The height of an object can be represented as a function of time.
It takes the rocket 25 seconds to hit the ground
The height function is given as:
[tex]\mathbf{h(t) = 400t - 16t^2}[/tex]
When the rocket hits the ground, we have:
h(t) = 0
So, the height function becomes
[tex]\mathbf{ 400t - 16t^2 = 0}[/tex]
Rewrite as:
[tex]\mathbf{ 16t^2 = 400t}[/tex]
Divide both sides by 16t
[tex]\mathbf{ t = 25}[/tex]
Hence, it takes the rocket 25 seconds to hit the ground
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a function, f(x)=4x+5, has a domain 0<=x<=50. What is the range? How do you do this??
Step-by-step explanation:
remember the domain is the interval or set of valid input (x) values. the range is the interval or set of the valid result (y) values.
so, the given domain tells us the interval to look at.
what are the functional values of the function between 0 and 50 ?
since the function is continuous (there are no gaps) in this interval, we can safely assume that all values between f(0) and f(50) are valid y values.
f(0) = 4×0 + 5 = 5
f(50) = 4×50 + 5 = 205
so, the range is 5 <= y <= 205
You and your friend are selling magazine subscriptions for a fundraiser after W weeks if you have sold (4w+1) subscriptions and your friend has sold (8w+6) subscriptions
Answer:
(4w+1)-(8w+6)
Step-by-step explanation:
Hope this helps :)
Can you help me I have a basketball game Tuesday and if I don’t pass I can’t play plz !!
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Explanation:
Angles A and B are supplementary which mean they combine to form a straight line. This further means the angles add to 180.
A+B = 180
(8x-27) + (4x+3) = 180
(8x+4x) + (-27+3) = 180
12x-24 = 180
12x = 180+24
12x = 204
x = 204/12
x = 17
Use this x value to find angles A and B
A = 8x-27 = 8*17-27 = 109B = 4x+3 = 4*17+3 = 71Note how A+B = 109+71 = 180 to help verify the answer.
Answer:
109
Step-by-step explanation:
supplementary angles equals 180 degrees
8x-27+4x+3=180
12x-24=180
12x=204
x=17
Then you put the 17 where the x is
8(17)-27=109
Which system of linear inequalities has the point (2, 1) in its solution set?
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2 On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 4, negative 2) and (0, 0). Everything below the line is shaded.
Nikola buys a bouquet of 8 sunflowers for $18
what is the cost for 1 sunflower?
1. Write the following statements in the from of equations. a. One third of a number plus 7 is 26
pls tell step by step
Answer:
1/3x+7=26
Step-by-step explanation:
1/3 of a number which could anything so mark as X
add 7
equals 26
1/3x+7=26
Given $P(10,12)$ and $Q(20,36)$, find the coordinates of a point whose distance from both $P$ and $Q$ is exactly $13.$
The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)
The distance between points, P and Q can be evaluated by the Pythagoras theorem as follows;
Distance, PQ = √(20-10)² + (36-12)²PQ = √(100+576)PQ = √676PQ = 26.Therefore, a point whose distance from both P and Q is exactly 13 is the midpoint of PQ.
Therefore,
x = (20 + 10)/2x = 15y = (36 + 12)/2y = 24.The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)
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10. The perimeter of a rectangular field is 100 ft and its width is 20 ft. Find
the length and the area of this rectangular field.
Answer:
Length is 30ft, area is 600ft squared
Step-by-step explanation:
how much better is Alex's money situation than if Amy's balance is $-28 and Alex's is $45?
Answer: Alex has $77 more than Amy
Explanation:
Draw a vertical number line. Plot -28 and 45 on this number line. Also, plot the number 0. Note the distance from -28 to 0 is 28 units. Then from 0 to 45 is another 45 units.
Overall, the distance is 28+45 = 77 units. This is the distance between the points -28 and 45 on the number line. It indicates Alex has $77 more compared to Amy. Effectively, Amy has $0 right now, but she's in debt $28. If we ignored the debt temporarily, then Alex has $45 more compared to Amy's balance of $0. Then we tack on the debt of 28 to bump to $77.
Another way to see this is to consider that Amy somehow gets $28. That 28 dollars is then immediately paid back to bring the balance back to $0. Then we'll tack on the $45 to get to 45+28 = 77.
If p is inversely proportional to the square of q, and p is 8 when q is 3, determine p when q is equal to 2.
Answer:
16/3
Step-by-step explanation:
formula :
p = kq
k = 8/3
so that is k
it will be like this "p = 8/3 x"
p = 8 × 2 / 3
p = 16/3
cant divide 3 with 16.
so, "p = 16/3" is the answer
What is an equation of the line that passes through the points (-6, -2) and
(-3, 2)?
Answer:
y = (4/3)x - 2/3
Step-by-step explanation:
From (-6, -2) to (-3, 2) we see the x-component changing by 3 units and the y-component by 4 units. Thus, the slope of this new line is
m = rise / run = 4/3.
Let's focus on the point (-3, 2). Here x = -3 and y = 2. Plugging these three values into the slope-intercept form of the equation of a line, we get:
2 = (4/3)(2) + b.
Then 2 = 8/3 + b, or 6/3 = 8/3 + b. Thus, b = 6/3 - 8/3, or -2/3.
The equation of the desired line is y = (4/3)x - 2/3
Answer:y=4/3x+6
Step-by-step explanation:
Given the graph below, which of the following could be the quadratic equation?
A.
[tex]3(x + 2 {)}^{2} + 5[/tex]
B.
[tex] - {x}^{2} + 8x + 18[/tex]
C.
[tex] - 2(x - 3 {)}^{2} + 1[/tex]
D.
[tex] {x}^{2} - 8x + 18[/tex]
Needs to be answered quickly
Answer:
only D as the correct answer
Step-by-step explanation:
The correct quadratic could not be B or C, because the negative sign in each indicates that the parabola opens down, which is not what we see here.
A is not appropriate either, because of the (x + 2)^2; that + sign tells us that the vertex lies 2 units to the left of the y-axis.
This leaves only D as the correct answer.
Does -19x go behind -12xi or in front of o -12xi in standard form?
x^2-19x-12xi or x^2-12xi-12x
Answer:
It's x² -12xi-12x
Step-by-step explanation:
You always do ax²+bx+c
Jason gets 15 gallons of gas at $3.90 a gallon. 15 gallons gives him 20 miles to the gallon. How many miles can Jason travel on 1 tank of gas?
Plsss some one help with this
Answer:
the answer is c and the entire equation means that the tickets each cost $15 and the service fee is $12
Find the perimeter. Simplify your answer.
Answer:
3a+ 16
Hope this helps!
8. The sum of two numbers is 52. Find the larger number if their ratio is 1: 3.
Answer:
39
Step-by-step explanation:
Lets solve for x:
We know the ratio is 1:3
1x+3x = 52
4x = 52
x = 13
Since the ratio is 1:3:
13(3) = 39
13:39
Which makes 39 the larger number
solve the proportion (someone pls help)
The tables of ordered pairs represent some points on the graphs of two lines. What is the solution to the system of equations represented by the two lines?
Answer:
(-9, 5)
Step-by-step explanation:
1. Find the equations of both lines (y = mx +b).
For the table on the left, we can see that the y-intercept is 23 (at x=0, y=23). Hence, b = 23. We can also see that the y-value for the left table increases by increments of 2, meaning that the slope (m) will be 2. Thus:
f1(x) = 2x + 23
For the right table, do the same thing. The table tells us that when x = 0, y = -58 (so b = -58). We also see that the y-value DECREASES in increments of 7, meaning that the slope, m = -7. Thus,
f2(x) = -7x - 58
2. Set the equations equal to each other to find the x-value at which the two equations will intersect.
2x + 23 = -7x - 58
9x = -81
x = -9
3. Plug your newfound x-value into any of the two equations to find the y-value at which both equations will intersect.
y = 2x + 23
y = 2(-9) + 23
y = 5
OR
y = -7x - 58
y = -7(-9) - 58
y = 5
ANSWER: At the point (-9, 5), the two lines intersect. Hence, the solution to the equation is (-9, 5).
Answer:
x = -9 and y =. 5
Step-by-step explanation:
(-2, 19) and (-1, 21)
Slope: (21-19)/(-1- -2) = 2
y-intercept = 21 - (2)(-1) = 23
a) y =2x + 23
(-2,-44) and (-1,-51)
Slope: (-51- - 44)/(-1- -2) = -7/1 = -7
y-intercept: -44-(-7)(-2)=-58
b) y = -7x - 58
Substitute y in equation a.
-7x-58 = 2x + 23
-9x = 81
x = -9
Substitute X by -9 in equation b: y = -7(-9) - 58= 5
y = 5
What is the least common multiple (lcm)of 2,3, and 6
Explanation:
List list the multiples of each value
multiples of 2 = {2, 4, 6, 8, 10, ...}multiples of 3 = {3, 6, 9, 12, 15, ...}multiples of 6 = {6, 12, 18, 24, ...}In each list, we see 6 show up. This is the smallest multiple that is in common; therefore, the LCM is 6
Side note: The LCM is useful to help add and subtract fractions.
solve the equation −4(m+6)=−8
.,........................
To reach his office on time, Mr Chin usually drives to work at an average speed of 75 km/h. However, if Mr Chin increases his average driving speed by 5 km/h, he will reach his office 10 minutes earlier. If the distance Mr Chin needs to travel to reach his office is represented by x km, form an equation in x and solve for x.
Answer: x = 200 km
Step-by-step explanation:
Distance(x) = Speed(s) x Time(t)
t is in hours
x=s*t
At 75km/h: 75*t = x
At 80km/h: 80*(t-(10/60)) = x [the -(10/60) is the 10 minutes saved, in hours]
We know the distance, x, is the same, so we can set these equal to each other:
75*t = 80*(t- (10/60))
75*t = 80*t - 13.3333
-5*t = -13.3333
t = 2 2/3 hours
Both situations should give the same distance with 2 2/3 and 2 2/3 - :
x = (75 km/hr) x ( 2 2/3 hr)= 200 km
x = (80 km/hr) x (2 2/3 - 1/6 hr) = 200 km
Enter a digit in each box to complete the addition problem
Answer:
4.5 + 19.75 = 24.25
Find your missing digits with the equation above
5y+40z what is the factor
Answer:
the factored form is 5(y + 8z)
Step-by-step explanation:
Because 5 divides evenly into both 5y and 40z, the GCF is 5 and the factored form is 5(y + 8z)
5, k+3, 2k+1 ,3k-2, 26 and 31 are in ascending order. if the median is 17. find the value of k.
Answer:
k = 7
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order.
If there is no exact middle value then the median is the average of the 2 values either side of the middle.
5 , k + 3 , 2k + 1 , 3k - 2 , 26 , 31
↑ middle
Then
[tex]\frac{2k+1+3k-2}{2}[/tex] = 17 ( multiply both sides by 2 to clear the fraction )
5k - 1 = 34 ( add 1 to both sides )
5k = 35 ( divide both sides by 5 )
k = 7
The value of k is 7 if 5, k+3, 2k+1,3k-2, 26, and 31 are in ascending order and the median of the data set is 17.
What is the median?A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.
We have:
5, k+3, 2k+1 ,3k-2, 26 and 31 are in ascending order
The median of the data set is 17.
The mid-terms are 2k+1 ,3k-2
(2k + 1 + 3k - 2)/2 = 17
5k -1 = 34
5k = 34 + 1
5k = 35
k = 35/5
k = 7
Thus, the value of k is 7 if 5, k+3, 2k+1,3k-2, 26, and 31 are in ascending order and the median of the data set is 17.
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What is the slope of this line?
−15
15
5
−5
Number graph ranging from negative 5 to 5 on both the x and y axis. A line passes through the point begin ordered pair 0 comma 2 end ordered pair and the point begin ordered pair 5 comma 3 end ordered pair
Step-by-step explanation:
if I understand your text right, we are looking at the line going through the points (0, 2) and (5, 3).
the slope is in a line equation always the factor of x.
anyway, it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point on the line to another.
so, we are simply going from (0, 2) to (5, 3).
x changes by +5 (from 0 to 5).
y changes by +1 (from 2 to 3).
so, the slope is y/x = 1/5.
Answer:
B. [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Please help im in a hurry
Answer:
I can't explain this discrepancy other than to suggest that they are talking about 2 different groups. The boss has included his salary in the average, but the employee is only concerned about the wage of the average worker.
Step-by-step explanation:
Josh is painting all the walls in his room that is 3m x 4m and 2.75m high, How much paint in square feet is needed?
Answer:
33
Step-by-step explanation:
3*4*2.75=33
13. Rachel is building a book shelf. The wood she is using is sold in sections that are 8 feet long and 16 inches
wide.
All of the boards Rachel needs will be 16 inches wide.
She needs 5 boards that each measure 48 inches long,
She needs 2 boards that each measure 32 inches long.
What is the minimum number of 8 foot sections of wood Rachel will need to make the book shelf?
.
.
A. 3
B. 4
C. 6
D. 7
Can anyone please answer this question properly with explanation
I need explanation
EXPLANATION
DONT ANSWER IF YOU DON’T HAVE A EXPLANATION PLEASE
Answer: See below.
Step-by-step explanation:
We'll assume the top and bottom lines are parallel. That means angles 4 and 5 are 90 degrees since the line coming down is perpendicular to the parallel line. The sum of angles 1 and 2 is also 90°. The interior angles of a triangle must add to 180°. So far we have two: 90° and 60°. The third must therefore be 30°(angle 2). Angle 3 must be 120° since it shares a straight line with the 60° angle and the straight line is 180° from one side to the other. Angle 1 must be (90°- angle 2), which makes it 60°.
1. 60°
2. 30°
3. 120°
4. 60°
5. 90°