Given the points P (3, 5) and Q (-5, 7) on the cartesian plane such that R (x, y) is
the midpoint of PQ, find the equation of the line that passes through R and
perpendicular
to PQ.
Answer:
-22=22
Step-by-step explanation:
3,5-5,7=
-22/22
The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.
The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.
The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.
So, the coordinates of the midpoint R are (-1/2, 6).
Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:
(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)
Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:
(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))
Simplifying the equation:
(y - 6) = (2 / -8) \(\times\)(x + 1/2)
(y - 6) = -1/4 \(\times\)(x + 1/2)
4(y - 6) = -x - 1/2
Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
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A scientist has two solutions what she has labeled solution a and solution b each contains salt she knows that solution a is 60% salt and solution b is 85% salt she wants to obtain 70 ounces of a mixture that is 80% salt how many ounces of each solution should she use
Solving a system of equations we can see that:
She needs to use 56 oz of the 85% solution.She needs to use 14 oz of the 60% solution.How many ounces of each solution should she use?We can use the variables:
x = mass of the 60% solution.
y = mass of the 85% solution.
We can write a system of equations.
x + y = 70
x*0.6 + y*0.85 = 70*0.8
We can isolate x on the first equation to get:
x = 70 - y
Replace that in the other one:
(70 - y)*0.6 + y*0.85 = 70*0.8
Now we can solve this for y.
y*0.25 = 70*0.8 - 70*0.6
y = 14/0.25 = 56
Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.
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General form of
Y= 1/3x +3 and has an x intercept of 3
Answer:
Step-by-step explanation:
y
=
1
3
x
−
3
Use the slope-intercept form to find the slope and y-intercept
Slope:
1
3
y-intercept:
(
0
,
−
3
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
x
y
0
−
3
3
−
2
Graph the line using the slope and the y-intercept, or the points.
Slope:
1
3
y-intercept:
(
0
,
−
3
)
x
y
0
−
3
3
−
2
image of graph
could someone help me with this and show work?
The volume of the shape is 490cm³
What is volume of prisms?A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.
The base of this prism is rectangular. The volume of a prism is expressed as;
V = base area × height
base area = 7 × 10 = 70cm²
height = 7cm
the volume of the shape = 70× 7 = 490cm²
therefore the volume of the shape is 490cm³.
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Three pizza are shared equally among 12 people.what fraction of a pizza will each person get?
A
4/1
B
3/1
Answer:
d) 1/12
Step-by-step explanation:
A flower bed has the shape of a rectangle 5 yards long and 4 yards wide. what is its area in square feet? be sure to include the correct unit in your answer.
Answer: 60 square feet
Step-by-step explanation: 5 times 4= 20 yards 20 times 3=60 feet
5*3=15
4*3=12
15*12= 180square feet
7. What do you know about the hypotenuse of triangle XYZ?
Answer:
Step-by-step explanation:
it is the diameter AB.
PLEASE HELP PLEASE PLEASE
Answer:
(2, 4)
Step-by-step explanation:
When plotting points you need to do the x first then the y,
To help you remember the order use the saying OVER AND UP.
For the x-axis is the line going from SIDE to SIDE,
For the y-axis is the line going UP to DOWN,
The Radio City Music Hall x value is 2 and the y value 4.
Therefore your coordinates/ordered pair is (2, 4).
A set of twins purchase a small, oddly shaped plot of land for their retirement. They want to divide the parcel along the grid lines into two identical plots. Can they do it and how?
The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.
To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.
For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.
If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.
However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.
To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.
If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.
the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.
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Note the full question may be :
To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.
-x^3-3x^2=6x+4 find all the zeros of the equation
This is consistent with the solutions for the equation \(x^{2}\) - 6x + 5 = 0 being x = 1 and x = 5.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.
The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation \(x^{2}\) - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.
The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation \(x^{2}\) - 6x + 5 = 0 being x = 1 and x = 5.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Use the domain {-3, -2, -1, 0, 1} and plot the points on the graph that would best satisfy the equation. The bold grid marks represent one unit, the horizontal red line represents the x-axis, and the vertical red line represents the y-axis.
y = 2-x
the side length of NS is 7.81 units.
I don't understand calculus at all bruh :/. I figured out some of this but I don't know if the answer is 0 or 2. Whoever figures this, out also please explain how you got it.
how did the greeks defend themselves from dorian rules?
Answer: the Dorians were far less advanced then the Mycenaean Greeks; economy collasped and trade stopped
What is the mean of 89, 73, 84, 91, 87, 77, 94
Answer:
85
Step-by-step explanation:
Mean = Sum of the terms / Number of terms
Mean = 89 + 73 + 84 + 91 + 87 + 77 + 94 / 7Mean = 595/7Mean = 85the equation p=1.5r graphed find price p, in dollars for r pounds of rice
Answer:
Hope that help you mark me brinilylist
Step-by-step explanation:
Given that 5 pounds of rice at a store cost $6.50.
Then 1 pound of rice at a store cost = $6.50/5= $1.3
So the equation for the cost can be written as:
C=1.3P just like we write equation y=mx
Now we have to graph the cost C, vs pounds of rice.
Variable for Pounds of rice is not given so let it be "P"
So let's make a table for the number of pounds (P) and cost (C) we can graph the points from that table to get the final graph.
The Attached graph is the final graph.
An antibiotic loses 15% of its effectiveness in each hour after it has been taken.
The doctor prescribed a 500mg dose; the first dose was taken at 8am.
Construct a model to represent the amount of antibiotic remaining after any
given number of hours, then use your model to determine the amount of
antibiotic that remains at 6:00pm. Round your answer to the nearest tenth of a
milligram.
12.5mg left at 6pm
Step-by-step explanation:
500mg x 15% = 75mg/hr
Taken at 8am and by 2pm that's 6/hrs 7 x 75mg/hr = 450mg
By 2pm only 50mg are left
Taken at 8am, by 6pm that's 10/hrs
With 50mg left and 4hrs to go
50mg ÷ 4 = 12.5mg
Describe and correct the error in listing the coordinates of the image after a dilation with a scale factor of 1/2.
Each coordinate was multiplied by 2 instead of divided by 2
the correct coordinates are
preimage image
A (2, 5) → (2 * 1/2, 5 * 1/2) → A' (1, 2.5)
B (2, 0) → (2 * 1/2, 0 * 1/2) → B' (1, 0)
C (4, 0) → (4 * 1/2, 0 * 1/2) → C' (2, 0)
How to find the coordinates of the imageDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we solve with scale factor of 1/2
preimage image
A (2, 5) → (2 * 1/2, 5 * 1/2) → A' (1, 2.5)
B (2, 0) → (2 * 1/2, 0 * 1/2) → B' (1, 0)
C (4, 0) → (4 * 1/2, 0 * 1/2) → C' (2, 0)
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hgggggggggggggggggggg
Seriously dude, c'mon
Juilo`s trail mix recipe has 2/3 cup of almonds. Paula`s trail mis recipe has 3/4 cup of almonds. Whose recipe has more almonds ?
analyze question
expand 2/3 to get 8/12
expand 3/4 to get 9/12
so, paulas trail got more almonds
1. Approximately what was the total expenditure on entertainment if separated amount of $11,406.30, $1,669.72, $2,506.81 and $1,930.20 were spent?
Answer:
The approximate expenditure spent on entertainment is $17,513
Step-by-step explanation:
To get the total entertainment expenditure, we simply add up all these values
We have;
11,406.30 + 1669.72 + 2506.81 + 1930.20 = 17,513.03
The total expenditure spent on entertainment is approximately $17,513
Professor A.B.C company opens his own company, Electronic Tutorial Services, and completes the following transactions in June:
6/1 A.B.C company invests 20,000 in the business.
6/3 Purchased 12,100 of equipment.
6/4 Paid 220 premium for an insurance policy.
6/6 Purchased office supplies on Account 140.
6/9 Purchased a new computer for 9,000. Paid 40% cash agreed to pay the remainder Later.
6/10 Billed student Omar 58 for tutorial services that were performed.
6/14 Paid for the supplies purchased on June 6th.
6/15 the owner suggested to purchased new Building for his company by 22,000
6/25 Received 85 cash from student Salim Ali for tutorial services performed.
6/30 Student billed on June 10 pays the amount due to A.B.C company.
6/30 A.B.C company withdraws 60 for personal use.
Required: Prepare the all Accounting Cycles
In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.
Accounting Cycles:
1. June 1:
- A.B.C company invests $20,000 in the business.
- Prepare the journal entry:
- Debit: Cash ($20,000)
- Credit: Capital ($20,000)
2. June 3:
- Purchased equipment for $12,100.
- Prepare the journal entry:
- Debit: Equipment ($12,100)
- Credit: Cash ($12,100)
3. June 4:
- Paid $220 premium for an insurance policy.
- Prepare the journal entry:
- Debit: Insurance Expense ($220)
- Credit: Cash ($220)
4. June 6:
- Purchased office supplies on account for $140.
- Prepare the journal entry:
- Debit: Office Supplies ($140)
- Credit: Accounts Payable ($140)
5. June 9:
- Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.
- Prepare the journal entry for the cash payment:
- Debit: Computer ($3,600) [40% of $9,000]
- Credit: Cash ($3,600)
- Prepare the journal entry for the remaining amount:
- Debit: Computer ($5,400)
- Credit: Accounts Payable ($5,400)
6. June 10:
- Billed student Omar $58 for tutorial services performed.
- Prepare the journal entry:
- Debit: Accounts Receivable ($58)
- Credit: Tutorial Services Revenue ($58)
7. June 14:
- Paid for the supplies purchased on June 6th ($140).
- Prepare the journal entry:
- Debit: Accounts Payable ($140)
- Credit: Cash ($140)
8. June 15:
- The owner suggested purchasing a new building for the company for $22,000.
- No journal entry is required at this point. It is a decision made by the owner.
9. June 25:
- Received $85 cash from student Salim Ali for tutorial services performed.
- Prepare the journal entry:
- Debit: Cash ($85)
- Credit: Accounts Receivable ($85)
10. June 30:
- Student billed on June 10 pays the amount due ($58).
- Prepare the journal entry:
- Debit: Cash ($58)
- Credit: Accounts Receivable ($58)
11. June 30:
- A.B.C company withdraws $60 for personal use.
- Prepare the journal entry:
- Debit: Withdrawals ($60)
- Credit: Cash ($60)
These transactions represent the accounting cycles for the given period.
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The sugar content of orange juice is decreased from 6% to 4%. How much percent does the sugar content decrease?
Answer:
33.33%
Step-by-step explanation:
amount of sugar at first 6x
now 4x
difference 2x,(6x-4x)
"ratio=2/6"
change in percentage:2/6×100%=33.33%
x = y+2
x+4y=7
Please help!
CAN SOMEONE HELP ME I NEED IT NOWW PLSSSS THE QUESTIONS ARE:
1) what is the exact length of the line segment
2) find the decimal approximation of the length
PLSSS I NEED HELPPPP
-2/3 + 9/2
what's the answer
Answer:
The answer would be 23/6
Option (c) p =10000 (1.04)-t . Given
To find the poulation, p of a town after t years is represented using the equation, p = .
Which of the following is an equivalent expression?
(a) p = 10000 (1/25)t
(b) p = 10000 (25/26)t
(c) p = 10000 ( 26/25)t
(d) p = 10000(25/1)t
The equivalent expression is p=10000(26/25)t
What is expression ?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.
Considering that the population, p, of a town after t years is represented using the equation p=10000(1.04)^-t
The equation is equivalent to
p=10000(26/25)t
26/25 = 1.04
Hence; p=10000(26/25)t
⇒ p=10000(1.04)^t
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If line m || line n and 24 measures 135º, what is the measure of 23?
Answer:
45°
Step-by-step explanation:
by liner pair {180°-135°}
= 45°
Can someone help please
let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so
\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)
\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)
Translate the following statements into probability notation. Use x as the random variable. some options are used more than once!
a. The probability of x being no more than a:
a. P(x≥a)
b. P(x=a)
c. P(x>a)
d. P(x≤a)
c. P(x
b. The probability of being at least a:
a. P(x
b. P(x≤ a)
c. P(x>a)∆
d. P(x = a)
e. P(x≥ a)
c. The probability of z being at most a:
a. P(x < a)
b. P(x ≤a)
c. P(x > a)
d. P(x =a)
e. P(x≥a)
d. The probability of z being no less than a:
a. P(x=a)
b. P(x≤a)
c. P(x ≥a).
d. P(x>a)
e. P(x > a)
e. The probability of a being more than a:
a. P(x < a)
b. P(x ≤ a)
c. P(x>a)
d. P(x≥a)
e. P(x= a)
f. The probability of 2 being exactly a:
a. P(x ≤a)
b. P(x =a)
c. P(x ≥ a)
d. P(x < à)
e. P(x > a)
a. The probability of x being no more than a: d. P(x≤a)
P(x)) The probability of being at least a?b. The probability of being at least a: e. P(x≥a)
c. The probability of z being at most a: b. P(x ≤a)
d. The probability of z being no less than a: c. P(x ≥a).
e. The probability of a being more than a: c. P(x>a)
f. The probability of 2 being exactly a: b. P(x =a)
Using mathematical symbols, probability notation is a means to represent events and their probabilities. In this instance, an is a specified value or constant, while x is utilised as a random variable. P(x=a), P(x>=a), P(x=a), P(x>a), P(xa), or P(x!=a) are the possible outcomes. Depending on the particular event under consideration, one may choose one of the inequality symbols (, >, =, >=, or =). For instance, P(x=a) denotes the likelihood that x will not exceed a, but P(x>a) denotes the likelihood that x will exceed a. To minimise confusion and assure accurate probability estimates, the proper notation must be used
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The answer for following questions are mentioned below.
What is probability notation?Probability notation is a way of representing the probability of an event or a random variable using mathematical symbols and formulas. It typically involves using capital letters, such as P, to denote probability, and variables, such as x, to denote random variables.
a. The probability of x being no more than a:
d. P(x≤a)
b. The probability of being atleast a:
e. P(x≥ a)
c. The probability of z being at most a:
b. P(x ≤a)
d. The probability of z being no less than a:
c. P(x ≥a).
e. The probability of a being more than a:
c. P(x>a)
f. The probability of 2 being exactly a:
b. P(x =a)
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Which graph matches the function given:
The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.
What is a piecewise function?A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.
The intervals of the piecewise function are;
f(x) = √(x + 5) if x < -2
f(x) = |x + 1| -2 ≤ x ≤ 2
f(x) = (x - 2)² if x > 2
The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²
The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2
The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.
The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.
The correct option for the graph of the piecewise function is therefore the third option.
Please find the attached the graph of the piecewise function created with MS Excel
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