the mid point of the points C and D is M = ( 4 , - 1 / 2 ).
We are given the coordinates of the point:
C ( 1 , - 6 )
D ( 7 , 5 )
We need to find the mid point M for it.
Here, we have:
x₁ = 1
x₂ = 7
y₁ = - 6
y₂ = 5
We know that the formula for mid point is given by:
M = ( x₁ + x₂ / 2, y₁ + y₂ / 2 )
Substituting the values, we get that:
M = ( 1 + 7 / 2 , - 6 + 5 / 2 )
M = ( 8 / 2 , - 1 / 2 )
M = ( 4 , - 1 / 2 )
Therefore, we get that, the mid point of the points C and D is M = ( 4 , - 1 / 2 ).
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Which of the following is equivalent to
(p3)(2p^2 - 4p)(3p^2 - 1)?
A.(p3)(6p^4 - 12p^3 - 2p^2 + 4p)
B.(p3)(6p^4 + 4p)
C.(2p^6 - 4p^3)(3p^2 - 1)
D.(2p^5 - 4p^4)(3p^5 - p^3)
The equivalent expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).
what is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
(p^3)(2p^2 - 4p)(3p^2 - 1)
Now further solving
(p^3)(2p^2 * 3p^2 - 2p^2 * 1 - 4p * 3p^2 + 4p)
=(p^3) (6p^4 - 2p^2 - 12 P^3 + 4p)
=(p3)(6p^4 - 12p^3 - 2p^2 + 4p)
Hence, the value of expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).
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the different between 8 and 4,divided by 2
Answer:
2
Step-by-step explanation:
8-4=4
4/2=2
Answer:
so you take 2×4=8 and 2×2=4 I think that's how to do it
Given that [tex]sin(x)+cos(x)=\frac{2}{5}[/tex], compute the following.
[tex]sin^4(x)+cos^4(x)[/tex]
90x - 128 = 24x + 50
Greetings from Brasil...
90X - 128 = 24X + 50
90X - 24X = 50 + 128
X = 89/33How do I write this out and answer it right
The numeric values of the expressions are given as follows:
3. 36.
5. 38.
7. 16/61.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
In item 3, we have that:
4|m - n|, m = -7, n = 2.
Hence the numeric value is:
4|-7 - 2| = 4|-9| = 4 x 9 = 36.
In item 5, we have that:
s²t - 10 with s = -8, t = 3/4.
Hence the numeric value is:
(-8)² x 3/4 - 10 = 48 - 10 = 38.
In item 7, we have that:
(a + b)^5/(a - 2b²), a = 6, b = -8.
Hence the numeric value is:
(-2)^5/(6 - 128)
-32/-122 (negative divided by negative is positive).
32/122 (simplify by 2).
16/61.
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Answer the questions about the following polynomial
-x^2/4+3x^5+1
(12x^5 + x² + 4) /4.
Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.
Given equation
x²/4+3x^5+1
Find common denominator
x²/4+3x^5 . 4/4+4/4
Combine fractions with common denominator
(x²+3x^5 . 4+4)/4
Multiply the numbers
(x²+12x^5 +4)/4
Rearrange terms
(x²+12x^5 +4)/4
(12x^5 + x² + 4) /4
Thus , solution of the given polynomial is (12x^5 + x² + 4) /4. we can also write it as -
3x^5 + x² / 4 + 1.
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Which point is a solution to the following system of inequalities? "-2x+3y>=1" "-5x+6y<=1"
a. (6,6)
b. (7,8)
c. (8,7)
d. (9,7)
By option verification,
i.e., substituting the options by given equation and verifying
Given -2x + 3y > = 1 and - 5x + 6y <= 1
Substituting option A i.e., ( x , y ) = ( 6,6)
-2x + 3y >=1 --> -2 * 6 + 3 * 6 >= 1
--> -12+ 18 >= 1
---> 6>=1
-5x + 6y<=1--> -5 * 6 + 6 *6 <=1
--> -30+ 36 <=1
-->6<=1
False
Substituting option B i.e., (x , y)= (7 ,8)
-2x + 3y>=1 --> -2* 7 + 3 * 8>=1
--> -14 + 24>=1
--> 10>=1
-5x + 6y<=1 --> -5 *7 + 6* 8<=1
--> -35 + 48<=1
--> 13<=1
False
Substituting option C i.e., (x, y) = ( 8 ,7)
-2x + 3y >=1 --> -2* 8 + 3* 7>=1
--> -16 + 21>=1
--> 5>=1
-5x + 6y <=1 --> -5 * 8 + 6 * 7 <=1
--> -40 + 42<=1
--> 2<=1
False
Substituting option D i.e., (x ,y ) = (9, 7)
-2x + 3y >= 1 --> -2* 9 + 3 * 7 >=1
--> -18 +21>=1
--> 3>=1
-5x + 6y <=1 --> -5* 9 + 6 * 7 <=1
--> -45 + 42<=1
--> -3<=1
True
Therefore (x ,y ) = (9, 7) is the solution of the given equation -2x + 3y>=1 and -5x = 6y <=1
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Answer: For the people who were just as confused with the answer above, the answer is D-
Step-by-step explanation:
What is the radius of D
A. 6 cm
B. 12 cm
C. 3 cm
D. 24 cm
Help me ASAP!
What is 4÷139 as a decimal answer ?
Please help me.
Answer:
0.025
Step-by-step explanation:
Divide 4 by 139 and get the number as a decimal
help me please i need to know how to do this
Answer:
12'
Step-by-step explanation:
Pythagoras theorem = a² = b²+c²
*a² is always the hypothenuse (the longest side if the triangle)
you could use b² as the base and c² as the height
to find the height i.e., c² you transpose and substitute what we know so that'll be
13'² = 5'² + c²
you expand which will then give you
169 = 25 + c²
you then take over the 25+ which when addition goes over the equal sign becomes subtraction so that'll now give you
169 - 25 = c²
144 = c²
we want to find for c not c² so to do that we find the square root of 144 which is equal to 12.
so the height is equal to 12'
hope this helps
Which equation does not belong with the other three? Explain your reasoning.
²³/x+ ²/3=y\
y = 0.5x -0.2
4x + 3 = y
y = x² +6
:: a linear equation
does not belong because it is
while the other three equations are
:: y = 0.5x -0.2 :: 4x +3=y :: y = x² +6
:: not a linear equation
:: not linear equations
x + = y
3/
:: linear equations
Answer:
3 = x ÷ 4
Step-by-step explanation:
Given expressions:
8 = x - 2 ⇒ x = 8 + 2= 10
3 = x ÷ 4 ⇒ x = 3*4 = 12
x - 6 = 5 ⇒ x = 5 + 6 = 11
x - 3 = 9 ⇒ x = 9 + 3 = 12
3 of them involves addition, one of them - multiplication
The second expression doesn't belong
Question 8 (1 point)
Solve the equation. Check for extraneous solutions.
7|14-8x|= 2x + 2;
Answer:
Step-by-step explanation:
The most appropriate choice for modulus function is given by-
values of [tex]x[/tex] = [tex]\frac{48}{29}[/tex] and [tex]\frac{50}{27}[/tex]
What is modulus function?
Modulus function returns the absolute value of a function.
[tex]|x| = \left \{ {{x, x \geq 0} \atop {-x, x < 0}} \right.[/tex]
Here,
For [tex]14 - 8x \geq 0[/tex]
[tex]7(14-8x) = 2x + 2\\98 - 56x = 2x + 2\\56x + 2x =98 -2\\58 x = 96\\x = \frac{96}{58}\\ \\x = \frac{48}{29}[/tex]
For [tex]14 - 8x < 0[/tex],
[tex]7(8x - 14) = 2x + 2\\56x - 98 = 2x + 2\\56x - 2x =98 +2\\54 x = 100\\x = \frac{100}{54}\\ \\x = \frac{50}{27}[/tex]
So, [tex]x = \frac{48}{29}[/tex] and [tex]x =\frac{50}{27}[/tex]
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I need help! Thank you
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 18 times t squared plus 54 times t end quantity over the quantity t squared plus 7 times t plus 10 end quantity comma where the time, t is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations.
The domain of the function C(t) is R - { -5. -2}.
What is a domain?The domain of a function is the set of all values for which the range of the function is defined.
To achieve an immediate response to a particular drug's effects the concentration, C, in mg/L, of a particular medication after being injected into a patient is given by the function
C(t) = [tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex] where t represents time in hours.
We know that a function is undefined when its denominator becomes zero.
∴ We have to factor the quadratic equation t² + 7t + 10 which is,
t² + 5t + 2t + 10 = 0.
t(t+5)+2(t+5) = 0.
(t+5)(t+2) = 0.
So, t = -5 or t = -2 are the two values of this equation which makes the function c(t) undefined.
∴ The domain of the function [tex]\frac{-18t^2 + 54t}{(t+5)(t+2)}[/tex] is all real numbers except -2 and - 5 which can be written as
Domain of C(t) is R - { -5, -2}, where R represents all real numbers.
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What is the gradient y= 12-x
Answer:
-1
Step-by-step explanation:
i just inserted it into an online graphing calculator called desmos.
what number can equal 2x² -50=
The number that can be equal to 2x² -50 = 2(x + 5)(x - 5).
What is defined as the quadratic equation?A quadratic equation has a single factor of degree two. It has the general form ax² + bx + c = 0,, at which x is the variable, a, b, and c are constants, and a = 0.This same standard form of a quadratic equation is given to us in the question as - ax² + bx + c = 0,When we compare the statement in the question to the definition discussed above, we can conclude that the given statement is correct. The standard form of the a quadratic equation is ax² + bx + c = 0,, where a, b, and c are constant real numbers. The constant 'a' cannot be zero as it will indeed reduce the degree of the equation to one.For the given equation;
= 2x² -50
Take 2 common;
= 2(x² - 25)
This could be written as;
= 2(x² - 5²)
Now use per the property of (a² - b²) = (a + b)(a - b).
= 2(x + 5)(x - 5)
Thus, the given expression 2x² -50 can be represented as 2(x + 5)(x - 5).
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Solve for y 2y - x = 34 (-y + 1)
The solution for y is given as : y = (34+x)/36
According to the question we have been the linear equation in two variable as :
2y - x = 34 (-y + 1)
We need to solve the above equation for y. For that we will do step by step.
First we will open the brackets on the right hand side of the equation we get
2y - x = -34y + 34
then we will combine the terms on the left hand side of the equation.
2y + 34y = 34 + x
36y = 34+x
dividing both the sides by 36 we get
36y/36 = (34+x)/36
y = (34+x)/36
Hence the solution for y is given as : y = (34+x)/36
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Tonya is paid a salary of $650 a month at her sales job. She also earns a commission on her sales in this way: 3% on all sales up to $32,000 in a month
and 8% on all higher sales. What were Tonya's total earnings for a month where her total sales were $80,000?
Tonya's total earnings for a month where her total sales were $80,000 is $5,450
What made up Tonya's total earnings?
Tonya's total earnings in any month comprises the basic salary of $650 , 3% of sales as sales commission on sales revenue of up to $32,000 and 8% as commission on sales in excess of $32,000
total earnings=basic salary+(3%*sales of up to $32,000)+(8%*sales of above $80,000)
basic salary=$650
3%*sales of up to $32,000=3%*$32,000
3%*sales of up to $32,000=$960
8%*sales of above $80,000=8%*($80,000-$32,000)
8%*sales of above $80,000=8%*$48,000
8%*sales of above $80,000=$3,840
Tonya's total earnings for a month=$650+$960+$3,840
Tonya's total earnings for a month=$5,450
Note that the total earnings based on the basic salary of $650 and sales revenue of $80,000 is $5,450
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A jar contains 0.25 liter of apple juice and 0.30 liter of grape juice. Melissa poured 0.75 liter of pineapple juice into the jar. She then drank 0.20 liter of the mixture
The expression to represent the total amount of juice left in the jar is: (.25 + .30+ .75) -.20 and the property used in each step is addition and extraction of Liquid from the mixture.
ExpressionExpression:
(AJ+GP+PJ)-M
Where:
Apple juice=AJ
Grape juice=GP
Pineapple juice=PJ
Mixture=M
Hence,
(.25 + .30+ .75) -.20
b. Simplifying the expression
(.25 + .30+ .75) -.20
=1.3-.20
=1.10
Therefore the expression to represent the total amount of juice left in the jar is: (.25 + .30+ .75) -.20 and the property used in each step is addition and extraction of Liquid from the mixture.
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Solve each equation. Check your answers. ln x=-2
After solving the equation ln x = -2, x is the value of equal to [tex]e^{-2}[/tex]
We have been asked to find x in ln x = -2
⇒ ln x = -2
⇒ x = [tex]e^{-2}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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What did i do wrong here
Answer: Everything lol
Step-by-step explanation:
Please help very quickly
The name of each midpoint and the segment it bisects include the following:
Point R bisects line segment PQ.Point X bisects line segment WY.Point Y bisects line segment WZ.Point D bisects line segment CA.What is a line segment?A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
In this scenario, the name of each midpoint and the segment it bisects include the following:
Point R bisects line segment PQ.Point X bisects line segment WY.Point Y bisects line segment WZ.Point D bisects line segment CA.Read more on midpoint and line segments here: https://brainly.com/question/28367319
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Complete Question:
Name each midpoint and the segment it bisects.
Identify each function as linear, quadratic, or exponential. Explain your reasoning.
c. y =2x+5
The given function is a linear function because variable have first degree power.
The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
A linear function is a function that represents a straight line on the coordinate plane. As an illustration, the equation y = 3x – 2 represents a linear function because it is a straight line in the coordinate plane.
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find the quotient of (−2/9)÷(−2 1/3÷1/9).
Answer: 2/189
Step-by-step explanation:
HELP ME PLEASE ITS THE LAST QUESTION
Answer:
10 hours
$352
Step-by-step explanation:
Given costs:
Pleasure Pontoons: $132 per day plus $22 per hour.Water Sportscrafts: $152 per day plus $20 per hour.Define the variables:
Let x = number of hours renting the boat.Let y = total cost (in dollars) of renting the boat.Create a system of equations using the given costs and defined variables:
[tex]\begin{cases}y=132+22x\\y=152+20x \end{cases}[/tex]
To find how many hours Ryan would need to rent the boat in order for the cost of both companies to be the same, substitute equation 1 into equation 2 and solve for x:
[tex]\begin{aligned}132+22x & = 152+20x\\132+22x-20x & = 152+20x-20x\\132+2x & = 152\\132+2x-132 & = 152-132\\2x & = 20\\\dfrac{2x}{2} & = \dfrac{20}{2}\\x & = 10\end{aligned}[/tex]
Therefore, the number of hours Ryan would need to rent the boat in order for the cost of both companies to be the same is 10 hours.
Substitute x = 10 into one of the equations to find the cost at both companies if Ryan rented a boat for this many hours:
[tex]\begin{aligned}x=10 \implies y & = 132+22(10)\\& = 132+220\\& = 352\end{aligned}[/tex]
Therefore, the cost at both companies if Ryan rented a boat for 10 hours would be $352.
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Please HURRY
Describe the trend in the scatter plot.
• positive correlation
no correlation
• negative correlation
O not enough information because the trend line is unclear
the angle of elevation to the top of a building in new york is 6° from the ground and 2 miles from the base of the building. use this information to calculate the height of the building.
The height of building is 0.2 miles.
The given points form a right angled triangle. Top of the building to base of building is the perpendicular, base of building to the angle of elevation is base and angle of elevation to top of the building is hypotenuse. So, considering this, tan of angle of elevation related the two sides of triangle as follows -
tan theta = perpendicular ÷ base
tan 6° = perpendicular ÷ 2
Perpendicular = 2 × tan 6°
Keep the value of tan 6°
Perpendicular = 2 × 0.1
Performing multiplication
Perpendicular = 0.2 miles
Hence, the height of the building is 0.2 miles.
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Giving 80 points to the person who answers correctly
The function f(t) represents water going into a swimming pool with respect to the number of hours(t) water is flowing in where(t) represents time. f(t)=t squared +8t+9 There is a leak in the pool and it’s losing water at a rate represented by d(t). d(t)=t squared +11t+4
a.Write a function w(t) to represent the amount of water in the pool using the two functions.
b. Use the new function to determine if the pool will leak all of the water
c. If the pool will drain of all water, how much time will it take?
d.Will f(t) and d(t) intersect on a graph? Explain what it means if they do.
e. What is the domain of f(t), d(t), and w(t)? Explain your answer.
Using operations with functions, we have that:
a) w(t) = -3t + 5.
b) The pool will leak all the water in 1.67 hours.
c) 1.67 hours.
d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
e) The domain of the function is 0 ≤ t ≤ 1.67.
What is the amount of water in the pool?The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.
For this problem, these following functions are given:
Flowing: f(t) = t² + 8t + 9.Draining: d(t) = t² + 11t + 4.Hence the amount of water in the pool is given by:
w(t) = f(t) - d(t)
w(t) = t² + 8t + 9 - t² - 11t - 4
w(t) = -3t + 5.
Hence:
The function is: w(t) = -3t + 5.
The pool will have leaked all the water when:
w(t) = 0.
Hence:
-3t + 5 = 0.
3t = 5
t = 1.67.
The pool will leak all the water in 1.67 hours.
Equaling f(t) and d(t), we have that:
t² + 8t + 9 = t² + 11t + 4.
3t = 5.
t = 1.67.
Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:
Time cannot be negative, hence t ≥ 0.When all the water has been drained, everything stops, hence t ≤ 1.67.Hence:
The domain of the function is 0 ≤ t ≤ 1.67.
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Drew is an artist. He paints portraits. The table below shows the number of portraits painted in hours. What is the constant of proportionality?
The constant of proportionality for the paints portraits is estimated as 5.
What is defined as the constant of proportionality?When two variables are proportional to one another, their relationship can be expressed as y = kx or y = k/x, in which k defines how the two factors are connected to one another. This k is recognized as the proportionality constant.The proportionality constant is the fixed value of the ratio of two proportional quantities. When the ratio or product of two varying quantities yields a constant, they are said to be in a proportional relationship.For, the given question;
The relation between the portraits and the time for their drawing made by Drew is-
In 5 hours ----> 1 portrait
Thus, 5/1 = 5
In 10 hours ------> 2 portrait
Thus, 10/2 = 5
In 15 hours -----> 3 portrait
Thus, 15/3 = 5 .....and so on.
Therefore, the constant of proportionality is found as 5.
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Find the unknown length for the similar rectangles below.