(x² + 3x + 2) ÷ (x + 2)​

Answer:

2 √3

Step-by-step explanation:

The value of sin 90° is 1, so we can simplify the expression as:

16 sin 10° sin 30° sin 50° sin 70° sin 90° = 16 sin 10° sin 30° sin 50° sin 70°

We can use the identity sin (90 - x) = cos x to rewrite sin 70° as cos 20°:

16 sin 10° sin 30° sin 50° sin 70° = 16 sin 10° sin 30° sin 50° cos 20°

We can use the identity sin (180 - x) = sin x to rewrite sin 170° as sin 10°:

16 sin 10° sin 30° sin 50° cos 20° = 8 sin 10° [2 cos 20° sin 30° sin 50°]

We can use the identity sin (2x) = 2 sin x cos x to simplify the expression inside the brackets:

8 sin 10° [2 cos 20° sin 30° sin 50°] = 8 sin 10° [sin 100° - sin 20°]

We can use the identity sin (180 - x) = sin x to rewrite sin 20° as sin 160°:

8 sin 10° [sin 100° - sin 20°] = 8 sin 10° [sin 100° - sin 160°]

We can use the identity sin (x + y) = sin x cos y + cos x sin y to rewrite sin 100° as sin (60° + 40°):

8 sin 10° [sin 100° - sin 160°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 160°]

We can use the identity sin (180 - x) = sin x to rewrite sin 160° as sin 20°:

8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]

Now, we can use the values of sin 60°, cos 40°, and sin 20°, which are:

sin 60° = √3/2

cos 40° = √[(1+cos 80°)/2] = √[(1+sin 10°)/4]

sin 20° = sin (60° - 40°) = sin 60° cos 40° - cos 60° sin 40° = (√3/2)(√[(1+sin 10°)/4]) - (1/2)sin 10°

Substituting these values into the expression, we get:

8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]

= 8 sin 10° [√3/2 × √[(1+sin 10°)/4] + 1/2 × sin 10° - (√3/2) × √[(1+sin 10°)/4]]

= 2 √3 sin 10° √[(1+sin 10°)/2]

Therefore, the value of the expression is:

16 sin 10° sin 30° sin 50° sin 70° sin 90° = 2 √3

Answer: 4

See the graph attached

Hope it helps

Answer:763.02

Step-by-step explanation:

r=9

R=r+9=18

[tex]A=R^{2}\pi-r^{2}\pi = \pi (R^{2}-r^{2})=\pi =243\pi \\\pi =3.14\\243\pi=763.02[/tex]

Answer:

763.02

Step-by-step explanation:

Area of a circle is πr²

so the area of the whole circle is the sum of both radius

9+9 = 18

so Area = 3.14 × 18² = 1017.36

then we subtract the white part to leave the shaded part

area of the white circle = 3.14 × 9² = 254.34

then 1017.36 - 254.34 = 763.02

Answer:

Option C

Step-by-step explanation:

The possible calculated length of the segment AC is a length of any value that exceeds around 7.15 feet.

If triangle ABC is an isosceles triangle, then the length of AC must be equal to the length of BC.

Let's denote the length of AC as "x".

To find the length of the diagonal line segment referred to as BD, which represents the height of the peaked roof, we can use the Pythagorean theorem:

BD² = AB² - (AC/2)²

BD² = 8² - (x/2)²

BD² = 64 - x²/4

In order for the roof to be peaked, BD must be less than x, otherwise the roof would be flat.

Therefore, we can set up the inequality:

x√(64 - x²/4) < x

64 - x²/4 < x²

Multiplying both sides by 4 gives:

256 - x² < 4x²

5x² > 256

Dividing both sides by 5 gives:

x² > 51.2

x > √(51.2)

x > 7.15 feet

As a result, any value greater than the square root of 51.2 (approximately 7.15 feet) is a possible length for AC.

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The possible lengths for AC are any values greater than 7.15 feet.

We are given that the triangle ABC is an isosceles triangle. This means that the length of segment AC must be equal to the length of segment BC.

Let x denote the length of AC.

With the aid of the Pythagorean theorem, the length of the diagonal line segment BD which denotes the height of the peaked roof is:

BD² = AB² - (AC/2)²

BD² = 8² - (x/2)²

BD² = 64 - x²/4

If the roof is to be peaked, then the length of segment BD must be less than x. Thus, we generate the inequality:

BD < x

√(64 - (x²/4)) < x

Square both sides to get:

64 - x²/4 < x²

256 - x² < 4x²

5x² > 256

x² > 51.2

x > √(51.2)

x > 7.15 ft

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The outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario can be written as S = { (1,3,5), (2,3,4), (2,4,3), (3,2,4), (3,4,2), (4,2,3), (4,3,2), (5,1,3)}

Outcome refers to the result of an action or event. It is the end result of the process and can be positive, negative, or a mix of both. Outcome can also refer to the impact of an event, such as the effect it has on the environment, the people affected, or the economy.

The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.

Each of the elements in this set represents a combination of numbers on the dice that will add up to 9 when rolled. For example, the first element of this set (1,3,5) means that if the three dice are rolled, the numbers shown on the dice will be 1, 3, and 5, and the sum of the numbers will be 9.

When determining the sample space for the outcome of rolling three dice, the order of the numbers does not matter. Therefore, the sets (2,3,4) and (4,2,3) are equivalent, since the sum of the numbers is still 9 regardless of the order.

In conclusion, the outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.

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Based on the information provided, the volume of the pyramid would be  5308.33 cubic centimeters.

The volume or the space occupied by the pyramid can be calculated using the following formula

V=(1/3)Ah

In this formula,  A is the area of the base and h is the height.

Area of the base: 6.5 x 3.5 = 22.75 squared centimeters.

Now, let's calculate the volume:

V = (1/3)*22.75 x 700 cm = 5308.33 cm^3 (Cubic centimeters)

Here 1 meter = 100 cm, then 7 m = 700 cm

Note: This question is incomplete; here is the missing information:

The base of a pyramid is 6.5 cm by 3.5cm and its height is 7m. What is its volume?

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Answer:

y = 2x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = 2 and point where line crosses y- axis (0, - 5 ) , then c = - 5

y = 2x - 5 ← equation of line

The time taken, in hours, for the bacteria to double in size, found using the given function is 26.25 hours.

What is a function?

A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

The given function is:

[tex]y = y_0e^{(0.0264t)}[/tex]

We are asked to find the time taken for the bacteria to double.

y = a number of bacteria at present time t.

y₀ = initial number of bacteria

When y = 2y₀

The function becomes,

[tex]2y_0 = y_0e^{(0.0264t)}\\\\2 = e^{(0.0264t)}\\\\ln (2) = 0.0264t\\\\0.693 = 0.0264t\\\\t = 26.25[/tex]

Therefore the time taken, in hours, for the bacteria to double in size, found using the given function is 26.25 hours.

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Answer: It will cost $58.80 to buy enough stain for the whole porch.

Step-by-step explanation: The area of Carmen's front porch is:

Area = length x width

Substituting the given values, we get:

Area = 12 ft x 7 ft

Area = 84 square feet

To find the cost of the stain, we need to multiply the area of the porch by the cost per square foot:

Cost of stain = Area x Cost per square foot

Cost of stain = 84 square feet x $0.70/square foot

Cost of stain = $58.80

Answer:

429

Step-by-step explanation:

Answer:

360 in^2

Step-by-step explanation:

Area of bottom rectangle : A = 7.5 x 17 = 127.5

Area of front rectangle: A = 6 x 17 = 102

Area of back rectangle: A = 4.5 x 17 = 76.5

Area of 2 triangles: 2(4.5 x 6) = 54

Total surface area = 127.5 + 102 + 76.5 + 54 = 360 in^2

Answer:

which of the following set of nos could not be the length of sides of aright angled triangles.

The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday

Given that

Combined hours = x - 2 + x + x - 3

When splitted, we have

Monday = x - 2

Wednesday = x

Friday = x + 3

To determine which statement is true, we need to compare the hours worked on Monday and Wednesday, and the hours worked on Wednesday and Friday.

By comparison, Option 1 is correct

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Answer:

Step-by-step explanation:

2 cups of water.

54,000 rounded to the nearest ten is 54,000  because the zeros after the 4 are insignificant

Rounding off in math is the process of approximating a number to a certain degree of accuracy. This involves changing the value of a number to one that is simpler or easier to work with, while still maintaining an acceptable level of accuracy.

For example, rounding off 3.75 to the nearest whole number would give you 4, while rounding off 3.75 to the nearest tenth would give you 3.8.

Rounding off 54000  to the nearest ten is still 54000 because the zeros after the 4 are insignificant

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Answer:

[tex]\frac{28.5km}{sec}[/tex]

In 10 seconds the earth will travel 288 km

Step-by-step explanation:

[tex]\frac{18miles}{sec}[/tex] x [tex]\frac{1.6km}{1 mile}[/tex] = [tex]\frac{28.8km}{sec}[/tex]

[tex]\frac{28.8km}{sec}[/tex] x [tex]\frac{10sec}{1}[/tex] = 288 km

Helping in the name of Jesus.

Using tautology, we can conclude that the argument here is invalid.

A compound statement known as a tautology is one that is true regardless of whether the individual statements inside it are true or false.

The Greek term "tautology," which means "same" and "logy," is where the word "tautology" comes from.

We need to build a truth-table and examine the truth value in the last column in order to determine whether a particular statement is a tautology.

It is a tautology if all of the values are true.

In the given case:

p is TRUE

and

q is FALSE

In this case:

p→q : is FALSE (the assumption “TRUE implies FALSE” is FALSE)

So, here:

p → (p→q) is equal to as p → FALSE

But p is TRUE so in that case it’s TRUE→ FALSE, which is in fact FALSE.

Since there a case where the expression is not true, then it’s not valid.

It’s invalid.

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Answer:

Para resolver este problema, primero debemos encontrar la cantidad total de raciones que tienen los 50 hombres para 20 días a razón de tres raciones diarias:

50 hombres x 3 raciones por día x 20 días = 3000 raciones

Esto significa que tienen un total de 3000 raciones de alimentos para los 50 hombres durante 20 días.

Luego, podemos calcular la cantidad de raciones diarias después de la disminución en 1/3:

3 raciones diarias - (1/3)(3 raciones diarias) = 2 raciones diarias

Esto significa que cada hombre ahora recibe 2 raciones diarias en lugar de 3.

Después de aumentar el número de hombres en 10, tenemos un total de 60 hombres:

50 hombres + 10 hombres = 60 hombres

Podemos calcular la cantidad total de raciones diarias para los 60 hombres durante los días que durarán las provisiones:

60 hombres x 2 raciones por día = 120 raciones diarias

Finalmente, podemos calcular la cantidad de días que durarán los víveres:

3000 raciones totales / 120 raciones diarias = 25 días

Por lo tanto, los víveres durarán 25 días después de disminuir las raciones en 1/3 y aumentar el número de hombres en 10.

Step-by-step explanation:

Answer:

3 hours

Step-by-step explanation:

65 - 85x = 320

85x = 320 - 65

85x = 255

x = 255 / 85

x = 3

Answer:

6 pencils

Step-by-step explanation:

120*4=480, 480/80=6

The range of this function is: (0, 2].

f(x) = bx, where b is a positive integer between 0 and 1, denotes an exponential function. Like in every exponential expression, B and x are referred to as the base and exponent, respectively. An excellent illustration of an exponential function is bacterial proliferation. Some microorganisms reproduce every hour.

As all real numbers are the domain of an exponential function, the following is the domain of this function:

(-∞, ∞)

We must examine the function's behaviour as x gets closer to positive and negative infinity in order to determine the range. The function approaches the horizontal asymptote at y = 2 as x increases to positive infinity. The function gets close to 0, but never quite achieves it as x increases to negative infinity. The scope of this function is as follows:

(0, 2].

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Answer:

the correct answer is 12

Answer:

12

Step-by-step explanation:

Answer:

6h65

Step-by-step explanation:

Add up all the values:

1h+2h+3h= 6

20+40+05= 65

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The measure of angle ABC is 40 degrees.

What is inscribed angle theorem ?

The inscribed angle theorem, also known as the central angle theorem, states that an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc, or in other words, the angle that connects the endpoints of the arc.

In other words, if we draw a chord of a circle and an angle with its vertex on the circumference of the circle and its sides passing through the endpoints of the chord, then the measure of the inscribed angle is half the measure of the central angle that subtends the same arc as the inscribed angle.

According to the question:

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc it intercepts.

Since chord AB is congruent to chord CB, we can conclude that angle A is congruent to angle C, because they both intercept the same arc AC. Thus, we have:

angle BAC + angle ABC + angle ACB = 180 degrees (by the angle sum property of triangles

Substituting the measure of arc AC, we get:

angle BAC + angle ABC + 70 degrees = 180 degrees

Simplifying, we get:

angle BAC + angle ABC = 110 degrees

Since angles A and C are congruent, we have:

2 x angle BAC + angle ABC = 180 degrees

Substituting angle BAC + angle ABC = 110 degrees, we get:

2 x 110 degrees - angle ABC = 180 degrees

Solving for angle ABC, we get:

angle ABC = 40 degrees

Therefore, the measure of angle ABC is 40 degrees.

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Answer:

Step-by-step explanation:

Only the one on the bottom right is a function. It's the only one that does not have 2 of the same x value for a single y value.

Using the simple interest formula it is seen that Mrs Jo saves an amount of $180 when she chooses option B over option A.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

To determine which option is better, we need to compare the total amount of interest paid for each option.

Option A -

The principal amount is $900 and the interest rate is 8%. The term is 5 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.08 × 5

Interest = $360

Total amount paid = Principal + Interest

Total amount paid = $900 + $360

Total amount paid = $1260

Option B -

The principal amount is $900 and the interest rate is 10%. The term is 2 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.10 × 2 = $180

Total amount paid = Principal + Interest

Total amount paid = $900 + $180

Total amount paid = $1080

Therefore, option B is the better option because it has a lower total amount paid by choosing option B.

Mrs. Jo will save -

$1260 - $1080 = $180

Therefore, Mrs. Jo will save $180 by choosing option B instead of option A.

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Answer:

Rational numbers, Real Numbers, Fractions, and Percentages.