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Andrew [12]
2 years ago
6

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

Mathematics
2 answers:
algol132 years ago
7 0

Answer:

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

brilliants [131]2 years ago
6 0

Answer:

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

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Hank has to drain his pool so repairs can be done on a crack on the bottom. The company coming to fix the pool is scheduled to a
Alik [6]

Answer:

The answer to the question: "Will Hank have the pool drained in time?" is:

  • <u>Yes, Hank will have the pool drained in time</u>.

Step-by-step explanation:

To identify the time Hank needs to drain the pool, we can begin with the time Hank has from 8:00 AM to 2:00 PM in minutes:

  • Available time = 6 hours * 60 minutes / 1 hour (we cancel the unit "hour")
  • Available time =  360 minutes

Now we know Hank has 360 minutes to drain the pool, we're gonna calculate the volume of the pool with the given measurements and the next equation:

  • Volume of the pool = Deep * Long * Wide
  • Volume of the pool = 2 m * 10 m * 8 m
  • Volume of the pool = 160 m^3

Since the drain rate is in gallons, we must convert the obtained volume to gallons too, we must know that:

  • 1 m^3 = 264.172 gal

Now, we use a rule of three:

If:

  • 1 m^3 ⇒ 264.172 gal
  • 160 m^3 ⇒ x

And we calculate:

  • x = \frac{160 m^{3}*264.172 gal }{1m^{3} } (We cancel the unit "m^3)
  • x = 42267.52 gal

At last, we must identify how much time take to drain the pool with a volume of 42267.52 gallons if the drain rate is 130 gal/min:

  • Time to drain the pool =\frac{42267.52gal}{130\frac{gal}{min} }(We cancel the unit "gallon")
  • Time to drain the pool = 325.1347692 minutes
  • <u>Time to drain the pool ≅ 326 minutes</u> (I approximate to the next number because I want to assure the pool is drained in that time)

As we know, <u><em>Hank has 360 minutes to drain the pool and how it would be drained in 326 minutes approximately, we know Hank will have the pool drained in time and will have and additional 34 minutes</em></u>.

7 0
2 years ago
Type the correct answer in the box. Round your answer to the nearest integer.
umka21 [38]

Answer:

m∠ADC = 132°

Step-by-step explanation:

From the figure attached,

By applying sine rule in ΔABD,

\frac{\text{sin}(\angle ABD)}{\text{AD}}=\frac{\text{sin}(\angle ADB)}{AB}

\frac{\text{sin}(120)}{35}=\frac{\text{sin}(\angle ADB)}{30}

sin(∠ADB) = \frac{30\text{sin}(120)}{35}

                 = 0.74231

m∠ADB = \text{sin}^{-1}(0.74231)

             = 47.92°

             ≈ 48°

m∠ADC + m∠ADB = 180° [Linear pair of angles]

m∠ADC + 48° = 180°

m∠ADC = 180° - 48°

m∠ADC = 132°

4 0
3 years ago
Fill in the missing numbers in these equations
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Give me the equations
6 0
3 years ago
Which equation represents a line with a slope of zero?
elena55 [62]
Y=4 because it only has a y-intercept
3 0
2 years ago
​= <br> The solution set is <br> ​ 1/2(10x+16)-13=-3/5(15x-35)
-BARSIC- [3]

Answer: 13/7 or as a decimal 1.857142857

How did i get the answer:

Step 1: Simplify both sides of the equation.

so 1/2 of 10 is 5, 1/2 of 16 is 8

-3/5 of 15 is -9 and -3/5 of -35 is POSITIVE 21

all together should look like 5x+8+−13=−9x+21

(now we have to combine like terms)

8+ -13= -5

5x -5 = -9x+21

Step 2: Add 9x to both sides

5x + 9x= 14x

14x -5 = 21

Step 3: Add 5 to both sides.

21+5= 26

14x=26

Step 4: Divide both sides by 14.

26/14= 1.85714286 or 13/7

8 0
2 years ago
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