Find the sum of a 22-term arithmetic sequence, where the first term is 7 and the last term is 240.

Answer:

Problem 1)  frequency:  160 heartbeats per minute, period= 0.00625 minutes (or 0.375 seconds)

Problem 2) Runner B has the smallest period

Problem 3) The sound propagates faster via a solid than via air, then the sound of the train will arrive faster via the rails.

Step-by-step explanation:

The frequency of the football player is 160 heartbeats per minute.

The period is (using the equation you showed above):

[tex]Period = \frac{1}{frequency} = \frac{1}{160} \,minutes= 0.00625\,\,minutes = 0.375\,\,seconds[/tex]

second problem:

Runner A does 200 loops in 60 minutes so his frequency is:

[tex]\frac{200}{60} = \frac{10}{3} \approx 3.33[/tex]   loops per minute

then the period is: 0.3 minutes (does one loop in 0.3 minutes)

the other runner does 200 loops in 65 minutes, so his frequency is:

[tex]\frac{200}{65} = \frac{40}{13} \approx 3.08[/tex]   loops per minute

then the period is:

[tex]\frac{13}{40} =0.325\,\,\,minutes[/tex]

Therefore runner B has the smaller period

Answer:

7 and 1

Step-by-step explanation:

Let the numbers be a and b.

A positive number is 7 times another number:

If 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number:

To solve this we substitute a with 7b in the second equation:

Then, finding a:

So the numbers are 7 and 1

ω in terms of m and k is expressed as  [tex]\omega = \sqrt{\frac{k}{m} }[/tex]

The given expression is as follows;

     [tex]T_s = 2\pi \sqrt{\frac{m}{k} } , \ \ \\\\ T_s = \frac{2\pi}{\omega}[/tex]

To find:

From the given expression above make ω the subject of the formula;

[tex]T_s = \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} } \\\\ \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} }\\\\ \frac{2\pi}{\omega} = \sqrt{4\pi^2\frac{m}{k} }\\\\square \ both \ sides \ of \ the \ equation;\\\\(\frac{2\pi}{\omega})^2 = 4\pi^2\frac{m}{k} \\\\\frac{4\pi^2}{\omega^2}= \frac{4\pi^2m}{k} \\\\\omega^2 4\pi^2m = k4\pi^2 \\\\divide \ both \ side \ by \ 4\pi ^2 \\\\\omega^2 m = k\\\\divide \ both \ sides \ by \ m\\\\\omega^2 = \frac{k}{m} \\\\[/tex]

[tex]take \ the \ square \ root \ of \ both \ sides \ of \ the \ equation\\\\\omega = \sqrt{\frac{k}{m} }[/tex]

Therefore, ω in terms of m and k is expressed as [tex]\omega = \sqrt{\frac{k}{m} }[/tex]

To learn more about subject of formula visit: https://brainly.com/question/15469690

Answer:

EAT THIS ANDAD Which polynomial has (3x + 2) as a binomial factor?

6x3 + 3x2 + 4x + 2

12x2 + 15x + 8x + 10

18x3 – 12x2 + 9x – 6

21x4 + 7x3 + 6x + 2

Step-by-step explanation:

Answer:

The amount of balls on each side would stay the same. The amount of balls would stay the same as long as both sides are throwing the same number of balls at the same time.

Step-by-step explanation:

Equation for east side: 20 (balls) -1 (thrown over to west) + 1 (thrown over from west) = 20 balls

Equation for west side: 40 (balls) -1 (thrown over to east side) +1 (thrown over by east side) = 40 balls

Answer:

[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]

Step-by-step explanation:

[tex]2x^2-8x=-7[/tex]

[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]

[tex]2x^2-8x+7=-7+7[/tex]

[tex]2x^2-8x+7=0[/tex]

[tex]ax^2 +bx+c=0[/tex]

[tex]\sf Apply \ quadratic \ formula.[/tex]

[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]

[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]

[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]

[tex]x=2\pm \frac{\sqrt{2}}{2}[/tex]

Answer:

D

Step-by-step explanation:

your function is not very clear but I'm assuming it's 2 multiplied by 7^x

first let y be equal to the function

to find the range interchange x and y and make the subject

at some point you'll have to use logarithm to get rid of the exponent

only log of positive numbers numbers exist hence y must be greater than 0

Answer:

see below (I hope this helps!)

Step-by-step explanation:

We can split this into 2 cases:

3x + 2 > 9 or -(3x + 2) > 9

3x > 7 or 3x + 2 < -9

x > 7/3 or x < -11/3

Answer:

19/90

Step-by-step explanation:

0.2(1)

We know that most recurring decimals like this have a 9

We know that it can't be anything over 99, or else all digits will repeat:

0.212121....

It will be a number over 90, which will be 19/90

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

15/4 x-y=-24

Step-by-step explanation:

the standard form is ax+by=c

two points (x1,x2) , (y2,y1)

x1=-8       x2=-6

y1=-4        y2=9

find slope m: y2-y1/x2-x1

m=9-(-6)/-4-(-8)

m=15/4

find b: take any point(-8,-6)

y=mx+b

-6=15/4 (-8)+b

-6=-30+b

b=-6+30

b=24

y=15/4 x+24

standard form: y-15/4x=24

OR : 15/4 x-y=-24

it depends upon a persons pace a average pace is 9-10 mins

Answer:

2c +7d

Step-by-step explanation:

2c+2d+5d

Combine like terms

2c + d(2+5)

2c +7d

Answer:

The simplified answer of this expression is 2c + 7d

Step-by-step explanation:

For this problem, you will have to combine like terms.

2c + 2d + 5d

Combine 2d and 5d.

2c + 7d

Answer:

the awnser is d 1000 pediatricians

Answer:

infinite solutions

Step-by-step explanation:

If we have and identity such as

3=3

Then we have infinite solutions since the identity is always true

Answer:

[tex] 0.88^x [/tex]

Step-by-step explanation:

Exponential decay formula is given as [tex] a(1 - r)^x [/tex], where,

a is the initial amount

r is the decay rate

x is the time interval

Therefore, the multiplier that corresponds to 12% decay is [tex] (1 - r)^x = (1 - \frac{12}{100})^2 = (1 - 0.12)^x = 0.88^x [/tex]

Answer:

-3

Step-by-step explanation:

-7+4=-3

The absolute value of -3 is 3

The negative sign in front of the absolute value bracket makes it -3

Answer:

(2,−6)+(9,9)

(12,−5)⋅(5,6)

(4,4)⋅(4,4)

Step-by-step explanation:

Try one of these answers

Answer:

Let's simplify step-by-step.

2x(3−1)+3

=4x+3

Step-by-step explanation:

2x[3-1]=6x-2x=4x

4x+3

Answer:

x = 50

Step-by-step explanation:

Since the angle is right = 90°, then

40 + x = 90 ( subtract 40 from both sides )

x = 50

Answer:

[tex]\boxed{\sf x = 50\ degrees}[/tex]

Step-by-step explanation:

x = 90 - 40    [Complementary angles add up to 90 degrees]

x = 50 degrees

Answer:

Step-by-step explanation:

9) 9xt

10) r-10

Answer:

Hey there!

We can write an equation:

x+x+1+x+2=7

3x+3=7

3x+4

x=4/3

The lines are 4/3, 7/3, and 10/3.

Let me know if this helps :)

[tex](3x^2 - 4x + 1) + (-x^2 + x - 9)=\\3x^2-4x+1-x^2+x-9=\\2x^2-3x-8[/tex]

Answer:

6 + 8x

46

Step-by-step explanation:

1. Write the expression

6 + 8x

2. Plug in 5 for x

6 + 8(5) → 6 + 40 = 46

Answer:

Expression=8x+6

The value of expression=46

━━━━━━━☆☆━━━━━━━

▹ Answer

a = 8

▹ Step-by-Step Explanation

a/4 + 4 = 6

Multiply both sides:

a + 16 = 24

Subtract 16 from both sides:

16 - 16 = a

24 - 16 = 8

a = 8

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

a = 8

Step-by-step explanation:

a/4 + 4 = 6

Subtract 4 from each side

a/4 + 4-4 = 6-4

a/4 = 2

Multiply each side  by 4

a/4 * 4 = 2*4

a = 8

Plugging in the values, we see that object 1 has more potential energy (the ball to the left)

Answer:

The answer is below

Step-by-step explanation:

The ratio of Keith's height and his nephew's height is 15:7. Let keith height be x cm and his nephews height be y cm.

[tex]\frac{x}{y}=\frac{15}{7} \\x=\frac{15}{7}y[/tex]

Keiths height increased by 16% , therefore Keith new height is (100% + 16%) × x = 1.16x

The nephew height is doubled, therefore his new height is 2y.

Given that Keith is now 34 cm taller than his nephew

1.16x = 2y + 34

but x = (15/7)y

[tex]1.16(\frac{15}{7} )y=2y+34\\\\\frac{87}{35} y=2y+34\\\\\frac{87}{35} y-2y=34\\\\\frac{17}{35}y=34\\ \\y=\frac{34*35}{17}\\ \\y=70\ cm[/tex]

The nephews new height = 2y = 2(70) = 140 cm

Keith new height = 2y + 34 = 140 + 34 = 174 cm

Their total current height = 140 cm + 174 cm = 314 cm

Answer:

-2, -1/2

Step-by-step explanation:

Step-by-step explanation:

The midpoint of a line segment between two points is given by

[tex]M = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

where ( x1 , y1) and ( x2 , y2) are the points

From the question

The midpoint of the line segment using points (-5,2) and (1, -3) is

[tex]M = ( \frac{ - 5 + 1}{2} , \frac{2 - 3}{2} )[/tex]

[tex]M = ( - \frac{ 4}{2} , - \frac{1}{2} )[/tex]

We have the final answer as

[tex]M = ( - 2, - \frac{1}{2} )[/tex]

Hope this helps you

Answer:

5%

Step-by-step explanation:

Total 'halwa' made = 1

Divided into four equal portion = 1/4

Arrival of an unexpected guest = 1/5

By what percentage has each family member's share been reduced:

Change in the sharing proportion:

Previous share ratio - new sharing ratio

(1/4 - 1/5) = (5 - 4) / 20 = 1/20

That means total reduction in the sharing = 1/ 20

Since each member comes contributed equally:

Reduction in each family member's share ;

(1 / 20) ÷ 4

(1 / 20) * 1/4 = 1/ 80

Percentage reduction:

(Reduction / original share) * 100%

[(1/80) ÷ (1/4)] * 100

(1/80 * 4/1) * 100%

(1/20) * 100%

= 5%

Reduction in each family members share = 5%

Answer:

Step-by-step explanation:

Base is right triangle, so:

B = ¹/₂•4•6 = 12 mm²

H = 7 mm

V = ¹/₃•B•H

V = ¹/₃•12•7 = 4•7 = 28 mm³

Answer:

V=28 mm³

Step-by-step explanation:

V= volume of the pyramide

G = square of the triangle

h = high of the pyramide

V = 1/3 * G* h

G=1/2 *a*b

G = 1/2 * 6 * 4

G = 12

V= 1/3 *12*7

V=28 mm³

Answer:

The answer to this question can be defined as follows:

In option A, the answer is "- 357.14 miles per hour".  

In option B, the answer is "-0.98".

Step-by-step explanation:

Given:

[tex]\frac{dx}{dt} =- 300 \text{ miles per hour}[/tex]

[tex]\frac{dy}{dt} =- 400 \text{ miles per hour}[/tex]

find:

[tex]\frac{ds}{dt} =?[/tex] when

[tex]x= 150 \\y= 200\\s=x+y\\\\[/tex]

  [tex]= 150+200 \\\\=350[/tex]

[tex]\to s^2=x^2+y^2\\[/tex]

differentiate the above value:

[tex]\to 2s\frac{ds}{dt}= 2x \frac{dx}{dt}+2y \frac{dy}{dt}[/tex]

[tex]\to 2s\frac{ds}{dt}= 2(x \frac{dx}{dt}+y \frac{dy}{dt})\\\\\to \frac{ds}{dt}= \frac{(x \frac{dx}{dt}+y \frac{dy}{dt})}{s}\\\\[/tex]

        [tex]= \frac{(150 \times -300 +200 \times -400 )}{350}\\\\= \frac{-45000+ (-80000) }{350}\\\\= \frac{- 125000 }{350}\\\\= - 357.14 \ \text{miles per hour}[/tex]

In option B:

[tex]\to d=rt\\\\ \to t= \frac{d}{r}[/tex]

[tex]\to \ \ d= 350 \ \ \ \ \ \ r= -357.14\\[/tex]

[tex]\to t= - \frac{350}{357.14}\\\\\to t= - 0.98[/tex]

Explanation:

f(x) = (x+5)^2 = x^2+10x+25 = x^2+10x^1+25x^0

The exponents for that last expression are 2, 1, 0

The mix of even and odd exponents in the standard form means f(x) is neither even nor odd. We would need to have all exponents even to have f(x) even, or have all exponents odd to have f(x) be odd.