Original price: $82
Discount: 10%
Sale price: ?

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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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 flowcharts for each proof are shown in the image attachments below.

For problem 1, we use the SSS (side side side) congruence theorem.

Problem 2 uses SAS (side angle side). It might help to rotate one of the triangles in problem 2 so the marked angles align.

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

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:

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.

Answer: rental is $415, and the standard deviation is $5.

Step-by-step explanation:

If about 99.7 percent of the monthly rentals fall between 400 and 430, it implies that this range encompasses three standard deviations from the mean.

To calculate the mean, we can find the midpoint of the given range:

Mean = (400 + 430) / 2 = 415

Since the range of three standard deviations covers about 99.7 percent of the data in a normal distribution, we can use this information to estimate the standard deviation (σ).

Standard deviation (σ) = (430 - 415) / 3 = 15 / 3 = 5

Therefore, based on the given information, the mean monthly rental is $415, and the standard deviation is $5.

To determine the annual interest rate paid, we need to calculate the simple interest for one month and then convert it to an annual rate.

The formula for simple interest is:

Simple Interest = Principal × Rate × Time

In this case, the principal amount is $720, and after one month, you pay back a total of $1272. Therefore, the interest paid is:

Interest = $1272 - $720 = $552

We can now calculate the monthly interest rate:

Rate = Interest / Principal = $552 / $720 ≈ 0.7667

To convert the monthly interest rate to an annual rate, we multiply it by 12:

Annual Rate = Monthly Rate × 12 = 0.7667 × 12 ≈ 9.20

Therefore, you paid an annual interest rate of approximately 9.20%.

Answer:

Step-by-step explanation:

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:

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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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.

Answer:  $62.40

Step-by-step explanation:

Original price $80

22% of 80%

.22(80) = 17.60   >This is the discount

Sale price = Original price -  discount

Sale price = 80 - 17.60

Sale price = $62.40

Answer:

[tex]\Huge \boxed{\text{\$62.40}}[/tex]

Step-by-step explanation:

In the sale, the prices decrease by 22%. This means that the sale price is 78% of the original price.

[tex]\Large \text{Sale price = (100 - 22)\% of old price}\\\text{Sale price = 78\% of \$80}\\\text{Sale price = 0.78 $\times$ 80}\\\text{Sale price = \$62.40}[/tex]

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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(a) The time taken by aircraft C to travel the distance from R to the longitude 180°W is 25.92 hours

(b) Since aircraft A departed at 08:45 hrs, the arrival time would be:

Arrival time is 13:14 hrs

Aircraft A would arrive at approximately 13:14 hrs, and aircraft B would arrive at approximately 21:01 hrs local time.

To calculate the position of aircraft C when aircraft A was passing the longitude 180°W, we need to determine the distance and direction between R (30°N, 10°W) and Q (50°N, 170°E) via the shortest route.

Distance between R and Q:

The latitude difference between R and Q is 50°N - 30°N = 20°. As each degree of latitude is approximately 111 km, the distance in terms of latitude is 20° × 111 km = 2,220 km.

The longitude difference between R and Q is 170°E - 10°W = 180°.

At the latitude of 40°N (midpoint between 30°N and 50°N), each degree of longitude is approximately cos(40°) × 111 km = 70.7 km.

The distance in terms of longitude is 180° × 70.7 km = 12,726 km.

Using the Pythagorean , the shortest distance between R and Q is:

Distance = √((2,220 km)² + (12,726 km)²)

≈ 12,960 km

Speed of aircraft C is 500 km/hr.

The time taken by aircraft C to travel the distance from R to the longitude 180°W is:

Time = Distance / Speed

= 12,960 km / 500 km/hr

≈ 25.92 hours

Since the aircraft A and aircraft C departed at the same time, when aircraft A was passing the longitude 180°W, aircraft C would also be at the same longitude, assuming they maintained a constant speed.

(b) To calculate the arrival local time of the two aircraft, we need to consider the time taken for each leg of their respective routes.

For aircraft A:

Distance from P to (50°N, 130°W) = (50°N - 30°N) × 111 km/degree

= 2,220 km

Time taken = Distance / Speed

= 2,220 km / 500 km/hr

= 4.44 hours

Since aircraft A departed at 08:45 hrs, the arrival time would be:

Arrival time = Departure time + Time taken

= 08:45 + 4.44 hours

≈ 13:14 hrs

For aircraft B:

Distance from (30°N, 170°E) to Q = (170°E - 130°W) × cos(40°) × 111 km/degree = 6,282 km

Time taken = Distance / Speed

= 6,282 km / 500 km/hr

= 12.564 hours

Since aircraft B departed at 08:45 hrs, the arrival time would be:

Arrival time = Departure time + Time taken

= 08:45 + 12.564 hours

≈ 21:01 hrs

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

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.

If the position of 5 m below sea level is expressed as -5, then the number that expresses the position of 7 m above sea level would be + 7.

In this particular instance, with the position residing 7 m above sea level, we articulate it as +7. This notation elegantly captures the notion of elevation, affirming the distance above the familiar sea level benchmark.

In the realm of vertical measurements, sea level occupies a crucial position as the reference point, embodying the zero mark on the vertical scale. It is from this fundamental reference point that we navigate the vast spectrum of altitudes.

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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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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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The value of the function f(-1) is 1/3. Option D

A function can be defined as a law, an expression or rule that is used to show the relationship between two variables.

These variables are listed as;

From the information given, we have the function written as;

f(x) = 3ˣ

To determine the function f(-1), we need to substitute the value of the variable x as -1 in the function f(x)

Substitute the values, we have;

f(-1) = 3⁻¹

Take the inverse of the value, we get;

f(-1) = 1/3

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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.