w-13=27
\(w - 13 = 27\)
how do i do this?​

The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.

We are given that;

Line a is parallel to line b

Line m is parallel to line n.

A) We want to prove that line a is perpendicular to n.

From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.

Now, we know that by definition of a right angle that ∠1 will also be a right angle.

Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.

B) We want to prove that line b is perpendicular to n.

The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Thus, b will be perpendicular to n.

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Answer:

d. (x - 1)(2x + 3)(3x - 4)

Step-by-step explanation:

6x³ - 5x² - 13x + 12

6x³ + x² - 12x - 6x² - x + 12

x(6x² + x - 12) - 1(6x² + x - 12)

(x - 1)(6x² + x - 12)

(x - 1)(6x² + 9x - 8x - 12)

(x - 1)(3x(2x + 3) - 4(2x + 3))

(x - 1)(2x - 3)(3x - 4)

Answer:

( x - 1 )( 2x + 3 )( 3x - 4 )

Step-by-step explanation:

Hope this helps!

Answer: \(y = -\frac{1}{2} x -8\)

Step-by-step explanation:

Going to build the equation in slope-intercept form, let me know if you need another form :)

Slope intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Simply plug in the slope for m to get: y = -1/2x + b.

Then simply plug in the point to get:

-6 = -1/2(-4) + b

-6 = 2 + b

b = -8

y = -1/2x -8

Hope it helps :)

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

First equation of system A multiplied by -3:

(-3)(x+6y=5)

(-3)(x)+(-3)(6)=(-3)(5)

-3x-18=-15

Sum of the second equation of system A and the first equation multiplied by -3:

(-3x-18)+(3x-7y)=(-15)+(-35)

-3x-18+3x-7y=-15-35

-25y=-50

System B

x+6y=5

-25y=-50

Hence,  To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

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Answer:

3

Step-by-step explanation:

5 times 3 is 15 + 4 is 19.

This is the least possible number. as any other number would be too big or too little.

The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.

A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.

A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.

A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.

A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.

In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

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The region bounded by\(x=3√3y,x=0,y=5\) is rotated about the y-axis to form a solid. The volume of this solid is V. The region, the solid and a typical disk or washer can be sketched using the given curves.

To calculate the volume V of the solid obtained by rotating the region bounded by \(x=3√3y,x=0,y=5\)about the y-axis, we will use the equation \(V=π∫a b[(R)^2-(r)^2]dy,\) where R is the outer radius, r is the inner radius, a is the lower limit of the integral and b is the upper limit of the integral. Substituting the given values, we get

\(V=π∫0 5[(3√3y)^2-(0)^2]dy\)

This simplifies to \(V=π∫0 5[9y^2]dy.\) Integrating this expression, we get \(V=π(5^3-0^3)\). Substituting the limits, we get \(V=π(5^3-0^3)\). This simplifies to V=125π. Hence, the volume of the solid is 125π.

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Answer:

No solutions.

Step-by-step explanation:

Steps:

I will solve your system by substitution.

y=1/4x−10;y=1/4x+1

Step: Solve y=1/4x−10 for y:

Step: Substitute 1/4x−10 for y in y=1/4x+1:

y=1/4x+1

1/4x−10=1/4x+1

1/4x−10+−1/4x=1/4x+1+−1/4x(Add (-1)/4x to both sides)

−10=1

−10+10=1+10(Add 10 to both sides)

0=11

The given system of equation of No solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have the equations:

y= 1/4 x - 10

y = 1/4x + 1

Now, Solve y=1/4x−10 for y by Substituting 1/4x−10 for y in y=1/4x+1 we get

y=1/4x+1

1/4x−10=1/4x+1

1/4x−10+−1/4x=1/4x+1+−1/4x

−10=1

0=11

thus, the equation have No solution.

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Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

Their ages are 5 years, 25 years

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let L and Y represent the age of the older person and younger person respectively.

Using the given information, we can write:

L = 4Y + 5 --- (1)

L + Y = 30 --- (2)

From (2):

L = 30 - Y --- (3)

Put (3) in (1):

L = 4Y + 5

30 - Y = 4Y + 5

4Y + Y = 30 - 5

5Y = 25

Y = 25/5

Y = 5 years

Put Y = 5 into (3):

L = 30 - Y

L = 30 - 5

L = 25 years

Their ages are 5 years, 25 years

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i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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Answer:

H0 : μ = 6.4

H0 : μ > 6.4

Sample mean = 7.24

Pvalue = 0.120

At each α - level ; 0.1, 0.05, 0.01 ; We fail to reject the null

Step-by-step explanation:

From the sample data :

Mean, xbar, = The test statistic :

ΣX / n = 361.8 / 50 = 7.24

Standard deviation, s = √Σ(x - xbar)²/ n-1 = 2.263

The hypothesis :

H0 : μ = 6.4

H0 : μ > 6.4

The test statistic, Z ;

(xbar - μ) / s/√n

(7.24 - 6.4) / s/√n

0.84 / 2.263/√10

Z = 0.84 / 0.7156234

Z = 1.174

Using the Pvalue from Zscore calculator to Obtain the Pvalue ;

Pvalue = 0.120

Decision region :

Reject H0 ; if Pvalue < α

At 90% ; α = 0.1

Pvalue > α ; We fail to reject the Null

At 95% ; α = 0.05

Pvalue > α ; We fail to reject the Null

At 99% ; α = 0.01

Pvalue > α ; We fail to reject the Null

An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is

The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

f(x) = a(b)^x

Where:

Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 13 = 87% = 0.87.

By substituting the parameters into the exponential equation, we have the following;

\(f(x) = 95(0.87)^x\)

When x = 12, we have;

\(f(12) = 95(0.87)^{12}\)

f(12) = 17.86 ≈ 18 milligrams.

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Answer:

F. 6π is the correct answer

As the diameter of the 2nd circle is 2x+3, its radius will be (2x+3)/2 which is equal to x + 1.5  

But as it is identical to the 1st circle their radii will be equal.

Therefore, 2x = x + 1.5

Therefore, 2x - x = 1.5

Thus we get that x = 1.5

Therefore, r (radius) = 2x = 2*1.5 = 3

Now we can find the circumfrence by the equation circumference = 2πr

Therefore, circumference = 2*π*3 = 6π

The circumference of each circle is 6π.

The Circumference (or) perimeter of circle = 2πR

where, R is the radius of the circle. π is the mathematical constant with an approximate (up to two decimal points) value of 3.14. Again, Pi (π) is a special mathematical constant; it is the ratio of circumference to diameter of any circle.

Given:

Circle 1: radius of 2x;

Circle 2: diameter = 2x+3

radius of circle 2 = x+1.5

Now, the two circles are identical then they have equal radius

2x = x + 1.5

2x - x = 1.5

x = 1.5

Now, circumference of circle = 2πr

= 2*π*3

= 6π

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Answer:

Volume

24

US liquid gallon

=  

90.8499

Liter

Step-by-step explanation:

Answer:

(100/500) *200 =40%

Step-by-step explanation:

The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.

The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:

dA = (1/2) \(R^{2}\) dθ

The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:

A = ∫(β=6π, α=-6π) (1/2) \(R^{2}\)dθ

= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ

= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 +    cos(6θ))/2)

= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)

= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)

= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))

= 6π

Correct Question :

Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )

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The resultant force acting on the block is 47.6N.

The acceleration of the block will be 23.8 m/s².

The speed of the block after 5 seconds of movement is 119 m/s.

In this question, we need to make use of Newton's second law, hence:

resultant force = mass × acceleration

So, for question a. The value of the resultant force  will be obtained by adding the two forces together:

resultant force = F₁ + F₂

                       = 25N + 22.6N

                        = 47.6N

b.  Its acceleration will be:

acceleration = resultant force / mass

                  = 47.6N / 2kg

                  = 23.8 m/s²

c. The speed of the block after 5 seconds of movement will be:

Velocity  (v) = u + at

velocity = initial velocity + acceleration x time

Based on the block was initially at rest, the initial velocity is 0.

Hence:

V = acceleration x time

    = 23.8 m/s² x 5s

     = 119 m/s

Hence the speed of the block after 5 seconds of movement will be: 119 m/s.

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See full text below

The block in the figure is at rest when the forces begin to act.

F₁ = 25N

F, = 22.6 N

m = 2kg

to. Find the value of the resultant force.

b. Determine its acceleration.

C. Calculate the speed of the block after 5 seconds of movement.

Answer:

Step-by-step explanation:

You divide 2837 by 3 then your is 947

Answer:

1. ∠4 = 152°

2. ∠5 = 152°

3. ∠8 = 152°

4. ∠6 = 28°

Step-by-step explanation:

1. ∠4 and 152° are vertical angles. Therefore, m∠4 = 152°.

2. ∠5 and 152° are corresponding angles. Therefore, m∠5 = 152°

3. ∠8 and 152° are alternate exterior angles, therefore, m∠8 = 152°

4. ∠6 and <8 are a linear pair. Therefore,

m∠6 + m∠8 = 180°

m∠6 = 180° - m∠8

m∠6 = 180° - 152°

m∠6 = 28°

Answer:

It's called the Natural Logarithm because so many processes in nature can be described mathematically using it.

For example:

1) The population of a colony of rabbits that reproduce at a constant rate

2) The decay rate of a charged capacitor

3) The decay rate of a radioactive isotope

4) The rate at which your money will grow if you apply an interest rate continuously over a period of time.

5) The population of seeds in a sun flower

6) etc.

Answer:

23

Step-by-step explanation:

im sorry i just  want some points but look it up im sure youll figure it out !

Answer:

A. \(n=100\)
B. \(k=0\)

Step-by-step explanation:

A. The equation "110% n = 11" can be solved as follows:

110% n = 11

To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).

(110% n) / 110% = 11 / 110%

n = 11 / 0.110

n = 100

So, the solution for n in the equation "110% n = 11" is n = 100.

B. The given equation is:

(328 x 128) x k = 328 x (82 x 128) x k

To solve for k, we can simplify the equation using the properties of multiplication.

Step 1: Perform the multiplications inside the parentheses:

41984 x k = 328 x 10576 x k

Step 2: Rearrange the equation by applying the associative property of multiplication:

41984 x k = 328 x (10576 x k)

Step 3: Divide both sides of the equation by 328:

(41984 x k) / 328 = 10576 x k

Step 4: Cancel out the common factor of k on the left-hand side:

(41984 / 328) x k = 10576 x k

Step 5: Simplify the left-hand side:

128 x k = 10576 x k

Step 6: Subtract 10576 x k from both sides of the equation to isolate k:

128 x k - 10576 x k = 0

Step 7: Factor out k on the left-hand side:

k x (128 - 10576) = 0

Step 8: Simplify further:

k x (-10448) = 0

Step 9: Divide both sides of the equation by (-10448):

k = 0

So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.

Answer:

above sea level

Step-by-step explanation:

as anything bellow sea level would be negative meters and if you go up the number gets larger.

Answer:dx fun fun

Step-by-step explanation:

Answer:

the answer is

\(1.8\pi \: or \: 5.6548667765\)

Step-by-step explanation:

so the equation to find arc length is A=

\(\pi \: d \frac{m}{360} \)

1. find the diameter by multiplying the radius by 2 to get 10.8

2. plug in the diameter and m stands for the angle measurement, in your case 60

3. when you solve you should get 1.8 pie or 5.6548667765

Answer:

The correct answer is 1.8 pi

Step-by-step explanation:

Verified by correct test results.

Answer:

sin of 52 radians = 0.98662759204

Step-by-step explanation:

Answer: 0.98

Step-by-step explanation:

Approximately 1, you shouldn't have to answer 0.988 etc on the test.

9514 1404 393

Answer:

Step-by-step explanation:

The quantities in Batch 2 are double those in Batch 1, as shown by the Blue quantities.

Batch 1 Green = 3/2 = 1 1/2

Batch 2 Yellow = 1/2 × 2 = 1