In order for the ratio of AP to PB to be 3/2, the coordinates of point P along the directed line segment AB are (14/5, -1).
What exactly is a section formula?The section formula returns the coordinates of a point that divides the line connecting two points in a ratio, either internally or externally.
Section formula is given as follows:
[tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]
In math, how do you find coordinates?Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to find the y-coordinate.It is given that the coordinates of the points A and B are A(-2, -4), B(6, 1) and AP/PB = 3/2
Let the coordinates of the point P be (a, b).
By using section formula,
(a, b) = [tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]
(a, b) = [tex](\frac{3(6)+2(-2)}{3+2} , \frac{3(1) +2(-4)}{3+2} )[/tex]
(a, b) = [tex](\frac{18 - 4}{5} , \frac{3-8}{5})[/tex]
(a, b) = [tex](14/5, -5/5)[/tex]
(a, b) = [tex](14/5, -1)[/tex]
Therefore, the coordinates of the point P along the directed line segment AB so that the ratio of AP to PB is 3/2 are (14/5, -1).
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156.24 is 36% of what
Answer:
434
Step-by-step explanation:
Steps:
156.24 ÷ 36% = 156.24 ÷ 0.36 = 434
Each number in a list of numbers can be found using the expression 6 − 23(n − 1), where n is a positive integer that gives the position of the number in the list. What is the thirteenth number in the list? A. −8 B. −2 C. 8 D. 13
The solution is Option A.
The value of the 13th number from the equation A = ( -2/3 ) ( n - 1 ) is A = -8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( -2/3 ) ( n - 1 ) be equation (1)
On simplifying the equation , we get
The thirteenth number in the list is n = 13
So , when n = 13
A = ( -2/3 ) ( n - 1 )
A = ( -2/3 ) ( 13 - 1 )
On further simplification , we get
A = ( -2/3 ) ( 12 )
A = ( -2 ) x 4
So , the value of A = -8
Hence , the thirteenth number in the list is A = -8
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Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Correct option are C,D, E. g(x) > h(x) for x = -1, For positive values of x, g(x) > h(x), For negative values of x, g(x) > h(x).
What are functions?A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
They have the same value if x=0.
The first and second choices are not viable
for x=-1
g(-1)=1
h(-1)=-1
3. is accurate
4th , false G(x)>H for all values other than zero (x)
the proper ones are
For x=-1, g(x) exceeds h(x).
G(x) > h for positive values of x. (x).
G(x) > h for negative values of x (x).
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Need to find the mean, median, mode, and midrange.
The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.
Explain about mean median mode?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The value that appears the most frequently on the list is the mode.
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ill give brainliest!!!!
Answer:
(f ⋅ g)(x) = f(g(x)) = 5·√(9 - x^2)
The domain is: -3 ≤ x ≤ 3
(g ⋅ f)(x) = g(f(x)) = √(9 - (5·x)^2)
The domain is: -0.6 ≤ x ≤ 0.6
Find the values of x and y that maximize the objective function
Answer: D
Step-by-step explanation:
A. [tex]P=2(4)-3=5[/tex]
B. [tex]P=2(0)-3=-3[/tex]
C. [tex]P=2(0)-0=0[/tex]
D. [tex]P=2(4)-0=8[/tex]
A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 14900 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 120-kilogram crates that can be loaded into the shipping container.
HURRY PLEASEEEEEEEEEEEEEEEEEEE!
A maximum of 105 number of 120 kilograms can be loaded in the container.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Weight of each crate = 120 kg
The greatest weight loaded in the container = 27500 kg
Weight already loaded in the container = 14900 kg
Now,
Since, Weight already loaded = 14900 kg
Let number of 120 kilograms loaded in the container = x.
Hence, Weight of x = 120 kg
So, After combined we get;
Weight nor be greater than the capacity of the container.
Hence, we can formulate;
14900 + 120x ≤ 27500
Subtract 14900 we get;
120x ≤ 27500 - 14900
120x ≤ 12600
x ≤ 12600 ÷ 120
x ≤ 105
Thus, A maximum of 105 number of 120 kilograms can be loaded in the container.
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Rabbit populations can double every 30
days. If there are 10 rabbits on a farm,
how many rabbits will be on the farm
after 120 days?
Future Amount = [?] rabbits
Hint: Future Amount =
←
+ r)t
(1 + r)t time
(1
periods
initial
growth
amount rate
Round to the nearest whole number.
Answer:
80
Step-by-step explanation:
→ Work out how many rabbits after 60 days
20 rabbits
→ Work out how many rabbits after 90 days
40 rabbits
→ Work out how many rabbits after 120 days
80 rabbits
Please help me, it is important
Answer: Your fourth point is going to be (-3,4). Hope this helps!
Step-by-step explanation:
What's the circumference of a circle with a diameter of 31 inches
Answer:
C≈97.39in
Step-by-step explanation:
Answer:97.39
Step-by-step explanation:
HELP ASAP
You are working as a car salesperson. You make $13.25 per hour. You are paid biweekly (two weeks of work). Your boss encourages competition between employees by letting you know that you will receive a commission of $150 for each new car you sell.
In the first week, you work 25 hours and sell 3 cars.
In the second week, you work 18 hours and sell 2 cars.
How much will your total pay be at the end of these two weeks?
Total pay be the at the end of the two weeks with rate of $13.25 per hour and commission of $150 for selling each new car is $1319.75.
As given,
Rate of salesperson per hour pay = $13.25
Commission on selling each new car =$150
Amount of the pay earned by salesperson:
First week :
25 (13.25) + 3 (150)
= 331.25 + 450
= $781.25
Second week:
18 (13.25) + 2(150)
= 238.5 +300
= $538.50
Total pay of salesperson at the end of two weeks
=$(781.25 +538.5)
=$1319.75
Therefore, total pay be the at the end of the two weeks with rate of $13.25 per hour and commission of $150 for selling each new car is $1319.75.
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in a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices
The probability that the randomly selected sample is vulnerable or critically endangered is equal to 0.76
The probability can be determined using the following formula;
probability = number of desired events or outcomes ÷ total number of events or outcomes
The total is known to be 45, the favorable or desired outcomes can be calculated as follows;
number of desired outcomes = number of vulnerable species + number of critically endangered species
number of desired outcomes = 12 + 22
number of desired outcomes = 34
Now we calculate the probability by using the above formula;
probability = 34 ÷ 45
probability = 0.76
Therefore, 0.76 is the probability that the randomly selected species is vulnerable or critically endangered.
Although a part of your question is missing, you might be referring to this question:
In a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices
11/45
0.24
0.83
0.76
12/45
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g(x)=3/4f(x) graphed
The function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is the following equation-
g(x) = 3/4 f(x)
Since, the functions are not given, we will assume them by ourselves. You can use the same procedure for any pair of functions of the form -g(x) = n f(x)
Assume that -
f(x) = 2x + 1
Now -
g(x) = (3/4) f(x)
g(x) = (3/4)(2x + 1)
g(x) = (3/2)x + 3/4
Now, both the graphs f(x) and g(x) are attached below. In general, g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4).
Therefore, the function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.
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10
-90+30+(−10)+ +... n = 16
3
Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 6x + ___?
1
3
6
9
Answer:
+ 9
Step-by-step explanation:
x² + 6x
to complete the square
add ( half the coefficient of the x- term )² to x² + 6x
x² + 2(3)x + 3²
= x² + 2(3)x + 9
= (x + 3)² ← a perfect square
Use the values In 8 ≈ 2.08 and In 1000≈6.91 to find the approximate value of log8 1000
The approximate value of log₈1000 is 0.30.
What are logarithms?The inverse of power is a logarithm. When you take the log of a number, you reverse the exponent.Logarithms normally use a base of 10 (but a different value can be provided), whereas natural logs always use a base of e. Use the following calculation to convert between logarithms and natural logs.[tex]log_{10}x[/tex] [tex]= ln(x) / ln(10)[/tex]
The given values are:
In 8 ≈ 2.08 and In 1000 ≈ 6.91
To find the approximate value of log₈1000,
log₈1000 = In 8/In 1000
= 2.08/6.91
≅ 0.30
Therefore, the approximate value of log₈1000 is 0.30.
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(20pts, 5pts each) The median of AMND from vertex N of the
isosceles trapezoid MNFD is 5cm. The diagonal ND is
perpendicular to the leg MN. The shorter base NF = 6cm and the
32cm².
A
MNFD
=
Find: MD, the altitude of the trapezoid h, the length of the
legs of the trapezoid and the ratio between the areas of AMND and
ANFD.
Answer:
MD = 10 cmh = 4 cmMN = FD = 2√5 cm ≈ 4.47 cmarea ratio = 5 : 3Step-by-step explanation:
Given isosceles trapezoid MNFD with short base NF = 6 cm, diagonal ND perpendicular to leg MN, and triangle MND median NX = 5 cm, you want ...
length MDaltitude h of the trapezoidlengths of MN and FDratio of areas of ∆MND and ∆NFDMDMD is the hypotenuse of right triangle MND. The median from the right angle of a right triangle is half the length of the hypotenuse, so ...
MD = 2·NX = 2·(5 cm)
MD = 10 cm
AltitudeIn the attached diagram, we see that right triangle XYN has side XY = 3 (half of NF), and hypotenuse NX = 5 (given). These are two sides of a 3-4-5 right triangle, so the remaining side, altitude h, is 4.
h = 4 cm
Side lengthsThe attache diagram shows congruent side lengths MN and FD are the hypotenuse of a right triangle with sides YM = 2 and YN = 4. The Pythagorean theorem tells us the length of side MN is ...
MN² = MY² +NY²
MN² = 2² +4² = 4 +16 = 20
MN = √20
MN = FD = 2√5 ≈ 4.47
Area ratioTriangle MND has a base length MD = 10 and a height h = 4. Triangle NFD has a base length NF = 6 and a height h = 4. The ratio of the areas of these two triangles is ...
[tex]\dfrac{A_{MND}}{A_{NFD}}=\dfrac{\frac{1}{2}\cdot10\cdot4}{\frac{1}{2}\cdot6\cdot4}=\dfrac{10}{6}=\boxed{\dfrac{5}{3}}[/tex]
The ratio between the areas is 5 : 3.
__
Additional comment
We are also given the area of the trapezoid as 32 cm². That can be used to find the longer base and/or the altitude, or to check the answers we have for those values. It is redundant information.
The midpoint X of MD is the center of the circumscribing circle of the trapezoid and right triangles MND and MFD. The midpoint of the hypotenuse of a right triangle is always the circumcenter, so knowing the length NX tells us the radius of that circle, hence MX and XD.
if you want to just give me the answer that would be fine. i just want to make sure i’m correct.
Okay, here we have this:
Considering that if the graph of the line rises from left to right, then it means that the slope is positive. On the other hand, if the graph of the line falls from left to right, the slope will be negative.
So, according with this finally we obtain that the correct answer is that the slope is negative.
Answer:
Negative
Step-by-step explanation:
Because MATH
Help! 100 points! Evaluate the function at: x=3
Answer: When x=3 y=-3
Step-by-step explanation:
The product of 8 and n decreased by 5 is _________________ 25. less than greater than less than or equal to greater than or equal to
The statement that represents the given inequality is:
The product of 8 and n decreased by 5 is less than 25.
Which sentence represents the inequality?The inequality is defined as follows:
8(n - 5) < 25.
The meaning of the expression n - 5 is given as follows:
n decreased by 5. (n is an unknown number).
The meaning of the expression 8(n - 5) is given as follows:
The product of 8 and n decreased by 5. (multiplication of two numbers is also called product).
The symbol of the inequality is given as follows:
<
Which represents the expression less than.
Considering the 25 on the other side of the inequality, the complete sentence is given as follows:
The product of 8 and n decreased by 5 is less than 25.
Missing informationThe complete problem is:
Sal wrote the statement below to represent the inequality 8(n - 5) < 25. Which words should Sal use to complete the verbal statement? The product of 8 and n decreased by 5 is ___________
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What is the difference between a relation and a function? Classify each of the following as a function or not a function. State the domain and range. {(0,0),(2,22),(3,33)}
The relation given can be classified as a function as every single input corresponds to a single output value.
What is the difference between a relation and function?The difference between a relation and a function lies in the fact that a relation can have many outputs for a single input, but a function has a single input for a single output. The statement above is the distinctive property between a relation and a function.
The relation given in the task content is a function as every single input has a single output as evident in the function.
Hence, the domain of the function is; {x | x : 0, 2, 3} while the range is; {y | y : 0, 22, 33}.
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Explain in detail with at least two sentences how to represent the difference of z1 and z2 geometrically, given that z1= −7i and z2 = 4+3i. Then, give the difference z1 − z2 in rectangular form.
Given that z₁= −7i and z₂ = 4+3i, the difference z₁ − z₂ in rectangular form is; -4 - 10i
What is the Vector in rectangular form?Addition of complex numbers is basically the same thing as adding two-dimensional vectors that are located on the x-y Cartesian plane.
Now, it is pertinent to note that when doing vector addition, we denote the x-component with i^ and y-component with j^.
We should also not that when adding complex numbers, the x-component is the real part and y-component is the imaginary part.
Geometrically, we can say that the addition of complex numbers can be equated to the addition of vectors in x-y plane.
Thus by the the parallelogram law of vector addition, we will be able to find the resultant vector.
In rectangular coordinates,
z₁ = -7i
z₂ = 4 + 3i
Then, z₁ - z₂ = -7i - (4 + 3i)
= -7i - 4 - 3i
= -4 - 10i
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Ms. Gartland bought x number of shirts for the new members of her chorus. The cost for x number of shirts, including $3.99 shipping, was $77.49. Each shirt cost $12.25. There was no sales tax on this purchase. Which equation could be used to find x?A. 3.99(+12.25)=77.49B. 3.99+12.25=77.49C. 12.25(+3.99)=77.49D. 12.25+3.99=77.49
the expression for the given situation is given as follows,
12.25x + 3.99 = 77.49 $
here, x = no. of shirt
so the correct answer is option D
write a real world situation for which the rate of change is -15
The most appropriate choice for velocity and accleration will be given by- Deacceleration of a car of 15 [tex]m/s^2[/tex] is a real world situation for which the rate of change is -15
What is velocity and acceleration?
Velocity
The distance travelled by a body per unit interval of time where the direction of the motion of a body is taken into account is known as velocity.
Velocity is a vector quantity as direction of motion of body is taken into account.
If d is the displacement of body and t is the time,
Velocity = [tex]\frac{d}{t}[/tex]
Acceleration
The rate of change of velocity of a body is called acceleration.
Acceleration is a vector quantity as direction of motion of a body is taken into account.
If [tex]\Delta[/tex]v is the change of velocity and t is the time,
Acceleration = [tex]\frac{\Delta v}{t}[/tex]
If velocity decreases then it is called Deacceleration
Here
Deacceleration of a car is 15 [tex]m/s^2[/tex]
That means rate of change of velocity of a car is -15 [tex]m/s^2[/tex]
This is a real world situation for which the rate of change is -15
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4 Given the table below, which student wrote a correct equation between the number of horses, x, and the cost of boarding, y? # of Horses Cost O C. Tori only 37 4 99 TORI 31x - 2y = 74 J A. Both Laquita and Tori go to 6 go to 1 8 161 10 192 12 223 LAQUITA y = 15.5x +37 B. Neither Laquita nor Tori D. Laquita only go to 9 go to 8
Both Laquita and Tori wrote a correct equation which is the correct answer would be an option (A).
Let the required line would be as
⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )
Here x₁ = 0 and y₁ = 37
x₂ = 4 and y₂ = 99
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 37 = (62/4)x
⇒ y - 37 = 15.5x
⇒ y = 15.5x +37
This equation is written by Laquita.
Multiply by 2 both sides of the equation,
⇒ 2y = 31x + 74
⇒ 31x - 2y = 74
This equation is written by Tori.
Therefore, both Laquita and Tori wrote a correct equation.
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Plot the intercepts to graph the equation
8x-3y=-24
Answer:
Step-by-step explanation:
A pump fills a pool at a constant rate. At the end of 1 minute, it has filled 10 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
A
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
22 2020
44 4040
66 6060
B
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
11 1010
22 3030
44 5050
C
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
22 2020
44 2222
66 2424
D
\text{Time} \newline \text{ (minutes)}Time
(minutes) \text{Water} \newline \text{ (gallons)}Water
(gallons)
11 1010
22 1111
44 1313
I'm sorry this is confusing :\
The answer is A, because if one minute corresponds to 10 gallons of water, then the amount of gallons is the minutes times 10.
The largest angle of a triangle measures 9degrees less than 5 times the measure of the smallest angle. The middle angle measures three times that of the smallest angle. Find the measures of the three angles.
Let the smallest angle be represented as
[tex]=x[/tex]Step 1: The largest angle of a triangle(let the largest angle =z) measures 9degrees less than 5 times the measure of the smallest angle, this statement is represented as
[tex]\begin{gathered} 5\text{ times the smallest angle gives} \\ =5\times x \\ =5x \\ 9\text{ degr}ees\text{ less will give the largest angle to be} \\ \text{largest angle =5x-}9 \\ z=5x-9 \end{gathered}[/tex]Step 2: let's calculate the middle angle (let the middle angle =y)
The middle angle measures three times that of the smallest angle, which means that
[tex]\begin{gathered} y=3\times x \\ \text{middle angle =y= 3x} \\ y=3x \end{gathered}[/tex]Recall that the total angles in a triangle give
[tex]=180^0[/tex]Therefore,
[tex]\begin{gathered} \text{largest angle + middle angle + smallest angle =180}^0 \\ z+y+x=180^0 \end{gathered}[/tex]Substituting we will have
[tex]\begin{gathered} 5x-9+3x+x=180^0 \\ \text{collect the sinmilar terms we will have} \\ 5x+3x+x=180^0+9^0 \\ 9x=189^0 \\ \text{divide both sides by 9} \\ \frac{9x}{9}=\frac{189^0}{9} \\ x=21^0 \end{gathered}[/tex]Hence,
the smallest angle is = 21 degrees
[tex]\begin{gathered} \text{The largest angle =5x-9} \\ =5\times21^0-9 \\ =105^0-9 \\ =96^0 \end{gathered}[/tex]Hence,
The largest angle = 96 degrees
[tex]\begin{gathered} \text{The middle angle=}3x \\ =3\times21^0 \\ =63^0 \end{gathered}[/tex]Hence,
The middle angle = 63 degrees
finishing a long race, a runner puts on a burst of speed 15 meters from the finish line. two seconds later, she comes to a stop 3 meters past the finish line. what was her average speed during those two seconds?
The average speed during the two seconds in which the runner moved from 15 meters from the finish line to 3 meters past the finish line is 9 m/s
The average speed of the runner can be determined by using the following formula;
speed = distance ÷ time
As she moved from 15 meters from the finish line to 3 meters past the finish line in 2 seconds, the total distance covered in these 2 seconds by her can be calculated as follows;
distance = 15 meters + 3 meters
distance = 18 meters
Now substituting the values for distance and time in the formula;
speed = 18 / 2
speed = 9 m/s
Hence the average speed of the runner during the two seconds is calculated to be 9 m/s.
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A large multiplex movie house has many theaters. The largest theatre has 36 rows. There are 20 seats in the first row. Each row has four seats more than the previous row. How many total seats are there in this theatre?
Answer:
2880 seats
Step-by-step explanation:
r1 r2 r3 r36
20 + 20+4 + 20+4+4 + ···+20+4×35
total seats = ((20 + 20+4×35)÷2)×36= 2880