Towns A,B,C, and D
are located as shown in the accompanying figure. Two highways link Town A to Town D. Route 1 runs from Town A to Town D via Town B
, and Route 2 runs from Town A to Town D via Town C. If a salesman wishes to drive from Town A to Town D and traffic conditions are such that he could expect to average the same speed on either route, which highway should he take to arrive in the shortest time?
Answers
If the salesman chooses highway route 1 he will arrive in the shortest time because the distance in route 1 is less than the distance in route 2.
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Route 1:
The distance between A and D
Distance of AB:
[tex]\rm AB=\sqrt{(400-0)^2+(300-0)^2}[/tex]
AB = 500 mi
Distance between BD:
[tex]\rm BD=\sqrt{(1300-400)^2+(1500-300)^2}[/tex]
BD = 1500 mi
In route 1 the distance traveled by salesman:
AD = 500 + 1500 = 2000 mi
Route 2:
[tex]\rm AC=\sqrt{(800-0)^2+(1500-0)^2}[/tex]
AC = 1700 mi
[tex]\rm CD=\sqrt{(1300-800)^2+(1500-1500)^2}[/tex]
CD = 500 mi
AD(through C) = 1700 + 500 = 2200 mi
Thus, if the salesman chooses highway route 1 he will arrive in the shortest time because the distance in route 1 is less than the distance in route 2.
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Related Questions
Tell whether you can reach each type of conclusion below using coordinate
methods. Give a reason for each answer.
6. AB = CD
9. AB bisects CD.
12. LA is a right angle.
15. Quadrilateral ABCD is a rhombus.
8. ABL CD
11. LA LB
14. AABC is isosceles.
16. AB and CD bisect each other.
7. AB || CD
10. AB bisects LCAD.
13. AB + BC = AC
Answers
The answer to all of them is yes.
6) The lengths of AB and CD using the distance formula. (because congruent segments have equal length)
7) The slopes of AB and CD are equal using the slope formula. (because parallel segments have equal slopesL
8) The slopes of AB and CD are negative reciprocals using the slope formula. (because perpendicular lines have slopes that are negative reciprocals)
9) The two segments that CD is split into by AB have equal length using the distance formula. (because a segment bisector splits a segment into two congruent segments, and congruent segments have equal length)
10) Angles CAB and DAB have the same measure using the angle between two lines formula. (Because an angle bisector splits an angle into two congruent angles, and congruent angles have equal measure)
11) Angles A and B have the same measure using the angle between two lines formula. (Because an angle bisector splits an angle into two congruent angles, and congruent angles have equal measure)
12) The lines that form angle A have slopes that are negative reciprocals using the slope formula. (because perpendicular lines have slopes that are negative reciprocals, and perpendicular lines form right angles)
13) The lengths of AB and AC combined equal the length of AC using the distance formula.
14) Two sides of triangle ABC have equal length using the distance formula.
15) All four sides of ABCD have the same length using the distance formula.
16) Letting AB and CD meet at E, the distance formula says AE=BE and CE=DE.
In the triangle below, what is the measure of
Answers
Answer:
D. 30°
Step-by-step explanation:
QP and QR have the same length "8" , therefore, the triangle is an isosceles triangle. Opposite angles are congruent.
- ∠R = ∠P
- ∠R = 30°
-----------------------------
Mr. Thompson has a 1-meter-square whiteboard. He creates a square with sides on his whiteboard to post a weekly puzzle. How many square meters of whiteboard space does he use for the weekly puzzle?
Answers
Answero
Step-by-step explanation:
i dont know
Due ti the board being 1 meter
Can someone help me out on this problem and show work
Answers
200/250 = 4/5 = 0.8
250
200 | 250 x 0.8 = 200
160 | 200 x 0.8 = 160
128 | 160 x 0.8 = 128
102.4 | 128 x 0.8 = 102.4
81.92 | 102.4 x 0.8 = 81.92
HOPES THIS HELPS! PLEASE MARK ME BRAINLIEST PLS
PLEASE HELP< GEOMTREY SUCKS!!!!!!!!!
Answers
Answer:
The measure of angle DCB = 125
Step-by-step explanation:
This is because angle ACD and angle DCB are supplementary.
Supplementary angles are two angles with a sum of 180 degrees, and we know these angles are supplementary by the fact that angle ACB = 180 degrees.
What is the value of X
Answers
Answer:
x = 10
Step-by-step explanation:
BF is two times AX so
2 ( 2x+10) = 5x+10
4x + 20 = 5x + 10
x = 10
The question is on the picture below
Answers
Answer: 54
Step-by-step explanation:
By the inscribed angle theorem, angle ZXY measures half of 108 degrees, which is 54 degrees.
A full can of milk weighs 70 pounds. If exactly half of the milk is poured out, it weighs 38 pounds. How much does the empty can weigh?
Answers
Answer:
6 pounds
Step-by-step explanation:
Let the can weigh x pounds
Let the milk weigh y when full, therefore half is [tex]\frac{y}{2}[/tex]
Now we for 2 simultaneous equations:
[tex]x + y =70[/tex] ....(i)
[tex]x+ \frac{y}{2}= 38[/tex] .... (ii)
we solve by eliminating the x in both equation throug subtraction
[tex]x - x + y- \frac{y}{2} =70-38\\y- \frac{y}{2} = 32\\\frac{y}{2} = 32\\y=2(32)\\y=64\\x+y=70\\x+64=70\\x=6[/tex]
There are 8 kids at a birthday party. If there are 5 girls and 3 boys at a party, what fraction of the kids are girls?
Answers
Answer:
5/8 fraction of kids are girls
P(A) = 1/2
P(ANB) = 1/5
What will P(B) have to be for A and B to be independent?
4/10
1/10
03/10
7/10
Answers
Answer:
4/10
Step-by-step explanation:
If A and B are independent events, P(A∩B) = P(A).P(B)
Therefore, P(B) = P(A∩B) /P(A)
P(A∩B) = 1/5, P(A) = 1/2
P(B) = 1/5 ÷ 1/2 = 1 /5 * 2/1 = 2/5 which is 4/10 if you multiply numerator and denominator by 2
2) Express 34m 5cm 6mm in millimeteres
Answers
Answer:
34079 millimeters
Step-by-step explanation:
__________________________________
I assume you mean millimeters, but
34 m = 34000 millimeter4 cm = 4 centimeters = 40 millimeter5 mm = 5 millimeterAll together adds up to 79 millimeter
34000 + 40 + 5 = 34079 mm
__________________________________
Hope this helped
(Edit) Sorry I didn't see meters
Solve for x
Help pls asap
Answers
Answer:
x = 8
Step-by-step explanation:
Because they are alternate exterior angles, the two angles must equal to each other. You can set up the equation:
9x-2 = 8x + 6
And then solve for x.
______________
9x - 2 = 8x + 6
9x - 8x = 6 + 2
x = 6 + 2
x = 8
Write the product in its simplest form:
c•9c
Answers
c squared
Convert 2077 to base eight
Answers
To convert 2077₁₀ to base eight is 4035₈
How to convert 2077 to base 8?Since 2077 is in base 10, to convert it to base 8, we successively divide it by 8 and keep the remainder. We divide until we have zero as the dividend then count the remainder from bottom to top.
So, to convert 2077 to base 8, we have
2077 ÷ 8 = 259 r 5
259 ÷ 8 = 32 r 3
32 ÷ 8 = 4 r 0
4 ÷ 8 = 0 r 4
So, counting the remainders from bottom to top, we have 4035₈
So, 2077₁₀ = 4035₈
So, to convert 2077₁₀ to base eight is 4035₈
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The coordinates of the vertices of quadrilateral ABCD are (0,-4) (-4,3) (3,4) (6,-1)
Answers
Based on the given coordinates of the quadrilateral ABCD, the slopes of the lines given at:
Slope of AB = -7/4Slope of BC = 1/7Slope of CD = -5/3Slope of AD = 1/2What are the slopes of the line?The slope of AB is:
= (3 - (-4)) / (-4 - 0)
= -7/4
The slope of BC:
= (4 - 3) / (3 - (-4))
= 1/7
The slope of CD:
= (-1 - 4) / (6 - 3)
= -5/3
The slope of AD:
= (-1 - (-4)) / (6 - 0)
= 1/2
The rest of the question is:
The slope of AB ¯ ¯ ¯ ¯ ¯ is , the slope of BC ¯ ¯ ¯ ¯ ¯ is , the slope of CD ¯ ¯ ¯ ¯ ¯ is , and the slope of AD ¯ ¯ ¯ ¯ ¯.
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On a quiz show, Linda won $10 less than three times as much as Charlie. If Linda won $800, how much did Charlie win?
Answers
Using a system of equations, it is found that Charlie won $270.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Amount earned by Linda.Variable y: Amount earned by Charlie.Linda won $10 less than three times as much as Charlie, hence:
x = 3y - 10
Linda won $800, hence the amount won by Charlie is found as follows:
800 = 3y - 10
3y = 810
y = 810/3
y = 270
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The scale on a map is 1 cm : 6 km. If two cities are 13 cm apart on the map, what is the actual distance between the cities?
Answers
Answer:
78 km!
Step-by-step explanation:
13 cm * 6 km per cm = 78 km in actual distance
Help I need this urgently!!!!
Answers
Which of the following inequality should be graphed with a dashed line? Select all that apply.
(I think B is one of the correct answers?)
Answers
Answer:
B, D
Step-by-step explanation:
Any inequality that does not include the "or equal to" case will be graphed with a dashed line.
ApplicationThe "or equal to" case is included when the inequality symbol is one of ≤ or ≥. When symbols > or < are used, the boundary line of the solution space is dashed (or the end point on the number line is an open circle).
The inequalities that will be graphed with a dashed line are ...
2x -4y < 12 . . . . choice Bx +7 > -1 . . . . . . .choice D-4,12-5-22,24-100,37 ordenar de menor a mayor
Answers
Answer: 24 - 100, 12 - 5 - 22, -4, 37
Step-by-step explanation:
Simplificar:
-4 = -4
12 - 5 - 22 = -15
24 - 100 = -76
37 = 37
Ordenar de menor a mayor:
-76, -15, -4, 37
\/
24 - 100, 12 - 5 - 22, -4, 37
12 - 5 - 22=-15
- 4, lo mismo
37, lo mismo
La orden es:
-76, -15, -4, 37
Let $m$ and $n$ be positive integers such that $m$ has exactly 5 positive divisors, $n$ has exactly 6 positive divisors, and $mn$ has exactly 14 positive divisors. How many distinct prime factors does $mn$ have
Answers
If [tex]A[/tex] is the set of positive divisors of [tex]m[/tex] and [tex]B[/tex] the set of positive divisors of [tex]n[/tex], then [tex]A\cup B[/tex] is the set of positive divisors of [tex]mn[/tex].
Use the inclusion/exclusion principle:
[tex]|A \cup B| = |A| + |B| - |A \cap B|[/tex]
where [tex]|\cdot|[/tex] denotes set cardinality (the number of elements the set contains). The set [tex]A\cap B[/tex] is the set of common divisors of [tex]m[/tex] and [tex]n[/tex]. Then
[tex]14 = 5 + 6 - |A\cap B| \implies |A\cap B| = 3[/tex]
so that [tex]m[/tex] and [tex]n[/tex] share 3 divisors [tex]d_1,d_2,d_3[/tex]; let [tex]k=d_1d_2d_3[/tex] be their product. They must be prime
This means we can write
[tex]m = p_1 p_2 k[/tex]
[tex]n = p_3 p_4 p_5 k[/tex]
[tex]\implies mn = p_1 p_2 p_3 p_4 p_5 k^2 = p_1 p_2 p_3 p_4 p_5 {d_1}^2 {d_2}^2 {d_3}^2[/tex]
so that [tex]mn[/tex] has up to 8 distinct prime factors.
Estimate the difference:7 3/4 x 2 2/5 . Show your work.
Answers
Answer:
16
Step-by-step explanation:
7 3/4 rounds to 8
2 2/5 rounds to 2
8 times 2=16
I really need help!!!
Solve each equation by using the Quadratic Formula. Round to the nearest tenth
if necessary.
72. x²-25=0
75. 2r²+r- 14 = 0
73. r²+25=0
76. 5v^2-7v = 1
Answers
Answer:
72. 5
73. -5
74.r =2.40753645…,−2.90753645
75. v =1.53066238…,−0.13066238
Step-by-step explanation:
g Consider a brand of coffee. The weight of a pod of coffee this brand makes has mean 42.05 grams and standard deviation 0.025 grams. Using the central limit theorem and the normal distribution, what is the probability that the mean weight of 25 pods of coffee is less than 42.035 grams
Answers
Using the normal distribution, it is found that there is a 0.0013 = 0.13% probability that the mean weight of 25 pods of coffee is less than 42.035 grams.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 42.05, \sigma = 0.025, n = 25, s = \frac{0.025}{\sqrt{25}} = 0.005[/tex]
The probability that the mean weight of 25 pods of coffee is less than 42.035 grams is the p-value of Z when X = 42.035, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{42.035 - 42.05}{0.005}[/tex]
Z = -3
Z = -3 has a p-value of 0.0013.
0.0013 = 0.13% probability that the mean weight of 25 pods of coffee is less than 42.035 grams.
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Which statement correctly explains how to prove △ABC∼△DEF?
Answers
Answer:
A
Step-by-step explanation:
calculate the ratios AB/DE BC/EF AND AC/DF。their ratios are 1/2
Answer:
Step-by-step explanation:
the first because the ratio is always from a small to a large triangle, and it is right, the second is wrong, the sides are not congruent, the third is also wrong, the last ratio is wrong
Solve: (6x2 + 5x + 1) + (x + 2).
Answers
Answer:
6x+6x2+3
Step-by-step explanation:
6x2+5x+1+x+2
Combine 5x and x to get 6x.
6x2+6x+1+2
Add 1 and 2 to get 3.
6x2+6x+3
The simplified form of the expression (6x² + 5x + 1) + (x + 2) is 6x^2 + 6x + 3.
To solve the expression (6x² + 5x + 1) + (x + 2)
we need to combine like terms.
First, let's remove the parentheses:
6x² + 5x + 1 + x + 2
Next, we combine like terms:
6x² + (5x + x) + (1 + 2)
Simplifying further:
6x^2 + 6x + 3
Therefore, the simplified form of (6x² + 5x + 1) + (x + 2) is 6x² + 6x + 3.
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The school that Natalie goes to is selling tickets to a play. On the first day of ticket sales the school sold 14 adult tickets and 3 student tickets for a total of $195. The school took in $306 on the second day by selling 15 adult tickets and 14 student tickets. What is the price each of one adult ticket and one student ticket
Answers
The price of an adult ticket is 12$.
And the price of a student ticket is 9$.
Let ‘x’ be the price of an adult ticket.
Let ‘y’ be the price of a student ticket.
On the first day of ticket sales, the school sold 14 adult tickets and 3 student tickets for a total of $195 i.e
14x + 3y = 195$ i)
15x + 14y = 306$ ii)
from equation i) we get the value of y,
y = (195 - 14x)/3
put this value of y in equation ii) we get,
= 15x +14{(195 - 14x)/3} = 306
= (45x +2730 - 196x)/3 = 306
= (45x +2730 - 196x) = 918
= -151x = -1812
= x =12$
then value of y we get ,
put value of x in y,
y = (195 - 14*12)/3
= 27/3
= 9$
hence, the price of an adult ticket is 12$.
And the price of a student ticket is 9$.
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Kamal sells 240 ice creams for a total of £640
1/3 of the ice creams he sells are large.
The cost of each large ice cream he sells is £3.80
All the other ice creams he sells are small.
He sells each small ice cream for the same cost.
Work out the cost of each small ice cream.
Answers
Answer:
2.10
Step-by-step explanation:
# of large ice creams: 240/3 = 80
# of small ice creams: 240 - 80 = 160
Total large ice cream cost: 80*3.8 = 304
Total small ice cream cost: 640 - 304 = 336
Cost of one small ice cream: 336/160 = 2.1
i need help fast please
Answers
Answer:
D
Step-by-step explanation:
Triangle PQR is scaled 3x the size of Triangle LMN. This means that if length LM is 3cm, just multiply it by 3 to get length PQ, 9cm
Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by step?
Thanks in advance!
Answers
If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate [tex]x^4[/tex].
We have
[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h[/tex]
Expand the numerator using the binomial theorem, then simplify and compute the limit.
[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}[/tex]
In general, the derivative of a power function [tex]f(x) = x^n[/tex] is [tex]\frac{df}{dx} = nx^{n-1}[/tex]. (This is the aptly-named "power rule" for differentiation.)