The coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)
What is the coordinate of the point which divides a line segment in a specified ratio?Suppose that there is a line segment [tex]\overline{AB}[/tex]such that a point P(x,y) lying on that line segment [tex]\overline{AB}[/tex] divides the line segment [tex]\overline{AB}[/tex] in m:n, then, the coordinates of the point P is given by:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
where we have:
the coordinate of A is [tex](x_1, y_1)[/tex]and the coordinate of B is [tex](x_2, y_2)[/tex]We're given that:
Coordinate of A is [tex](x_1, y_1)[/tex] = (-7,2)Coordinate of B is [tex](x_2, y_2)[/tex] = (9.-6)The point P lies on AB such that AP:BP=3:1 (so m = 3, and n = 1)Let the coordinate of P be (x,y), then we get the values of x and y as:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{3(9) + 1(-7)}{3+1} , \dfrac{3(-6) + 1(2)}{3+1} \right)\\\\(x,y) = \left( \dfrac{20}{4} , \dfrac{-16}{4} \right) = (5,-4)[/tex]
Thus, the coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)
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Please help!! Can somebody give me a step by step answer for 3m = 531. I’ve been wanting to know how to do the questions but I don’t know how to solve them.
[tex]3m = 531 \\ divide \: both \: sides \: by \: 3 \\ \frac{3m}{3} = \frac{531}{3} \\ m = 177[/tex]
Find two positive numbers whose difference is 27 and whose product is 874.
richard has two circular sprinklers to water his rectangular backyard as shown.
Answer:
109.88 ft² (nearest hundredth)
Step-by-step explanation:
Formulae
Area of a rectangle = width × lengthArea of a circle = πr²To find the area of the lawn that is not watered, subtract the area of the 2 circles from the area of the rectangle.
From inspection of the diagram
width of rectangle = 2rlength of rectangle = 4rarea = 512 ft²Substituting the values into the area of a rectangle formula, and solving for r:
⇒ 512 = 2r × 4r
⇒ 512 = 8r²
⇒ r² = 64
⇒ r = ±8
As distance is positive, r = 8 ft
Area of one circle = π8² = 64π ft²
Therefore,
Area not watered = area of rectangle - 2 × area of circle
= 512 - 2(64π)
= 109.88 ft² (nearest hundredth)
Pablo's father is 4 years older than his mother and Pablo is a third his mother's age.
If their combined age is 74 years
which number has a 9 with a value ten times greater than the 9 in 4 903
Answer:
49030
Step-by-step explanation:
we multiply it by ten so
4903×10=49030
15 POINTS TO ANYBODY THAT SOLVE THIS EQUATION
Answer:
This is how i had my answer
Hope it helped
Answer:
r=6
Step-by-step explanation:
The point A(5.
7) is reflected over the
What are the coordinates of point B?
point (6,
6) and its
image is point B.
The point (6, 6) is the mid-point of A and B. Then the coordinate of the point B is (7, 5).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point A (5, 7) is reflected over the point (6, 6) and its image is point B. Then the point (6, 6) is the mid-point of the A and B. Then the coordinate of the point B will be
[tex]\rm (x_2 , y_2) = (2x -x _1, 2y - y_1)\\\\(x_2 , y_2) = (2 \times 6 - 5, 2 \times 6- 7)\\\\(x_2 , y_2) = (12-5,12-7)\\\\(x_2 , y_2) = (7, 5)[/tex]
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5. Change the following mixed numbers to improper
fractions.
a. 3 5/6
b. 2 7/8
C. 5 1/5
D. 7 1/9
Hi can someone please help me
Answer:
Last and second lastv
Step-by-step explanation:
According to the rational factorization.
Find the equation of the tangent to the curve y = 4x³- 5x² + x - 3 at the point where it crosses the y axis.
Answer:
y = x-3
Step-by-step explanation:
When the graph of this equation crosses the y - axis , the value of x is = 0.
sub in zero to find this y value = -3
so the point is (0, -3)
Now find the drivative of this equation....the derivative tells you the slope of the original graph at any given point
derivative = 12x^2-10x+1 this , when x = 0 shows slope = 1
the equation then becomes y = (1) x -3 or just y = x-3
See image below
Answer:
-3
Step-by-step explanation:
put x= 0
solve:
-0.4k-6=1.2
If you answer this you're a God
Answer:
The answer is k = -18
Step-by-step explanation:
This is so easy... so first you do -2k/5 - 6 = 1.2
-2k + 5(-6)/5 = 1.2
and then all that divided by 5
A factory makes aquariums. Each aquarium is in the shape of a triangular prism, as shown below. If the factory makes 288 aquariums, how much water will be needed to fill all of them (in cubic feet)?
Answer:
384
Step-by-step explanation:
Mill rate is the tax rate that is applied to the assessed value of a real estate property by a municipality. Your tax is calculated by multiplying the mill rate by the assessed value of a property and dividing by 1,000. If your town's mill rate is 8 and your assessed home value is $188,000, how much will your town tax bill be?
If your town's mill rate is 8 and your assessed home value is $188,000, your town tax bill will be $1504.
What will be your town tax rate?Tax is a complusory amount levied by the government or an agency of the government on the sales of goods and services. It is a fomr of transfer of wealth to the government.
Town tax = (8 x $188,000) / 1000 = $1504
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Find an equation of the line passing through the pair of points (3,5) and (6,11). Write the equation in the form Ax+By=C
Answer: (4,8)
Step-by-step explanation:
please help me!! i've been stuck on this question for the past few days.
Answer:
It transforms down 6.
The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C equals five ninths times the quantity F minus thirty two.. Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.
Answer:
see below
Step-by-step explanation:
The label on the car's antifreeze container claims to protect the car between -40°C and 125°C.
So inequality which models this situation will be -40°C < T < 125°C
Now we have to show this inequality in Fahrenheit temperature with the help of [tex]C=\frac{5}{9} (F-32)[/tex]
So the compound inequality in Fahrenheit temperature will be
[tex]-40 < \frac{5}{9} (F-32) < 125[/tex]
Solve and show your work for each question.
Note: Remember per the rule of 9s if you have a repeating and non-repeating component you need to handle them separately.
What is 0.47 expressed as a fraction in simplest form?
What is 0.4¯7 expressed as a fraction in simplest form?
What is 0.¯47 expressed as a fraction in simplest form?
Answer:
show work on how you did it
The computation of the figure illustrates that 0.47 expressed as a fraction in simplest form is 43/90.
How to compute the fraction?From the information given, let a = 0.47. Now 10a = 4.777 .... equation i
100a = 47.77 ..... equation ii
Subtract equation i from ii
100a - 10a = 47 - 4
90a = 43
Divide both side by 90
90a/90 = 43/90
a = 43/90
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Maggie takes three electives: art, Spanish, and creative writing. She calculated the mean absolute deviation of the points she earned throughout the year in each class. art: mean absolute deviation of 2.1
Spanish: mean absolute deviation of 0.8
creative writing: mean absolute deviation of 2.7
In which elective were her scores the most spread out?
Answer:
0.8 seconds sorry if im wrong
Step-by-step explanation:
Which of the following options have the same value as 10 % , percent of 33?
Answer:
3.3
Step-by-step explanation:
33 x .10 = 3.3
Choose the graph that represents the equation y=x-2
Step-by-step explanation:
The choices are not given but the graph looks like the above picture.
Answer:
just use Desmos graphing calculator, it works great.
Step-by-step explanation:
Find the minimum value of X²+6X-5
Answer:
x = -3, y = -14
Step-by-step explanation:
Graph it
help me please…………..
Ryan invested $257 in an account paying an interest rate of 3.9% compounded weekly.
What is the equation?
Answer:
The equation is 257/x = x/3.9
Step-by-step explanation:
Please help. I need the answer
Answer:
B
Step-by-step explanation:
[tex]m-5\neq 5-m[/tex]
The others follow the rules of the commutative property of multiplication/addition.
Answer:
B
m - 5
Step-by-step explanation:
1) division
2) m - 5 . Since subtraction is not commutative
pls help i need an A my mom is going to get mad at me pls help i will give 62 points
Answer:
I would say the second one
Step-by-step explanation: Good luck! :)
Question 14 of 25 The image shows the location of ladders around a circular pool. 10 C 8 2 0 2 B (6y-2 85 -12 -10 0 2 Cody walks clockwise around the pool from point D to point E. How many degrees of arc does he walk? If your answer is a decimal, express your answer to the nearest hundredth.
The degrees of arc which Cody he walks clockwise around the pool from point D to point E is 105 degrees.
What is inscribed polygon in circle?The inscribed polygon in a circle is the polygon of which each corner point is on the circle.
The image shows the location of ladders around a circular pool. Cody walks clockwise around the pool from point D to point E. In the given image the value of x i,
[tex]2x+8=86\\2x=86-8\\x=\dfrac{78}{2}\\x=39^o[/tex]
Thus, the angle C and angle B are the supplementary angle. Thus,
[tex]m\angle C=m\angle D\\7y-4=360-(3y-6)\\7y+3y=360+6+4\\10y=370\\y=37[/tex]
3y-6 is the inscribed angle which intercept the arc DE. Thus,
[tex]\text {arc } DE= 3y-6\\\text {arc } DE= 3(37)-6\\\text {arc } DE= 105[/tex]
Thus, the degrees of arc which Cody he walks clockwise around the pool from point D to point E is 105 degrees.
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Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a decimal to the nearest hundredth.
The probability that the next customer will pay with a credit card will be 0.26 or 26%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.
Then the probability that the next customer will pay with a credit card will be
[tex]\rm P = \dfrac{32}{123}\\\\ P = 0.26[/tex]
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Answer:
The answer is .26
Step-by-step explanation:
32/123
0.260162...
13.
Hamza made 6 calls in
one day. Each call cost the
same amount of
money. The next day he made a
call that cost $4. Which expression
represents the total cost of the calls Hamza made during the two
days?
Answer:
6x +4 where x is amount for standard call
Step-by-step explanation:
Answer:
4c+6
Step-by-step explanation:
Right on my test
Hey can somebody help me on this?
Answer: 7
Step-by-step explanation: g = 8 ( given ) g/2+3 plugging the value of g 8/2+3
8+3x2
2
8+6
2
14
7
= 2
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
[tex]\sf \sin A=\boxed{\dfrac{5}{13}}\quad\cos A=\boxed{\dfrac{12}{13}}\quad\tan A=\boxed{\dfrac{5}{12}}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuseGiven:
[tex]\theta[/tex] = AO = BC = 5A = AC = 12H = AB = 13[tex]\implies \sf \sin A=\dfrac{5}{13}\quad\cos A=\dfrac{12}{13}\quad\tan A=\dfrac{5}{12}[/tex]