I got carried away I need a lil help.<br><br>calculate 57% of $295 to the nearest cent

A sequence of three real numbers forms an arithmetic progression with a ﬁrst term of 9. If 2 is added to the second term and 20

Alexxandr [17]

Answer:

The smallest possible value for the third term of the geometric progression is 1.

Step-by-step explanation:

Given : A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression.

To find : What is the smallest possible value for the third term of the geometric progression?

Solution :

The arithmetic progression is given by $a,a+d,a+2d$

First term a=9

Second term - 2 is added to second term i.e. $a+d+2=9+d+2=11+d$

Third term - 20 is added to the third term i.e. $a+2d+20=9+2d+20=29+2d$

The geometric progression is given by $a,ar,ar^2$

First term a=9

Second term - $ar=11+d$

Third term $ar^2=29+2d$

r is the common ratio which is second term divided by first term,

So, $r=\frac{ar}{a}=\frac{11+d}{9}$

or third term divided by second term,

So, $r=\frac{ar^2}{ar}=\frac{29+2d}{11+d}$

Equating both the r,

$\frac{11+d}{9}=\frac{29+2d}{11+d}$

Cross multiply,

$(11+d)\times (11+d)=(29+2d)(9)$

$11^2+11d+11d+d^2=261+18d$

$121+22d+d^2-261-18d=0$

$d^2+4d-140=0$

Solving by middle term split,

$d^2+14d-10d-140=0$

$d(d+14)-10(d+14)=0$

$(d+14)(d-10)=0$

$d=-14,10$

Substituting the value of d in the third term,

Third term $ar^2=29+2d$

When d=-14,

Third term $ar^2=29+2(-14)=29-28=1$

When d=10,

Third term $ar^2=29+2(10)=29+20=49$

Therefore, The smallest possible value for the third term of the geometric progression is 1.

7 0

3 years ago

Simplify using the distributive property 6(y-8)

densk [106]

Answer:

6y - 48

Step-by-step explanation:

Using distributive property 6(y-8)

= 6(y) - 6(8)

= 6y - 48

6 0

3 years ago

Which process contributes to the formation of tornados? a. water droplets freeze, giving off energy b. the storm begins to rotat

Mashutka [201]

Answer:

D. A cold, dry air mass interacts with a warm, moist air mass.

Step-by-step explanation:

Tornadoes are very scary and kind of cool to look at. They have a great scientific reason behind them which we can easily understand. First, a funnel cloud forms that reaches down to the ground (you probably have seen this in video as a cloud that is heavily densed and circling). Then , warm air rises, resulting in a decrease in air pressure and finally, a cold, dry air mass interacts with a warm, moist air mass.

6 0

3 years ago

Find the value of x. If necessary, round to the nearest tenth.

Ghella [55]

Answer:

x = 10.3 in

Step-by-step explanation:

To find the value of a, use the area formula for a triangle. The formula is A = 1/2 *b*h. Here b = x and h= x. The formula becomes A = 1/2 *x². Substitute A = 53 and solve for x by using inverse operations.

A = 1/2x²

53 = 1/2x²

106 = x²

√106 = x

10.3 = x

5 0

3 years ago

a middle school has 520 students, 75% of the students ride the bus to school. How many students do not ride the bus to school?

Nata [24]

Answer:

130 students do not ride the bus to school.

Step-by-step explanation:

520 * .75 = 390

390 students ride the bus to school.

520-390=130

130 students do NOT ride the bus to school.

Hope this helps! :)

6 0

3 years ago

I got carried away I need a lil help.calculate 57% of $295 to the nearest cent​

I got carried away I need a lil help.calculate 57% of $295 to the nearest cent