Find the values of t6 and d for the arithmetic sequence with t6= 4 and t10= -4

t1 = 14  d= -2

Step-by-step explanation:

tn = t1 + d ( n-1)

t6 = t1 + d(6-1)

4 = t1+ 5d

t10 = t1 +d (10-1)

-4 = t1 +d9

Take the two equations and subtract to eliminate a1

4 = t1+ 5d

- (-4 = t1 +d9)

4 = t1+ 5d

+4 =- t1 -d9

8  =   -4d

Divide each side by -4

8/-4 = -4d/-4

-2 =d

Now we can find t1

4 = t1+ 5d

4 = t1 + 5(-2)

4 = t1 -10

Add 10 to each side

4+10 = t1

14 = t1

A

Step-by-step explanation:

t1 = a

tn = a + (n-1)d

t6 = a + 5d = 4

a = 4 - 5d

t10 = a + 9d = -4

4 - 5d + 9d = -4

-8 = 4d

d = -2

a = 4 - 5(-2)

= 4 + 10

= 14

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles