Answers
Answer:
[tex] \rm\displaystyle D) \left (1,3\right)[/tex]
Step-by-step explanation:
well to figure out the point we can consider the following formula:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{m x_{2} + n x_{1} }{m + n} , \frac{m y_{2} + n y_{1} }{m + n} \right)[/tex]
from the given we acquire that,
[tex](x _{1}, y_{1}) = ( - 1,7)[/tex][tex](x _{2}, y_{2}) = ( 4, - 3)[/tex][tex]m : n = 2 : 3[/tex]therefore substitute:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{(2) (4)+ 3( - 1) }{2 + 3} , \frac{(2) ( - 3) + (3)(7)}{2 + 3} \right)[/tex]
simplify multiplication:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{8 - 3 }{2 + 3} , \frac{ - 6+ 21}{2 + 3} \right)[/tex]
simplify:
[tex] \rm\displaystyle \text C(x,y)= \left (\frac{5}{5} , \frac{ 15}{5} \right)[/tex]
simplify division:
[tex] \rm\displaystyle \text C(x,y)= \left (1,3\right)[/tex]
hence our answer is D)
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
Points => (-1, 7) & (4, -3)
Ratio => 2 : 3
(x₁, y₁) = (-1, 7)
(x₂, y₂) = (4, -3)
(m₁, m₂) = (2, 3)
Formula = [tex]\large\left (\frac{m_{1} x_{2} + m_{2} x_{1} }{m_{1} + m_{2}} , \frac{m_{1} y_{2} + m_{2} y_{1} }{m_{1} + m_{2}} \right)[/tex]
Points which divide the line segment
= [tex]( \frac{2 \times 4 + 3 \times - 1}{2 + 3}, \frac{2 \times -3 + 3 \times 7}{2 + 3})[/tex]
[tex] =( \frac{8 - 3}{5} , \frac{ - 6 + 21}{5}) \\ = ( \frac{5}{5} , \frac{15}{5} ) \\ = (1,3)[/tex]
Answer => (1, 3) [option D]
Related Questions
John finds that the sum of two numbers is 24 and their difference is one sixth of the
sum. Find the smallest number between the two numbers.
Answers
Given:
The sum of two numbers is 24 and their difference is one sixth of the sum.
To find:
The smaller number between the two numbers.
Solution:
Let x and y be the two numbers where x>y.
The sum of two numbers is 24.
[tex]x+y=24[/tex] ...(i)
Their difference is one sixth of the sum.
[tex]x-y=\dfrac{1}{6}\times 24[/tex]
[tex]x-y=4[/tex] ...(ii)
Adding (i) and (ii), we get
[tex]2x=28[/tex]
[tex]x=\dfrac{28}{2}[/tex]
[tex]x=14[/tex]
Putting [tex]x=14[/tex] in (i), we get
[tex]14+y=24[/tex]
[tex]y=24-14[/tex]
[tex]y=10[/tex]
The two numbers are 14 and 10.
Therefore, the smaller number between the two numbers is 10.
x/5 = 2/3 = 5/y find the ratio from x to y
Answers
Answer:B
Step-by-step explanation:because im smart
Which of the following is a radical equation?
Answers
Answer:
[tex]\sqrt{x} +3 =13[/tex]
Step-by-step explanation:
A radical equation is any equation in which a variable is under a root. This is the only equation in which x is under the square root, so this is the radical equation.
Can someone help me with this math homework please!
Answers
Answer:
addition one is: (1/2) + 5x - (1/2)= 8 - (1/2)
muliplcation one is: (4x)(1/4)=(3) (1/4)
subtracting one is: 3x-4+4=12+4
division one is: 55/11 = 11x/11
Step-by-step explanation:
Hope this helps and good luck :)))
The inequality x ≤ -8 would represent which of the following values?
{8, 5, 0}
{-6, -7, -8}
{-10, -9, -8}
None of these choices are correct.
Answers
Answer:
{-10. -9, -8}
Step-by-step explanation:
x ≤ -8 would be all values of x less than or equal to -8
x = -8, -9, -10
find 3 rational numbers between (-3-4) and (3/4)
Answers
Answer:
The three Rational between 3 and 4
A rational number between 3 and 4 is 1/2 (3 + 4) = 7/2. Hence, 13/4, 7/2 and 15/4 are the three rational numbers lying between 3 and 4.
Step-by-step explanation:
PLEASE HELP!!!
Verify sin(180°- θ) = sin θ
SHOW WORK!!!
Answers
Answer:
see explanation
Step-by-step explanation:
Using the identity
sin(x - y) = sinxcosy - cosxsiny , then
sin(180 - θ)
= sin180cosθ - cos180sinθ
= (0) cosθ - (- 1)sinθ
= 0 + sinθ
= sinθ
which choice is equivalent to the expression below when x less than or equal to 0
Answers
Answer:
b
Step-by-step explanation:
Which one of the following groups would be unbiased when asked, “What is your favorite kind of pizza?”
Group of answer choices
health & fitness fanatics leaving the gym
guests leaving a gourmet pizza restaurant
kids at the playground
families attending a sporting event
Answers
Answer:
kids at playground
children are too young to know calorie count and the health benefits of certain foods. So they would simply choose the one they think tastes best
Someone please help me with this algebra problem
Answers
Step-by-step explanation:
8.4 is the ans
4x+8y=40
4x + 6.4=40
4x=40-6.4
4x=33.6
x=33.6÷4
x=8.4
Answer:
4x+8y=40
4x+(8+0.8)=40
4x+6.4=40
4x+6.4-6.4 =40-6.4
4x=33.6
4x÷4=33.6÷4
X=8.4
Jamal bought a diamond ring at a 20% discount. He paid $2640 for the ring. Naomi bought a similar ring but was given a discount of $924. What was the percentage discount given to Naomi?
Answers
Answer: 72%
Step-by-step explanation:
Set Jamal's original ring price = x
[tex]x - x(0.2) = 2640\\x(1-0.2)=2640\\x(0.8)=2640\\x=\frac{2640}{0.8}=3300[/tex]
Jamal's original ring price = $3300
Set Naomi's discount = y
[tex]3300-3300(y)=924\\=3300(1-y)=924\\1-y=\frac{924}{3300} \\-y=\frac{924}{3300} -1\\y=1-\frac{924}{3300}=1-0.28=0.72[/tex]
Naomi's discount is 0.72 = 72%
( 4.2 + 3 ) + (5.7 x - 2 ) + ( 5 — 2.6 x)
Answers
Solve by combining like terms
In a survey of 600 students in a school. 150 student were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee Find how many Students were taking neither tea nor coffee
Answers
Answer:
125
Step-by-step explanation:
600=150+225+100+X=475+X
600-475=125=X
X=125
Answer: 325 I believe!
Step-by-step explanation:
The diagram is not drawn to scale
Find the value of x to the nearest tenth.
Options:
A: 25.0
B: 16.0
C: 9.0
D: 17.3
Answers
Answer:
3x-2 = 25 3x = 25+2 3x = 27 x =9the answer is option cNeed help ASAP !!!!!!
Answers
answer:
to test whether agraph is linear
Out of 100 students, 80 passed in Science, 71 passed in Math, 10 failed in both subjects nd 7 did not appear in an examination. Find the number of students who passed in both subjects by representing the above information in a Venn-diagram.
Answers
Answer:
68Step-by-step explanation:
Total students = 100Failed and didn't appear = 10 + 7 = 17Total passed = 100 - 17 = 83Passed in Science and in Math = 80 + 71 = 151Passed in both subjects = 151 - 83 = 68The total number of students,
→ 100 students
No. of students were absent & failed,
→ 7 + 10
→ 17 students
No. of students totally passed,
→ 100 - 17
→ 83 students
No. of students passed in Science,
→ 80 students
No. of students passed in Mathematics,
→ 71 students
Then add both science and math,
→ 80 + 71
→ 151 students
No. of students passed in both subjects,
→ 151 - 83
→ 68 students
Therefore, the number of students who passed in both subjects are 68 students.
Match each percent with the fraction or decimal equivalent. 5% 0.25 15% 0.07 6.5% 1 20 25% 0.065 7% 3/20
Answers
Answer:
5% = 1/20
15% = 3/20
6.5% = 0.065
25% = 0.25
7% = 0.07
Step-by-step explanation:
I hope this helps! Just ask me if you have any questions.
Have a nice dayy! :)
Answer:
.05 25% .15 7% .065 100% 2000% .25
Step-by-step explanation:
Percentages to decimals :
example
5% = .05
First remove the % sign: 5
Where is the decimal? Here : 5.00
Now move the decimal to the left two places. Fill the gaps with zeros : .05
Another way to do it is by divide the number by 100. Use a calculator if necessary.
Example 2: 6.5%
Move decimal two places to left: .065
Example 3: .56%
Move decimal to places to the left: .0056
Decimals to percentages. Do the exact opposite. Move decimal to places to the right then add the % sign.
Example: .25 becomes 25%
.07 becomes 07% or just 7%
Determine the value of x
2.12 units
2.02 units
12.38 units
0.49 units
Answers
Answer:
2.02
Step-by-step explanation:
Hello, I took the quiz. The correct answer is 2.02
Pier is a teacher
There are 13 boys and 17 girls in the class
Pier chooses one student at random
Workout the probability the student is a boy
Answers
Answer:
I think its 43%
Explanation
math
The probability of Pier choosing a boy is 0.43 or 43%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The total number of students in the class is:
13 boys + 17 girls
= 30 students
The probability of Pier choosing a boy is the number of boys in the class divided by the total number of students:
Probability of choosing a boy.
= number of boys / total number of students
Probability of choosing a boy.
= 13 / 30
Probability of choosing a boy.
= 0.4333 or approximately 0.43
Therefore,
The probability of Pier choosing a boy is 0.43 or 43%.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ2
What is the constant of variation, k, of the direct variation, y = for, through (5,8)?
Answers
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.
Usually represented with the variable [tex]k[/tex], it is given by:
[tex]\frac{y}{x}=k[/tex] for coordinates (x, y).
This relationship can be written as [tex]y=kx[/tex] which is also the layout for a proportional relationship.
Since coordinates are written (x, y), for point (5, 8), substitute [tex]x=5, y=8[/tex] to get the constant of variation:
[tex]8=5k,\\k=\boxed{\frac{8}{5}}[/tex]
Answer:
8/5
Step-by-step explanation:
Given that y varies directly with x , therefore ,
[tex]\implies y \propto x[/tex]
Let k be the constant . Therefore ,
[tex]\implies y = k x[/tex]
When the point is (5,8) ,
[tex]\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =\dfrac{8}{5}}}}[/tex]
Hence the constant of variation is 8/5.
find the discriminantof the quadratic equation root 2 X square + 7 x + 5 root 2
Answers
[tex]\displaystyle\ 2x^2+7x+5\sqrt{2} =0 \\\\\boxed{D=7^2-4\cdot2\cdot 5\sqrt{2} =49-40\sqrt{2} }[/tex]
A farmer in China discovers a mammal
hide that contains 71% of its original
amount of C-14.
N = Noekt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answers
Answer:
Step-by-step explanation:
I'm assuming you're looking for the age of the mammal hide, since there's no question here, but there's also nothing else to solve for. Remember a few things before we move on. First, if we are not told the initial amount with which we start, we have to assume that it's 100%. Second, remember that natural log and e are inverses of each other so they eliminate each other in application. Now to set up the problem. It looks like this:
[tex]71=100e^{-.0001t}[/tex] and begin by dividing both sides by 100 to get
[tex].71=e^{-.0001t}[/tex] and take the natural log of both sides. The other important thing to remember about the rules for logs and natural logs is that when you take the natural log of something, you are "allowed" to move the exponent down out front, which is why we do this. We cannot currently solve for t when it's stuck up there where it is right now. Taking the natural log allows us to bring that exponent down AND eliminate both the natural log and the e at the same time:
ln(.71) = -.0001t and we divide to solve for t:
[tex]\frac{ln(.71)}{-.0001}=t[/tex] and
[tex]\frac{-.3424903089}{-.0001}=t[/tex] so
t = 3424.9 years, or rounded, 3425 years.
Graph: Y - 3 = 1/2 (x+2)
Answers
Answer:
see graph
Step-by-step explanation:
Personally I put into slope intercept form before graphing
y - 3 = 1/2 (x+2)
y -3 = 1/2x + 1
y = 1/2x + 4
4 is y-intercept
1/2 is slope. [tex]\frac{Rise= 1}{Run= 2}[/tex]
Sila jogged 12 kilometers today and wants to know how far she traveled in feet. What error did Sila make while converting from kilometers to feet? StartFraction 12 kilometers Over 1 EndFraction times StartFraction 0.62 miles Over 1 kilometer EndFraction times StartFraction 5280 feet Over 1 mile EndFraction = 392,832 feet Sila put a wrong number in her calculator when multiplying the numerators. Sila's first fraction should be StartFraction 1 kilometer Over 0.62 miles EndFraction. Sila's last fraction should be StartFraction 1 mile Over 5280 feet EndFraction. Sila forgot to divide by 0.62.
Answers
Answer:
Sila put a wrong number in her calculator when multiplying the numerators.
Step-by-step explanation:
StartFraction 12 kilometers Over 1 EndFraction times StartFraction 0.62 miles Over 1 kilometer EndFraction times StartFraction 5280 feet Over 1 mile EndFraction = 392,832 feet
Correct calculation:
12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile
= (12km * 0.62 miles * 5280 feet) / (1 * 1 km * 1 mile)
= 39,283.2 feet
Sila's calculation:
12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile
= 392,832 feet
The marked price of a fan is Rs 1,620 and selling price is Rs 1,539. Find the discount amount.
Answers
Answer:
rs. 81
Step-by-step explanation:
given,
mp. = 1620
sp. = 1539
now,
discount = mp - s.p = 1620 - 1539 = 81
if two angles are supplementary, then what is the measurement of the missing angle, if one angle is 120?
Answers
Answer: 60°
Step-by-step explanation:
If two angles are supplementary, that means they add up to 180°.
Therefore, if one angle is 120°, the other missing angle can be calculated by:
180° - 120° = 60°
jordan wants to save to buy a car and decides to open a banking account that is offering an interest rate of 4.5% compounded annually how much will jordan have in the account after 5 years it he deposits $7,000 today?
Answers
Answer:
8,723.27$
Step-by-step explanation:
Jorge compro en la papeleria 3 Borradores y 2 lápices, por ellos pago $47.50. si la suma de lo que cuesta un borrador y un lápizes $20 ¿cuanto vale cada borrador y cada lápiz?
Por favor es urgente
Answers
Answer:
Cost of each pencil = $12.5
Cost of each eraser = $7.5
Step-by-step explanation:
Given:
Number of eraser bought = 3
Number of pencil bought = 2
Total amount paid = $47.50
Cost of one pencil and one eraser = $20
Find:
Each cost
Computation:
Let;
Cost of each eraser = e
Cost of each pencil = p
So,
e + p = 20
e = 20 - p .................................... eq1
3e + 2p = 47.50
3(20 - p) + 2p = 47.50
60 - 3p + 2p = 47.50
-p = -12.5
Cost of each pencil = $12.5
e = 20 - p
e = 20 - 12.5
e = 7.5
Cost of each eraser = $7.5
Select the correct answer.
A distribution center is redesigning two of its shipping boxes. The volume of these two boxes needs to be the same, and their dimensions are shown.
Write a system of equations to represent the volume of each box, y. Which statement describes the number and viability of the systems solutions?
Answers
Answer:
The system has two solutions, but only one is viable because the other results in negative side lengths.
Step-by-step explanation:
correct on edmentum or plato
Given: triangle RST is circumscribed about circle A.
m∠APT = _____°
Answers
Answer:
90
Step-by-step explanation:
From the given drawing, we have;
ΔRST is circumscribed about circle A
The center of the circle A = The point A
The line RT = A tangent to the circle A
The radius to the circle A = The line AP
According to circle theory, a line which is tangent to a circle is perpendicular to the radius of the circle drawn from the point of tangency
Where two lines are perpendicular to each other, then the angle formed between them = 90°
The angle formed between a tangent and the radius of the circle = m∠APT
Therefore;
m∠APT = 90°