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4 years ago

What must be the value of x if (x,4) lies on the line 3x +y = 10

1 answer:

7 0

If (x, 4) lies on the line 3x+y=10, we can just substitute the values in
x=x and 4=y
3x+4= 10
Subtract 4 from each side
3x= 6
Divide by 3 on each side
x=2
so the x in (x,4) must be 2

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Nancy leaves the school and drives toward her town at 27 mph. greg leaves the same school 2 hours later and drives the same rout

Paul [167]

Nancy's rate=27 mph
Greg's rate=45 mph
t=Greg's time
t+2=Nancy's time
Since they both traveled same distance then:
27(t+2)=45t
27t+54=45t
18t=54
t=3 hours
Greg will pass Nancy after 3 hours

6 0

3 years ago

1. What is the solution to the system below?<br> x+y=5<br> 1x- y=3

Alika [10]

Answer:

(4,1)

Step-by-step explanation:

x+y=5

x- y=3

Add the equations together to eliminate y

x+y=5

x- y=3

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

2x = 8

Divide each side by 2

2x/2 = 8/2

x = 4

Now we can find y

x+y = 5

4+y = 5

Subtract 4 from each side

4+y-4 = 5-4

y =1

5 0

3 years ago

Find the value of x and y

djverab [1.8K]

Answer:

x = 8, y = 27

Step-by-step explanation:

Since both opposite lines are equal in length to each other, these opposite lines are parallel to each other. The top line is parallel and same length as the bottom line and the left and right lines are also parallel and equal in length.

Based on that, the two left side angles must equal 180 and the right side two angles must equal 180.

(2y + 24) + (3y + 21) = 180

That's the same as 2y + 24 + 3y + 21 = 180

Simplify to 5y + 45 = 180

Subtract 45 from both sides

5y = 135

y = 27

(16x - 26) + (9x + 6) = 180

16x - 26 + 9x + 6 = 180

25x - 20 = 180

25x = 200

x = 8

7 0

3 years ago

A radioactive substance decreases in the amount of grams by one-third each year. If the starting amount of the

katovenus [111]

Answer:

The sequence is geometric. The recursive formula is $a_{n}=2/3a_{n-1}$

Step-by-step explanation:

In order to solve this problem, you have to calculate the amount of the substance left after the end of each year to obtain a sequence and then you have to determine if the sequence is arithmetic or geometric.

The substance decreases by one-third each year, therefore:

After 1 year:

$1452-\frac{1}{3}(1452)$

Using 1452 as a common factor and solving the fraction:

$1452(1-\frac{1}{3})=1452(\frac{2}{3})=968$

You can notice that in general, after each year the amount of grams is the initial amount of the year multiplied by 2/3

After 2 years:

$968(\frac{2}{3})=\frac{1936}{3}$

After 3 years:

$\frac{1936}{3}(\frac{2}{3})=\frac{3872}{9}$

The sequence is:

1452,968,1936/3,3872/9....

In order to determine if the sequence is geometric, you have to calculate the ratio of two consecutive terms and see if the ratio is the same for all two consecutive terms. The ratio is obtained by dividing a term by the previous term.

The sequence is arithmetic if the difference of two consecutive terms is the same for all two consecutive terms.

-Calculating the ratio:

For the first and second terms:

968/1452=2/3

For the second and third terms:

1936/3 ÷ 968 = 2/3

In conclussion, the sequence is geometric because the ratio is common.

The recursive formula of a geometric sequence is given by:

$a_{n}=ra_{n-1}$

where an is the nth term, r is the common ratio and an-1 is the previous term.

In this case, r=2/3

7 0

3 years ago

Gracie is shipping a cube shaped box. It measures 14in x 14in x 14in. What is the surface area of the box?

DanielleElmas [232]

14× 14 = 196 area of 1 of the squares. on a cube there are 6 squares so multiply 196 by 6

196 × 6 = 1176 sq in

8 0

3 years ago