Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
What is the value of x in the equation 3x-4y=65, when y=4?
x=13 1/4
x=21 2/3
x =23
x = 27
Hello there! :)
Answer:
[tex]\huge\boxed{x = 27}[/tex]
Given the equation:
3x - 4y = 65 where y = 4
Substitute in 4 for "y":
3x - 4(4) = 65
Simplify:
3x - 16 = 65
Add 16 to both sides:
3x - 16 + 16 = 65 + 16
3x = 81
Divide both sides by 3:
3x/3 = 81/3
x = 27.
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.
Answer:
83 adult tickets and 217 student tickets.
Step-by-step explanation:
Let number of adult tickets sold = [tex]x[/tex]
Given that total number of tickets = 300
So, number of student tickets = 300 - [tex]x[/tex]
Cost of adult ticket = $15
Cost of student ticket = $11
Total collection from adult tickets = $[tex]15x[/tex]
Total collection from student tickets = [tex](300-x)\times 11 = 3300-11x[/tex]
Given that overall collection = $3630
[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]
So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.
Now , collection = $3632
What are the solutions to the system of equations? {y=2x2+6x−10 y=−x+5
Answer:
I think this is mistake because y=2x^2+6x-10 y=x+5 this is the right
In the expression 3x^2+y+-5 which of the following choices is the exponent in the term 3x^2?
A. 3
B. 2
C. X
D. None of these choices
Answer:
2
Step-by-step explanation:
3x^2
The coefficient is 3
The variable is x
The exponent is 2
A zoo train ride costs $4 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who took the ride was 27, and the total money collected was $60. What was the number of children and the number of adults who took the train ride that day, and which pair of equations can be solved to find the numbers? 1) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 2) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 3) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60 4) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60
Answer:
11 adults and 16 children
Step-by-step explanation:
a + c = 27 and 4a + c = 60
3a = 60 - 27 = 33
a= 11
so c = 16
The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains point (3, −2). A. y = 2x + 4 B. y = negative 1 over 2 , x − 1 over 2 C. y = − 1 over 2 , x − 7 over 2 D. y = 2x − 8
Answer:
The answer is option DStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
y = 2x + 4
comparing with the above equation for a line
The slope / m = 2
Since the lines are parallel their slope are also the same
Slope of parallel line = 2
So we have
The equation of the line using point
( 3 , -2) and slope 2 is
y + 2 = 2( x - 3)
y + 2 = 2x - 6
y = 2x - 6 - 2
We have the final answer as
y = 2x - 8Hope this helps you
Answer:
y=2x-8
Step-by-step explanation:
Which of these relations are functions?
х
O
-2 6 2 -6
-5 21 15-15
y
11
y
4
2
O
x
4
-2
4
o
{(-5,-7), (-2,-7), (7,17), (-5,21)}
y
For each value of y, the number of value of x must be one. Then the correct options is D.
The complete question is attached below.
What is relation function?The relation function is given as, for every independent value, there is a dependent value.
Let the function be y = f(x).
For each value of x, the number of value of y may one or two.
But for each value of y, the number of value of x must be one.
Then the correct options is D.
More about the relation function link is given below.
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If f(x) = 3x + 5 and g(x) = -2x2 - 5x + 3, find (f + g)(x).
Answer:
A
Step-by-step explanation:
(f+g)(x) simply means you add f(x) and g(x).
[tex]-2x^2-5x+3x+3+5=(f+g)(x)[/tex]
We can then simplify by combining like terms to get
[tex]-2x^2-2x+8[/tex]
A is correct!
In a circle, an arc measuring 130° is what percentage of the circumference of the circle
Answer:
≈ 36.1%
Step-by-step explanation:
In any circle the following ratio is equal
[tex]\frac{arc}{circmference}[/tex] = [tex]\frac{centralangle}{360}[/tex] = [tex]\frac{130}{360}[/tex] , thus
percentage = [tex]\frac{130}{360}[/tex] × 100% ≈ 36.1%
an arc measuring 130° is approximately 36.11% of the circumference of the circle.
To find the percentage of the circumference that an arc measuring 130° represents, we need to calculate the ratio of the arc length to the circumference of the circle and then convert it to a percentage.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
Let's assume the radius of the circle is r.
The circumference of the circle is C = 2πr.
To find the length of the arc corresponding to 130°, we need to calculate the fraction of the total angle (360°) that 130° represents:
Fraction of the angle = (130° / 360°) = (13/36).
Since the fraction of the angle is equal to the fraction of the arc length to the circumference, the length of the arc can be calculated as:
Arc length = Fraction of the angle * Circumference = (13/36) * (2πr).
Now, to find the percentage of the circumference that the arc length represents, we divide the arc length by the circumference and multiply by 100:
Percentage = (Arc length / Circumference) * 100
Percentage = [(13/36) * (2πr)] / (2πr) * 100
Percentage = (13/36) * 100
Percentage = 36.11%
Therefore, an arc measuring 130° is approximately 36.11% of the circumference of the circle.
Learn more about arc length here
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Write an expression in simplified form for the area of each rectangle. Width: 7 Length: 5n-9
Answer:
35n - 63
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 7(5n-9)
Distribute
A = 35n - 63
Area of rectangle = Length * Width
Length is 5n-9
Width is 7
⇛Area = 5n-9(7)
⇛Area = 33n - 63
Solve for X in the diagram below
PLS HELP BRAINLIST AND A THANK YOU WILL BE REWARDED :)
The 3 angles need to equal 180
The middle angle is given as 100.
180 -100 = 80
There is an x on each side so you have 2x
2x = 80
X = 80/2
X = 40 degrees
if a man works 400km in 6 minutes.How long will he work in 9 minutes
Answer:
600 kmStep-by-step explanation:
400 km = x
6 min 9 min
cross multiply:
6x = 400 ( 9)
x = 3600 / 6
x = 600 km
please help me with this problem
Answer:
Step-by-step explanation:
I'm not sure but i think your right
Find the value of x in the triangle
Answer:
x=62
Step-by-step explanation:
a triangle equals 180
so knowing that you subtract 56 from 180
That gives you 124
Then you divide it by 2 because the sides are equal.
That gives you 62
so x=62
BELL RINGER #2
A consultant charges $45 for each hour she works on a consultation, plus a flat $30
consulting fee. How many hours of work are included in a $210 bill for a consultation?
A. 2 4/5
B. 4
c. 4 2/3
D. 5 1 / 2
E. 7
Answer:
A. 2 4/5
Step-by-step explanation:
To find how many hours she worked for $210, you must get the amount of money she gets in 1 hour.
Because she charges $43 dollars every hour, and fines a fee of $30 flat, we must add both of the amount to get how many she earns in 1 hour.
So:
$45 + $30= $75
She earn $75 in 1 hour.
Next, divide $210 dollars that she earned for working for hour(s) to the amount of money she earned in 1 hour to find how many hours she worked.
So:
$210 ÷ $75= 2.8 hours
The answer is 2.8 hours
Because the given answers is in fraction, we must change the decimal into a fraction.
To change a decimal into a fraction, you must place the decimal over its place value.
Because 8 in the decimal 2.8 is in the tenths place, you must place it over 10
So:
2.8 into a decimal is 2 8/10
Simplify (only simplify if possible):
Divide 8 and 10 to their GCF which is 2.
So:
8 ÷ 2= 4
10 ÷ 2= 5
So the fraction and the answer is now:
2 4/5
I hope this helps! I'm sorry if it's wrong and too complicated.
After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year and an increase of 8% per year, the population is 34,560. Which equation can be used to predict, y, the number of people living in the town after x years? (Round population values to the nearest whole number.) y = 32,000(1.08)x y = 32,000(0.08)x y = 34,560(1.08)x y = 34,560(0.08)x
Answer:
y = 32,000(1.08)^x
Step-by-step explanation:
The exponential growth equation is y = a(1 + r)^x, where a is the initial amount, r is rate as a decimal, and x is the time.
In this situation, 32,000 is the initial amount (a) and 0.08 is the rate (r)
If we plug these into the equation, we get the equation y = 32,000(1.08)^x
So, y = 32,000(1.08)^x is the correct answer.
Answer:
A
Step-by-step explanation:
on edge 2020
Omar wanted to fill his bathtub. His faucet poured water at a rate of 9 liters per minute. Omar forgot to plug the drain. So 12 liters were wasted before he plugged the drain and continued to fill the tub. Suppose the tub held 150 liters of water. How long was the faucet on before the tub was filled?
Answer:
162/9 = 18 minutes
Step-by-step explanation:
how to write x divided by 16 in algebraic expression
Answer:
x/16 the line means your dividing the x by 16
Step-by-step explanation:
twice x,plus 8,is the same as -10
Answer:
greater than or equal to -36
Step-by-step explanation:
2x >= -36-16
2x >= -52
x >= -26
Answer:
x = -9
Step-by-step explanation:
2x + 8 = -10
2x = -8 -10
2x = -18
x = -9
67) Interest on a Loan: Jeff Hubbard borrowed $800 from his brother for 2 years. At the end of 2 years, he repaid
the $800 plus $128 in interest. What simple interest rate did he pay?
Answer:
0.08%
Step-by-step explanation:
2 years,
the $800 plus $128 in interest. What simple interest rate did he pay?
128/2
$64 a year
64/800=0.08
so 0.08%
37. What is the slope of the equation ?
-3
y = x + 2
HELP! answer if you can!
Answer:
Slope =1Step-by-step explanation:
Method 1 : Standard form method
[tex]y = x + 2\\\mathrm{Convert\:to\:standard\:form}:\quad x-y=-2\\\\\mathrm{Slope}\:\mathbf{m}\:\mathrm{of\:a\:line\:of\:the\:form}\:\\\mathbf{Ax+By=C}\:\mathrm{equals}\:\mathbf{-\frac{A}{B}}\\\\\mathbf{A}=1,\:\mathbf{B}=-1\\m=-\frac{1}{-1}\\m=1[/tex]
Method 2 : Slope -intercept Form
[tex]\mathrm{Slope\:of\:}y=x+2:\\\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:} :\\\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}\\\\m=1[/tex]
Helpp mee plss in this one
Apples are cut into 8 pieces to be shared among some children. Twenty-two bags of seven apples are used. How many pieces of apple are cut?
Answer: 1232 pieces
Work Shown:
1 bag = 7 apples
22 bags = 22*7 = 154 apples
So we have 154 apples to work with in total.
Each of those apples is cut into 8 pieces, giving us 8*154 = 1232 pieces
We can write it as one single calculation to say 22*7*8 = 1232
Find the distance between the two points (8, 3), (0, -3)
Answer:
The answer is 10 unitsStep-by-step explanation:
The distance between two points can be found by
[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]
where
(x1 , y1) and (x2 , y2) are the points
The distance between (8, 3), (0, -3) is
[tex] \sqrt{ ({8 - 0})^{2} + ({3 + 3})^{2} } [/tex]
[tex] = \sqrt{ {8}^{2} + {6}^{2} } [/tex]
[tex] = \sqrt{64 + 36} [/tex]
[tex] = \sqrt{100} [/tex]
We have the final answer as
10 unitsHope this helps you
A pair of shoes is on sale for 30% off. The original price is p. Which expression can be used to find the price of the shoes after the discount?
a) 0.30p
b) 0.70p
c) 1.30p
d) 30p
Answer:
Step-by-step explanation:
the answer is b
If the angles of a pentagon are x 2x 3x 4x 5x .Find the value of X
Mark Brainliest if correct:
x = 36
Step-by-step explanation:
x + 2x + 3x + 4x + 5x = 540 (Sum of interior angles in pentagon)
15x = 540
x = 36
Help please Which is the equation of a trend line that passes through the points (3, 95) and (11, 12)? Round values to the nearest ten-thousandths. y = negative 10.375 x + 126.125 y = negative 0.096 x + 13.056 y = 0.096 x + 10.944 y = 10.375 x 63.875
Answer:
y = -10.375x + 126.125
Step-by-step explanation:
(12-95)/(11-3) = -83/8 = -10.375
y = mx + b
12 = -10.375(11) + b
12 = -114.125 + b
b = 126.125
y = -10.375x + 126.125
The solution is, y = -10.375x + 126.125, is the equation of a trend line that passes through the points (3, 95) and (11, 12).
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
given that,
a trend line that passes through the points (3, 95) and (11, 12).
so, the slope is,
(12-95)/(11-3) = -83/8 = -10.375
now, we have,
y = mx + b
12 = -10.375(11) + b
12 = -114.125 + b
b = 126.125
so, we get,
y = -10.375x + 126.125
Hence, The solution is, y = -10.375x + 126.125, is the equation of a trend line that passes through the points (3, 95) and (11, 12).
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7. Verify the following: i) (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0 ii) (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc iii) (p – q) (p² + pq + q²) = p³ – q³. EXPLAIN
1. (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0
We know that (a+b)(a-b) = a²-b²
(ab + bc)(ab -bc) can be written as a²b² - b²c²
(bc + ca)(bc -ca) can be written as b²c² - c²a²
(ca + ab)(ca - ab) can be written as c²a² - a²b²
→ a²b² - b²c² + b²c² - c²a² + c²a² - a²b²
→ a²b² - a²b² - b²c² + b²c² - c²a² + c²a²
→ 0
2. (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc
→ a³ + ab² + ac² -a²b - abc -ca² + a²b + b³ + bc² - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a
→ a³ + b³+ c³ + (- abc - abc - abc) + (ab² - ab² )+ (ac² - ca² ) -(a²b + a²b )+ (bc² - bc² )+ (a²c - c²a) + (b²c - b²c)
→ a³+b³+c³ - 3 abc .
3. (p – q) (p² + pq + q²) = p³ – q³.
→ p³ + p²q + pq² - p²q - pq² - q³
→ p³ - q³ +(p²q - p²q) + (pq² - pq²)
→ p³ - q³
As a burglar reaches for something on the mantel, accidentally knocks over a clock. It falls to the floor, breaks, and stops. The next morning, however, pol.ice aren't able to determine what time the robbery took place. Why not?
Answer: There is no way of finding out if the clock worked before then, and if it stopped at P.m or A.m.
Step-by-step explanation:
Let's say the robber broke the clock at 3 a.m, the police would first of all not have any idea if the clock was indeed broken before the robber knocked it over, and the clock has no way of saying whether it was broken at 3 a.m. or 3 p.m, therefore it's rendered useless.
Factorise 7a³b²_14a²b³
Answer:
7a²b²(a - 2b)
Step-by-step explanation:
Given
7a³b² - 14a²b³ ← factor out 7a²b² from each term
= 7a²b²(a - 2b)