The figure below shows a striaght line AB intersected by another straight line t: Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3. (10 points)

Answer: 30

Step-by-step explanation:

(Assuming the line is a tangent)

Answer:

1023/4

Step-by-step explanation:

shown in the picture

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

32

Step-by-step explanation:

4y + 8 and y = 6 ( plug in 6 to y )

4 x 6 + 8

24 + 8 = 32

Answer: \(1024\pi\) square units

Step-by-step explanation:

\(A=\pi r^{2}\\\\A=\pi(32)^{2}\\\\A=\boxed{1024\pi}\)

The area of circle C is 1024π square units.

The correct option is D.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

The area of a circle is given by the formula A = πr², where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

Given that the radius of circle C is r = 32 units, we can use the formula to find its area:

A = πr²

A = π(32)²

A = 1024π

Since π is an irrational number, we can also approximate the answer as 3,221.2 square units, rounded to one decimal place.

Therefore, the area of circle C is 1024π square units.

To learn more about the circle;

https://brainly.com/question/29142813

#SPJ5

The ramp has a volume capacity of around 37.5 cubic feet.

Calculating the volume of a triangular prism shaped ramp follows a specific formula. First, identify the shape and refer to the equation:

Volume = (1/2) * Base Area * Height

To begin, the base is always in a right-angled triangle form, where its area depends on its width denoted as W, and height noted specifically as H.

Based on these computations, knowing that its triangular base measures 5 feet at its length while taking its height equates 3 feet therefore assessing how much it covers can be found using:

Triangle Area = (1/2) * Base * Height

Substituting values into solving areas leads us to have an answer of over 7 square feet.

Next is computing the volume of the said triangular prism. Placing all given data results in the same formula:

Volume = (1/2) * Base Area * Height

With one-half of the product of both areas which resulted in 7.5 square feet and then multiplying the figure by 10 ft, this yields us an approximate volume of 37.5 cubic feet.

In conclusion, we have determined that the ramp has a volume capacity of around 37.5 cubic feet.

Read more about volume here:

https://brainly.com/question/27710307

#SPJ1

Length (L) = 10 feet

Width (W) = 5 feet

Height (H) = 3 feet

Mr. González designed a ramp for his car with a length of 10 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the ramp in cubic feet?

120 ways

We would be using permutation as the position each finihes is considered.

Total people in the race = 6

There are 3 place finishers:

The number of possilble ways = 6P3

\(5x - 6 = 4x + 8 \\ = > 5x - 4x = 8 + 6 \\ = > x = 14\)

14

Hope it helps

(i) Each of u, v, and w are vectors in Rⁿ, so they each have size n × 1 (i.e. n rows and 1 column). So u and v both have size n × 1, while wᵀ has size 1 × n.

M is an n × n matrix, so the matrix A has been partitioned into the blocks

\(A=\begin{pmatrix}M_{n\times n}&\mathbf u_{n\times 1}\\\mathbf w^\top_{1\times n}&\alpha\end{pmatrix}\)

where α is a scalar with size 1 × 1. So A has size (n + 1) × (n + 1).

(ii) Multiplying both sides (on the left is the only sensible way) by the given matrix gives

\(\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}M&\mathbf u\\\mathbf w^\top&\alpha\end{pmatrix}\begin{pmatrix}\mathbf x\\x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}\mathbf v\\v_{n+1}\end{pmatrix}\)

\(\begin{pmatrix}M^{-1}M&M^{-1}\mathbf u\\-\mathbf w^\top M^{-1}M+\mathbf w^\top&-\mathbf w^\top M^{-1}\mathbf u+\alpha\end{pmatrix}\begin{pmatrix}\mathbf x\\x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}\mathbf v\\v_{n+1}\end{pmatrix}\)

and of course M ⁻¹ M = I (the identity matrix), so

-wᵀ M ⁻¹ M  + wᵀ = -wᵀ + wᵀ = 0ᵀ (the zero vector transposed)

(iii) Simplifying the system further gives

\(\begin{pmatrix}I&M^{-1}\mathbf u\\\mathbf 0^\top&-\mathbf w^\top M^{-1}\mathbf u+\alpha\end{pmatrix}\begin{pmatrix}\mathbf x\\x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}\mathbf v\\v_{n+1}\end{pmatrix}\)

\(\begin{pmatrix}\mathbf x+x_{n+1}M^{-1}\mathbf u\\(\alpha-\mathbf w^\top M^{-1}\mathbf u)x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}\mathbf v\\-\mathbf w^\top M^{-1}\mathbf v+v_{n+1}\end{pmatrix}\)

So now, setting y = M ⁻¹u and z = M ⁻¹ v gives

\(\begin{pmatrix}\mathbf x+x_{n+1}\mathbf y\\(\alpha-\mathbf w^\top\mathbf y)x_{n+1}\end{pmatrix}=\begin{pmatrix}\mathbf z\\-\mathbf w^\top \mathbf z+v_{n+1}\end{pmatrix}\)

Given that α - wᵀy ≠ 0, it follows that

\(x_{n+1}=\dfrac{v_{n+1}-\mathbf w^\top\mathbf z}{\alpha-\mathbf w^\top\mathbf y}\)

(iv) Combining the result from (iii) with the first row gives

\(\mathbf x+x_{n+1}\mathbf y=\mathbf z\)

\(\mathbf x=\mathbf z-x_{n+1}\mathbf y\)

\(\mathbf x=\mathbf z-\dfrac{v_{n+1}-\mathbf w^\top\mathbf z}{\alpha-\mathbf w^\top\mathbf y}\mathbf y\)

Both of you are correct because using either way can solve the equation for the value of x.

In the case of solving for x in  2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.

Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :

Multiplying :

2/5 x = 14

5 / 2 x 2 / 5 x = 14 x 5 / 2

x = 35

Dividing :

2/5 x = 14

2 / 5 x / 2 / 5 = 14 / 2 / 5

x = 35

Find out more on solving for x at https://brainly.com/question/2763008

#SPJ1

Answer:

(a) 0.0178 <= p <= 0.0622

(b) p <= 0.0586

Step-by-step explanation:

We have that the sample proportion is:

p = 12/300 = 0.04

(to)

For 95% confidence interval alpha = 0.05, so critical value of z will be 1.96

Therefore, we have that the interval would be:

p + - z * (p * (1-p) / n) ^ (1/2)

replacing we have:

0.04 + - 1.96 * (0.04 * (1-0.04) / 300) ^ (1/2)

0.04 + - 0.022

Therefore the interval would be:

0.04 - 0.022 <= p <= 0.04 + 0.022

0.0178 <= p <= 0.0622

(b)

For upper bounf z-critical value for 95% confidence interval is 1.645, so upper bound is:

p + z * (p * (1-p) / n) ^ (1/2)

replacing:

0.04 + 1.645 * (0.04 * (1-0.04) / 300) ^ (1/2)

0.04 + 0.0186 = 0.0586

p <= 0.0586

Answer:

(0.5,1)

Step-by-step explanation:

The midpoint formula is \((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

Let's do x first

-1+2=1

1 ÷2=0.5

y

5+-3=2

2÷2=1

(0.5,1)

Hope this helps :-)

The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer:

like terms =2x,-6x

.....

like terms =5y²,18y²

remaining are unlike terms.

Answer:

like term=2x-6x

like term=5y square-18y square

There are some symbols missing in your integral. I suspect you meant something along the lines of

\(\displaystyle \int_C (x+5y)\,\mathrm dx + x^2\,\mathrm dy\)

but we can consider a more general integral,

\(\displaystyle \int_C f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy\)

One way to compute the integral is to split up C into two component paths C₁ and C₂, parameterize both, directly compute the integral over each path, then sum the results.

Parameterize C₁ and C₂ respectively by

〈x₁(t), y₁(t)⟩ = (1 - t ) 〈0, 0⟩ + t 〈5, 1⟩ = 〈5t, t⟩

〈x₂(t), y₂(t)⟩ = (1 - t ) 〈5, 1⟩ + t 〈5, 0⟩ = 〈5, 1 - t⟩

where 0 ≤ t ≤ 1. Then

\(\displaystyle \int_C f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy = \int_{C_1} f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy + \int_{C_2} f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy \\\\ = \int_{C_1} \left(f(x_1(t),y_1(t))\frac{\mathrm dx_1}{\mathrm dt} + g(x_1(t),y_1(t))\frac{\mathrm dy_1}{\mathrm dt}\right)\,\mathrm dt \\ + \int_{C_2} \left(f(x_2(t),y_2(t))\frac{\mathrm dx_2}{\mathrm dt} + g(x_2(t),y_2(t))\frac{\mathrm dy_2}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_0^1 \left(5f(5t,t) + g(5t,t) - g(5,1-t)\)

If f and g agree with what I suggested earlier, the integral reduces to

\(\displaystyle \int_0^1 \left(5(5t+5t) + (5t)^2 - 5^2\right)\,\mathrm dt = \int_0^1 \left(25t^2 + 50t - 25\right)\,\mathrm dt = \boxed{\frac{25}3}\)

Another way would be to close the path with a line segment from (5, 0) to (0, 0) and apply Green's theorem. Compute the resulting double integral, then subtract the contribution of the line integral over this third line segment. Provided that f(x,y) and g(x,y) don't have any singularities along this closed path C* or inside the triangle (call it T ) that it surrounds, we have

\(\displaystyle \int_{C^*} f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy = -\iint_T \frac{\partial g}{\partial x}-\frac{\partial f}{\partial y} \,\mathrm dx\,\mathrm dy\)

where T is the region,

\(T = \left\{(x,y) \mid 0\le x\le 5 \text{ and } 0\le y\le \dfrac x5\right\}\)

The double integral has a negative sign because C* has a negative, clockwise orientation.

Then

\(\displaystyle \int_{C^*} f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy = -\int_0^5\int_0^{x/5} \frac{\partial g}{\partial x}-\frac{\partial f}{\partial y} \,\mathrm dy\,\mathrm dx\)

If f and g are as I suggested, then

\(\displaystyle \int_{C^*} f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy = \int_0^5\int_0^{x/5} (5-2x) \,\mathrm dy\,\mathrm dx = -\frac{25}6\)

From this, we subtract the integral along the line segment C₃ from (5, 0) to (0, 0), parameterized by

〈x₃(t), y₃(t)⟩ = (1 - t ) 〈5, 0⟩ + t 〈0, 0⟩ = 〈5 - 5t, 0⟩

again with 0 ≤ t ≤ 1.

Then the remaining line integral is

\(\displaystyle \int_{C_3} f(x_3(t),y_3(t))\,\mathrm dx_3 + g(x_3(t),y_3(t))\,\mathrm dy_3 = \int_{C_3} x_3(t)\frac{\mathrm dx_3}{\mathrm dt}\,\mathrm dt \\\\ = \int_0^1 -5(5-5t)\,\mathrm dt = -\frac{25}2\)

and so the original line integral is again -25/6 - (-25/2) = 25/3.

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

Know more about triangle,

https://brainly.com/question/13677972

#SPJ1

Answer:

y = 1

Step-by-step explanation:

Answer:

6 meters

Step-by-step explanation:

Every 7 floors, it goes up by 22.4 meter intervals.

Let's count down,

the 7th floor would be 50.8 - 22.4, which is 28.4.

the 0th floor would be 28.4 - 22.4, which is 6.

Answer:

6

Step-by-step explanation:

Answer:

\(f - g = x - 10 - 4 + x = 2x - 14 \\ f - g(5) =10 - 14 = - 4 \)

Answer:

40-26.50=m

Step-by-step explanation:

Answer:

1.) 4

2.) -11

3.) -4

4. 19

Step-by-step explanation:

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

Read more about Partial Differential Equations at: https://brainly.com/question/28099315

#SPJ1

Answer:

it a shape of a w and nothing

Step-by-step explanation:

have some bubble tea

Answer:

We should attempt synthetic division to find when

x

3

−

k

x

2

+

2

k

x

−

15

x

−

3

has a remainder of

0

, which would signify that it is a factor of the polynomial.

The synthetic substitution would be set up as:

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

−−−

−−−

−−−

|

0

Treating the synthetic division like any other synthetic division problem, we see that

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

3

−−−−−−−−

−

3

k

+

9

−−−−−−−−

−

3

k

+

27

−−−−−−−−−

1

−

k

+

3

−

k

+

9

|

0

If the remainder equals

0

, then we know that

−

3

k

+

27

+

(

−

15

)

=

0

Solve this to see that

k

=

4

.

Thus,

(

x

−

3

)

is a factor of

x

3

−

4

x

2

+

8

x

−

15

.

Answer:

Simplifying an expression means to reduce something into its simplest, smallest, or lowest answer possible.

Answer:

25/6

Step-by-step explanation:

Take the number on the left multiply by the denominator and add the numerator which is 4×6+1 =25

Reuse the same denominator which is 6 so 25/6

Work backwards: 25/6 to 4 1/6 (25 divide by 6 is 4 remainder 1 so 4 on the left and 1 as the numerator)

Answer:

25/6

Step-by-step explanation:

put the denominator as it is

Answer:

john

Step-by-step explanation:

ku

Answer:

XL = PC

AC = NX

PC = XL

Angle L = Angle C

Angle C = Angle L

Angle X = Angle P

Step-by-step explanation:

Answer:

15.1

Step-by-step explanation:

If you add all the numbers up including 15.1 then divide it by 5 (number of fish) you will get 13.8. Which is the average. Hope this helped!