Quadrilateral CDEF is inscribed in circle A, so m arc CDE + m arc CFE= 360°. ∠CFE and ∠CDE are inscribed angles, which means that their measures are _________________. So, _________________. Using the substitution property of equality, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary. twice the measure of their intercepted arcs; 2 ⋅ m arc CDE= m∠CFE and 2 ⋅ arc CDE = m∠CDE twice the measure of their intercepted arcs; marc CDE= 2 ⋅ m∠CFE and arc CFE = 2 ⋅ m∠CDE one half the measure of their intercepted arcs; m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2 ⋅ m∠CDE one half the measure of their intercepted arcs; 2 ⋅ m arc CDE= m∠CFE and 2 ⋅ arc CFE= m∠CDE

Answers and Step-by-step explanations:

9. Subtract root x from both sides: [tex]\sqrt{x+12} =6-\sqrt{x}[/tex]

Square both sides: x + 12 = 36 - 12[tex]\sqrt{x}[/tex] + x

Subtract x and 36 from both sides: -24 = -12[tex]\sqrt{x}[/tex]

Divide both sides by -12: 2 = [tex]\sqrt{x}[/tex]

Square both sides again: x = 4

10. Switch the places of the two root expressions: [tex]\sqrt{4x-1} =1-2\sqrt{x}[/tex]

Square both sides: 4x - 1 = 1 - 4[tex]\sqrt{x}[/tex] + 4x

Subtract 4x and 1 from both sides: -2 = -4[tex]\sqrt{x}[/tex]

Divide by -4 from both sides: 1/2 = [tex]\sqrt{x}[/tex]

Square both sides again: x = 1/4

11. Square both sides: 4x^2 = 4x - 1

Move all the terms to one side: 4x^2 - 4x + 1 = 0

Factorize: (2x - 1)(2x - 1) = 0  ⇒  x = 1/2

12. Square both sides: 4x - 1 = 4 - 8x + 4x^2

Move all the terms to one side: 4x^2 - 12x + 5 = 0

(2x - 5)(2x - 1) = 0  ⇒  x = 5/2 or x = 1/2

Hope this helps!

Answer:

9. x = 4

10. x = ¼

11. x = ½

12. x = ½

Step-by-step explanation:

9. sqrt(x + 12) = 6 - sqrt(x)

Square both sides

x + 12 = 36 - 12sqrt(x) + x

12sqrt(x) = 24

sqrt(x) = 2

x = 4

10. 2sqrt(x) = 1 - sqrt(4x - 1)

Square both sides

4x = 1 - 2sqrt(4x - 1) + 4x - 1

-2sqrt(4x - 1) = 0

sqrt(4x - 1) = 0

4x - 1 = 0

x = ¼

11. 2x = sqrt(4x - 1)

4x² = 4x - 1

4x² - 4x + 1 = 0

4x² - 2x - 2x + 1 = 0

2x(2x - 1) - (2x - 1) = 0

(2x - 1)(2x - 1) = 0

x = ½

12. sqrt(4x - 1) = 2 - 2x

4x - 1 = (2 - 2x)²

4x - 1 = 4 - 8x + 4x²

4x² - 12x + 5 = 0

4x² - 2x - 10x + 5 = 0

2x(2x - 1) - 5(2x + 1) = 0

(2x - 1)(2x - 5) = 0

x = ½ , 5/2

x = 2.5 is rejected because it doesn't satisfy the equation

* when solving equations involving radicals, make sure to verify your answers by plugging in the values in the initial equation

Answer:

probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG = 0.8668

Step-by-step explanation:

mean, μ = 80 mg/mi

Standard deviation, [tex]\sigma = 4 mg/mi[/tex]

probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG

[tex]P(X > x ) = P(z > \frac{x - \mu}{\sigma})[/tex]

[tex]P(X > x ) =1 - P(z < \frac{x - \mu}{\sigma})[/tex]

[tex]P(X > 86 ) =1 - P(z < \frac{86 - 80}{4})[/tex]

P(X > 86) = 1 - P(z < 1.5)

From the standard normal table, P(z < 1.5) = 0.9332

P(X > 86) = 1 - 0.9332

P(X > 86) = 0.0668

Answer:

In the picture above

Step-by-step explanation:

I hope that it's a clear solution and explanation.

Goodluck.

Answer:

370

Step-by-step explanation:

4^2 = 16

5^2 = 25

25 x 16 = 400

400 - 30 = 370

Your welcome! :D

The total possible outcomes of a serving would be 16.

Step-by-step explanation:

Given that,

The total number of beverages = b = 4 ( water, milk, juice,

or tea)

Ice options = i = 2 (with or without ice)

Serving options = s = 2 (glass or plastic cup)

We have to find the total possible outcome x, that can be calculated using

x = b x i x s

Putting the values in the equation, we get

x = 4 x 2 x 2

x = 16

Hence, the total possible outcomes of a serving would be 16.

Given:

The base of the triangle = 5 mm

The other side of the of the triangle = 9 mm

The 3rd side of the triangle = 9 mm

The height of the triangle = 7 mm

The height of the prism = 12 mm

To find the surface area of the the prism.

Formula:

The surface area of a triangular prism is

[tex]SA = bh+(s_{1} +s_{2} +s_{3})H[/tex]

Where,

h be the height of the triangle

H be the side of the prism

b be the base of the triangle

[tex]s_{1} ,s_{2} ,s_{3}[/tex] are the sides of the triangle.

Now,

Putting, b=5, H= 12, h=7, [tex]s_{1} =5,s_{2} =9,s_{3} =9[/tex] we get,

[tex]SA = (5)(7)+(5+9+9)(12)[/tex]

or, [tex]SA = 35+276[/tex]

or, [tex]SA = 311[/tex] sq mm

Hence,

The surface area of the triangular prism is 311 sq mm.

Answer:

d) 1/3

Step-by-step explanation:

fish = 3 + 2 + 1 = 6

bluegill = 2

p = 2/6 = 1/3

Answer:

1/3

Step-by-step explanation:

The total number of fish that were caught

3 trout + 2 bluegill + 1 bass = 6

P (bluegill) = number of bluegill/ total

                 =2/6

                  = 1/3

The total surface area will be 1360.2 square centimeters.

To find the amount of gift wrap needed to cover Jenny's gift box shaped like a triangular prism, we first need to calculate the surface area of the prism.

The box has two triangular bases and three rectangular sides.

Therefore,

Calculate the total surface area of the triangular prism: 2(base area) + (base perimeter * prism height)

Substitute the values:

= 2(1/2 * base side * base height) + (base side * 3base side + prism height)

Solve to find the total surface area:

= 2(1/2 * 12 cm * 10.4 cm) + (12 cm * 3 * 12 cm + 68 cm)

= 1360.2

After calculations, the total surface area will be 1360.2 square centimeters.

The amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.

To find the amount of gift wrap needed to cover a triangular prism, we need to calculate the total surface area of the prism.

Given information:

- Each side of the base is 12 cm.

- The triangular base has a height of 10.4 cm.

- The prism is 68 cm tall.

Calculate the area of the triangular base.

Area of a triangle = (1/2) × base × height

Area of the triangular base = (1/2) × 12 cm × 10.4 cm

Area of the triangular base = 62.4 cm²

Calculate the perimeter of the triangular base.

Perimeter of a triangle = sum of all sides

Perimeter of the triangular base = 12 cm + 12 cm + 12 cm = 36 cm

Calculate the area of the rectangular faces.

Area of a rectangle = length × width

Area of each rectangular face = 36 cm × 68 cm = 2,448 cm²

Total area of the rectangular faces = 2 × 2,448 cm² = 4,896 cm²

Calculate the total surface area of the triangular prism.

Total surface area = Area of the triangular base + Area of the rectangular faces

Total surface area = 62.4 cm² + 4,896 cm²

Total surface area = 4,958.4 cm²

Therefore, the amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.

Answer:

The likelihood that a math teacher is selected is 2 out of 5 possible cases or 40% chance.

Step-by-step explanation:

Please kindly check the attached files for explanation

Final answer:

It is likely that a math teacher will be chosen for the dunking booth since the probability is 8 out of 20 or 40%, which is close to a 50% chance.

Explanation:

To determine if it is likely that a math teacher will be chosen for the dunking booth, we need to look at the probability of selecting a math teacher from the total group of teachers. The total number of teachers is the sum of the English, math, science, and social studies teachers, which is 3 + 8 + 5 + 4 = 20. Since there are 8 math teachers, the probability of selecting a math teacher is 8 out of 20, or 40%.

This probability can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4, giving us 2 out of 5, or 40%. This indicates that there is a likelihood of 2 in 5 that a math teacher will be chosen, which can be considered likely since it is close to a 50% chance.

Answer:

-5x+5

Step-by-step explanation:

(6x-3)-(11x-8)=

6x-11x-3+8=

-5x+5

The subtraction of (6x -3) - (11x - 8) is 5(x - 1)

The subtraction method of algebraic terms takes a process whereby you first open the brackets, followed by rearranging variables with common-like terms.

Given that:

(6x -3) - (11x - 8)

Open brackets

= 6x - 3 - 11x + 8

Collecting like terms by rearrangement

= 6x - 11x - 3 + 8

= -5x + 5

Multiply through by (-)

= 5x - 5

Factorize out (5)

= 5(x - 1)

Therefore, we can conclude that the subtraction of (6x -3) - (11x - 8) is 5(x - 1)

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3 + 7 + 5 = 15 total marbles.

3 red, picking a red would be 3/15, reduced to 1/5

5 blue, picking a blue would be 5/15, reduced to 1/3

7 white, picking a white would be 7/15

Picking all 3 would be: 1/5 x 1/3 x 7/15 = 7/225

Answer:

7/225

Step-by-step explanation:

To find probability, we take the number of ways the specific event can occur and divide it by the number of ways any event can occur.

The probability of drawing a red marble is: (# of red marbles) / (total # of marbles) = 3/(3 + 7 + 5) = 3/15 = 1/5.

The probability of drawing a blue marble is: (# of blue marbles) / (total # of marbles) = 5/(3 + 7 + 5) = 5/15 = 1/3.

The probability of drawing a white marble is: (# of white marbles) / (total # of marbles) = 7/(3 + 7 + 5) = 7/15.

Now, we want these events to all occur for us. So, we must multiply them by each other: (1/5) * (1/3) * (7/15) = 7/225.

Thus, the probability is 7/225.

Hope this helps!

Answer:         1,424,600,000 =  1.4246 × 10^9

Step-by-step explanation:  ten to the power of 9 =1000000000

                                               1000000000 x  1.4246 = 1 ,424,600,000

Answer with Step-by-step explanation:

We are given that

[tex]f(x)=5x+9[/tex]

[tex]g(x)=3x^2[/tex]

f(x) is linear function

Domain of f(x)=R

g(x) is a quadratic function

Domain of g(x)=R

[tex](f+g)(x)=f(x)+g(x)=5x+9+3x^2[/tex]

Domain of (f+g)=R

(f-g)(x)=f(x)-g(x)=[tex]5x+9-3x^2[/tex]

Domain of (f-g)=R

[tex]fg(x)=f(g(x))=f(3x^2)=5(3x^2)+9=15x^2+9[/tex]

Domain of fg=R

[tex]\frac{f}{g}=\frac{5x+9}{3x^2}[/tex]

The function is not defined where g(x)=0

[tex]3x^2=0[/tex]

[tex]x=0[/tex]

Domain of f/g=R-{0}

Answer:

The GCF for 84 and 90 is 6.

Step-by-step explanation:

The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Then the greatest common factor is 6.

Answer:

GCF=6

Step-by-step explanation:

In order to find the GCF of 84 and 90 you must find the prime factors of each term.

Answer:

50.24 mm²

Step-by-step explanation:

Area = pi × r²

3.14 × 4²

50.24 mm²

Answer:

The correct answer is C! I just got it right:)

Answer:

2155 or 5/11

Step-by-step explanation:

(5/11)4741=5×431=2155 boys

Answer:

y=2x-4

Step-by-step explanation:

Slope intercept form is:

y=mx+b

We need to isolate y to be able to write the equation in slope intercept form

-4x+2y=-8

Add 4x to both sides

-4x+4x +2y= -8+4x

2y= 4x-8

Divide both sides by 2

2y/2=4x/2-8/2

y=2x-4

Now it is in y=mx+b or slope intercept form.

Approximately 140 months have passed since Laura retired.

To find the number of months that have passed since Laura retired, we need to calculate the total number of months Laura's retirement savings can cover her living expenses, and then subtract that from the balance in her account.

First, we calculate the number of months Laura's retirement savings can cover her living expenses by dividing her total savings by the monthly withdrawal amount: $414,731.00 ÷ $2,224.00 = 186.41 months.

Then, we subtract the number of months from the balance in Laura's account to find the number of months that have passed since Laura retired: 186.41 - X = $381,371.00, where X is the number of months. So, X = 186.41 - $381,371.00 = 140.41.

Therefore, approximately 140 months have passed since Laura retired.

Answer:

f(x)=6

Step-by-step explanation:

By Substitution

f(x or coefficient of x)

=6 since X doesn't exist in question above

Final answer:

The value of f(x) is 6, indicating a constant function where the output is the same irrespective of the input. For constant functions, the total differential is zero as there is no change in the function value with varying x.

Explanation:

The question is asking for the value of f(x) when f(x) is equal to 6. This is a type of question that involves understanding how functions work. In this particular case, the question seems to be abstract, suggesting that f(x) = 6 for all x, indicating a constant function. A constant function is one where the output value is the same no matter what the input value is.

Considering this, without additional context or a specific function definition besides f(x) = 6, we presume that the student is being asked to recognize this as a constant function. Therefore, the value of f(x) is always 6, regardless of the value of x.

However, if we are considering a function that changes with respect to x, the total differential would be involved to find infinitesimal changes in f(x) as x changes. For a constant function like this one, the differential would be zero since the function's value does not change as x changes.

Answer:

-47.0

Step-by-step explanation:

The question pertains to Physics, specifically kinematics. The pumpkin's horizontal velocity and distance traveled are given, but without vertical distance, we can't compute the time of flight or height of the building. More information is needed.

The subject of your question is Physics, specifically kinematics, which is the study of motion. Given that the pumpkin was thrown horizontally with a velocity of 2.5 m/s and it landed a horizontal distance of 12m from the base of the building, we could find the height of the building or the time the pumpkin was in the air.

The time it takes the pumpkin to hit the ground depends solely on the vertical motion. So we must find the time it takes for an object to fall from the height of the building. This time of flight can be calculated by using a kinematic formula: 2gh = v², where g is the gravitational acceleration (9.8 m/s² on Earth).

However, as the vertical distance travelled by the pumpkin isn't provided in this problem, we can't calculate the time using the given data. More information is needed to solve this problem appropriately.

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Answer:

120 ways

Step-by-step explanation:

Answer:

$7544 is the amount paid

Step-by-step explanation:

In this question, we are asked to calculate the amount Leeco pay Macy given the data in the question.

Firstly, we calculate the Discount amount.

That would be 1% ( from 1/10)

that is 7,600 * 1% = $76

Now, we proceed to subtract this value from cost of office equipment; 7,600 - 76 = $7,524

Afterwards, we can now add the freight charges = $7,524 + 20 = $7544

Answer: LeeCo. pay Macy 7544 dollars

Step-by-step explanation:

Given that the office equipment was sold at $7,600

And  Sale terms were 1/10, n/30 FOB New York. Macy agreed to prepay the $20 freight.

Then,

7600 - 7600(0.01) + 20

= 7600 - 76 + 20

= 7544 dollars

LeeCo. pay Macy $7544

Answer:

54

Step-by-step explanation:

multiply 9 x 6 to get the answer above

The area of the picture frame, after subtracting the area of the displayed picture, is 30 square inches.

To find the area of the picture frame, we need to subtract the area of the picture it displays from the area of the entire frame.

The area of the entire frame can be calculated by multiplying its length by its width:

[tex]\[ \text{Area of frame} = \text{Length} \times \text{Width} \][/tex]

Given that the frame is 9 inches long and 6 inches wide:

[tex]\[ \text{Area of frame} = 9 \times 6 = 54 \text{ square inches} \][/tex]

Now, we need to subtract the area of the picture it displays. Since the picture is 6 inches long and 4 inches wide:

[tex]\[ \text{Area of picture} = \text{Length} \times \text{Width} = 6 \times 4 = 24 \text{ square inches} \][/tex]

So, the area of the picture frame is:

[tex]\[ \text{Area of frame} - \text{Area of picture} = 54 - 24 = 30 \text{ square inches} \][/tex]

Therefore, the area of the picture frame is 30 square inches.

Answer: The answer is B

Step-by-step explanation:

Answer:

A.  9.42

Step-by-step explanation:

Answer: 3

P's coordinates are:  

Y  X

1,  4

1,  2

2,  2

Once we multiply it by 3 it's equal to Q's coordinates.

Y   X

3,  12

3,  6

6,  6

Therefore, P was enlarged 3 times more.

The point P was enlarged by a factor of 3 in both the x and y directions to obtain point Q.

From the graph, the coordinates of point P are given as:

P:

(1, 4)

(1, 2)

(2, 2)

From the given coordinates, we can observe that the x-coordinates of Q are three times larger than the x-coordinates of P, and the y-coordinates of Q are also three times larger than the y-coordinates of P.

After multiplying each coordinate of P by 3, we obtain the coordinates of point Q:

Q:

(3, 12)

(3, 6)

(6, 6)

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Answer:

the answer to this is -7/6

Answer:

The population of Lasvegas = 1202000.

Population of Sacramento = 1479000

Step-by-step explanation:

Let the population of each be

 Las​ Vegas Nevada = L

and​

Sacramento, California = S

Initially L + S = 2681 000 people

Sacramento had 277 thousand more residents than Las Vegas

This mean that:

L = Population of Las Vegas

L+ 277,000 = population of Sacramento

2,681,000=L+(L+277,000)

2,681,000=2L + 277,000

2,681,000-277,000=2L

2,404,000=2L

2,404,000/2=L

1,202,000=L

The population of Lasvegas = 1202000.

1,202,000+277,000=1,479,000

Population of Sacramento = 1479000

Check base on the question.

2,681,000=1,202,000+1,479,000

2,681,000=2,681,000

Final answer:

To solve the problem, we used algebra to define variables for the population of Las Vegas and Sacramento, set up an equation based on the given information, and solved for the populations of both metropolitan areas.

Explanation:

The question involves solving a basic algebra problem to find the population of Las Vegas and Sacramento metropolitan areas when given the total combined population and the difference in populations between the two areas.

Let x represent the population of Las Vegas. Then, Sacramento's population would be x + 277277 thousand.

Solving the equation x + (x + 277277) = 26812681 will give us the populations of both areas.

Combine like terms to get 2x + 277277 = 26812681.

Subtract 277277 from both sides to get 2x = 26535404.

Divide both sides by 2 to find the population of Las Vegas, x = 13267702 thousand.

To find Sacramento's population, add 277277 to Las Vegas' population to get 13544979 thousand.

Therefore, the population of the Las Vegas metropolitan area was 13267702 thousand, and Sacramento's metropolitan area had a population of 13544979 thousand.