the graph of f passes through (-6,4) and is perpendicular to the line that has an x-intercept of 3 and a y-intercept of-6
Answers
To solve this problem, first, we have to find the slope of the line that has an x-intercept of 3 and a y-intercept of 6. The intercepts can be written as (3,0) and (0,6). Let's use the slope formula
\(m=\frac{y_2-y_1}{x_2-x_1}\)Where,
\(\begin{gathered} x_1=3 \\ x_2=0 \\ y_1=0 \\ y_2=6 \end{gathered}\)Let's use these values to find the slope.
\(m=\frac{6-0}{0-3}=\frac{6}{-3}=-2\)The slope of the line that has the given intercepts is m = -2.
Now, we have to find the perpendicular slope of m = -2 using the following rule
\(m\cdot m_{\text{perp}}=-1\)Let's replace the slope we found and find the other one.
\(m_{\text{perp}}=-\frac{1}{m}=-\frac{1}{-2}=\frac{1}{2}\)The slope of the perpendicular line is 1/2.
Once we have the slope of the new perpendicular line, we use the point-slope formula
\(y-y_1=m_{\text{perp}}\cdot(x-x_1)\)Where,
\(\begin{gathered} x_1=-6 \\ y_1=4 \\ m_{\text{perp}}=\frac{1}{2} \end{gathered}\)Let's use these values above to find the equation of the new perpendicular line.
\(\begin{gathered} y-4=\frac{1}{2}(x-(-6)) \\ y-4=\frac{1}{2}(x+6) \\ y-4=\frac{1}{2}x+\frac{6}{2} \\ y=\frac{1}{2}x+3+4 \\ y=\frac{1}{2}x+7 \end{gathered}\)Therefore, the equation of the new perpendicular line that passes through (-6,4) is
\(y=\frac{1}{2}x+7\)The image below shows the graph of this function
Related Questions
On the coast of Oregon, mussels cover most of the rocky shoreline. Two mussel predators include Pisaster (ochre stars) and Nucella (whelks). A sixty-day removal study was conducted, and the results are presented in the graph. Which of the following conclusions is best supported by the data in the graph?
Answers
Because Pisaster is a keystone species, the proportion of living mussels was comparable to the control after Nucella removal.
Is the ochraceous Pisaster a keystone species?Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.
Pisaster ochraceous: prey or predator?Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.
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The volume of a cube is 512ft³ Find the side length of the cube
Answers
We have that the cube has a volume of 512 ft^3.Then,
volume of cube = edge cubed
v = a³
512m³ = a³
∛512m³ = ∛a³
8m = to
Answer: The length of each side is 8 feet ✔ .
Write an equivalent fraction with a denominator of 10
1/2 = ?/10
Answers
Answer:
5/10
Step-by-step explanation:
An equivalent fraction will have the numerator and denominator multiplied by the same value.
ApplicationThe denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...
\(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)
BASKETBALL Oliver shot 8 free throws at practice, making 6 free throws and missing 2 free throws. If Oliver is equally likely to make a free throw as he is to miss a free throw, find the probability of this outcome by expanding (m + n)8.
Round to the nearest percent if necessary.
Answers
Therefore, the probability of Oliver making 6 free throws and missing 2 free throws is: 1/28(256) = 0.091 or 9.1% (rounded to the nearest percent).
What is Probability?Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
by the question.
We can use the binomial theorem to expand (m + n)8, where m represents the probability of making a free throw and n represents the probability of missing a free throw:
(m + n)8 = 8C0m8n0 + 8C1m7n1 + 8C2m6n2 + 8C3m5n3 + 8C4m4n4 + 8C5m3n5 + 8C6m2n6 + 8C7m1n7 + 8C8m0n8
where 8C0, 8C1, ..., 8C8 are the binomial coefficients.
Substituting m = 1/2 and n = 1/2, we get:
(1/2 + 1/2)8 = 8C0(1/2)8(1/2)0 + 8C1(1/2)7(1/2)1 + 8C2(1/2)6(1/2)2 + 8C3(1/2)5(1/2)3 + 8C4(1/2)4(1/2)4 + 8C5(1/2)3(1/2)5 + 8C6(1/2)2(1/2)6 + 8C7(1/2)1(1/2)7 + 8C8(1/2)0(1/2)8
Simplifying, we get:
1/28(1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1) = 1/28(256)
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Please Help with math word problem.
A community drama centre sells tickets to a play. They sell 216 tickets. Adult tickets cost $10.25 and students tickets cost $8. The total number of sales was $2117.25. How many students tickets were sold, how many adult tickets were sold?
Please show me how its done
Will make brainlist, thanks
Answers
Answer:
Adult Tickets: 173
Student Tickets: 43
Explanation:
To solve this problem, you'll need to set up a system of equations.Assume a = # of adult tickets soldAssume s = # of student tickets sold2: a + s = 216; 1: 10.25a+ 8s= 2117.25
2: <<As the total number of tickets sold from both sides is equal to 216>>
1: <<Each adults ticket (a) costs $10.25 and each student ticket (s) costs $8, and the total amount of money earned (2117.25) from sales is the combination of these two))>>
Note that there are two ways to solve systems of equations (by elimnation and substitution), in this case I'll use elimnation as substitution requires one of the variables in one of the two equations to be isolated.In this case, I'll elimnate a.a + s = 216
10.25a + 8s = 2117.25
In order to elimnate a, it has to be equal to - 10.25 so that it cancels out + 10.25 (so you have to multiply everything on the first equation by 10.25 ((what you do to one part, you'll do to all the other parts)).-10.25a -10.25s = -2214
10.25a + 8s = 2117.25
a cancels, and now you solve accordingly.-2.25s/-2.25 = -96.75/-2.25
s = 43
You could solve for a using this same method, but it's easier to use the first formula <<a+s=216>> to find a.a + 43 = 216
- 43 -43
a = 173
A triangle LMN with ln = 12 cm,Nm= x cm, Nk = 6cm and Km 8cm
Calculate the value of
(i) x
(ii) o
Answers
The value of x is 9 cm, and angle O is 0 degrees.
To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:
(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:
LN = 12 cm
NK = 6 cm
KM = 8 cm
Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.
Using the Law of Cosines, we can write the equation for side NM (x):
x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)
We don't know the value of angle N yet, so we need to find it using the Law of Sines.
(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:
sin(A) / a = sin(B) / b = sin(C) / c
In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.
We can write the equation for angle O:
sin(O) / 8 = sin(N) / 6
Now, let's solve these equations step by step to find the values of x and angle O.
To find angle N, we can use the Law of Sines:
sin(N) / 12 = sin(180 - N - O) / x
Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:
sin(N) / 12 = sin(O) / x
Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):
sin(N) / 12 = (6 / 8) * sin(N) / x
Now, we can solve this equation for x:
x = (12 * 6) / 8 = 9 cm
So, the value of x is 9 cm.
To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:
sin(O) / 8 = sin(N) / 6
sin(O) / 8 = sin(O) / 9
9 * sin(O) = 8 * sin(O)
sin(O) = 0
This implies that angle O is 0 degrees.
Therefore, the value of x is 9 cm, and angle O is 0 degrees.
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The figure for the given question is provided here :
The effect of ______ variables on an observed association is a common cause of Simpson's paradoxlurking
Answers
The effect of confounding variables on an observed association is a common cause of Simpson's paradox lurking
What are Confounding variables?Confounding variables are variables that are related to both the independent and dependent variables, and they can distort or mask the true relationship between the variables of interest.
Simpson's paradox occurs when the direction or magnitude of an association between two variables is reversed or disappears when a third variable (a confounding variable) is taken into account.
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Solve (x+1)2 =13/4 using the square root property
Answers
Answer:
Starting with the equation:
(x + 1)^2 = 13/4
We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.
Taking the square root of both sides, we get:
x + 1 = ±√(13/4)
Simplifying under the radical:
x + 1 = ±(√13)/2
Now we can solve for x by subtracting 1 from both sides:
x = -1 ± (√13)/2
Therefore, the solutions to the equation are:
x = -1 + (√13)/2 or x = -1 - (√13)/2
Step-by-step explanation:
Please help! Look at photo
Answers
Answer:
EZ. You first have to to divide 108 by 36 which will be 3. Then multiply that to the ingredients amount and that will be ur answer which is 3
Describe several methods you could use to determine the rational zeros of a polynomial function. Which would you choose to use first? Explain.
Answers
Answer:
The Rational Zero Theorem helps us to narrow down the list of possible rational zeros for a polynomial function. Once we have done this, we can use synthetic division repeatedly to determine all of the zeros of a polynomial function.
Step-by-step explanation:
Answer:
The Rational Zero Theorem helps us to narrow down the list of possible rational zeros for a polynomial function. Once we have done this, we can use synthetic division repeatedly to determine all of the zeros of a polynomial function.
Step-by-step explanation:
. If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2
Answers
By linear equality , g >1.5 is must be true.
What are equality and inequality along a line?
Equal (=) is the symbol used in linear equations. Example. Using the inequality symbols (>,, is greater than or equal to, and is less than or equal to), linear inequalities are expressed.
x - 5 > 3x - 10 is an illustration of a linear inequality. As the larger than symbol is employed in this inequality, the LHS is strictly greater than the RHS. After being solved, the inequality appears as 2x 5 x (5/2).
If h> 3 and h - 2g= 0
H=2g
2g>3
g >1.5
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(PLEASE ANSWER THIS SERIOUSLY! ITS FOR A TEST) Move the yellow dots in order to make the segments intersect. Let the intersection be called point X. Make the lines intersect in such a way that ∠TXV is an obtuse angle less than 135°. Afterwards, use the protractor to determine the precise measure of all four angles. You should redraw the lines if ∠TXV is not the proper size.
Answers
Answer:)Angle FIH and GIE after keeping angle EIH at 140° is 40° while ∠FIG will is the opposite angle of ∠EIH so it will remain the same as 140°.
Step-by-step explanation:We need to intersect both lines and make ∠EIH > 135°
So,Let's keep ∠EIH = 140°
Then,∠FIG = 140° (opposite angle)∠FIH = ∠GIE = x (opposite angle)
Now,The Sum of all angles around I will be 360 degrees.
So,140 + x + 140 + x = 360 ,2x + 280 = 360, 2x = 80 ⇒ x = 40°.
A geometric sequence is given: 0.5, 0.75, 1.125, what is the common ratio?
Answers
We may deduce that the common ratio of the given sequence is 1.5 since sequence we receive the same number when we divide any phrase by its previous term.
what is a sequence?A sequence is a collection of numbers, sometimes known as "terms." Terms like 2, 5, and 8 are examples. Certain sequences may be made infinitely long by utilising a specific pattern they follow. To continue the process, take the example of 2,5,8 and add 3. There are formulae that show where to search in a series for words. In mathematics, a sequence is a collection of items that are in some order (or events). It is similar to a set in that it has components (also called elements or terms). The length of a series is defined as the total number of ordered items, which may be infinite. The act of arranging two or more elements in a logical sequence.
To obtain the common ratio of a geometric series, divide any term in the sequence by the term before it.
0.75 / 0.5 = 1.5
1.125 / 0.75 = 1.5
We may deduce that the common ratio of the given sequence is 1.5 since we receive the same number when we divide any phrase by its previous term.
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You own Company X. When you started the company, you initially invested $12,000.
You also borrowed $12,000 through a five-year (long-term) loan, of which you have
paid back $2,018. You have retained $1,291 in earnings to be reinvested in the
company, and you decided to put $1,000 of it aside for a long-term investment. The
company owns land and a building worth $8,878 and equipment worth $4,230. As of
today, the company has $8,250 in cash, $1,225 in inventory, and is due to receive
accounts worth $675. However, the company owes its suppliers $485 and has a
$500 loan to pay off in the next six months.
Answers
You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.
What does "company" mean?Businesses, a noun in plural. a group of people who are connected or who have joined together. a guest or guests: We're having people over for dinner. a collection of individuals together for social purposes. association, camaraderie, and fellowship She is a lot of joy to be around.
The Old French word "compagnie," which was first used in the Salic code and meaning "one who eats bread with you," is where the English word "company" originates. To describe a "society, friendship, closeness, or body of troops," it was first used in 1150.
You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.
Total Amount to be when start the company is $12000 + $12000
= $24000
Out of which company owns land and a building worth $8,878 and equipment worth $4,230 and have retained $1,291 in earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term investment.
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Which of the following graphs best represents the solution to the following systems of equations?
3x+5y=10
Answers
3
x
+
5
y
=
10
Step 1: Add -5y to both sides.
3
x
+
5
y
+
−
5
y
=
10
+
−
5
y
3
x
=
−
5
y
+
10
Step 2: Divide both sides by 3.
3
x
3
=
−
5
y
+
10
3
x
=
−
5
3
y
+
10
3
Answer:
x
=
−
5
3
y
+
10
3
The product of 4 and the difference of a number and 7.
Answers
Answer:
simplified: 4x−28
Step-by-step explanation:
The product of 4 and the difference of a number and 7 can be written as 4(x-7) where x is the number you are looking for.
Write the decimal expansion for 4/9
Answers
Answer:
0.44444444
Step-by-step explanation:
Answer:
the decimal expansion of 4/9 = 0
Step-by-step explanation:
if c= the number of cars in a parking lot which algebaraic expression represents the phrase below the number of cars increased by 9
Answers
Answer:
C+9
Step-by-step explanation:
Factor the trinomial: 2x^2+7x+3
Answers
Answer:
(x+3)(2x+1)
Step-by-step explanation:
2x^2 + 7x + 3
1st step) Multiply the 2 from 2x^2 with the 3
2nd step) Then when you get x^2 + 7x + 6, find the factors of 6 that add up to the 7 from 7x.
3rd step) The factors that add up to the 7 from 7x are 6 and 1. - these factors can be represented as (x+6)(x+1).
4th step) After this, since you multiplied the 2 from 2x^2 with the 3(shown in the first step), you must divide each each factor by the 2 from 2x^2.
5th step) Finally, you should get (x+3)(2x+1). - when dividing 1 and 2, the denominator(2) should be next to/multiply with x, and when dividing the numerator(6) and the 2 from 2x^2 together, you should get x+3 since 6 divided by 2 is 3.
Find the shaded area of the figure. Please help would really appreciate it
Answers
==========================================================
Work Shown:
Let,
A = area of unshaded rectangle (the 6 by 10 rectangle)B = area of the unshaded triangle (that has the "8 cm" inside it)C = area of parallelogramD = shaded area = C - (A+B) = C - A - BWe can see that A = 60 since the rectangle has base 10 and height 6, so 10*6 = 60.
The upper horizontal part of the parallelogram is 10+8 = 18 cm long. This means the bottom horizontal part of the parallelogram is the same length. The bottom portion shows 9 cm until we reach the triangle. This means that 18-9 = 9 cm is the base of the unshaded triangle (that has the "8 cm" inside it).
That triangle has area of 0.5*base*height = 0.5*9*8 = 36 square cm. So B = 36
The parallelogram has base 18 cm and height 12 cm, so it has area of 18*12 = 216. This means C = 216
We can then finally compute the value of D
D = C - A - B
D = 216 - 60 - 36
D = 120 square cm
A segment has a midpoint at (2,-7) and an endpoint at (8,-5). What what are coordinates of the other midpoint
Answers
The coordinates of the other endpoints is (-4, -9).
What is midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
Midpoint: (2, -7) = (x, y)
Endpoints: (a, b) and (8, -5) = (c, d)
Now,
x = (a + c)/2
2 = (a + 8)/2
4 = a + 8
a = 4 - 8
a = -4
y = (b + d)/2
-7 = (b - 5)/2
-14 = b - 5
b = -14 + 5
b = -9
Thus,
The other endpoint is (-4, -9).
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Given the vector u equal to 7 (cos 330°, sin 330°) and vector v equal to
4 (cos 90º, sin 90°), find the sum u + v and write your answer in magnitude and
direction form with the magnitude rounded to the nearest tenth and the direction
rounded to the nearest degree, 0° ≤ 0 < 360°.
Answers
The magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree 5.4<cos335°<, sin335°
What is direction ?
Direction is characterized as the course that anything follows, the route that must be taken to go to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.
The basis of the x, y, and z directions of a line or unit vector is identified by the number triplet known as the direction number. They are easily identified as a percentage of a unit vector.
u = 7cos300°i + 7sin300j
v = 4cos70i + 4sin70 j
u = 7*0.5i + 7*(-√3/2)j
= 3.5i - 6.062j
v = 1.368i + 3.758j
u + v =(3.5+1.368)i +(-6.062+3.758)j
= 4.868i +(-2.304)j
Magnitude of (u+v) = √(4.868)² +(2.304)²
= 5.385 ≈ 5.4
For direction
tanФ = y/x
= -2.304/4.868
Ф = -25.327
∴(u+v) is in 4th Quandrant
∴ Ф = 360 - 25.327
= 334.672
≈ 335°
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There was a green house. Inside the green house there was a white house. Inside the white house there was a red house. Inside the red house there were lots of babies. What is it?
Answers
Answer:
A watermelon my woman
Step-by-step explanation:
What is the slope of the line that passes through the points (-5,-7) and (4,-1)? Write your answer is simplest form
Answers
Answer:
2/3
Step-by-step explanation:
-7 - -1 = -6
-5 - 4 = -9
-6/-9= 2/3
Hope this helped!
Answer:
2/3
Step-by-step explanation:
-1-(-7) / 4-(-5)
6/9 = 2/3
0.2 of the money in my savings account is $1500. How much money do I have in my
savings account?
Answers
Answer:
$300
Step-by-step explanation:
A bag with 8 marbles has 4 red marbles, 3 blue marbles, and 1 yellow marble.A marble is chosen at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
SOMEONE PLEASE HELP ME IM SO STUCK
Answers
Answer:
1/4
Step-by-step explanation:
First you add all of the marbles in the bag which is 16 marbles. The fraction of red marbles to the total would be 4/16. In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.
Why do most Canadians live near its southern United States border?
Answers
Answer:
Step-by-step explanation:
1
A red die is tossed and then a green. die is tossed.
What is the probability that the red die shows a
number larger than 4 or the green die shows a
number less than 2?
The two events are not mutually exclusive. So to find the
probability of the union, use:
P(A or B) = P(A) + P(B) - P(A and B)
[?]
P(A or B)
=
8
P(B)
Green die
What is the probability of the red die rolling a
P(A)
Red die
+
-
8)
P(B)
P(A)
Red die Green die
number greater than 4?
Enter your answer in simplest form.
Enter
Answers
On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667
What is probability?A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.
red die, there are 3 numbers greater than 3 out of 6 numbers
Probability (A) = 3/6 = 1/2.
green die, there are 2 numbers less than 3 out of 6 numbers
Probability (B) = 2/6 = 1/3.
events are independent
P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)
16.67% probability = 0.1667
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Kinetic energy is the energy of a moving object. The kinetic energy of an object can be found by using the following formula, where represents the mass of the object in kilograms and represents the velocity of the object in meters per second. What is the kinetic energy of a 42 kg mass traveling at 25 meters per second?
Answers
13125
Step-by-step explanation:
The formula for kinetic energy is 1/2 times mass times velocity squared
in this situation the formual is 1/2 × 42 × 25 squared
42 divided by two is 21 so the new problem is
21 × 25 squared which is also
21 × 25 × 25= 13125 joules
HELP ME HELP ME HELP ME HELP HELP MEEEE
Answers
Answer:
Infinatly many solutions
Step-by-step explanation:
mark me brainlyest
Answer:
i would say a or b but probably b
Step-by-step explanation: