Answer: 900,000 for the city/2,304,000
Step-by-step explanation:
I used the exponential growth formula with initial population rate of growth and time passed.
In 2002, the population of the city was 416,000 and the population of the suburbs was 884,000.
Explanation:In 2000, the city's population was 400,000 and the suburban population was 900,000. Each year, 5% of the city's population moves to the suburbs (and 95% stays in the city), and 4% of the suburban population moves to the city (and 96% remains in the suburbs). To calculate the population of the city in 2002, we need to subtract 5% of the city's population in 2000 from the 2000 city population and add 4% of the suburban population. To calculate the population of the suburbs in 2002, we need to subtract 4% of the suburban population in 2000 from the 2000 suburban population and add 5% of the city population.
Population of city in 2002 = (City population in 2000) - 5% of (City population in 2000) + 4% of (Suburban population in 2000)
Population of suburbs in 2002 = (Suburban population in 2000) - 4% of (Suburban population in 2000) + 5% of (City population in 2000)
By substituting the given values, we can calculate the population of the city and suburbs in 2002.
Population of city in 2002 = 400,000 - 0.05 * 400,000 + 0.04 * 900,000
Population of city in 2002 = 400,000 - 20,000 + 36,000
Population of city in 2002 = 416,000
Population of suburbs in 2002 = 900,000 - 0.04 * 900,000 + 0.05 * 400,000
Population of suburbs in 2002 = 900,000 - 36,000 + 20,000
Population of suburbs in 2002 = 884,000
Learn more about Population calculation here:https://brainly.com/question/2894353
#SPJ3
Is there enough information given to find the value of X. Explain your reasoning. Ty!
Without a given equation or inequality to work with, it is impossible to determine the value of 'x' based on the presented information.
Explanation:The provided question seems to be missing some key elements that would offer us enough information to determine the value of x. In mathematics, to find the value of a variable, such as x, you generally need some form of an equation or inequality where x is a part of and other elements present in the equation give indirect details about x. This could include clues as to its relationships with other values, or boundaries for its possible amount. Without an equation, it is impossible to ascertain the value of x based on the given question.
This reasoning is based on the fundamental principles of algebra, a branch of mathematics. For example, if given an equation like '3x + 2 = 8', we could apply algebraic principles to solve for x. However, in this case, no such equation has been provided, and so we cannot calculate the value of x. Thus, there is not enough information provided.
Learn more about Determining Variable Value here:https://brainly.com/question/33446292
#SPJ2
How do you do this question?
Answer:
(B) only I and II
Step-by-step explanation:
An odd relation is symmetrical about the origin. All of the relations are odd.
An even relation is symmetrical about the y-axis. Only the first two relations are even.
_____
The graph shows the first relation is that of a circle. It is symmetrical about its center at the origin and about any diameter, including the y-axis.
The second relation is a degenerate hyperbola. It graphs as the pair of lines y=x and y=-x. It is symmetrical about both the origin and the y-axis. (It also has other lines of symmetry.)
The third relation is a line with slope -1 (represented by dots). It is symmetrical about the origin, but not the y-axis. It is only an odd relation.
HELP ASAP! I need help! I’m stuck and don’t know what to do!
Answer:
last choice
Step-by-step explanation:
Let's look at (8,-2)
We are moving this point 7 units right and 2 units down so that becomes
(15,-4)
But you are also reflecting it across y-axis so the x becomes opposite and y stays the same so you have the final image point after the transformations is (-15,-4).
So it can only be choice D, the last choice.
(-4,0) reflected across y=0 is it
A)(-4,0)
B)(4,0)
C)(-4,-2)
D)(0,0)
En una comunidad se intercambian productos alimenticios A, B, C y D con la modalidad del trueque, utilizando un mismo recipiente llamado a "medida" para cada producto. Si una medida de A más una de C se cambia por 5 medidas de B; una medida de A más una de B se cambia por una de C; y una medida de B más una de C se cambia por una de D, ?Cuántas medidas de B se cambian por una de D?
Answer: se necesitan 4 medidas de B para obtener una de D
Step-by-step explanation:
Las medidas serán entendidas como unidades de.. (A , B o C)
Entonces, de esta manera
1A + 1C = 5B
1A + 1B = 1 C
1B + 1C = 1D
Para lograr el cometido debo combinar las 3 relaciones de cambio de tal manera que se cancelen totalmente las partes A y C utilizando los multiplicadores adecuados
Entonces,
Uso 5 unidades de B para conseguir una de A y una de C
5B = 1A + 1C
Con esa A y otra de B obtengo otra C
1A + 1B = 1C
Por último con esas dos unidades de C y dos unidades mas de B consigo 2 de D
2B+ 2C = 2D
En total utilicé 5 + 1 + 2 = 8 unidades de B para obtener 2 de D
Entonces para obtener una de D necesitaría 4 unidades de B
What is the total surface area of the square pyramid below?
question above
Answer:
132 m².
Step-by-step explanation:
What's the surface area of each lateral face of this pyramid?
Each lateral face of this pyramid is a triangle, with
a height of 8 meters on a base 6 meters.The base of this pyramid is a square. As a result, all four lateral sides are congruent. The area of each of these triangle is thus
[tex]\displaystyle \frac{1}{2}\times \text{Base}\times \text{Height} = \rm \frac{1}{2} \times 6 \times 8 = 24\; m^{2}[/tex].
The base of this pyramid is a square. The length of a side of this square is 6 meters. The area of the base will be
[tex]\text{Side}^{2} = \rm 6^{2} = 36\; m^{2}[/tex].
Put the five faces together to get the total surface area of this square pyramid:
[tex]\rm 4\times 24 + 36 = 132\; m^{2}[/tex].
Solve for x
12
6√3
5
12.5
First, lets focus on finding out the other two legs of the large triangle.
To do this, we use Pythagoras' Theorem.
So the left leg = √(16² + x²)
So the right leg = √(9² + x²)
Notice, the larger triangle is also a right angled triangle, that means the sum of the two legs squared = hypotenuse squared.
Since we have just worked out the two legs, we can substitute them into:
a² + b² = c²
(√(16² + x²) )² + (√(9² + x²) )² = (16 + 9)²
Notice that the power of two cancels out with the squareroots so we get:
(16² + x² ) + (9² + x² ) = (25)² (simplify and collect like terms)
256 + x² + 81 + x² = 625
337 + 2x² = 625 (subtract 337 from both sides to isolate the x )
2x² = 288 (divide both sides by 2)
x² = 144 (square root both sides)
x = √144
x = 12
_______________________________________
Answer:
x = 12
_______________________________________
Note: if you have any questions, please ask and I will be more than happy to help and give further explanations!
I can confirm that the other person is right, the answer is 12.
Two consecutive even integers add up to 1830 . What are the two numbers.
Answer:
914 and 916
Step-by-step explanation:
let the first integer be x
The next largest consecutive even integer is hence x+2
given that the 2 integers add up to 1830,
x + (x+2) = 1830
2x + 2 = 1830
2x = 1828
x = 914
Hence the first number is 914
the second number is 914 + 2 = 916
Check Answer:
914 + 916 = 1830 (verified)
[tex]2n+2n+2=1830\\4n=1828\\n=457\\\\2n=914\\2n+2=916[/tex]
914 and 916
Find the area of the kite
For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 3 + 3 = 6 meters and one has height of 2m and the other height of 4m.
So, the total area is given by:
[tex]A = \frac {1} {2} * 6 * 2 + \frac {1} {2} * 6 * 4\\A = \frac {1} {2} 12+ \frac {1} {2} *24\\A = 6 + 12\\A = 18[/tex]
Thus, the area of the kite is [tex]18m ^ 2[/tex]
ANswer:
[tex]18m ^ 2[/tex]
4. (08.07 MC) Which graph shows the quadratic function y = 3x2 + 12x + 14? (5 points) The following graph is labeled A: A four quadrant graph with a parabola opening up, passing through the points negative 3, 1, negative 2, negative 2, and negative 1, 1 with the vertex at 2, negative 2. The following graph is labeled B: A four quadrant graph with a parabola opening up, passing through the points 1, 4, 2, 1, and 3, 4 with the vertex at 2, 1. The following graph is labeled C: A four quadrant graph with a parabola opening up, passing through the points negative 3, 5, negative 2, 2, and negative 1, 5 with the vertex at negative 2, 2. The following graph is labeled D: A four quadrant graph with a parabola opening up, passing through the points 1, 1, 2, negative 2, and 3, 1 with the vertex at 2, negative 2. A B C D
Answer:
C
Step-by-step explanation:
You have a vertex of (-2,2) since -b/(2a)=-12/(2*3)=-12/6=-2
and then plug it in for the y-coordinate 3(-2)^2+12(-2)+14=2
So you have a vertex of (-2,2).
The parabola is open up since 3 is positive.
So far it looks like the choice is C because it is the only one that says the vertex is (-2,2) and it does have that it is open up.
Let' s look at (-3,5) and (-1,5).
So if we plug in -3 into 3x^2+12x+14 we get 3(-3)^2+12(-3)+14=5 check mark
what about x=-1? 3(-1)^2+12(-1)+14=5
Bingo! C checks out!
Which is the graph of f(x) = (4)x?
Answer:
f(x)=4x
Step-by-step explanation:
In order to make the graph of f(x)= 4x we will find out few coordinates first and then plot them on the graph. In order to find the coordinates we will find the values of f(x) for random values of x .
Let us see:
x=1 ; f(x) = 4(1) = 4
x=2 ; f(x) = 4(2)=8
x=0 ; f(x) = 4(0)=0
x=-1 ; f(x)= 4(-1) = -4
x=-2 ; f(x)=4(-2)= -8
Hence our coordinates are
(-2,-8) ; (-1,-4) ; (0,0) ; (1,4) ; (2,8)
Now we plot those coordinates on x - y plane and join them to make our line. Please see the graph in the attachment.
A distribution has the five-number summary shown below. What is the third quartile, Q3, of this distribution?
22, 34, 41, 55, 62
Please answer this multiple choice question for 22 points and brainliest!!
Answer:
A
Step-by-step explanation:
Degree: that's the power on the x term. 2
Coefficient on the x term. That is 3
Constant term. That has no x -4
The minus is included.
The answer is A
In a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If Tim randomly draws one marble from each bag, what is the probability that they are both yellow?
Answer :
[tex]\frac{7}{15}[/tex]×[tex]\frac{2}{15}[/tex] = [tex]\frac{14}{225}[/tex]
Step-by-step explanation:
P([tex]Event_{1}[/tex]) = choosing yellow marble from paper bag = [tex]\frac{favourable outcomes}{possible outcomes}[/tex] = [tex]\frac{7}{15}[/tex]
P([tex]Event_{2}[/tex]) = choosing yellow marble from cloth bag = [tex]\frac{favourable outcomes}{possible outcomes}[/tex] = [tex]\frac{2}{15}[/tex]
∵ Resultant outcome is dependent upon both the events and both events are independent from each other, so we can apply intersection rule [ P(A∩B)=P(A)×P(B) ] here
∴ Probability ( Both marbles are yellow) = P([tex]Event_{1}[/tex]) × P([tex]Event_{2}[/tex]) = [tex]\frac{7}{15}[/tex] × [tex]\frac{2}{15}[/tex]
The probability that Tim will draw a yellow marble from both bags is found by multiplying the probability of drawing a yellow marble from each bag, giving a result of 14/225 or approximately 0.0622.
Explanation:The question is asking to find the probability of Tim drawing two yellow marbles, one from each bag, so this is a question about probability.
We know that there are 7 yellow marbles out of 15 in the paper bag, so the probability of drawing a yellow marble from this bag is 7/15. In the cloth bag, there are 2 yellow marbles out of 15, making the probability of drawing a yellow marble from this bag 2/15.
To find the overall probability that both marbles Tim draws are yellow, we multiply the two independent probabilities: (7/15) × (2/15) = 14/225.
So the probability that Tim will draw a yellow marble from both bags is 14/225, or approximately 0.0622 when expressed as a decimal.
The selling price of x number of a certain stereo can be modeled by the function R(x) = 160x. The total cost of making x stereos is C(x) = 71x – 0.02x2. What is the percent markup for 31 stereos?
23%
127%
227%
278%
Answer:
127% markup
Step-by-step explanation:
So we need to plug in 31 into each
R(31)=160(31)=4960
C(31)=71(31)-.02(31)^2=2181.78
So the selling price is 4960 for 31 stereos.
The total cost for making 31 stereos is 2181.78.
So that is a markup for sure.
So you find the difference and then divide it by the total cost.
(4960-2181.78)/2181.78=1.27 approximately
so there is 127% markup
A car travels down a highway at a constant speed shown in the graph below.
Find the speed of the car.
__________ kilometers per hour
Answer:
80 per hour
Step-by-step explanation:
because every hour it goes up 80 every time
The speed of the car is 80 km/h.
What is the speed of the car?Speed exists as the time rate at which an object exists moving along a path, while velocity exists as the rate and direction of an object's movement. Put another way, speed exists as a scalar value, while velocity is a vector.
Speed exists the rate at which an object’s position changes, measured in meters per second.
The speed of the car is 80 km/h.
Therefore, 80 km/h stands as the correct answer.
To learn more about Speed refer to:
https://brainly.com/question/13262646
#SPJ2
Need help with a math question
Answer:
(x+1)^2+(y-7)^2=8
Step-by-step explanation:
You should try the next one and I can check work or tell you if it is right.
The diameter length can be found be computing the distance that (-3,5) is to (1,9) which is sqrt(4^2+4^2)=sqrt(32).
The radius is half the diameter so it is sqrt(32)/2.
The center of the circle is the midpoint of a diameter. So compute the (Average of x, average of y)=(-1,7)
So plug into (x-h)^2+(y-k)^2=r^2 we get
(x+1)^2+(y-7)^2=32/4
simplifying gives
(x+1)^2+(y-7)^2=8
(I had to type this twice; my cat jump on my keyboard)
ANSWER
[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]
EXPLANATION
The given circle has P(-3,5) and Q(1,9) as its diameter.
The center can be obtained using the midpoint rule.
[tex]( \frac{ - 3 + 1}{2} , \frac{5 + 9}{2} )[/tex]
[tex]( - 1,7)[/tex]
The radius is obtained using the distance formula,
[tex]r = \sqrt{( - 1 - - 3 )^{2} + {(7 - 5)}^{2} } [/tex]
[tex]r = \sqrt{( 2)^{2} + {(2)}^{2} } = \sqrt{8} [/tex]
The equation is given by
[tex] {(x - h)}^{2} + {(y - h)}^{2} = {r}^{2} [/tex]
We substitute the center and radius to get:
[tex]{(x - - 1)}^{2} + {(y - 7)}^{2} = { (\sqrt{8}) }^{2} [/tex]
[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]
A bouncy ball is dropped such that the height of its first bounce is 5.5 feet and each successive bounce is 64% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
Final answer:
To find the height of the 7th bounce of a bouncy ball, where each bounce is 64% of the height of the previous one, use the geometric sequence formula. For the first bounce's height of 5.5 feet and a common ratio of 0.64, calculate the 6th power of 0.64, then multiply by 5.5 and round to the nearest tenth.
Explanation:
The student is asking about finding the height of the seventh bounce of a bouncy ball, which follows a geometric sequence in which each term is 64% of the previous one. To find the height of the 7th bounce, we will use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
The first term a1 is the height of the first bounce, which is 5.5 feet, and the common ratio r is 0.64 (since 64% is 0.64 in decimal form). Using this information, the height of the 7th bounce is calculated as follows:
Calculate the 6th power of the common ratio: 0.646
Multiply this value by the height of the first bounce: 5.5 × 0.646
Round the result to the nearest tenth
Calculating the exact value and rounding to the nearest tenth gives us the height of the seventh bounce.
The diameter and height of this cylinder are equal to the side length, s, of the cube in which the cylinder is inscribed. What is the expression for the cylinders volume?
Answer:
V = (π/4)s³
Step-by-step explanation:
The volume of a cylinder can be found using the formula ...
V = πr²h
In this problem, we have r=s/2 and h=s. Filling in these values, the volume is ...
V = π(s/2)²·s = (π/4)s³
Answer:
Its A
Step-by-step explanation:
V= 1/4 pi S^3
What are the coordinates of the center of a circle whose equation is (x + 7)2 + (y – 5)2 = 16?
Answer:
(-7, 5)
Step-by-step explanation:
Comparing the equation to the standard form equation of a circle of radius r centered at (h, k):
(x -h)² +(y -k)² = r²
you see that h=-7 and k=5.
The center of the circle has coordinates (-7, 5).
_____
Like a lot of math, it's about pattern matching.
What is the value of the discriminant, b2 ? 4ac, for the quadratic equation 0 = x2 ? 4x + 5, and what does it mean about the number of real solutions the equation has?
Answer:
Discriminant D = -4 , no real solution
Step-by-step explanation:
Here our equation is
[tex]x^{2}-4x+5=0[/tex]
Discriminant (D)= [tex]b^2-4ac[/tex]
where
a = coefficient of term containing [tex]x^{2}[/tex]
b= coefficient of the term containing [tex]x[/tex]
c is the constant term
hence
a=1 , b =-4 and c=5
Hence
[tex]D=b^2-4ac\\D=(-4)^2-4*1*5\\D=16-20\\D=-4\\[/tex]
Hence D is less than 0 , therefore we do not have any real solution to this quadratic equation.
Answer:
b on edge-The discriminant is −4, so the equation has no real solutions.
Step-by-step explanation:
(PLEASE dont ignore, NEED help❗️❗️❗️)
Answer:
Part 21) The distance from Football Field to the Park is [tex]10.95\ miles[/tex]
Part 22)
a) The value of a is [tex]20\ units[/tex]
b) The value of b is [tex]20.10\ units[/tex]
Step-by-step explanation:
Part 21)
Let
A -----> Football Field
B -----> Park
C -----> Home
D -----> Library
x -----> the distance from Football Field to the Park
In the right triangle ABD
[tex]cos(A)=10/x[/tex] -----> equation A
In the right triangle ABC
[tex]cos(A)=x/12[/tex] ----> equation B
equate equation A and equation B
[tex]10/x=x/12[/tex]
solve for x
[tex]x^{2}=120\\ \\x=10.95\ miles[/tex]
Part 22)
see the attached figure with letter to better understand the problem
step 1
Find the value of a
In the right triangle ABD
[tex]tan(ABD)=a/200[/tex] ----> equation A
In the right triangle ADC
[tex]tan(DAC)=2/a[/tex] ----> equation B
remember that angle ABD is congruent with angle DAC
therefore
equate equation A and equation B
[tex]a/200=2/a[/tex]
solve for a
[tex]a^{2}=400\\ \\a=20\ units[/tex]
step 2
Find the value of b
In the right triangle ADC
Applying the Pythagoras Theorem
[tex]b^{2}=a^{2}+2^{2}[/tex]
substitute the value of a
[tex]b^{2}=20^{2}+2^{2}[/tex]
[tex]b^{2}=404[/tex]
[tex]b=20.10\ units[/tex]
5. A rock is tossed from a height of 2 meters at an initial velocity of 30 m/s at an angle of 20° with the ground. Write parametric equations to represent the path of the rock.
Answer:
x = 30t cos 20 or x = 28.19t.
y = 30t sin 20 - 4.9t^2 + 2 or y = -4.9t^2 + 10.26t + 2.
Step-by-step explanation:
The horizontal component of the velocity = 30 cos 20 m/s so the distance at time t seconds = 30t cos 20.
The vertical component is obtained from the equation of motion
s = ut - 1/2* 9.8t^2 + 2
u = 30 sin 20
Vertical component = 30t sin 20 - 4.9t^2 + 2.
Answer:
x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2
Step-by-step explanation:
The path the rock took can be represented by the following equation x(t) = v0 * cos(θ) * t y (t) = v0 * sin (θ) * t – 0.5 * g * t^2 + h. v0 is the initial velocity (30 m/s), θ is the angle of launch (20 degrees), g is the acceleration due to gravity (9.8 m/s^2) , h is the initial height (2m ) , and t is time. When we switch the values, we get x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2
What is the circumstance of the circle P .
Answer:
6π ft
Step-by-step explanation:
I believe you meant CIRCUMFERENCE, the distance around the outer edge of this circle. The appropriate formula for the circumference is C = 2πr, where r is the radius. In the illustration we see that line segment PA has length 3 ft. Thus, the circumference of this circle is C = 2π(3 ft) = 6π ft (the next to last answer choice).
Answer:
=6π ft
Step-by-step explanation:
The circumference of a circle is calculated using the formula C=2πr where r is the radius and C the circumference of the circle.
In the circle provided r= 3ft
C= 2π × (3ft)
=6π ft
We do not use the approximate value of pi as the question demands us to leave pi unsolved.
Please help, lots of points! Please answer the question in the picture.
Answer:
Im positive the answer is A: x^3-3x+2
Answer:
a x^3-3x+2
Step-by-step explanation:
f(x) = -3x+2
g(x)= x^3
(f+g)(x)= -3x+2+x^3
= x^3-3x+2
What are the x- and why negative intercepts of the line
2x + 3y= -12
X-intercept -6 y-intercept -4
X-intercept -6 y-intercept 4
X-intercept -4 y-intercept 6
X-intercept 4 y-intercept -6
Answer:
Step-by-step explanation:
try using the equation of y=mx+b
Muscles, a membership-only gym is hoping to open a new branch in a small city in Pennsylvania that currently has no fitness centers. According to their research approximately 12,600 residents live within driving distance of the gym. Muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. Based on the past survey research, Muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. Based on this information and the results of the sample survey, about how many residents should Muscles expect to join its new branch?
A) 134
B) 504
C) 1,680
D) 3,780
Answer:
B) 504
Step-by-step explanation:
They should expect 30% of 40 out of every 300 of the 12,600, so ...
0.30 × 40/300 × 12,600 = 504
About 504 residents might be expected to join.
To estimate the number of residents that Muscles can expect to join its new branch, multiply the total number of residents within driving distance by the percentage of respondents who would actually join the gym. Muscles can expect about 1,680 residents to join its new branch.
Explanation:
To estimate the number of residents that Muscles can expect to join its new branch, we can multiply the total number of residents within driving distance by the percentage of respondents who would actually join the gym.
First, we need to calculate the percentage of respondents who would join the gym:
Percentage = (Number of respondents who would join the gym / Total number of respondents) * 100
Percentage = (40 / 300) * 100 = 13.33%
Next, we multiply the estimated percentage by the total number of residents within driving distance:
Number of residents who would join the gym = (Percentage / 100) * Total number of residents within driving distance
Number of residents who would join the gym = (13.33 / 100) * 12,600 = 1,678.5
Therefore, Muscles can expect about 1,680 residents to join its new branch.
Learn more about Calculating the number of residents who would join the gym here:https://brainly.com/question/35865378
#SPJ2
Given the function f(x) = 3x + 1, evaluate f(a + 1).
A. 3a + 1
B. a + 2
C. 3a + 4
Answer:
Given the function f(x) = 3x + 1, evaluation of f(a + 1) gives:
C. 3a + 4
Step-by-step explanation:
Given function:
f(x) = 3x + 1
We have to find f(a+1).
For this purpose, we will take x = a+1 and
substitute it in the function f(x) = 3x+1:
f(x) = 3x + 1
f(a+1) = 3(a+1) +1
f(a+1) = 3(a) + 3(1) +1
f(a+1) = 3a+3+1
f(a+1) = 3a + 4
So the function f(a+1) is equal to option C. 3a + 4.
the answer is
3a + 4
Please help me with this problem
For a system of linear equations to have a solution, it means that they would cross over at some point, thus if we are looking for a system of linear equations that do not have a solution (ie. they do not cross over), we are looking for two parallel lines.
Now for two lines to be parallel, they must have the same gradient. Thus, we must find the value of a for which both the equations have the same gradient. In order to do this, we should first write both equations in the form y = mx + c, where m is the gradient and c the y-intercept.
1) Equation 1:
(1/2)x - (2/3)y = 7
(3/4)x - y = 21/2 (Multiply both sides by 3/2)
(3/4)x = 21/2 + y (Add y to both sides)
(3/4)x - 21/2 = y (Subtract 21/2 from both sides)
Thus, the first equation may be written as y = (3/4)x - 21/2
2) Equation 2:
ax - 8y = -1
(a/8)x - y = -1/8 (Divide both sides by 8)
(a/8)x = -1/8 + y (Add y to both sides)
(a/8)x + 1/8 = y (Add 1/8 to both sides)
Thus, the second equation may be written as y = (a/8)x + 1/8
Now that we know the equations of the two lines, we can compare their gradients.
Equation 1: m = 3/4
Equation 2: m = a/8
Remember, for the two lines to be parallel, their gradients must be the same. Thus, we must equate the two gradients above to find the value of a:
3/4 = a/8
24/4 = a (Multiply both sides by 8)
6 = a
Therefor, if the system of linear equations has no solution, and a is a constant, the value of a is 6 (answer D).
The diameter of each wheel of a bicycle is 28 inches. If you are traveling at a speed of 15 miles per hour on this? bicycle, through how many revolutions per minute are the wheels? turning?
Answer:
180.07 rev / min
Step-by-step explanation:
Diameter (D) of each wheel =28 inches
Circumference (C) = π x 28 = 28π inches
Conversions:
1 mile = 63,360 inches
1 hour = 60 min
Hence 15 miles / hour
= (15)(63,360) inches / hour
= (15)(63,360) / 60 inches / min
= 15,840 inches per min
Number of revolutions per min = Number of inches per min ÷ circumference in inches
=15,840 inches/min ÷ 28π inches
= 180.07 revolutions per min
To find the number of revolutions per minute a bicycle's wheels make, convert the speed from miles per hour to inches per minute, calculate the wheel's circumference, and divide the traveling speed in inches per minute by the circumference. A bicycle with 28-inch diameter wheels going 15 miles per hour makes approximately 180 revolutions per minute.
Explanation:To determine how many revolutions per minute the wheels of a bicycle with a 28-inch diameter are turning when traveling at 15 miles per hour, we first need to convert the speed to inches per minute. There are 5280 feet in a mile and 12 inches in a foot, so first we calculate:
15 miles/hour * 5280 feet/mile * 12 inches/foot = 950400 inches/hour
Since there are 60 minutes in an hour, we then convert to inches per minute:
950400 inches/hour / 60 minutes/hour = 15840 inches/minute
Next, we need to find out the circumference of the bicycle wheel, as this will tell us how far the bike travels with each revolution. The formula for the circumference (C) of a circle using the diameter (d) is:
C = π * d
For a wheel with a diameter of 28 inches:
C = π * 28 inches ≈ 87.96 inches
Now, to find the number of revolutions per minute, we divide the traveling speed in inches per minute by the circumference:
15840 inches/minute / 87.96 inches/revolution ≈ 180 revolutions per minute (rounded to the nearest whole number).