sf{TheAnimeGirl}\)

In this case, Anika can choose to read the books over the summer in 604800 different orders.

Different orders can be chosen by Anika to read the books over the summer. This can be calculated using the permutation formula.

The formula for permutation is:

P(n,r) = n!/(n-r)!

Where:

P = permutation

n = total number of items

r = number of items taken at a time

In this case, n = 9 (total number of books) and r = 9 (number of books taken at a time).

Therefore,P(9,9) = 9!/(9-9)! = 9!/0! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 = 604800

Hence, Anika can choose to read the books over the summer in 604800 different orders.

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If all three conditions are met, the function is continuous at x=-8. If any of the conditions fail, the function is discontinuous at x=-8

To determine whether the function is continuous or discontinuous at x=-8, we need to examine the three conditions for continuity:

1. The function must be defined at x=-8.
2. The limit of the function must exist as x approaches -8.
3. The limit of the function as x approaches -8 must equal the function's value at x=-8.

If all three conditions are met, the function is continuous at x=-8. If any of the conditions fail, the function is discontinuous at x=-8.

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By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.

To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.

First, let's examine the given figure and information.

We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.

To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.

Supplementary angles are defined as two angles whose measures sum up to 180 degrees.

We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.

Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.

Now, let's assume that segments HI and JK are not parallel.

In this case, if we extend lines HA and JA, they will eventually intersect at point P.

Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.

However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.

Therefore, our assumption that segments HI and JK are not parallel must be incorrect.

Consequently, we can conclude that segment HI is indeed parallel to segment JK.

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The unit vector normal to the plane defined by a and b is λ = -32i/49 + 49j/49 - 44k/49.

To find the unit vector normal to a plane defined by two non-collinear vectors, we can use the cross product. The cross product of two vectors a and b produces a vector that is orthogonal to both a and b, and has a magnitude equal to the area of the parallelogram defined by a and b.

To obtain a unit vector, we divide the cross product by its magnitude.

Given that a = 7i + 8j - 2k and b = 9i - 4j - 5k, we can find the cross product as follows:

a x b = det( i j k)

7 8 -2

9 -4 -5 )

= (8 x (-5) - (-2) x (-4)) i

- (7 x (-5) - (-2) x 9) j

+ (7 x (-4) - 8 x 9) k

= 18i + 59j + 50k

To obtain the unit vector normal to the plane, we need to divide this vector by its magnitude:

|18i + 59j + 50k| = √(18^2 + 59^2 + 50^2) = √(6885)

So, the unit vector normal to the plane is:

λ = (18i + 59j + 50k)/√(6885)

= (-32i + 49j - 44k)/49

We can see that this matches the given result, so we can conclude that the unit vector normal to the plane defined by a and b is λ = -32i/49 + 49j/49 - 44k/49.

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Answer:

"OC. Invasive species reduce the availability of natural resources for native species by outcompeting the native species for those resources"

Step-by-step explanation:

    Most invasive species reproduce / spread faster than the native species, so the availability of natural resources is reduced for the native species.

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

It is OC. Invasive species reduce the availability of natural resources for native species by outcompeting the native species for those resources

Step-by-step explanation:

Invasive species usually reduce the availability of natural resources for the native species by competing the native species for those resources and their population will increase making the resources less available for the native species living there,effecting their population.

- I hope this answers your question. Good Luck!! :))

Answer:

Step-by-step explanation:

Less than 1/3/5

- 1/3/5*1/3

- 3/4*1/3/5

Greater than 1/3/5

- 1/2/3*1/3/5

- 1/3/5*1/1/4

Check the picture below.

since the triangle is equilateral, is also equiangular.

\(a\sqrt{3}=\sqrt{6}\implies a=\cfrac{\sqrt{6}}{\sqrt{3}}\implies a=\cfrac{\sqrt{2\cdot 3}}{\sqrt{3}}\implies a=\cfrac{\sqrt{2}\sqrt{3}}{\sqrt{3}}\implies a=\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ 2a=x\implies {\Large \begin{array}{llll} 2\sqrt{3}=x \end{array}}\)

Answer:

74 degrees

Step-by-step explanation:

You can see this is a supplementary angle, which means that it is a straight line with a line sticking out. This means the two angles add up to 180 degrees, so 180 - 106 = 74, which is your answer.

Answer:

x = 74°

Step-by-step explanation:

x + 106 = 180    {linear pair}

Subtract 106 from both sides

        x = 180 - 106

       x = 74°

The number of ways is 432

From the question, we have

Each number has a different color from each of its proper divisors.

number of ways = 3*2*1*3*3*2*2*2

=432

Multiplication:

Mathematicians multiply two or more numbers to determine the sum of the parts. It is a fundamental mathematical procedure that is commonly used in real-world situations. Multiplication is used when groups of like sizes need to be combined. Multiplication is a mathematical operation that illustrates the fundamental idea of adding the same number again. The product of two or more numbers is what occurs from multiplying them, while the components are the quantities that are multiplied. Multiplying the numbers makes it simpler to repeatedly add the same quantity.

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