Derive a formula to find the perimeter of an isosceles triangle in which one of the equal
sides is 3x + 2 and unequal side is 14

Given data:

Base of the sale = 12 feet

Height = 16 feet

Finfing the value of x,

The triangle is a right angle triangle , so by using the Pythagorean Theorem

Here, Hypotenues = x

Perpendicular = 16

Base = 12

Thus, the value of x is 20

Answer: Answer is 15 hours

Step-by-step explanation:Given 6 men dig 5 holes in 25 hours

Therefore 10 men will take to dig 5 holes is

workers(1) × time(1) = workers(2)×time(2)

(This formula is used when Total work is same)

where workers(1)= 6 men

Time (1) = 25 hours

workers (2) = 10 men

We have find out Time(2)=T(2)

by applying above formula

6×25=10×T2

after simplify

T2= 15 hours

The markup amount of the purchase is $1114

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

Discount = 30%

Selling price = $780

The markup amount is calculated using the following equation

Selling price = Markup amount * (1 - discount)

Make the markup the subject

Markup = Selling price/(1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Markup = 780/(1 - 30%)

Evaluate

Markup = 1114

Hence, the markup is $1114

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Answer:

2) 92.1327412287*

3) $288.71**

Step-by-step explanation:

2)Triangle = 1/2(8)11=44

Rectangle =8x3=24

Semicircle = 1/2\(\pi\)r²=1/2\(\pi\)4²=24.1327412287

44+24+24.13=92.1327412287

3) 92.1327412287x3.10=288.711497809

*I don’t know what they want it rounded to.  I used the real pi, but if the directions say to use 3.14 for pi, it would change the answer

**If the first answer changes, so does the second.

Answer:

2/0 or infinity

Step-by-step explanation:

a. Parameterize C₁ by

\((x(t),y(t)) = (1-t)(-13,-7) + t(0,6) = (-13+13t,-7+13t)\)

with 0 ≤ t ≤ 1. Then both dx = 13 dt and dy = 13 dt, so that the line integral along C₁ is

\(\displaystyle \int_C y^2\,dx + x\,dy = \int_0^1 (-7+13t)^2(13\, dt) + (-13+13t)(13\,dt)\)

\(\displaystyle \int_C y^2\,dx + x\,dy = 13 \int_0^1 (169t^2 - 169t + 36) \, dt\)

\(\displaystyle \int_C y^2\,dx + x\,dy = 13 \left(\frac{169}3-\frac{169}2+36\right) = \boxed{\frac{611}6}\)

b. Parameterize C₂ by

\((x(t),y(t)) = (36-t^2,t)\)

with -7 ≤ t ≤ 6. Then dx = -2t dt and dy = dt, so the line integral is

\(\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 t^2(-2t\,dt) + (36-t^2)\,dt\)

\(\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 (36-t^2-2t^3) \, dt\)

\(\displaystyle \int_C y^2\,dx + x\,dy = \left(36\cdot6-\frac{6^3}3-\frac{6^4}2\right) - \left(36\cdot(-7)-\frac{(-7)^3}3-\frac{(-7)^4}2\right) = \boxed{\frac{5005}6}\)

Answer:just add all the number together and that’s ur answer

Step-by-step explanation:87

Answer: you should plot it a -3.2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

Answer:

Step-by-step explanation:

2x = x+30

subtract x on both sides

x = 30

As it is a isosceles triangle opposite sides are equal.

\(\\ \sf\longmapsto 2x=x+30\)

\(\\ \sf\longmapsto 2x-x=30\)

\(\\ \sf\longmapsto (2-1)x=30\)

\(\\ \sf\longmapsto x=30\)

After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

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By the Pythagorean theorem,

\(\sin^2 t +\cos^2 t = 1 \\ \\ \sin^2 t +(-3/4)^2 = 1 \\ \\ \sin^2 t =7/16 \\ \\ \sin t=-\frac{\sqrt{7}}{4}\)

(I took the negative case because of the range of values of t)

Using the cosine double angle formula,

\(\cos 2t=2\cos^2 t -1 =2(-3/4)^2 - 1 =1/8\)

Using the sine double angle formula,

\(\sin 2t=2\left(-\frac{3}{4} \right)\left(-\frac{\sqrt{7}}{4} \right)=\frac{3\sqrt{7}}{8}\)

Using the cosine half-angle formula,

\(\cos \frac{t}{2}= -\frac{\sqrt{1+\cos A}}{2}=-\frac{\sqrt{1+\frac{3\sqrt{7}}{8}}}{2}\)

(I took the negative case because of the range of values of t)

Using the sine half-angle formula,

\(\sin \frac{t}{2}=\frac{\sqrt{1-\cos A}}{2}=\frac{\sqrt{1-\frac{3\sqrt{7}}{8}}}{2}\)

(I took the positive case because of the range of values of t)

Answer:

1332 i think

Step-by-step explanation:

287+379=666

666*2=1332

Answer: See explanation

Step-by-step explanation:

The sampling methods include:

1. Simple random sampling: Here, the individuals in the population have an equal chance of being selected as the selection is done randomly and anyone can be picked from the population

2. Systematic sampling: This is when the selection of the individuals is done at regular intervals. For example from the population, every 10th person might be picked.

3. Stratified sampling: Here, the total population is first divided into a smaller group called the strata before the sampling is done.

4. Clustered sampling: Here, the sampling unit is the subgroups of the population and not the individuals.

Answer:

C) an open top cone

Step-by-step explanation:

A = 139°

B = 139°

You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.

The angle around a point always add up to 360°, so add the 41° angles.

41 + 41 = 82°

Then minus this by 360°.

360 - 82 = 278°

And to work out one angle, which gives you the angle for both, divide 278 by two.

278 ÷ 2 = 139°

Both A and B have an angle of 139°

Example:

To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:

3x - 5 = -2x + 7

5x = 12

x = 12/5

Then, plug x = 12/5 into either equation and solve for y:

y = 3(12/5) - 5

y = 36/5 - 25/5

y = 11/5

Therefore, the point of intersection is (12/5, 11/5).

If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:

slope = tan(41 degrees) ≈ 0.87

y = mx + b

y = 0.87x + 0

Then, you can use the same method as before to find the point of intersection with another line.

_______________________________________________________

The answer is 139 degrees, using the method I gave.

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Answer:

30×pi ft

Step-by-step explanation:

ST is the diameter.

the formula for the circumference of a circle is

C = 2×pi×r

r = radius = diameter / 2

so,

C = 2×pi×30/2 = pi×30

therefore, the first answer option is correct.

Answer:

The number of enrollments increased by 5%.

Step-by-step explanation:

Given that:

Number of students at the beginning of the year = 480

Number of students at the end of the year = 504

Change = 504 - 480 = 24

This indicates increase.

Percent of change = \(\frac{Change}{Old\ number\ of\ students}*100\)

Percent of change = \(\frac{24}{480}*100\)

Percent of change = 5%

Hence,

The number of enrollments increased by 5%.

The required values of x and y are x = 2 and y = 11.

We have been given that parallelogram PQRS which has:

PT = ​y, TR = 5x+​1, QT = 2​y, TS = 6x+10

We know that the diagonals of a parallelogram bisect each other.

So, PT = TR and QT = TS

Substitute the values and we have a system of equations:

y = 5x + ​1    ....(i)

2y = 6x + 10 ....(ii)

Substitute the value of the equation y = 5x + ​1 in equation (ii), and solve for x

2(5x + ​1) = 6x + 10

10x + 2 = 6x + 10

10x - 6x = 10 - 2

4x = 8

x = 8/4

x = 2

Substitute the value of x = 2 in equation (i), and solve for y

y = 5(2) + ​1

y = 10 + 1

y = 11

Therefore, the required values of x and y are x = 2 and y = 11.

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Answer:

Angle LKM is 110

Step-by-step explanation:

Since all the angles in a triangle equal 180, and 60 is one angle you can see its an equilaterial triangle.

so x=60

Then 3(60)-70=110

So LKM=110

Answer:

125, i don't know if I'm right though so try it? :)

Step-by-step explanation:

Well an exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees

180-60=120

120=x+(180-(3x-70))

x=65

3*65=195

195-70=125

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

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Answer:

E. 1/3

Step-by-step explanation:

In this sequence, the numbers are descending and are 1/3 of the previous number.

243 / 3 = 81

81 / 3 = 27

9 / 3 = 3

3 / 3 = 1

1 / 3 = 1 / 3 (the next term)

Answer:

19

Step-by-step explanation:

Given:

\( \frac{b^7}{a^5c^6} \)

log a = 3,

log b = 4,

log c = -1

Required:

Numerical value of the log expression

SOLUTION:

To solve this, we need to recall the rules to apply in each step:

\( \frac{b^7}{a^5c^6} \)

Step 1: Apply log of quotients => i.e. \( log \frac{a}{b} = log(a) - log(b) \)

\( log(b^7) - (log(a^5c^6)) \)

Step 2: Apply log of products. i.e. log ab = log a + log b.

\( log(b^7) - (log(a^5) + log(c^6)) \)

Step 3: Apply log of exponents. i.e. \( log(a^n) = nlog(a) \).

\( 7log(b) - (5log(a) + 6log(c)) \)

Step 4: Substitute log a = 3, log b = 4, log c = -1, into the equation.

\( 7(4) - (5(3) + 6(-1)) \).

\( 28 - (15 - 6) \).

\( 28 - 9 \).

\( = 19 \).

The value of \(\rm{log\ 10^{19}\) is 19.

A log function is a way to find how much a number must be raised in order to get the desired number.

\(a^c=b\)

can be written as

\(\rm{log_ab=c\)

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.  

\(\rm{log\ 1000 = 3\)

log a = 3,

log b = 4,

log c = -1,

log a = 3

\(10^3 = a\\1000 = a\\a=1000\)

lob b = 4,

\(10^4=b\\10000=b\\b=10,000\)

log c = -1,

\(10^{-1} = c\\\\\dfrac{1}{10} = c\\\\c = 0.1\)

\(\rm{log\dfrac{b^7}{a^5c^6}\\\)

\(=\rm{log\dfrac{10,000^7}{1,000^5\times 0.1^6}\\\)

\(=\rm{log 10^{19}\)

Hence, the value of \(\rm{log\ 10^{19}\) is 19.

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

Divide total dollars by total pounds:

$35 /5 = $7 per pound

Answer: $7

The area of the rectangle is 81 square units. (option a)

To find the area of a rectangle, we need to know its length and width. We can determine these values by looking at the difference between the x-coordinates and the y-coordinates of the vertices.

In this case, we have the following coordinates: (-4,5), (5,5), (-4,-4), and (5,-4).

The length of the rectangle is the difference between the x-coordinates of the left and right vertices:

=> 5 - (-4) = 9.

The width is the difference between the y-coordinates of the top and bottom vertices:

=> 5 - (-4) = 9.

To find the area of the rectangle, we multiply its length by its width:

=> 9 x 9 = 81.

So, the correct answer is the (a), 81 square units.

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a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

linear function

Step-by-step explanation:

straight line then add up

Answer:

  41.3%

Step-by-step explanation:

The probability of interest is found by dividing the number of students passing either course by the total number of students.

The number passing only one of the courses is the number passing that course, less the number passing both courses. This is shown in the attached 2-way table.

__

The number passing either course will be the sum of the number passing one course (including the number passing both courses), and the number passing only the other course. It can also be found as the sum of the numbers passing either course, less the number passing both courses (since the latter would be counted twice).

Here those passing either (or both) Math or English will be ...

  90 +(85 -78) = 85 +(90 -78) = (90 +85) -78 = 97

So, the probability is ...

  p(passing either M or E) = 97/235 = 0.41277 ≈ 41.3%