Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the questions below. Show all your work for full credit. Use the correct units with your answers
Answers
Answer:
Step-by-step explanation:
From what I understand about parabolic motion in the English system, the equation for flight is
[tex]s(t)=-16t^2+v_{0}t+h_{0}[/tex]
where [tex]v_{0}t[/tex] is the initial upwards velocity and
[tex]h_{0}[/tex] is the initial height from which the object was launched. Filling in that equation with those values gives you
[tex]s(t)=-16t^2+64t+3[/tex]. That's a.
In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function. The absolute max is the heighest that the ball will go. Completing the square is the way to solve this. Begin by setting the equation equal to 0, the moving the 3 over by subtraction:
[tex]-16t^2+64t=-3[/tex]
Now factor out the -16 since the leading coefficient HAS to be a positive 1:
[tex]-16(t^2-4t)=-3[/tex]
Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:
[tex]-16(t^2-4t+4)=-3[/tex]
BUT since you added in a 4*-16 on the left you have to add it in on the right:
[tex]-16t^2(t^2-4t+4)=-3-64[/tex]
which simplifies to
[tex]-16(t-2)^2=-67[/tex]
Now bring the 67 over by addition and you have your vertex:
[tex]s(t)=-16(t-2)^2+67[/tex].
The vertex is (2, 67). The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.
How long it will be in the air is found by factoring to find the zeros. These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046
So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at
x = 4.05 seconds. Which makes sense if you know anything about parabolic motion and physics. The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark. Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds. And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters). Sorry it's so long, but it's not a question that can be answered with just a few sentences.
Related Questions
In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm and DH = 4 cm.
Answers
Answer:
[tex]AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm[/tex]
Step-by-step explanation:
Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.
By the Pythagorean theorem,
[tex]AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm[/tex]
AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:
[tex]\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD[/tex]
Consider right triangle CAH.By the Pythagorean theorem,
[tex]CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8[/tex]
The length cannot be negative, so CD=8 cm and
[tex]CA=\sqrt{3}CD=8\sqrt{3}\ cm[/tex]
In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,
[tex]AB=2CA=16\sqrt{3}\ cm[/tex]
By the Pythagorean theorem,
[tex]BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm[/tex]
The midpoint of AB =
Answers
Answer:
(-.5, 0)
Step-by-step explanation:
y ---- 2÷2=1, y-1= 1-1=0
x ---- 3÷2 =1.5, x-1.5= 1-1.5= -.5
Answer:
( -0.5, 0 )
Step-by-step explanation:
Add the 0 before 5, it matters if its right or wrong. The Answer is ( -0.5 , 0 ). ADD THE 0 !!!!!
What is the answer and why?
Answers
Answer:
g(10) is undefined
Step-by-step explanation:
A vertical asymptote is a place where a function is literally undefined. That is commonly because the function is a rational function with a denominator of zero at that point (division by zero is undefined), but it can also be for any of a variety of other reasons.
Suppose the initial height of a Pumpkin is 12 feet and the pumpkin is being launched with a velocity of 61 feet per second. Use this information to find out the maximum height the pumpkin will go before landing.
Please show your work
(98 points)
Answers
The answer is:
The maximum height before landing will be 69.7804 feet.
Why?Since there is no information about the angle of the launch, we can safely assume that it's launched vertically.
So, we can calculate the maximum height of the pumpkin using the following formulas:
[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]
[tex]v=vo-gt[/tex]
Where,
y, is the final height
[tex]y_o[/tex], is the initial height
g, is the acceleration of gravity , and it's equal to:
[tex]g=32.2\frac{ft}{s^{2} }[/tex]
t, is the time.
Now, we are given the following information:
[tex]y_{o}=12ft\\\\v=61\frac{ft}{s}[/tex]
Then, to calculate the maximum height, we must remember that at the maximum height, the speed tends to 0, so, calculating we have:
Time calculation,
We need to use the following equation,
[tex]v=vo-gt[/tex]
So, substituting we have:
[tex]v=61\frac{ft}{s}-32.2\frac{ft}{s^{2}}*t\\\\-61\frac{ft}{s}=-32.2\frac{ft}{s^{2}}*t\\\\t=\frac{-61{ft}{s}}{-32.2\frac{ft}{s^{2}}}=1.8944s[/tex]
We know that it will take 1.8944 seconds to the pumpkin to reach its maximum height.
Maximum height calculation,
Now, calculating the maximum height, we need to use the following equation:
[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]
Substituting and calculating, we have:
[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]
[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}[/tex]
[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}\\\\y_{max}=12ft+115.5584ft-16.1\frac{ft}{s^{2}}*(3.5887s^{2})\\\\y_{max}=127.5584ft-57.7780ft=69.7804ft[/tex]
Hence, we have that the maximum height before the landing will be 69.7804 feet.
Have a nice day!
The z-statistic for a sample of delmar's practice times is 1.41. how should this statistic be interpreted in terms of the hypothesis test?
Answers
Answer:
Part 1: Answer C) There is not enough evidence to reject H0
Part 2: Answer C) There is not enough evidence to accept or reject his claim.
Step-by-step explanation:
Just did it on edge
The z-statistic of 1.41 means the sample mean is 1.41 standard deviations to the right of the population mean, if we assume the null hypothesis is true. The corresponding p-value is approximately 0.1587, which is greater than the commonly used threshold (0.05), leading us to not reject the null hypothesis.
Explanation:The z-statistic of 1.41 in the sample of Delmar's practice times can be used to draw conclusions about the sample's relationship to the population in a hypothesis test. It represents how many standard deviations an element (or group of elements, like a sample mean) falls from the mean or average of a population. A z-statistic of 1.41 means that the sample mean falls 1.41 standard deviations to the right of the population mean, assuming the null hypothesis to be true.
This information is useful in determining the p-value, which is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true. If the p-value is smaller than the predetermined significance level (let's assume α=0.05), we would reject the null hypothesis. The p-value corresponding to z=1.41 in a two-tailed test is approximately 0.1587. Since this p-value is greater than 0.05, we would not reject the null hypothesis and state that we do not have enough evidence to suggest that Delmar's practice times are significantly different from the population.
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A sack of potato with 14 lbs. 9 oz. After Wendy makes potato salad for a picnic does sac wait 9 lbs. 14 oz. What is the week of the potato Wendy's use for the potato salad
Answers
Answer:
Your answer should be 4 pounds 6 ounces.
Step-by-step explanation:
If you subtract how much the potato sack was before she made the potato salad from how much it was after, this gives you how much the potato she used weighed.
zoes living room rug is 3 feet wide and 7 feet long she will cover the rug with 6 inch cardboard pieces for a painting project how many cardboard pieces will zoe need
Answers
Zoe will need 84 pieces if they are 6” by 6”
For this case we have that by definition, 1 foot equals 12 inches.
So:
[tex]3 \ ft = 36 \ in\\7 \ ft = 84 \ in[/tex]
So, the area of the Zoes carpet is:
[tex]A = 36 * 84 = 3024 \ in ^ 2[/tex]
If the cardboard pieces are[tex]6 \ in\ by\ 6 \ in[/tex], then the area is:
[tex]36 \ in ^ 2[/tex]
To indicate the number of necessary pieces we divide:
[tex]\frac {3024} {36} = 84[/tex]
Thus, 84 pieces of cardboard are needed
Answer:
84
What is the tangent ratio for ∠A?
Answers
Answer:
Tan <A = 1/2
Step-by-step explanation:
SOH CAH TOA
TOA (opposite/adjacent)
So, the answer is 1/2
because the opposite of <A is 1 and the adjacent is 2.
For this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. Then, according to the figure we have:
[tex]tg (A) = \frac {1} {2}[/tex]
Answer:
[tex]tg (A) = \frac {1} {2}[/tex]
Evaluate 7 − (−1).
6
−6
8
−8
Answers
Simplify brackets
7 + 1
Simplify
8
Answer: C. 8
Answer:
minus and minus is plus
7+ 1 is 8 :)
For real number a, which of the following equations are true ? Select all that apply.
Answers
ANSWER
[tex] \lim_{x \to \: a}(x) = a[/tex]
[tex]\lim_{x \to \: a}(a) = a[/tex]
[tex]\lim_{x \to \: 5}(x) = 5[/tex]
EXPLANATION
For real number 'a',
[tex] \lim_{x \to \: a}(x) = a[/tex]
is true because we have to plug in 'a' for x.
[tex]\lim_{x \to \: a}(a) = a[/tex]
This is also true because limit of a constant is the constant.
[tex]\lim_{x \to \: 5}(4) = 5[/tex]
is false. The correct value is
[tex]\lim_{x \to \: 5}(4) =4[/tex]
[tex]\lim_{x \to \: 5}(x) = 5[/tex]
is also true because we have to substitute 5 for x.
[tex]\lim_{x \to \: a}(a) = x[/tex]
is also false
The limit should be
[tex]\lim_{x \to \: a}(a) = a[/tex]
Answer:
A, B, D
Step-by-step explanation:
Answers for the rest of the quick check
1. A,B,D
2. 16, D
3. 10a, B
4. 3, D
Good Luck :)
Question 5 of 8 2 Points Which values are solutions to the inequality below? Check all that apply. x2 > 10
A. -2
B. 3
C. 4
D. -4
Answers
Answer:
4 and -4
Step-by-step explanation:
> means greater than
x² > 10
4² > 10 → True, 16 is greater than 10
-4² > 10 → True, 16 is greater than 10
How do you evaluate trig functions without a calculator
Answers
You can't in theory. Only a few "nice" values are known, because they lead to particular triangles. For example, we have
[tex]\sin(0)=0,\quad \cos(0)=1[/tex][tex]\sin(30)=\frac{1}{2},\quad \cos(30)=\frac{\sqrt{3}}{2}[/tex][tex]\sin(45)=\cos(45)=\frac{\sqrt{2}}{2}[/tex]You can add other angles using symmetries, for example, you can compute sin(60) using sin(90-x) = cos(x), or similar stuff.
You can also use the double/half angles identities to add another couple of angles in our list, but that's it.
A gym surveyed 100 female members. These members were chosen at random from the gym's membership database. Participants were asked the question, "Do you prefer to use the easy weight-lifting machines or the harder free weights?"
A report of the survey results stated that female members at the gym prefer the weight-lifting machines over the free weights.
Select ALL statements that correctly evaluate the report.
Answers
Answer:
Step-by-step explanation:
The sample is not biased. The members were selected at random from the gym's female population.
The question is biased. It described the weight lifting machines as "easy" and the free weights as "harder".
The second and third choices are correct.
Which inequality statement best represents the graph?
f(x) > –x2 + x – 1
f(x) < x2 + x – 1
f(x) < –x2 + x – 1
f(x) > x2 + x – 1
Answers
Answer:
f(x) < –x2 + x – 1
Step-by-step explanation:
The graph is going down so we know that there is a maximum, therefore the A value has to be negative. This rules out f(x) < x2 + x – 1 and f(x) > x2 + x – 1 . The shaded area of the graph is below which indicates that f(x) has to be less than the function. This means the correct answer is f(x) < –x2 + x – 1 .
Answer:
[tex]y>-x^2 +x-1[/tex]
Step-by-step explanation:
Lets find the inequality that best describes the given statement
The graph of the parabola is upside down so the value of 'a' is -1
It means the equation for the parabola becomes [tex]y=-x^2 +x-1[/tex]
Now to get inequality , lets pick a point from the shaded part .
Lets pick (0,0), plug in 0 for x and 0 for y
[tex]y=-x^2 +x-1[/tex]
[tex]0=-(0)^2 +(0)-1[/tex]
[tex]0=-1[/tex]
0 is greater than -1
[tex]y>-x^2 +x-1[/tex]
Solve the inequality. SHOW YOUR WORK.
–6b > 36 or 2b > –4
**WHOEVER SHOWS THEIR WORK AND IS CORRECT WILL BE MARKED AS BRAINLEST**
Answers
-6b > 36
Divide both sides by -6;The result is b!b > -6or 2b > -4Divide both sides by 2The result is b!b > -2A triangle has an angle that measures 50°. The other two angles are in a ratio of 5:8. What are the measures of those two angles?
Answers
Answer:
Step-by-step explanation:
sum of angle of triangle is 180 degree
5x+8x+50degree =180 degree
13x= 180-50
13x= 130
x= 130/13
x=10
5x= 5*10=50degree
8x= 8*10 =80degree
The value of other two angles of triangle are 50 and 80 degrees.
Angles of triangle:Let us consider that other two angles of triangle are 5x and 8x.
Given that, one angle of triangle is 50 degree.
By property of triangle, sum of all three angles is equal to 180 degrees.
[tex]5x+8x+50=180\\\\13x=130\\\\x=130/13=10[/tex]
Other two angles of triangle are,
[tex]5x=5*10=50\\\\8x=8*10=80[/tex]
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A number generator was used to simulate the percentage of people in a town who ride a bike. The process simulates randomly selecting 100 people from the town and was repeated 20 times. The percentage of people who ride a bike is shown in the dot plot.
Which statement is true about the population of the town?
Answers
Answer:
Step-by-step explanation:
Of the 20 trials, 18 of them ended up between 60 and 75. So most likely, 60% to 75% of the town rides a bike.
The true statement about the dot plot is (c) Most likely, 60% to 75% of the town rides a bike.
How to interpret the dot plot?From the dot plot, we have the following sample between 60 and 75%
Sample = 3 + 4 + 6 + 5
Evaluate
Sample = 18
The above means that 18 out of the 20 trials fall between 60 and 75%
This means that between 60 and 75% of the town rides a bike
Hence, the true statement about the dot plot is (c)
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A line in the Cartesian plane passes through the points (5,8) and (9,15). What is the slope of the line?
A. 4⁄7
B. –7⁄4
C. –4⁄7
D. 7⁄4
Answers
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{15}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{15-8}{9-5}\implies \cfrac{7}{4}[/tex]
Can you guys please help
Answers
if you add 3 to it it would be 6
All of the following are equivalent, except _____.
2x + x
x(2 + 1)
2x²
3x
Answers
2x+x = 2x^2
X(2+1) = 2x^2
2x^2 stays the same
Therefore the answer is d 3x is not the same as the rest
Answer:
2x^2
Step-by-step explanation:
2x+x=3x
x(2+1)=2x+x=3x
3x
Solve the system of equations given below
Answers
[tex]
y-15=3x \\
-2x+5y=-3 \\ \\
-2x+y-15=0 /\cdot2 \\
-2x+5y-3=0 /\cdot(-2) \\ \\
-4x+2y-30=0 \\
4x-10y+6=0 \\ \\
-8y-24=0 \\
\boxed{y=-3} \\ \\
-3-15=3x \\
\boxed{x=-6}
[/tex]
The answer is C. (-6, -3)
Hope this helps.
r3t40
For this case we have the following system of equations:
[tex]y-15 = 3x\\-2x + 5y = -3[/tex]
We multiply the first equation by -5:
[tex]-5y + 75 = -15x[/tex]
Now we add the equations:
[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]
We find the value of the variable "y" according to the first equation:
[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]
The solution of the system is: (-6, -3)
Answer:
(-6, -3)
Option C
Jalen randomly chooses a number from 1 - 10 . What Is the probability he chooses a number greater than 3?
A. 3/5
B. 1/5
C. 7/9
D. 7/10
Answers
The answer will be D. 7/10 because you have 10 numbers and you want to have a number greater than 3 so it would be 10-3=7 and 7 would go over 10 because there are 7 numbers greater than 3 but less than 10.
The probability he chooses a number greater than 3 is 7/10, the correct option is D.
What is Probability?Probability is the likeliness of an event to happen.
Jalen randomly chooses a number 1-10
Probability = ( No. of favourable outcomes)/ Total Outcomes
The chances of getting the number more than 3 is 7
Total numbers are 10
The probability he chooses a number greater than 3 is 7/10.
Therefore, the correct option is D.
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Select the correct answer from each drop-down menu. The equation (y-2)^2/3^2 - (x-2)^2/4^2=1 represents a hyperbola whose foci are blank and blank .
Answers
Answer:
The foci are (2 , 7) and (2 , -3)
Step-by-step explanation:
* lets revise the equation of the hyperbola
- The standard form of the equation of a hyperbola with
center (h , k) and transverse axis parallel to the y-axis is
(y - k)²/a² - (x - h)²/b² = 1
- The coordinates of the vertices are ( h ± a , k )
- The coordinates of the co-vertices are ( h , k ± b )
- The coordinates of the foci are (h , k ± c), where c² = a² + b²
* Now lets solve the problem
∵ The equation of the hyperbola of vertex (h , k) is
(y - k)²/a² - (x - h)²/b² = 1
∵ The equation is (y - 2)²/3² - (x - 2)²/4² = 1
∴ k = 2 , h = 2 , a = 3 , b = 4
∵ The foci of it are (h , k + c) and (h , k - c)
- Lets find c from the equation c² = a² + b²
∵ a = 3
∴ a² = 3² = 9
∵ b = 4
∴ b² = 4² = 16
∴ c² = 9 + 16 = 25
∴ c = √25 = 5
- Lets find the foci
∵ The foci are (h , k + c) and (h , k - c)
∵ h = 2 , k = 2 , c = 5
∴ The foci are (2 , 2 + 5) and (2 , 2 - 5)
∴ The foci are (2 , 7) and (2 , -3)
Answer:
The foci are (2 , 7) and (2 , -3)
Step-by-step explanation:
solve for x and show all your work
3x + 4 = 16
Answers
Answer:
x=4
Step-by-step explanation:
16-4=12
3x=12
3*4=12
Answer: [tex]x=4[/tex]
Step-by-step explanation:
You need to find the value of the variable "x".
To solve for "x", the first step is to apply the Subtraction property of equality, which states that:
[tex]If\ a=b\ then\ a-c=b-c[/tex]
Then, you need to subtract 4 from both sides of the equation:
[tex]3x + 4 = 16\\3x + 4-4 = 16-4\\3x=12[/tex]
And finally, you can apply the Division property of equality, which states that:
[tex]If\ a=b\ then\ \frac{a}{c}=\frac{b}{c}[/tex]
Then you can divide both sides of the equation by 3, getting:
[tex]\frac{3x}{3}=\frac{12}{3}\\\\x=4[/tex]
Graph the solution set of the system of inequalities or indicate that the system has no solution.
y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x ≤ 1
Answers
The graph of inequality have many solution .
What is graph of inequality?The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
According to the question
The system of inequalities:
y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x ≤ 1
values to the graph of inequalities we will have to make inequalities into equal sign
y ≥ 2x – 4
y = 2x – 4
x y
0 -4
1 -2
2 0
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.
x + 2y ≤ 7
x + 2y = 7
x y
0 3.5
1 3
2 2.5
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≤ or < is used, shade below the line.
y ≥ -2
y = -2
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.
x ≤ 1
x = 1
Now,
As per graph of inequalities rules:
The solid line for ≤ and ≥.If the symbol ≤ or < is used, shade below the line.
Therefore, the darker part in graph is common part of all 4 inequalities with point (1,-2) and (1,3) .
Hence, The graph of inequality have many solution .
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Help!
Use the given conditions to write an equation for the line in point-slope form.
Passing through (-5, -7) and (-8, -6)
A) y− 7 = −13(x−5) or y −6 = −13(x−8)
B) y+7= −13(x+8) or y+6 = −13(x+5)
C) y+7 = −13(x+5) or y+6 = −13(x+8)
D) y+7 = −13(x+5) or y +6 = −13(x+7)
Answers
[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-6-(-7)}{-8-(-5)}\implies \cfrac{-6+7}{-8+5}\implies \cfrac{1}{-3}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-7)=-\cfrac{1}{3}[x-(-5)]\implies y+7=-\cfrac{1}{3}(x+5)[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-(-6)=-\cfrac{1}{3}[x-(-8)]\implies y+6=-\cfrac{1}{3}(x+8)[/tex]
Which value is not in the domain of the function?
Answers
Answer:
The answer is the second choice.
Step-by-step explanation:
The value of the domain which is not part of the function is x = -2.
Given data:
The domain of a function is the set of values that are allowed to plug into the function which are the inputs.
The domain of the three line segments is represented as:
Domain of line 1 ranges from [ -5 , -2 ).
Domain of line 2 ranges from ( -2 , 2 ).
Domain of line 3 ranges from [ 2 , 5 ].
So, the value -2 is not included in the domain values of the function.
Hence, x = -2 is not in the domain of function.
To learn more about domain and range:
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The amount of a sample remaining after t days is given by the equation p(t)=A(1/2)^t/h, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
Answers
Answer:
9.4 days
Step-by-step explanation:
Filling in the given numbers, we can solve for t:
0.18 = 1·(1/2)^(t/3.8)
log(0.18) = (t/3.8)log(1/2)
t = 3.8·log(0.18)/log(0.50) ≈ 9.4 . . . . days
The best estimate of the age of the sample is 9.4 days.
Answer:
9.4 days
Step-by-step explanation:
Which of the following are true statemetns about a 30-60-90 triangle?
I think it is a and b but I'm not sure
Answers
Answer:
Use the hyper link
Step-by-step explanation:
I took a picture on the unit.
Answer:
A.The longer leg is √3 times as long as the shorter
B. The hypotenuse is twice as long as the shorter leg
Step-by-step explanation:
The 30-60-90 is a special triangle with two acute angles 30° and 60°
The side across from the 30°= shorter leg
The side across from 60°=longer leg
The side across from 90°=hypotenuse
If we take the shorter side to be x and hypotenuse to be 2x then the longer leg will be;
Apply Pythagorean relationship
a² + b² =c²
c²-a²=b² where-----------c=2x and a=x
(2x)² - x² = b²
4x² - x² =b²
3x² = b²
√3x²=b
x√3 =b
Hence longer leg is √3 times longer than the shorter leg which is x and the hypothenuse 2x is twice the shorter leg which is x
use a cube and a cylinder to build a new shape. Repeat. Draw to show how you can combine these two new shapes to make a larger shape
Answers
Check the picture below.
If these two shapes are combined then the new shape is generated. Then the new shape will be given below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A cube and a cylinder are given.
If these two shapes are combined then the new shape is generated. Then the new shape will be
The shape is given below.
More about the geometry link is given below.
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