Students in a school are asked to pick either football, rugby or tennis to play in their lessons. the number of students who picked football and rugby are in the ratio of 4:3 the number of students who picked rugby and tennis in the ratio of 9:19 57 students picked tennis work out how many student picked football
Answer: 36 Students picked football
Step-by-step explanation: When calculating values by the use of given ratios, it is important to note that the ratio of one value as compared to the other is the same as the actual value compared to the other.
The ratio of students who picked rugby and tennis is given as ratio 9 : 19, which means for every 28 students (that was derived by 9 + 19), 9 would choose rugby and 19 would choose tennis. However, we have been given the total number of students who chose tennis as 57, hence the value 57 would now replace the ratio of 19. However the total number of those who chose rugby is not yet known, so we can write out an equation as shown below;
19/28 = t/x
Where t is the number of tennis players as represented by ratio 19 and x is the total number of both tennis and rugby players as represented by 28.
By cross multiplication we now have
19 * x = 28 * 57
x = (28 * 57)/19
x = 1596/19
x = 84
If a total of 84 students play both rugby and tennis, and 57 of them play only tennis, then the number of rugby players is derived as
r = x - t
r = 84 - 57
r = 27
Having determined that 27 students played rugby, and the ratio of football to rugby players is given as 4 : 3, the relationship can be mathematically represented as follows;
3/7 = r/y
Where r is the total number of rugby players and y is the total number of both football and rugby players
3/7 = 27/y
By cross multiplication you now have
3 * y = 7 * 27
y = (7 * 27)/3
y = 189/3
y = 63
If the total number of football and rugby players is 63 and out of these 27 play rugby only, then the number of football players is derived as;
f = y - r
f = 63 - 27
f = 36
Therefore the number of students who chose football is 36
Which statement is true about f(x) + 2 = 1/6 |x-3| ?
A) The graph of f(x) has a vertex of (–3, 2).
B) The graph of f(x) is a horizontal compression of the graph of the parent function.
C) The graph of f(x) opens downward.
D) The graph of f(x) has range of f(x) ≥ –2.
Answer:
Option D.
Step-by-step explanation:
Statement given,
f(x) + 2 = [tex]\frac{1}{6}|x - 3|[/tex]
Or f(x) = [tex]\frac{1}{6}|x-3|[/tex] -2
Parent function, g(x) = |x|
Absolute value function g(x) when shifted 3 units right,
g'(x) = |x - 3|
Vertically compressed by [tex]\frac{1}{6}[/tex] units and shifted 2 units down, then the new function will be
f(x) = [tex]\frac{1}{6}|x - 3|-2[/tex]
Characteristics of the graph of this function:
1). Vertex at (3, -2).
2). Vertical compression of the parent function by [tex]\frac{1}{6}[/tex].
3). Graph opens upwards.
4). Range of the graph f(x) is f(x) ≥ -2.
Therefore, Option D will be the answer.
Find f(2) if f(x) = (x + 1)2
Answer:
2x
Step-by-step explanation:
f(2)=(2x+1)2
f(2)=(4x+2)
÷ both by two
f(2)=(2x)
// have a great day //
(7x + 30) and 11x
I'm not sure what and is...is it adding or an equal sign?
for equal sign
(7x+30)=11x
30=11x-7x
30=4x
30/4=x
7.5=x
for plus sign
evalute
(7x+30)+11x
7x+11x+30
18x+30
factorize
(7x+30)+11x
18x+30
6(3x+5)
hope it help yuh..
Can someone please explain what I did wrong here? Thank you!
Answer:
you didn't do anything wrong who ever said you did is stupid
The answer is attached.
please help me, I just needa pass this lesson!!!
Answer:
Plot the points (0,2) and (3,3)
Step-by-step explanation:
(0,2) is the y-intercept and the slope is always rise over run so go up 1 unit and right 3 units, that gets you to (3,3)
you could also plot any point other than (3,3) that is on the same line
The equation a=180(n-2)/n represent the angle measures,a in a regular n-sided polygon. When the equation is Solved for n,n is equal to a fraction with a denominator of a-180. What is the numerator of the fraction.
Answer:
The
numerator is 360
Step-by-step explanation:
What we need to do here is make n the subject of the formula;
a = 180(n-2)/n
an = 180n-360
180n - an = 360
n(180-a) = 360
n = 360/(180-a)
H(a)= 3a - 4; Find h(8)
Answer:
20
Step-by-step explanation:
You plug 8 into the equation where a is. 8 x 3 = 24 - 4 = 20.
A water grist mill has a radius of 8ft and takes 6 seconds to make a complete rotation. A bucket starts at position (8,0). What are the coordinates of the bucket's location after 4 seconds? Round values to the nearest tenth.
(8.7, −3.5)
(−4, −6.9)
(4, −6.9)
(−8.7, −3.5)
Answer:
(−4 -6.9 )= x, y rotation 240 degree anti clockwise
Step-by-step explanation:
We are told radius = 8 so the center point or point of origin is 0.0
360/3 = 120 degree x 2 = 240 degree is where we need to be.
(8,0) circulating anti clockwise = -8,0 at 180 = 180 degree.
This is 3 seconds.
We divide 8/3 to find the 4th and know it will be negative in the 3rd quadrant across the negative y axis, the lower and left point on the graph.
We know both are negative if going anti clockwise 240 degree.
We also know that the hands of a clock or mechanics of a mill cannot increase in length they shorten so they cannot be 8.7 even though triangles slants do increase this is independent of completing the lengths in a triangle. The lengths shorten.
-4 = x this is because it crosses -4 x axis to reach to -6.9 y coordinate.
Y= 6.9 as the length of 8 is shortened by 1.1 units between each 180 degree line we have 210deg (shows (-6.35, -2.4) also; 240 deg (-6.9, -4 ) and a 270 deg (this shows (0,8)
if 240/6.9 = 34% reduction
As 8 6.9 of 8 as a percentage = 86.25
As a ratio decrease we have 13.75% with the size of the coordinates at 240 degrees from 180 degrees the highest point is 270 degrees and is half again 1.1/2 = 0.55 increase in coordinates of y.
y would show -6.35 at 210 degrees and x would show 1.1 whole ratio change and show -2.4 at 210 degrees. The reason for this is that it is cutting the axis line and is a narrowing crossing for x axis shortly before 180 degree change.
The shortest point of the hand and central to 240 and 180 is 210 degree.
What is the area of the rhombus shown below?
Answer:
A. 97.5 square units
Step-by-step explanation:
==>Given:
Rhombus ABCD with the following dimensions:
diagonal 1 (d1) = BD = 15
diagonal 2 (d2) = AC = 13
AB = 9.9
==>Required:
Area of the rhombus
==>Solution:
Since we know the length of the 2 diagonals, area of the rhombus can be calculated using A = ½ × d1 × d2
Area = ½ × 15 × 13
A = ½ × 195
A = 97.5 square units
Answer:
A
Step-by-step explanation:
6= -3 + r
solve for r
Answer:
6=-3+r
r=9
Step-by-step explanation:
Answer:
9=r
Step-by-step explanation:
6=-3+r
+3 = +3
add 3 to both sides
9=r
Make a magic square using only first nine odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17. (In a magic square, the numbers in each row, in each column, and along each diagonal have the same sum.)
Answer: [tex]\left[\begin{array}{ccc}11&13&3\\1&9&17\\15&5&7\end{array}\right][/tex]
Step-by-step explanation:
A magic cube is something like:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Where the numbers that we must use are:
1, 3, 5, 7, 9, 11, 13, 15, 17
If we take the addition of those 9 numbers, we get 81.
Now, we divide it by 3 (the number of numbers in each row or column) and get:
81/3 = 27
so the sum in each row, column and diagonal must be 27.
1 + 9 + 17 = 27
13 + 11 + 3 = 27
5 + 7 + 15 = 27
9 + 13 + 5 = 27
You can keep playing with this, and then start forming our number cube, some of the hints tat we can use is that the median of the group is 9, so it must be in the middle of the cuve, and the extremes, 1 and 17, must be in the same column or row as 9.
so we start with:
[tex]\left[\begin{array}{ccc}x&x&x\\1&9&17\\x&x&x\end{array}\right][/tex]
and start to fill the empty spaces, now we can use that
1 + 11 + 15 = 27 and get:
[tex]\left[\begin{array}{ccc}11&x&x\\1&9&17\\15&x&x\end{array}\right][/tex]
now for the diagonals:
11 + 9 + 7 = 27
15 + 9 + 3 = 27
[tex]\left[\begin{array}{ccc}11&x&3\\1&9&17\\15&x&7\end{array}\right][/tex]
and for the last one:
11 + 3 + 13 = 27
15 + 7 + 5 = 27
[tex]\left[\begin{array}{ccc}11&13&3\\1&9&17\\15&5&7\end{array}\right][/tex]
A car travels 0.75 miles every minute.explain how you could use proportional reasoning too find how far the car travels in a hour
Answer:
The car travels 45 miles in one hour.
Step-by-step explanation:
Knowing that one hour is 60 minutes and that the car travels 0.75 miles every minute, you can multiply 60 and 0.75 which gives you 45 miles per hour meaning in one hour the car travels 45 miles.
HELP PLEASE WITH THE IMAGE BELOW it would mean a lot if someone helped me answer this question and maybe even explain how you got it.
Answer:
65/97 = 0.67
Step-by-step explanation:
using trigonometric ratios
Cosine of angle = [tex]\frac{adj}{hyp}[/tex]
Use cross products to identify the equation needed to solve this proportion: 5/x = 2/9
Answer:
x=22.5
Step-by-step explanation:
We are given the proportion:
5/x=2/9
Cross multiply. Multiply the numerator (top number) of the first fraction by the denominator (bottom number) of the second. Then multiply the denominator of the first by the numerator of the second.
5*9=2*x
45=2x
2 and x are being multiplied. The opposite of multiplication is division. Divide both sides by 2. This will cancel out the 2 being multiplied by x, and leave x by itself.
45/2=2x/2
45/2=x
22.5=x
If we substitute 22.5 in for x, the final proportion will be:
5/22.5=2/9
Answer: 22.5 = x
Step-by-step explanation: First, write the problem, 5/x = 2/9. Next, cross multiply. Write the equation, 5 x 9 = 2x. After, write the equation in a multiplying fraction sentence. 45/2 = 2x/2. Lastly, solve for x by dividing 45 by 2. You should end up with a result of 22.5 = x.
A figure is located entirely in the third quadrant if it is reflected over the y axis in which quadrant will it's image lie
Answer:
It will land in quadrant 1 (quadrant 1)
Step-by-step explanation:
ran 42 miles per hour in 8 hours whats his miles per hour
Q4: Katie and Tyler are working at their lemonade stand. An hour ago, their pitcher of lemonade was 78 full. Since then, they have sold 12 of a pitcher of lemonade. What fraction of a pitcher do they have left?
Answer:
3/8 of the pitcher of lemonade remains.
Step-by-step explanation:
They tell us that at first they had 7/8 of a pitcher full of lemonade, and they ask us to know what fraction is left if they have taken 1/2 of the pitcher of lemonade for a while, which means that it would be a subtraction between what had at the beginning and what they have taken, would be:
7/8 - 1/2 = (14 - 8) / 8 * 2 = 6/16 = 3/8
Which means that 3/8 of the pitcher of lemonade remains.
work out the area of a circle with diameter 1.8cm take pie to be 3.142 and give your answer to 1 decimal place.
You buy 1.65 pounds of apples and 1.85 pounds of plums. Apples and plums sell for the same price per pound. The total cost, after using a 65cents-off coupon, is $3.20. If c represents the cost of the fruit in dollars per pound, what equation could you use to find the value of c?
Answer:the value is 20
Step-by-step explanation:
Please help
AOB = ?
BOC = ?
BOD = ?
Answer: in between a and b it could be 12x
in between b and c it could be 55x
in between d and c it could be [tex]4x^{o}[/tex] than probably half that
in between b and c it could be [tex]x^{o}[/tex]
or this
From the diagram, we know that it is an angle that adds up to 360
So
x+4x+2x+10+5x+50=360
Gather like terms
12x+60=360
Move sixty to the other side as a negative number
12x=300
Divide both sirs by twelve
x is equal to 25
AOB is 2x+10
Sub x in 2*25+10
AOB is 60
BOC is 5x+50
5*25+50, which is 175
BOD is x+2x+10
Which is 3x+10
Sub x
3*25+10 which is 85
Step-by-step explanation:
i think it could be like this
Which number is irrational?
-4
2/9
8.26
11
Answer:
C. Square Root of 11
Edg 2020
Answer:
C
Step-by-step explanation:
edge 2020
Please answer correctly !!!!!!! Will mark brainliest answer !!!!!!!!!!
Answer:
f⁻¹(f(6.022)) = 6.022
f⁻¹(-10) + f(-6) = -6 + -10 = -16
Step-by-step explanation:
f⁻¹(f(x)) = x
so f⁻¹(f(6.022)) = 6.022
inverse function flips y and x coordinates so look at table where f(x)=-10 and read x so f⁻¹(-10) = -6
f⁻¹(-10) + f(-6) = -6 + -10 = -16
Which of the following best describes the graph shown below?
Answer:
B. This is a graph of a one to one function
Answer:B
Step-by-step explanation:
5 Write the first five terms of the sequence with nth term.
a 4n
b 2n+1
c 3n -2
d 1/2n +1
e 20 -5n
f -2n +3
Answer:
its a lot u'll see at the end
Step-by-step explanation:
a) 4n = 4,8,12,16,20
b) 2n+1= 3,5,7,9,11
c) 3n-2= 1,4,7,10,13
d) 1÷2n+1= [tex]\frac{3}{2}[/tex], [tex]\frac{5}{4} ,\frac{7}{6} ,\frac{9}{8} ,\frac{11}{10} ,[/tex]
e) 20-5n= 15,10,5,0,-5
f) -2n+3= 1,-1,-3,-5,-7
took me a while hope it is helpful
How do you solve [tex]x^2 + 7x + 2 = 0[/tex]?
Answer:
-7 ± √6
x = ----------------
2
Step-by-step explanation:
You have several options here. One would be "completing the square," and another would be "quadratic formula."
Here the coefficients of this quadratic are a = 1, b = 7 and c = 2.
The discriminant is therefore b^2 - 4(a)(c), or 7^2 - 4(1)(2) = 6.
The roots are thus:
-7 ± √6
x = ----------------
2
Given ƒ(x) = 9x + 54, find x when ƒ(x) = 18. A) −6 B) −4 C) 3 D) 8
Answer:
-4 =x
Step-by-step explanation:
ƒ(x) = 9x + 54
Let f(x) = 18
18 = 9x+54
Subtract 54 from each side
18-54 = 9x + 54-54
-36 = 9x
Divide each side by 9
-36/9 = 9x/9
-4 =x
Answer: B
Step-by-step explanation:
Well, they told you what f(x) equals. So make the function of f(x) equal to the value they gave, 18
[tex]18=9x+54[/tex]
Subtract 54 from both sides to get:
[tex]-36=9x[/tex]
Divide both sides by 9 to get x = -4
this question is my thing
Answer:
Below
Step-by-step explanation:
8 is classified as a rational number because it can be made into a fraction. 8.8 = 8 8/10 = 88/1
What is the result of subtracting the second equation from the first?
-2x+y=0
7x+3y=2
Answer:
5x -2y = -2
Step-by-step explanation:
-2x+y=0
-7x+3y=2
Subtract the second equation from the first
-2x+y=0
7x-3y=-2
------------------
5x -2y = -2
(Number 8)!!!!!!!!!!!!!!!!
Answer:
B=29
Step-by-step explanation:
you have on the right hand side [tex](7x^{3} y^{3/4}) ^{2}[/tex] which is equal to [tex]49x^{6}yx^{3/2}[/tex] so B=49
