Find the circumference and area of a circle with the radius 3.5 feet. Use 22/7 for π.

Supplementary angles add up 180°.

So:

M

(2x-24) + (5x-27) = 180

Solve for x:

2x - 24 + 5x - 27 = 180

Combine like terms:

2x + 5x - 24 -27 = 180

7x -51 = 180

7x = 180 +51

7x = 231

x= 231/7

x= 33

Replace x on m

m< B = 5x-27 = 5 (33) - 27 = 165-27 = 138

m

The area of the sidewalk is 388 square feet.

To find the area of the sidewalk you can find the area of each individual shape and add them together.

Area of the first triangle T = (1/2) x 6 ft x 11 ft = 33 sq. ft.

Area of the second triangle = (1/2) x 6 ft x 18 ft = 54 sq. ft.

Area of the rectangle = 6 ft x 30 ft = 180 sq. ft.

Area of the square = 11 ft x 11 ft = 121 sq. ft.

Therefore, the total area of the sidewalk is:

33 sq. ft. + 54 sq. ft. + 180 sq. ft. + 121 sq. ft. = 388 sq. ft.

So, the area of the sidewalk is 388 square feet.

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Answer:

You see that 73 degrees and angle 'a' must add up to be = to 180 degrees since both angles form that straaight line on the left. So 180 degrees - 73 = 107 degrees which is measure of angle 'a'

Step-by-step explanation:

Answer:

107°

Step-by-step explanation:

The two angles below form a linear pair.

They are characterized by forming a sum of 180°, which is the standard angle measure of any line.

⇒ a + 73° = 180°

⇒ a = 107°

Answer:

13 and 7

Step-by-step explanation:

13 - 7 = 6

13 + 7 = 20

hope this helps...

Speed = Distance / time

Distance = Speed x time

In t hours, first plane travels = 600 t miles

In t hours, the second plane travels =150 t miles

After t hours the distance between the two planes is:

(600t+150t)= 750t ( since both travel in opposite directions)

When the distance is 900 miles:

750t= 900

Solve for t:

t= 900/750

t= 1.2 hours

After 1.2 hours.

1.2 x 60 = 72 minutes = 60 +12 = 1 hour and 12 minutes

Since both leave at 10 pm:

10am + 1 hour and 12 minutes : 11:12 am

They will be 900 miles apart at 11:12 am

Each one traveled:

Plane 1:

Distance: Speed x time = 600 mph x 1.2 = 720 miles

Plane 2:

Distance = Speed x time = 150 mph x 1.2 = 180 miles

Answer:

all incorrect

Step-by-step explanation:

I did it in my head so I'm sorry if wrong

Answer:

The last one is incorrect

Step-by-step explanation:

-4c^2 - 2c^2 = -6c^2

9c - c = 8c

9c - c is equal to 8c so that means the polynomial is wrong since they put 10c instead of 8c.

Answer:

Step-by-step explanation:

Answer:

C and D

Step-by-step explanation:

Hope this helps :)

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

In the given triangle equations AC² = AB² + BC², AB² = AD² + BD² and BC² = CD² + BD² are true.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.

Given that,

ABC is a right-angle triangle. And BD is perpendicular to AC.

To show the equations which are true,

Use the Pythagorean theorem,

(Hypotenuse)² = (base)² + (height)²

In triangle ABC,

AC² = AB² + BC²

In triangle ABD,

(AB)² = AD² + BD²

And in triangle BCD,

BC² = CD² + BD²

Therefore, options (2), (3), and (6) are correct. Those are the only equation satisfying the Pythagorean theorem.

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Answer:

24 because it would be that

Step-by-step explanation:

The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

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To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.

First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):

W(y1, y2) = | y1 y2 |

| y1' y2' |

We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:

y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))

y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))

Substituting these values into the Wronskian:

W(y1, y2) = | sin(x) / √x cos(x) / √x |

| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |

Expanding the determinant:

W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))

Simplifying:

W(y1, y2) = -1 / (2√x)

Now, we can find the particular solution using the variation of parameters formula:

y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx

Here, g(x) = 3x√xsin(x). Substituting the values:

y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx

Simplifying the integrals:

y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)

Integrating:

y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C

Simplifying:

y_p(x) = 3x(sin^2(x) - cos^2(x)) + C

The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:

y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C

where C1, C2, and C are arbitrary constants.

Answer:

1) A

2) A

3) D

4) B

5) D

Step-by-step explanation:

__________________________________________________________

FACTS TO KNOW BEFORE SOLVING :-

If any 2 parallel lines are cut by a transversal line , then :-

__________________________________________________________

Q1)

According to the figure on the right side of the question paper ,

So,

∠7 + ∠8 = 180°

⇒ ∠2 + ∠8 = 180°    (∵ ∠2 = ∠7)

Hence , we can conclude that interior angles of same side are supplementary angles. So the correct option is A.

Q2)

According to the figure on the question paper ,

So ,

∠1 + ∠3 = 180°

⇒ ∠5 + ∠3 = 180°  (∵ ∠1 = ∠5)

Hence , we can conclude that exterior angles on the same side are supplementary angles. So , the correct option is A.

Q3)

According to the figure , (∠2 , ∠7) & (∠1 , ∠8) are alternate interior angles. But as (∠1 , ∠8) is there as an option , so the correct option is D.

Q4)

According to the figure , m∠1 = 129°.

Also , ∠1 & ∠7 are interior angles on the same side.

⇒ They are supplementary angles.

⇒ ∠1 + ∠7 = 180°

⇒ ∠7 = 180° - 129° = 51°

So , the correct option is B.

Q5)

According to the figure , m∠2 = 3x - 10 and m∠6 = 2x + 20

Also , ∠2 = ∠6 (∵ Corresponding angles are equal)

⇒ 3x - 10 = 2x + 20

⇒ 3x - 2x = 20 + 10

⇒ x = 30

So , ∠2 = 3×30 - 10 = 80° = ∠6 (∵ Corresponding angles are equal)

Hence , the correct option is D.

Answer:

(-1,-4)

Step-by-step explanation:

Because it is near -1 in x axis and -4 y axis

Answer:

54

Step-by-step explanation:

66+60=126

180-126=54

So ummm. I kind of got this wrong, and I had to delete my answer, I swear, I am SOOOO sorry. If there is a way I can give your points back I will do so.

So um yeah, just ignore this.

Answer:

115-2*180

= 245

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

there are 2 triangles so the angles in all add up to 360. (108*2) then you subtract all the known angles.

Answer:

A, E, G

Step-by-step explanation:

Answer:

A

E

G

Step-by-step explanation:

When you divide A, E, and G with the common factor, they all equal 5 : 9

The formula for the 'B' variable is V/MK

To solve for the variable B is to make it the subject of formula.

Subject of formula is the variable that is expressed in terms of the other variables in a given formula, expression, function or equation.

Example;

In the equation,  2x + y = 4, let's make 'y' the subject of formula

y = 4 - 2x

Given the expression;

V=BMK

To make 'B' the subject, we need to divide both sides by the coefficients of B, we have;

V/MK = BMK/MK

B = V/MK

Thus, the formula for the 'B' variable is V/MK

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Answer:

Step-by-step explanation:

This graph of Wildlife Population shows the changes in populations of bears, dolphins and whales from 2017 to 2022.  The bear population shows a steady increase from approximately 10 individuals to approximately 185 individuals in that 5 year period.  The whale population fluctuates up and down, from a low of 55 to a high of 100 individuals.  The dolphin population shows an exponential decrease.  To summarize, the bear population is increasing, the whale population is somewhat stable and the dolphin population is in decline.  This data seems odd because it includes marine animals (dolphins and whales) as reported by a completely landlocked state, Nebraska.

The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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Answer:

The answer is that the simplest fraction form of 34% is 17/50

Step-by-step explanation:

Both the numerator and denominator of the fraction 34/100 can only be divided by 2, to satisfy creating its simplest form.

34% = 17/50

Have an awesome day! :D

Answer:

\(\frac{17}{50}\)

Step-by-step explanation:

To write any fraction as a percent, remember perCENT means per 100. Think of 100 cents in a dollar. So 34 perCENT means 34 of 100, which you write as \(\frac{34}{100}\).

Simplest form means to reduce, so you see if there is any number you can divide out of the top and the bottom.

\(\frac{34}{100}\) = \(\frac{17*2}{50*2}\)= \(\frac{17}{50}\)

Answer:

$1307.69

Step-by-step explanation:

Let the original investment be x.

Note that a 30% increase in a value is equal to multiplying a value by 130% and a withdrawal is to take out money. The final amount is $1500. Let’s write the equation with the information we have.

Equation:

130%x - 200 = 1500

(130/100)x = 1700

x = 1700(100/130) = $1307.69

I hope this helps! :)

The measure of one exterior angle in this regular polygon (pentagon)​ is equal to 72°.

In Geometry, the measure of the sum of the angles of a convex quadrilateral, pentagon, and a nonagon is equal to 360 degrees. This ultimately implies that, the sum of all the exterior angles of a regular polygon must add up to 360 degrees.

Mathematically, the exterior angle of a regular polygon can be calculated by using this mathematical expression:

Exterior angle = 360/number of sides

Note: The given regular polygon is a pentagon and it has 5 sides.

Therefore, by substituting we have the following:

Exterior angle = 360/5

Exterior angle = 72 degrees.

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The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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I would try to help you but thats a bit hard to explain.

Answer:

C

Step-by-step explanation:

1014=0.75s

1014/0.75=s is the same as 1014/s=0.75

Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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