Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
Step-by-step explanation:
Since we have given that
Total number of students and teachers = 409
Let the number of vans be x
Let the number of buses be x+5
Number of students and teachers each bus transported = 55
Number of students and teachers each van transported = 12
According to question,
[tex]55(x+5)+12x=409\\\\55x+275+12x=409\\\\67x=409-275\\\\67x=134\\\\x=\frac{134}{67}\\\\x=2[/tex]
Total number of students and teachers who rode to the zoo in buses will be
[tex]55(x+5)\\\\=55(2+5)\\\\=55\times 7\\\\=385[/tex]
Total number of students and teachers who rode to the zoo in vans will be
[tex]12x\\\\=12\times 2=24[/tex]
Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.
To find the total number of students and teachers who rode to the zoo in buses, we need to determine the number of buses and multiply it by the number of students and teachers each bus transported. Each bus transported 55 students and teachers, while each van transported 12. By solving the equation using the given information, we can find the total number of students and teachers in each type of vehicle.
Explanation:To find the total number of students and teachers who rode to the zoo in buses, we need to determine the number of buses and multiply it by the number of students and teachers each bus transported.
Let x be the number of vans.
Since there were 5 buses more than vans, the number of buses can be represented as x + 5.
Each bus transports 55 students and teachers, so the total number of students and teachers in buses is (x + 5) * 55.
Each van transports 12 students and teachers, so the total number of students and teachers in vans is x * 12.
Since there were a total of 409 students and teachers, we can create an equation: (x + 5) * 55 + x * 12 = 409.
Solving this equation will give us the value of x, which represents the number of vans. Once we know x, we can calculate the total number of students and teachers who rode to the zoo in buses and vans.
HELP ASAP : Find the largest value of n such that 5x^2+nx+48 can be factored as the product of two linear factors with integer coefficients
Answer:
[tex]n=241[/tex]
Step-by-step explanation:
We are given
[tex]5x^2+nx+48[/tex]
Let's assume it can be factored as
[tex]5x^2+nx+48=(5x-s)(x-r)[/tex]
now, we can multiply right side
and then we can compare it
[tex]5x^2+nx+48=5x^2-5rx-sx+rs[/tex]
[tex]5x^2+nx+48=5x^2-(5r+s)x+rs[/tex]
now, we can compare coefficients
[tex]rs=48[/tex]
[tex]5r+s=-n[/tex]
[tex]n=-(5r+s)[/tex]
now, we can find all possible factors of 48
and then we can assume possible prime factors of 48
[tex]48=-+(1\times 48)[/tex]
[tex]48=-+(2\times 24)[/tex]
[tex]48=-+(3\times 16)[/tex]
[tex]48=-+(4\times 12)[/tex]
[tex]48=-+(6\times 8)[/tex]
Since, we have to find the largest value of n
So, we will get consider larger value of r because of 5r
and because n is negative of 5r+s
so, we will both n and r as negative
So, we can assume
r=-48 and s=-1
so, we get
[tex]n=-(5\times -48-1)[/tex]
[tex]n=241[/tex]
What does the t represent at the end of the vector?
The uppercase T means "transpose". A matrix transpose is where you swap the rows and columns. Anything that is row becomes a column, and vice versa. What this means is that instead of a row vector, you end up with a column vector. The dimensions are important so you can properly multiply matrices.
what is the approximate value of y - x
Answer:
17.2°
Step-by-step explanation:
using the tangent ration in the right triangle
tan y° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19.1}{14.1}[/tex], hence
y = [tex]tan^{-1}[/tex]([tex]\frac{19.1}{14.1}[/tex]) ≈ 53.6°
tan x° = [tex]\frac{14.1}{19.1}[/tex], hence
x = [tex]tan^{-1}[/tex]([tex]\frac{14.1}{19.1}[/tex]) ≈ 36.4°
y - x = 53.6° - 36.4° = 17.2°
Answer:
D) y -x = Approximate 17.1 degree.
Step-by-step explanation:
Given : Triangle .
To find : Approximate value of y - x.
Solution : We have given a right angle triangle with
Opposite side = 19.1 in.
Adjacent side = 14 .1 in.
Tan( y ) = [tex]\frac{Opposite}{adjacent}[/tex].
Plug the values
Tan( y ) = [tex]\frac{19.1}{14.1}[/tex].
tan(y) = 1.354.
Taking tan inverse both sides.
y = [tex]tan^{-1}(1.354)[/tex].
y = 53.55 degree.
Now, by the sum of angle of triangles is 180 degree.
Angle c + angle y + angle x = 180.
Plug the variable
90 + 53.55 + x = 180.
83.55 + x = 180
On subtracting both sides by 83.55
x = 36.45 degree
Then ,
y - x = 53 .55 - 36 . 45
y - x = 17.2
Approximate 17.1 degree
Therefore, D) y -x = Approximate 17.1 degree.
A car rental agency advertised renting a car for $ 23.95$23.95 per day and $ 0.34$0.34 per mile. If TrevorTrevor rents this car for 22 days, how many whole miles can he drive on a $ 100$100 budget?
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
$23.95 x 2 = $47.90
$100 - $47.90 = $52.10
$52.10 ÷ .34 = 153.23 miles can be driven
If you need to round the number will be 153 miles
The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. Find the side of the square, if it’s known that the area of the square is 30 cm2 less than the area of the rectangle.
Quickly 10 points
[tex]a-the\ side\ of\ square\\a^2-the\ area\ of\ square\\\\a+3-the\ one\ side\ of\ rectangle\\a-2-the\ second\ side\ of\ rectangle\\(a+3)(a-2)-the\ area\ of\ rectangle\\\\\text{The equation:}\\\\(a+3)(a-2)=a^2+30\qquad\text{use distributive property}\\\\(a)(a)+(a)(-2)+(3)(a)+(3)(-2)=a^2+30\\\\a^2-2a+3a-6=a^2+30\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\a-6=30\qquad\text{add 6 to both sides}\\\\\boxed{a=36}\\\\Answer:\ \boxed{36\ cm}[/tex]
is this right i dont know smo help
Answer:
D. multiplication property
Step-by-step explanation
Am not so sure but i think its that
solve for a 1/4(20-4a)=6-a
[tex]1/4(20-4a)=6-a \ /\cdot4\\20-4a=24-4a\\-4a+4a=24-20\\0=4\\false[/tex]
a boat can travel 176 kilometers on 88 liters of gasoline. How much gasoline will it need to go 250 kilometers
Answer:
176 km/88 liters = 2 km/liter
(250 km)(1 liter/2 km) = 125 liters
at a constant speed a car travels 75 miles in 60 minutes how far does the car travel in 18 minutes
Answer:
22.5 miles
Step-by-step explanation:
first divide 75 by sixty and that will be your traveled per minute then multiply that by 18 and that is you answer. Good luck, please mark me brainliest.
Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval. The distance traveled by the car in 18 minutes is 22.5 miles.
Given Information-
The car traveled with the constant speed is 75 miles in 60 minutes.
What is the constant speed?Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval.
As the car traveled with the constant speed is 75 miles in 60 minutes. Let x the total miles traveled by the car in one minutes is.
[tex]x=\dfrac{75}{60}[/tex]
[tex]x=\dfrac{5}{4}[/tex]
Thus the the total miles traveled by the car in one minutes is 5/4 miles. Let n be the total miles traveled by the car in 18 minutes. Thus,
[tex]x=\dfrac{5}{4}\times 18[/tex]
[tex]x=\dfrac{45}{2}[/tex]
[tex]x=22.5[/tex]
Hence the distance traveled by the car in 18 minutes is 22.5 miles.
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A 24 foot ladder leans against the wall of a building. The foot of the ladder is 5 feet from the base of the wall. How many feet above the ground is the point where the ladder touches the wall?
Answer:
The answer is approximately about 23.5 feet about the ground touching the wall.
Step-by-step explanation:
The ladder makes a right triangle with the wall and ground, therefore you use pythagorean theorem. If you draw what is being described, you can see that the 24 ladder is the hypotenuse or "c", while the ground and wall are "a" and "b" for the equation.
you set it up like so:
√(24²-5²) = a²
which will result in √(551) or ≈23.5 feet
The number of feet above the ground where the ladder touches the wall is 23.47 ft.
The information above forms a right angle triangle. The base of the right angle triangle is 5 ft and the hypotenuse of the right angle triangle is 24 ft.
Let's find the height of the triangle to know how many feet above the ground where the ladder touches the wall.
Using Pythagoras theorem,
c² = a²+b²where
c =hypotenuse
a and b are either adjacent side or opposite sides.
Therefore,
b² = 24² - 5²
b² = 576 - 25
b = √551
b = 23.4733891886
b ≈ 23. 47 ft.
Therefore, the feet above the ground where the ladder touches the wall is 23.47 feet.
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All of my points to anyone who can help me with these..! Marking Brainliest as well
Answer:
Question one 186
Question two 240
Step-by-step explanation: You multiply the variable (the letter) by the number that the person is using
Answer:
1. 186
2. 240
Step-by-step explanation:
1. D =3w+60
D =3(42)+60
D =186
2. I =48t
I =48(5)
I =240
The letter X shown above has which type of symmetry?
1. Line Symmetry only
2. Point Symmetry only
3. Point and Line Symmetry
4. No Symmetry
The letter X shown ''Point and Line Symmetry''.
What is Line segment?
Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The letter is X.
Now,
We know that;
A point symmetry is defined as a type of symmetry in which a geometrical figure is divided into two equal and symmetrical parts by a central point.
Thus, Letter X has Point symmetry.
And, The line symmetry is defined as a type of symmetry that divides a geometrical figure into two equal and symmetrical parts.
Thus, Letter X has Line symmetry.
Therefore, The letter X shown ''Point and Line Symmetry''.
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Given: ∆ABC is isosceles m∠ACB = 120° M ∈ AB , CM = 12 m∠BMC = 60° Find: AB
Look at the picture.
This is isosceles triangle. Therefore, the angles at the base are congruent.
m∠ BAC = m∠ABC.
We know, the sum of the measures of the angles in a triangle is equal 180°.
Therefore:
m∠BAC + m∠ABC + m∠ACB = 180°
2m∠ABC + 120° = 180° subtract 120° from both sides
2m∠ABC = 60° divide both sides by 2
m∠ABC = 30°
m∠MCB = 90° → ΔMCB is a right triangle (30 - 60 - 90).
The sides of that triangle are in proportion: 1 : √3 : 2.
Therefore MC : BC : MB = 1 : √3 : 2
MC = 12 → BC = 12√3 and MB = 2 · 12 = 24
ΔCDB is the right triangle (30 - 60 - 90) too.
Therefore CD : BD : BC = 1 : √3 : 2
CD = 1/2 BC → CD = 1/2(12√3) = 6√3
BD = CD√3 → BD = 6√3(√3) = 6(3) = 18
AB = 2BD therefore your answer is:
AB = 2(18) = 36AB length is 24 cm
Further Explanation The first step, find the length of BM
Given length CM = 12 cm
and length CB = 12 sqrt 3
sin 60 ° = CB / BM
1/2 sqrt 3 = 12 sqrt 3 / BM
BM = 1/2 sqrt 3 * 12 sqrt 3
BM = 18 cm
Then find the length of the MA
sin 30 ° = CM / MA
1/2 = 12 / MA
MA = 1/2 * 12
MA = 6 cm
So, the length of AB is BM + MA = 18 cm + 6 cm = 24 cm
A triangle is the name of a shape made from three sides in the form of a straight line and three angles. The mathematician Euclid who lived around 300 BC found that the sum of the three angles on a triangle on a flat plane was 180° degrees. This allows us to calculate the magnitude of one angle when the other two angles are known.
Classification of triangles
According to the length of the sides:
The equilateral triangle is a triangle whose sides are the same length. As a result, all angles are equal, which is 60 °. Isosceles triangle is a triangle whose two sides are the same length. This triangle has two equal angles. An arbitrary triangle is a triangle whose sides have different lengths. Big all the angles are also different.According to the biggest angle:
A right triangle is a triangle whose angle is equal to 90°. The side in front of the 90° angle is called the hypotenuse or the hypotenuse. An acute triangle is a large triangle, all angles <90° An obtuse triangle is a large triangle with an angle of> 90°
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Details
Class: Middle/High School and College
Subject: Mathematics
Keyword: degrees, angles, triangle
What is the solution to the inequality −3x < 7.5?
Answer:
The solution of the inequality is [tex](-2.5,\infty)[/tex].
Step-by-step explanation:
The given inequality is
[tex]-3x<7.5[/tex]
If an inequality divided by a negative number,then the sign of inequality change. Divide both sides by -3.
[tex]\frac{-3x}{-3} >\frac{7.5}{-3}[/tex]
[tex]x >-2.5[/tex]
Therefore the solution of the given inequality is all real numbers greater than -2.5.
In interval notation it can be defined as
[tex](-2.5,\infty)[/tex]
Answer:
x > −2.5
Step-by-step explanation:
i got the correct answer
A swimming pool has 2.5 million liters of water in it. Some water evaporated and then the pool only has 2 millions liters in it. What percent of the water evaporated?
Answer:
20% was evaporated
Step-by-step explanation:
Formula:
((New value-old value)/(old value))*100
((2-2.5)/(2.5))*100 = 20
Answer:
20% of the water evaporated
Step-by-step explanation:
We know that 500,000 evaporated because 2,500,000-2,000,000 is 500,000.
100% - 2,500,000
500,000 - x%
2,500,000/500,000 = 100/x
x=(500,000)(100)/2,500,000
x= 20%
20% of the water evaporated.
Tate has 5 more than twice as many pennies as Mia. If Mia has x pennies, how many does Tate have
Answer:
Tate has 7x pennies.
Step-by-step explanation:
Tate has 2x pennies because Mia has x pennies and Tate has twice the pennies of Mia so
5+2x= 7x
Jay is letting her bread dough rise. After three hours, her bread dough is 11/5 of its original size.
What percent of its original size is Jay's bread dough?
Answer:
original size of Jay's bread dough is raised to 220%
Step-by-step explanation:
Let 1 be the original size of the bread
her bread dough is 11/5 of its original size.
[tex]1* \frac{11}{5} = 2.2[/tex]
The original size of the bread is raised to 2.2
To get percentage we multiply by 100
2.2*100 = 220%
original size of Jay's bread dough is raised to 220%
what is this song of 2.5 x 10 to the 4th power + 3.4 * 10 to the 4th power
Oliver is watching a farmer plant a vegetable garden. He notices two hours after they began that the farmer had planted seven rows of the garden. Three hours later, he noticed that the farmer had now planted seventeen and a half rows of the garden. Assume that the farmer works at a constant rate.
Part B)Create an equation to represent the rate at which the farmer plants his vegetables, where x equals the hours worked and y equals the number of rows planted.
Answer:
y = 3.5x
Step-by-step explanation:
The equation for a straight line is
y = mx +b
We know that when
x₁ = 2, y₁ = 7 and when
x₂ = 5, y₂ = 17.5
Step 1. Determine the slope
m = (y₂ - y₁)/(x₂ - x₁) Substitute values
m = (17.5 – 7)/(5 – 2) Remove parentheses
m = 10.5/3
m = 3.5
===============
Step 2. Determine the y-intercept.
y = 3.5x + b Insert x₁ and y₁
7 = 3.5×2 + b
7 = 7 + b Subtract 7 from each side
b = 0
===============
Step 3. Write the equation
y = mx + b
y = 3.5x + 0
y = 3.5x
The equation is y = 3.5x.
12-packs Of Skwunch apple juice cost $3.00 after a 40% discount. Which equation would allow you to find the original price of the 12-pack? PLEASE HELP!!!!!!
Answer:
3.00 = original price * (1-.4)
or
3 = original price*.6
Step-by-step explanation:
We know the cost after the discount.
Price after discount = original price - original price * discount rate
Factoring out the original price
Price after discount = original price (1- discount rate)
We know the price after discount = 3.00 and the discount rate =.40
Substituting these values in
3.00 = original price * (1-.4)
3 = original price*.6
Divide each side by .6
3/.6 = original price
5.00 = original price
Which is the graph of x is greater than or equal to 2
The intersection of two planes is a point and two lines intersect in a point. True or false
Statement: Two planes intersect to form a point
This is false. Two planes intersect to form a single straight line.
-----------------
Statement: two lines intersect to form a point
This is true assuming the two lines have different slopes
-----------------
Because the first statement is false, the overall argument is false.
Final answer:
The intersection of two planes is a line, not a point, which makes the statement false. Two lines intersecting in a point is true provided they are not parallel.
Explanation:
The statement that the intersection of two planes is a point is false. According to geometric principles, specifically the line of intersection of two planes, when two planes intersect, they do so along a line, not just a single point. This line of intersection is represented by the points where their respective great circles cross. The intersection of two lines, however, is indeed a point, provided that the lines are not parallel. This is in agreement with Theorem 1, which states that two straight lines of a plane have either one point or no point in common; similarly, two planes have no point in common or a straight line in common.
Relevant Theorems on Intersections
Theorem 1 and Theorem 2 outline the foundational concepts regarding intersections in geometry. Understanding these theorems helps explain why two intersecting planes result in a line and not a single point.
what is the equation
Graham and Max will meet at the same altitude after approximately 22 minutes.
Explanation:
To find out how many minutes it will take Graham and Max to meet at the same altitude, we need to set up an equation.
Let's assume that after t minutes, Graham and Max will meet at the same altitude. This means that the altitude of Graham is equal to the altitude of Max.
Equation: 14,040 - 50t = 12,500 + 20t
To find t, we can solve this equation:
14,040 - 50t = 12,500 + 20t
Subtract 20t from both sides: 14,040 - 70t = 12,500
Subtract 12,500 from both sides: 14,040 - 12,500 - 70t = 0
Combine like terms: 1,540 - 70t = 0
Subtract 1,540 from both sides: -70t = -1,540
Divide by -70 on both sides: t = -1,540/-70
Simplify: t ≈ 22 minutes
Therefore, it will take approximately 22 minutes for Graham and Max to meet at the same altitude.
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a sea bird is 28 meters above the surface of the ocean what is the elevation
91.8 ft above sea level
ANY HELP WITH THIS WOULD BE AMAZING TYSM!!!
Match the equation with its graph -2x+7y=14
Answer:
x= 1
Step-by-step explanation:
- = negative. so negative 2 blank + 7 equals 14.
x is 1 because the more you add positively to a negative number the close it gets to zero. negative 21 + 7 is negative 14 but I you got an 8ntegr the n it would be 14.
The graph of the function -2x + 7y = 14 is attached
How to plot the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
-2x + 7y = 14
We start by making the variable y the subject
-2x + 7y = 14
So, we have
7y = 2x + 14
Divide through by 7
y = 2/7x + 2
And it also means that the equation is a linear equation
A linear equation is represented as
y = mx + c
Where
m = slope
i.e. m = 2/7
Hence, the equivalent equation to plot is y = 2/7x + 2
See attachment for graph
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In college math class of 50 student are 23 are boys 27 are girls on the final exam 15 boys and 14 girls made an A. What is the probability of choosing a boy or an girl A student is choosen at random from the class
Answer:
The probability of choosing an A student is 58% (0.58 or 29/50)
Step-by-step explanation:
The fact that 23 students are boys and 27 are girls is irrelevant to the question so we can ignore that.
There are 50 students in all and out of these students 15 boys and 14 girls made an A.
We can first add 15+14 which equals 29. So 29 students out of 50 made in A on the exam.
29/50 equals 0.58 or 58%.
I'LL GIVE BRAINLIEST! :D
How do you write these equations in slope intercept form?
y - 2x = -4
y - 3 = -1/2x
2x + 3y = 6
Answer:
y= 2x-4 , y= -1/2x +3 , y= -2/3x+2
Step-by-step explanation:
slope intercept form: y=mx+b
y-2x=-4
add 2x to both sides
y= 2x-4
y-3= -1/2x
add 3 to both sides
y= -1/2x +3
2x+3y=6
subtract 2x from both sides
3y= -2x+6
divide both sides by 3
y= (-2x+6)/3
y= -2/3x+2
NOTES:
Slope-Intercept form is y = mx + b ; where m is the slope and b is the y-intercept.
To convert an equation into slope-intercept form, solve for y
******************************************************************************************
Answer: y = 2x - 4
Step-by-step explanation:
y - 2x = -4
+2x +2x
y = 2x - 4
********************************************************************************************
Answer: y = [tex]-\frac{1}{2}x[/tex] + 3
Step-by-step explanation:
y - 3 = [tex]-\frac{1}{2}x[/tex]
+3 +3
y = [tex]-\frac{1}{2}x[/tex] + 3
********************************************************************************************
Answer: y = [tex]-\frac{2}{3}x[/tex] + 2
Step-by-step explanation:
2x + 3y = 6
-2x -2x
3y = -2x + 6
÷3 ÷3 ÷3
y = [tex]-\frac{2}{3}x[/tex] + 2
PLEASE HELP ME ON NUMBER 13 I NEED IT!!!!!
Answer:
a. x+y=10, 2x+3y=24
b.this systems of equations have a unique solution since there is only one value for x and one value for y where each equation is present in. There is no same slope or y-intercept
c. 4 magnet gift boxes
Step-by-step explanation:
simplify (b^9)^3
A.b^24
B.b^6
C.b^27
D.b^9
Answer:
C. b^27
Step-by-step explanation:
By the definition of exponents
[tex](b^9)^3=b^9*b^9*b^9[/tex]
And since for any real numbers [tex]r,x,[/tex] and [tex]y[/tex]
[tex]r^x*r^y=r^{(x+y)}[/tex]
This makes
[tex](b^9)^3=b^9*b^9*b^9=b^{{9+9+9}}=\boxed{b^{27}}[/tex]
Which is choice C.
Alternatively, we could use the identity
[tex](r^x)^y=r^{xy}[/tex]
in which case
[tex](b^9)^3=b^{(9*3)}= \boxed{b^{27}}[/tex]
which is the same answer.
Answer:b²⁷
Step-by-step explanation:
An author has 18 pages to send to a publisher. The author has only small envelopes and can't fit all the pages into a single envelope. It ends up taking 6 envelopes to hold all the pages. If each envelope has the same number of pages in it, how many pages are there in each envelope? A) 2 pages B) 3 pages C) 4 pages D) 5 pages