Answer:
7
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
The height of the rock after t seconds is given by the following equation:
[tex]H(t) = -16t^2 + 96t + 112[/tex]
How long will it take in seconds for the rock to hit the ocean?
This is t for which:
[tex]H(t) = 0[/tex]
So
[tex]-16t^2 + 96t + 112 = 0[/tex]
Simplifying by -16
[tex]t^2 - 6t - 7 = 0[/tex]
So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]
[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]
[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]
[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]
Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.
Watch help video
Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = 2x(x - 3)
Answer:
Submit Answer
What is the answer for this?
Answer:
Proved
Step-by-step explanation:
Given
[tex](2 * 10^2) * (3 * 10^5) = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Required
Prove
On the right hand side, we have:
[tex]2 * 10^2 * 3 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Rewrite:
[tex]2 * 3* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
[tex]6* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Apply law of indices
[tex]6* 10^{2+5} = 3.5 * 10^7 + 2.5 * 10^7[/tex]
[tex]6* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Express 6 as 3.5 + 2.5
[tex](3.5 + 2.5)* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Open bracket
[tex]3.5 *10^7+ 2.5*10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Proved
Which of the following is true for a circle that has an area of approximately 113 square feet?
a
The diameter is 6 feet and the circumference is 38 square feet.
b
The radius is 6 feet and the circumference is 38 square feet.
c
The diameter is 6 feet and the circumference is 38 feet.
d
The radius is 6 feet and the circumference is 38 feet.
Answer:
radius is 6, diameter is 12, circumference is 38
Step-by-step explanation:
The area of a circle hs the following formula:
A = π*r², where r is the circle radius (distance from center to edge of circle)
So, we have A = 113 = π*r²
Divide both sides by π: 113/π = r²
Approximately: 35.97 = r²
Square-root both sides: 5.997 = r
So, the radius is about 6 feet
The circumference of a circle has the following formula:
C = π * D, where D is the diameter of the circle (distance from one side of circle to opposite side, through the center)
But the length of a diameter is just that of two radiuses. (This is obvious when the 2 radii are collinear.)
Since r = 6 feet, D = 12 feet, and the circumference C = 12 * π = 37.699, about 38 feet.
*** So the radius is about 6 feet, the diameter is about 12 feet, and the circumference is about 38 feet,
It lloks like b and d are identical. Typo. maybe?
SOMEONE ANSWER MY FREAKING QUESTIONS!!!!!!
please
Answer: i dont know trie asking linder0917
Step-by-step explanation:
ok
A stamp collector has 55 stamps from the United States, 30 stamps from Canada, and 15 from Mexico. If he were to close his eyes and randomly select 20 from his collection, about how many would you expect to be from Mexico?
A pet store sold 12 siamese cats. If the ratio of siamese cats to house cats sold was 2 : 1, what is the combined amount of cats sold?
Answer:
32 cats in total
Step-by-step explanation:
so 18 siamese
the ratio was9:7=siameese:house
18=9 units
divide 9
2=1 unit
house=7 units
7 times 2=14
14 house cats
combined=siameese+house=18+14=32
Solve the solution of this inequality
9−4d≥−3
Answer: d
≤
3
Step-by-step explanation: that’s the answer buddy
Answer: X is less than or equal to 3.
I am 100% sure it's right.
Step-by-step explanation:
que expresision algebraica es P (x)=3x - 5x +6?
23rd term of -11,-7,-3 in arithmetic sequence
Answer:
The 23rd term for the sequence is -99
Step-by-step explanation:
We can use an explicit rule to find the 23rd term.
Given Info:
=> Sequence: -11,-7,-3
=> f(1) = -11
=> Common difference (d) = -4
Explicit rule: f(1) + d(n-1)
So,
-11 -4 (n-1)
Substitute 23 for n
=> -11 - 4(23-1)
=> -11 - 4(22)
=> -11 - 88
=> -99
hope this helps and is right :)
p.s. i really need brainliest
Solve for x...............
Answer:
x = 12 degrees
Step-by-step explanation:
They all have to add up to 360, so:
[tex]5x + 4 + 4x+9+7x+4+9x-6+4x+1=360\\29x + 12 = 360\\29x = 348\\x = 12[/tex]
Is the association between x and y positive or negative?
A. none B.positive C, negative
Answer:
A.non at all so, please choose the right answer
Answer:
A.non at all so, please choose the right answer
Help me please......
Answer: 46
Step-by-step explanation:
Let the 3 consecutive even numbers be x, (x-2) and (x+2) respectively.
According to the question,
x + (x - 2) + (x + 2) = 132
or, x + x - 2 + x + 2 = 132
or, 3x = 132
or, x = 132 ÷ 3
or, x = 44
So, first even number = 44
Required third number = 44 + 2
= 46
Can somebody help please #asap help w number 8
Answer:
y=4x bc each one is 4 so for one box it cost $4
Answer:
The expression will be y = 4x.
Step-by-step explanation:
First, we have to form expressions for number of boxes and total amount she earn :
Let x be the number of boxes,
Let y be the total amount,
Given that the costs of each box is $4 so in order to find the total amount, you have to multiply the number of boxes by 4 :
y = 4x
what is the area of triangle ABC?? i need this asap
Answer:
A) 36√3
Step-by-step explanation:
First, figure out the height. Since it's an equilateral triangle, it would be
6²+B²=12²
36+B²=144
B²=144-36
B²=108
B=√108
B=√36x√3
B=6√3
Now we can get the area.
1/2(6√3)(12) = 36√3
-2(x+2)=1/4(-8x-16) how many solutions does it have
Answer:
infinite
Step-by-step explanation:
for brainliest!!!! please help :)
Answer:
area = 572.3 m²
Step-by-step explanation:
area = PiR²
r = 27/2
area = (3.14)(13.5²)
area = 572.3 m²
What is the distance between - 10
and 2 on the number line?
12 units
-8 units
5 units
8 units
Answer:
12 units
Step-by-step explanation:
Draw a number line and mark x = -10 and x = 2. You can readily see that the distance from -10 to the origin is 10 units, and from the origin to 2 is 2 units, in both cases measured from left to right. Adding these two positive quantities together, we get 10 + 2, or 12.
The distance from -10 to 2 on the number line is 12 units.
Find the value of x.
А.
6
B
5
y
x = V[?]
Answer:
I thought this was going to be easy been sitting here for 20min
find the measure of the angle pic added
22. According to ghost hunters, large cities have, on average, 9 haunted houses each. As far as we know, it is unpredictable which houses will be haunted; and just because one house is haunted, that does not mean any of its neighbors will or will not be haunted. a) What is the standard deviation of the number of haunted houses in a large city
Answer:
The standard deviation of the number of haunted houses in a large city is 3.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval, which is the same as the variance.
According to ghost hunters, large cities have, on average, 9 haunted houses each.
This means that [tex]\mu = 9[/tex]
a) What is the standard deviation of the number of haunted houses in a large city?
Square root of the variance, so:
[tex]\sqrt{9} = 3[/tex]
The standard deviation of the number of haunted houses in a large city is 3.
Jerry buys a new cell phone and signs up for a yearly cell phone plan. The cell phone costs $329 and the yearly plan costs 490 per year for every year he uses the cell phone. The only costs associated with the cell phone are the purchase price and the cost of the yearly cell phone plan.
a) Describe the annual cost of the cell phone per year as a function of the number of years he uses the cell phone.
b) What happens to the average price per year the longer Jerry holds onto this plan and explain why?
Answer:
(329 + 490X) / X = Cost
Thus, the average annual price decreases as the cell phone is used for more years, because the fixed cost (the cost of the value of the cell phone) is divided each time by a greater number of years.
Step-by-step explanation:
Since Jerry bought a new cell phone and signed up for a yearly cell phone plan, and the cell phone costed $ 329 and the yearly plan costs $ 490 per year for every year he uses the cell phone, to determine the annual cost of the cell phone per year as a function of the number of years he uses the cell phone, the following mathematical reasoning must be performed:
(329 + 490X) / X = Cost
So, for example, if the cell phone was used for 3 years, the function would apply as follows:
(329 + 490x3) / 3 = X
(329 + 1470) / 3 = X
1,799 / 3 = X
599.66 = X
Thus, the average annual price decreases as the cell phone is used for more years, because the fixed cost (the cost of the value of the cell phone) is divided each time by a greater number of years.
Using the provided measures determine the measure of angle K.
A)30.5°
B)34.90
C)41.2°
D)58.0°
Answer:
B. 34.90°
Step-by-step explanation:
✔️First, find GF using Trigonometric function:
Reference angle = 58°
Adjacent length = GF
Hypotenuse = 6 cm
Apply CAH, thus:
Cos 58 = Adj/Hyp
Cos 58 = GF/6
GF = 6*Cos 58
GF = 3.17951558 ≈ 3.18 cm
✔️Find angle K using the Sine Rule:
[tex] \frac{sin(K)}{GF} = \frac{sin(G)}{KF} [/tex]
Substitute
[tex] \frac{sin(K)}{3.18} = \frac{sin(64)}{5} [/tex]
Multiply both sides by 3.18
[tex] sin(K) = \frac{sin(64)}{5}*3.18 [/tex]
[tex] sin(K) = 0.5716 [/tex]
[tex] K = sin^{-1}(0.5716) [/tex]
K = 34.8618741° ≈ 34.90°
After a discount of 40%, the sale price of a ride pass at a fun park is $30. What is the original
price?
Answer:
30 divided by 0.40 = 75
The original price was $75
Step-by-step explanation:
30 divided by 0.40 = 75
The original price was $75
Please help please thank
Answer:
3/4 of an hour
Step-by-step explanation:
the longest is 1 hour. the shortest is 1/4 of an hour. 1 minus 1/4 is 3/4
Solve for x.
X -8 = -11
PLZ HELP I NEED ANSWER ASAP
Answer:
x= -3
Step-by-step explanation:
Write 2 9/10 as an improper fraction.
pls hurry!
and pls explain how to do it
Answer:
29/10
Step-by-step explanation:
Answer:
[tex] \frac{29}{10} [/tex]
Step-by-step explanation:
[tex]2 \frac{9}{10} \\ \frac{2 \times 10 + 9}{10} [/tex]
Compare and contrast how to graph: x = 5 and y = 3.
4x - 8 = 32
?!!!! please help me plss
Answer:
The answer is X=10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
4x - 8 = 32
4x = 40
x = 10
f(x)=2x + 2
g(x)= x – 5
Find f(x) + g(x)
I need help understanding how to do a problem like this
Thank you
Answer:
3x - 3
Step-by-step explanation:
f(x) + g(x)
(2x + 2) + (x - 5)
3x - 3
Please help and show work