What is the common difference for this arithmetic sequence?
-6,-1,4,9,14,...
A. 6
B. 4
C. 5
D. 3
SUBMIT

If y = x + 6√(x + 4), then

y' = 1 + 3/√(x + 4)

Substituting y and y' into the DE gives

(y - x) y' = (x + 6√(x + 4) - x) (1 + 3/√(x + 4))

… = 6√(x + 4) (1 + 3/√(x + 4))

… = 6√(x + 4) + 18

on the left side, while on the right you get

y - x + 18 = x + 6√(x + 4) - x + 18

… = 6√(x + 4) + 18

so both sides match and the given function is indeed a solution to the DE.

9514 1404 393

Answer:

  19 hours

Step-by-step explanation:

Add up the numbers:

  3×3.5 +2×2.0 +4.5 = 19

Jacob trains 19 hours per week.

Answer:

a) 3.19

b) 3.29

c) 96.81

Step-by-step explanation:

Question a:

Levere's: 10.63s

Ross: 10.98s

10.98 - 10.63 = 0.35s shorter than 10.98s, so:

0.35*100%/10.98 = 3.19% shorter.

Question b:

35s longer than 10.63s, so:

0.35*100%/10.63 = 3.29% longer.

Question c:

3.19% shorter, so 100 - 3.19 = 96.81% of Ross.

Answer:

U={-2,-1,0,1,2,3,4,5,6,7,8}

Answer:

[tex]P(G_1) = \frac{5}{13}[/tex]

[tex]P(G_2) = \frac{1}{3}[/tex]

[tex]P(X \ge 1) = \frac{25}{39}[/tex]

Step-by-step explanation:

Given

[tex]G = 5[/tex]

[tex]R = 4[/tex]

[tex]B = 4[/tex]

[tex]n = 13[/tex]

Solving (a): [tex]P(G_1)[/tex]

This is calculated as:

[tex]P(G_1) = \frac{G}{n}[/tex]

[tex]P(G_1) = \frac{5}{13}[/tex]

Solving (b): [tex]P(G_2)[/tex]

This is calculated as:

[tex]P(G_2) = \frac{G - 1}{n - 1}[/tex] -- this is so because the selection is without replacement

[tex]P(G_2) = \frac{5 - 1}{13 - 1}[/tex]

[tex]P(G_2) = \frac{4}{12}[/tex]

[tex]P(G_2) = \frac{1}{3}[/tex]

Solving (c): [tex]P(X \ge 1)[/tex]

Using the complement rule, we have:

[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]

To calculate [tex]P(X = 0)[/tex], we have:

[tex]G = 5[/tex] --- Green

[tex]G' = 8[/tex] ---- Not green

The probability that both selections are not green is:

[tex]P(X = 0) = P(G'_1) * P(G'_2)[/tex]

So, we have:

[tex]P(X = 0) = \frac{G'}{n} * \frac{G'-1}{n-1}[/tex]

[tex]P(X = 0) = \frac{8}{13} * \frac{8-1}{13-1}[/tex]

[tex]P(X = 0) = \frac{8}{13} * \frac{7}{12}[/tex]

Simplify

[tex]P(X = 0) = \frac{2}{13} * \frac{7}{3}[/tex]

[tex]P(X = 0) = \frac{14}{39}[/tex]

Recall that:

[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]

[tex]P(X \ge 1) = 1 - \frac{14}{39}[/tex]

Take LCM

[tex]P(X \ge 1) = \frac{39 -14}{39}[/tex]

[tex]P(X \ge 1) = \frac{25}{39}[/tex]

The range is the an interval on the y-axis where the function is defined.

You can see that your function is y-wise going all the way down to negative infinity but then stops and continues the path along 2 on the upper bound.

The inequality describing the interval is thusly B,

[tex]-\infty\lt y\lt2[/tex]

Hope this helps :)

Answer:

breathing, jk buddy

Step-by-step explanation:

Answer:

85 rounded to the nearest dollar would be $1. 73 rounded to the nearest dollar would also be $1

Step-by-step explanation:

Answer:

2x^2 - 9x -1 = 0

Solution: x = 9 ±√89/4

2x^2 -9x +6 = 0

Solution: 9 ± √33/4

Step-by-step explanation:

Given the equation;2x^2 - 9x -1 = 0

From the quadratic formula;

-b ±√ b^2 -4ac/2a

We have;

x= -(-9) ± √(-9)^2 - -4(2)(-1)/2(2)

x = 9 ±√89/4

Also;

Given the equation: 2x^2 -9x +6 = 0

From the quadratic formula: -b ±√ b^2 -4ac/2a

We have;

x= -(-9) ± √(-9)^2 - 4(2)(6)/2(2)

x= 9 ± √33/4

1.) 2x^2-9x+6 2.)  2x^2-8x+5 3.) 2x^2-9x-1   4.) 2x^2-8x-3

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Leg = x

Hypotenuse = 16

[tex] x\sqrt{2} = 16 [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16\sqrt{2}}{2} [/tex]

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

Answer:

Sin43 = x/13

x= 13* sin43

x= 8.865

Answer:

8.9

Step-by-step explanation:

using sine rule

[tex] \frac{x}{sin \: 43} = \frac{13}{sin \: 90} [/tex]

cross multiply

x sin 90=13 sin 43

x=13 sin 43

x=8.9

Answer:

[tex]-5, 18, \sqrt{13}[/tex]

Step-by-step explanation:

We can solve the first equation, f of -3. The value of the function f is [tex]\frac{1+x^2}{x+1}[/tex], and plugging in -3 gets us [tex]\frac{1+9}{1-3}[/tex], this results in 10 divided by negative 2, which is negative 5.

Now, we must solve g of negative one third. The function g is defined as [tex]|9x-15|[/tex]. Plugging in negative one third into the question gets us [tex]|9(-\frac{1}{3})-15|[/tex]

9 times negative one third is -3, and -3 minus 15 is -18. The absolute value of -18 is 18.

Now, we must solve h of negative 2, and h is defined as [tex]\sqrt{-3-8x}[/tex]. Plugging in negative 2, we have [tex]\sqrt{-3-8(-2)}[/tex]. Negative 8 times negative 2 is positive 16, and 16 minus 3 is 13. The answer is the square root of 13

These are variables on your graph

Answer:

Answer:

11

Step-by-step explanation:

Unknown number = x

If twice the difference of x and 8 is 6:

2(x-8) = 6

2x-16 = 6

2x = 6 + 16

2x = 22

x = 22/2

x = 11

Answer from Gauthmath

Answer:

Regular Polygons are never concave by definition.

Step-by-step explanation:

Im sorry I don't know the answer to the question

Answer:

✔ positive

✔ 1

✔ closely

✔ increases

ED2021

Answer:

The solution set is {-2, 3}.

Step-by-step explanation:

We can do this by elimination after manipulating the 2 equations so that the coefficients of  y  will disappear after addition:

5x - 2y = -16        Multiply this by -5:

-25x + 10y = 80 ...........(A)

4x - 5y = -23       Multiply this by 2:

8x - 10y = -46..............(B)

Now add A and B:

-17x = 34

x = 34/-17

x = -2.

Now substitute x = -2 into the first original equation:

5(-2) - 2y = -16

-2y = -16 +10 = -6

y = -6/-2

y = 3.

Confirm these results by substitution in the second original equation:

4(-2) - 5(3)

= - 8  - 15 = -23.

Checks OK.

Answer:

true

Step-by-step explanation:

the incenter of a triangle is the common intersection of the angle bisectors.hence always remains inside the triangle.

Answer:

3h33j333jj3

Step-by-step explanation:b3n3n3nn3n33

Answer:

50

Step-by-step explanation:

Sum Even numbers

n = 50

d = 2

a1 = 2

The last number is

an = a1 + (n-1)d

an = 2 + (50 - 1)*2

an = 2 + 49 * 2

an = 2 + 98

an = 100

Sum of the even numbers

Sum = (a1 + a50)*n/ 2

Sum = (2 + 100)*50/2

sum = 102 * 25

sum = 2550

Sum of the first 50 odd numbers

a1 = 1

n = 50

d = 2

l = ?

Find l

l = a1 + (n - 1)*2

l = 1 + 49*2

l = 99

Sum

Sum = (1 + 99)*50/2

Sum = 2500

The difference and answer is 2550 - 2500  = 50

The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the

tunnel with a cross section that is the shape of half of a sine curve and the

height of the tunnel at the edge of the road, (approximately 7.07 ft.) are

found by applying the following steps

(a) The equation for the sine curve is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is approximately 7.07 feet

The reason for the above answers are presented as follows;

(a) From a similar question posted online, the missing part of the question

is, what is the height of the tunnel at the edge of the road

The known parameters;

The shape of the tunnel = One-half sine curve cycle

The height of the road at its highest point = 10 ft.

The opening of the tunnel at road level = 24 ft.

The unknown parameter;

The equation of the sine curve that fits the opening

Method;

Model the sine curve equation of the tunnel using the general equation of a sine curve;

The general equation of a sine curve is y = A·sin(B·(x - C) + D

Where;

y = The height at point x

A = The amplitude = The distance from the centerline of the sine wave to the top of a crest

Therefore;

The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.

D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)

The period is the distance between successive points where the curve passes through the center line while rising to a crest

Therefore

The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.

T = 48 ft.

We get;

48 = 2·π/B

B = 2·π/48 = π/24

By plugging in the values for A, B, C, and D, we get;

y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)

The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is given by substituting

the value of x at the edge of the road into the equation for the sine curve

as  follows;

The width of the shoulders = 6 feet

∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.

Therefore, we get;

y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2

y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2

The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.

Learn more about the sine curve here;

https://brainly.com/question/3827606

Answer:

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.

Step-by-step explanation:

Probability of a defective part:

0.04 of [tex]\frac{100}{180}[/tex], that is, coming from A.

0.05 of [tex]\frac{80}{180}[/tex], that is, coming from B. So

[tex]p = 0.04\frac{100}{180} + 0.05\frac{80}{180} = \frac{0.04*100 + 0.05*80}{180} = 0.0444[/tex]

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.

Answer:

español :/

Step-by-step explanation:

Answer:

256/5 pi

Step-by-step explanation:

= angle/360 × pi×r^2

= 72/360 × pi × 16^2

= 51.2 pi

= 256/5 pi

Answer:

B.

Step-by-step explanation:

Since C and A are parallel

and B is perpendicular to C

then B is also perpendicular to A

meaning they have the same angle so 90 Degrees.

All you do is first you ha

Answer: 4 13/30 cups

Step-by-step explanation:

Since Lila used 1 2/5 times as much lemonade as Naomi did (3 1/6 cups), we have to multiply 1 2/5 by 3 1/6:

1 2/5 ⋅ 3 1/6 = ?

19/6 ⋅ 7/5 = 133/30

133/30 = 4 13/30

4 13/30 cups