Answer:
Child ticket = $16.
Step-by-step explanation:
Let adult tickets = a;
child ticket = c.
2a + c = 94 — eq no. 1,
2a + 2c = 110 — eq no. 2,
then,from eq 1,
c = 94 - 2a. —eq no. 3.
Substitute eq 3 into eq 2,
2a + 2(94 - 2a) = 110
2a - 4a = 110 - 188
-2a /-2 = -78 / -2
a = 39.
Substitute value of a into eq 3,
c = 94 - 2(39)
= 94 - 78
c = 16.
Thus, child ticket = $16.
which of these expressions are equivalent to p/3?
A. p-2/3
B. 1/3p
C. p-3
D. 3/p
E. 3p/p
This is assuming that p is not in the denominator. To make it more clear that p is not in the denominator, I recommend you write (1/3)p.
Taking 1/3 of a number is the same as dividing by 3.
Example:
27/3 = 9
27*(1/3) = 9
helpyffhvjvjnvhdfuguig
Answer:
x = 0, x = 4
Step-by-step explanation:
12x - 21 = 5x + 7(x - 3)
First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.
Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.
Factor out a 5x --> 0 = 5x(x - 4)
If you want to solve for x, set 5x = 0 and x - 4 = 0.
For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.
For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.
Plug the values back into the original equation to check if it works
12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21
12(4) - 21 = 5(4) + 7((4) -3) --> 27 = 27
Hope this helps!
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = 6x − x2, y = 8; about x = 2
Answer:
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
Step-by-step explanation:
Given that:
y = 6x - x² , y = 8 about x = 2
To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8
6x - x² - 8
6x - x² - 8 = 0
-x² + 6x - 8 = 0
x² - 6x + 8 = 0
(x -4) (x - 2 ) = 0
So;
x = 2 , x = 4
Thus, the region bound of the integral are from a = 2 and b = 4
Therefore , the volume of the solid can be computed as :
[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]
[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]
[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]
[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
PLEASE HELP!!! ASAP!!!
Answer:
28 units²
Step-by-step explanation:
→ Work out the size of the triangle if it was a full rectangle
Height = 4 and Base = 2
→ Work out area of triangle
0.5 × Height × Base ⇒ 0.5 × 4 × 2 ⇒ 2 × 2 ⇒ 4
→ Minus the area of the triangle from the "imaginary full' rectangle
Area of rectangle = Length × Width ⇒ 8 × 4 ⇒ 32
32 - 4 = 28
Answer:
[tex]\huge\boxed{28\ units^2}[/tex]
Step-by-step explanation:
The figure consists of a triangle, a square and a rectangle.
Area of Triangle:
[tex]\sf \frac{1}{2} (Base)(Height)\\Where \ Base = 2 , Height = 4 \\=> \frac{1}{2} (2)(4)\\=> 4\ units^2[/tex]
Area of Square:
[tex]\sf (Length)(Length)\\(4)(4)\\=> 16\ units^2[/tex]
Area of rectangle:
[tex]\sf (Length)(Width)\\Where \ Length = 4 , Width = 2\\=> (4)(2)\\=> 8 \ units^2[/tex]
Area of the whole figure:
=> 4 + 16 + 8
=> 28 units²
Find the equation of a line that is perpendicular to line g that contains (P, Q).
coordinate plane with line g that passes through the points negative (3, 6) and (0, 5)
3x − y = 3P − Q
3x + y = Q − 3P
x − y = P − Q
x + y = Q − P
Answer:
x-y is parallel, im confused on what your asking for and what you mean by "negative"
Step-by-step explanation:
The equation of a line that is perpendicular to line g that contains (P, Q). is 3x − y = 3P − Q
What is Equation of line?The general form of the equation of a line with a slope m and passing through the point (x1, y1) is given as: y - y1 = m ( x- x1)
Further, this equation can be solved and simplified into the standard form of the equation of a line.
Given:
Line g passes through (3,6) and (0,5).
Slope of lone= y2 - y1/ (x2 - x1)
Perpendicular lines have opposite, reciprocal slopes, so negative change in x over change in y.
slope of line= -(-3 - 0)/(6 - 5)
= - -(-3)/1 =
slope of line = 3
Now, Two lines are perpendicular if they have the same slope.
Line parallel to line g has a slope of 1. Since it passes through (P, Q),
y - y1 = m ( x- x1)
y- Q =3 ( x- P)
y- Q = 3x- 3P
3x − y = 3P − Q
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(08.01) Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point
Answer:
the answer is D
Step-by-step explanation:
y=x-1
2=3-1
2=2
y=-3x+11
2=-3(3)+11
2=-9+11
2=2
Answer:
Step-by-step explanation:
If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.
Which statement BEST explains why the sine of an acute angle is equal to the cosine of the angles complement?
Answer:
In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B. Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.
Step-by-step explanation:
Calculate the surface area of a cube when the length of a side a = 15cm.
Surface area = 6a^2
Answer:
[tex]\boxed{ \sf 1350 \ cm^2}[/tex]
Step-by-step explanation:
Surface area of a cube = 6a²
a = side length
The side length is given 15 cm.
[tex]6(15)^2[/tex]
[tex]6(225)[/tex]
[tex]1350[/tex]
The surface area of the cube is 1350 cm².
how many ways can you order a sandwich if you can order it with or without ham, mustard, mayo, or cheese?
Which side of the quadrilateral ABCD has a length equal to 10? Question 5 options: Which side of the quadrilateral ABCD has a length equal to 10? Question 5 options: A. BC B. DA C. BA D. CD
Answer:
Side DA
Step-by-step explanation:
The point A has coordinates of (-2,6) and the point D has coordinates of (-2,-4). Since both points have the same x-coordinate, we can subtract point A's y-coordinate from point D's y-coordinate.
6 - ( -4) = 10 (Basically adding 4 to six since the 2 minus signs make a plus sign)
That's your answer!
Hope that helps and maybe earns a brainliest!
Have a great day! :)
The side of the quadrilateral ABCD has a length equal to 10 is AD.
What is distance?Distance is the amount of space between two points. The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is given by:
[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The coordinate of vertex A = (-2, 6) while for D is D(-2, -4). Hence:
[tex]AD=\sqrt{(-4-6)^2+(-2-(-2))^2}=10\ units[/tex]
The side of the quadrilateral ABCD has a length equal to 10 is AD.
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Which statement best compares the two functions?
The minimum of function A occurs 1 unit higher than the minimum of function B.
The minimum of function A occurs 3 units higher than the minimum of function B.
The minimum of function A occurs 5 units lower than the minimum of function B.
The minimum of function A occurs 7 units lower than the minimum of function B.
Answer:The minimum of function A occurs 1 unit higher than the minimum of function B.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Trust
The five-number summary for the number of touchdowns thrown by each quarterback in the British Football League is shown in the following table. About what per cent of quarterbacks in the British Football League threw more than 13 touchdowns?
Answer:
25%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 70% more of the substance? (Round your answer to one decimal place.) hr
Step-by-step explanation:
half life time-50%-8.4hr
so for 10%- 8.4/5=1.68 hr
now for 70%
1.68 × 7 = 11.76 hrs
to one decimal place - 11.8hrs
11.8 hours ago, there were 70% more of the substance if an isotope of lead has a half-life of 8.4 hours.
What is half-life?Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.
Half-life period - 50% -8.4hours
so for 10%- 8.4/5 = 1.68 hour
now for 70%
1.68 × 7 = 11.76 hours
To one decimal place - 11.8hours
Hence, 11.8hours is the answer.
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Drag each object to show whether distance is proportional to time in the situation represented.
Answer: please find the answer in the explanation.
Step-by-step explanation:
1.) The distance is not proportional to time. Because the distance was constant from time = 3 seconds to 10 seconds.
2.) A person running down a field to score a touchdown. Not enough information.
3. A dog jogging at a constant speed for 20 minute. The distance is proportional to time because of the constant speed.
4.) The distance is proportional to time because their is increase in distance covered and increase in time taken.
5.) A truck passing through the 4 cities at a constant speed. The distance is proportional to time because the speed is constant.
6.) A horse running around a race track. Distance is not proportional to time because this is not a linear motion.
what is the first step to solving this problem: 3x-10=2(x+3)
Answer:
x = 16
Step-by-step explanation:
3x - 10 = 2(x+3)
First step is solve this:
2(x+3) = 2*x + 2*3 = 2x + 6
then:
3x - 10 = 2x + 6
3x - 2x = 6 + 10
x = 16
Check:
3*16 - 10 = 2(16+3)
48 - 10 = 2*19 = 38
Answer:
x = 16
Step-by-step explanation:
you start off by isolating the variable
Drag the tiles to the correct boxes to complete the pairs.
The tables show proportional relationships between x and y. Match each table with its constant of proportionality.
ху
ху
ху
ху
1 10
4 20
215
1
4
2 20
8 40
430
2
8
330
12 60
645
312
4
15
Answer:
can you send a picture please? i have no clue how to answer this. it seems confusing with the numbers
attachment help for question c no explanation only answer thank you
Answer:
Tablets.
Step-by-step explanation:
You didn't want an explanation so....here you go....no explanation.
Hope that helps and maybe earns a brainliest.
Have a great day!
Please help! Dad will murder me if I don't have this done by the time he gets home! 100 points for whoever solves this!
Answer:
3(4)to the 3
Step-by-step explanation:
Please answer ASAP
Randomly pick 6 points from a square of side = 1. Show that you can always find 2 points from these 6 that their distance is less or equal to [tex]\frac{\sqrt{2} }{2} }[/tex]
Randomly pick 5 points from a sphere. Show that you can always find a closed semi-sphere ( half a sphere and boundary) that contains 4 points.
Problem 1.
My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.
Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.
Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.
===================================================
Problem 2.
For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.
If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.
Evaluate the expression. *
23 – (12 + 6) + 8
Please help
Answer:
13
Step-by-step explanation:
23-(12+6)+8
23-18+8
31-18
13
answer is 13
Step-by-step explanation:
Using the BODMAS rule,bracket of division or multiplication, addition or subtraction.
This applies the rule:
therefore,
23- (12+6)+8 ,calculate within bracket first
=23-(18)+8
now remove the bracket,by multiply by the -1
=23-18+8
the start calculate from the left to right
=23-10
=13
therefore the answer is 13
plz help me i need help
Kaitlyn can build a shed in 6 days. Mark can build the same shed in 8 days. Which equation can be used to find d, the number of days it would take Kaitlyn and Mark to build the shed together? Rate (Sheds per Day) Time (Days) Fraction Completed Kaitlyn One-sixth d One-sixth dd Mark One-eighth d One-eighth dd One-sixth d minus one-eighth d = 48 One-sixth d + one-eighth d = 48 One-sixth d minus one-eighth d = 1 One-sixth d + one-eighth d = 1
Answer:
One-sixth d + one-eighth d = 1
Step-by-step explanation:
When they work together, their rates of completion add. They want to build one shed, so the number of sheds being built is ...
(Kaitlyn's sheds per day)×(days Kaitlyn works) +(Mark's sheds per day)×(days Mark works) = 1 shed
(1/6)d + (1/8)d = 1 . . . . matches the last choice
What is the area of triangle PQR to the nearest tenth of a square meter? Drawing is not to scale. A. 24.1 m2 B. 34.4 m2 C. 48.2 m2 D. 68.8 m2
Answer:
b
Step-by-step explanation:
The area of triangle PQR which is an SAS triangle, to the nearest tenth, is: A. 24.1 m²
What is the Area of an SAS Triangle?The area of an SAS triangle = ½ × bc × sin(A).
Given the following:
PQ (b) = 14 mRQ (c) = 6 mAngle Q (A) = 35°Area of triangle PQR = ½ × (14)(6) × sin(35)
Area of triangle PQR = 24.1 m²
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Find the value of m∠ACD. A. 30º B. 15º C. 60º D. 90º
Answer:
A. 30 degrees
Step-by-step explanation:
Set the two angles equal to each other:
3x-15 = 45-x
Solve for x:
4x -15 = 45
4x = 60
x = 15
Finally, plug in the x to one of the equations (preferably 45 - x since it's easier to solve) and solve for x.
45 - 15 = 30
Answer:
A 30 degrees
Step-by-step explanation:
4x = 2x + 2x + 5(x-x) does this have one solution, no solution or infinite solutions
Answer:
infinite solutions
Step-by-step explanation:
4x = 2x + 2x + 5(x-x)
Simplify
4x = 2x + 2x + 5*0
4x = 2x + 2x
4x = 4x
Divide by x
4 =4
This is always true so this has infinite solutions
Please help me on this question
Answer:
The area can be expressed as: [tex]\pi r^2+lw[/tex].
We have l=10, because 18-2(4)
We have w=8, as given.
Thus, the rectangle area is 80.
There are two semicircles, but they add to form a full circle, which makes things a lot easier. We have the circle area formula, and substituting the values gives us 50.24 as the circle volume
80+50.24=130.24.
Rounded to 1 decimal place that is 130.2
Hope this helps :)
Plzz help I’ll mark brainliest
Answer:
6cot 50
Step-by-step explanation:
Tan 50=6/x
x= 6/(tan 50)
x= 6cot 50°
Answer:
? = 6 cot 50
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 50 = 6 /?
? tan 50 = 6
? = 6 / tan 50
We know that 1 / tan 50 = cot 50
? = 6 cot 50
PLEASE HELP ME!! I WILL GIVE BRAINLIEST!!
Find the output, y, when the input, x, is -5.
Answer:
[tex]\boxed{y = -2}[/tex]
Step-by-step explanation:
Hey there!
To find y when x is -5 we go to -5 on the x-axis.
When at -5 find where the blue line is vertical to -5,
which is -2.
Hope this helps :)
need help with these questions!!! please explain bc I don't really get it!
Answer:
1. b. 2. a. 3. a.
Step-by-step explanation:
1. (f + g)x = f(x) + g(x)
= x^2 + 2x + 4
(f + g)(-1) = (f + g)(x) where x = 1 so it is
(-1)^2 + 2(-1) + 4
= 1 - 2 + 4
= 3.
2. We find (f o g)(x) by replacing the x in f(x) by g(x):
= √(x + 1) and
(f o g)(3) = √(3 + 1)
= √4
= 2.
3. (f/g) c = f(x) / g(x)
= (x - 3)/(x + 1)
The domain is the values of x which give real values of (f/g).
x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.
The domain is (-∞, -1) U (-1, ∞)
How many units away is 1 from -6 on a number line?
Answer:
7 units
Step-by-step explanation:
(number line:)
<- -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ->
←there are 7 units from 1 to -6 (you don't count the 0)
(I'm not sure if you understood my explanation, but I do am sure about the answer, so if there is something you didn't understand let me know, and which part are you confused about so I can help you out!)
Answer:
[tex]\huge\boxed{\sf 7\ units}[/tex]
Step-by-step explanation:
To find that how much far they are from each other, we can subtract both of them.
=> 1 - (-6)
=> 1 + 6
=> 7 units
So, they are 7 units apart from each other.
