What is the slope of the line below? If necessary, enter your answer as afraction in lowest terms, using the slash (/) as the fraction bar. Do not enteryour answer as a decimal number or an equation.
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To find the slope of a line use two points (x,y) in the next formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In the given line you have the points: (-4, -9) and (-2, -3)
[tex]m=\frac{-3-(-9)}{-2-(-4)}=\frac{-3+9}{-2+4}=\frac{6}{2}=3[/tex]Then, the slope of the given line is 3Related Questions
What is the x values that satisfies the linear equations on the graph?
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In the linear equations shown on the coordinate grid, the values of x that satisfies both equations is 2 (option b).
The graph of both equations intersect at the point where x equals 2.
can someone please help me find the value of x?
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Since we have a right triangle, we can relate the angle 28 with x and side 34 by meand of the sine function, that is,
[tex]\sin 28=\frac{34}{x}[/tex]where x is the hypotenuse. By moving x to the left hand side, we have
[tex]x\cdot\sin 28=34[/tex]and by moving sin28 to the right hand side, we get
[tex]x=\frac{34}{\sin 28}[/tex]since sin28=0.4694, we have
[tex]x=\frac{34}{0.4694}[/tex]then, x is given by
[tex]x=72.42[/tex]by rounding down, the answer is option D: x=72.4
Suppose a mutual fund yielded a return of 14% last year. Its CAPM beta (β) is 1.2. The risk-free rate was 5% last year and the stock market return was 10% last year. What is the alpha (α) of the mutual fund?
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The Jensen's Alpha of the mutual fund is given as follows:
α = 3.
Jensen's AlphaThe Jensen's Alpha of a mutual fund is calculated according to the rule presented as follows:
α = [Rp - (Rf + Bp x (Rm - Rf))]
The parameters of the problem are defined as follows:
Rp is the expected portfolio return.Rf is the risk free rate.Bp is the beta of the portfolio.Rm is the expected market return.Hence, in the context of this problem, the values of the parameters are given as follows:
Rp = 14, Rf = 5, Bp = 1.2, Rm = 10.
Hence the Jensen's Alpha of the mutual fund is given as follows:
α = [Rp - (Rf + Bp x (Rm - Rf))]
α = [14 - (5 + 1.2 x (10 - 5))]
α = 3.
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Solve the inequality below to determine and state the smallest possible value of x in the solution set. - 7(x + 4) + 3x < 8x - 2(2x - 2)
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given the inequality :
- 7(x + 4) + 3x < 8x - 2(2x - 2)
so,
-7x - 28 + 3x < 8x - 4x + 4
combine like terms:
-7x + 3x - 8x + 4x < 28 + 4
-8x < 32
Divide both sides by -8
Do not forget to flip the inequality sign
so,
x > -4
so, The solution is the interval ( -4 , ∞ )
On the number line the solution will be :
The smallest possible interger of x = -3
Write the equation of the line when the slope is 1/5 and the y-intercept is 13.
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Given:
• Slope, m = 1/5
,• y-intercept = 13
Let's write the equation of the line.
To write the equation of the line, apply the slope-intercept equation of a line:
[tex]y=mx+b[/tex]Where:
m is the slope
b is the y-intercept.
Thus, we have:
m = 1/5
b = 13
Plug in the values in the equation:
[tex]y=\frac{1}{5}x+13[/tex]Therefore, the equation of the line is:
[tex]y=\frac{1}{5}x+13[/tex]1. Knowledge: Use your Factoring Flowchart or Concept Map to factor the following Quadratic Polynomials. Copy down the question and show any necessary steps if it is a multi-step factoring process (not just a single-step solution). Question F to I
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Solution
We are asked to factorize the following questions
Question F:
[tex]\begin{gathered} 4+6x+2x^2 \\ \text{ 2 is common among the terms, so we can factorize it out} \\ \\ 2(2+3x+x^2) \\ \text{ The term }3x\text{ can also be written as }2x+x.\text{ And the terms }2x\text{ and }x\text{ multiply to get }2x^2 \\ \text{ Thus, we have,} \\ \\ 2(2+3x+x^2)=2(2+2x+x+x^2) \\ \text{ In this new expression, }2\text{ is common to }2+2x\text{ while }x\text{ is common to }x+x^2 \\ \text{ Thus, we can factorize them out} \\ \\ 2(2+2x+x+x^2)=2(2(1+x)+x(1+x)) \\ \text{ Lastly, }(1+x)\text{ is common to }2(1+x)\text{ and }x(1+x) \\ \\ 2(2(1+x)+x(1+x))=2((2+x)(1+x)) \\ \\ \therefore4+6x+2x^2=2(2+x)(1+x) \end{gathered}[/tex]Question G:
[tex]\begin{gathered} 3x^2-1x-10 \\ \text{ The term }-1x\text{ can also be written as }-6x+5x\text{ and the terms }-6x\text{ and }5x\text{ multiply to get} \\ -30x^2.\text{ Thus, we have,} \\ \\ 3x^2-1x-10=3x^2-6x+5x-10 \\ 3x\text{ is common to }(3x^2-6x)\text{ and }5\text{ is common to \lparen}5x-10) \\ \text{ Thus, we can factor them out} \\ \\ 3x^2-6x+5x-10=3x(x-2)+5(x-2) \\ (x-2)\text{ is common to both terms, so we can factor again} \\ \\ 3x(x-2)+5(x-2)=(x-2)(3x+5) \\ \\ \therefore3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]Final Answer
The answers to questions F and G are:
[tex]\begin{gathered} 4+6x+2x^2=2(2+x)(1+x) \\ \\ 3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]
Find the slope of the line that contains the two points.ROUND YOUR ANSWER TO TWO DECIMAL PLACES.
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The slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of the given points. Replace the given values and solve for m:
[tex]m=\frac{8-(-4)}{-6-0}=\frac{8+4}{-6}=\frac{12}{-6}=-2[/tex]The slope of the line that contains the two given points is -2.
Miguel is judging an essay contest. He has to select the best, second best, and third best. If there are 6 essays entered, how many ways could he choose the top essays?
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There are 120 ways to choose the top essays.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
There are 6 essays entered.
And, He has to select the best, second best, and third best.
Now,
Since, There are 6 essays entered.
Hence, The number of ways to choose the top essays = [tex]^{6} P_{3}[/tex]
= 6! / 3!
= 6×5×4
= 120
Thus, The number of ways = 120
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Which of the following equations shows the correct way to apply the Associative Property of Addition? (1 point)0 6x (2 + 3) = 6 x 2) + 3O 9+8 = 8+9O 6+2 = 4+4O 3+ (4+5) = (3+4) +5
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This property indicates that when there are or more digits in these operations, the result does not depends on the way the terms are grouped. Therefore:
[tex]\begin{gathered} 3+(4+5)=(3+4)+5 \\ 3+9=7+5 \\ 12=12 \end{gathered}[/tex]therefore, the answer is the last option 3+ (4+5) = (3+4) +5
a wood cutter measures a piece of wood to be 830 grams.There are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pounds.Whats is the mass of the wood in pounds
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The mass of the wood in pounds is 1.826 pounds.
How to calculate the value?From the information, the wood cutter measures a piece of wood to be 830 grams and there are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pound.
Therefore,the mass will be represented as x
This will be:
830 grams = 0.83 kilograms
0.83/1 = x/2.2
Cross multiply
x = 2.2 × 0.83
x = 1.826 pounds.
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What is the slope and y-intercept?
y=7x+2
Options:
Blank # 1
Blank # 2
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Answer:
Step-by-step explanation:
18098
Rewrite the equation by completing the square. x^{2}-6x-16 = 0
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Answer:
Step-by-step explanation:
x^2 - 6x - 16 = x^2 - 6x + 9 - 9 - 16 = (x - 3)^2 - 25
Form a polynomial whose zeros and degree are given.Zeros: -4, multiplicity 2; -3, multiplicity 1; degree 3O x3 + 8x2 + 40x + 48O x3 - 11x2 + 24x - 48O x3 + 11x2 + 40x + 48O x3 - 11x2 + 40% - 48
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The boxplot shown below results from the heights (cm) of males listed in a data set. What do the numbers in that boxplot tell us?
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Given:
The boxplot is given.
To fill in the blanks:
Explanation:
As we know,
The minimum value is represented by the line at the far left end of the diagram.
So, the minimum height is 153cm.
The first quartile on the left side is represented by the line between the minimum value ad the median.
So, the first quartile is 166.6cm.
The second quartile (or median) is represented by the line at the centre of the box.
So, the second quartile is 173.2cm.
The third quartile on the right side is represented by the line between the maximum value ad the median.
So, the third quartile is 180.1cm.
The maximum value is represented by the line at the far right end of the diagram.
So, the maximum height is 193cm.
Final answer:
The minimum height is 153cm, the first quartile is 166.6cm, the second quartile is 173.2cm, the third quartile is 180.1cm, and the maximum height is 193cm.
the mean salary offered to students who are graduating from coastal state university this year is $24,215, with a standard deviation of $3712. A random sample of 80 coastal state students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is $24,250 or more?
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Given that the mean and standard deviation of the population are $24,215 and $3712 respectively,
[tex]\begin{gathered} \mu=24215 \\ \sigma=3712 \end{gathered}[/tex]The sample size taken is 80,
[tex]n=80[/tex]Consider that the salary of students in the sample is assumed to follow Normal Distribution with mean and standard deviation as follows,
[tex]\begin{gathered} \mu_x=\mu\Rightarrow\mu_x=24215 \\ \sigma_x=\frac{\sigma}{\sqrt[]{n}}=\frac{3712}{\sqrt[]{80}}\approx415 \end{gathered}[/tex]So the probability that the mean salary (X) is $24250 or more, is calculated as,
[tex]\begin{gathered} P(X\ge24250)=P(z\ge\frac{24250-24215}{415}) \\ P(X\ge24250)=P(z\ge0.084) \\ P(X\ge24250)=P(z\ge0)-P(0From the Standard Normal Distribution Table,[tex]\begin{gathered} \emptyset(0.08)=0.0319 \\ \emptyset(0.09)=0.0359 \end{gathered}[/tex]So the approximate value for z=0.084 is,
[tex]\emptyset(0.084)=\frac{0.0319+0.0359}{2}=0.0339[/tex]Substitute the value in the expression,
[tex]\begin{gathered} P(X\ge24250)=0.5-0.0339 \\ P(X\ge24250)=0.4661 \end{gathered}[/tex]Thus, there is a 0.4661 probability that the mean salary offer for these 80 students is $24,250 or more.
Lucky Champ owes $209.10 interest on a 6% loan he took out on his March 17 birthday to upgrade an oven in his Irish restaurant, Lucky's Pub and Grub. The loan is due on August 17. What is the principal? (Use 360 days a year.)
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Based on the interest owed on the loan and the date that the loan is due and when Lucky Champ took it, the principal for the loan is $8,200.
How to find the principal?First, find the period of the loan:
= 14 days in March + 30 + 31 + 30 + 31 + 17 days in August
= 153 days
The interest can be found by the formula:
= Principal x Interest rate x Period
The Principal can therefore be found by the formula:
= Interest owed x Number of days in year / Number of days x 100 / 6
= 209.10 x 360 / 153 x 100 / 6
= $8,200
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Calculate the net price and trade discount (use net price equivalent rate and single equivalent discount rate) for the following: Sony Hd flat-screen list price: 899 chain discount: 5/4 net price: Trade discount
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The net price and trade discount for the good is.539.4 and 359.6 respectively.
How to calculate the net price?From the information given, tuw.Sony Hd flat-screen list price is 899 and has a discount: 5/4 net price:
The net price will be:
= List price × (1 - Discount rate)
= 899 × (1 - 40%)
= 899 × 60%
= 899 × 0.6
= 539.4
The trade discount will be:
= List price - Net price
= 899 - 539.4
= 359.6
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Complete question:
Calculate the net price and trade discount (use net price equivalent rate and single equivalent discount rate) for the following: Sony Hd flat-screen list price: 899 chain discount: 5/4 net price and discount 40%
Theoretical Probabilities. Use the theoretical method to determine the probability ofthe following outcomes and events. State any assumptions that you make. Drawing a red card (heart or diamond) from a standard deck of cards
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Recall that the theoretical probability that an event occurring is given by the following quotient:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]We know that there are 26 red cards in a standard deck, therefore:
[tex]P(\text{Drawing a red car)=}\frac{26}{52}=0.5.[/tex]Answer: 0.5.
Can you help me with my math homework?"There are 600 seats in the auditorium. This is 112 less than the number of seats in the gymnasium. How many seats are in the gymnasium? Let s= the number of seats in the gymnasium"
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According to the problem, there are 600 seats in the auditorium.
112 less than the number of seats in the gymnasium.
So, to find the number of seats in the gymnasium, we just have to add 122 and 600 because the auditorium has 112 seats less.
[tex]s=600+112=712[/tex]Hence, there are 712 seats in the gymnasium.If t = (- pi)/3 find the terminal point P(x,y) on the unit circle
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Find the corresponding possitive angle by adding to the angle t 2pi:
[tex]-\frac{\pi}{3}+2\pi=\frac{-\pi+6\pi}{3}=\frac{5\pi}{3}[/tex]Identify the coordiantes using a unit circle:
Then, for angle t=-pi/3 the coordinates are:x=1/2y=-√3 /2Supposed g is a one-to-one function with the following valuesg(-7)= -6g(11)= -1
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Given:
The function g(x) is one-one.
[tex]g(-7)=-6[/tex][tex]g(11)=-1[/tex]Required:
We need to find the values of the inverse image of the function g(x).
Explanation:
Recall that the image of distinct elements of the function is distinct.
There exist an inverse of g(x) since g(x) is one to one.
The inverse image of the given can be written as follows.
Consider the equation
[tex]g(-7)=-6[/tex][tex]g^{-1}g(-7)=g^{-1}(-6)[/tex][tex]g^{-1}(-6)=-7[/tex][tex]g(11)=-1[/tex][tex]g^{-1}g(11)=g^{-1}(-1)[/tex][tex]g^{-1}(-1)=11[/tex]Final answer:
[tex]g^{-1}(-6)=-7[/tex][tex]g^{-1}(-1)=11[/tex]A model of a 51 foot long airplane is 25 in long how is is a tire that is 1/6 tinch
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The length of the tire on the airplane given the length of the tire on the model is 17 / 50 foot.
What is the length of the tire?The first step is to determine the scale of the model. In order to determine the scale, divide the length of the airplane by the length of the plane in the model.
Scale of the model = length of the airplane / length of the model
51 / 25 = 1 inch represents 2 1/25 foot
The next step is to multiply the scale determined in the previous step by the length of the tire.
Length of the tire on the airplane = scale x length of the tire in the model
1 / 6 x 2 1/25
1/6 x 51 / 25 = 17 / 50 foot
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If 1 is added to a number and the sum is tripled, the result is 5 more than the number. Find the number
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Answer;
[tex]n=1[/tex]Explanation;
Here, we want to get a number
Since the number is not known at the moment, we can start by identifying the number with an a;phabet
Let us call this n
If 1 is added to the number
mathematical representation;
[tex]1+n[/tex]And the sum is tripled;
[tex]3(1+n)[/tex]The result is 5 more than the number
5 more than the number is simply;
[tex]5+n[/tex]So, we equate this to what we had initially as follows;
[tex]5+n=3(1+n)[/tex]We can now solve this equation for n
[tex]\begin{gathered} 5+n=3+3n \\ 5-3=3n-n \\ 2n=2 \\ n=\frac{2}{2} \\ n=1 \end{gathered}[/tex]Neptune is about how many times as far from the Sun as Mars is fronthe Sun?Neptune = 2,600, 000,000MarS= 143,000,000Solution:
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1.) A gourmet shop wants to mix coffee beans that cost $3.00 per pound with coffee beans that
cost $4.25 per pound to create 25 pounds of a new blend that costs $3.50 per pound. Find the
number of pounds of each needed to produce the new blend.
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Explanation:
3.00 x 15 = 45$ ( old blend )
4.25 x 10 = 42.5$ ( new blend )
25 pound in total cost $87.50
To find the average cost per pound divide total cost by # of pounds.
87.50 divided by 25 pounds is $3.50
There are 9,321 leaves on a tree. Explain why the digit 3 stays the same when9,321 is rounded to the nearest hundred.
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To round the nearest hundred the digit in the hundred column and test digit in the tens column.
To round the nearest hundred the digit in the hundred column is rounding digit and the digit in the tens column is test digit.
We find the rounding digit in hundred column is 3. Then we look out the test digit 2 to the right of the 3 in the tens column. Because 2<5 we round down and leave the 3 in the hundred column. Then replace the two rightmost digits with 0's.
The 9,321 rounded to the nearest hundred is 9,300.
Determine if the 2 lines are parallel, perpendicular, or neither based on their slope-intercept equations.
Equations of lines G & H;
Line G: y=-6x + 14
Line H: y=6x-14
O Perpendicular
O Not Enough Information
O Parallel
O Neither
POSS
10 11
12 13 14 15
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Answer:
perpendicular because the slopes are opposite
Step-by-step explanation:
Give the degree of the polynomial.
-v^8u^9 + 6x - 16u^6x^2v^6 - 5
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Answer: nonic
Step-by-step explanation:
How do you find the square root of -6 by imaginary numbers
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To find the square root of a negative number use the next:
[tex]\sqrt{-1}=i[/tex]For -6:
You can write -6 as the product of 6 and -1:
[tex]\sqrt{\left(6\right)*\left(-1\right)}[/tex]The square root of a product is the same as the product of the square root if each of the factors:
[tex]=\sqrt{6}*\sqrt{-1}[/tex]As the square root of 6 is not a exact number (it has many decimals) you leave the square root of 6 as it is. The square root of -1 is i; then, the square root of -6 is:
[tex]\begin{gathered} =\sqrt{6}*i \\ =\sqrt{6}i \end{gathered}[/tex]Then, the square root of -6 is: (√6)iWhich of the following tools did the Greeks limit themselves to in their
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The Greeks limited themselves to using only compass and ruler in their formal geometric constructions.
Answer: Options B and D.