a. Use the properties of right triangles and AABC to prove the Law of Sines.
b. Find the length of BC, rounded to the nearest tenth of a unit.
In your final answer for parts A and B, Include all of the necessary steps and calculations.

The time taken by the ball to get to the ground exists for 7 seconds.

Let, the function [tex]f(x) = -16(x^{2} - 6x- 7)[/tex] represent the height of the ball.

Where x exists the number of seconds.

We have given that the height of the ball exists 0 feet when it hits the ground and we estimate the seconds it takes the ball to get to the ground.

Consider f(x) = 0 and find the value of x.

[tex]0 = -16(x^{2} - 6x - 7)[/tex]

[tex]x^{2} - 6x - 7 = 0[/tex]

Using middle-term separation,

[tex]x^{2} - 7x + x-7 = 0[/tex]

x(x-7) + 1(x-7)=0

(x - 7)(x + 1) =0

x = 7, -1

x = -1 exists rejected as time exists not negative.

x = 7 exists accepted.

The time taken by the ball to get to the ground exists for 7 seconds.

Therefore, the correct answer is option B.7.

To learn more about the value of x refer to:

https://brainly.com/question/4165116

#SPJ9

The coterminal angles are given as follows:

a) 0º.

b) 120º.

The coterminal angle of a negative angle between 0 and -360º = -2pi is found adding 360º = 2pi to the angle, hence:

-2pi + 2pi = 0, which is the answer to item a.

The coterminal angle is found taking the remainder of the division of the angle by 360º.

The remainder of the division of 480º by 360º is of 120º, hence the coterminal angle of 480º is of 120º.

More can be learned about coterminal angles at https://brainly.com/question/23093580
#SPJ1

Answer:

y= -1/3x + 1

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y= -1/3x + 1

Answer: [tex]y=-\frac{5}{3}x-1[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we want to find is -5/3.

Since the y-intercept is (0,-1), the equation is [tex]y=-\frac{5}{3}x-1[/tex]

The equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y + 3 = 0.

A line of the standard form y = mx + c , where m is the slope of the line and c is a y-intercept. Another way to express the equation for a line is in standard form.

Slope: A line's slope provides information on the steepness and direction of the line.

By figuring out the difference between both the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of such a straight line through them. The letter "m" denote the slope of the line.

Relation between slope of two perpendicular lines are-

Calculation for the equation of the line.

Consider the given equation;

y=3/5x-3 (compare this with the standard equation)

The slope 'm' is 3/5

Use the relation of slopes of two perpendicular line.

The slope of orthogonal line will be -1/m

Slope = -5/3

Put the slope in the slope point equation of line.

(y - y1) = m(x - x1)

where (x1,y1) = (0,-1)

Substitute the coordinates in the equation

y - (-1) = (-5/3)×(x - 0)

y + 1 = -5x/3

Further simplifying the equation,

5x + 3y +3 = 0

Therefore, the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y +3 = 0.

To know more about standard form equation of the line, here

https://brainly.com/question/5470278

#SPJ4

===================================================

Explanation:

If it increases by 5%, then we use the multiplier 1.05

Think of it like saying 100% + 5% = 1 + 0.05 = 1.05

Similarly, an increase of 20% means we involve 1.20

Combine those multipliers to get: 1.05*1.20 = 1.26

This is a net increase of 26%

Interestingly, we get fairly close to 25% which is what many students might go for (since 5 + 20 = 25). This is a beginner's trap.

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

An example:

Let's say the temperature is 20 degrees Celsius (68 degrees Fahrenheit)

An increase of 5% means it moves to 1.05*20 = 21 degrees C

A 20% increase means we go to 1.20*21 = 25.2 degrees C

The shortcut would be to do a 26% increase to get 1.26*20 = 25.2 to help confirm we have the correct combined increase.

Answer:

-1728:512

Step-by-step explanation:

(-12)³ = -1728

8³ = 512

ratio is -1728:512

14) theorem

15) sides

16) separately

17) equilateral

18) supplementary

A simple main effect analysis looks at the mean difference at each level of the independent variable.

Given With a simple main effect, the analysis examines.

Simple effects are also called the main effects of design of experiments. The main effect can be defined as the effect of the explanatory variables measured on a particular criterion or response variable of the study. It's easy to say that what happens within the level of the explanatory variables is the difference. In a factorial experiment, the simple main effect is that one independent variable is at a specified level of another. The main effect of one independent variable is averaged across the levels of the other independent variable. For a simple main effect, the results are analyzed as if a separate experiment was performed at each level of the other independent variables.

Therefore, a simple main effect analysis looks at the mean difference at each level of the independent variable.

Learn more about analysis from here brainly.com/question/15179003

#SPJ4

The area of the shaded region is B. 52 square inches.

It should be noted that the shaded region is in the shape of a rectangle.

Length = 18 - 4 - 1= 13 inches

Width = 6 - 2 = 4 inches

The area is:

= Length × Width

= 13 × 4

= 52 inches²

Learn more about area on:

brainly.com/question/25292087

#SPJ1

Answer:

1 - 3090

2 - 12

3 - 2.16

Step-by-step explanation:

hope you find this helpful...

Answer:

2 sides and angle between them are congruent to the same 2 sides and angle on the other triangle

Step-by-step explanation:

Total possible outcomes are 312

We need to find that if you roll a 6-sided die and draw a card from a deck of 52 cards,what are total possible outcomes

Probability is a measure of the possibility that an event will occur. Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it. Probability can range from 0 to 1, where 0 means an event is impossible and 1 means a certain event

An outcome is the result of an event that depends on probability. Probability refers to the likelihood that something will happen, and an event can have more than one possible outcome.

Enumeration of possible outcomes is the process of determining the number of possible outcomes for an event. There are various methods to carry out this process. The best way to calculate the number of possible outcomes of an event depends on the type of event and the structure of the event

If a 6-sided die and draw a card from a deck,

then each side has total possible outcome 52

so, total number of possible outcomes for 6 - sided dice are 52 * 6

= 312

Hence total number of possible outcomes are 312

Learn more about possible outcomes here:

https://brainly.com/question/28052707

#SPJ4

The length and width of the rectangle are 18 in and 1 in, respectively.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : b*h, where b = base and h =height.

For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=b*h

18=(W+17)*W

18=W²+17W

W²+17W-18=0

Solving this quadratic equation, you have:

[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}[/tex]

[tex]w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]

w1=1 and w2= -18

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², see.

18=l*w

18=l*1

l=18 in

Read more about the area of rectangle here:

https://brainly.com/question/25292087

#SPJ1

The additional information needed to determine that ABCD is a parallelogram is: A. AB ≅ CD.

One of the criteria for proving that a quadrilateral is a parallelogram is that one of the pairs of opposite sides are congruent and also parallel to each.

We are already given that side AB is parallel to side CD, therefore, the additional information we would need to prove that quadrilateral ABCD is a parallelogram is: A. AB ≅ CD.

Learn more about parallelogram on:

https://brainly.com/question/3050890

#SPJ1

Answer:

(C)=22.5

Step-by-step explanation:

Hi! ❄

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

First, let's subtract by 23 both sides.

[tex]\sf{\dfrac{3}{2}c=15}[/tex]

Now we multiply the equation by 2.

[tex]\sf{3c=30}[/tex]. See how on the left hand side, the 3/2c*2 turned into 3c? That's because multiplication and division are operations that undo each other.

And Now we just divide by 3 both sides.

[tex]\sf{c=10}[/tex]

Hope this made sense !!

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

[tex]\star\tiny\pmb{calligraphy}\star[/tex]

The time, date and the day when the journey finished is 2:30 pm on Thursday 9th January

68 hours = 68/24

= 2 days and 20 hours

6;30 pm on Monday 6th January + 2 days and 20 hours

= 2:30 pm on Thursday 9th January

Learn more about time:

https://brainly.com/question/25800303

#SPJ1

The equation which can be used to determine x, the number of players the team can bring to the

tournament is 1353 = 943.50 + 31.50x and x = 13 players

1353 = 943.50 + 31.50x

1353 - 943.50 = 31.50x

409.50 = 31.50x

x = 409.50 / 31.50

x = 13 players

Learn more about equation:

https://brainly.com/question/13763238

#SPJ1

p→r

The law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost  similar to the transitive property.

now if we want to define general case then we can say tha

a→b

and

b→c  => a→c

now according to statements given in the problem

p→q and q→r ⇒ p→r

which completes the syllogism.

hence ,  p→r is the required answer.

learn more about syllogism here:

https://brainly.com/question/5142648

#SPJ4

The null hypothesis be is =15 and the alternative hypothesis be  is ≠15

According to the statement

Mean length of time on death row is 17.4 years

Standard deviation of 6.3 years.

Now we determine the hypothesis with mean time 15 years then

P value outcome is 0.00015

So, The null hypothesis be  is =15 and the alternative hypothesis be is ≠15

Learn more about HYPOTHESIS here https://brainly.com/question/12416923

#SPJ4

Answer:

10%.

Step-by-step explanation:

There are a total of 40 numbers.

Number of permutations of 3 numbers from 40

= 40 P 3

= 40! / (40-3)!

= 59,280.

The total of even numbers is (38 - 2) / 2 + 1 = 19.

Number of permutations of 3

=  19P 3

=  5814

So Prob(all even) = 5814/59280

= 0.098077

= 9.8%

= 10% to nearest whole number.

Answer:

[tex]\frac{\sqrt{3} }{6}[/tex]

Step-by-step explanation:

using the 30- 60- 90 triangle for exact values , then

tan60° = [tex]\sqrt{3}[/tex] , and

cot60° = [tex]\frac{1}{tan60}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]

cos60° = [tex]\frac{1}{2}[/tex]

cot60° cos60°

= [tex]\frac{1}{\sqrt{3} }[/tex] × [tex]\frac{1}{2}[/tex]

= [tex]\frac{1}{2\sqrt{3} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= [tex]\frac{1}{2\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= [tex]\frac{\sqrt{3} }{6}[/tex]

The answer is [tex]\boxed {\frac{1}{2\sqrt{3}}}[/tex]

The needed trigonometric values :

Hence, the value of the expression is :

The reasonable value for the range of the given function is: A. 75.

The range of a function is the output that a corresponding input value would give as a relation.

In this scenario, the grade you get is a function of number of hours you study. Range is the grade (output), while the domain is hours of study (input).

The given possible range values in the options are, 75, 1.25, -30, 1/2.

A reasonable value of a a grade cannot be a negative number, neither can it be 1.25, nor 1/2.

Therefore, the reasonable value of the range is: A. 75.

Learn more about the range of a function on:

https://brainly.com/question/7644636

#SPJ1

The equation p=4+3y is maximised at (4,5) and the maximised value is 31.

Given equation p=4x+3y and constraints x>0,x<4, y<5.

We have to maximise the equation p=4x+3y with constraints x>0,x<4,y<5.

To find out the points we have to make graphs of the constraints first.

From the graph we have found that points are (0,0),(0,5),(4,0),(4,5).

The above points are common points of graphs of all constraints.

The value of equations are as under:

At (0,0) , p=4*0+3*0=0

At (0,5), p=4*0+3*5=15

At (4,0),p=4*4+3*0=16

At (4,5),p=4*4+3*5=16+15=31

Maximum value of p is 31 and that is for (4,5).

Hence the equation is maximised at (4,5) and the maximum value is 31.

Learn more about equation at https://brainly.com/question/2972832

#SPJ4

Answer:

In math, calculus deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two basic types of calculus are differential calculus and integral calculus.

Step-by-step explanation:

hope it helps

sorry if I'm wrong

The sum of the first 30 terms of the arithmetic series is 1560

From the question, we are to determine the sum of the first 30 terms of the series

Using formula,

[tex]S_{n} = \frac{n}{2}(a + l)[/tex]

Where [tex]S_{n}[/tex] is the sum of the nth term

n is the number of terms

a is the first term

and [tex]l[/tex] is the last term

From the given information,

n = 30

a = 3

[tex]l[/tex] = 101

Thus,

[tex]S_{30} = \frac{30}{2}(3+ 101)[/tex]

[tex]S_{30} = 15(104)[/tex]

[tex]S_{30} = 15 \times 104[/tex]

[tex]S_{30} = 1560[/tex]

Hence, the sum of the first 30 terms of the arithmetic series is 1560

Learn more on Sum of an Arithmetic progression here: https://brainly.com/question/24295771

#SPJ1

Answer: base = 12, altitude = 16

Step-by-step explanation:

The mean of the scores to the nearest 10th digit will be 74.9.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.

Then the mean is given as,

Mean = (Total score) / (total student)

The total score will be

Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2

Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190

Total score = 2470

The total number of students will be

Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2

Total student = 33

Then the mean will be

Mean = 2470 / 33

Mean = 74.85 ≈ 74.9

More about the mean link is given below.

https://brainly.com/question/521501

#SPJ2

Answer:

1. (x + 8)(x + 3)

2. (x - 9)²

Step-by-step explanation:

Given trinomials:

1. [tex]x^2+11x+24[/tex]

2. [tex]x^2-18x+81[/tex]

..................................................................................................................................................

When factoring trinomials of the form ax² + bx + c:

..................................................................................................................................................

1) x² + 11x + 24

Step 1: Multiply the leading coefficient (1) and the last term (24).

[tex]\implies 1 \times 24 = \boxed{24}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (11).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:24 & \sf Sum\:of\:factors\\\cline{1-2} 1, 24\ \| -1, -24 & 25\ \| -25 \\\cline{1-2} 2, 12\ \| -2, -12 & 14\ \| -14 \\ \cline{1-2} 3, 8\ \| -3, -8 & 11\ \| -11 \\\cline{1-2} 4, 6 \ \| -4, -6 & 10\ \| -10 \\\cline{1-2}\end{array}[/tex]

[tex]\implies 3x+8x=11x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2+3x+8x+24[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2+3x)}^x+\overbrace{(8x+24)}^8\ \ \textsf{[ Factor out $x$ and $8$. ]}[/tex]

[tex]\implies x\overbrace{(x+3)}^{\textsf {Factor out}}+8(x+3)[/tex]

[tex]\implies \boxed{(x+8)(x+3)}[/tex]

The factored form of the given trinomial is [tex](x+8)(x+3)[/tex].

..................................................................................................................................................

2) x² - 18x + 81

Step 1: Multiply the leading coefficient (1) and the last term (81).

[tex]\implies 1 \times 81 = \boxed{81}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (-18).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:81 & \sf Sum\:of\:factors\\\cline{1-2} 1, 81\ \| -1, -81 & 81\ \| -81 \\\cline{1-2} 3, 27\ \| -3, -27 & 30\ \| -30 \\ \cline{1-2} 9, 9\ \| -9, -9 & 18\ \| -18 \\\cline{1-2}\end{array}[/tex]

[tex]\implies (-9x)+(-9x)=-18x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2-9x-9x+81[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2-9x)}^x+\overbrace{(-9x+81)}^{-9}\ \ \textsf{[ Factor out $x$ and $-9$. ]}[/tex]

[tex]\implies x\overbrace{(x-9)}^{\textsf {Factor out}}-9(x-9)[/tex]

[tex]\implies (x-9)(x-9)[/tex]

[tex]\implies \boxed{(x-9)^2}[/tex]

The factored form of the given trinomial is [tex](x-9)(x-9)\ \textsf{or}\ (x-9)^2[/tex].