If sin A 0.3, cos A = 0.7, sin B = (1/√5)
and cos B: (-1/√5) find the exact value of cos(A - B).
(i know the answer but i want to know how to solve it as well)
Answers
The exact value of cos(A - B) is -2√5 /25.
What are Sine and Cosine?In math, the trigonometric functions of an angle are sine and cosine. In the context of a right triangle, the sine and cosine of an acute angle are defined as the ratio of the lengths of the adjacent leg to the hypotenuse, and the sine of the specified angle is the ratio of the opposite leg's length to the hypotenuse's length.The concepts of sine and cosine can be expanded to include any real value in terms of the lengths of particular line segments in a unit circle.The sine and cosine can be extended to any positive or negative value, even complex numbers, according to more recent definitions of the terms, which also represent them as infinite series or as the solutions to specific differential equations.Therefore,
sin A = 0.3
sin B = (1/√5)
cos A = 0.7
cos B = (-1/√5)
cos(A-B) = cos a cos b + sin a sin b
⇒ cos(A-B) = 0.7(-1/√5) + 0.3((1/√5))
⇒ cos(A-B) = -0.7/√5 + 0.3/√5
⇒ cos(A-B) = -0.4/√5
On multiplying, √5 on the numerator and denominator,
⇒ cos(A-B) = -0.4 x √5 / 5
⇒ cos(A-B) = -2√5 /25
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Related Questions
Need help on this question with some explanation "Graph the image of the figure on the right under the given translation". T(3,2) (x,y) . Thanks in advance!
Answers
ANSWER
[tex]A[/tex]EXPLANATION
The given translation
[tex](3,2)[/tex]This means the shape will be translated 3units to the right and 2 units up.
That is;
[tex]\begin{gathered} (x+3) \\ (y+2) \end{gathered}[/tex]Maria has already written Two-fifths of her 1,000 word essay. If she continues writing at the same pace of 6One-half words per minute, which expression shows the amount of time it will take her to write the rest of the essay?
1000 times two-fifths times StartFraction 13 Over 2 EndFraction
1000 times two-fifths divided by StartFraction 13 Over 2 EndFraction
1000 times three-fifths times StartFraction 13 Over 2 EndFraction
1000 times three-fifths divided by StartFraction 13 Over 2 EndFraction
Answers
1000 times three-fifths divided by Start Fraction 13 Over 2 End Fraction is the required expression.
What is Expression?An expression is a combination of numbers, variables and operators.
Given that,
Maria has already written Two-fifths of her 1,000 word essay.
It means she has completed 2/5 of essay.
She has 3/5 more to do.
she continues writing at the same pace of 6One-half words per minute
So Her speed is 13/2 words per minute.
So 1000*3/5 (600 words) at 13/2 words per minute
we need to divide the number of words by the speed to work out the time: 1000*3/5/(13/2),
Hence 1000 times three-fifths divided by Start Fraction 13 Over 2 End Fraction is the required expression.
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Answer:
c
Step-by-step explanation:
Write the equation in the form of f(x) for the following problems. You have solutions of: x=-4 and 3 and a point at (0,-60).
Answers
Equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .
As given in the question,
For the function f(x):
Standard form of the equation with solution x =a and x=b is:
f(x) = k(x-a)(x-b)
Solutions for the given function f(x) is x =-4 and x=3 and a point (0,-60)
is given by:
f(x) = k(x-(-4))(x-3)
= k(x+4)(x-3)
Point at (0,-60) we get,
-60 = k ( 0+4)(0 -3)
⇒-60 = -12k
⇒ k =5
Required equation is :
f(x) = 5(x+4)(x-3)
Therefore, equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .
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Consider the arithmetic sequence an = 5 + 3 (n − 1)
a. What are the first 5 terms of the sequence?
b. What is the 9th term in the sequence?
c. Rewrite the explicit formula as a function.
d. What is f(15)?
e. f(n) = 65 what is n?
Answers
The answers to the subparts of the arithmetic sequence are shown:
(A) a₅ = 17(B) a₉ = 28What is an arithmetic sequence?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.So, the formula is: aₙ = 5 + 3 (n − 1)
Where n is the number of terms.So, 5th term or n = 5:
a₅ = 5 + 3 (n − 1)a₅ = 5 + 3 (5 − 1)a₅ = 5 + 3 (4)a₅ = 5 + 12a₅ = 17Similarly, the 9th term or n = 9:
a₉ = 5 + 3 (n − 1)a₉ = 5 + 3 (9 − 1)a₉ = 5 + 3 (8)a₉ = 5 + 24a₉ = 28Therefore, the answers to the subparts of the arithmetic sequence are shown:
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The correct question is given below:
Consider the arithmetic sequence an = 5 + 3 (n − 1)
a. What are the first 5 terms of the sequence?
b. What is the 9th term in the sequence?
I have a graph with the question. If the parent function is y= 2 to the power of x plus 2, which is the function of the graph
Answers
The parent function of the graph is
[tex]y=2^x[/tex]The function of the grapg will be
[tex]y=2^{x\text{ + a}}\text{ + b}[/tex]at x equals infinity y equals 1
Therefore
[tex]\begin{gathered} \text{x =}\infty\text{ then y = 1} \\ \text{this implies} \\ b\text{ = 1} \end{gathered}[/tex]Therefore the function will now be
[tex]y=2^{x\text{ + a}}\text{ + 1}[/tex]from the graph
x = 2 when y = 2
Therefore,
[tex]\begin{gathered} 2=2^{2\text{ + a}}\text{ + 1} \\ 2-1=2^{2\text{ + a}} \\ 1=2^{2\text{ + a}} \\ \text{recall 1 = 2}^0 \\ 2^0=2^{2\text{ + a}} \\ 2\text{ + a = 0} \\ a\text{ = - 2} \end{gathered}[/tex]Therefore, the function is
[tex]y=2^{x\text{ - 2}}\text{ + 1}[/tex]Taylor works on an art project that uses only rectangular pieces of paper. The first rectangle ha length 3/8 and width of 3in. Detriment wether the dimensions of each rectangle described as a proportional to the dimensions of tailors first rectangle
Answers
By comparing the dimensions above with the dimensions of Taylor's first rectangle, we have the following:
No, a length of 6 in, width 3/4 in. is not proportional.Yes, a length of 1/2 in, width 4 in. is not proportional.No, a length of 1 1/8 in, width 9 in. is not proportional.No, a length of 3 in, width 5 5/8 in. is not proportional.What is a direct proportion?Mathematically, a direct proportion (direct variation) can be represented the following mathematical expression:
y = kx
Where:
y and x are the variables or dimensions.k represents the constant of proportionality.For the dimensions of the rectangular pieces of paper to be proportional, the length and width must remain in a constant ratio.
Next, we would determine the constant of proportionality (k) as follows:
k = y/x
k = (3/8)/3
k = 3/24
k = 1/8
For dimension 1, we have:
k = y/x
k = (6)/(3/4)
k = 24/3
k = 8 (No).
For dimension 2, we have:
k = y/x
k = (1/2)/4
k = 1/2 × 1/4
k = 1/8 (Yes).
For dimension 3, we have:
k = y/x
k = (1 1/8)/9
k = (9/8)/8
k = 9/8 × 1/8
k = 9/64 (No).
For dimension 4, we have:
k = y/x
k = (3)/(5 5/8)
k = 3/(45/8)
k = 3 × 8/45
k = 24/45 (No).
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Complete Question:
Taylor works on an art project that uses only rectangular pieces of paper. The first rectangle has length 3/8 in. and width 3 in. Determine which dimensions below are proportional to the dimensions of Taylor's first rectangle.
Explain the meaning of the expression tan 32°= 0.624
Answers
The meaning of the expression tan 32°=0.624 is the adjacent side of ratio is 0.624m.
What is ratio?
the ratio is the number that can be used to express one is quantity as a fraction of the other ones. The two of numbers in a ratio can only be compared when they have the same unit. We are make use of ratios o compare two things.
Sol- let's take an example first
In a triangle abc
C is 32°
tan 32° = AB/BC =0.624m
By applying the theorem we know that
In a right triangle , tan 32° is the ratio of the constant to the adjacent side the ratio is
0.624 m.
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Please help me find the quadratic inequality for this
y ≥ x2 - 4x + 1
Answers
Answer:
x/> -y/2 + 1/2
8v < 40 solve the inequality for v and simplify your answer as much as possible
Answers
Hey there!
8v < 40
DIVIDE 8 to BOTH SIDES
8v/8 < 40/8
v < 40/8
v < 5
It is an open circle starting at 5 and it is going down to the left side of the number line
Therefore, your answer should be:
v < 5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
what is the answer for n? 5i + 7i =n
Answers
Answer: [tex]n=12i[/tex]
Step-by-step explanation:
Combine like terms.
Rewrite the following equation as a function of x.
1+ 3y - 29 = 0
O A. f(x)
f(x) = 9,2808 2
OB. f(x) = -9,280 +
O c. f(x) = -9,280 + 20
O D. f(x) = 9,280
1
20x
Answers
( 9 times 10 to the power of -7) (5 times 10 to the power of -4)
Answers
5 x 10^-4 = 1/2000
Mr. Reed is drawing a blueprint of a rectangular patio. The width of the patio is 40 3/4 feet shorter than twice its length. The perimeter of the patio is 86 1/2 feet. What is the length of the patio?
Answers
Answer:
length = 28 feet
Step-by-step explanation:
let length = x
width = 2x - 40 3/4
= 2x - 163/4
= 2x - 40.75
perimeter of a rectangle = 2(l+w)
according to the question:
86 1/2 = 2(l+w)
86.5 = 2(x + 2x - 40.75)
86.5 = 2(3x - 40.75)
86.5 = 6x - 81.5
86.5 + 81.5 = 6x
thus, x = 28
determine the equation of line from the graph
Answers
Answer:
y=2x+0
Step-by-step explanation:
This is slope intercept form. The slope is 2 you can tell by the two points on the graph at (0,0) and (1,2). The points move up 2 and over 1. That makes the slope 2/1 but since the bottom half is just a one it can be simplified to 2.
And the +0 just means that its y intercept is 0,0
however it is not required to put +0 at the end
Answer:y=2x+0
Step-by-step explanation:
One of the rows in the table has an error and does not have the same ratio as the other rows. Which explains how to correct the error in the table?
Conversion Chart
Feet
Centimeters
Row 1
3
91.44
Row 2
6
172.88
Row 3
7
213.36
Row 4
9
274.32
Row 1 should show 3 feet is equivalent to 92.44 centimeters.
Row 2 should show 6 feet is equivalent to 182.88 centimeters.
Row 3 should show 7 feet is equivalent to 223.36 centimeters.
Row 4 should show 9 feet is equivalent to 284.32 centimeters.
Answers
The correct option regarding the error in the proportional relationship is given as follows:
Row 2 should show 6 feet is equivalent to 182.88 centimeters.
Direct proportional relationshipA direct proportional relationship is a function in which the output variable y is calculated by the multiplication of the input variable x and the constant of proportionality k, as follows:
y = kx.
In the context of this problem, the input and the output are given as follows:
Input: Length in feet.Output: Length in centimeters.The constant is calculated dividing the output by the input of each of the lengths, hence:
Row 1: k = 91.44/3 = 30.48.Row 2: k = 172.88/6 = 28.81.Row 3: k = 213.36/7 = 30.48.Row 4: k = 274.32/9 = 30.48.Due to the different ratio, the mistake is in Row 2, and the correct value should be of:
6 x 30.48 =182.88 centimeters.
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A volume of the cone is 1/3 the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?
Answers
The volume of the sphere is 4/3 times the volume of the cylinder.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
We have,
The volume of the cone is 1/3 the volume of a cylinder.
The volume of a cone is given as:
V = (1/3)πr²h ____(1)
The volume of a cylinder is given as:
V = πr²h _____(2)
From (1) and (2) we get,
(1/3)πr²h = 1/3 πr²h
The volume of a sphere:
V = 4/3 πr³
Since the height of the sphere and the radius is the same we can have
V = 4/3πr²h
So,
Volume of sphere = 4/3 x πr²h
The volume of the sphere = 4/3 x the Volume of the cylinder.
Thus,
The volume of the sphere is 4/3 times the volume of the cylinder.
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Just need the answer A, B , C or D
Answers
Answer:
A. 2.25 feet.
Explanation:
We know the following equation:
[tex]v=\sqrt[]{2gh}[/tex]Where v is the speed, g is the gravity and h is the height. So, replacing v by 12 feet per second and g by 32 feet per second square, we get:
[tex]12=\sqrt[]{2(32)h}[/tex]So, solving for h, we get:
[tex]\begin{gathered} 12=\sqrt[]{64h} \\ 12^2=(\sqrt[]{64h})^2 \\ 144=64h \\ \frac{144}{64}=\frac{64h}{64} \\ 2.25=h \end{gathered}[/tex]Therefore, the answer is A. 2.25 feet.
which of the statements are true of the residuals in a regression equation? multiple choice question. they measure the impact of firm-specific events. they are not part of regression analysis. they reflect systematic risk. they represent alpha.
Answers
The residuals in a regression equation measure the impact of firm-specific events.
Residuals = Actual y value - Predicted y value
Residual analysis is a helpful set of methods for assessing the quality of a fitted model. Checking the underlying assumptions is crucial because most linear regression estimators depend on independent errors with the same distribution and a correctly stated regression function in order to be consistent. Regression is a statistical technique used in finance, investing, and other fields that aim to ascertain the strength and nature of the relationship between a single dependent variable (often represented by Y) and a number of other factors (known as independent variables).
The residuals in a regression equation measure the impact of firm-specific events.
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gary gets an average of 15 text messages during his 8 hour work day. in order to find the probability that gary will get exactly 3 text messages in a 2 hour portion of his work day using the poisson distribution, what is the time interval of interest?
Answers
The probability that Gary will get exactly 3 text messages in a 2-hour portion of his work day using the Poisson distribution, what is the time interval of interest: 2 hours
Gary will get calls according to Poisson distribution with an average # of calls per hour = 15.
Let x be the Poisson random Variable Such that X ~Poisson (15).
We need to find P(x≤3) in 2 hours.
Thus, the time interval of interest is 2 hours.
What is probability ?
Probability is the likelihood of an event occurring. It can range from an impossible event to a probability to an absolute certainty. In mathematics, probability is on a scale of 0-1. Zero means the event is impossible, like rolling seven dice with only the numbers 1-6. One is an event that will happen, that's for sure. An example of a specific event is tomorrow is Friday if today is Thursday. It will definitely happen. The median is 0.5 or half and these events are equally likely. A good example of half probability is tossing a coin. It gets straight heads or tails.
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Hello, I was wondering if the fraction 5/2 x and 5x/2 have the same value.
Answers
We have:
[tex]\frac{5}{2}x\text{ and }\frac{5x}{2}[/tex]These fractions are equal because the x is found by multiplying and it is as if we have this:
[tex]\frac{5}{2}\times\frac{x}{1}\text{ and }\frac{5\times x}{2}[/tex]And as we already know:
[tex]\frac{5}{2}\times\frac{x}{1}=\frac{5\times x}{2\times1}=\frac{5\times x}{2}=\frac{5x}{2}[/tex]50 POINTS!!!!!
decide whether the statement about the diagram is true explain your answer
ES ≅ ST
Answers
Answer: No
Step-by-step explanation:
The segments are not indicated to be congruent.
Pythagorean Theorem1 2 3 4 5OA 29.5 unitsOB23.4 unitsC. 24.4 unitsOD. 33.4 units
Answers
we know that the perimeter is the sum of all the sides, therefore:
[tex]\begin{gathered} P=10+9+3+\sqrt{7^2+9^2} \\ P=22+\sqrt{49+81} \\ P=22+\sqrt{130} \\ P=22+11.4=33.4 \end{gathered}[/tex]Therefore the answer is D. 33.4 units
a jar contains 22 red marbles number 1 to 22 and 52 blue marbles number 1 to 50 to a marble is drawn at random from the drawer find the probability of the given event around solution to three decimal places
Answers
We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.
PART 1
Let the probability that the marble is red be P(r).
Therefore,
[tex]P(r)=\frac{Number\text{ of red balls}}{\text{Total number of balls}}[/tex]This gives,
[tex]\begin{gathered} P(r)=\frac{22}{22+52}=\frac{22}{74} \\ \therefore P(r)=\frac{11}{37}=0.297 \end{gathered}[/tex]Therefore, the probability that the marble is red is:
ANSWER= 0.297
PART 2:
Let the probability of picking odd-numbered balls be P(o)
Therefore,
[tex]P\mleft(o\mright)=\frac{Number\text{ of odd balls}}{\text{Total number of balls}}[/tex]We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.
Therefore,
[tex]\begin{gathered} P(o)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore P(o)=0.5 \end{gathered}[/tex]The probability of picking odd-numbered balls is
ANSWER = 0.5
PART 3:
Let the probability of picking a red or odd-numbered ball be P(r U o)
[tex]P(r\cup o)=P(r)+p(o)-p(r\cap o)[/tex]Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).
p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.
Therefore,
[tex]\begin{gathered} P(r\cap o)=\frac{nu\text{mber of red and odd balls}}{\text{Total number of balls}} \\ =\frac{11}{74} \\ =0.149 \end{gathered}[/tex]This implies that,
[tex]\begin{gathered} P(r\cup o)=P(r)+p(o)-p(r\cap o) \\ P(r\cup o)=0.297+0.5-0.149 \\ \therefore P(r\cup o)=0.648 \end{gathered}[/tex]Hence, the probability of picking a red or odd-numbered ball is
ANSWER = 0.648
PART 4:
Let the probability of picking a blue or even-numbered ball be P(b U e)
Therefore,
[tex]P(b\cup e)=p(b)+p(e)-p(b\cap e)[/tex]From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,
[tex]\begin{gathered} p(b)=\frac{Number\text{ of blue balls}}{\text{Total number of balls}} \\ \therefore p(b)=\frac{52}{74}=0.703 \end{gathered}[/tex]p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.
[tex]\begin{gathered} p(e)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore p(e)=0.5 \end{gathered}[/tex]p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls
[tex]\begin{gathered} p(b\cap e)=\frac{Number\text{ of blue and even balls}}{\text{Total number of balls}} \\ P(b\cap e)=\frac{26}{74}=0.351 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(b\cup e)=p(b)+p(e)-p(b\cap e) \\ P(b\cup e)=0.703+0.5-0.351 \\ \therefore P(b\cup e)=0.852 \end{gathered}[/tex]Therefore, the probability of picking a blue or an even ball is:
ANSWER = 0.852
Last night, the two dinner specials at Rhianna's favorite restaurant were salmon filet and steak. The restaurant served 52 specials in all, 25% of which were salmon filets. How many salmon filets did the restaurant serve?
Answers
There were 13 salmon fillets that the restaurant served.
How do we calculate how many salmon fillets the restaurant served?The solution to this math problem involves fractions, especially percentage. A percentage is a fraction of a hundred. The literal meaning of percentage is "per 100". Percentage is often referred to as percent. The symbol or sign for percentage is %. The number beside the symbol/sign is the numerator, so for example, 10% can also be written as 10/100.
We're given that 25% of the dinner specials served by the restaurant were salmon fillets. In order to find out how many salmon fillets were served, we only need to multiply 52 by 25%.
52 × 25% =
52 × 25/100 =
(52 × 25)/100 =
1,300/100 = 13
There were indeed thirteen salmon fillets served by the restaurant.
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what is the answer
5+3=3+5
Answers
Answer:
They are equal
Step-by-step explanation:
5+3=8 and 3+5=8
If you are seeking the answer in terms of evaluation, then the answer would be 8 = 8. Both sides of the equation are equal, so in addition to this, the given equation is true.
5 + 3 = 8
3 + 5 = 8
So, if you were to attempt breaking down the equation, you could easily write it as 8 = 8.
Hope this helps!
A 6-foot- tall electric pole casts a shadow that is 24 feet long. What is the ratio
of the pole's height to its shadow?
Answers
The ratio of the pole's height to its shadow is 1:4.
What is a ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, the ratio of height:shadow:
The height of the pole is 6 feet.The shadow the pool creates is 24 feet.The ratio will be:
6:246/241/41:4
Therefore, the ratio of the pole's height to its shadow is 1:4.
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Tell whether the data in the table can be modeled by a linear equation. Explain. A table listing pairs of x and y values. First pair. Negative 3 and 16. Second pair. Negative 1 and 10. Third pair. 1 and 4. Fourth pair. 3 and negative 2. Fifth pair. 5 and negative 8. The data be modeled by a linear equation because the rate of change constant. Question 2 If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.
Answers
The table is a linear function and the equation is y = -3(x - 1) + 4
How to determine if the table represents a linear equation?From the question, we have the pairs to be
First pair = (-3, 16)Second pair.= (-1, 10)Third pair = (1, 4)Fourth pair = (3, -2)Fifth pair = (5, -8)From the above representations, we can see that:
As the values of x increase by +2, the values of y constantly increase by -6
This means that the table has a constant rate
By the definition of a linear function, the table represents a linear function
The linear equation of the functionIn (a), we have
x = +2
y = -6
The slope is calculated as
Slope = y/x
So, we have
Slope = -6/2
Evaluate
Slope = -3
The equation is then calculated as
Y = Slope * (X - x) + y
Where
(x, y) = (1, 4)
So, we have
y = -3(x - 1) + 4
Hence, the linear function is y = -3(x - 1) + 4
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What is the slope of -2,1 and 2,1
Answers
Is should be 50% slope
Answer:
m=0
Step-by-step explanation:
(-2,1) (2,1)
x1=-2,x2=2,y1=1,y2=1
Gradient/slope
m=y2-y1/x2-x1
m=1 - 1/2-(-2)
m=0/2+2
m=0/4
m=0
3/4 of a number is 30. What is the number? )) What is the number?
Answers
To find the number we can create the following equation and solve for x:
[tex]\frac{3}{4}\cdot x=30[/tex]Let x be the missing number, use inverse operations to solve the equation:
[tex]\begin{gathered} x=30\cdot\frac{4}{3} \\ x=\frac{120}{3} \\ x=40 \end{gathered}[/tex]The number is 40.
the area of a rectangular garden in square is xsquare -5x-300 If x=45 what is the width and the height of the garden 12a.widthheight 12b.please pot it step by step show all your work thank you
Answers
If a rectangle has an area of A and sides b and h, then:
[tex]A=b\cdot h[/tex]Solving for the base:
[tex]b=\frac{A}{h}[/tex]Basically, the sides b and h could have any value provided that b*h=A.
Nevertheless, this problem seems to want from us to factorize the expression:
[tex]x^2-5x-300[/tex]So that each side is a binomial.
Part a)
To factorize that expression, find two numbers so that if they are added up, the sum is equal to -5, and if they are multiplied, the product is equal to -300.
Since the product is negative, one number must be negative. Since the sum is negative, the biggest number should be the negative one.
Consider the factors of 300:
[tex]300=2\cdot2\cdot3\cdot5\cdot5[/tex]Using those factors, we can find pairs of numbers that give 300 as a result from multiplying.
After a bit of trial and error, notice that 15*20=300. If we choose 20 as the negative number, then 15*(-20)=-300 and 15+(-20)=-5. Therefore:
[tex]x^2-5x-300=(x+15)(x-20)[/tex]So, we can choose the width and the height to be those factors. Since (x+15) is greater then (x-20), then:
[tex]\begin{gathered} \text{Width}=x+15 \\ \text{Height}=x-20 \end{gathered}[/tex]Part b)
If x=45, then:
[tex]\begin{gathered} \text{Width}=60feet \\ \text{Height}=25feet \end{gathered}[/tex]