Given:
The given equation is:
[tex]-3t^2+24t=h[/tex]
Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.
To find:
The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.
Solution:
We have,
[tex]-3t^2+24t=h[/tex]
The height of the ball is at least 36 feet above the ground. It means [tex]h\geq 36[/tex].
[tex]-3t^2+24t\geq 36[/tex]
[tex]-3t^2+24t-36\geq 0[/tex]
[tex]-3(t^2-8t+12)\geq 0[/tex]
Splitting the middle term, we get
[tex]-3(t^2-6t-2t+12)\geq 0[/tex]
[tex]-3(t(t-6)-2(t-6))\geq 0[/tex]
[tex]-3(t-2)(t-6)\geq 0[/tex]
The critical points are:
[tex]-3(t-2)(t-6)=0[/tex]
[tex]t=2,6[/tex]
These two points divide the number line in 3 intervals [tex](-\infty,2),(2,6),(6,\infty)[/tex].
Intervals Check point [tex]-3(t-2)(t-6)\geq 0[/tex] Result
[tex](-\infty,2)[/tex] 0 [tex](-)(-)(-)=(-)<0[/tex] False
[tex](2,6)[/tex] 4 [tex](-)(+)(-)=+>0[/tex] True
[tex](6,\infty)[/tex] 8 [tex](-)(+)(+)=(-)<0[/tex] False
The inequality is true for (2,6) and the sign of inequality is [tex]\geq[/tex]. So, the ball is above 36 feet between 2 to 6 seconds.
[tex]6-2=4[/tex]
Therefore, the required inequality is [tex]-3t^2+24t\geq 36[/tex] and the ball is 36 feet above for 4 seconds.
A purchase costs $25.79 plus a tax of $1.29. Find the sales tax rate.
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%.
9. Find the remainder when the polynomial: p(x) = x⁴ + 2x³- 3x² + x - 1 is divided by (x - 2)
pls it's urgent
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
Match function with its corresponding graph
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
A person walks on average 4000 steps per day. If one step is about 2 feet long, how much would the average person walk per week? HELP
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.
The diagram shows three points P, Q and R on horizontal ground.
PQ = 50 m, PR = 100 m and angie PQR = 140°.
Calculate angle PRO.
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
If n(a)=40,n(b)=60 and n(a∪b)=80.find the value of (a∩b.
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
What is the measure of m?
Answer:
12
Step-by-step explanation:
bc it is
Please someone tell me the answer of these questions
Answer:
VERTICALLY OPP ANGLES
Step-by-step explanation:
which inequality is represented on the number line shown?
Answer: A x> -2
Step-by-step explanation:
Given an arithmetic progression 17,13,9,..... find the number of terms required so that its sum is - 33 .
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]
Emma rides a bicycle 16 miles east and then 15 miles north. About how far is she from her starting point?
Step-by-step explanation:
starting pt.
root 16²+15²
= 256 + 225
=481
distance= 22 miles aprox.1.Evaluate
a.(243/32)^-0.4
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
X+3y=2 and y=2x+3
Please explain using substitution method.
- 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
9x mũ 2 + 6x + 1 cho mình hỏi câu này ạ
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..
đưa về phương trình tích: f(x)=3x^2-2x-1
f(x)=3x²+x-3x-1
=x(3x+1)-(3x+1)
=(x-1)(3x+1)
Triangle Q R S is shown. Line R Q extends through point P. Angle Q S R is 35 degrees. Angle S R Q is 58 degrees. Exterior angle S Q P is x degrees. What is the value of x?
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
A changes
16. By accident, 6 burned out bulbs have been mixed in with 16 good ones, Ken is replacing old bulbs in his house. If he selects two bulbs at random from the box of 22, what is the
probability they both work?
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:
Choice A is only true if Ken puts the first selection back. You would compute (16/22)*(16/22) = 64/121. However, it sounds like he's not doing replacement. So whatever is selected is not put back. This is why I ruled out choice A.Choice B is ruled out as well because 16/22 = 8/11 refers to the probability of one working bulb (instead of 2 in a row)It's not clear how the fraction of choice D is formed, but we can rule it out because choice C is the answer.y=8200(0.96)^x growth or decay find
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:
The perimeter of a rectangle is 18cm . if the length is (x+2), find it's width.
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
the length of a rectangular box is 8cm. If its diagonal is 10cm. Find its width
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.
An angle measures 51.4° less than the measure of its complementary angle. What is the measure of each angle?
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
Find X round to the nearest tenth.
Answer: 83 degrees
Step-by-step explanation:
(16^2 + 8^2 - 17^2)/(2)(16)(8) = 83
Find the value of x in each case:
Please help me
It's an easy 40 points if you answer this
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
Pls answer all questions
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
22=2×1188=2×2×2×11HCF=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
Un avión puede volar con la velocidad de 400 km por hora en atmósfera tranquila si cuando se dirige hacia el este el viento viene del Sur con la velocidad de 40 km por hora cuál es la dirección de su vuelo
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
factor and solve the problem in the photo ……. pleaseeee helppppp i havent done algebra in 2 years
Answer:
Not factarable, all terms must be in x. or y
Step-by-step explanation:
At a particular restaurant, each slider has 225 calories and each chicken wing has 70 calories. A combination meal with sliders and chicken wings has a total of 7 sliders and chicken wings altogether and contains 1110 calories. Write a system of equations that could be used to determine the number of sliders in the combination meal and the number of chicken wings in the combination meal. Define the variables that you use to write the system.
Answer:
X+y=7
Step-by-step explanation:
i remember doing something like this but mines had the word onion rings .
What's 672 divided by 32
James is having a BBQ. Burgers come in packs of 12
and buns come in packs of 8. How many packs of each
will James need to buy so that he has no spares?
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
I can’t figure out which formula goes with which sequence. Help……. Please???
1st sequence:
1,3,9,27,….
What is the formula?
2nd sequence:
400,200,100,50,…
What is the formula?
3rd sequence:
4,8,16,32,…
What is the formula?
4th sequence:
400,100,25,6.25,…
What is the formula?
5th sequence:
1,5,25,125,…
What is the formula?
6th sequence:
1000,500,250,125,…
What is the formula?
7th sequence:
2,10,50,250
What is the formula?
I need to know the correct geometric sequence formula for each of these sequences. Thanks!!!
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
