The perimeter of a regular pentagon with the side length of 4 meters

Answer:

B 1/5 1/4 1/3

Step-by-step explanation:

The first digit Maggie's bank picked from the 5 digit available, so 1/5.

The second digit will be picked from the 4 remaining digits available, so 1/4.

For the final digit, the bank will have only 3 options to choose from, so 1/3.

So the possibility for the 3-digit assigned PIN to be 123 is

[tex]\frac{1}{5} * \frac{1}{4} *\frac{1}{3} =\frac{1}{60}[/tex]

1/60, so the formula is the one presented in the B option: 1/5 1/4 1/3

Answer: option C

Step-by-step explanation:

The volume of a rectangular prism can be calculated with this formula:

[tex]V=l*w*h[/tex]

Where "V" is the volume of the prism "l" is the lenght, "w" is the width and "h" is the height.

You know that the volume of this prism is 93 cubic centimeters and you need to find the height. Then, you have to solve for "h":

[tex]h=\frac{V}{l*w}[/tex]

You can observe that the volume is in the numerator and the product of the lenght and the width of the rectangular prism is in the denominator, then, the option that matches this form is the option C:

[tex]h=\frac{93}{15.5}[/tex]

Answer:

H= 93/15.5

Step-by-step explanation:

Answer:

The radius of circle is 5 cm

Step-by-step explanation:

Given a right triangle △ABC with right angle C is inscribed in a circle in which

m∠C = 90°, AC = 8 cm, BC = 6 cm

we have to find the radius of circle.

As ACB is right angles triangle where angle C is right angle.

⇒ side AB must be the diameter of circle as angle made at semi circle is 90°

[tex]Radius=AO=\frac{1}{2}AB[/tex]

By Pythagoras theorem

[tex]AB^2=AC^2+CB^2[/tex]

[tex]AB^2=8^2+6^2=64+36=100[/tex]

[tex]AB=10cm[/tex]

[tex]Radius=AO=\frac{1}{2}AB=\frac{1}{2}\times 10=5cm[/tex]

Hence, the radius of circle is 5 cm

Answer:

a. [tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]

Step-by-step explanation:

The given vector is v= 4i - 5j

The magnitude of this vector is;

[tex]|v|=\sqrt{(-4)^2+(-5)^2}[/tex]

[tex]|v|=\sqrt{16+25}[/tex]

[tex]|v|=\sqrt{41}[/tex]

The unit vector u in the direction of v is;

[tex]u=\frac{v}{|v|}[/tex]

[tex]u=\frac{4i - 5j}{\sqrt{41}}[/tex]

[tex]u=\frac{4i }{\sqrt{41}}-\frac{5j}{\sqrt{41}}[/tex]

We rationalize to get

[tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]

ANSWER

domain:

[tex]x \geqslant - 3[/tex]

Range

[tex]y \leqslant - 2[/tex]

EXPLANATION

The given function is

[tex]f( x) = - \sqrt{x + 3} - 2[/tex]

This base of this function is

[tex]y = \sqrt{x} [/tex]

This function has been shifted to the left 3 units and down 2 units.

This function is reflected in the x-axis.

Therefore graph starts at (-3,-2) and move down forever.

The domain is obtained using the expression under the radical sign.

It must be greater than or equal to zero.

[tex]x + 3 \geqslant 0[/tex]

[tex]x \geqslant - 3[/tex]

The range is

[tex]y \leqslant - 2[/tex]

Answer:

The answer is D. 51,200

Step-by-step explanation:

64000/x=100/80

(64000/x)*x=(100/80)*x       - we multiply both sides of the equation by x

64000=1.25*x       - we divide both sides of the equation by (1.25) to get x

64000/1.25=x

51200=x

x=51200

The number of people who were supporters of the home team is 51,200, the correct answer is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The home team= 80%

Visiting team= 20%

Now,

If 80% of the people attending the football game were supporters of the home team, then we can find the number of people who were supporters of the home team by multiplying the total number of people attending the game by 80%:

= 0.8 * 64,000

= 51,200

Therefore, by algebra the answer will be 51,200.

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Answer:

C.

Step-by-step explanation:

A - Perpendicular lines always touch each other at least once.

B - Parallel lines never touch.

D- Not always true.

C is true. If they are not in the same plane they are skewed lines.

The true statement is C: Parallel lines are always in the same plane. Perpendicular lines do intersect, while parallel lines do not, and perpendicular lines can certainly be in the same plane. Hence, correct option C.

The question seeks to determine the accuracy of given statements about geometric relationships between. Perpendicular lines and parallel lines. Based on the provided theorems, the true statement is: C. Parallel lines are always in the same plane.

This is because if two lines are parallel, they will be equidistant from each other at all points, which can only occur if they are in the same plane. Statements A, B, and D are false.

Perpendicular lines do intersect at a 90-degree angle.

Parallel lines, by definition, never intersect as they are always equidistant.

Perpendicular lines can be in the same plane or in different planes, although a line that is perpendicular to a plane must lie in another plane.

Answer:

42.5

Step-by-step explanation:

110 - 25 divided by 2 because

angle ABC = (angle AC- angle DE)÷2

Answer:

The third table

Step-by-step explanation:

A linear function must increase or decrease at a constant rate. All the tables either add 1 or subtract 1 each time x increases except for the third one which at one point adds two. This is not a consistent increase and therefore is not linear

Answer:

3ed tabel

Step-by-step explanation:

adds 1 to both sides so its a non leirn

Answer:the probability is 0.5

Step-by-step explanation:

It would be 37’000 because 20% of 185000 is 37’000 which you get by 20 x 185000 and dividing the answer to 100.

Answer:

D and E

Step-by-step explanation:

2 and 3 are verticle angles

1 and 4 add up to more than 180

angles 1 2 and 3 add up to more than 180

Based on the figure, the statements are true include;

D. m∠3 ≅ m∠4 = m∠1 ≅ m∠2

E. m∠1 ≅ m∠4 are vertical angles.

In Mathematics and Euclidean Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two lines intersect each other are always congruent, which means being equal to each other.

By applying the vertical angles theorem to the lines, we have the following congruent angles:

m∠1 ≅ m∠4

m∠2 ≅ m∠3

Based on linear pair theorem, we have the following supplementary angles;

m∠3 + m∠4 = 180°

m∠1 + m∠2 = 180°

m∠3 ≅ m∠4 = m∠1 ≅ m∠2 (transitive property).

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Answer:

The length of the other diagonal is 10 units

Step-by-step explanation:

we know that

The area of a Rhombus is equal to

[tex]A=\frac{1}{2}[D1D2][/tex]

where

D1 and D2 are the diagonals of the rhombus

we have

[tex]A=65\ units^{2}[/tex]

[tex]D1=13\ units[/tex]

substitute in the formula and solve for D2

[tex]65=\frac{1}{2}[(13)D2][/tex]

[tex]130=[(13)D2][/tex]

[tex]D2=130/13=10\ units[/tex]

Answer:

10

Step-by-step explanation:

2x+6=20

move 7 to the right side.

The sign changes from positive to negative. whenever moving a number to the other side the sign changes.

2x+6-6=20-6

2x= 14

Divide by 2 for both of the numbers

x=7

check answer:

Substitute x into the equation

2(7)+6=20

20= 20

Answer: x=7

The solution of the given linear equation in one variable is x = 7.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.

Given is a linear equation in one variable, 2x+6 = 20,

We need to find its solution,

Since, the given linear equation has only one variable, so it will have only one solution.

The equation is =

2x+6 = 20

Solving for x,

2x = 20-6

2x = 14

x = 7

Hence, the solution of the given linear equation in one variable is x = 7.

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Answer:

Step-by-step explanation:

(1) 4x = 200

(2) 50

Answer:

4x = 200

50

Step-by-step explanation:

One scarf = $4

Number of scarves = x

Amount she needs to earn = $200

Equation

4x = 200

Number of scarves

= 200 ÷ 4

= 50

Is the answer 25? Thats what I got.

The correct answer is b

Answer:

x=30

Step-by-step explanation:

Add up all of the values of the angles and set it equal to 180 degrees since a triangle is always made up of angles that have a sum of 180 degrees.

x+2x+3x=180

6x=180

x=30

First plug in g(x) into f(x)

F((g(x))=2(2x+3)

And now you plug in -8

F(g(-8))=2(-16+3)

F(g(-8))=2(-13)

F(g(-8))=-26

Find the jets speed per hour by dividing distance by time:

600 miles /  5 hours = 120 miles per hour. ( Rate of speed)

Now multiply the speed by time:

120 miles per hour x 14 hours = 1,680 miles.

Answer:

120 miles per hour

Step-by-step explanation:

Answer:The starting value is 20,300, and the value is decreasing by 9.5% each year.

Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.

A decrease by 9.5% corresponds to multiplying by 91.5% each year.

We write . We plug in 11 years for t.

$7,671.18

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Step-by-step explanation:

Answer:

The starting value is 20,300, and the value is decreasing by 9.5% each year.

Step-by-step explanation:

Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.A decrease by 9.5% corresponds to multiplying by 91.5% each year.We write . We plug in 11 years for t.

Answer:

option b

1 , 16, 121 , 13456

Step-by-step explanation:

Given in the question a function, f(x) = (x - 5)²

initial value [tex]x_{0}[/tex] = 4

First iteration

f(x0) = f(4) = (4 - 5)² = (-1)² = 1

x1 = 1

Second iteration

f(x1) = f(1) = (1 - 5)² = (-4)² = 16

x2 = 16

Third iteration

f(x2) = f(16) = ( 16 - 5)² = (11)² = 121

x3 = 121

Fourth iteration

f(x3) = f(121) = (121 - 5)² = (116)² = 13456

x4 = 13456

Answer:

Step-by-step explanation:

[tex](3a^3)^x=27a^9\\\\(3a^3)^x=3^3a^{3\cdot3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(3a^3)^x=3^3(a^3)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\(3a^3)^x=(3a^3)^3\iff x=3[/tex]

Answer:

35 in²

Step-by-step explanation:

The irregular shaped can be divided into two squares and one rectangle, so the area will be the additions of the area of the squares and the rectangle

area of square A = L *B = 3 *3 = 9in²

area of square B = L * B = 4*4 = 16in²

area of rectangle C = L * B = 5 *2 = 10in²

th area of the irregular shape = 9 in² + 16 in² + 10 in² = 35 in²

Answer:

Center: (-9, -2)

Radius = 6

Step-by-step explanation:

The general equation of the circle is:

[tex]x^{2} + y^{2}+2gx+2fy+c=0[/tex]

The center of the circle is given as (-g, -f) and the radius of this circle is calculated as:

[tex]r=\sqrt{g^{2}+f^{2}-c}[/tex]

The given equation is:

[tex]x^{2} +y^{2}+18x+4y+49=0[/tex]

Re-writing this equation in a form similar to general form:

[tex]x^{2} +y^{2}+2(9)(x)+2(2)(y)+49=0[/tex]

Comparing this equation with general equation we get:

g = 9

f = 2

c = 49

Thus center of the given circle is (-g, -f) = (-9, -2)

The radius of the circle will be:

[tex]r=\sqrt{9^{2}+2^{2}-49}=6[/tex]

Thus the radius of the given circle is 6.

Answer:

Step-by-step explanation:

b+s=18

s=18-b

1.50 b+2.50 s=38

multiply by 4

6.00 b+10.00 s=152

divide by 2

3 b+5 s=76

3 b+5(18-b)=76

3 b+90-5 b=76

-2b=76-90

-2b=-14

divide by -2

b=7

s=18-7=11

There are total 11 packets of squash seeds and 7 packets of basil seeds.

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.

According to the given question.

Cost of one packet of basil seeds = $1.50

Cost of one packet of squash seeds = $2.50

Cost of 18 packets of seeds = 38

Also, b represents the number of packets of basil seeds and s represents of numbers of squash seeds.

Therefore, from the given conditions we get some system of equations

[tex]s + b = 18..(i)[/tex]

and [tex]b(1.50) + s(2.50) = 38...(ii)[/tex]

From equation (i)

[tex]s = 18-b[/tex]

Substitute the value of s in the equation (ii)

⇒[tex]1.50b+(18-b)2.50 =38[/tex]

⇒ [tex]1.50b + 45 - 2.50b = 38[/tex]

⇒[tex]-b = 38-45[/tex]

⇒ [tex]-1b =- 7[/tex]

⇒[tex]b = 7[/tex]

So, [tex]s = 18 - 7 =11[/tex]

Hence, there are total 11 packets of squash seeds and 7 packets of basil seeds.

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Your probability of getting a specific number on a die is 1/6. Since you have 2 dice the probability for each is 1/6. Multiply those together to find the probability that the numbers would be the same. So, 1/36 is the correct answer.

Answer:

The answer in the attached figure

Step-by-step explanation:

step 1

Find the area of one blue square

[tex]A=6^{2}=36\ ft^{2}[/tex]  

step 2

Find the area of one orange triangle

[tex]A=(1/2)8^{2}=32\ ft^{2}[/tex]

Part 1) [tex]256\ ft^{2}[/tex]

Divide the total area by the area of one orange triangle

[tex]256/32=8\ triangles[/tex]

Part 2) [tex]180\ ft^{2}[/tex]

Divide the total area by the area of one blue square

[tex]180/36=5\squares[/tex]

Part 3) [tex]168\ ft^{2}[/tex]

Let

x----> the number of blue squares

y ------> the number of orange triangles

we know that

[tex]36x+32y=168[/tex]

Construct a table and prove different values for x and for y

we have

x=2, y=3

Two blue squares and three orange triangles

Area of blue squares

[tex]A1=2*(36)=72\ ft^{2}[/tex]

Area of an orange triangles

[tex]A2=3*(32)=96\ ft^{2}[/tex]

so

the area total is

[tex]72+96=168\ ft^{2}[/tex]

Answer:

D

Step-by-step explanation:

5 divided by 3 is 1.6666 which is the same as 1 and 2/3

The correct answer is D

Answer:

Part 1) The area of the shaded region is [tex]2.1\pi\ m^{2}[/tex]

Part 2) The length of the arc AB is [tex]2.5\pi\ in[/tex]

Part 3) The area of the shaded region is [tex]56.53\pi\ in^{2}[/tex]

Step-by-step explanation:

Part 1) Find the area of the shaded region

step 1

Find the area of the circle

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=3\ m[/tex]

substitute

[tex]A=\pi (3)^{2}[/tex]

[tex]A=9\pi\ m^{2}[/tex]

step 2

we know that

The area of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the area of the shaded region with a central angle of 84 degrees

[tex]\frac{9\pi }{360} =\frac{x }{84}\\ \\x=(9\pi)*84/360\\ \\x=2.1\pi\ m^{2}[/tex]

Part 2) What is the length of arc AB?

step 1

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ in[/tex]

substitute

[tex]C=2\pi (5)[/tex]

[tex]C=10\pi\ in[/tex]

step 2

we know that

The length of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the length of the arc AB with a central angle of 90 degrees

[tex]\frac{10\pi }{360} =\frac{x }{90}\\ \\x=(10\pi)*90/360\\ \\x=2.5\pi\ in[/tex]

Part 3) Find the area of the shaded region given that XY measures 8 in

step 1

Find the area of the circle

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]XY=r=8\ in[/tex]

substitute

[tex]A=\pi (8)^{2}[/tex]

[tex]A=64\pi\ in^{2}[/tex]

step 2

we know that

The area of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the area of the shaded region with a central angle of (360-42)=318 degrees

[tex]\frac{64\pi }{360} =\frac{x }{318}\\ \\x=(64\pi)*318/360\\ \\x=56.53\pi\ in^{2}[/tex]