Given:
A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G.
To find:
The coordinates of point G.
Solution:
Section formula: If a point divide a line segment with end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in m:n, then the coordinates of that point are
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Point G divide the line segment FH in 8:2. Using section formula, we get
[tex]G=\left(\dfrac{8(8)+2(-8)}{8+2},\dfrac{8(6)+2(-2)}{8+2}\right)[/tex]
[tex]G=\left(\dfrac{64-16}{10},\dfrac{48-4}{10}\right)[/tex]
[tex]G=\left(\dfrac{48}{10},\dfrac{44}{10}\right)[/tex]
[tex]G=\left(4.8,4.4\right)[/tex]
Therefore, the coordinates of point G are (4.8, 4.4).
The ratio of the number of boys to the number of girls at school is 4:5. If there are 120 boys, how many total students are there? (Write the number only) *
Answer:
150
Step-by-step explanation:
So first you divide 120 by 4 so you know how much times 4 was increased, 4 was increased by 30 times
Next you multiply 5 by 30 because 4 was multiplied by that much
The answer is 150 girls
Which graph represents the solution to the compound inequality?
–6 < 3x – 12 ≤ 9
Answer:
second graph
Step-by-step explanation:
Solving the inequality
- 6 < 3x - 12 ≤ 9 ( add 12 to all 3 intervals )
6 < 3x ≤ 21 ( divide the intervals by 3 )
2 < x ≤ 7
The graph has an open circle at 2 and a closed circle at 7
This is represented on the second graph
Cannnn SOMEONE HELP PLEASEEE
Answer:
C
Step-by-step explanation:
please answer this quickly
Answer:
Step-by-step explanation:
A rectangular garden is 5m longer
than it is wide.
The area of the garden is 600m2
Calculate the width and length of the garden.
Answer:
The width of the garden is 22.12 m and its length is 27.12 m
Step-by-step explanation:
Equations
Let x = width of the garden
The length is 5 m longer than the wide, thus:
x + 5 = length of the garden
The area of the rectangular garden is
A=x(x+5)=600
Operating:
[tex]x^2+5x-600=0[/tex]
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Where a=1 b=5 c=-600:
[tex]\displaystyle x=\frac{-5\pm \sqrt{5^2-4(1)(-600)}}{2(1)}[/tex]
Operating:
[tex]\displaystyle x=\frac{-5\pm \sqrt{25+2400}}{2}[/tex]
[tex]\displaystyle x=\frac{-5\pm \sqrt{2425}}{2}[/tex]
There are two solutions:
x = 22.12
x = -27.12
The negative solution is not valid because x is the width of the garden, thus
x = 22.12 m
And
y = 22.12 + 5 = 27.12 m
The width of the garden is 22.12 m and its length is 27.12 m
Select all the equations for which (-6,-1) is a solution. *
y = 4x + 23
3x = (1/2)y
2x + 6y = -6
2x - 13y = 1
The number of incidents in which police were needed for a sample of 10 schools in one county is:
6
40
49
4
42
47
17
8
32 11
Find the first and third quartiles for the data.
Part: 0/2
Part 1 of 2
First quartile Q, is
Answer:
3Step-by-step explanation:
expand My eBay and thought you might be a good time to get the latest flash player is required for video playback is unavailable right now because this video is not available for remote playback is unavailable right now because this video is not available for remote playback is unavailable right now because this video is not available for remote playback is unavailable right for me as soon is unavailable and nice and clean this is unavailable for video for me and
help plzzzzzzzzzzz WILL MARK BRAINLIST
Answer:
7
Step-by-step explanation:
(-1^2)x 3 = 3
-1 x 4 = -4
3--4 = 7
Jon makes $76 in 12 hours of work for his mom. How much would Jon make in 20 hours of work.
Answer:
around 126
Step-by-step explanation:
What is the sticker price?
60% gross margin means they increase by the price by 60%
Multiply the purchase price by 1 + the gross margin:
16 x (1 + 0.60) = 16 x 1.60 = 25.60
The sticker price is $25.60
evaluate each expression if m = 13 and n = 8
1.) 2m - n
2.) 3m + 2n
3.) 12 + 3 x m - n
4.)
Answer:
1.) 18
2.) 55
3.)43
Step-by-step explanation:
Christopher is going to use a computer at an internet cafe. The cafe charges
$0.20 for every minute using a computer on top of an initial charge of $7.
Make a table of values and then write an equation for C, in terms oft,
representing the total cost of using a computer for t minutes at the internet
cafe.
Answer:
0 7
1 7.20
2 7.40
3 7.60
Step-by-step explanation:
The distance between two cities on a map is 4 Inches. The actual distance between the two citles is 24 miles.
a. What is the scale used on the map?
b. If the scale on a different map of the same area Is Inch = 1 mlle, how many Inches separate the same two cities?
-6a - 4 + 7a + 2 —— i dont really understand haha
Answer:
−2
Step-by-step explanation:
Is this right. Please help me I will make you Brainliest
A (Decode this message)
Answer:
don't cry because it is over smile because it happened
Step-by-step explanation:
What is the value of y?
40°
y +30
A. 1100
B. 10°
C. 55°
D. 850
Answer:
the answer is c or 55
Step-by-step explanation:
good luck on your quiz!
Kristin's credit rating was lowered, and the credit card company raised her APR from 14% to 15.2%. If her average daily balance this month is x dollars, express algebraically the increase in this month's finance charge due to the higher APR. Fill in the blank 1
Answer:
0.0022x
Step-by-step explanation:
Given that,
The credit card company raised her APR from 14% to 15.2%.
Her average daily balance this month is x dollars.
We need to find the algebraically the increase in this month's finance charge due to the higher APR. It can be calculated as follows :
[tex]y=x\times \dfrac{12\%}{14}-x\times \dfrac{15.2\%}{14}\\\\=x\times \dfrac{12}{1400}-x\times \dfrac{15.2}{1400}\\\\=-0.0022x[/tex]
So, the required increase in the month's finance is 0.0022x.
Answer:
0.001x
Step-by-step explanation:
factor the expression 9r2-4
Answer: Hieee! So the answer to this problem is (3r-2)(3r+2) I think...
Step-by-step explanation:
Answer:
9(r - 5)(r - 1)
Step-by-step explanation:
enter a negative number that has a greater absolute value than 5
Answer:
-10 ||10||
Step-by-step explanation:
5.3 - 4.2
What does this equal
the answer is 1.1
i hoped this help
-21 – (-14) =+=
Helpppp
Answer:
-21 - (-14) = -21 + 14 = -7
Step-by-step explanation:
A - and a - make a +. So -21 - (-14) makes -21 + 14. Solve to get -7.
Hope it helps!
A rectangular glass window is divided into two equivalent right triangles by a diagonal brace. What is the length of the diagonal brace?
A. 9 inches
B. 12 inches
C. 15 inches
D. 21 inches
Answer:
15
Step-by-step explanation: 9 square plus 12 squared equal 225 and then find the square root of 225 which equals 15
Factor as the product of two binomials. x^2-9x+20
Answer:
(x-4)(x-5)
That is the answer, hope it helps.
please helppppppppppppppppppppppppppp don't get me wrong
Kelli is searching for a new daycare center for her child. At Lori's Local Daycare, there is a ratio of 2 caretakers for every 7 children. If there are 189 total children, then how many people are at the daycare facility?
Answer:
243 people
Step-by-step explanation:
Kelli is searching for a new daycare center for her child. At Lori's Local Daycare, there is a ratio of 2 caretakers for every 7 children. If there are 189 total children, then how many people are at the daycare facility?
The ratio is given as:
Caretakers : Children
2 : 7
= In fraction = 2/7
If there are 189 total children, then how many people are at the daycare facility?
Step 1
We calculate the number of caretakers is there are 189 children
7 children = 2 caretakeras
189 children = x
Cross Multiply
7x = 189 × 2
x = 189 × 2/7
x = 54 caretakers
Step 2
The total number of people at the daycare
= 189 children + 54 caretakers
= 243 people
What's 4 x 90 divided by 3 x 7?
Answer:
17.14
Step-by-step explanation:
360/21=17.14
Answer:
(4 × 90) ÷ (3 × 7)
= 360 ÷ 21
= 17.14
hello , how to do 6(iii)?
Answer:
[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}[/tex]
Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:
[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]
Therefore:
[tex]\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]
Next, the surface area of a sphere S is given by:
[tex]\displaystyle S=4\pi r^2[/tex]
Therefore:
[tex]\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}[/tex]
We can divide both sides by 2:
[tex]\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}[/tex]
We can substitute this into dV/dt. Rewriting:
[tex]\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)[/tex]
So:
[tex]\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}[/tex]
Since dV/dt = 0.03 or 3/100:
[tex]\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}[/tex]
Therefore:
[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)[/tex]
Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
expand and simplify (3X+1)(2X+4)
Answer:
6x square +14x+4
Step-by-step explanation:
hope this helps................
Answer:
6x^2+14x+4
Step-by-step explanation:
6x^2+12x+2x+4
6x^2+14x+4
A. Solve the following linear equations.
2.) y - 18 = 32
3.)x/1.3=-6
4.) b/4=3/8
5.)3x-53=-16
6.)8x-7+2x=6+5x+2
7.) 7x-1=9-5x
Answer:
2. y = 50
3. x = 7.8
4. x = 3/5
5. x = 23
6. x = ?
I don't know 6 answer...