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?

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

Answer:

5/8 fraction of kids are girls

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.

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.

Using a system of equations, it is found that Charlie won $270.

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:

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

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

To convert 2077₁₀ to base eight is 4035₈

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

Learn more about convert to base eight here:

https://brainly.com/question/13556214

#SPJ1

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

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

Answer:

78 km!

Step-by-step explanation:

13 cm * 6 km per cm = 78 km in actual distance

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°

-----------------------------

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.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ6

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

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.

Answero

Step-by-step explanation:

i dont know

Answer: 54

Step-by-step explanation:

By the inscribed angle theorem, angle ZXY measures half of 108 degrees, which is 54 degrees.

Answer:

34079 millimeters

Step-by-step explanation:

__________________________________

I assume you mean millimeters, but

All together adds up to 79 millimeter

34000 + 40 + 5 = 34079 mm

__________________________________

Hope this helped

(Edit) Sorry I didn't see meters

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

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]

Based on the given coordinates of the quadrilateral ABCD, the slopes of the lines given at:

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 ¯ ¯ ¯ ¯ ¯.

Find out more on the slope of line at https://brainly.com/question/3493733.

#SPJ1

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

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.

The "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 ...

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.

The 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 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.

More can be learned about the normal distribution at https://brainly.com/question/4079902

#SPJ1

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 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$.

Learn more about solving equations here

https://brainly.com/question/1202328

#SPJ4

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.)

Answer:

16

Step-by-step explanation:

7 3/4 rounds to 8

2 2/5 rounds to 2

8 times 2=16

Answer:

72. 5

73. -5

74.r =2.40753645…,−2.90753645

75. v =1.53066238…,−0.13066238

Step-by-step explanation: