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Travka [436]
3 years ago
6

Find the x- and y- intercepts of the line with the given equation -6x+8y=-36

Mathematics
2 answers:
Likurg_2 [28]3 years ago
5 0

Answer:

Y int at

(

0

,

3

2

)

X int at

(

3

,

0

)

Step-by-step explanation:

The line is easier to visualize when the equation is in slope-intercept form:

4

x

+

8

y

=

12

Divide each side by 4:

x

+

2

y

=

3

2

y

=

−

x

+

3

y

=

−

1

2

x

+

3

2

Y-intercept (plug in 0 for x):

y

=

−

1

2

(

0

)

+

3

2

y

=

3

2

X-intercept (plug in 0 for y):

0

=

−

1

2

x

+

3

2

−

3

2

=

−

1

2

x

x

=

3

user100 [1]3 years ago
3 0

Answer:

x-intercept (6,0)

y-intercept (0,-4.5)

Step-by-step explanation:

the x-intercept will be when y=0

and the y-intercept will be when x=0

so

y=0\\\\-6x+8(0)=-36\\\\-6x=-36\\\\x=6

so the x intercept will be at (6,0)

x=0\\\\-6(0)+8y=-36\\\\8y=-36\\\\y=-\frac{9}{2}\\\\y=-4.5

so the y intercept will be at (0,-4.5)

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Find the number of elements in A 1 ∪ A 2 ∪ A 3 if there are 200 elements in A 1 , 1000 in A 2 , and 5, 000 in A 3 if (a) A 1 ⊆ A
lina2011 [118]

Answer:

a. 4600

b. 6200

c. 6193

Step-by-step explanation:

Let n(A) the number of elements in A.

Remember, the number of elements in A_1 \cup A_2 \cup A_3 satisfies

n(A_1 \cup A_2 \cup A_3)=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)

Then,

a) If A_1\subseteq A_2, n(A_1 \cap A_2)=n(A_1)=200, and if A_2\subseteq A_3, n(A_2\cap A_3)=n(A_2)=1000

Since A_1\subseteq A_2\; and \; A_2\subseteq A_3, \; then \; A_1\cap A_2 \cap A_3= A_1

So

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-200-200-1000-200=4600

b) Since the sets are pairwise disjoint

n(A_1 \cup A_2 \cup A_3)=\\n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\200+1000+5000-0-0-0-0=6200

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-2-2-2-1=6193

8 0
2 years ago
. Un turist a parcurs un traseu în trei zile. În prima zi turistul a parcurs
Dahasolnce [82]

Answer:

The total length of route travelled in 3 days = 30 km

Lungimea traseului parcurs în cele trei zile = 30 km

Step-by-step explanation:

English Translation of the Question

A tourist traveled a route in three days. On the first day the tourist covered 40% of the length of the route, on the second day the tourist covered 5/6 of the remaining distance after the first day, and on the third day the remaining 3 km. Calculate the length of the route traveled in the three days.

Let the total length of the route be x.

Lungimea traseului parcurs în cele trei zile = x

- On the first day, the tourist covers 40% of the total length of the route;

În prima zi turistul a parcurs 40% din lungimea traseului

That is, 40% of x = 0.4x

- On the second day, the tourist covered 5/6 of the remaining journey.

în a doua zi turistul a parcurs 5/6 din distanța rămasă de parcurs după prima zi

The remaining journey after day 1 = x - 0.4x = 0.6x

(5/6) of the remaining journey = (5/6) × 0.6x = 0.5x

- On the third day, the toursit travels the total remaining length of the route = 3 km

iar în a treia zi restul de 3 km

The total remaining length of the route = x - 0.4x - 0.5x = 0.1x

0.1x = 3

x = (3/0.1) = 30 km

The Hope this Helps!!!

3 0
3 years ago
Martin starts at 300 and counts by fives to 420. What are the last 6 numbers Martin will say?
Neko [114]
The last six numbers are:
390, 395, 400, 405, 410, 415
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3 0
3 years ago
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Find the exact value cos5pi/6
Lelechka [254]

Answer:

-  \frac{ \sqrt{3} }{2}

Step-by-step explanation:

Unit circle

5 0
3 years ago
team rise over run finished the last 12 miles in 1/2 an hour what was their average speed in miles per hour
saveliy_v [14]

Answer:

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Step-by-step explanation: it’s been half an hour and they ran the 12 miles so in an hour which is double half an hour they ran two times what they did in half an hour

4 0
3 years ago
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