1 N b In Fig. R49 b, PT is a tangent at T to circle LMNT such that PT || LN. i Show that ANTL is isosceles. ii Find NTM. T M 498 L 36° P​

The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)

What in mathematics is a quadrilateral?

A quadrilateral, a two-dimensional shape, is made up of four sides, four vertices, and four angles. The most prevalent shapes are concave and convex. Also included in the list of convex quadrilateral subgroups are trapezoids, parallelograms, rectangles, rhombuses, and squares.

Given: quadrilateral HIJK to that translated H'I'J'K'

To determine the algebraic rule, we need to get the coordinates of  HIJK and H'I'J'K' and then subtract them to get the translation:

H => (x, y) = (4, 6)  |  H' => (x, y) = (5, -2)

I =>  (x, y) = (6, 4)   |  I' =>  (x, y) = (7, -4)

J => (x, y) = (4, 2)   |  J' => (x, y) = (5, -6)

K => (x, y) = (4, 2)  |   K' => (x, y) = (3, -6)

Using points H and H' (you can use any point):

The difference in x is 5-4 = +1 => x+1

The difference in y is -2-6 = -8 => y-8

Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer

Learn more about quadrilateral

brainly.com/question/29934440

#SPJ1

Answer:

12 meters

Step-by-step explanation:

30 times 40 = 1200

100 cm in a meter

1200/100= 12

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

For such more questions on velocity

https://brainly.com/question/25749514

#SPJ8

Answer:

Step-by-step explanation:

Sorry for the shadow.

The solution of Neumann problem, ∇²u= 0 if r < R , Uₙ (R,θ) = f(θ) is u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ) with boundary conditions uᵣ (r,θ) = ∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ) and

Aₙ=∫(f(θ)cosnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Bₙ=∫(f(θ)sinnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Given that

The solution of Numann problem

∇²u= 0 if r < R , Uₙ (R,θ) = f(θ)

Use polar co-ordinates (r,θ)

uᵣᵣ + 1/r uᵣ+ 1/uᵣ (uθθ) = 0 ,0 < r< R,

0 <θ <2π and ∂u/∂r(R,θ) = f(θ) is directional derivative

r²d²u/dr² + rdu/dr + d²u/dθ² = 0

Let , r = ε⁻ᵗ , u(r(t),θ)

uₜ = uᵣ(rₜ) = - e⁻ᵗ uᵣ

uₜₜ =( - e⁻ᵗ uᵣ )ₜ = ε⁻ᵗuᵣ + e⁻²ᵗ uᵣᵣ

= r uᵣ+ r²uᵣᵣ

Thus we have, uₜₜ + uθθ = 0

Let u(t,θ) = X(t)Y(θ)

Which gives X''(t)Y(θ) + X(t)Y"(θ) = 0

X"(t)/X(t) = - Y"(θ)/Y(θ) = λ

From Y"(θ) + λ Y(θ) = 0

We get, Yₙ(θ) = aₙ cosnθ + bₙ sinnθ

λ= n² , n =0, 1, ...

With these values of λn we solve,

X"(t) - n² X(t) = 0

If n = 0 , X₀(t) = c₀t + d₀

X₀(r) = -c₀log (r) + d₀

If n not equal to 0 then

Xₙ (t) = cₙeⁿᵗ + dₙ e⁻ⁿᵗ

Xₙ(r) = cₙ(r)⁻ⁿ + dₙ (r)ⁿ

We have u₀(r, θ) = X₀(r)Y₀(θ)

= a₀ ( - c₀(log r) + d₀)

uₙ(r,θ) = Xₙ(r) Yₙ(θ)

= (cₙ r⁻ⁿ+ dₙrⁿ)(aₙ cosnθ + bₙ sinnθ)

But u must be positive at t =0

So, cₙ = 0 ; n = 0,1,2....

u₀ (r,θ) = a₀ d₀

uₙ(r,θ) = dₙ rⁿ( aₙ connθ + bₙ sinnθ)

By superposition , we can write as

u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ)

Boundary conditions gives

uᵣ (r,θ)=∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ)

the coefficients aₙ , bₙ for n ≥ 1 are determined are Fourier series for f(θ)

but a₀ is not determined from f(θ) therefore , it may take arbitrary value. By using Fourier series,

Aₙ= Integration of(f(θ)cosnθ dθ/π n R⁽ⁿ⁻¹⁾) where θ∈[-π, π]

Bₙ= Integration of (f(θ) sinnθ dθ/π nR⁽ⁿ⁻¹⁾) where θ∈[-π, π]

To learn more about Directional derivative, refer:

https://brainly.com/question/12873145

#SPJ4

The statement that a rate is a type of ratio that has both terms expressed in different units is true.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A rate is a type of ratio that has both terms expressed in different units.

This is true.

Example:

The unit rate of running a distance of 5 km in 4 hours.

Rate = 5km/4 hours

Unit rate = (5/4) km / 1 hour

Thus,

A rate is a type of ratio that has both terms expressed indifferent unit is true.

Learn more about unit rates here:

https://brainly.com/question/11258929

#SPJ1

For this derivative, you could set

\(\boxed{u = x^2 - 4x}\)

Then

\(y = \sin(x^2-4x) = \sin(u)\)

so that

\(\boxed{\dfrac{\mathrm dy}{\mathrm du} = \cos(u)}\)

and

\(\boxed{\dfrac{\mathrm du}{\mathrm dx} = 2x - 4}\)

Then the chain rule gives

\(\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \cos(u)(2x-4) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = (2x-4)\cos(x^2-4x)}\)

Answer:

a^2 plus b^2 = c^2

Step-by-step explanation:

That's the Pythagorean theorem apply.

Answer:

one solution

⇒ The system of linear equation represented on the graph has only one solution.

The quadratic equation with the given zeros is:

y = 2.5*x^2 - 5x - 7.5

For a quadratic equation with the zeros h and k, and a leading coefficient a is:

y = a*(x - h)*(x - k)

Here we know that the zeros are 3 and -1, replacing these values we will get:

y = a*(x - 3)*(x + 1)

Finally, we also know that the quadratic goes through (1, -10)

Replacing these values we will get:

-10 = a*(1 - 3)*(1 + 1)

-10 = a*(-2)*2

-10 = -4a

10/4 = a

5/2 = a = 2.5

Then the quadratic equation is:

y = 2.5(x - 3)*(x + 1)

Expanding that we will get:

y = 2.5*(x^2 - 3x + x - 3)

y = 2.5*x^2 - 5x - 7.5

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

Answer:WY=24 hope this helps

Step-by-step explanation:refer the attachment

remember that,

the diagonals of Parallelogram bisect each other so WA=AY

thus our equation is

move left hand side expression to right hand side and change its sign:

rewrite 2x and 4x-6x:

factor out x:

factor out -6:

group:

recall that,

When the product of factors equals 0 then at least one factor is 0 so

since the length cannot be negative negative x isn't available

therefore

since WA and AY are the part of WY we acquire:

substitute the got value of x:

simplify square:

simplify multiplication:

simplify addition:

simplify substraction:

Answer: WY = 24

Mark me brainliest thank you.

Based on the given data, the probability that exactly 2 insects will survive is 0.1402 rounded to four decimal places.

The probability mass function for the binomial distribution is given by:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (surviving insects), k is the specific number of successes we're interested in (k=2 in this case), n is the total number of trials (n=11), p is the probability of success (p=0.3), and (n choose k) is the binomial coefficient, which is the number of ways to choose k objects from a set of n objects.

Plugging in the values, we get:

P(X=2) = (11 choose 2) * 0.3² * 0.7²

= (55) * 0.09 * 0.02825

= 0.1402

Therefore, the probability that exactly 2 insects will survive is 0.1402 (rounded to four decimal places).

To know more about probability, visit:https://brainly.com/question/30034780

#SPJ1

Answer:

a 120 degree angle is 90 (right angle) + 30 (an acute angle)

Answer:

-4 < x ≤ 1.5

Step-by-step explanation:

First we will need to determine what signs to use for our inequality:

According to the picture, we have one of each

So we need to write an equality for each point and then combine them

The first inequality will be x > -4 because here the shading is "pointing" to the right just as the inequality sign >

The second inequality will be x ≤ 1.5 because here the shading is "pointing" to the left just as the inequality sign ≤

Now to combine, we arrange the two number values that we have from least to greatest with the smallest number being on the leftmost side of the inequality and the larger number being on the rightmost side of the inequality.

Then we put x in the middle and add the signs that we have

So our complete inequality will read -4 < x ≤ 1.5

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

Find out more on unemployment at https://brainly.com/question/13280244

#SPJ1

The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Scale model train: 14.2 cm

Scale factor:

The actual train length of the train can be calculated using the formula:

Then:

Answer:

x = 37.5

Step-by-step explanation:

By Basic Proportionality Theorem:

\( \frac{x}{20} = \frac{46 - 16}{16} \\ \\ \frac{x}{20} = \frac{30}{16} \\ \\ x = \frac{20 \times 30}{16} \\ \\ x = \frac{600}{16} \\ \\ x = 37.5\)

Answer:

x=37.5

Step-by-step explanation:

16/20=30/x

cross multiply

16x=600

x=37.5

Ans5 and 2

Step-by-step explanation:

(a) 45 tens is equal to 450. :- True

(b) 12.3 is equal to 123 ones. :- True

(c) 80 tens is greater than 6 hundreds. :- True

(d) 43,200 is less than 50 thousands. :- True

(e) 60 hundreds = 6,000 :- True

Consider the first statement,

45 tens are equal to 450

So, 45 tens mean 45 times 10 is written as:

45 × 10 = 450

Hence, it's true.

Consider the second statement,

12.3 is equal to 123 ones.

Now, 123 ones is equal to 123 times 1.

123 × 1 = 123

Hence, the statement is true.

Consider the third statement,

80 tens is greater than 6 hundreds.

Now 80 tens = 80 × 10 = 800

Now, 6 hundreds = 6 × 100 = 600

Now, 800 > 600

Hence, the statement is true.

Consider the fourth statement.

43,200 is less than 50 thousands.

Now, 50 thousands = 50 × 1000 = 50,000

We know,

50,000 > 43,200

Therefore, the statement is true.

Consider the fifth statement,

60 hundreds = 6000

Now, 60 hundreds = 60 × 100 = 6000

Therefore, the statement is true.

Learn more about thousands and hundreds here:

https://brainly.com/question/15226779

#SPJ9

Answer:

Center ( -8, 1 )

Radius ( 13 )

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

For such more questions on range

https://brainly.com/question/30389189

#SPJ8

Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

To know more about Range .

https://brainly.com/question/30389189

#SPJ11

The test statistic t-value is calculated for this scenario.

What is test statistic?

The degree to which your data's distribution resembles that predicted under the null hypothesis of the statistical test you are applying is shown by a test statistic.

The central tendency and variance surrounding the central tendency can be used to characterise the distribution of data, which is how frequently each observation happens. It's critical to select the appropriate statistical test for your hypothesis since different statistical tests predict various types of distributions.

In the given case population, the standard deviation is unknown. sample standard deviation and sample mean are given so we can calculate the t value.

Hence, the t-value is calculated for this scenario.

To learn more about test statistics

https://brainly.com/question/15525560

#SPJ1

Answer:

x-intercepts: x =-1, x=-3 when y=0

y-intercept, y=3, when x =0

axis of symmetry x = -2

Step-by-step explanation:

We are given the function: \(g(x) = x^2+4x+3\)

We need to draw the graph for

of the given function.

For finding x-intercept put y=0, in the given function, we will put g(x) =0

We know that: g(x)=y

\(y=x^2+4x+3\)

Putting y=0, we get:

\(0=x^2+4x+3\)

Now, we need to solve the equation by factorization, to find value of x

\(0=x^2+4x+3\\We\:can\:write\\x^2+4x+3=0\\x^2+3x+x+3=0\\x(x+3)+1(x+3)=0\\(x+1)(x+3)=0\\x+1=0\:or\:x+3=0\\x=-1\:or\:x=-3\)

So, we get x-intercepts: x =-1, x=-3 when y=0

For, finding y-intercept, put x =0

Putting x=0

\(g(x)=x^2+4x+3\\We\:know\:g(x)=y\\y=x^2+4x+3\\y=(0)^2+4(0)+3\\y=3\)

So, we get y-intercept, y=3, when x =0

The formula used to calculate axis of symmetry is: \(x = \frac{-b}{2a}\)

We have b=4 and a = 1

Putting values and finding axis of symmetry

\(x =-\frac{b}{2a} \\x=-\frac{4}{2(1)}\\x=-2\)

So, we get axis of symmetry x = -2

We will also be requiring vertex of the function:

We can find h = -b/2a (same as axis of symmetry) we get h =-2

k can be found as k=f(h)

Put h=-2 in the function:

g(-2)=(-2)^2+4(-2)+3

g(-2)=4-8+3

g(-2)=-1

So, we get k = -1

The vertex (h,k) is (-2,-1)

Now, the graph is attached in figure below.

Answer:

57

Step-by-step explanation:

Step 1:

3 = n ÷ 19

Step 2:

3 × 19 = n

Answer:

57 = n

Hope This Helps :)

Answer:

A) x= -4

Step-by-step explanation:

-7x+3x=7+9

-4x= 16

x= 16÷ -4 = -4

Answer:

5,800,000,000,000

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

??????????????????????

Answer:

Today: Tuesday, 08 December 2020

2/5 + 1/4

= 8/20 + 5/20

= 13/20