The product of two numbers is 144 and their difference is 10 what are the numbers​

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

By using the concept of compact set, it can be proved that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

What is compact set?

A set K is said to be compact if every open cover of K has a finite subcover.

Let K⊆Rn is compact  f:K→R is continuous, and ϵ>0

Let there exist \(x_n, y_n\) ∈ K such that |f(\(x_n\))−f(\(y_n\))| > n∥\(x_n\)−\(y_n\)∥+ϵ,

Since K is compact there is a subsequence \(x_{nk}\) and \(y_{nk}\) of \(x_n, y_n\) respectively such that \(x_{nk}\) converges to x and \(y_{nk}\) converges to y.

So,  |f(\(x_{nk}\))−f(\(y_{nk}\))| > \(n_k\)∥\(x_{nk}\)−\(y_{nk}\)∥+ϵ,

Since f is continuous,

We can write

|f(x)−f(y)| > \(n_k\)∥x - y∥+ϵ,

This is true for infinite many \(n_k\)

So ||x - y|| = 0

|f(x) - f(y)| > ϵ, a contradiction since f is continuous

So,  there is a number A>0 such that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

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The following is an excerpt from A First Training in Probability by Sheldon Ross. (74) = 35 is the right response.

Total moves required are 7, as follows:

Three steps up as well as four steps right.

Remember that perhaps the number of paths equals the number of arranged 7-tuples with 3 U's and 4 R's. As instance, the word URRURRU indicates to travel up, right, up, right, right, up.

There are 7 ways to arrange these letters, 7 ways to arrange the corresponding Us, and 7 ways to arrange the comparable Rs, for a total of 7!3!4! (74).

For each NxN grid, we may write the following as a generalization of our formula: It should be noted that there's a simpler method of writing this: D = N! / (K! * (N-K))! additionally known as the binomial coefficient.

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Using the proportional rule of Similar Triangles, the length of SD is 12 m.

Given a truss bridge.

From it,

The triangles BCD and RSD are similar.

For similar triangles, corresponding sides are proportional.

Corresponding sides are,

BC and RS, CD and SD, BD and RD.

BC / RS = CD / SD = BD / RD.

Consider BC / RS = CD / SD.

2 / 1 = 24 / SD

2 (SD) = 24

SD = 12

Hence the length of SD is 12 m.

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The complement of 0.87 is calculated by subtracting the given number from 1. Mathematically, this can be expressed as 1 - 0.87 = 0.13.

The complement of any number x is calculated by subtracting x from 1. This means that the complement of 0.87 is 0.13.

The complement of a number is used to find the remaining portion of a whole. For example, if the given number is 0.87, then the complement of 0.87 is 0.13. This means that 0.87 is 87% of the whole and 0.13 is the remaining 13%. Thus, the complement of 0.87 is 0.13.

Complements can also be used to find the probability of something happening. For example, if the probability of an event occurring is 0.87, then the probability of it not occurring is 0.13. This is because the sum of the probabilities must equal 1 (100%). Therefore, the complement of 0.87 is 0.13.

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Step-by-step explanation:

i don't know

I don't have a calculator

Answer:

1. Even Chance

2. Even Chance

3. No Chance

4. No Chance

5. Even Chance

(NOT SURE)

(but im sure)

We will see that the probability of x taking on a value between 75 to 90 is P = 0.5

We know that x is a continuous random variable uniformly distributed between 65 and 85.

This means that the probability that x value y in the range is such that:

1 = P(y)*(85 - 65) = P(y)*20

1/20 = P(y).

Now, the probability of x taking a value between 75 and 85 is:

P(75 to 85) = (1/20)*(85 - 75) = 10/20 = 0.5

And the probability between 85 and 90 is zero (because the maximum value that x can take is 85, so this part does not affect).

Then we conclude that the probability of x taking a value between 75 to 90 is:

P(75 to 90) = P(75 to 85) + P(85 to 90) = 0.5 + 0 = 0.5

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Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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The double integral of 4xy dx dy over the region D, bounded by x = 1, 2x + y = 9, y = 1, and y = 36 in the first quadrant of the xy-plane, can be computed using a change of variables. The final answer is 540.

To perform the change of variables, let's define a new coordinate system u and v such that:

u = x

v = 2x + y

Next, we need to determine the new limits of integration in terms of u and v. From the given boundaries, we have:

For x = 1, the corresponding value in the new system is u = 1.

For 2x + y = 9, we can solve for y to get y = 9 - 2x. Substituting the new variables, we have v = 9 - 2u.

For y = 1, we have v = 2u + 1.

For y = 36, we have v = 2u + 36.

Now, let's calculate the Jacobian determinant of the transformation:

J = ∂(x, y) / ∂(u, v) = ∂x / ∂u * ∂y / ∂v - ∂x / ∂v * ∂y / ∂u

  = 1 * (-2) - 0 * 1

  = -2

Using the change of variables, the double integral becomes:

∫∫(4xy) dxdy = ∫∫(4uv)(1/|-2|) dudv

           = 2∫∫(4uv) dudv

           = 2 ∫[1,9] ∫[2u+1,2u+36] (4uv) dvdx

           = 2 ∫[1,9] [8u^3 + 35u^2] du

           = 2 [(2u^4/4 + 35u^3/3)]|[1,9]

           = 2 [(8*9^4/4 + 35*9^3/3) - (2*1^4/4 + 35*1^3/3)]

           = 2 (7776 + 2835 - 1 - 35/3)

           = 540

Therefore, the double integral of 4xy dx dy over the given region D is equal to 540.

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The number of distinct possibilities for the values in the first column of a short bingo card is = 10000

According to the data given in the question,

The middle square is contained with the word = WILD

Number of remaining squares = 24

Total number of choices given to an individual = 4

Number of options provided for each choice made = 10

Let N denote the number of choices,

In order to find the number of choices we will use the following formula,

N = \(Number of options^{Number of choices}\)

N = \(10^{4}\)

N = 10000

Therefore, the number of distinct possibilities for the values in the first column of a short bingo card is = 10000

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The probability that at least 6 of these will have a mechanical defect is 0.1612.

For the given question;

At least six of the seven chosen has to have a mechanical defect.

So we add this same cases with exactly 6 mechanical defects and the cases with exactly 7 mechanical defects.

Number of possible approaches = ⁶C₂ + ¹⁹C₇ = 6!/2!4! + 19!/7!2!

= 27132 + 50388

= 77, 520

Calculated the total number of options to pick the seven keyboards as;

²⁵C₇ = 25!/7!18!

²⁵C₇ = 480,700.

As a result, the necessary probability = 77, 520/480,700 = 0.1612.

Thus, the probability that at least 6 of these will have a mechanical defect is 0.1612.

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The complete question is-

Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects.

If a sample of 7 keyboards is randomly selected, what is the probability that at least 6 of these will have a mechanical defect? (Round the answer to four decimal places.)

The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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The question refers to the plot of the plate's function of the angle of inclination. When the hot side is tilted both upward and downward over the range of +90°, the discontinuous formulas must be used in different ranges of 0.

It refers to the plot of the function of the angle of inclination of a plate. It is a graph that shows the relationship between the angle of inclination and the plate's function. A plate is tilted on its hot side both upward and downward over a range of +90°. The graph shows that different discontinuous formulas are needed for different ranges of 0. A discontinuous formula refers to a formula that consists of two or more parts, each with a different equation. The two or more parts of a discontinuous formula have different ranges, such that each range requires a different equation. These formulas are used in cases where the same equation cannot be applied throughout the entire range.

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Answer:

\(h = 15.163\ meters\)

Step-by-step explanation:

(Assuming the correct angles are 30° and 45°)

We can use the tangent relation of the angle of elevation to find two equations, then we can use these equations to find the height of the pole.

Let's call the initial distance of the boy to the pole 'x'.

Then, with an angle of elevation of 30°, the opposite side to this angle is the height of the pole (let's call this 'h') minus the height of the boy, and the adjacent side to the angle is the distance x:

\(tan(30) = (h - 1.5) / x\)

Then, with an angle of elevation of 45°, the opposite side to this angle is still the height of the pole minus the height of the boy, and the adjacent side to the angle is the distance x minus 10:

\(tan(45) = (h - 1.5) / (x - 10)\)

So rewriting both equations using the tangents values, we have that:

\(0.5774 = (h - 1.5) / x\)

\(1 = (h - 1.5) / (x - 10) \rightarrow (h - 1.5) = (x - 10)\)

From the first equation, we have that:

\(x = (h - 1.5) / 0.5774\)

Using this value of x in the second equation, we have that:

\(h - 1.5 = \frac{ (h - 1.5) }{0.5774} - 10\)

\(h + 8.5 = \frac{ (h - 1.5) }{0.5774}\)

\(0.5774h + 4.9079 = h - 1.5\)

\(0.4226h = 6.4079\)

\(h = 15.163\ meters\)

Solvable problems for which no polynomially bounded algorithms exist are called NP-hard problems.

In computer science, the class of problems known as NP (nondeterministic polynomial time) consists of decision problems that can be verified in polynomial time, meaning that the time it takes to verify a solution to the problem grows at most polynomially with the size of the input. NP-hard problems are a subset of NP that are at least as hard as the hardest problems in NP.

An algorithm for an NP-hard problem is considered polynomially bounded if the time it takes to solve the problem grows at most as a polynomial function of the size of the input. This means that for large inputs, the running time of the algorithm does not increase too quickly. NP-hard problems are of particular interest because, although they may not have a polynomial time solution, they can be used to model many real-world problems and can provide insights into the complexity of computational problems.

Examples of NP-hard problems include the traveling salesman problem, the subset sum problem, and the knapsack problem. These problems have been shown to be NP-hard through a process called reduction, in which a problem can be transformed into another problem that is known to be NP-hard. By showing that the original problem can be reduced to an NP-hard problem, it can be concluded that the original problem is also NP-hard.

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By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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Step-by-step explanation:

\(\sf{\bold{\blue{\underline{\underline{Given}}}}}\)

\(\tt{\angle{c}=110°}\)

and,

\(\tt{BC=AC}  \)

⠀⠀⠀⠀

\(\sf{\bold{\red{\underline{\underline{To\:Find}}}}}\)

☆Find the \(\angle{B} ~and~\angle{A}  \)

\(\sf{\bold{\purple{\underline{\underline{Solution}}}}}\)

Here,

BC =AC

so,

⠀⠀⠀

\(\angle{A}=\angle{B}  \)

we know that,

\(\tt{\boxed{\pink{\angle{A}+\angle{B}+\angle{C}=180°}}}  \)

But \(\angle{C}=110°  \)(Ģìvéñ)

so..

\(\angle{A}+\angle{B}+110°=180°  \)

\(\angle{A}+\angle{A}+110°=180°  \)

\(\because{\angle{A}=\angle{B} }  \)

\(2\angle{A}=180°-110°  \)

\(2\angle{A}=70°  \)

\(\angle{A}=\dfrac{70°}{2}  \)

\(\boxed{\orange{\angle{A}=35°}}  \)

But...

\(\angle{A}=\angle{B}  \)

soo,

\(\boxed{\orange{\angle{B}=35°}}  \)

\(\sf{\bold{\green{\underline{\underline{Answer}}}}}\)

⠀⠀⠀⠀

\(\boxed{\green{\angle{A}=35°}}  \)

\(\boxed{\green{\angle{B}=35°}}  \)

Answer:yes?

Step-by-step explanation:

it has #s in it lol

Answer:

no it isnt

Step-by-step explanation:

Answer:

m = -1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

9m - m + 3 = -2(m + 1)

Step 2: Solve for m

The nth term for a, b, c, d, e, are 2n+13, -3n + 18, 15- n, -2n, -5n respectively.

Arithmetic progression, also known as arithmetic sequence, is a series of numbers in which each term is obtained by adding a constant value, called the common difference (d), to the previous term. The constant difference can be either positive, negative, or zero. An arithmetic progression is denoted by {a, a + d, a + 2d, a + 3d, ...}, where 'a' is the first term and 'd' is the common difference.

For example, the following sequence is an arithmetic progression: {1, 3, 5, 7, 9, 11, ...}, where 'a' = 1 and 'd' = 2, since we are adding 2 to each previous term to obtain the next term.

Arithmetic progressions have several important properties. The nth term of an arithmetic progression can be calculated using the formula: a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number. The sum of the first 'n' terms of an arithmetic progression can be calculated using the formula: Sn = (n/2)(2a + (n-1)d), where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms.

a) 15, 13, 11, 9, 7, ...

nth term: 2n + 13

b) 15, 12, 9, 6, 3, ...

nth term: -3n + 18

c) 15, 14, 13, 12, 11,...

nth term: 15 - n

d) -2, -4, -6, -8, -10, ...

nth term: -2n

e) -5, -10, -15, -20, -25, ...

nth term: -5n

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We have to make a suspicion based on the given data. The standard deviations of the three bunches are not given within the address, so we cannot straightforwardly decide whether the condition of equal standard deviations is met. Be that as it may, ready to make a few taught surmises based on what we know almost each gather.

The primary gather, which did not think about, is likely to have a bigger change in scores than the other two bunches since understudies with shifting levels of arrangement and capacity took the test. Subsequently, we might anticipate the standard deviation of this group to be bigger than that of the other two bunches.

It is conceivable that the condition of rise to standard deviations isn't met. In case the condition of equal standard deviations isn't met, we may require to utilize an altered adaptation of ANOVA, such as Welch's ANOVA, which does not expect a rise in changes. 

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Answer: Side-Angle-Side Theorem (SAS)

Step-by-step explanation:

The Side-Angle-Side Theorem (SAS) states that if two sides and the angle between those two sides of a triangle are equal to two sides and the angle between those sides of another triangle, then these two triangles are congruent.

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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Answer:

60/24

Step-by-step explanation:

Answer:

StartFraction 60 hours Over 1 EndFraction times StartFraction 24 days Over 1 hour EndFraction

Step-by-step explanation:

I'm sorry if this is wrong

Answer:

b must be positive

Step-by-step explanation:

if a is less than -1

that means to get smaller numbers

b needs to be positive

so that when a is multiplied by b you would have

numbers that are more negative

Answer:

b > 1

Step-by-step explanation:

Given:

Substituting a = -1 into ab < a

⇒ (-1)b < -1  

⇒ -b < -1

⇒ b > 1

If a < -1 then a is negative.  If ab < a then ab is also negative.  

In order for ab to be negative (when a is negative) b must be positive.

For ab < a then b > 1.

Proof

If b = 0.5 and a = -1.5 then ab = -0.75

As -0.75 > -1.5 then ab > a so this cannot be true.

If b = 1.5 and a = -1.5 then ab = -2.25

As -2.25 < -1.5 then ab < a so this is true.

Therefore b > 1

Answer:

total area of the house and walla and stuff is 322ft²

Step-by-step explanation:

Answer:

wall area to be painted = 322 ft²

Step-by-step explanation:

The front wall and back wall have the same length and width.

The left wall and the right wall have the same length and width.

We need to add 2 times the area of the front wall plus 2 times the area of the left wall and then subtract the areas of the door and windows.

wall area to be painted =

= 2 × 12 ft × 8 ft + 2 × 10 ft × 8 ft - 22 ft² - 2 × 2 ft × 2 ft

= 192 ft² + 160 ft² - 22 ft² - 8 ft²

= 322 ft²

Answer: The triangles are not congruent.

Step-by-step explanation:

We are given that the two triangles both contain a congruent angle and two congruent sides. The triangles have two congruent sides with a non-included congruent angle among them.

However, because the two triangles only have two congruent sides, and the angle shared by each triangle is not included between the two sides, the triangle would be "congruent" by SSA, which is not a triangle congruency theorem or postulate.

Therefore, the two triangles are not congruent.

I hope this helps!