Newton's first law of motion states that; An object continues to be in its state of rest or uniform motion unless acted upon by an external force in which case, it acts otherwise.
An example of this law is an orange placed on a table.
In essence, the orange continues in its state of rest unless acted upon by a force of push or otherwise by an individual or perhaps wind as the case may be.
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Answer:
K) I, II, and III
Step-by-step explanation:
Given the quadratic equation in standard form, h = -at² + bt + c, where h is the height or the projectile of a baseball that changes over time, t. In the given quadratic equation, c represents the constant term. Altering the constant term, c, affects the h-intercept, the maximum value of h, and the t-intercept of the quadratic equation.
I. The h-interceptThe h-intercept is the value of the height, h, when t = 0. This means that setting t = 0 will leave you with the value of the constant term. In other words:
Set t = 0:
h = -at² + bt + c
h = -a(0)² + b(0) + c
h = -a(0) + 0 + c
h = 0 + c
h = c
Therefore, the value of the h-intercept is the value of c.
Hence, altering the value of c will also change the value of the h-intercept.
II. The maximum value of hThe maximum value of h occurs at the vertex, (t, h ). Changing the value of c affects the equation, especially the maximum value of h. To find the value of the t-coordinate of the vertex, use the following formula:
t = -b/2a
The value of the t-coordinate will then be substituted into the equation to find its corresponding h-coordinate. Thus, changing the value of c affects the corresponding h-coordinate of the vertex because you'll have to add the constant term into the rest of the terms within the equation. Therefore, altering the value of c affects the maximum value of h.
III. The t-interceptThe t-intercept is the point on the graph where it crosses the t-axis, and is also the value of t when h = 0. The t-intercept is the zero or the solution to the given equation. To find the t-intercept, set h = 0, and solve for the value of t. Solving for the value of t includes the addition of the constant term, c, with the rest of the terms in the equation. Therefore, altering the value of c also affects the t-intercept.
Therefore, the correct answer is Option K: I, II, and III.
Find the equation of the line which passes through (0,7) at a gradient of 3
Answer:
y=3x+7
Step-by-step explanation:
y=mx+c
we have (0,7). (x,y)
so y-7/x-0=3
multiply by (x-0) both sides to get
y-7=3x take -7 to the other side of equal sign
it will be: Y=3X+7
Review the incomplete equation below. Select the number that makes the equation true.
35 × 64 = 1800 +_____ + 120 +20
Answer:
300
Step-by-step explanation:
find what's 35 x 64 its 2240
then you add up 1800 and 120 and 20 n you get 1940
Then you subtract to see what's missing and you get
300
if you don't understand pls tell me
From a group of 15 men and 12 women, how many ways can you select a group of 2?
Answer:
The total number of ways this can be done together is 105 × 66 = 6930
This is a combination question question it has to do with selection.
In order to group 2 men from 15 men, this can be expressed using the combination formula as shown;
15C2 = 15!/(15-2)!2!
15C2 = 15!/13!2!
15C2 = 15×14/2
15C2 = 105 ways
Similarly in order to group 2 women from 12 men, this can be expressed using the combination formula as shown;
12C2 = 12!/(12-2)!2!
12C2 = 12!/10!2!
12C2 = 12×11/2
12C2 = 66 ways
The total number of ways this can be done together is 105 × 66 = 6930
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Suppose `h\left(t\right)=-5t^{2}+10t+3`is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.
a. How high above the water is the springboard? Explain how you know.
Answer:
Step-by-step explanation:
a) The height of the springboard above the water should be h(0) : Read, the height at t = 0
h(0) = -5(0) + 10(0) + 3
h(0) = 0 + 0 + 3
h(0) = 3
a) 3 meters
b) The time it takes the diver to hit water should be, the positive 0 solution for t. Remember, in a quadratic equation, there are two values for t where a parabola crosses the horizontal axis, which in this case would be t. Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac) / 2a
Substitute t for x, and use the coefficients for a, b, c:
t = (-10 ± √((102 - 4(-5)(3)))/2(-5)
t = (-10 ±√(100 + 60))/-10
t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:
t = (-10 ±√(10*16))/-10
t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:
t = -2(5 ± 2√10)/-10
t = (5 ± 2√10)/5
Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):
t ≈ 2.265
b) approx. 2.265 seconds for diver to hit water.
c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).
-5tt + 10t + 3 = 3
-5t2 + 10t = 0 ; factor out t
t(-5t + 10) = 0
We know t = 0:
We also know that -5t + 10 = 0
-5t = -10
t = 2
c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.
d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).
h = -10/2(-5)
h = -10/-10
h = 1
h(1) = -5(1)2 + 10(1) + 3
h(1) = -5 + 10 + 3
h(1) = 8
d) At t = 1 second, diver will have reached peak of dive.
e) At t = 1 second, diver will have reached a maximum height of 8 meters.
A grocery store clerk can scan 1 product every 1/2 of a second. At what rate can she scan products?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
An executive has 6 skirts, 8 jackets, and 6 blouses that all coordinate. If an outfit consists of one skirt, one
jacket, and one blouse, how many different outfits does she have?
Work Shown:
6*8*6 = 288
Why does this work? Consider a table that is 6 rows by 8 columns. The rows represent the number of skirts and 8 is the number of jackets. That produces 6*8 = 48 different skirt & jacket combos. We can extend this idea out to any number of items instead of just 2.
Answer:
6
Step-by-step explanation:
you keep counting until you reach the lowest number of whatever you need to make it equal
6-1-1-1-1-1-1
6-1-1-1-1-1-1
8-1-1-1-1-1-1
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:
y = 2 1/2 x + 5
Step-by-step explanation:
We were recently going over this. Slope formula: y2 - y1 / x2 - x1. In our case the slope is 2 1/2, and the y-intercept is 5.
Tell me if I'm wrong :)
35 if the answer is correct
Answer:
A.
Step-by-step explanation:
The attached graph has a y-intercept of -1 and a slope of 2, as the equation says it must.
__
The equation is in slope-intercept form, where the coefficient of x is the slope of the line. That is, the ratio of "rise" to "run" is 2: the line rises 2 grid squares for each grid square it runs to the right.
Eric is helping his younger sister learn division. He is having a hard time explaining what a remainder is. Help Eric out by describing what a remainder is in your own words. What is the remainder when 76 is divided by 3?
Answer:
1
Step-by-step explanation:
The remainder is what’s left when you divide. The part you cannot divide.
You can divide 75 by 3 = 25, so the remainder is 1.
In a recent survey of 288 people, 72 said that their favorite color of car was white. What percent of the people surveyed didn't like white cars?Write 2 over 5 as a percent.
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Answer:
75%
Step-by-step explanation:
The number for whom white was not a favorite was ...
288 -72 = 216
The percentage whose favorite was not white was ...
216/288 × 100% = 75% . . . didn't like white
In a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $50 and standard deviation of $14. Construct a confidence interval at a 98% confidence level.
Answer:
21
Step-by-step explanation:
if star x 2 equals square, then star x 8 equal
Answer:
Square times 4
Step-by-step explanation:
Square divided by 2 equals star right? Now we can plug in star in terms of square and we get square divided by 2 times 8, which is just Square times 4
(b) If the population doubled in size over 30 months and the current population is 20,000, what will the population be 4 years from now?
Answer:
The population will be 160,000 in 3 years.
Step-by-step explanation:
The deepest point in the world is the Mariana Trench in the western Pacific Ocean. It is 36,198 ft below sea level. What integer represents this depth?
Answer:
-36,198 feet below sea level
Step-by-step explanation:
Find the product -5.5(-1/5)?
a. -1.1
b. 2.75
c. 1.1
d. -0.275
Answer:
c. 1.1
Step-by-step explanation:
-5.5(-1/5) = 5.5/5 = 1.1
What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.
Rewrite 5/6 and 6/7 so they have a common denominator
Answer:
a command demonimater of 6 and 7 is 42
35/42 and 36/42
Hope This Helps!!!
Triangle PQR, triangle RST and two angle measures are shown below
Line segment QT intersects line segment PS at point R.
What is the value of x?
(look at picture to get a better understanding)
Answer:
x=50
Step-by-step explanation:
60+70=130
180-130=50
according to vertical angles x equals 50 degrees
sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday ?
Answer:
12x-15 dollars
Step-by-step explanation:
She worked for x hours, and earned $12 for every hour. This would be 12x. Then, she got charged $15 dollars, so -15. It would then be 12x-15 dollars.
Calculate the perimeter of a square with a side length of 3ft
The perimeter of a square is the length of one side multiplied by 4 ( the number of sides)
3 ft x 4 sides = 12 ft.
Perimeter = 12 ft.
How are expressions 1/4 of 12 and 12 divided by 4
5b + 6 - 6b + 2 = 19
Answer:
i got b= -11
Step-by-step explanation:
Answer:
b=-11Step-by-step explanation:
5b + 6 - 6b + 2 = 19
5b-6b+6+2=19
-b+8=19
b=8-19
b=-115(-11) + 6 - 6(-11) + 2 = 19
-55 + 6 + 66 + 2 = 19
-55+74=19
19=19
The temperature in antartica is 20 degrees below freezing at night. During the day, the temperature increases
by 30 degrees. What is the daytime temperature?
Answer:
42
Step-by-step explanation:
A local hamburger shop sold a combined total of 813 hamburgers and cheeseburgers on Saturday. There were 63 more cheeseburger sold than burgers. How many hamburgers were sold on Saturday?
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Answer:
375 hamburgers
Step-by-step explanation:
Let h represent the number of hamburgers. Then h+63 is the number of cheeseburgers, and the combined total is ...
h +(h +63) = 813
2h = 813 -63 = 750
h = 750/2 = 375
375 hamburgers were sold on Saturday.
_____
Additional comment
In a "sum and difference" problem like this, the smaller number is half the difference between the sum and the difference. h = (813 -63)/2 = 375. This generic solution applies to all "sum and difference" problems.
8y + 15x + 3y - 12x - 3x
Answer:
11y is the exact value.
Step-by-step explanation:
what is 3/4 ÷ 1/6 plz help
Answer:
4.5
Step-by-step explanation:
Please look at picture for question.
Answer:
The answer is D ane B
Step-by-step explanation:
The expression [tex](8z-4)(-7)[/tex] you would have to distribute -7 to get [tex]-56z+28[/tex]
The same goes for 40 in the expression [tex](-1.4z+0.7)*40[/tex]
if something traveled 36 feet in 22 frames in a 60 fps video, how fast would that be in mph?
i calculated that the answer will be roughly 24.9 miles per hour.
A radio station runs a promotion at an auto show with a money box with 12 $100 tickets, 11 $50 tickets, and 11 $25 tickets. The box contains an additional 20
"dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that exactly two $100 prizes and no other money winners are chosen.
Answer:
I wanna have fun sike lol
Step-by-step explanation: