Which pairs of angles in the figure below are vertical angles?
Check all that apply.

Answer:

48 cm²

Explanation:

Let the breadth be b, then the length is 3b

P = 2(Length + Breadth)

32 = 2(3b + b)

32 = 2(4b)

8b = 32

b = 4

Breadth is 4 cm

Length: 3b = 3(4) = 12 cm

Area of rectangle:

Length × Breadth

12 × 4

48 cm²

Given :-

To Find :-

Solution :-

Using formula;

Where;

We have;

By putting all values in formula we get;

→ 2(3x + x) = 32

→ 2(4x) = 32

→ 2 × 4x = 32

→ 8x = 32

→ x = 32/8

After dividing 32 with 8, we get;

→ x = 4

Hence;

Now, using formula;

Where;

We have;

By putting all values in formula we get;

→ Area of rectangle = 12 × 4

By multiplying 12 with 4, we get;

→ Area of rectangle = 48 cm²

Answer:

[tex]\fbox {2,400 pounds}[/tex]

Step-by-step explanation:

Information we have :

What we need to find :

Solving :

Answer:

Anita= 25 years old

Sumbo= 10 years old

Step-by-step explanation:

Start by forming 2 equations that represent the given information.

Let Anu's and Sumbo's ages be A and S respectively.

A= S +15 -----(1)

A² +S²= 725 -----(2)

Now, solve for A and S by substitution.

Substitute (1) into (2):

(S +15)² +S²= 725

Expand:

S² +2(S)(15) +15² +S²= 725

2S² +30S +225= 725

-725 on both sides:

2S² +30S -500= 0

Divide both sides by 2:

S² +15S -250= 0

Factorise:

(S +25)(S -10)= 0

S +25= 0             or            S -10= 0

S= -25 (reject)     or            S= 10

Sumbo's age cannot be a negative value hence -25 is rejected.

Substitute S= 10 into (1):

A= S +15

A= 10 +15

A= 25

Answer:

Speed of light 186000 miles/second.

it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.

Step-by-step explanation:

Earth travels around the sun in a slightly oval-shaped orbit, known as an ellipse. Therefore, the planet's distance from the sun changes throughout the year.

However, the average distance from Earth to the sun is about 93 million miles (150 million kilometres). Scientists also call this distance one astronomical unit (AU).

A universe is a big place, and sometimes researchers use astronomical units to communicate how far celestial objects are separated from one another. For example, Jupiter orbits about 5 AU from the sun.

The distance between the earth and the sun d= velocity of light × time taken to reach light from the sun to earth

Distance from Earth to Sun=93000000 miles.

Speed of light = 186000 miles/second.

=>  [tex]\frac{93000,000}{186000}[/tex]

=> 500 seconds.

=> 8.333 minutes

it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.

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By solving a system of equations, we will see that the parking lot is 210ft by 200ft.

For a rectangle of length L and width W, the perimeter is:

P = 2*(L + W)

And the area is:

A = L*W

Here we know that the perimeter is 820 ft and the area is 42,000 ft²

Then we can write the two equations (ignoring units).

820 = 2*(L + W)

42,000 = L*W

We can isolate L in the first equation to get:

820/2 = L + W

410 - W = L

Now we can replace that in the other equation:

42,000 = (410 - W)*W = 410*W - W^2

Now we want to solve the quadratic equation:

-W^2 + 410*W - 42,000 = 0

The solutions are given by:

[tex]W = \frac{-410 \pm \sqrt{410^2 - 4*(-1)*(-42000)} }{-2} \\\\W = \frac{-410 \pm 10 }{-2}[/tex]

Then the solutions are:

W = (-410 + 10)/(-2) = 200

W = (-410 - 10)/2 = 210

If we take W = 200, then:

L = 410 - W  = 410 - 200 = 210

So we can conclude that the parking lot is 200ft by 210ft.

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Answer: C, 210 ft

Step-by-step explanation: edge :)

There are 210 different three-digit whole numbers that can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated.

To calculate how many different three-digit whole numbers can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated, we need to use the permutation formula.

The number of permutations of n objects taken r at a time, where order matters and objects cannot be repeated, is given by:

P(n,r) = n! / (n-r)!

In this case, we have 7 digits to choose from, and we want to form a three-digit number, so r = 3. Therefore, the number of different three-digit whole numbers that can be formed is:

P(7,3) = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210

Each of these numbers will be unique, as we are not allowed to repeat any of the digits.

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Answer: 10

Step-by-step explanation:

[tex]\frac{5}{x+5} (2x-5(2))\\\frac{5}{x+5} (2x-10)\\\frac{10x-50}{x+5}\\\frac{10(x+5)}{x+5} \\\frac{10}{1} \\10[/tex]

The three consecutive integers are 15 16 and 17.

Step 1:

Let  X be the first integer. Since they are consecutive, it means that the second number will be X + 1 and the third number will be X + 2 and sum of the first and the third should add up to 32. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) be the three consecutive integers.

Step 2:

The sum of the first and the third should add up to 32.

X + ( X + 2 )= 32

2X + 2= 32

2X = 32 - 2

2X = 30

X = 30/2

X=15

Hence the first number is 15, the second number is 15 + 1, and the third number is 15 + 2.

Therefore, three consecutive integers in which the sum of the first and the third is 32 are 15 16, and 17.

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Using a system of equations, the total number of marbles that they have is given by:

A. 27.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

Eve has two more marbles than Solene, hence:

x = y + 2.

Solene has twice as many marbles as Steve, hence:

Steve has 7 less marbles than eve, hence:

z = x - 7.

Hence:

[tex]\frac{y}{2} = x - 7[/tex]

y = 2(x - 7)

y = 2(y + 2 - 7)

y = 2y - 10

y = 10.

Then:

Hence the total is given by:

T = 12 + 10 + 5 = 27.

Which means that option A is correct.

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The zeroes of the function will be [tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]

A quadratic function is given by ax² +bx+c = f(x)

The given quadratic function is

f(x) = 6x² +12x - 7

The zeroes of the function will be given by

f(0) = 0

6x² +12x - 7 = 0

The zeroes are given by

[tex]\rm \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

here

a = 6

b = 12

c = -7

Therefore the zeroes of the function will be

[tex]\rm \dfrac {-12 \pm \sqrt{12^2 -4*6*(-7)}}{2 *6}[/tex]

[tex]\rm \dfrac {-12 \pm \sqrt{312}}{12}[/tex]

[tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]

Therefore these are the two zeroes of the function.

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Answer:

the answer is B. 140 units²

The value of expression is n=3 and r= 16

An expression is a set of terms combined using the operations +, – , x or , /.

Given:

[tex](4k^{7})^{3} = 4^{n}* (k^{7})^{3} = 64 k^{21}[/tex]

[tex](64 k^{21}) = 4^{n}* k^{21} = 64 k^{21}[/tex]

[tex]4 ^{3} * k^{21}= 4^{n}* k^{21}[/tex]

On comparing

n=3

Now,

[tex](-3r^{-4})^{-4} = (-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}[/tex]

[tex](-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}\\1/ (-3)^{4} * 1/(r^{-4})^{4} = 1/81* r^{m}\\1/ (-3)^{4} * (r^{16}) = 1/81* r^{m}[/tex]

1/81 * r^16 = 1/81 * r^{m}

On compairing

r = 16.

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Answer:

answer in picture

Step-by-step explanation:

Answer:

A set is a well-defined collection of distinct mathematical objects.

Answer:

D. Sqroot6

Step-by-step explanation:

6 is not a perfect square. So it is a non-repeating decimal that never ends

sqroot6 ~=

2.4494897428...

this is an irrational number.

The rest on the numbers can be written as a ratio:

0.45=45/100=9/20

0.63636363

= 63/99 = 7/11

sqrt25 = 5 = 5/1

that means they are rational.

The answer is simple

First find the angle measures of first triangle:

statement:

we know that the sum of 45 and 30 sums up to the opposite angle and that is equal to 75, then to find the next remaining angle:

180-(75+20)=85

The you find the supplement of 85:

180-85=95

so x = 95

Hope it helps

Answer:

x = 9 or B

Step-by-step explanation:

Formula

(x + 2)^2 = 121                        

Comment

The easiest way to do this is to take the square root immediately, which is usually possible.

Solution

√(x + 2)^2 = √121                     Take the square root

x + 2 = 11                                   Subtract 2 from both sides

x + 2 -  2 = 11 - 2

x = 9

Answer: B) 9 inches by 9 inches

Step-by-step explanation:

Edg 2022

i beilive this is unknown

The expression written in equivalent form with a common denominator is -1/6

Fractions are written as ratio of two integers. For instance a/b is a fraction.

Given the sum of the fractions shown;

-3/4 and 5/8

Sum = -3/4 + 5/8

Sum = 5/8 - 3/4

Sum = 5-6/8

Sum  = -1/8

Hence the sum of the given fraction -1/3 and 5/8 is -1/6

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The angle θ to the diameter that she should row is; θ = 56.44°

It should be noted that;

a = 90° - θ. Thus;

b = 2θ

For any circle, the angle subtended (in radians) is equal to the arc length (d_w ) divided by the radius (1.2). Thus; d_w = 4θ .

The time required to walk this distance is given by;

t_w = 4θ/5 = 0.8θ

The distance rowed is given by: cos θ = d_r/2.4

d_r = 2.4cos θ while the time needed for it is;

t_r = 2.4cos θ/3.5

t_r = 0.6857θ

Thus, total time is;

T(θ) = t_r + t_w

T(θ) = 0.6857θ + 0.8θ

T(θ) = 1.4857θ

Now we need the critical numbers:

T'(θ) = 1 - 1.2 sin θ

At T'(θ) = 0, we have;

1 - 1.2 sin θ = 0

1/1.2 = sin θ

θ = sin⁻¹(1/1.2)

θ = 56.44°

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Answer:

2:45

Step-by-step explanation:

1 1/2 hour is 1 hour and 30 minutes.

If we add 30 minutes to 1:15, we get 1:45

if we add 1 hour to 1:45, we get 2:45, which is our answer.

Answer:

B. 47 7/12

Step-by-step explanation:

=126 1/4 - 78 2/3

Change the two mix fraction to improper fractions.

= 505/4 - 236/3

= 1515-944/12

= 571/12

= 47 7/12

27

Solution:

21 + ( -3 ) ( -2 )

21 + 6

27

Therefore, The answer is 27.

Answer:

eyyyyyyyyyy wassupppppppp

Answer:

240%

Step-by-step explanation:

Volume of a prism is Bh (area of the base * height)

Let's start with the small prism.

B=125

h=12

Volume = 125*12 = 1500 cubic cm

Bigger prism base are is 160% of 125. 1.6 * 125 = 200

Height is 6 cm more = 12+6 = 18

V = 200 * 18 = 3600

To find the percentage, divide 3600 by 1500. You get 2.4, which is 240%

The reflection is

A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.

For reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

and, for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y value the same.

So, by considering the above value rules the reflection of the given points as follows over respective axis.

E(7, 1) ⇒ (7, -1)

Here, the reflection is over x-axis because the y value is changing

F(-3, 5) ⇒ (-3, -5)

Here, the reflection is over x-axis because the y value is changing

G(6, -2) ⇒ (-6, -2)

Here, the reflection is over y-axis because the x value is changing.

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Answer: [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]

Step-by-step explanation:

We have [tex]y=2x^{2}[/tex] and [tex]y=3x-1[/tex].

Since both of the equations are set equal to y, we can conclude that:

[tex]2x^2 = 3x-1\\\\2x^{2}-3x+1=0\\\\(2x-1)(x-1)=0\\\\x=\frac{1}{2}, 1[/tex]

If [tex]x=\frac{1}{2}[/tex], then [tex]y=3\left(\frac{1}{2} \right)-1=1[/tex]

If [tex]x=1[/tex], then [tex]y=3-1=2[/tex]

Therefore, the solutions are [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]

The number of the meals possible is 350.

The complete question is given below:-

A menu has 5 choices of appetizers, ten main courses, and seven desserts. How many meals are possible?

The arrangement of the different things or numbers in a number of ways is called the combination.

Given that:-

The number of the combination of the meals will be calculated as:-

N = 5 x 10 x 7

N = 350

Therefore the number of the meals possible is 350.

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The attached diagram represents the Venn diagram of the sets

The sets are given as:

From the above representation, we have the following highlights:

Using the above highlights, we can now draw the Venn diagram

See attachment for the Venn diagram

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Answer:

36 seconds will be the answer... by looking down here↓:

Step-by-step explanation:

6 secs x 6 cycles = 36 seconds

9 secs x 4 cycles = 36 secs

12 ses x 3 cycles = 36 secs

Answer:

3x^2 + 3xz

Step-by-step explanation:

Under the assumption that I need to distribute,

(x + z)(x + 2x)

(x + 2x) is (3x)

3x(x + z) becomes 3x*x and 3x*z

3x*x = 3x^2

3x*z = 3xz

combine, 3x^2 + 3xz

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