Answers
The midpoints of the segment is (4, -3.5).
What is Section Formula?The coordinates of the point A(x, y) which divides the line segment joining the points P(a , b) and Q(c , d) internally in the ratio m : n are given by the formula: P ( x , y ) = ( a x n + c x m / (m+n) , bn + dn / (m+n))
Given:
Points (-4, -7) and (12, -6).
So, the ratio is line is m:n = 1:1
let (x, y) be the midpoint.
Now, using section formula
x = (-4 x 1 + 12 x 1)/ (1+1)
x= (-4 +12) /2
x= 8/2
x= 4
and, y = (-7 x 1 -6 x 1)/ 2
y = -7-6/2
y = -13/2
y = -3.5
Hence, the midpoints are (4, -3.5).
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Related Questions
projectile is fired vertically upward and has position given by s(t) = 16t^2 320t _ 336 for 0
Answers
The time when the projectile has an instantaneous velocity of zero is a = 10 seconds.
The instantaneous velocity of a projectile at time t can be found by taking the derivative of its position function with respect to time. The velocity function is given by:
v(t) = ds(t)/dt = -32t + 320
The time at which the projectile has an instantaneous velocity of zero is when the velocity function is equal to 0. We can find this time by solving the equation:
-32t + 320 = 0
32t = 320
t = 10
Therefore, the time at which the projectile has an instantaneous velocity of zero is a = 10.
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--The given question is incomplete; the complete question is
"A projectile is fired vertically upward and has a position given by s(t) = -16T^2+320t+336 for 0 ≤ t ≤ 21.
Identify the time at which the projectile has an instantaneous velocity of zero; call this time = a."--
what is the measurement of Arc FQ?
Answers
The measure of arc FQ is given as follows:
155º.
How to obtain the measure of arc FQ?The measure of arc FQ is obtained applying the two secant theorem in the context of this problem.
From the theorem we have that the angle of 40º represents half the difference between the angle measures of arcs FQ and TR = 75º.
Applying the two secant theorem, the angle measure of arc FQ is given as follows:
(FQ - 75)/2 = 40
FQ - 75 = 80
FQ = 75 + 80
FQ = 155º.
Meaning that the last option represents the correct option in the context of this problem.
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pls help meee i dont understand this
Answers
Answer:
I think the y= (-7)
3. The Erie Canal runs 584 kilometers from Albany to Buffalo. Salvador travels on the canal from Albany. He
must travel 396 kilometers more before he reaches Buffalo. How many kilometers has he traveled so far?
Answers
Answer:
Salvador has traveled 584 - 396 = 188 kilometers so far.
Write a numerical tatement to repreent the problem. Then implify the numerical expreion to anwer the quetion. After dieting for 30 day, Ignacio ha lot 12 pound. What number decribe hi average weight change per day?
Answers
The number which describes the average change in weight per day of Ignacio is equal to 0.4 pounds per day.
Number of days Ignacio done the dieting is equal to 30 days
Total weight lost by Ignacio in 30 days = 12 pounds
Let 'x' be the change in weight per day of Ignacio after dieting.
Weight lost in 30 days = 12 pounds
Average weight change per day is:
⇒ 1 day = ( 12 / 30 ) pounds per day
⇒ 1 day = ( 2/ 5 ) pounds per day
⇒ 1 day = ( 0.4 ) pounds per day
Therefore, the average weight change per day by Ignacio is equal to 0.4pounds per day.
The above question is incomplete, the complete question is:
Write a numerical statement to represent the problem. Then simplify the numerical expression to answer the question. After dieting for 30 day, Ignacio has lost 12 pound. What number describe his average weight change per day?
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Can somebody translate:
2 more than the quotient of a number and 4 is equal to 5
Answers
Answer: x/4+2=5
Step-by-step explanation:
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon
of gas. During one particular week, the two cars went a combined total of 2475 miles, for a total gas consumption of 65 gallons. How many
gallons were consumed by each of the two cars that week?
First car: ___ gallons
Second car:___ gallons
Answers
Answer:
first car: 25 gallons
second car: 40 gallons
Step-by-step explanation:
1) 35 miles/gallon consumption=distance/volume
2) 40 miles/gallon distance=consumption*volume
2475 miles = d1 + d2
= 35*v1 + 40*v2
v1 + v2 = 65
v2 = 65 - v1
2475 = 35*v1 + 40*(65 - v1)
2475 = 35*v1 + 2600 - 40*v1 /-2600
-125 = -5*v1
v1 = 25 gallons
v2 = 65 - v1
v2 = 40 gallons
Fill in the blanks
Divide
A.5
B.54
C.546
Goes in the _____ Place
A.hundreds
B.tens
C.ones
Answers
Answer:
hundreds
Step-by-step explanation:
You have the option of buying 20 tickets at the fair for $15 or 45 tickets for $27. Which is the best deal?
Answers
Answer:
the 45 tickets
Step-by-step explanation:
In the 20 tickets deal, you'll spend USD 1.333333333333333 per ticket; in the 45 tickets deal, you pay USD 0.6 per ticket.
please help me with this question.
Answers
Answer: The last option.
Step-by-step explanation:
The statement that can be used to prove that vertical angles ∠1 and ∠3 are congruent is;
m∠1 + m∠2 = m∠2 + m∠3
This is because we know that m∠1 + m∠2 is a straight line and that m∠2 + m∠3 is a straight line. Straight lines are equal to 180 degrees, so the vertical angles must be congruent.
find the domain of each function. (enter your answers in interval notation.) (a) (b) g(t) = sin(e−t) g(t) = 1 − 6t
Answers
(a) The domain of the function-
[tex]g(t)=sin(e^{-t})[/tex]
is (-∞,∞)
(b) the domain of the given function -
[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)
The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive. (For a function that has fractional values.)
(a) The domain of the function-
[tex]g(t)=sin(e^{-t})[/tex]
is (-∞,∞)
(b) the domain of the function -
[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)
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consider the vectors a = (−1, −2, 3), b = (3, 0, −2), v = (2, −5, −4) and the plane p given by 2x y = z 13. 1. what should the real number y be, so that (1, y, −9) is perpendicular to v?
Answers
The value of y if (1, y, −9) is perpendicular to vector v is 38/5.
Given vector v = 2i - 5j - 4k and vector c = 1i + yj - 9k
In the question, we are told that we need to find y if vector v and vector c are perpendicular. So, if two vectors are perpendicular their dot product is zero
So, vector v.vector c = 0
(2i - 5j - 4k ).(i + yj - 9k) = 0
2(1) - 5(y) - 4(-9) = 0
2 - 5y + 36 = 0
5y = 38
y = 38/5
Hence, the value of y is 38/5.
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Find the length of the circumferences of the circles whose diameters is 49
Answers
The diameters is 49 be the circumference of the circle is 154 cm.
What is meant by circumference of the circle?When it comes to geometry, a circle's or ellipse's circumference is its perimeter. In other words, the circumference would be the length of the circle's arc if it were opened out and straightened out to a line segment. The radius surrounding any closed figure is known as its perimeter more generally.
The distance in a straight line around a circle is known as its circumference. Or, to put it another way, the circumference of a circle is the length of a straight line formed by opening up the circle.
A circle's perimeter is referred to as its circumference. By calculating the length it would take to walk around the world, we may determine the size of the earth.
Given : Diameter of the circle [tex]$=49 \mathrm{~cm}$[/tex] and value of [tex]$\pi=\frac{22}{7}$[/tex]
The circumference of the circle is given by [tex]$C=2 \pi r$[/tex] or in the form of a diameter the circumference of the circle is [tex]$C=\pi d$[/tex]
Now, we have given [tex]$\mathrm{d}=49 \mathrm{~cm}$[/tex] and value of [tex]$\pi=\frac{22}{7}$[/tex]
Substitute the value in the formula,
[tex]$& C=\pi d \\[/tex]
substitute the values in the above equation, we get
[tex]$& C=\frac{22}{7} \times 49 \\[/tex]
simplifying the equation, we get
C = 22 × 7
C = 154 cm
Therefore, the circumference of the circle is 154 cm.
The complete question is:
Find the circumference of circle whose diameter is 49cm, pi = 22 by 7
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Find the percentage error in x when it is estimated to be y and y>x
Answers
Answer:
The percentage error in x can be calculated as follows:
Percentage error = (Estimated value - Actual value) / Actual value * 100
Let x be the actual value and y be the estimated value such that y > x.
Percentage error = (y - x) / x * 100
This formula calculates the absolute error in terms of a percentage of the actual value.
machine builds 300 bobble-head toys in 5 hours. The machine builds the same number of bobble-head toys each hour. Which table shows the relationship between the amount of time the machine runs and the number of bobble-head toys built?
Answers
Answer: Graph A is your answer
Step-by-step explanation:
Graph A becuase since it makes the same bobble-heads each hour and in 2 hours it made 120 then it makes 60 an hour. So 60x5 is 300 so Graph shows the relationship between the amount of time the machine runs and the number of bobble-head toys built.
Write your own word problem that involves a multistep linear equation. Then translate your problem into its resulting math equation. What steps would you then follow to solve for the variable? Be sure to list your steps in the correct order.
Answers
Word problem with steps for linear equation is given below.
What is linear equation?An equation containing variables with its highest power as one is called linear equation.
Question:
Mother is as five times as old as daughter. After 3 years, the mother will be four four times as old as her daughter. What are their present age?
Solution
Let x represents the age daughter.
Mother is as five times as old as daughter. i.e., 5x
After 3 years, the mother will be four four times as old as her daughter.
⇒5x+3=4(x+3)
5x+3=4x+12
⇒5x-4x=12-3
⇒x=9.
Their present age of daughter is 9 and mother is 5*9=45.
Hence, present age of mother and daughter is 45 and 9 respectively.
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a bag contain red, yellow, and green sweets, in theses ratios = red : yellow = 3:2, yellow : green = 1:5, find the ratio of red : green
Answers
Answer:
3:10
Step-by-step explanation:
In order to find the ratio of red to green sweets, we first need to find the ratio of yellow to green sweets. We know that the ratio of yellow to green is 1:5 and we also know that the ratio of red to yellow is 3:2.
We can use this information to find the ratio of red to green by cross-multiplying the ratio of red to yellow and the ratio of yellow to green.
So (3:2) x (1:5) = (3:10)
This means the ratio of red to green is 3:10.
Alternatively, we can find the ratio of red to green by using the following formula:
(red:yellow) x (yellow:green) = (red:green)
So (3:2) x (1:5) = (3:10)
The ratio of red to green is 3:10.
Answer:
Step-by-step explanation:
The ratio of red : yellow = 3:2 and yellow:green = 1:5
So, the ratio of red : yellow : green = 3:2:5
To find the ratio of red: green, we can find the ratio of red : yellow : green and then divide the red and green portions.
So, the ratio of red: green = (3/(3+2+5)) : (5/(3+2+5)) = 3/10 : 5/10 = 3:5
4 of 8 Work out the area of the shaded shape. 5m 12m 8m 9m The diagram is not drawn to scale. 2
Answers
The area of the shaded shape is 60 [tex]m^{2}[/tex].
What is the area of shaded shape?This question uses the area formula for rectangles, which states that the area of a rectangle is equal to its length multiplied by its width.
The formula for the area of a rectangle is A = lw, where l is the length of the rectangle and w is the width of the rectangle
To work out the area of the shaded shape, we need to calculate the area of the rectangle (5m x 12m) and subtract the area of the smaller rectangle (8m x 9m).
The area of the rectangle = 5m x 12m = 60[tex]m^{2}[/tex]
The area of the small rectangle = 8m x 9m = 72[tex]m^{2}[/tex]
Therefore, the area of the shaded shape = 60[tex]m^{2}[/tex] - 72[tex]m^{2}[/tex] = -12[tex]m^{2}[/tex]
The answer is 60[tex]m^{2}[/tex].
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A bank charge a 10$ fee to open an account. Which are the following equation bet repreent the total amount in account,m, when tarting with d, in dollar
Answers
The following equation is m=d-10+k×i represent the total amount in account(m) in dollar.
Although the question does not specify the options, but I have specified my answer as follows:
Given:
The equation representing the total amount in the account, m, when starting with d dollars and being charged a 10$ fee.
Account Opening Charges: $10
Starting amount: $d
The total amount in the account: $m
Let us say the depositor deposits an amount $k for 'i' number of months
Banks deduct their charges from the account balance itself, hence account opening charges are deducted from the bank balance.
I have assumed an amount $k invested every month. You can remove that term as per the requirement of the question.
The total amount at a point in time = starting amount - Account Opening Charges + monthly deposit till that time
⇒m=d-10+k×i
This equation shows that the total amount in the account will be equal to the initial deposit minus the fee charged by the bank.
Therefore, the following equation is m=d-10+k×i.
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Find all points (a, b, c) in space for which the system has at least one solution.
x + 2y + 3z = a
4x + 5y + 6z = b
7x + 8y + 9z = c
Answers
The system of equations has at least one solution if the determinant of the coefficient matrix is not equal to zero.
A system of linear equations is a set of two or more linear equations with the same variables. These equations can be solved to find the values of the variables that satisfy all the equations simultaneously.
In this problem, we have a system of three linear equations: x + 2y + 3z = a, 4x + 5y + 6z = b, and 7x + 8y + 9z = c.
The goal is to find all the points (a, b, c) in space for which the system has at least one solution.
To find the points (a, b, c) in space, we need to find out if the system of equations is consistent or inconsistent. If the system is consistent, it means that there exists at least one solution to the system of equations.
This can be determined by finding the determinant of the coefficient matrix, which is the matrix formed by the coefficients of the variables in the system of equations.
If the determinant is not equal to zero, then the system is consistent, and it has at least one solution.
This means that the points (a, b, c) in space are those for which the system of equations is consistent and has a solution.
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what would be the answer to 23 x 10^5
Answers
Answer:
2300000
Step-by-step explanation:
Use the Binomial Theorem and substitution to expand each Binomial. Show your step.
A) (3x+y)^4
B) (x-2y)^6
Answers
The value of the equation from binomial expansion is
a) A = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴
b) B = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶
What is Binomial Expansion?The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
A = ( 3x + y )⁴
On simplifying the equation , we get
From binomial expansion , ( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Substituting the values in the equation , we get
( 3x + y )⁴ = ⁴C₀ ( 3x )⁴ ( y )⁰ + ⁴C₁ ( 3x )³ ( y ) + ⁴C₂ ( 3x )² ( y )² + ⁴C₃ ( 3x ) ( y )³ + ⁴C₄ ( 3x )⁰ ( y )⁴
On further simplification , we get
( 3x + y )⁴ = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴
Hence , the equation is A = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴
b)
B = ( x - 2y )⁶
On simplifying the equation , we get
From binomial expansion , ( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Substituting the values in the equation , we get
( x - 2y )⁶ = ⁶C₀ ( x )⁶ ( -2y )⁰ + ⁶C₁ ( x )⁵ ( -2y ) + ⁶C₂ ( x )⁴ ( -2y )² + ⁶C₃( x )³(-2y)³ + ⁶C₄ ( x )² ( -2y )⁴ + ⁶C₅ ( x )¹ ( -2y )⁵ + ⁶C₆ ( x )⁰ ( -2y )⁶
On further simplification , we get
( x - 2y )⁶ = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶
Hence , the equation is
B = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶
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A 40% sugar solution is added to an 85% sugar solution to create 1000 mL of a 60% solution. How
much of each solution is used?
Answers
Number of ml of 40% sugar = x = 1000mL
Number of ml of 85% sugar used = y = 800mL
How to find the value of x?A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x. To determine the answer, simplify the values.
Let the number of ml of 40% sugar be x and 85% sugar used be y
System of equations is given as:
x + y = 1800mL ....... (1)
x = 1800 - y
40% × x + 85% × y = 60% × 1800mL
0.4x + 0.85y = 1080.... (2)
We substitute 1800 - y for x in (2)
0.4(1800 - y) + 0.85y = 1080
simplifying the above equation, we get
720 - 0.4y + 0.85y = 1080
- 0.4y + 0.85y = 1080 - 720
0.45y = 360
y = 360/0.45
y = 800mL
Solving for x
x = 1800 - y
substitute the value of y in the above equation, we get
x = 1800 - 800
x = 1000mL
Therefore, the number of ml of 40% sugar = x = 1000mL
Number of ml of 85% sugar used = y = 800mL.
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Points K and M are points of tangency. Find the value of x.
Answers
Applying the two-tangents theorem, the value of x is: 5.
What is the Two-tangents Theorem?The Two-Tangents Theorem says that if a single point outside a circle is used to draw two tangent lines, they will have the same length.
Since point J is formed by the two tangents, KJ and MJ, therefore:
KJ = MJ
Substitute:
4x + 7 = 7x - 8, find x
Combine like terms:
4x - 7x = -7 - 8
-3x = -15
-3x/-3 = -15/-3
x = 5
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Pls Help
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale of 67 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
Answers
From the equation 1) X+Y=67
2) 7X+ 9Y= 543
Based on the scatter plot below, which is a better prediction for y when x = 5?
is it one or 6
Answers
According to the scatter plot below, when x = 5, the value of y is 1.
What is scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables). With a particular confidence interval, a scatter plot might imply several types of relationships between variables. Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).
Here,
Based on the scatter plot below, when x=5 then value of y is 1.
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find f if f'(x) = 1/x^2
Answers
The function f(x) is 3/x³ if f'(x) is 1/x²
Given that,
f'(x) is 1/x²
To find : f(x)
Differentiation is the opposite of integration. In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:: y = x2 => dy/dx = 2x. So, ∫ (dy/dx) dx = ∫ 2x dx = x2 together represent the integration of the function with respect to the x.
f(x) ---> differentiation ------> f'(x)
f'(x)---> integration ------> f(x)
f(x) = ∫ f'(x)
f(x) = ∫ 1/x²
f(x) = 3/x³
Therefore, function f(x) is is 3/x³ if f'(x) is 1/x² .
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4. Which type of data is displayed below? Create a tal ly chart out of it. 10 19 17 14 11 18 16 17 18 15 13 12 14 15 16 18 19 20 16 15 11 10 15 2o 12 14
Answers
Step-by-step explanation:
The data displayed below is numerical data.
Tally Chart:
10 |
19 |
17 |
14 |
11 |
18 |
16 |
17 |
18 |
15 |
13 |
12 |
14 |
15 |
16 |
18 |
19 |
20 |
16 |
15 |
11 |
10 |
15 |
20 |
12 |
14 |
Note: The above tally chart is just a representation of the data, the actual tally chart should be made on paper with tally marks.
HELP ME PLSS!?!?
In the mall you receive a coupon for $5 off of a pair of jeans when you arrive at the store you find that all jeans are 25% off
.let x represent the original cost of the jeans
.the function f(x)=x-5 represents the cost of the jeans if you use the coupon
.the function g(x)=0.25x represents the cost of the jeans if you apply the store discount of 25% first
Write a function:j(x) that represents how much you would pay if you use the store discount first followed by the mall coupon??
Answers
Answer:
j(x) = f(g(x)) = f(0.25x) = 0.75x - 5
ms. avila got blue ribbons to give to participants at the school science fair. she ordered 120 blue ribbons from the smart start school supplier. since this was a bulk order, smart start reduced the price of each blue ribbon by $0.75. the total came to $60. which equation can you use to find the amount of money, b, smart start normally charges for a blue ribbon?
Answers
The equation 120(b - 0.75) = 60 can you use to find the amount of money, b, smart start normally charges for a blue ribbon
Ms. Avila ordered 120 blue ribbons from the smart start school supplier.
Smart start reduced the price of each blue ribbon by $0.75.
The total came to $60.
To express the problem in equation we have to read the question carefully and write the equation according to question.
Let the price of 1 blue ribbon = b
If he reduce the price by 0.75, then the price of blue ribbon = (b - 0.75)
She buy total blue ribbons = 120
So the price of 120 blue ribbons = 120(b - 0.75)
But the total cost is $60.
So the equation is:
120(b - 0.75) = 60
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