Find the area and the perimeter of the shaded regions below. Give
your answer as a completely simplified exact value in terms of T (no
approximations). The figures below are based on semicircles or
quarter circles and problems b), c), and d) are involving portions of
a square.

Pls explain as best as you can i cant understand this stuff

Answer:

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: \{ 0,4 \}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: - {a}^{2} + 4a = 0[/tex]

[tex]\qquad \tt \rightarrow \: - ( {a}^{2} - 4a) = 0[/tex]

[tex]\qquad \tt \rightarrow \: {a}^{2} - 4a = 0[/tex]

[tex]\qquad \tt \rightarrow \:a(a - 4) = 0[/tex]

The two cases are :

or

We can conclude :

[tex]\qquad \tt \rightarrow \:solution \: (a) = \{ 0,4\}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex] \quad \quad \quad \quad\huge \tt \pink ❆ AnSweR \pink ❆[/tex]

[tex]\quad\quad \tt-a^2+4a= 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \quad\quad\tt⇢-1(a^2 - 4a) = 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢-1(a-4)a = 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢a-4=0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢a = 0[/tex]

-----------------------------------------------------------

[tex] \boxed{ \tt \blue{a = 0}}[/tex]

[tex]\boxed{ \tt\blue{a = 4}}[/tex]

Answer:

12.56637ft

Step-by-step explanation:

Formula: c=2π*r

c=2π*2 = 12.56637ft

Answer: y = -2/3x+23/3

Step-by-step explanation:

Parallel is the key point here. They gave points (7,3), 7 is the x value, 3 is the y value.

Take your equation

y = -2/3x+3 and substitute the 7 for the x value and 3 for the y value.

Like this...

3 = -2/3(7)+b

3 = -14/3 +b

Add 14/3 to 3

The answer is 23/3

So y = -2/3x+ 23/3

***Don't change -2/3 because it's asking for parallel***

***If 2 lines are parallel their slopes are equal***

The answer is [tex]11c^3[/tex].

By the inscribed angle theorem, [tex]m\angle AEB=30^{\circ}[/tex] and [tex]m\angle ACB=30^{\circ}[/tex].

Answer:

49/100

Step-by-step explanation:

So you can find the area of shaded area by finding the area of the circle inside the entire circle that has a diameter of 3 cm and 4 cm and then find the area of the most inner circle which only has a diameter of 4 cm and then subtract these 2. After that you want to find the area of the entire circle and then divide the area of the shaded area by the entire circle. The formula for the area of a circle is given as: [tex]\pi r^2[/tex]

Area of the two "inner" circles of a diameter of 4 and 3 cm. This gives you an entire diameter of 7 cm with a radius of 3.5. The area of this circle is [tex]\pi(3.5)^2[/tex] which is [tex]12.25\pi[/tex].

The area of the most inner circle only has a diameter only 4 cm. The radius is 2, thus the area of this circle is [tex]\pi (2)^2[/tex] which is [tex]4\pi[/tex]. Now subtract this from the 12.25 pi to find the area of the shaded area. This gives you the equation: [tex]12.25\pi-4\pi[/tex] which equals [tex]8.25\pi[/tex].

Now to find the area of the entire circle you add up all the "diameters" which gives you 4 cm + 3 cm + 3 cm = 10 cm. So the radius is 5. This gives you the equation: [tex]\pi(5)^2[/tex] which is equal to [tex]25\pi[/tex].

Now to find the fraction of circle that is shaded we divide the area of the shaded area and the area of the entire circle. This gives you the equation: [tex]\frac{12.25\pi}{25\pi}[/tex] but since it wants it as a fraction, I'm assuming it wants integers in the decimal and numerator place. So we can represent 12.25 as 12 + 1/4. And then convert the 12 into 1/4ths by multiplying by 4 and then adding that to the numerator. This makes the fraction [tex]\frac{49}{4}=12.25[/tex]. So now all we have to is divide the two values: [tex]\frac{\frac{49}{4}}{\frac{25}{1}}[/tex]. If you're wondering where the pi's when you can just cancel them out since they're both in the numerator and denominator. Now all we have to do is keep the 49/4, change the operator to multiplication, and flip the 25/1 to 1/25. This gives you the equation: [tex]\frac{49}{4} * \frac{1}{25}[/tex] which becomes [tex]\frac{49}{100}[/tex] which is the answer

The equation for the ellipse centered at the origin is C. x²/4 + y²/49 = 1.

Let the equation of the ellipse be:

x²/b² + y²/a² = 1

The co vertices are at (2, 0) and (-2, 0). The major axis is 14 units. Therefore, 2a = 14. This implies that a = 7 and a² = 7 × 7 = 49.

Therefore, since x²/b² + y²/a² = 1, this will be x²/4 + y²/49 = 1.

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The simplified expression are as follows;

6mn³ - mn² +  3mn³ + 15mn² =  9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

A simplified expression is express to its lowest term.

Therefore,

6mn³ - mn² +  3mn³ + 15mn²

combine like terms

6mn³  +  3mn³ - mn² + 15mn²

9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

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Simplified value of  subtraction of 7x+27x+2 from -5x^2-2x−5x 2 −2x. is [tex]-10x^{2} -38x-2[/tex].

Given Expressions  7x+27x+2 and  -5x^2-2x−5x 2 −2x.

Expressions refers to the combination of numbers, variables and symbols. It represents the relationship between variables. They are solved for finding out the value of variables. It is mainly not in equal to form. Subtraction is possible when subtracting the coefficients of same variable.

We have to subtract 7x+27x+2 from -5x^2-2x−5x 2 −2x. and to do this we need to first solve the expressions itself.

7x+27x+2=34x+2------------------1

[tex]-5x^{2} -2x-5x^{2} -2x[/tex]=[tex]-10x^{2} -7x-2x[/tex]--------------------2

Now subtract 1 from 2

=[tex]-10x^{2} -7x-2x[/tex]-34x+2

=[tex]-10x^{2} -38x-2[/tex].

Hence the simplified value of subtraction is [tex]-10x^{2} -38x-2[/tex].

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The sum of the expression (–x² + x) and (x² – 3x – 1) will be –2x – 1. Then the correct option is D.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression can be written as

(–x² + x) and (x² – 3x – 1)

Then the sum of the expression (–x² + x) and (x² – 3x – 1) will be

(–x² + x) + (x² – 3x – 1) = –2x – 1

Then the correct option is D.

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Answer:

32°, 58°

Step-by-step explanation:

Let one acute angle measure x.

The other acute angle measures 2x - 6.

The sum of the measures of the acute angles of a right triangle is 90.

x + 2x - 6 = 90

3x - 6 = 90

3x = 96

x = 32

2x - 6 = 2(32) - 6 = 58

Answer: 32°, 58°

Answer:

16 ounce can sells for 85 cents

Step-by-step explanation:

29cents / 6 ounce = 4.833cents/ounce

65cents / 16 ounce = 4.0625cents/ounce

4.0625 < 4.833

then:

the better deal is:

16 ounces per 65 cents

Answer:

11:37

Step-by-step explanation:

11 thin-crust pizzas

11+24=37 total pizzas

=>11:37

The value of x would be 35.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

In order to calculate the value of x in the parallelogram, we have to find the following;

Let ∠m = 2x - 10

∠n = 2x + 50

So, ∠m + ∠n = 180

2x-10 + 2x+50 = 180

4x + 40 = 180

4x = 180 - 40

4x = 140

x = 35

Hence, the value of x is 35.

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(1,18)

Let's verify

Verified

Answer:

y=x^2+7x+4

Step-by-step explanation:

because the sign before x^2 is positive, the graph would concave up, if there's only one intercept, it has to be the vertex. the vertex is the critical point.

solve every make the derivative of each function equals zero, you get the x where the vertex shall be, then get this"x" into y=x-5 see if the y in y=x-5 is equal to y=x^2+6x+9 or other options.

let me give u an example.

for y=x^2+x-4, the critical point shall be 2x+1=0,x=-1/2, and the y is -4.25,

if you plug x=-1/2 into y=x-5, it's -5.5, -5.5 doesn't equal to -4.25

Answer:

D

Step-by-step explanation:

y = x2 + 7x + 4

To calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.

The average speed thus calculated is 393.2722 miles per hour.

The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.

Thus, Average speed = Total Distance/Time taken.

In the question, we are informed that a horse holds the all-time record for running a 2-kilometer race in 1 min and 59.4 sec.

We are asked for the necessary conversions required to calculate the average speed of the horse for the race in miles per hour.

The necessary conversions that will be required will be:

Distance: 2 kilometers to miles.

Time: 1 minute 59.4 secs to hours.

To convert from kilometers to miles, we follow the conversion rate:

1 kilometer = 0.621371 miles.

Thus, distance = 2 kilometers = 2 * 0.621371 miles = 1.24274 miles.

For the time, we first convert seconds to time, using the conversion rate:

1 second = 1/60 minutes,

Therefore, 59.4 seconds = 59.4/60 minutes = 0.99 minutes.

Thus, the total time = 1.99 minutes.

To convert from minutes to hours, we follow the conversion rate:

1 minutes= 1/60 hours.

Thus, time = 1.99 minutes = 1.99/60 hours = 0.03316 hours.

Thus, the average speed of the horse = Distance/Time = 1.24274/0.003316 miles per hour = 393.2722 miles per hour.

Thus, to calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.

The average speed thus calculated is 393.2722 miles per hour.

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The solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.

The interval notations are used to represent numbers between two numbers excluding or including the numbers as per the use. We use the following four interval notations:

[a, b] ⇒ All numbers between a and b including both a and b.

(a, b) ⇒ All numbers between a and b excluding both a and b.

(a, b] ⇒ All numbers between a and b excluding a but including b.

[a, b) ⇒ All numbers between a and b including a but excluding b.

We are asked to write the solution for x ≥ 0 and x ≥ -5 in the interval notation.

We first write each inequality in interval notation:

x ≥ 0 ⇒ x are all numbers greater than 0 including 0. This can be written in the interval notation as [0, ∞). We don't include ∞ as it is indeterminant.

x ≥ -5 ⇒ x are all numbers greater than -5 including -5. This can be written in the interval notation as [-5, ∞). We don't include ∞ as it is indeterminant.

Now, we are asked to solve for x ≥ 0 or x ≥ -5. Since it is 'or', we take unions of the two sets, that is the solution is:

[0, ∞) ∪ [-5, ∞) = [5, ∞).

Therefore, the solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.

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The two inside angles add up to the external angle's total. The m∠1 will be 69°. Option D is correct.

An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).

From the exterior angle property, the sum of the exterior angle is the sum of the two interior angles.

The m∠1 will be 69°.

Hence, option D is correct.

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Yosef's average weekly fuel cost would be $2537.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Yosef drove 12,900 miles last year. His truck's fuel efficiency averages 15 mpg.

Karla used 12900/15 = 860 gallons to drive 12900 miles.

The average cost of gas last year was $2.95 per gallon.

Therefore, Yosef's average weekly fuel cost would be

2.95 x 860 = $2537

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Answer:

F=9/5c+32

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf \$ \ 8.79\ per\ hour}[/tex]

Step-by-step explanation:

Work hours = 2:00 pm - 11:00 pm

So,

9 hours = $79.11

Using unitary method

9 hours = $79.11

Divide both sides by 9

1 hour = $79.11/9

1 hour = $8.79

So, Kenya is being paid $8.79 per hour.

[tex]\rule[225]{225}{2}[/tex]

The expression equivalent to -21.8 - (-18.3) would be option A; -21.8+18.3.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple.

The given expression is

-21.8 - (-18.3)

So, open the bracket and distribute the negative;

-21.8  (+18.3)

Thus, the expression equivalent to -21.8 - (-18.3) would be option A; -21.8+18.3.

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Answer: A

Step-by-step explanation: –21.8 – (–18.3) = -3.5 and –21.8 + 18.3 = -3.5

Answer:

19

Step-by-step explanation:

Given:

To find how many full bags of sweets the machine can fill, divide the total number of sweets by the number of sweets per full bag:

⇒ 4275 ÷ 28 = 152.6785714...

Therefore, the machine can fill 152 full bags.

To calculate how many sweets are left, subtract the product of the number of full bags and the number of sweets per bag from the total number of sweets:

⇒ 4275 - (152 · 28)

⇒ 4275 - 4256

⇒ 19

Therefore, there are 19 sweets left after the machine has filled as many bags as possible.

The solution will be a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Inequalities are equations that are separated by an equal sign. Given the inequality expression

3(8 – 4x) < 6(x – 5)

Expand

3(8) - 3(4x) < 6x - 6(5)

24 - 12x < 6x - 30

Collect the like terms

-12x - 6x < -30 - 24

-18x < -54

x > 3

Hence the solution will be a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

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