Point D is 1n of the way from C(−2.5, 1.25) to E(5, 15). What are the coordinates of D if n = 5?
Answers
Answer:
Coordinates of D are (-1, 4)
Step-by-step explanation:
I have assumed that what you wrote as 1n is actually 1/n otherwise the question does not make sense
1/n with n = 5 ==> that D is 1/5th of the distance from C on the CD line segment
Point D is 1/5th of the way from C to D
I will represent the (x, y) coordinates of points C, D and E as
[tex](x_C, y_C), (x_D, y_D) , (x_E, y_E)[/tex] respectively
Then the x-distance from C to E = [tex]x_E - x_C[/tex] and the y-distance from C to E will be [tex]y_E - y_C[/tex]
[tex]\text{1/5th of }[/tex] [tex]x_E - x_C = \dfrac{x_E - x_C}{5}[/tex] but this is relative to the location of [tex]x_C[/tex].
So we have to add this to [tex]x_C[/tex] to get the absolute x-coordinate of D
So
[tex]\displaystyle \large x_{D}=x_{C}+\dfrac{x_{E}-x_{C}}{5}[/tex]
and similarly
[tex]{\displaystyle y_{D}=y_{C}+\dfrac{y_{E}-y_{C}}{5}}[/tex]
Putting in the values for these coordinates we get
[tex]x_{D}=-2.5+\dfrac{5-(-2.5)}{5} \\\\= -2.5 + \dfrac{5 + 2.5}{5}\\\\\= -2.5 + \dfrac{7.5}{5}\\\\= - 2.5 + 1.5\\\\= -1.0[/tex]
[tex]y_{D}=1.25+\dfrac{15-1.25)}{5} \\\\= 1.25+ \dfrac{15 - 1.25}{5}\\\\\ = 1.25+ \dfrac{13.75}{5}\\\\= 1.25+ 2.75\\\\= 4.0[/tex]
So the coordinates of D are:
[tex]\boxed{D(-1, 4)}[/tex]
The graph shows the point D is indeed 1/5th of the distance from C to D
Related Questions
Natalie is paid for writing numbers on pages of a book. She is paid for writing each digit of the number. If she wrote 702 digits, how many pages is the book?
Answers
Answer:
I think 1,000??
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
17/23+3/23=
Answers
Answer:
17/23+3/23 = 10/23 =2.3
Step-by-step explanation:
brainliest
I have something on my page, please can you help me?
thankyou
find x: -3 = 4x - 12x^2 + 7x^3
Answers
Answer:
x = 0.3384663
Step-by-step explanation:
Sal is selling two types of printed socks.he sells type a at r45 a pair.he sells type b at r30 if he sold 16 pairs in total,and had a total income of r585,how many pairs of sock did sal sell
Answers
Sal sold 7 pairs of type a socks and 9 pairs of type b socks
Let the number of type a socks sold by Sal be x
Let the number of type b socks sold by Sal be y
The selling price of type a socks = 45
The selling price of type b socks = 30
Total pairs sold = 16
Total income = 585
Therefore, the equations will be
x + y = 16-------(1)
45x + 30y = 585--------(2)
Multiplying equation (1) by 30 we get
30x + 30y = 480 ------(3)
Equating equations (2) and (3) we get,
15x = 105
x = 7
Putting x = 7 in (1) we get
y = 9
Sal sold 7 pairs of type a socks and 9 pairs of type b socks
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the function f(x) is shown. the function g(x)= 2x - 6 compare slopes
Answers
Answer: The slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3
Step-by-step explanation:
Define slope?
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
We can write:
m=(y2-y1) / (x2-x1)
If,
g(x) = 2x - 6
The slope of g(x), m = 2
Let, x1=0
y1=2
x2=-1
Y2=1
So, we take (x1, y1) and (x2, y2) Then consider (0, 2) and (-1, 1)
Solve it:
Replace with x1, y1 and x2, y2
m = [1-(-2)/(-1)]
m=[(1+2) /(-1) ]
m=3/(-1)
m=-3
Thus, the slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3.
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Find a vector function r(t), that represents the curve of intersection of the two surfaces. the cylinder x2 y2=36 and the surface z=4xy
Answers
Given:
[tex]\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}[/tex]
Express 16 as [tex]4^{2}[/tex]: [tex]x^2+y^2=16[/tex]
[tex]x^2+y^2=4^2\\x^2+y^2=4^2 \times 1[/tex]
Trignometry,
[tex]\cos ^2(t)+\sin ^2(t)=1[/tex]
Now, substitute [tex]\cos ^2(t)+\sin ^2(t)[/tex] for 1:
[tex]\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)[/tex]
Law of indicates:
[tex]\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2[/tex]
Taking positive square roots as follows:
[tex]x=4 \cos (t), y=4 \sin (t)[/tex]
Recall that, z = xy.
Now, we have:
[tex]\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}[/tex]
Now, substitute the values:
[tex]r(t)=x_t i+y_t j+z_t k[/tex]
So, the vector r(t) is: [tex]r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i[/tex]
Therefore, the vector function r(t) is written as: [tex]r(t)=x_t i+y_t j+z_t k[/tex]
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What is the measure of the central angle that defines the shaded area below if the shaded area takes up 70% of the circle?
Answers
=252
If the price of an apple is $0.50, the marginal utility per dollar spent on the fifth apple is: ________
a) 20
b) 30
c) 40
Answers
The marginal utility per dollar spent on the fifth apple is 60. The correct option is D.
What is marginal utility?The marginal utility simply refers to the change or extra satisfaction derived from the change in consumption.
Hence, the marginal utility of the fifth apple equals :
Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)
= (250 - 220) = 30
Hence, marginal utility per dollar: Marginal utility/price per apple
Price per apple = $0.5
Marginal utility of 5th apple = 30
Marginal utility of 5th apple = 30 / 0.5
Marginal utility of 5th apple = 60
Therefore, the marginal utility per dollar spent on the fifth apple is 60. The correct option is D.
Complete question :
If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:
a) 20
b) 30
c) 40
d) 60
Number of apples ____total utility
2__________________130
3__________________180
4__________________220
5__________________250
6__________________270
7__________________280
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7 • 12 = 12 • 7 is an example of the ____ property of multiplication.
O commutative
O associative
O distributive
O multiplicative identity
Answers
Answer:
A, commutative
Step-by-step explanation:
Commutative property of Multiplication is when you can switch around the numbers when multiplying.
Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin(x) at the point 6 , 1 .
Answers
[1/2, sqrt(3)/2] and [-1/2, -sqrt(3)/2] are the unit vectors that are parallel to the tangent line to the curve.
Explain what a unit vector is?
A quantity with both magnitude and direction is referred to as a vector. A unit vector is one with a magnitude of 1. It also goes by the name Direction Vector.y=2sin(x)
dy/dx equals 2 cos x at pi/6 for x.
pi/6 = 2 cos pi/6 = 2 sqrt(3)/2 = sqrt = dy/dx(pi/6) (3)
the line sqrt(3) (x-pi/6) is the tangent to y at pi/6.
Atan Theta = sqrt is the angle with the x axis (3)
θ = pi/3 radians at 60 degrees
the vectors of units at (pi/6,1) [cos(60), sin(60)] and [-cos(60), -sin(60)] are parallel to this line.
[1/2, sqrt(3)/2] as well as [-1/2, -sqrt(3)/2]
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1. Draw the graph of y = 3 – x/2 using a table of points from x = -3 to 3.
Answers
Answer:
Step-by-step explanation:
x = -3 to 3
means that they are asking for the graph from -3 to 3 on the x-axis
gradient is (-1/2) which means rise is -1 when run is 2
y-intercept is 3.
go to 3 on the y axis which means the coordinate (0,3) go downwards by 1 and to the right by 2. This will lead you to coordinate (2,-1). Now connect both points by a straight line.
One more than the product of 14 and Mabel's age
Use the variable m to represent Mabel's age.
Answers
Answer: 14m + 1
Step-by-step explanation:
We will write an expression for this question.
One more➜ + 1
than the product of ➜ multiplication, *
Mabel's age ➜ m
One more than the product of 14 and Mabel's age
14 * m + 1, 14m + 1
A recent report stated that less than 35 percent of adult residents in a certain city will be able to pass a physical fitness test. Consequently, the city's Recreation Department is trying to convince the City Council to fund more physical fitness programs. The council is facing budget constraints and is skeptical of the report. The council will fund more physical fitness programs only if the Recreation Department can provide convincing evidence that the report is true. The Recreation Department plans to collect data from a sample of 185 adult residents in the city. A test of significance will be conducted at a significance level of a= 0.05 for the following hypotheses.
H0:p=0.35
Ha:p<0.35
where p is the proportion of adult residents in the city who are able to pass the physical fitness test.
The Recreation Department recruits 185 residents who volunteer to take the physical fitness test. The test is passed by 77 of the 185 volunteers, indicating that more than 35 percent of the city is in shape. Describe the primary flaw in the study described in part and explain why it is a concern.
Answers
The primary flaw is that the sample will slightly overestimate the physical fitness of the people of the town.
The given hypothesis are,
[tex]H_0:p=0.35\\H_1:p < 0.35[/tex]
Type II error is accepted in null hypothesis when it is not actually true.
In the given question null hypothesis p= 0.35
The conclusion is that in the given sample proportion is not equal to 0.35, though we know that proportion is not equal to 0.35 we accept the null hypothesis, that is wrong.
Now given n=185,x=77 P=0.53 then Q=1-0.35=0.65
[tex]H_0:P=0.35\\H_1:P < 0.35[/tex]
Now test statistic [tex]Z=\frac{p-P}{\sqrt{\frac{PQ}{n}}}[/tex]
Solving for Z using the given values we get :
Z=1.99
Now 1.99>-1.65
So we accept [tex]H_0[/tex]
The primary flaw in the system is that the sample is not randomly selected rather they are volunteers. So it is reasonable to think that the physical fitness of the town will be slightly over estimated by the experiment.
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4 (c) The high mountains of the world
Answers
Andes
Rockies
Given that 12q x + 16p + 10p = 192x + 312. Find the values of p and q
Answers
Answer:
p = 12, q = 16,
Step-by-step explanation:
Pls help me im stuck
Answers
Mr. drew wants to build a square sandbox with an area of 64 square feet. what is the total length of wood mr. drew needs to make the sides of the​ sandbox?
Answers
Mr. Drew needs woods of a total length of 32 feet to make the sides of the sandbox.
What do we mean by square shape?A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and 4 equal angles (90-degree angles, /2-radian angles, or right angles). It can also be described as a rectangle with two adjacent sides of equal length. It is the only frequent polygon with internal, central, and external angles that are all equal (90°) and diagonals that are all identical in length. ▢ABCD denotes a square with vertices ABCD.So,
A square with an area of 64ft² has sides that are √64 = 8 ft long.Because there are four of them, the perimeter is 8 × 4 feet = 32 feet.Therefore, Mr. Drew needs woods of a total length of 32 feet to make the sides of the sandbox.
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5. Using the data from question 2, you can compute the mean food and lodging
cost of a 10-day vacation by multiplying the per-day mean by 10. The
standard deviation for the 10-day vacation can be found by multiplying by
10 also.
a. What is the mean for food and lodging for a 10-day vacation?
Answers
Multiplying the underlying mean of $247 for a single day by 10 to account for the 10 days, the mean for food and lodging for a 10-day vacation is of $2470.
What is the mean per day cost?This problem is incomplete, but researching it on a search engine, it is found that the mean for a single day was of $247.
What is the mean for the entire trip?The entire trip was of 10 days, hence the mean is given as follows, multiplying the mean by the constant:
247 x 10 = $2,470.
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Information from the records of conundrum company for september was as follows: sales $307,500 selling and administrative expenses 52,500 direct materials used 66,000 direct labor 75,000 variable factory overhead 50,000 factory overhead 51,250 inventories sept. 1 sept 30 direct materials $ 8,000 $10,500 work in process 18,750 21,000 finished goods 17,250 14,250 conundrum company produced 20,000 units. the prime costs per unit (rounded to the nearest cent) for september were
Answers
The prime costs per unit (rounded to the nearest cent) for September were $7.05 per unit.
What is the total cost?In economics, total cost is the sum of all costs a company incurs in generating a certain output level.
It is typically expressed as the sum of all fixed costs (for example, the costs of a building lease and heavy machinery) that do not vary with the amount of output produced and all variable costs (the costs of labour & of raw materials).The concept of total cost is used to describe average cost (the total cost divided by the amount of units produced) and marginal cost (the marginal cost of a provided unit of output is the increase in total cost required to produce that unit).Now, as per the question;
Prime cost = (cost of direct material + cost of direct labour)/number of units.
Cost of direct materials used = $66,000
Cost of direct labour = $75,000
Number of units = 20,000
Substituting the values;
= ($66,000 + $75,000) / 20,000 units
= $141,000 / 20,000 units
= $7.05 per unit
Thus, the prime cost per unit in September is found to be $7.05 per unit.
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_____ is the process of drawing conclusions about unknown characteristics of a population from which data were taken.
Answers
Answer:
Statistical inference
Step-by-step explanation:
. The expression 3x+1 is equal to 9 for a certain value of x. Which of the following is the value of the
expression 12x+4 for the same value of x?
(1) 18
(3) 36
(2) 28
(4) 112
Answers
Answer:
(3) 36
Step-by-step explanation:
3x + 1 = 9
Minus 1 from both sides.
3x = 8
Divide both sides by 3.
x = 2 2/3
Plug it in.
12 (2 2/3) + 4
32 + 4
36
Is the following relation a function? Justify your answer.
Yes, because each output value has only one input value
Yes because each input value has only one output value
No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Answers
Answer:
No, because there is an output value with more than one input value.
Step-by-step explanation:
If you are using the same function equation, than you should not get the same output if you use two different inputs.
Solve 3.78 + (−13.2). anyone know the answer :,)
Answers
Answer:
-9.42
Step-by-step explanation:
Rewrite (4^7)^3 using a single exponent
Answers
Answer:
[tex]4^{21}[/tex]
Step-by-step explanation:
7 * 3 = 21
Add it as the exponent.
The cost per unit of an item is called what?
Answers
Answer:
The cost per unit of an item is called unit cost
Look at the diagram and evaluate. Which of the statements below is TRUE?
A). EH < EF
B). F is the midpoint of EG
C). GH< EF
D). FH> EG
Answers
The correct statement regarding the segments on the number line is:
C). GH< EF
Why the third statement is correct?For the first statement, the lengths are EH = 19 - 6 = 13 and EF = 11 - 6 = 5, hence EF < EH.For the second statement, we have that EF = 5 and EG = 9, since 5 is not the half of 9, it is not the midpoint.For the third statement, GH = 19 - 15 = 4 < EF = 5, hence it is the correct statement.For the fourth statement, EG = 9 > FH = 8, hence it is also not correct.More can be learned about segments at https://brainly.com/question/18315903
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Question
Find the equation of the line with slope
1/4
and y-intercept (0, -2).
Answers
Answer:
y=1/4 -2
Step-by-step explanation:
y =mx + c
m= slope
c= y-intercept
putting the valves of x and y ( 0,-2)
-2 = 1/4(0) + c
solve for C
C = -2
substituting back to the general equation of
y= 1/4x + C
y = 1/4x - 2( ans).
Find the output (y) of the function y
20x + 38 if the input (2) is -9.
Answers
A function assigns the values. The output(y) of the function y=20x + 38 if the input is -9 is -142.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function y=20x+38, therefore, if the input of the function is -9, then the output can be calculated by substituting the value of x as -9. Therefore, we can write the function as,
y = 20x + 38
y = 20(-9) + 38
y = -180 + 38
y = -142
Hence, the output(y) of the function y=20x + 38 if the input is -9 is -142.
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Better taxi service charges $3.00 for the first mile plus $0.20 for each additional mile. Best
taxi service charges $6.00 for the first two miles plus $0.10 for each additional mile. How
many miles will a person travel in order to spend an equal amount of money using either
service?
Answers
30 miles will a person travel in order to spend an equal amount of money using either service.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
Better taxi service charges $3.00 for the first mile plus $0.20 for each additional mile.
Best taxi service charges $6.00 for the first two miles plus $0.10 for each additional mile.
So, if equal amount of money spends on both services
3+0.2x = 3(2)+0.1x
3 +0.2x = 6 +0.1x
0.2x - 0.1x = 6-3
0.1x = 3
x = 30 miles
Hence, 30 miles will a person travel in order to spend an equal amount of money using either service.
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Find EFgiven E(-7, -2) and F(11, 3)
Answers
According to the given statement;
EF=18.682.
What is Distance Formula?
The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.
Distance formula used to find the distance measure between two lines, the sum of the lengths of all the sides of a polygon, perimeter of polygons on a coordinate plane, the area of polygons and many more.
According to the given value;
(-7, - 2) ; x1 = - 7 ; y1 = - 2
F = (11, 3) ; x2 = 11 ; y2 = 3
EF = √((x2 - x1)² + (y2 - y1)²)
EF = √((11 - -7)² + (3 - -2)²)
EF = √((11 + 7)² + (3 + 2)²)
EF = √(18² + 5²)
EF = √324 + 25
EF = √349
EF = 18.6815
EF = 18.682 units (3 decimal places )
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