25 marks. please help Pythagoras theorem. please help... ​

Answer:

x = 8

Step-by-step explanation:

Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Secant:  a straight line that intersects a circle at two points

Tangent: a straight line that touches a circle at only one point

Given:

⇒ x² = 16 · 4

⇒ x² = 64

⇒ x² = √(64)

⇒ x = ±8

As distance is positive, x = 8

Answer:

X^2-9=0 is x2 = 9

Step-by-step explanation:

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Answer: 14/45

Step-by-step explanation:

The equivalent expression of the product expression \(\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}\) is \(\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}\)

The expression is given as:

\(\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}\)

Rewrite the expression as a product

\(\frac{m^3}{m^2 - 16} * \frac{m^4}{m^2 - 9}\)

Evaluate the product

\(\frac{m^7}{(m^2 - 16)(m^2 - 9)}\)

Rewrite the denominator as a difference of two squares

\(\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}\)

Hence, the equivalent expression of the product expression \(\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}\) is \(\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}\)

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Step-by-step explanation:

5(r + 9) - 2(1 - r) = 1

5r + 45 - 2 + 2r = 1

7r + 43 = 1

7r = -42

r = -6.

Answer:

r = -6

Step-by-step explanation:

Given equation,

→ 5(r + 9) - 2(1 - r) = 1

Now the value of r will be,

→ 5(r + 9) - 2(1 - r) = 1

→ 5r + 45 - 2 + 2r = 1

→ 5r + 2r + 43 = 1

→ 7r = 1 - 43

→ 7r = -42

→ r = -42/7

→ [ r = -6 ]

Hence, the value of r is -6.

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Answer: 3/8

Step-by-step explanation:

there are 8 slots and three of them are blue if you need decimal form then here: 0.375.  The percentage is: 15% i think

I hope i helped you! :)

The value trigonometric rations of sinA = √5/2 and cosA = 1/2.

Given that,

SinA = √3 cosA

Divide both side by cos A

⇒ SinA/cosA = √3

Since we know that,

Tan A = SinA/cosA

Therefore,

   SinA/cosA = √3

⇒          tan A = √3

Squaring both sides, we get

⇒          tan² A = 3

⇒      sec²A - 1 = 3

⇒           sec²A = 4

Taking square root both sides, we get

⇒             secA = 2

⇒           1/cosA = 2

⇒              cosA = 1/2

Now again squaring both sides we get

⇒              cos²A = 1/4

⇒           sin²A - 1 = 1/4

⇒                sin²A = 1/4 + 1

⇒                sin²A = 5/4

Taking square root both sides, we get

⇒                sinA = √5/2

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The parameter often associated with enzyme affinity for substrates is Km.

Km, also known as the Michaelis constant, is a parameter commonly used to quantify the affinity of an enzyme for its substrate. It is an important parameter in enzyme kinetics and plays a crucial role in determining the efficiency of an enzyme-substrate interaction.

Km represents the substrate concentration at which the rate of the enzymatic reaction is half of its maximum velocity (Vmax). In other words, enzymes with lower Km values have higher affinity for their substrates, as they can achieve half of their maximum velocity at lower substrate concentrations. Therefore, Km serves as an indicator of the enzyme's ability to bind and convert substrates into products efficiently.

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Answer: \(1728\ in.^3\)

Step-by-step explanation:

Given

The dimension of the rectangular base aquarium is \(24\ in.\times 8\ in.\times 10\ in.\)

The gap between top and water level is \(1\ in.\) i.e. water is filled up to a height of \(10-1=9\ in.\)

Now, the dimensions of the water in the aquarium is \(24\ in.\times 8\ in.\times 9\ in.\)

The volume of a rectangular base prism is \(l\times b\times h\)

The volume of water in the aquarium is

\(\Rightarrow V=24\times 8\times 9=1728\ in.^3\)

The triangle with a = 17, c = 20, and B = 42° is an ambiguous case for solving triangles.

In the ambiguous case, given two sides and an angle opposite one of them, there can be two possible triangles or no triangle at all. To determine the possible triangles, we need to apply the Law of Sines.

Using the Law of Sines, we can find the value of angle A by using the ratio: sin(A) / a = sin(B) / b, where b is the unknown side. Once we find the value of angle A, we can calculate the remaining side lengths using the Law of Cosines. However, in this case, since angle A can have two possible values (acute and obtuse angles), we will have two possible triangles. The corresponding side lengths can be calculated using the Law of Cosines for each triangle.

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Given thet SU = UT = 6 units, hence 6 + 6 = 12 showing that the expression SU + UT = RT is TRUE. Option A is correct

A line is defined as the distance between two points

Since the point T bisects RT and TU = 6 units, hence the point U bisects TS.

The sum of the segment SU and UT will be RT

Given that SU = UT = 6 units, hence 6 + 6 = 12 showing that the expression SU + UT = RT is TRUE

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Answer:Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

Step-by-step explanation:

The point-slope form of the line is y -3 = 5(x + 1).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The slope of the line shown in the graph is 5.

And line passes through point (-1, 3).

So,

If a line passes through a point (x₁ ,y₁) and have a slope m,

then the equation of line is,

y - y₁ = m(x - x₁)

So,

y -3 = 5(x + 1)

Therefore, the equation of the line is y -3 = 5(x + 1).

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Answer:

\( \frac{ \sqrt{96} }{2} = \frac{ \sqrt{16 \times 6} }{2} = \frac{4\sqrt{6} }{2} = \boxed{2 \sqrt{6}}\\ \)

a. The integral converges for all values of p in the interval p > -1.

b. For p > -1,  \(\int\limits^1_0 {xp}ln(x) \, dx\) = (1/4) (1 - p²).

a. To determine the values of p for which the integral converges, we use the integral test for convergence. Specifically, we compare the given integral to the corresponding improper integral of the integrand from 0 to 1, which is:

∫0+xp ln(x) dx = limh→0+ ∫h1 xp ln(x) dx

Using integration by parts with u = ln(x) and dv = xp dx, we get:

∫xp ln(x) dx = (1/2) xp ln²(x) - (1/4) xp + (1/4) ∫x dx

= (1/2) xp ln²(x) - (1/4) xp² + (1/4) x² + C

where C is the constant of integration.

Now, applying the limit as h approaches 0 from the right, we get:

limh→0+ [(1/2) hpln²(h) - (1/4) hp² + (1/4) h² + C - (1/2) ln²(h) + (1/4) h]

Since ln(h) goes to negative infinity as h goes to 0 from the right, we have:

limh→0+ (1/2) hpln²(h) = 0

Therefore, the integral converges if and only if the improper integral of xp from 0 to 1 converges, which is the case if p > -1.

b. For p > -1, we can evaluate the integral using the formula we obtained earlier:

∫xp ln(x) dx = (1/2) xp ln²(x) - (1/4) xp² + (1/4) x² + C

Evaluating the definite integral from 0 to 1, we get:

∫01xpln(x)dx = (1/2) p ln²(1) - (1/4) p² + (1/4) - (1/2) ln²(0) + (1/4) (0)

= 0 - (1/4) p² + (1/4)

= (1/4) (1 - p²)

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Instantaneous voltage equation: v = X(1 - e^(-t/Y))
X = 11
Y = 1

a) Differentiate v with respect to t to give an equation for dv/dt:

Using the chain rule and the fact that the derivative of e^(ax) is a*e^(ax), we get:

dv/dt = X * (-1/Y) * e^(-t/Y) = -11/Y * e^(-t/Y)

Since Y = 1:

dv/dt = -11 * e^(-t)

b) Calculate the value of dv/dt at t = 2s and t = 4s:

For t = 2s:
dv/dt = -11 * e^(-2) ≈ -11 * 0.135 = -1.485

For t = 4s:
dv/dt = -11 * e^(-4) ≈ -11 * 0.018 = -0.198

c) Find the second derivative (d^2v/dt^2):

To find the second derivative, we differentiate dv/dt once more:

d^2v/dt^2 = d/dt(-11 * e^(-t)) = 11 * e^(-t)

In summary:

a) dv/dt = -11 * e^(-t)
b) At t = 2s, dv/dt ≈ -1.485; at t = 4s, dv/dt ≈ -0.198
c) d^2v/dt^2 = 11 * e^(-t)

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Step-by-step explanation:

2 1/3

=2*3+1/3

=7/3

Answer: C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given equation for ballistic motion graphs as a parabola that opens downward. When the equation is graphed using a graphing calculator, the graph shows the weight reaches a maximum height of 19 ft after 1 second. Since the weight does not reach 20 feet, there is no prize.

__

The time at the vertex of the function h(t) = at^2 +bt +c is given by t=-b/(2a). For the given function that time is ...

  t = -(32)/(2(-16)) = 1

The height at t=1 is ...

  h(1) = -16(1^2) +32(1) +3 = 19

The vertex is (t, h) = (1, 19).

__

1. The maximum height is 19 feet

2. It takes 1 second for the weight to reach the maximum height.

3. The contestant will not win a prize.

Sally's class haven't raised $2,000 as the amount made is $958. The estimated value is $1900. The amount needed is $42.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. The amount made will be:

= $997 + $961

= $1958

They have not made $2000. The amount left is:

= $2000 - $1958

= $42

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Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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Answer:

155÷8= 19,375

The unit price of each wagon can be obtained by dividing (155 by 8)

luck in your tasks.

Answer:

(-2,1)(-1,1)(0,1)(1,1) or y=2 x=[-2,1]

Step-by-step explanation:

Brainliest Please

when you want to solve an elimination question

3x -2y = 11. ( equation 1)

-3x - y = 6. ( equation 2)

To proceed in the solution, we have to make one of the variable' s coefficient equal on both equation.

I want to make the coefficient of variable X equal on both equation and to do this , the coefficient of X in equation 1 will be used to multiply the whole of equation 2 .while the coefficient of X in equation 2 will be used to multiply the whole of equation 1.

(-3) 3X - 2y = 11 ( equation 1)

(3) -3X - y = 6 ( equation 2)

-9X +6y = -33 ( equation 1)

- 9x - 3y = 18 ( equation 2)

( now , we have to eliminate X and inorder to do that , we substrate equation 1 from 2)

-9X -(-9X) ,+6y -(-3y) ,-33-18

-9X +9x , +6y +3y , -51

9 y = -51

y = -51/9

y = -5⅔

Substitute y = -5⅔ in equation 1

3x -2(-5⅔) = 11

3X - 2 ( -17/3) = 11

3X + 34/3 =11

divide through by the LCM which is 3

3( 3x) + 3 ( 34 /3 ) = 3*11

9x +34 = 33

9x = 33-34

9x = -1

X= -1/9

therefore, y = -5⅔ , X = -1/9

please mark me brainlest

Answer:

y = -2x + 6 and y = 1/3x - 7

Step-by-step explanation:

For A, using rise over run, you can count 2 units up and 1 unit left of any given point to get to the next point. Because left is the negative direction on a graph, the 1 unit is negative. To calculate slope, divide the rise (2) over the run (-1) and substitute the slope as m into y = mx + b. In the formula, b is the y-intercept (where the line crosses the x axis). The y-intercept of A is 6, so replace b in the formula with 6:

y = -2x + 6

The slope of B is 1/3 and the y intercept is -7, so substitute those values into the formula again to get the answer for B:

y = 1/3x - 7