Find the measure of the angles between the hands of the clocks at a) 8:54 b) 5:11 and c) 8:03I have the answers, but I need an explanation

Remember that the sine of an angle in a right triangle is equal to the quotient between the side opposite to the angle and the hypotenuse of the triangle.

Since the sine of the given angle θ is equal to 3/5, we can represent θ as part of a right triangle whose hypotenuse has a measure of 5 and the side opposite to θ has a measure of 3:

The length of the side adjacent to θ must be equal to 4 in order to satisfy the Pythagorean Theorem:

On the other hand, the cosine of an angle is defined as the quotient between the side adjacent to the angle and the hypotenuse of the triangle. Then, the cosine of θ must be equal to 4/5:

The rest of the trigonometric relations are defined in terms of the sine and the cosine as follows:

Since sinθ=3/5 and cosθ=4/5, then:

The art club has a goal to raise at least $500 by selling paintings to the student body for $15 each. They have already spent $70 buying

paint. Which inequality could be used to find the number of paintings the art club needs to sell to reach their goal?

we have that

Let

x -----> the number of paintings

so

the inequality that represent this situation is given by

solve for x

We need to know about area and perimeter of a rectangle to solve the problem. The perimeter of the garden as a percentage of its area is 50.5%

The perimeter of a rectangle is the total of all it's sides. The perimeter can be calculated by adding up the sides of the rectangle. The area of a rectangle can be calculated by multiplying the length with the breadth of the rectangle. The diagonal and width of a rectangle are given, we need to find the length using Pythagoras' theorem.

diagonal =11.5m

width=7 m

length=[tex]\sqrt{11.5^{2} -7^{2} }[/tex]=[tex]\sqrt{132.25-49} =\sqrt{83.25}[/tex]=9.12 m

perimeter=2x(l+b)=32.24 m

area= lxb= 9.12x7=63.84 [tex]m^{2}[/tex]

perimeter as percentage of area=32.24/63.84 x100=50.5%

Therefore the perimeter of the rectangle as a percentage of area is 50.5%.

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The point of maxima and minima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.

The differentiation of a function is defined as the rate change of its value at around a point. It can be written in mathematical form as g'(x) = (g(x + h) - g(x)) /(x + h - x).

Its geometric meaning is that it is the slope of the function at a given point.

Given that,

Initial height of the launching pad is 4 feet,

Initial velocity of rocket is 48 feet/sec,

Height of the rocket as a function of time, h(t) = -16t² + 48t + 3

In order to find the time for maximum height equate h'(t) = 0 as follows,

-32t + 48 = 0

⇒ t = 48 / 32

⇒ t = 3 / 2

⇒ t = 1.5

To find the maximum height find h(t) for t = 1.5 as follows,

h(1.5) = -16 × 1.5² + 48 × 1.5 + 3

= -36 + 60 + 3

= -36 + 63

= 27

Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.

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Answer:

The slope is -2

Step-by-step explanation:

Use the rise÷run formula to find the slope of any linear equation

In this case, -2÷1 = -2

Therefore, the slope is -2

You can check the attached image for more info

ANSWER

5

EXPLANATION

The given shape is a rhombus

The sum of interior angles of a rhombus add up to 360 degrees

The opposite angles of a rhombus are equal to each other.

hence, adding up all the interior angles, we have;

collecting like terms, we have;

Therefore the value of x is 5

28.68235294117647 days (29 days ) will be taken by nate and his family to take a cross country trip of 2438 miles .

Divide is the polar opposite of multiply. You get four in each group when you divide twelve into three equal groups then multiply three groups of four to create twelve. Determining how many equal groups are formed or how many individuals are in each group following a fair distribution is the fundamental goal of splitting.

speed  = 85miles / day

distance = 2438

time = 2438 / 85 = 28.68235294117647 days

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The area of any shape after dilation is equal to the area of the original shape multiplied by the square of the scale factor:

Where

A_new indicates the area of the shape after the dilation

A_original is the area of the original shape

k is the scale factor

The first step is to determine the area of the original shape and the new shape, using the formula:

The original shape has dimensions 4 and 5, so its area is:

Next is to determine the area of the shape after the dilation (A_new)

The scale factor is k=1.2

Now that we calculated both areas, we can determine the increase percentage.

- First, calculate the increase (I), which is the difference between the area of the new shape and the area of the original shape:

-Second, divide the increase by the original area and multiply the result by 100

This means that the area increased 44% after the dilation

To transform the graph of g(x) = lnx into the graph of of f(x) = ln(x-4) + 3 we have to translate 4 units to the right and 3 units up.

What is graph transformation?

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

As given in the question,

Parent function  g(x)=ln x

resultant function  f(x)=ln(x-4)+3

By the translation rules :

If f(x) needs to be translated in f(x-h), it mean function shifted right by h unit

and if f(x) needs to be translated in f(x)+k it mean function shifted up by k unit.

As per these rules, graph of  g(x) = lnx function shifted right by 4 unit and function shifted up by 3 unit.

Therefore, Translate 4 units to the right and 3 units up.

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The roots of [tex]x^{2}[/tex] +12x -c = 0 in surd form is -6 ± [tex]\sqrt{c + 36}[/tex]

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients of [tex]x^{2}[/tex] and x respectively and c is the constant term.

[tex]x^{2}[/tex] + 12x - c = 0

taking c to the other side, we have

[tex]x^{2}[/tex] + 12x = c

adding the square of half the coefficient of x, which is 6

[tex]x^{2}[/tex] + 12x + [tex]6^{2}[/tex] = c + [tex]6^{2}[/tex]

The left side is now a perfect square which can be simplified as [tex](x + 6)^{2}[/tex]

So,

[tex](x + 6)^{2}[/tex] = c + 36

taking the square root of both sides, we have

x + 6 = [tex]\sqrt{ c + 36}[/tex]

Therefore,

x = -6 ±[tex]\sqrt{c + 36}[/tex]

In conclusion, the solution to the equation is x = -6 ±[tex]\sqrt{c + 36}[/tex]

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August 2, 1776, in the Pennsylvania State House.

Step-by-step explanation:After much debate, the Second Continental Congress ultimately agreed to the Declaration of Independence, and then signed it

With 95% confidence, candidate A can win the election within 50.18% and 55.82%.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.

According to the question, n = 1200

The support rate for candidate A ([tex]p_{A}[/tex]) = 53% ≅ 0.53

So, [tex]z_{c}[/tex] for 95% confidence = 1.96

Confidence interval for [tex]p_{A}[/tex]

= ( [tex]p_{A}[/tex]   ±   [tex]z_{c}[/tex] ([tex]\sqrt{\frac{p_{A}( 1 - p_{A} ) }{n} }[/tex]) )

= ( 0.53  ±  1.96([tex]\sqrt{\frac{0.53(1-0.53)}{1200} }[/tex]) )

= ( 0.53  ±  1.96([tex]\sqrt{\frac{0.53*0.47}{1200} }[/tex]) )

= ( 0.53  ±  1.96([tex]\sqrt{\frac{0.2491}{1200} }[/tex]) )

= ( 0.53  ±  1.96([tex]\sqrt{0.0002075833}[/tex]) )

= ( 0.53  ±  1.96(0.014407751) )

= ( 0.53  ±  0.028239191 )

= ( 0.53 - 0.02823,0.53 + 0.02823 )

= ( 0.50177,0.55823 )

( 0.50177,0.55823 ) ≅ ( 50.18%,55.82%)

Candidate A can win the election between 50.18% and 55.82% with a confidence level of 95%.

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Answer:

30 square units.

Step-by-step explanation:

Divide the full polygon into two halves. The left half is 5 wide by 5 tall, making the area of the left 25 square units. The right half is 4 wide by 5 tall, and is perfectly cut in half. We can calculate the area normally, and then cut it in half: (5×4)/2 = 10 square units. Add the two polygons together, totalling 30 square units.

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following system of equations

In the case x = 7, it is parallel to the y axis, through the point 7 in x, and in the case y = 0, it is the same x axis, therefore the intercept is the point (7 , 0)

The solution is:

Answer:

58

Step-by-step explanation:

3x-14=58

+14 +14

3x=72

x=24

solved that now we'll input the factor

3(24)-14

72-14

"58" is your answer

The given graph is of the equation y = x - 2

Select x-values and enter them into the equation to graph a function. You will obtain a y-value once those values have been entered into the equation. The coordinates of a single point are made up of the x and y values.

Step 1 is to determine the variables.

Step 2: Establish the range of the variable

Determine the graph's scale in step three.

Step 4 is to give each axis a number, a label, and a title.

5. Select the data points and plot them on the graph.

6. Create the graph.

After understanding the "how" of drawing a graph you will surely understand how to decide which equation's graph it is.

The given graph is of the equation

y = x - 2

because as in the graph

the slope cuts the points x = 4 and y = 2

and when we substitute this value in the above mentioned equation we get

2 = 4 - 2

which satisfies the condition .

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No, 6 will not be included

Let the number greater than 6 be represented by x

The statement "x greater than 6" can be written as:

x > 6

Therefore, 6 will not be included in the list

Answer: 1

Step-by-step explanation:

Well, what they have asked is to find the zero of this equation, or the value of the variable when the equation is equal to 0.

So, h(x) = 4x-4 = 0

4x = 4

x = [tex]\frac{4}{4}[/tex]

x = 1

Answer:

The rational numbers between 2 & 3 include:

1. 4120

2. 4220

3. 4320

4. 4420

5. 4520

6. 4620

7. 4720

8. 4820

9. 4920

10. 5020

Step-by-step explanation:

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According to the problem, the transformation is a translation.

It is important to know that translations are rigid transformations, which means the figures won't change their shape or size. In other words, the images are congruent to the pre-images.

Hence, triangle C is congruent to triangle C', triangle D is congruent to triangle D', but the figures are not congruent because their shape is different.

First, let us define what (fg)(x) is:

Given:

So the solution to (fg)(x) will be:

Answer:

Step-by-step explanation:

four and one quarter yards. explanation: add 1 1/6 + 3/12 = 1 5/12. now, multiply that by 3.

Using the arithmetic operations the total yards of metal is needed 4(1/4).

The study and application of numbers in all other branches of mathematics is the focus of the branch of mathematics known as arithmetic operations. In essence, it consists of addition, subtraction, multiplication, and division operations.

According to the given:

First pieces of metal =  1 (1/6)

                                 = 7/6

Then Second pieces of metal = 3/12

Adding both the pieces, we have

=7/6 + 3/12

= (14 + 3)12

= 17/12.

now multiply that by 3.

We get,

= (17/12)3

= 17/4

= 4(1/4)

Using the arithmetic operations the total yards of metal is needed 4(1/4).

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Answer:2580

Step-by-step explanation:215*12=2580

In this case, we have to add mixed numbers to find the shortest path from the shown alternatives. We need to work with mixed numbers, fractions, and even decimals.

To answer this question, we know that:

1. The path from Hampton to Middletown is 8 + 1/4 mi.

2. Now, we have two alternatives to go from Middletown to Campbell:

First, we have a path that is equivalent to 6 + 1/8 mi (direct). On the other path, we need to go from Middletown to Danville, and then to Campbell. The measure of the latter path is then:

Thus, we have:

Which is equivalent to:

If we compare the measures of the two paths, we have that:

a. The path from Middletown to Campbell (directly) is equal to:

b. The path from Middletown to Danville, and then from Danville to Campbell is equal to 6.75 miles (it is longer).

Therefore, the shortest path, in this part of the "journey", is equal to 6.125 miles or 6 + 1/8 miles.

Now, the complete measure of the path from Hamptom to Lexington is the sum of:

1. The measure of the path from Hamptom to Middletown (8 + 1/4 miles) plus

2. The measure of the path from Middletown to Campbell (6 + 1/8 miles) (directly) plus

3. The measure of the path from Campbell to Lexington (5 + 3/4 miles).

And this is, numerically, as follows:

We can express the latter result as a fraction as follows:

Therefore, the shortest route from Hamptom to Lexington is:

1. As a fraction:

2. Or as a mixed number:

[Notice that we sum two fractions with the same denominator above:

.]

A method that is frequently used to make algebraic expressions simpler.

A method that is frequently used to make algebraic expressions simpler.

1. 10s2 + 10s2 - 13st =s*(20s-13t)

2. 13st + - 2st - t2 = 11st-t2

3. x2+ x2 + x3 = 2x2+x3

4. 6 x - 6 x + 2 =2

5. 24x - 3s - 4t =24x - 3s - 4t

6. 86 + 86x - 1 =86x+85

7. 4x + 3x - 2 = 7x-2

8. 7s - 4s + 3s = 6s

9. 12 +11x - 10 x =x+12

10. 12x + 24 x - 3 x - 4 =33x-4

11. 16t + 8t - 12t =12t

12. 17g + 19g - 2g +g =35g

13. 16 + 16 -16 + 16x = 16+16x

14. 4s - 3s + 3s =4s

15. 12t - 11t + t =2t.

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Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].

[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]

Answer:

B.C.

Step-by-step explanation: