Rate of change of distance is also known as speed.
Given,
Distance (s) = 400km = 400 × 1000m = 400,000m
Time (t) = 10h = 10 × 3600s = 36,000s
We know that,
Speed (v) = Distance/Time
[tex]=> v = \frac{s}{t} \\ => v = \frac{400000m}{36000s} \\ => v = \frac{400m}{36s} \\ => v = \frac{100m}{9s} \\ => v = \frac{100}{9}m {s}^{ - 2} \\ [/tex]
A heron can travel an average of 400 km in 10 hours. Then the rate of change of distance that is speed is [tex]11.12 ms^{-2}[/tex].
What is the meaning of the term “distance”?Distance is a measurement of how far apart two things or locations are, either quantitatively or occasionally qualitatively. Distance in physics or common language can refer to a physical length or an estimate based on other factors.
The term is frequently used metaphorically to refer to a measurement of the amount of difference between two similar objects, or a degree of separation as exemplified by distance between people in a social network.
The concept of a metric space is used in mathematics to formalize the majority of such concepts of distance, both literal and figurative.
[tex]Distance (s) = 400km \\= 400 \times 1000m \\= 400,000mTime (t) = 10h \\= 10 \times 3600s \\= 36,000s\\\\Speed = Distance / Time\\= 400000 / 36000\\= 11.12 ms^{-2}[/tex]
Therefore, the rate of change of distance that is speed is [tex]11.12 ms^{-2}[/tex].
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Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each. His total annual cost is a function of the number of books that he purchases in a year. Let b represent the number of books he purchases in a year. Which function, C(b), represents his yearly cost
mA = (4x - 2) and mzB = (11x + 17)°. Find x if the angles are
supplementary
A.) 165
B.) 180
C.) 15
D.) 11
If a pine tree grows 3 inches per year,how long will it take for the tree to reach a height of 8 feet
Answer:
32 years
Step-by-step explanation:
8x12 because there are 12 inches in a foot
8x12=96
96/3
96/3=32
Answer:
32 years
Step-by-step explanation:
y = years
1 foot = 12 inches
12 × 8 = 96
Now, plug in random numbers into the expression below to find how long it takes for the tree to grow 8 feet.
3y
3 × 10 = 30
3 × 20 = 60
3 × 30 = 90
3 × 31 = 93
3 × 32 = 96
It will take the pine tree 32 years to grow 8 feet, or 96 inches.
Solve the system of equations using substitution.
y = x + 6
y = –2x – 3
Answer:
x = -3
y= 3
Step-by-step explanation:
y = x + 6 -----------------------(I)
y = -2x - 3 ---------------------(II)
Substitute y =x +6 in equation (II)
x + 6 = -2x - 3
Add 2x to both sides
x + 2x +6 = -3
Combine like terms
3x + 6 = - 3
Subtract 6 from both sides
3x = - 3 - 6
3x = -9
Divide both sides by 3
x = -9/3
x = -3
Plug in s = -3 in equation (I)
y = -3 + 6
y = 3
Can someone help me with this math homework please!
In case of Nina:
slope of graph = speed = 48-32/6-4 = 16/2 =8
y-32 =8(x-4)
y-32=8x-32
y=8x
d=8t
at x= 0 i.e at t= 0
d= 0m
In case of Ryan:
slope =speed = 47.5-35=6-4 = 12.5/2 =6.25
y-35=6.25(x-4)
y-35=6.25x-25
y=6.25x+10
d=6.25t+10
at t = 0, d= 10m
RYAN had a head start of 10 m
PLEASE HELP 30 POINTS
Find the value of x in the triangle below.
804
155
55°
o
75
80°
Ο Ο
85
Answer:
75°
Step-by-step explanation:
First, we need to know that the interior angle sum of a triangle is always 180°.
Now, to find the missing angle aside from x, we need to complete the sum 180-155=25, seeing 155° lies on a straight line. Remembering the interior angle sum of a triangle is always 180°, it is thus clear that 25+80+x=180. If we complete this equation, x=75.
Hope this helps!
what are the points for the equation y +2 = - 3/4 (x+4)
Answer:A(1,-5)
B(6,-8)
Step-by-step explanation:
need some help with this
Answer:
y=4x-7
Step-by-step explanation:
here,
the equation of straight line in slope intercept form is;
y=mx+c
( m= slope
c= y-intercept )
soo..
the question has asked for slope 4 i.e. m=4
and y- intercept -7 i.e. c= -7
now.
the required equation is
y= 4x-7
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When AG = 16 ft, find the area of the region that is NOT shaded. Round to the nearest tenth.
Answer:
730.88
Step-by-step explanation:
Area of the entire circle = pi * r^2
r = 16
Area = 3.14 * 16^2
Area = 803.84
1/4 of the circle contains the shaded area. It's area = 1/4 * 803.84
Area of 1/4 circle =
200.96
the area of the triangle
Area = 1/2 AG * G?
AG and G? are equal
Area = 1/2 * 16^2
Area = 128
Area of 1/4 circle - area of the triangle = area of the shaded portion
shaded portion = 200.95 - 128
Shaded Portion = 72.96
So the area of the unshaded part
unshaded = 803.84 - 72.96
Unshaded = 730.88
Use the ordered pairs to give a function rule. Give the rule in slope intercept form {(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)}
Answer:
[tex]y = -0.25x -1.5[/tex]
Step-by-step explanation:
Given
[tex](x,y) = \{(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)\}[/tex]
Required
The function rule (in slope intercept)
First, we calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{-1.25 -1.5}{-1 - -12}[/tex]
[tex]m = \frac{-2.75}{11}[/tex]
[tex]m = -\frac{2.75}{11}[/tex]
[tex]m = -0.25[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = -0.25(x - -12) + 1.5[/tex]
[tex]y = -0.25(x +12) + 1.5[/tex]
Open bracket
[tex]y = -0.25x -3 + 1.5[/tex]
[tex]y = -0.25x -1.5[/tex]
3.)The lateral surface area of a right circular cylinder is 120cm² and the circumference of the bases is 12cm.Find the altitude of the cylinder
Answer:
Lateral surface area= circumference*height
120=12*h
h=10cm
Answer:
h=10 cm
Step-by-step explanation:
cicumference of a circle C=2πr=12
lateral surface area of cylinder=2πrh
120=12h
h=120/12=10 cm
simplify -8/2 ÷ 6/-3
Answer: the answer is 2 or C
-8/2 x -3/6
*Always do the recipical*
(-8 x -3) / (2 x 6)
-8 x -3= +24
2 x 6= 12
24/12= 2
The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Given that the expression is,
-8/2 x -3/6
The expression will be solved as below,
E = (-8 x -3) / (2 x 6)
The numerator will get reciprocal and multiplied to the denominator,
E = 24 / 12
Divide the number 24 by 12 and get the solution,
E = 2
Therefore, the solution of the expression will be 2. The correct option is B.
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The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?
Answer:
Yes it can
Step-by-step explanation:
To check wether it's a right angle triangle we need to apply the Pythagoras theorem
h^2= a^2 +b^2
Hypotenuse is always the longest side so
5^2 = 3^2 + 4^2
This is correct, so the triangle is a right angle triangle
Answer from Gauthmath
a)out of 300 students In a class 60% of the students took physics and 35 students took chemistry and 20% of the students did not take any of this subject. how many students take both the subject
Answer:
25 students take both subjects.
Step-by-step explanation:
Solve for 60% of 300 students:
60/100 = x/300
Cross multiply:
60 × 300 = 100 × x
18000 = 100x
Divide both sides by 100:
180 = x
Solve for 20% of 300 students:
20/100 = x/300
20 × 300 = 100 × x
6000 = 100x
60 = x
Solve for the percentage of students in chemistry:
x/100 = 35/300
x × 300 = 100 × 35
300x = 3500
x = 11.66666...7
x = about 11.7%
Find the difference in percentages:
100 - 60 - 20 - 11.7
8.3
8.3% take both subjects
Solve for 8.3% of students:
8.3/100 = x/300
8.3 × 300 = 100 × x
2490 = 100x
24.9
About 25 students
Check your work by adding all the students together (to get to 300):
25 + 60 + 180 + 35
300 students total
This is correct!
*Please Help!*
What is the volume of water, to the nearest tenth of a cubic metre, that would fill this spa tub?
First cylinder= 0.75m diameter, 0.80m height
Cylinder Underneath= 1.25m diameter, 0.70m height
Semi Sphere that holds both cylinders= 3m long
Answer:
The volume of water that will fill the spa tub is 5.9 cubic meters.
Step-by-step explanation:
Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)
i. volume of first cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius and h is the height of the cylinder.
r = [tex]\frac{0.75}{2}[/tex] = [tex]\frac{3}{8}[/tex]
= 0.375 m
h = 0.80 m
volume of the first cylinder = [tex]\frac{22}{7}[/tex] x [tex](\frac{3}{8} )^{2}[/tex] x 0.8
= 0.3536 cubic meters
ii. volume of the cylinder underneath = [tex]\pi[/tex][tex]r^{2}[/tex]h
r = [tex]\frac{1.25}{2}[/tex] = [tex]\frac{5}{8}[/tex]
= 0.625
h = 0.70 m
volume of the cylinder underneath = [tex]\frac{22}{7}[/tex] x [tex](\frac{5}{8}) ^{2}[/tex] x 0.7
= 0.8594 cubic meters
iii. volume of the semi sphere = [tex]\frac{2}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
where r is the radius = 1.5 m
volume of the semi sphere = [tex]\frac{2}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](1.5)^{3}[/tex]
= 7.0714 cubic meters
Thus,
volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)
= 5.8584
The volume of water that will fill the spa tub is 5.9 cubic meters.
A particular strain of bacteria triples in population every 45 minutes Assuming you start with 50 bacteria in a Petri dish how many bacteria will there be in 4.5 hours
Answer:
4.5 hours in minutes = 270
Every 45 minutes, bacteria triples
You start with 50
Divide 270 (total time) by 45 (every time bacteria triples)
270/45 = 6
36,450 bacteria
Which of the following accurately describes the median of a set of data? Multiple choice question. The midpoint of the data when it is arranged in order. The difference in the largest and smallest values. The most numerous observation in a set of data. The arithmetic average of the values in the set.
Answer:
The midpoint of the data when it is arranged in order.
Step-by-step explanation:
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
For example, the median of the following set of numbers is 5
1, 2, 5, 10, 20
Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Given JIH~ LMN. what is the value of LN?
Answer:
7 units
Step-by-step explanation:
In similar triangles, corresponding sides are same ratio.
[tex]\frac{LN}{JH}=\frac{LM}{JI}\\\\\frac{LN}{14}=\frac{5}{10}\\\\LN=\frac{5}{10}*14\\\\LN=7[/tex]
Evaluate the following expression using the values given: (1 point)
Find 3x − y − 3z if x = −2, y = 1, and z = −2.
Use the parabola tool to graph the quadratic function f(x)=−x2+4. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
see below
Step-by-step explanation:
f(x) = -x^2 +4
The vertex form is
y = a(x-h)^2 +k
Rewriting
f(x) = -(x-0)^2 +4
The vertex is (0,4) and a = -1
Since a is negative we know the parabola opens downward
f(x) = -(x^2 -4)
We can find the zeros
0 = -(x^2 -2^2)
This is the difference of squares
0 = -(x-2)(x+2)
Using the zero product property
x-2 =0 x+2 =0
x=2 x=-2
(2,0) (-2,0) are the zeros of the parabola and 2 other points on the parabola
We have the maximum ( vertex) and the zeros and know that it opens downward, we can graph the parabola
Answer:
Your vertex is (4,0)
Step-by-step explanation:
Three red balls, 5 green balls and a number of blue balls are put together in a sac. One ball is picked at random from the sac. If the probability of picking a red ball is 1|6, find the a) The number of blue balls in sac. B) the probability of picking a green ball
Answer:
total balls = 18 .... 3/x = 1/6
blue = 10 ... 18-(5+3) = 10
p of green = 5/18 = .277
Step-by-step explanation:
expand this question (x+5)(x-3)
I need help what’s the answer?
Answer:
30 words per minute
Step-by-step explanation:
Take the number of words and divide by the number of minutes
150/5 = 30
300/10 =30
450/15 = 30
600/20 = 30
30 words per minute
Answer:
janae types 30 words each minutes.
Step-by-step explanation:
if 5minutes = 150 words
[tex]1 \: minute = \frac{150words}{5minutes} [/tex]
[tex] = \: 30words[/tex]
Help this is due in 10 mins
Answer:
Only A is true
for sure
....................
Can somebody help me Answer to this ??
X=7
c is the answer:
[tex]3x + 50 = 10x + 1 \\ 10x - 3x = 50 - 1 \\ 7x = 49 \\ x = \frac{49}{7} \\ x = 7[/tex]
18 Ib. Then her dog loses another 1 lb. Finally, it
Cece dog
gains lb. What is the total change in her dog's weight? how your work. Pleasss help
Answer:
17 lb I guess 8 don't think the question is full
Step-by-step explanation:
the question is half
find the cost of four score of plate at 50k each and three dozens of spoon at 20k each
can i get some help? i tried figuring it out myself already but i must have done something wrong. please help!
First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.
N will represent nickels
D will represent dimes
N + D = 30
---The problem tells us that there are 30 total coins
0.05N + 0.10D = 2.95
---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95
Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.
N + D = 30
N = 30 - D
Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.
0.05(30 - D) + 0.10D = 2.95
1.5 - 0.05D + 0.10D = 2.95
1.5 + 0.05D = 2.95
0.05D = 1.45
D = 29
Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.
N = 30 - D
N = 30 - 29
N = 1
Therefore, there are 29 dimes and 1 nickel.
Hope this helps!
Use the given conditions to write an equations for the line in slope- intercept form. passing through (1,-8) and (-7,8)
Answer:
y = -2x - 6
Step-by-step explanation:
Going from the first point to the second, we see x decreasing by 8 from 1 to -7 (this is the 'run') and y increasing by 16 from -8 to +8 (this is the 'rise'). Thus, the slope of the line through these two points is m = rise/run = 16/(-8) = -2.
Using the point-slope formula y - k = m(x - h) and the point (1, -8), we get:
y + 8 = -2(x - 1), or
y = -8 - 2x + 2, or
y = -2x - 6 (in slope-intercept form)
Please help me i need the answer right now. The lesson is Rational Root Theorem.
Step-by-step explanation:
1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the
x+4.(3x+1)(x)The volume is 720.Volume of Rectangular prism is LxWXH. So the volume is equal to the terms all multiplied. which is[tex](3x + 1)(x + 4)[/tex]
[tex](3 {x}^{2} + 13x + 4)x = 720[/tex]
Multiply it by x.
[tex]3 {x}^{3} + 13 {x}^{2} + 4x = 720[/tex]
[tex] 3{x}^{3} + 13 {x}^{2} + 4 x - 720[/tex]
The possible roots
The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be
[tex]x = 5[/tex]
2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.
Let check via synethic division to see which are roots.
Let try 1 and -1 first. If we plug 1 into the equation, we get
[tex]1 - 2 - 5 + 6 = 0[/tex]
So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in
[tex] {x}^{2} - x - 6[/tex]
We can then factor this into
[tex](x - 3)(x + 2)[/tex]
So our roots or factors is
[tex](x - 1)(x - 3)(x + 2)[/tex]
