Tell me about algebra

The volume of the given cylinder is 2543 cubic yards.

For the given cylinder,

Height of the cylinder  = 10 yard

Radius of cylinder = 9 yard yard

Then we have to calculate the volume of this cylinder.

Since we know that,

Volume of the cylinder  = πr²h

Where,

r represents radius of cylinder = 9 yard

h represents height of cylinder = 10 yard

Noe therefore,

Volume of the cylinder = π(9)²(10)

                                       = 3.14x 81 x 10

                                       = 2543 cubic yards

Thus,

⇒ Volume = 2543 cubic yards.

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Answer:

To convert 7.55 dollars into dimes and quarters, we need to make use of the fact that there are 10 dimes in a dollar and 4 quarters in a dollar. Here's how to do it:

Step-by-step explanation:

1. First, convert the dollar amount into cents: 7.55 dollars x 100 cents/dollar = 755 cents.

2. Next, use long division to find how many quarters are in 755 cents: 755 ÷ 25 = 30 with a remainder of 5.

3. The quotient of 30 tells us that we can use 30 quarters, which equals $7.50.

4. The remainder of 5 cents is less than a quarter, so we cannot use another quarter. Instead, we can use 1 dime, which is worth 10 cents.

Therefore, 7.55 dollars is equivalent to 30 quarters and 1 dime.

The distance from X to Z will be 386 km when rounded to 3 significant figures.

The distance from Y to XZ will be 141 km when rounded to 3 significant figures.

To obtain the distances, we need to extend the distances traveled by the airplane and this yields another triangular form. Angle Y = 105°, z = 200 km, and Z = 30°.

y/Sine Y = z/Sine Z

y/Sine 105° = 200/Sine 30°

y = 200 × 0.966/0.5

386 km to 3 significant figures

Also for the distance from Y to XZ,

We assume that the distance from Y to XZ is d

Sine 45°/1 = d/200

d = 200 sine 45°

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Answer: The answer is A.

Step-by-step explanation: The surface area of a triangular prism is given by A = b h + ( b 1 + b 2 + b 3 ) l units 2 where is the base of a triangular face, is the height of a triangular face, , , and are the sides of the triangular base, and is the length of the prism.

A) first multiply 18 x 7 = 116, then subtract 500 - 116 = 384, so the answer is 384

B) first divide 384 from 18 which should give you 18, so the answer is 18

Answer:

To determine if the given relation is a function, we need to check if there is a unique y-value for every x-value in the relation.

The given relation is:

y^2 + 4 = x

To test for functionality, we need to solve for y in terms of x:

y^2 = x - 4

y = ± √(x - 4)

Notice that for each x-value, there are two possible y-values, one positive and one negative. This means that for a single x-value, there are two potential y-values, violating the condition of a unique y-value for every x-value.

Therefore, the given relation is not a function since it fails the vertical line test, as there are x-values with multiple corresponding y-values.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Unless we restrict its domain, a quadratic function doesn't have the inverse.

The number of squares that are in 384 sq ft is 0

From the question, we have the following parameters that can be used in our computation:

Area expression = 384 sq ft

The above expression is an area expression

This means that it cannot be compared to quantities other then squares

The term "how many squares" is not an area expression

Hence, there are no squares in 384 sq ft

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It can be seen that each side of the isosceles triangle measures approximately 29.81 meters.

The angles at the base of an isosceles triangle have equivalent magnitudes. It can be deduced intelligently that if one of the base angles measures 34°, the remaining base angle must also be 34°.

Let's denote the length of each side as "x."

In a right triangle formed by half of the base, the height, and one of the sides, we can use the tangent ratio:

tan(34°) = height / (x/2)

tan(34°) = 15 / (x/2)

To isolate x, we can rearrange the equation:

x/2 = 15 / tan(34°)

x = (15 / tan(34°)) * 2

By employing a calculator, we have the capability to determine the numerical worth of x.

x ≈ 29.81 m

Therefore, each side of the isosceles triangle measures approximately 29.81 meters.

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The question in English:

The angle at the base of an isosceles triangle 34° the height measures 15m

Calculate the length of the sides equal

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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The solution to the compound inequality -28 < -4r < 16 is 7 > r > -4

from the question, we have the following parameters that can be used in our computation:

-28 < -4r < 16

Divide through the inequality by -4

so, we have the following representation

-28/-4 < -4r/-4 < 16/-4

When the quotients are evaluated, we have

7 > r > -4

Hence, the solution to the compound inequality is 7 > r > -4

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Answer:

70 cm³

Step-by-step explanation:

let the total volume be x

copper : zinc = 3:2

copper ==>

3/5 *x = 42

make x the subject if formula

x = 42*5/3

:. x = 70 cm³✅✅

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The rationalized form of the expression √(3/5) is √15/5.

To rationalize the denominator of the expression √(3/5), we need to eliminate the square root in the denominator.

We can achieve this by multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of √5 is also √5, so we can multiply the expression by (√5)/(√5):

√(3/5)×(√5)/(√5)

Multiplying the numerator and denominator, we have:

√(3 × 5)/(√(5×5))

Which simplifies to:

√15/√25

√15/5

Therefore, the rationalized form of √(3/5) is √15/5.

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The calculated value of the missing side length in the triangle is (c) 12

From the question, we have the following parameters that can be used in our computation:

The simiar triangles

Using the theorem of corresponding sides, we hav

?/8 = 9/6

Multiply both sides by 8

So, we have

? = 8 * 9/6

Evaluate

? = 12

Hence, the missing side length in the triangle is (c) 12

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Answer:

please see answers below

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ².

angles in a triangle add up to 180°.

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C

angle C = 90° (little square means 90).

if angle A is 30, then angle B must be 180 - 90 - 30 = 60°.

using the Sine rule:

a/Sin A  =  c/Sin C

multiply both sides by Sin A:

a = (c Sin A) / Sin C

= (12 Sin 30) / Sin 90

= 6.

so a = 6.

Using Pythagoras (In a right-angled triangle, a ² + b ² = c ²),

c² = a² + b²

b² = c² - a²

= 12² - 6²

= 144 - 36

= 108

so b² = 108

b = √108

angle B is correct

The equation for the circle is

(x - 1)² + (y + 2)² = 9

Then the radius is 3 units and the center is (1, -2), the graph is on the image at the end.

Remember that for an equation for a circle of radius R and center (a, b), the equation is:

(x - a)² + (y - b)² = R²

Here we have the equation of the circle:

x² + y² - 2x + 4y - 4 = 0

We need to complete squares, we will get:

(x² - 2x) + (y² + 2*2y)  = 4

Now we can add in both sides (-1)² and (2)², then we will get:

(x² - 2x + (-1)²) + (y² + 2*2y +  (2)²)  = 4 +  (2)² + (-1)²

(x - 1)² + (y + 2)² = 4 + 4 + 1

(x - 1)² + (y + 2)² = 9 = 3²

Then we can see that the center is (1, -2), and the radius is 3.

The graph of this circle is on the image at the end.

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Answer: C

Step-by-step explanation:

If I plugged in 0 for x,  You get 4 for y.   This is the y-intercept

(0,4)

The only graph that goes through (0,4) is C.

With f(1), we're being given an x-value of 1.

Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.

f(1) = 1 - 2 = -1

The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.

Given an equation,

3√2 sec θ + 7 = 1

We have to find that whether 3π/4 is a solution for the given equation or not.

Solving the given equation, we get,

3√2 sec θ + 7 = 1

3√2 sec θ = 1 - 7

3√2 sec θ = -6

sec θ = -6 / 3√2

sec θ = -2 / √2

sec θ = -√2

Now, we know that, sec θ = 1/ cos θ

So the equation becomes,

1/ cos θ = -√2

cos θ = -1/√2

Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.

cos 3π/4 =  cos (π - π/4) = -cos (π/4) = -1/√2

So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.

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The area of the shaded region is equal to 45 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 8 × 6

Area of rectangle = 48 square units.

Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;

L₁ = 8 - 5 = 3 units.

L₂ = 6 - 4 = 2 units.

Area of right triangle = 1/2 × 3 × 2

Area of right triangle = 3 square units.

For the area of the shaded region, we have:

Area of the shaded region = 48 square units - 3 square units.

Area of the shaded region = 45 square units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

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

In ΔNOP, we are given:

Use the law of cosines to find side o:

Now, use the law of sines to find ∠N:

So,  ∠N is approximately 10°.

Answer:

We can get 10 cheeseburgers.

Step-by-step explanation:

To find out how many cheeseburgers we can buy if:

we can divide the money we have by the cost of each cheeseburger.

To make the division simpler, we can multiply both numbers by 10.

$25 / $2.50 = $250 / $25

From this form of the division, we can clearly see that the amount of money we have is 10 times the cost of one burger because it is 25 with a 0 on the end, which is the result of multiplying by 10.

Therefore, we can get 10 cheeseburgers.

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer:

tan^(-1)(|cos(x)| / (1 + sin(x)))

Step-by-step explanation:

√(1 - sin(x)) / √(1 + sin(x))

(√(1 - sin(x)) / √(1 + sin(x))) * (√(1 + sin(x)) / √(1 + sin(x)))

√((1 - sin(x))(1 + sin(x))) / (1 + sin(x))

√(1 - sin^2(x)) / (1 + sin(x))

Then, using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can substitute cos^2(x) for 1 - sin^2(x):

√(cos^2(x)) / (1 + sin(x))

|cos(x)| / (1 + sin(x))

tan^(-1)(|cos(x)| / (1 + sin(x)))

*Note : the absolute value |cos(x)| is used to ensure the argument of the inverse tangent is always positive.

A) Area of figure is,

⇒ A = 3π (3 + √73) + 4.5π

B) Area of figure is,

A = 89 feet²

We can simplify as;

A) In figure A,

It is make with one cone and one semicircle.

Hence, Area of cone is,

A = πr (r + √h² + r²)

A = π × 3 (3 + √8² + 3²)

A = 3π (3 + √64 + 9

A = 3π (3 + √73)

And, Area of semicircle is,

⇒ A = 1/2 (π × 3²)

⇒ A = 4.5π

Hence, Total area is,

⇒ A = 3π (3 + √73) + 4.5π

B) Figure B is make with a trapezoid and triangle.

Area of trapezoid is,

A = 1/2 (7 + 13) × 5

A = 20 × 5 / 2

A = 50 feet²

And, Area of triangle is,

A = 1/2 × 6 × 13

A = 39 feet²

Hence, We get;

Area of figure is,

A = 50 + 39

A = 89 feet²

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a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

We have,

a)

The composite figure has a cone and a semicircle.

So,

Area of cone = 1/3πr²h = 1/3 x 3.14 x 3 x 3 x 8 = 753.8 cm³

Area of semicircle = 1/2 x πr² = 1/2 x 3.14 x 3 x 3 = 14.13 cm²

b)

The composite figure has a trapezium and a triangle.

Area of the trapezium

= 1/2 x ( sum of the parallel side) x h

= 1/2 x (7 + 13) x 5

= 1/2 x 20 x 5

= 10 x 5

= 50 ft³

Area of the triangle.

= 1/2 x base x height

= 1/2 x 6 x 8

= 3 x 8

= 24 ft²

Thus,

a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

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