Graph the piecewise function given below.

The area of the right triangle is 18.02 cm².

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, let's find the area of the right angle triangle as follows;

let's find the height and base of the triangle.

using trigonometric ratios,

cos 75 = adjacent / hypotenuse

cos 75 = base / 12

base = 3.10582854123

Therefore,

sin 75 = opposite / hypotenuse

sin 75 = h / 12

height = 11.5911099155

height = 11.59

Therefore,

area of the triangle = 1 / 2 × 3.11 × 11.59

area of the triangle = 36.0483518371 / 2

area of the triangle = 18.0241759186

area of the triangle = 18.02 cm²

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Answer: $9.72

Step-by-step explanation:

Answer:

Option D

The answer is $9.72

Step-by-step explanation:

Here, We are given that;

For first 1/4 mile = $1.25,

For each additional 1/4 mile = $0.35,

For each additional passanger = $1.25.

Now,

4 1/2 = 9/2 = 4.5 miles

Here, the price is different for the first 1/4 mile.

So,

4.5 – 0.25 = 4.25 miles

↬ If it costs $0.35 for 0.25 mile then it will cost $1.4 for 1 mile.

0.35 × 4 = $1.4

Now, for 4.25 miles

1.4 + 1.4 + 1.4 + 1.4 + 0.35 = $5.95

Now, For first 1/4 mile and for each additional passanger.

$5.95 + $1.25 + $1.25 = $8.45

Here, The total fare with 15% tip

8.45 × 15 ÷ 100 = $1.2675

Now,

$8.45 + $1.2675 = $9.7175 ≈ $9.72

Thus, The answer is $9.72

-TheUnknownScientist 72

The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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Answer:

A(t) = π(8t)²

Step-by-step explanation:

Radius of a circular wave increases by 8 cm each second.

Every second radius of circular wave so the sequence of increase in radius will be,

8, 16, 24, 32.........(8t)

Here 't' = time

Since, area of a circle = πr²

Therefore, area of the circular wave after 't' seconds since the wave begins,

A(t) = π(8t)²

(a) The closed form for ∑2 is 2.

(b) The closed form expression for ∑3 is 24.

(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.

(d) The value of -3 matches the manual computation of the four terms.

Our closed form solution is correct.

To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:

∑2 = n(a + l) / 2

In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.

We also know that there is only one term, so n = 1.

Substituting these values into the formula, we have:

∑2 = 1(2 + 2) / 2

= 4 / 2

= 2

The formula for the sum of the first n terms of an arithmetic series is:

∑n = n(a + l) / 2

In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).

Substituting these values into the formula, we get:

∑3 = 3(3 + 13) / 2

= 3(16) / 2

= 48 / 2

= 24

The formula we developed in class is:

∑n = n(a + a + (n - 1)d) / 2

In this case, we have a = 0 (the first term) and d = -1 (the common difference).

Substituting these values into the formula, we get:

∑n = n(0 + 0 + (n - 1)(-1)) / 2

= n(0 - n + 1) / 2

= n(1 - n) / 2

To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):

∑3 = 3(1 - 3) / 2

= 3(-2) / 2

= -6 / 2

= -3

Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:

0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1

= 0 - 1 - 2 - 3

= -6

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Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

The quadratic equation is,

The quadratic equation ax^2 + bx + c = 0 can be solved by quadratic formula as,

The value of a is 4, value of b is -2 and value of c is 5.

Solve the quadratic equation by quadratic formula.

So answer is,

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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The number of people in Indiana residents is given by the equation

A = 5,750,000 or 5.75 million

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of people in Indiana residents aged 5 years and older be A

Now , the equation will be

Substituting the values in the equation , we get

The percentage of population residents aged 5 years and older = 5.6 %

The number of residents aged 5 years and older = 322,000

So , the total population A is calculated as

( 5.6 % ) of A = 322,000

On simplifying the equation , we get

( 5.6 / 100 ) A = 322,000

Divide by 6.6 on both sides of the equation , we get

A / 100 = 57,500

Multiply by 100 on both sides of the equation , we get

A = 5,750,000

A = 5.75 million

Hence , the population of Indiana is A = 5,750,000 or 5.75 million

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The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer:

true

Step-by-step explanation:

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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Answer:

4b = 50; 1a = 80

Step-by-step explanation:

So let's say that bananas = b and apple = a

Then we could set up the equations that are:

4b = 50 (cents)

1a = 80 (cents)

That means we have 2 equations of 4b = 50 and 1a = 80

Answer:

Step-by-step explanation:

banana = b = 50¢ = $.50

apple = a = 80¢ = $.80

Total cost of fruit = f

She bought 4 bananas for .50 each so we multiply 4*.50 to find the total cost of the bananas and she bought 1 apple for .80, so we add them together to get the total cost of the fruit, f.

4b + a = f     Now substitute the values.

(4*.50) + .80 = f       This is you expression, let's solve for fun.

(4*.50) + .80 = f

2 + .80 = f

$2.80 = f   Sylvia spend $2.80 on the fruit.

Answer:

$886.47

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The ratio is 4:1, so every 1 tablespoon of sugar is equal to 4 tablespoons of cocoa.  Just multiply the number of spoons of sugar by 4.

Answer: the answer is e

Step-by-step explanation:

If ax + b = 0, is x > 0

(1) a + b > 0

(2) a - b > 0

Answer:

x² + y² = 49

Step-by-step explanation:

The circle being centred at the origin simplifies things a lot.  Also, given an x-intercept point makes it easy to find the origin.

The equation for a circle is:

(x - x₁)² + (y - y₁)² = r²

Where (x₁, y₁) is the centre point of the circle.

In this case, the centre of the circle is (0, 0), giving us:

x² + y² = r²

We are told that the circle intercepts (-7, 0), which tells us that it has a radius of 7.

We can simply plug that into the given equation and say:

x² + y² = 7²

x² + y² = 49

***NOTE***

This is not part of the answer to the question, just an expansion of it.

Generically speaking, The equation for a circle is:

(x - x₁)² + (y - y₁)² = r²

Which applies when the centre of the circle is not at the origin.  For example, if the given circle was centred around the point (6, 8), with the same radius of 7, then the circle's equation would be (x - 6)² + (y - 8)² = 49.

The other complication that could show up is if the given border point does not have the same x or y coordinate as the circle's centre.  For example, if we are given a centre point of (-4, 6) and a border point of (-1, 2), we would first need to use the Pythagorean theorem to find the circle's radius:

r² = (x - x₁)² + (y - y₁)²

r² = (-4 - (-1))² + (6 - 2)²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

We can then plug that into the proper equation, giving us:

(x + 4)² + (y - 6)² = 25

You can also expand and group terms to express that in general form:

x² + 8x + 16 + y² - 12y + 36 = 26

x² + y² + 8x - 12y  + 26 = 0

Again, note that this part of the answer is not related to the original question, but an expansion on it.

For an equilateral triangle , all the sides are equal. Therefore, the perimeter of the equilateral triangle above is the sum of all it sides.

The sum is calculated below

The answer is C.

The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.

Here we have the summatory:

\(\sum^{5}_{n = 1} 2^{n - 2}\)

So we just need to add the 5 terms (between n = 1 and n = 5)

So we will get the sum:

S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]

S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]

S = [0.5 + 1 + 2 + 4 +8]

S = 15.5

So the correct option is the second one.

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Answer:

10x + 5

A is the correct answer

Step-by-step explanation:

when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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Answer:

C. 45%

Step-by-step explanation:

Divide 36 by 80 to get 0.45 (45%)