The coordinates of point S are (12,₋9)
Given, coordinates of T are (0,5)
midpoint of ST is (6,₋2)
When it is necessary to determine the precise center point between two specified points, the midpoint formula is used. So you may use this method to determine the point that divides a line segment specified by two points in half.
coordinates of S are = ?
we know the midpoint formula is (x₊x₁)/2 , (y₊y₁)/2
The midpoint calculation is the same as averaging two numbers. As a result, by adding any two integers together and dividing by two, you may find the midpoint between them.
substitute the given values in the formula.
(6,₋2) = (x₊0)/2 , (y₊5)/2
for the x value of S:
x/2 = 6
x = 12
for the y value of S:
y₊5/2 = ₋2
y ₊ 5 = ₋4
y = ₋4 ₋ 5
y = ₋9
Therefore the coordinates of S are (12,₋9)
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A ball is thrown from a height of 205 feet with an initial downward velocity of 11 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.
h=205-111-161²
How long after the ball is thrown does it hit the ground?
By free fall motion, the ball will take a time of 3.252 seconds to hit the ground.
How much time does a ball take to hit the ground?
The ball experiments a free fall motion, that is an uniform accelerated motion due to gravity, in which effects from Earth's rotation and air viscosity are neglected. The height of the ball (h), in feet, is modelled by a quadratic equation:
h = 205 - 11 · t - 16 · t²
Where t is the time, in seconds.
If we know that h = 0 ft, then the time needed for the ball to hit the ground is:
205 - 11 · t - 16 · t² = 0
16 · t² + 11 · t - 205 = 0
16 · [t² + (11 / 16) · t - 205 / 16] = 0
16 · (t - 3.252) · (t + 3.940) = 0
For time is a whole number, only the first root offers a reasonable answer.
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At lunch, Noah buys two tacos for $2.35 each, chips and salsa for $1.85, and lemonade for $1.60. To pay for his meal, he uses $5.00 from a gift card he has, and then he pays for the rest with a $20.00 bill. Which equations show how much change Noah receives? Explain you answer I will mark you as the brainlyest
2.35(2)+1.85+1.60= $8.15 total before gift card
8.15-5.00= $3.15 because the gift card was $5
now you do
20.00-3.15 to get the total change which is $16.85
Thanks hope you see this susususususususususuusususususuusususus
If Rachel were to paint her living room alone, it would take 2 hours. Her sister Fran could do the job in 5 hours. How many hours would it take them working together?
Express your answer as a fraction reduced to lowest terms, if needed.
Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours
Given that
Rachel can paint half of the living room in 1 hour
Fran can paint [tex]\frac{1}{5}[/tex]th part of the living room in 1 hour
Let's assume together they paint the living room in x hours
⇒ together they can paint [tex]\frac{1}{x}[/tex]th part of the living room in 1 hour
By proportions,
⇒[tex]\frac{1}{2}[/tex]+[tex]\frac{1}{5}[/tex]= [tex]\frac{1}{x}[/tex] {using operation proportions and addition}
⇒[tex]\frac{7}{10}[/tex]=[tex]\frac{1}{x}[/tex]
⇒x=[tex]\frac{10}{7}[/tex]
⇒ together they can paint [tex]\frac{7}{10}[/tex]th part of the living room in 1 hour
It means, Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours
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TASK CARD 17
Half of a number increased by six is
15. What is the number?
The number is 18
Let x be the number
Half of a number = x/2
Half of a number is increased by 6 = x/2 + 6
Half of a number increased by 6 is 15 = x/2 + 6 = 15
Algebra: The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.
Solving the equation we get:
= (x + 12)/2 = 15
= x + 12 = 30
x = 18
Hence, the number is 18
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What is the decimal form of the given fraction 48/100
Answer:
0,48
Step-by-step explanation:
whenever we convert a fraction to a decimal, it is easier to convert the denominator to a power of 10 and then move the comma the amt of zeros left of the number
List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these.
The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis, y-axis and it is graphically shown.
What is a symmetry of a function?A symmetry of a function is a transformation that leaves the graph unchanged. Symmetric function is a function having several variables which remain unchanged for any type of permutation of the variable.
For the given situation, Symmetry with respect to x-axis
The point becomes (x, -y) as the point flips by itself up or down which changes its y coordinate to negative of whatever it was. And there is no motion is done horizontally so no change in x coordinate.
The interecpets are; (0, 6) (0, -6)
Thus this intercepts is symmetric to y-axis. this intercepts is not symmetric about origin.
Hence we can conclude that the intercepts is symmetric about x - axis.
Therefore, The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis and it is graphically shown.
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Write the first 5 terms
an= -2n-3
Answer:
qfgggghbvvcccvvv kknnbvvvvvvvvvvvbhg
Residents of city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 2. If there were 1748 no votes, what was the total number of votes
The scatter plot shows the rental price versus area (in square feet) for 20
apartments that recently rented in an apartment complex.
The equation of the least squares regression line is given as:
Predicted Rental Price = 391+0.98· Area
Use the drop-down menus to complete the statements below about what this linear model tells you about the rental cost of apartments in the complex.
The linear model tells you about the rental cost of apartments in the complex that is $410.6
What is a linear equation?A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = MX + c. Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
A linear equation is given as y = MX + b
where m is the rate of change, b is the initial value of y, and, x are variables.
Assume that y represents the monthly rental price and x represents the square footage.
Given the equation:
Predicted Rental Price = 391+0.98· Area
For the rental price versus area (in square feet) for 20 apartments.
Predicted Rental Price = 391+0.98· Area
Predicted Rental Price = 391 +0.98· (20)
= 410.6
The linear model tells you about the rental cost of apartments in the complex that is $410.6
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Answer this question please
Answer:
[tex] \sf \large \: x<19 \: or \: x>−5[/tex]
Step-by-step explanation:
Let's solve your inequality step-by-step.
|x−7|<12
Solve Absolute Value.
|x−7|<12
We knowx−7<12andx−7>−12
x−7<12(Condition 1)
x−7+7<12+7(Add 7 to both sides)
x<19
x−7>−12(Condition 2)
x−7+7>−12+7(Add 7 to both sides)
x>−5
Answer:
x<19 and x>−5
how many proper subsets are there of the set {O,P,Q,R,S,T,U,V,W}
Answer:
37 subsets
Step-by-step explanation:
yeah just copy that and that's all
in Zoe's class, 4/5 of the students have pets. Of the students who have pets, 5/8 have rodents. what fraction of the students in Zoe's class have pets that are rodents?
Answer:
1/2
Step-by-step explanation:
5/8 students of the 4/5 students have rodents. The word "of" tells us to multiply. 5/8 * 4/5 is equal to 5*4/8*5, which is 20/40 and therefore simplifies to 1/2.
graph y=16-8x. .............
Answer: graph 'y=16-8x'
Step-by-step explanation:
First, alter the equation by making it a 'y=...' statement (y=-8x+16).
Secondly, plot your first point at positive 16.
Third, make sure that your slope is going down 8 from positive 16, so you plot your second point at positive 8, and move that second point to the right by 1.
Let me know if this helps!
michas savings account pays a simple annual interest rate of 2.25% suppose he deposits $6,000 in the account and makes no additional deposits or withdrawals for 4 years what will the total value of the account be after 4 years
The amount in the bank account at the end of 4 years will be = $6540
The amount deposited by Michas in the savings account = $6000
Interest rate = 2.25% annually
No. of years principal is invested = 4 years
Calculating the amount in the bank account after 4 years, using the formula:
Simple interest = P*R*T/100
where P = principal invested
R = rate of interest annually
T = number of years amount is invested
So, Simple interest on the principal invested for 4 years= 6000*2.25*4/100 = 540
The amount in the bank account at the end of 4 years will be = 540 + 6000 = $6540
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factorizar por el método de diferencia de cuadrado.
Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "q2" was replaced by "q^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(9 • (p2)) - (23•5q2)
STEP
2
:
Equation at the end of step
2
:
32p2 - (23•5q2)
STEP
3
:
Trying to factor as a Difference of Squares:
3.1 Factoring: 9p2-40q2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : 40 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
(2,-1)(-3,3) standard form
How i can do , somebody can explain step for step please ;(
[tex]\left( \cfrac{-5x^2}{y^3} \right)^{\underline{2}}\implies \left( \cfrac{(-5)^{\underline{2}}x^{2\cdot \underline{2}}}{y^{3\cdot \underline{2}}} \right)\implies \cfrac{(-5)(-5)x^4}{y^6}\implies \cfrac{25 x^4}{y^6}[/tex]
Find the slope-intercept form of the line with a slope of 2 and through (1,−7)
Answer:
y = 2x -9
Step-by-step explanation:
Bob Ross bought a Blackberry on the Web for $90.49. He saw the same Blackberry in the mall for $120.21. How much did Bob save by buying on the Web?
Note: Round your answer to the nearest cent.
Answer:
$29.72
Step-by-step explanation:
$120.21-$90.49=$29.72
3 in
←
4 in
**
2 in What is the area of the shape?
PLEASE PLEASE HELP!
Movies.
Your parents drop you off at the movies and you have $40 to spend. Admission to the movies costs you $14.50 and you buy a drink and popcorn for $7.75. You want to play a video game that costs $0.75.
1. Write a verbal inequality model that represents this situation.
2. Write an algebraic inequality model that represents this situation.
3. Show all work to solve the inequality.
4. Graph the inequality.
5. Describe the possible numbers of times you can play the same video game.
Answer:
3
Step-by-step explanation:
and the answer is 17
Answer:
1. The total cost of movie and the total cost of refreshments purchased and the total cost of video games played cannot exceed 40
2. 14.50 + 7.75x + 0.75y ≤ 40
3. y ≤ 34 - 10.333x
4. See attached graph
5.
one refreshment means you can play 23 times
two refreshments means you can play 13 times
three refreshments means you can play 3 times
Step-by-step explanation
We have to assume that you can see one movie but but buy multiple refreshments and play multiple video games. A refreshment is considered to be one drink and one popcorn.
If not we have a situation where we have three unknowns and it will be difficult to solve in a 2D context
1. Verbal inequality model
The total cost of one movie and the total cost of refreshments purchased and the total cost of video games played cannot exceed 40
2. Algebraic Inequality Model
Since the cost of a movie is 14.50 and you are seeing only 1 movie, the cost is 14.50(1) = 14.50
Assume you are going to buy x refreshments. Total cost of refreshments = 7.75x
Assume you are going to play y video games. Total cost of video games played = 0.75y
This cannot be greater than 40 i.e ≤ 40
So the algebraic inequality is
14.50 + 7.75x + 0.75y ≤ 40
3. Solving the inequality
Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤ 25.50
Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤ 25.50
Subtract 7.75x from both sides:
0.75y ≤ 25.50- 7.75x
Divide both sides by 0.75
y ≤ 25.50/0.75 - 7.75x/0.75
which is
y ≤ 34 - 10.333x
3. Graph of Inequality
This is an inequality in 2 variables and can be graphed.
See attached graph. The shaded portion represents the inequality
y ≤ 34 - 10.333x
Note that since neither x nor y can be < 0, we should not consider any portion of the shaded area which would mean two more constraints x ≥ 0 and y ≥ 0 but in this case I have stuck to only the above one inequality
5. Possible number of times you can play the same video game
Again we consider only 1 movie and multiple refreshments and video games
Using the inequality y ≤ 34 - 10.33x
If x = 1 refreshment,
y ≤ 34 - 10.33 x 1
y ≤ 23.67 or max 23 times you can play the video game max
If x = 2,
y ≤ 34 - 10.33 x 2
y ≤ 13.34 or maximum 13 times
If x = 3
y ≤ 34 - 30.99
y ≤ 3.01 or maximum 3 times
Find the equation of the line using the given information
the slope equals zero and it passes through the point (x,y) = (1, -4)
The equation of line which passes through (1, -4) and whose slope is 0 is y = -4.
According to the given question.
A line passes throught the point (1, -4) and its slope is 0.
Let the equation of the line be y = mx + b.
Where,
m is the slope of the line
and b is the y intercept.
Since, the line is passing through (1, -4) and slope is 0 i.e. m = 0.
Therefore, m = 0 and (x, y) = (1, -4) must statisfy y = mx + b.
-4 = 1(0) + b
⇒ -4 = b
⇒ b = -4
Therefore, the equation of line which passes through (1, -4) and whose slope is 0 is y = -4.
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Pls help ASAP!!
Which expression is equivalent to −3(4x + 3y)?
A: 3y(4x − 3)
B: 4x(−3 + 3y)
C: −12x + 3y
D: −12x − 9y
Answer:
d
Step-by-step explanation:
solve for x? divide after getting your last resolution!!
x+18=7x
please refer to the picture!!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
According to given information,
g(x) = 4when, x is not equal to -2, that means g(x) = 4 for all values of x except " - 2 "
Therefore,
[tex]\qquad \sf \dashrightarrow \: g( - 5) = 4[/tex]
and
[tex]\qquad \sf \dashrightarrow \: g(3) = 4[/tex]
And, when x = -2, it's value is 2, hence :
[tex]\qquad \sf \dashrightarrow \: g( - 2) = 2[/tex]
Find the slope-intercept form of the line that is perpendicular to −2x+6y=−1 and passes through the point (−2,4)
The equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.
Given the equation of line and point;
−2x + 6y = −1(-2,4)First, find the slope intercept form ( y = mx + b )of the given equation to determine the slope.
−2x + 6y = −1
Solve for y
6y = 2x - 1
y = (2/6)x - 1/6
y = (1/3)x - 1/6
Hence, the slope m = 1/3
Now, the equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Slope of the perpendicular will be;
m_perpendicular = -3
Next, find the equation of the perpendicular line using the point slope formula y - y₁ = m( x - x₁ ).
Plug in the slope m = -3 and the point (-2,4).
y - y₁ = m( x - x₁ )
y - 4 = -3( x - (-2) )
y - 4 = -3( x + 2 )
y - 4 = -3x - 6
y = -3x - 6 + 4
y = -3x - 2
Therefore, the equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.
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A pump can dispose of sludge at the rate of 6,000 lb/h. How many pounds can be disposed of per minute?
Amount of sludge dispose per minutes is 100 lb.
What is Rate of change?
A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.
Here it is given that :
A pump can dispose of sludge at the rate of 6,000 lb/h, that is in one hour pump dispose 6000 lb of sludge.
it is known that 1 hour = 60 minutes
Therefore, to find the amount of sludge dispose by pump in ome minute we divide 6000 with 60 :
amount of sludge dispose in one hour = 6000 lb
amount of sludge dispose in 60 minutes = 6000 lb
amount of sludge dispose in 1 minutes = 6000 lb/60 = 100 lb
Therefore, amount of sludge dispose per minutes is 100 lb
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select ALL expressions equal to -10(4x - 5).
A. 4x - 50
B. -40x -50
C. -40x + 50
D. -50 -40x
E. 50 - 4x
F. 50 - 40x
Answer: C, F
Step-by-step explanation: this is a form of distribution meaning you have to distribute -10 to the numbers inside the parenthesis. -10x4= -40x and -10 x -5= 50 therefor it is -40x+50. This answer can work as commutative meaning -40x+50 can also be written as 50-40x
7) 6003-457 =
How to solve this equation and borrow
Answer:
6003-457= 5546
Step-by-step explanation:
because when is second 603 - 457 when you subtract 7 from 3 it can't be possible so here is very tools so we will say so you go and borrow one from the 6 today's 0 nearest sex making it 10 and you borrow long from the time we
Please help meeeeeeee
Answer: 19
Step-by-step explanation: 13+6=19