What are the coordinates of the point on the directed line segment from (-4,-1) to (6,4) that partitions the segment into a ratio of 3 to 2?
Using proportions, it is found that the coordinates of the desired point are (2,2).
The first point is A(-4, -1).The second point is B(6, 4).The desired point is C(x,y).The point C partitions the segment AB into a ratio of 3 to 2, hence:
[tex]C - A = \frac{3}{5}(B - A)[/tex]
This proportion is applied using both the x and y coordinates of the points, hence:
[tex]x - (-4) = \frac{3}{5}[6 - (-4)][/tex]
[tex]x + 4 = 6[/tex]
[tex]x = 2[/tex]
[tex]y - (-1) = \frac{3}{5}[4 - (-1)][/tex]
[tex]y + 1 = 3[/tex]
[tex]y = 2[/tex]
The coordinates of the desired point are (2,2).
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A car travels 10 km southeast and then 15 km in a direction 60° north of east. Find the magnitude of the car's resultant vector.
Answer:
-10sin45+15cos60=Hor distance = 5.92 km
-10cos45+15sin60=ver distance = .429 km
resultant is sqrt(5.922+.4292)= 5.94 km at angle arctan(.429/5.92)= 1.77 degrees north of east
Step-by-step explanation:
What’s the domain and range for this? And is it a function? Yes or No
You are given the domain and range ( the numbers in each oval):
If There is more than one arrow connected to a number, that number is listed the same amount
Domain (-4,0,6,6)
Range (12,18,18,40)
To be a function each input value ( Domain) can only have one output value (range)
Because the 6 has two different outputs ( 12, 18) this is not a function.
Answer:
The input 6 (domain) leads to two outputs thus it is not a function.
Step-by-step explanation:
If 12g of a radioactive substance are present initially and 8yr later only 6g remain, how much if the substance will be present after 13 years?
The weight of substance remaining after 13 years is 2.25 g.
Given:
Present weight of substance = 12 g
After 8 years weight remains = 6 gm
Now, weight loss in 8 year will be,
12-6=6 gm
So, weight loss in 1 year will be,
[tex]\dfrac{6}{8} =\dfrac{3}{4}[/tex]
Total weight loss in 13 year will be,
[tex]\dfrac{3}{4}\times13=9.75[/tex]
The weight of substance remaining after 13 years will be,
[tex]12- 9.75 = 2.25 \;\rm g[/tex]
Therefore, the weight of substance remaining after 13 years is 2.25 g.
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PLEASE HELP! Give explanations down below please! Thanks I am timed
Answer:
you need to divide all number
How do you factor x³-9?
Answer:
(x² + 3)(x-3)
Step-by-step explanation:
Since the exponent is uneven you can take 2 and 1 and add them to the x's multiply to get 3 and since 9 is a perfect square you can square root it and get 3 which you put on both sides. Since the 9 is negative one of the symbols have to be negative, usually put in the second parenthesis.
Hope this helps!
Please help me with this question.
sooooooooooooooooooooooooooooo easy
Answer:
11/12..................
Answer:
J) 11/12
Step-by-step explanation:
Find the 75th term of the arithmetic sequence
16, 15, 14,
Answer:
[tex]a_{75}=-58[/tex]
Step-by-step explanation:
This is an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
where d is the common difference and n is the index of any given term.
For the given sequence, the common difference is -1:
[tex]15-16=-1\\14-15=-1[/tex]
Knowing both the common difference and the first term, you can write the equation for this sequence:
[tex]a_n=16+(n-1)(-1)[/tex]
Then you can use that equation to find the 75th term:
[tex]a_{75}=16+(75-1)(-1)\\a_{75}=16+(74)(-1)\\a_{75}=16-74\\a_{75}=-58[/tex]
A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. He collects data for 15 randomly selected students and determines the value for s was 0.67.
The interpretation of the value of s being 0.67 is that: the typical distance between the observed grade points and predicted grade points was about 0.67 points.
The given parameters are:
n = 15s = 0.67Variable sIn regression, the variable s represents the average distance that the observed values fall from the regression line
The grade pointsIn this case, we have:
The observed grade points and The predicted grade pointsHence, 0.67 represents the typical distance between the observed grade points and predicted grade points.
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What is the area, in square centimeters, of the shape below?
Express your answer as a fraction in simplest form.
Therefore, the area of the triangle is 4/9 cm².
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Jacoby made and sold x candy bars in one week. His profit, P, in dollars is calculated using the formula P = R-C
where R represents his revenue and C represents his costs. If R = 3x^2 – x+ 6 and C = -7x^2– 7x + 2. what is
the expression that represents his profit in dollars?
Answer: P = 10x^2 +6x + 4
Step-by-step explanation:
P = R-C
R = (3x^2 - x + 6)
C = (-7x^2 -7x + 2)
P = (3x^2 - x + 6) - (-7x^2 -7x + 2)
P = 3x^2 - x + 6 + 7x^2 +7x - 2
P = 10x^2 +6x + 4
1. Classify the following polynomials as monomial, binomial trinomial and polynomial:
i) a2 + a – 6
Answer:
trinomial
Step-by-step explanation:
a monomial has 1 term
a binomial has 2 terms
A trinomial has 3 terms
a² + a - 6 ← has 3 terms so is a trinomial and also a polynomial
A person swims 6.4 meters per
second north while being
pushed by a current moving
west at 2.1 meters per second.
What is the magnitude of the
swimmer's resultant vector?
Answer:
4.3
im not sure
correct me if im wrong
Answer
6.7
Step-by-step explanation:
Works on acellus
solve 2 2/3 x 3 3/5 using an area model of 4 squares.
Answer:
9 3/5 is the answer it's in photo above how to
A typical tip at a restaurant is 18% of the total bill. If the bill is $60, what would the typical tip be?
The typical tip would be $_________.
HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPP
Answer:
a, h and k have values 1, -5 and -10 respectively
Can someone please answer this no bots answer this please… I’ll give you brainliest
Answer:
Part one:
Y=13.5x+1
Part two:
Y=12x+40
Part three:
After 15 seconds Sam: 203.5ft Alice:220ft
Alice won
Step-by-step explanation:
If sine theta almost-equals 0.3090 , what is the approximate value of csc Theta?
0.5559
1.3090
3.2362
10.4733
Step-by-step explanation:
csc(Theta) = 1/sin(Theta) = 3.2362
Answer:
C. 3.2362
Explanation:
can someone please help me
Answer:
angle A=30°
angle B=60°
angle C=90°
Step-by-step explanation:
given : A=30°,C=90° the mark states it is 90°
find :C=?
A+B+C=180°
30°+90°+x°=180°
=120°+x°=180°
=120°-120°+x°=180°-120°
=x°=60°
What is the domain and range of this? Is it a function yes or no?
i need atleast 5 volunteers for the magic trick
What magic trick??
Are you gonna do a magic??
Sorry for a lot of questions.
Combine the like terms to create an equivalent expression:
-k+3k
Answer:2k
Step-by-step explanation:
-k+3k
-1k+3k
(-1+3)k
2k
Answer:
2k
Step-by-step explanation:
-k is the same as -1k so you can just solve it like that. Also, when adding terms with variables you just add the number in front (if they have the same variable). So -1k + 3k = 2k. Pretty much the same as -1 + 3, you just add a variable..
What is the answer to 2(2x-5)
Answer: The answer is 4x - 10.
Explanation: The explanation is in the image. The explanation is showing using the distributive property to multiply 2 by 2x - 5.
Answer:
4x-5
Step-by-step explanation:
solve for x and graph the solution on the number line
Answer:
[tex]\boxed{\sf x\ge \:-1}[/tex]
Step-by-step explanation:
[tex]\sf 4x\ge \:-4[/tex]
Divide both sides by 4:
[tex]\sf \cfrac{4x}{4}\ge \cfrac{-4}{4}[/tex][tex]\sf x\ge \:-1[/tex]__________________________________
Find the area of this figure
Show work, please
Answer:
80 in2
Step-by-step explanation:
Here is my work shown in screeny
Find the slope of this line.
Answer:
5/2
Step-by-step explanation:
To find a slope you use rise over run.
The graph shows that you rise 5 for every 2 right.
Help Plssss it is due tommorrow!!!!! I think it is A i am not sure help
Answer: congruent bases
Step-by-step explanation:
what makes a trapezoid a trapezoid is that the bases are different! the side on top and bottom are different.
NO LINKS PLS
The ratio of sugar to flour used in a pudding recipe is 2:1. Which figure shows equivalent ratios?
A graph is drawn. The title is Pudding Recipe. The axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y-axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 1,2 and 2,4 and 3,6.
A graph is drawn. The title is Pudding Recipe. The axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 2,2 and 4,3 and 6,4.
A graph is drawn. The title is Pudding Recipe. The x axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 2,1 and 4,2 and 6,3.
A graph is drawn. The title is Pudding Recipe. The axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 2,2 and 4,4 and 6,6.
Answer:
Answer #3
Step-by-step explanation:
The ratio of sugar to flour is 2:1, so the x values need to be twice as big as the y values in the points.
Pentagon TEXAS has vertices at T(1, 8), E(3, 8), X(6, 2), A(3, 2), and S(1, 4). What is the area of Pentagon TEXAS?
341.5 square units
18.5 square units
17 square units
19 square units
The area of the pentagon is 19 square units
The coordinates of the pentagon are given as:
[tex]T = (1, 8)[/tex]
[tex]E =(3, 8)[/tex]
[tex]X =(6, 2)[/tex]
[tex]A=(3, 2)[/tex]
[tex]S = (1, 4)[/tex]
The area of the pentagon is then calculated using:
[tex]Area = \frac 12|(x_1y_2+x_2y_3+x_3y_4+x_4y_5+x_5y_1) -(y_1x_2+y_2x_3+y_3x_4+y_4x_5+y_5x_1)|[/tex]
So, we have:
[tex]Area = \frac 12|(1 \times 8 +3 \times 2+6\times2+3 \times 4 + 1 \times 8) -(8\times3+8\times6+2\times3+2\times1+4\times1)|[/tex]
Simplify the expressions in both brackets
[tex]Area = \frac 12|46 -84|[/tex]
[tex]Area = \frac 12|-38|[/tex]
Remove absolute bracket
[tex]Area = \frac 12 \times 38[/tex]
[tex]Area = 19[/tex]
Hence, the area of the pentagon is 19 square units
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