A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h is the height of the ball above the ground, measured in feet. Write an inequality to model when the height of the ball is at least 36 feet above the ground. For how long is the ball at or above 36 feet?​

Answer:

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]

Simplify:

[tex]-66 = k(17 + x_k)[/tex]

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

[tex]x_ n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]

Then the last term is given by:

[tex]x_k = 17 - 4(k-1)[/tex]

Substitute:

[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Answer:

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]

[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]

Answer: A x> -2

Step-by-step explanation:

The triangle is missing and so i have attached it.

Answer:

x = 93°

Step-by-step explanation:

From the triangle attached, we can say that;

<SQP + <SQR = 180°

This is because sum of angles on a straight line equals 180°.

Secondly, we know that sum of angles in a triangle also equals 180°.

Thus;

<SQR + <QSR + <SRQ = 180

From the attached triangle, we see that;

<QSR = 35°

<SRQ = 58°

Thus;

<SQR + 35° + 58° = 180°

<SQR + 93° = 180°

<SQR = 180° - 93°

<SQR = 87°

From earlier on, we saw that;

<SQP + <SQR = 180°

Plugging in <SQR = 87°, we have;

<SQP + 87° = 180°

<SQP = 180° - 87°

<SQP = 93°

We are told in the question that <SQP is denoted by x.

Thus;

x = 93°

Answer:

The value of x is answer D: 93

For a geometric sequence

a, ar, ar ², ar ³, …

the n-th term in the sequence is ar ⁿ ⁻ ¹.

The first sequence is

1, 3, 9, 27, …

so it's clear that a = 1 and r = 3, and so the n-th term is 3ⁿ ⁻ ¹.

The second sequence is

400, 200, 100, 50, …

so of course a = 400, and you can easily solve for r :

200 = 400r   ==>   r = 200/400 = 1/2

Then the n-th term is 400 (1/2)ⁿ ⁻ ¹.

Similarly, the other sequences are given by

3rd: … 4 × 2ⁿ ⁻ ¹

4th: … 400 (1/4)ⁿ ⁻ ¹

5th: … 5ⁿ ⁻ ¹

6th: … 1000 (1/2)ⁿ ⁻ ¹

7th: … 2 × 5ⁿ ⁻ ¹

Answer:

56000 ft

Step-by-step explanation:

4000 steps a day.

7 days in a week.

2 ft per step

so, we calculate how many steps in a week

4000 × 7 = 28000

and then we calculate the distance by saying each of these steps is 2 ft

so,

28000 × 2 = 56000 ft

as a little extra thought :

there are 5280 ft in a mile.

so, the person walks

56000 / 5280 miles = 10.61 miles

in a week.

Step-by-step explanation:

starting pt.

root 16²+15²

= 256 + 225

=481

f(x)=3x²+x-3x-1

=x(3x+1)-(3x+1)

=(x-1)(3x+1)

Answer:

answer is 21..............

Explanation:

p(x) = x⁴ + 2x³- 3x² + x - 1

Factor of p(x)

x-2=0

x=2

Then by using synthetic division

Answer:

can you translate in english,would be better...

answer maybe wrong because of the language but stil....

9x(2+6x+1)

=9x(9x)

81x..

Answer:

Step-by-step explanation:

The diagonal of this rectangular box serves as the hypotenuse of the 2 right triangles that exist within this rectangle. The length is one leg, the hypotenuse is...well, the hypotenuse, so we need to use Pythagorean's Theorem to find the missing leg.

[tex]10^2=8^2+x^2[/tex] and

[tex]100-64=x^2[/tex] and

[tex]x^2=36[/tex] so

x = 6. The width is 6.

- X + 3Y = 2  (*)

⇔X = 2 - 3Y  (1)

- Y = 2X + 3   (2)

(1),(2)⇒ Y = 2(2 - 3Y) +3

       ⇔ Y = 4 - 6Y + 3

       ⇔ Y = 1  (**)

(*),(**)⇒ X + 3×1 =2

       ⇔ X = -1

Answer:

2 packs of Burgers, 3 Packs of Buns

Answer:

He will need to buy 2 packs of burgers. And 3 packs of buns.

Step-by-step explanation:

The lowest common number that 12 and 8 Share is 24. 12×2=24 8×3=24

Answer:

Step-by-step explanation:

We can see that there are roots at (-2,0) and (-1,0)

also, the root at (-2,0) should bounce right off

and the root at (-1,0) should go through

With all that being said it has to be B

Answer:

84,3 ° Sureste

Step-by-step explanation:

El diagrama vectorial que tipifica la pregunta se muestra en la imagen adjunta.

La dirección del avión es la dirección de la velocidad resultante.

Si esta dirección es θ

θ = tan ^ -1 (400/40)

θ = 84,3 ° Sureste

Answer: 8/11

Step-by-step explanation:

This is because there are a total of 22 bulbs. 16 of those bulbs work, giving us the fraction: 16/22. If you simplify 16/22 by dividing the numerator and denominator by 2, you get 8/11.

=================================================

Explanation:

There are 16 working bulbs out of 6+16 = 22 bulbs total.

The probability of randomly selecting a working bulb is 16/22

After that first bulb is selected and not put back, the probability of randomly selecting another working bulb is 15/21. Take note that I subtracted 1 from each part of the original fraction.

So we get the answer of

(16/22)*(15/21) = 240/462 = 40/77 which is choice C.

------------

Extra info:

Answer:

X+y=7

Step-by-step explanation:

i  remember  doing something like this but mines had the word onion rings .

Answer:

12

Step-by-step explanation:

bc it is

Answer:

VERTICALLY OPP ANGLES

Step-by-step explanation:

Answer:

70.7 deg, 19.3 deg

Step-by-step explanation:

The sum of the measures of complementary angles is 90 deg.

One angle measures x.

The other angles measures 51.4 deg less than x, or x - 51.4.

The sum of their measures equals 90.

x + x - 51.4 = 90

2x - 51.4 = 90

2x = 141.4

x = 70.7

x - 51.4 = 70.7 - 51.4 = 19.3

Answer: 70.7 deg, 19.3 deg

Answer: 83 degrees

Step-by-step explanation:

(16^2 + 8^2 - 17^2)/(2)(16)(8) = 83

Answer:

The sales tax rate is 5%.

Step-by-step explanation:

To determine the sales tax rate if you already know the amount of tax being added to the purchase price, divide the amount of tax by the purchase price. In this example, divide $1.29 (amount of tax being added) by $25.79 (purchase price). When you do that, you will see that the answer is 0.0500, or 5%.

Answer:

This would be a .04 or 4% decay.....

for every "time unit" (x in this case) you will be multiplying

the amount by .96 ... in other words if you started with one dollar

the results would be 96 cents... after two "time" steps you would have

only 92 cents (.96 *.96)

Step-by-step explanation:

5:-c

The 3multiples are 25,50,75

6:-c

[tex]\\ \sf\longmapsto 6\:of\:2+9-5[/tex]

[tex]\\ \sf\longmapsto 6(11-5)[/tex]

[tex]\\ \sf\longmapsto 6(6)[/tex]

[tex]\\ \sf\longmapsto 36[/tex]

7:-a

12,17

8:-c

HCF=2×2×11=44

9:-c

LCM of 9 and 5 is 45 hence its true

10:-c

HCF of two consecutive numbers is 1

Answer:

m<PQR = 18.7°

Step-by-step explanation:

Apply the Law of Sines,

[tex] \frac{Sin A}{a} = \frac{Sin B}{b} [/tex]

Where,

Sin A = Sin 140

a = 100 m

Sin B = Sin R (<PRQ)

b = 50 m

Substitute

[tex] \frac{Sin 140}{100} = \frac{Sin R}{50} [/tex]

Cross multiply

[tex] 100*Sin(R) = 50*Sin(140) [/tex]

Divide both sides by 100

[tex] Sin(R) = \frac{50*Sin(140)}{100} [/tex]

[tex] Sin(R) = 0.32139 [/tex]

[tex] R = Sin^{-1}(0.32139) [/tex]

R ≈ 18.7° (nearest tenth)

m<PQR = 18.7°

The angle PRO is 1.7 degrees.

Given that,

The diagram shows three points P, Q, and R on horizontal ground.

PQ = 50 m, PR = 100 m and angle PQR = 140°.

We have to determine,

The angle PRO.

According to the question,

The value of angle PRO is determined by using the sin rule-following all the steps given below.

[tex]\rm \dfrac{sina}{a} = \dfrac{sinb}{b}[/tex]

Where,  Sin A = Sin 140 , a = 100 m , Sin B = Sin R (<PRQ) , b = 50 m

Substitute all the values in the formula,

[tex]\rm \dfrac{sin140}{100} = \dfrac{sinR}{50}\\\\ \dfrac{0.64}{100} = \dfrac{sinR}{50}\\\\0.0064 = \dfrac{sinR}{50}\\\\0.0064 \times 50 = sinR\\\\0.321 = sinR\\\\R = sin{-1}(0.321)\\\\R = 18.7 \ degree[/tex]

Hence, The angle PRO is 1.7 degrees.

For more details refer to the link given below.

https://brainly.com/question/12895249

Answer:

4/9

Step-by-step explanation:

negative exponent means 1/...

so, this is

(32/243)^(4/10) = (32/243)^(2/5)

that means to the power of 2 and then pulling the 5th root.

so, let's pull the 5th root first, and then we square

(32/243)^(2/5) = (2⁵/3⁵)^(2/5) = (2/3)^2 = 4/9

Answer:

20

Step-by-step explanation:

we know,

n(aUb)=n(a)+n(b)-n(a∩b)

so,

80=40+60-n(a∩b)

or, 80-(40+60)=-n(a∩b)

or, -n(a∩b)=80-100

or, -n(a∩b)=-20

or, n(a∩b)=20

Answer:

W = 7 - x

Step-by-step explanation:

The perimeter is P= 2L + 2×W , where L is the length and W is the width.

If L = (x+2) , replacing L with the expression x+2 we have

P= 2×(X+2) + 2W ⇔ 18 = 2x + 4 + 2W ⇔ 2W =18 - 2x - 4 ⇔ 2W = 14 - 2x

⇔ W = 7 - x

Answer:

x = 45

Step-by-step explanation:

The angles labeled with the pink x are the same.  Line V and Line X are parallel and alternate interior angles are equal when the lines are parallel.

We know the 3 angles inside the triangle and the sum of the angles of a triangle are 180

x+x+ 2x = 180

4x= 180

4x/4 = 180/4

x = 45

Answer:

Not factarable, all terms must be in x. or y

Step-by-step explanation: