Answers
As given by the question
There are given that the point (-6, 1) and slope (m) is -6.
Now,
To graph, the line, first, finds the equation of the line by using the given point and slope.
Then,
From the formula of point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where,
[tex]x_1=-6,y_1=1,\text{ and m=-6}[/tex]Then, put all given values into the above formula:
So,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1_{}=-6(x-(-6)_{}) \\ y-1=-6(x+6) \end{gathered}[/tex]Then,
[tex]\begin{gathered} y-1=-6(x+6) \\ y-1=-6x-36 \\ y-1+1=-6x-36+1 \\ y=-6x-35 \end{gathered}[/tex]Then, the graph of the above equation is shown below:
Related Questions
Lesson 6.07: In a random sample of 74 homeowners in a city, 22 homeowners said they wouldsupport a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The samplingmethod had a margin of error of +3.1%. SHOW ALL WORK!A) Find the point estimate.B) Find the lower and upper limits and state the interval.
Answers
Confidence interval is written in the form,
(point estimate +/- margin of error)
The given scenario involves population proportion
The formula for the point estimate is
p' = x/n
where
p' = estimated proportion of success. p' is a point estimate for p which is the true proportion
x represents the number of success
n represents the number of samples
From the information given,
n = 74
x = 22
p' = 22/74 = 0.297
The formula for finding margin of error is expressed as
[tex]\begin{gathered} \text{margin of error = z}_{\frac{\alpha}{2}}(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}} \\ q^{\prime}\text{ = 1 - p'} \\ q^{\prime}\text{ = 1 - 0.297 = 0.703} \end{gathered}[/tex]A) The point estimate is 0.297
B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031
Thus,
the lower limit would be 0.297 - 0.031 = 0.266
Expressing in percentage, it is 0.266 x 100 = 26.6%
the upper limit would be 0.297 + 0.031 = 0.328
Expressing in percentage, it is 0.328 x 100 = 32.8%
Thus, the confidence interval is between 26.6% and 32.8%
Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by commas.
Answers
To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible.
What is a matrix?matrix, a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations.
The elements of the matrix, also known as the entry, are the numerals.
A matrix will be invertible only and only if the determinant is non-zero.
Given the matrix A.
The determinant of A is that |A| will be,
|A| = -3(8 - 8) - 0(-k + 2) - 3(-4k + 8) ≠ 0
0 + 0 + -3(-4k + 8) |A| ≠ 0
-4k + 8 ≠ 0
-4k ≠ -8
k ≠ 2
Hence "To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible".
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A golf course charges you $54 for a round of golf using a set of their clubs, and $42 if you have your own clubs. You decide to buy a set of clubs for $280 and your friend wants to just use the course's clubs.a. Write an equation to describe the cost for x number of rounds for you.b. write an equation to describe the cost for x number of rounds for your friend.c. How many rounds must you play to recover the cost of the clubs? (Find the break-even point).
Answers
Answer
You must play 24 rounds to recover the cost of the club
Step-by-step explanation:
The amount golf charged for using their set clubs = $54
They charged $42 for using personal course
let x be the number of rounds played
let y be the total cost of the clubs
Since you will be buying a set of clubs worth $280
Then, the first equation is
a. y = 280 + 42x
b. y = 54x
c . Calculate the number of rounds that must be played to recover the cost of the clubs
To calculate this, we need to equate equations a and b together
280 + 42x = 54x
Collect the like terms
280 = 54x - 42x
280 = 12x
Isolate x by dividing through by 12
280/12 = 12x/12
x = 23.3333
Hence, you must play 24 rounds to recover the cost of the club
I need to help finding the length of the arc shown in red..
Answers
We have the next formula to find the length is
[tex]\text{arc length }=\text{ 2}\pi r(\frac{\theta}{360})[/tex]where
r=10
theta=45°
[tex]\begin{gathered} \text{arc length=}2\pi(10)\frac{45}{360}=\frac{5}{2}\pi \\ \end{gathered}[/tex]the arc length is 5/2 pi cm
50 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
Answers
The expression that represents the area of the rectangle is 6x²+29x+35.
Given that, a rectangle has sides measuring (2x + 5) units and (3x + 7) units.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Part A:
Now, area = (2x+5)(3x+7)
= 2x(3x+7)+5(3x+7)
= 6x²+14x+15x+35
= 6x²+29x+35
So, the area of a rectangle is 6x²+29x+35
Part B:
A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
Here, the degree of the expression 6x²+29x+35 is 2.
Part C:
Closure property of multiplication states that if any two real numbers a and b are multiplied, the product will be a real number as well.
Here, we obtained product of two binomials is trinomial
Therefore, the expression that represents the area of the rectangle is 6x²+29x+35.
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The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?
Answers
We have that the volume of sphere is
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot r^3 \\ \end{gathered}[/tex]and the volume of a cube is
[tex]V_c=s^3[/tex]so if s=r=3. The volume of the sphere is greater.
If they have the same volume, we get that
[tex]\begin{gathered} \frac{4}{3}\pi\cdot r^3=125\rightarrow \\ r^3=\frac{3}{4\cdot\pi}\cdot125\approx29.84\approx30 \\ r=\sqrt[3]{30}\approx3.10 \end{gathered}[/tex]when s=r=2 we have that
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot8=\frac{32}{3}\pi \\ V_c=8 \end{gathered}[/tex]so the volume of the sphere is greater
Express M in terms of B and n: B = 3Mn 2
Answers
We are given the expression B=3Mn/2 and told to express M in terms of B and n. This means that we should apply mathematical operations on both sides of the equation so we "isolate " M on one side of the equality sign. We begin with the given equation
[tex]B=\frac{3\cdot M\cdot n}{2}[/tex]First, we multiply both sides by 2, so we get
[tex]2\cdot B=3\cdot M\cdot n[/tex]Next, we divide by 3 on both sides, so we get
[tex]\frac{2\cdot B}{3}=M\cdot n[/tex]Finally, we divide both sides by n, so we get
[tex]\frac{2\cdot B}{3\cdot n}=M[/tex]In this case, we have succesfully expressed M in terms of B and n
Find the equation of the tangent line to the curve y = x^3- 4x - 5 at the point (2, -5).Tangent Line Equation:
Answers
Let's find the derivative of y:
[tex]\begin{gathered} y=x^3-4x-5 \\ \frac{dy}{dx}=3x^2-4 \end{gathered}[/tex]Evaluate the derivative for x = 2:
[tex]\frac{dy}{dx}\begin{cases} \\ x=2\end{cases}=3(2)^2-4=12-4=8[/tex]Now, we have the slope, let's use the point-slope formula to find the equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ _{\text{ }}where\colon \\ (x1,y1)=(2,-5) \\ m=8 \\ y+5=8(x-2) \\ y+5=8x-16 \\ y=8x-21 \end{gathered}[/tex]Answer:
y = 8x - 21
Section 11 - Topic 5Probability and Independence• In your own words, describe what the word independeyou.Now describe dependent..
Answers
In probability , there are two events independent events and dependent events.
Independent Events :
Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.
Example
. Choosing a marble from a jar AND landing on heads after tossing a coin.
Dependent Events :
If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
Example
Buying ten lottery tickets and winning the lottery.
The graph of f(a) = > has been transformed to create the graph of g(s) =
Answers
EXPLANATION
The graph of the parent function: f(x) = 1/x has the following form:
Translating the function two units to the left, give us the Image function:
This function is obtained by adding two units to the denominator.
In conclusion, the solution is -2
What is the length of the arc ? ( Precalc )
Answers
We're going to use the following formula:
[tex]L=2\cdot\pi\cdot r\cdot\frac{\theta}{360}[/tex]If we replace our values:
[tex]L=2\cdot\pi\cdot3\cdot\frac{60}{360}=\pi[/tex]Therefore, the length is pi.
The dog looked at the cat warily A with interestb viciously c hungrily d with caution
Answers
Answer
Option D is correct.
The dog looked at the cat with caution.
is the same as
The dog looked at the cat warily.
Explanation
The word warily means 'using caution' or 'cautiously'.
Hope this Helps!!!
At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)
Answers
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
(3h+1)^2=h^2+35^2
9h^2+6h+1=h^2+1,225
solve for h
9h^2-h^2+6h+1-1,225=0
8h^2+6h-1,224=0
Solve the quadratic equation
Using a graphing tool
the solution is
h=12 ftAli borrowed Php22,000 for 3months at the discount rate of 5 ¼ % from a bank. Find the (a) bank’s discount and (b) proceeds.
Answers
If an M amount is borrowed for a time t at a discount rate of r per year, then the discount D is calculated as
[tex]\begin{gathered} D=M\cdot r\cdot t \\ \\ \text{where} \\ r\text{ is expressed in decimals} \end{gathered}[/tex][tex]\begin{gathered} \text{Given} \\ M=22000 \\ r=5\frac{1}{4}\%\rightarrow5.25\%\rightarrow0.0525 \\ t=\mleft(\frac{3}{12}\mright)\text{or }0.25\text{ (3 months out of 1 year or 12 months} \end{gathered}[/tex]Substitute the following values to get the bank's discount.
[tex]\begin{gathered} D=Mrt \\ D=(22000)(0.0525)(\frac{3}{12}) \\ D=288.75 \end{gathered}[/tex]Therefore, the bank's discount is Php 288.75.
To calculate for proceeds, subtract the amount borrowed by the bank's discount.
[tex]\begin{gathered} P=M-D \\ P=22000-288.75 \\ P=21711.25 \end{gathered}[/tex]The proceeds given to Ali is Php 21,711.25.
You start at (9,2). you move left 9 units. where do you end
Answers
If you start at (9,2) and then move left 9 units, you'll end up at (0, 2)
John starting playing video games as soon as he got home from school. He played videogames for 45 minutes. Then, it took John 30 minutes to finish his homework. When Johnfinished his homework, it was 4:25 P.M. What time did John get home from school?
Answers
Given:
After coming from school to home,
He played video games for 45 minutes.
Then he took 30 minutes to finish his homework.
When John finished his homework, it was 4:25 PM.
To find:
The time at which John got home from school
Explanation:
According to the problem,
Total time to play video games and do homework is,
[tex]\begin{gathered} 45mins+30mins=75mins \\ =1hr15mins \end{gathered}[/tex]So, the time he got home from school will be,
[tex]4:25P.M.-1hr15mins=3:10P.M.[/tex]Final answer:
The time he got home from school is 3:10 P.M.
The area of an equilateral triangle is decreasing at a rate of 3 cm2/min. Find the rate (in centimeters per minute) at which the length of a side is decreasing when the area of the triangle is 100 cm2.
Answers
The rate at which the length of a side is decreasing when the area of the triangle is 100 cm² is equal to -0.227 centimeters per minute.
What is rate of change?Rate of change is a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.
How to calculate the area of an equilateral triangle?Mathematically, the area of an equilateral triangle can be calculated by using this formula;
A = (√3/4)s²
Where:
A represents the area of an equilateral triangle.s represents the side length of an equilateral triangle.Next, we would determine the side length of a square by making s the subject of formula as follows:
s = (√4A)/√3
s = (√4 × 100)/√3
Side length, s = 15.20
Note: The rate of change (dA/dt) is negative because it is decreasing.
By applying chain rule of differentiation, the rate of change (dA/dt) in area of this equilateral triangle with respect to time is given by:
dA/dt = (√3/4)(2s)ds/dt
dA/dt = (√3/4) × (2 × 15.20) × -3
dA/dt = -0.227 centimeters per minute.
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Priya is mixing drops of food coloring to create purple frosting for a cake. She uses 24 drops of red dye and 16 drops of blue dye. Find the ratio of drops of red dye to total drops of dye. Express as a simplified ratio.
Answers
Priya uses 24 drops of red dye,
She also uses 16 drops of blue dye,
[tex]\begin{gathered} \text{Total drops of dye=}24+16 \\ =40\text{drops of dye} \end{gathered}[/tex]We are told to find the ratio of drops of red dye to the total drops dye.
[tex]=\frac{\text{red drops of dye}}{\text{total drops of dye}}[/tex][tex]\begin{gathered} =\frac{24}{40}=\frac{3}{5} \\ =3\colon5 \end{gathered}[/tex]Hence, the ratio of drops of red die to the total drops of die to the simplest rato is
3 : 5.
Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
Answers
We will have the following:
[tex]\sin (2\theta)=-\frac{1}{2}\Rightarrow2\theta=2\pi n_1+\frac{7\pi}{6}[/tex][tex]\Rightarrow\theta=\pi n_1+\frac{7\pi}{12}[/tex]Now, we will solve for the following:
[tex]\Rightarrow\pi n_1+\frac{7\pi}{12}\le2\pi\Rightarrow\pi n_1\le\frac{17\pi}{12}[/tex][tex]\Rightarrow n_1\le\frac{17}{12}[/tex]This value in degrees is:
[tex]\frac{17}{12}\text{radians}=81.169\text{degrees}[/tex]So, the solution is located in the interval:
[tex]\lbrack0,81\rbrack[/tex]Please help me I need the answer asap.
Answers
Therefore the right answer is option D = 1. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.
What are linear equations?An equation with the form Ax+By=C is referred to as a linear equation. It consists of two variables combined with a constant value that exists in each of them. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).Hence,
The correct Option is D = 1
Given
[tex]x^2+x-1\\[/tex] = 0
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = ?
From [tex]x^2+x-1\\[/tex] = 0
[tex]x^2 = 1-x[/tex]
Therefore,
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = [tex]\frac{x^2}{2x^2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{1}{2}[/tex]
= 1
Therefore the right answer is option D = 1
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Evaluate the expression when m=9 and n=7.
5m +n
Correction: m = 7 and n = 9
Answers
We have the expression:
[tex]5m+n\text{.}[/tex]We must evaluate the expression for:
• m = 7,
,• n = 9.
Replacing the values of m and n in the expression above, we get:
[tex]5\cdot7+9=35+9=44.[/tex]Answer
44
What is the volume of this triangle right prism 8 cm 15 cm 12 cm
Answers
The volume of a triangle right prism is given by the formula
how do you work the problem 3k+16=5k?
Answers
We have the following:
[tex]3k+16=5k[/tex]solving for k
[tex]\begin{gathered} 5k-3k=16 \\ k=\frac{16}{2} \\ k=8 \end{gathered}[/tex]The value of k is 8
A set of pool balls contains 15 balls numbered 1-15.
Without replacement: What is the probability that an odd number ball is picked
out of a box twice without the first one being replaced?
With replacement: What is the probability that an even number ball is picked with
the first ball drawn being inserted back into the box?
Answers
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
the first case I assume means that we need the probability to pick 2 odd-numbered balls in a row, if we do not put the first drawn ball back into the box.
starting condition :
15 basks in total.
1, 3, 5, 7, 9, 11, 13, 15 = 8 odd numbered balls
2, 4, 6, 8, 10, 12, 14 = 7 even numbered balls
the probability for the first ball to be odd numbered :
8/15
now we have
14 remaining balls in total.
7 remaining odd numbered balls.
the probability of the second ball being odd numbered is
7/14 = 1/2
so, the probability of both as one combined event is
8/15 × 1/2 = 4/15 = 0.266666666...
now back to the starting condition.
the probability to pick an even numbered ball is
7/15
we put the ball back in and pull a second time.
the probability to an even numbered ball is
7/15
so, the probability of both as one combined event is
7/15 × 7/15 = 49/225 = 0.217777777...
I got the last question right that was similar so I’m unsure what I’m doing wrong for this one
Answers
Solve x:
[tex][/tex]How many different lineups can Coach Lay create using 10 girls to fill 5 spots on the basketball court. Positions do not matter.
Answers
This is the formula for combinations
In this case, n = 10 and k = 5
C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252
Answer:
252 different line u
the day of the lowest show the most ever in a single day by random sample of 13 students calculate the 38th and the 60th percentile of data
Answers
We have that the sample consist in n=13 students. The percentile formula is given by
[tex]P_x=\frac{x}{100}\times n\text{ position}[/tex]where x denotes the percentaje. In the first case, p=38, then, we have
[tex]\begin{gathered} P_{38}=\frac{38}{100}\times13\text{ position} \\ P_{38}=4.94\text{ position} \end{gathered}[/tex]then, we get
[tex]P_{38}=41[/tex]that is, P_38 corresponds to 41 miles driven.
In the second case, by substituting x=60 in our formula, we get
[tex]\begin{gathered} P_{60}=\frac{60}{100}\times13\text{ position} \\ P_{60}=7.8\text{ position} \end{gathered}[/tex]which gives
[tex]P_{60}=56[/tex]that is, P_60 corresponds to 56 miles driven.
Then, the answers are:
[tex]P_{38}=41[/tex]This means that approximately 38% of the data lie below 41, when the data are ranked.
[tex]P_{60}=56[/tex]This means that approximately 60% of the data lie below 56, when the data are ranked.
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 9.5 ft by 5.5 ft by 9 ft. The container is entirely full. If, on average, its contents weigh 0.99 pounds per cubic foot, and, on average, the contents are worth $4.37 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
Answers
step 1
Find out the volume of the rectangular container
[tex]V=L\cdot W\cdot H[/tex]Substitute given values
[tex]\begin{gathered} V=9.5\cdot5.5\cdot9 \\ V=470.25\text{ ft3} \end{gathered}[/tex]step 2
Find out the weight of the container
Multiply the volume by the density of 0.99 pounds per cubic foot
0.99*470.25=465.5475 pounds
step 3
Multiply the weight by the factor of $4.37 per pound
so
4.37*465.5475=$2,034.44
therefore
The answer is $2,034.44The table gives a set of outcomes and their probabilities. Let A be the event the outcome is divisible by 3". Find P(A). 12 Outcome Probability Tim elaps 1 0.14 PAUS 2 0.02 3 0.19 Smart out of 4 0.01 5 0.04 7 6 0.17 7 0.15 8 0.28
Answers
Here, we want to get the probability that a selected outcome is divisible by 3
What we have to do here is ti select numbers that are multiples of 3 and add their probabilities
From the given table, the outcomes that are multiples of 3 are;
3 and 6 only
So, we proceed to add the probabilities of these outcomes
Mathematically, we have this as;
[tex]P(A)\text{ = 0.19 + 0.17 = 0.36}[/tex]Anna's room is a rectangle. Its length is 15 feet and its width is 4 yards. What is the perimeter of the room?
Answers
Answer:
38
Step-by-step explanation:
Perimeter is basically each side added together. 15 + 15 + 4 + 4 is 38. Therefore, it's 38.