To find the cost of a single cinema ticket, multiply the amount each friend paid, £6.15, by 4 to get the total cost for 3 paid tickets. Divide this total, £24.60, by 3 to find that the cost of one ticket is £8.20.
The question pertains to a group of 4 friends who buy cinema tickets using an offer where they buy 3 tickets and get 1 free. Since each friend pays £6.15, we need to determine the actual cost of a single ticket.
Under the offer, they are buying a total of 4 tickets for the price of 3. Therefore, we can calculate the cost of 3 tickets by multiplying £6.15 by 4, which gives us a total of £24.60. To find the cost of a single ticket, we divide the total cost of £24.60 by the number of tickets bought, which is 3.
Here is the calculation step:
Total cost for 4 friends = 4 × £6.15 = £24.60
Cost of a single ticket = [tex]\frac{24.60}{3}[/tex] tickets = £8.20
Therefore, the cost of one ticket without the offer is £8.20.
What is the measure of ∠ACD?
A.30°
B.63°
C.147°
D.150°
Please help :)
The measure of ∠ACD is 150°. So the answer is D.150°.
The ∠ACD is an exterior angle of triangle ABC. We can use the fact that the sum of the measures of the interior angles of a triangle is 180° to solve for the measure of ∠ACD.
Identify the interior angles of triangle ABC: We are given the measures of two interior angles: ∠A = 33° and ∠B = 117°.
Find the sum of the interior angles of triangle ABC: ∠A + ∠B + ∠C = 180°
Substitute the known values and solve for ∠C: 33° + 117° + ∠C = 180°
Combine like terms: 150° + ∠C = 180°
Isolate ∠C: ∠C = 180° - 150°
Calculate the measure of ∠C: ∠C = 30°
Find the measure of ∠ACD: Since ∠ACD is an exterior angle of triangle ABC and ∠C is an interior angle, we know that ∠ACD and ∠C are supplementary angles. Therefore, their measures add up to 180°.
Calculate the measure of ∠ACD: ∠ACD = 180° - ∠C = 180° - 30° = 150°
Therefore, the measure of ∠ACD is 150°. So the answer is D. 150°.
(35 pts)Evaluate the reasoning provided by both students A and B and correct the errors Make sure to provide proper reasoning. Only answer if you know your answer is correct please.
Answer:
see the explanation
Step-by-step explanation:
we know that
A Rational Number is a number that can be made by dividing two integers
we have
[tex]\frac{\sqrt{2}}{8}[/tex]
[tex]\sqrt{2}[/tex] ----> is not a integer
so
The given number cannot be rewritten as the quotient of two integers
therefore
The given number is irrational
Student A is incorrect because is a irrational number and not all fractions are rational
Student B reasoning is incorrect, because there are fractions that have as numerator an irrational number and can be rational numbers
example
[tex]\frac{\sqrt{2}}{3\sqrt{2}}=\frac{1}{3}[/tex] ----> is a rational number and the numerator is a irrational number
Student A incorrectly claims √2/8 is rational because it can be written as a fraction. Student B is correct, stating that √2/8 is irrational because √2 is irrational, and dividing it by 8 doesn't change its irrationality.
Let's evaluate the reasoning of both students A and B and correct any errors:
Student A:
Student A's reasoning is incorrect. They claim that √2 / 8 is rational because it can be written as a fraction. However, being able to write a number as a fraction doesn't necessarily make it rational. The key point is whether the number can be expressed as a ratio of two integers, and in this case, √2 cannot be expressed as a simple fraction. √2 is known to be an irrational number, and when you divide an irrational number by 8, the result remains irrational.
Student B:
Student B's reasoning is correct. They state that √2 / 8 is irrational because √2 is irrational. This is accurate. The division of an irrational number by a rational number does not change its irrationality. Therefore, √2 / 8 is indeed an irrational number.
In summary, Student B provides the correct reasoning, while Student A's reasoning is flawed.
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A classmate plotted the following points:
A(-3, 2), B(-1, 4), and C(1, 2).
Where should the classmate plot point
D so that the quadrilateral formed has
perpendicular sides?
Answer:
D(-1,0)
Step-by-step explanation:
Plot points A(-3, 2), B(-1, 4), and C(1, 2) on the coordinate plane (see attached diagram).
Two sides AB and BC are of equal length and are perpendicular, because
[tex]AB=\sqrt{(-3-(-1))^2+(2-4)^2}=\sart{(-2)^2+(-2)^2}=\sqrt{4+4}=2\sqrt{2}\ units\\ \\BC=\sqrt{(-1-1)^2+(4-2)^2}=\sart{(-2)^2+2^2}=\sqrt{4+4}=2\sqrt{2}\ units\\ \\\text{Slope AB}=\dfrac{4-2}{-1-(-3)}=\dfrac{2}{2}=1\\ \\\text{Slope BC}=\dfrac{2-4}{1-(-1)}=\dfrac{-2}{2}=-1\\ \\\text{Slope AB}\cdot \text{Slope BC}=1\cdot (-1)=-1\Rightarrow \text{lines AB and BC are perpendicular}[/tex]
If the quadrilateral ABCD has all sides perpendicular, then ABCD is a square. The diagonals of the square bisects each other. Find the coordinates of the point of intersection of these diagonals. This is the midpoint of segment AC:
[tex]x=\dfrac{-3+1}{2}=-1\\ \\y=\dfrac{2+2}{2}=2[/tex]
If point O(-1,2) is the point of intersection of diagonals, then it is the midpoint of the diagonal BD. Find coordinates of point D:
[tex]x_O=\dfrac{x_B+x_D}{2}\Rightarrow -1=\dfrac{-1+x_D}{2},\ -1+x_D=-2,\ x_D=-1\\ \\y_O=\dfrac{y_B+y_D}{2}\Rightarrow 2=\dfrac{4+y_D}{2}, 4+y_D=4,\ y_D=0[/tex]
Thus, D(-1,0)
NS SECTION ONE
In the number 416.98, which digit has the greatest value
the 4 because it's in the hundred place value
I THINK THAT"S HOW YOU DO IT, BUT YOU KNOW JUST TRYING TO HELP YOU :)
If a number is not a whole number then it is not a natural number
Answer:
false
Step-by-step explanation:
a natural number is a number you count by, you wouldn't cound by decimals or fractions
how can you use a formula for one measurement to write a formula for a different measurement?
Answer:
Write the formula for one measurement, then solve the formula for the different measurement you want to find and use this new formula to find that measurement.
Step-by-step explanation:
We can understand this through an example.
If we need to find the lenght of a rectangle whose width is 4 feet and whose perimeter is 28 feet, we can use a formula for one measurement to write a formula for a different measurement:
- We need to write the formula for the perimeter of a rectangle:
[tex]P=2l+2w[/tex]
Where "l" is the lenght and "w" is the width.
- Since we know the width and the perimeter of the rectangle and we need to find the lenght, we can solve for "l":
[tex]P=2l+2w\\\\P-2w=2l\\\\l=\frac{P-2w}{2}[/tex]
Now we get a new formula for calculate a differente measurement (the lenght of the rectangle).
- Substituting values, we get:
[tex]l=\frac{28ft-2(4ft)}{2}=10\ ft[/tex]
A lithium atom has positively charged protons and negatively charged electrons. The sum of the charges represents the charge of the lithium atom. Find the charge of the atom.
Answer:
The answer to your question is: zero
Step-by-step explanation:
# of protons = 3 they are in the nucleus (blue)
# of electrons = 3 they are in red
Charge = protons + electrons
Charge = +3 + (-3)
Charge = +3 - 3
Charge = 0
What is the area of a rectangle with a base of 12 mm and a height of 1.4 mm? A. 13.4mm2 B. 16.8 mm2, C. 134 mm2, 168 mm 2
Answer:
D. 168 mm²Step-by-step explanation:
The formula of an area of a rectangle:
[tex]A=l\cdot w[/tex]
l - length (base)
w - width (height)
We have l = 12mm, h = 14mm.
Substitute:
[tex]A=(12)(14)=168\ (mm^2)[/tex]
Solving an Equation with Absolute value |x-3|=5 . Equation 1:
Answer:8
Step-by-step explanation: add 3 on both sides to cancel it from the left, and then x=8.
Ayodele received a raise in her hourly pay, from $24.50 to $25.48. Find the percent change.
Answer:
4%
Step-by-step explanation:
The raise in her hourly pay is
$25.48-$24.50 =$0.98
Cross multiplying (rule of three)
24.50------100%
0.98--------x%
and so, x= 0.98*100/24.5 = 4%
Answer: The required percent change is 4%.
Step-by-step explanation: Given that Ayodele received a raise in her hourly pay, from $24.50 to $25.48.
We are to find the percent change.
The percent change is given by
[tex]p=\dfrac{\textup{increse in the amount}}{\textup{original amount}}\times100\%.[/tex]
In the given situation, we have
[tex]\textup{increase in the amount}=\$(25.48-24.50)=\$0.98.[/tex]
Therefore, the percent change is given by
[tex]p=\dfrac{0.98}{24.50}\times100\%=\dfrac{98}{24.50}\%=4\%.[/tex]
Thus, the required percent change is 4%.
What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)? y = – Five-halvesx – 1 y = – Five-halvesx + 5 y = Two-fifthsx – 1 y = Two-fifthsx + 5
Answer:
[tex]y= \frac{-5}{2}x-1[/tex]
Step-by-step explanation:
the line equation is 5x + 2y = 12
Solve for y to find out slope m
y=mx+b
[tex]5x + 2y = 12[/tex]
Subtract 5x from both sides
[tex]2y =-5x+12[/tex]
Divide both sides by 2
[tex]y=\frac{-5}{2} x+6[/tex]
slope = -5/2
Slope of parallel lines are same . So slope of parallel line is [tex]\frac{-5}{2}[/tex]
m=-5/2 , point (-2,4)
[tex]y-y_1= m(x-x_1)[/tex]
[tex]y-4= \frac{-5}{2}(x+2)[/tex]
[tex]y-4= \frac{-5}{2}x-5[/tex]
Add 4 on both sides
[tex]y= \frac{-5}{2}x-1[/tex]
Answer:
Answer is A
Step-by-step explanation:
Trust the process
hi i need help plz it is 7/3 add 1/3. plz plz help
Answer: 8/3
Step-by-step explanation: To add like fractions, or fractions that have the same denominator, simply add the numerators and keep the original denominator.
7 + 1 = 88/3 is the answer.What numbers can you times to make24
Answer:
6 and 4
2 and 12
1 and 24
3 and 8
Step-by-step explanation:
Answer:
1, 2, 3, 4, 6, 8, 12, 24.
Step-by-step explanation:
The question is basically saying "what are the factors of 24?"
Compare the expressions using <, >, or =. Show all your work.
(18 – 3) ÷ (6 - 1) _____ 4 • (10 – 3) – 4 • 2
Answer:
The answer would be <
Step-by-step explanation:
(18-3)÷(6-1)
18-3=15
6-1=5
15÷5=3
________
4×(10-3)-4×2
10-3=7
4×7-4×2
28-8=20
Based on the graph, what was the average speed, in miles per minute, of the train during the interval of 30 to 40 minutes?
Answer: 35 miles
Step-by-step explanation:
Answer:
Step-by-step explanation:
60
8. A cookie recipe calls for of a cup of flour and makes 2 dozen cookies.
a. If you plan to make 8 dozen cookies, how many cups of flour do you need?
- b. How many cookies can you make if you have 10 cups of flour and want to use it all?
Answer:
a. Number of flour cups needed = 4 cups
b. Number of cookies that can be baked = 240 cookies
Explanation:
We are given that:
1 cup of flour is needed to make 2 dozen cookies
To solve the two parts of this question, we will simply use cross multiplication
Part a:
1 cup of flour .......................> 2 dozen cookies
x cups of flour ....................> 8 dozen cookies
[tex]x = \frac{8*1}{2} = 4[/tex] cups
Therefore, 4 cups of flour are required to make 8 dozen cookies
Part b:
1 cup of flour .................> 2 dozen cookies
10 cups of flour ............> y dozens of cookies
[tex]y=\frac{10*2}{1} = 20[/tex] dozens of cookies
This means that, 10 cups of flour can make 20 dozen cookies
However, here we are asked about the number of cookies, not the number of dozens
We know that 1 dozen contains 12 parts
This means that:
1 dozen cookies = 12 cookies
Therefore:
20 dozens cookies = 20 × 12 = 240 cookies
Hope this helps :)
Look at this diagram:
Which diagram shows AABC rotated 120° counterclockwise about B?
Answer:
second one diagram rotated 120
In a 120° counterclockwise rotation about point B, diagram AABC would shift each point along a circular path 120° in a counterclockwise direction around point B. The positions of points A and C would change, while point B would stay as it is. The correct diagram would reflect these changes.
Explanation:Without a specific diagram to refer to, I can provide only a general explanation of how to determine the diagram that represents AABC rotated 120° counterclockwise about point B.
Rotations in a plane are performed counterclockwise with a positive degree measure. So, a 120° counterclockwise rotation about a fixed point B would take every point on triangle AABC and shift it along a circular path 120° in a counterclockwise direction around point B. The result would be a new triangle A'B'C'. If point B is the origin of rotation, it would remain unchanged. However, points A and C would change their positions after the rotation.
To determine the correct diagram, you would look for a triangle that has been shifted around point B in a counterclockwise direction with positions of points A and C reflecting a 120° rotation.
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So far, Carmella has collected 14 boxes of baseball cards. There are 315 cards in each box. Carmella estimates that she has about 3,000 cards, so she buys 6 albums that hold 500 cards each.
a. Will the albums have enough space for all of her cards? Why or why not?
b. How many cards does Carmella have?
c. How many albums will she need for all of her baseball cards?
Answer:
4410 cards, 9 albums
Step-by-step explanation:
Number of cards in a box = 315
Number of boxes = 14
b) Total number of cards = Number of boxes × Number of cards in 1 box
=[tex]315\times 14 = 4410[/tex]
a) Carmella estimated she had 3,000 cards so she bought a 6 album of 500 cards.
No, 6 albums are not enough as she estimated wrong number of cards. There are total of 4410 cards but she estimated it to be 3000 cards.
c) Total number of albums required = [tex]\displaystyle\frac{\text{Total number of cards}}{\text{Number of card 1 album can hold}}[/tex]
[tex]=\frac{4410}{500} = 8.82 \approx 9[/tex]
Thus, she will require 9 albums to put all her cards.
Thirty-six is at least one half of a number.
What is the inverse of the function below?
F(x)=3^x
A.
B.
C.
D.
Answer:
[tex]Log_{(3)}X[/tex]
Step-by-step explanation:
[tex]f(x)=3^{X}[/tex]
[tex]y=3^{X}[/tex]
exchange the variables x and y
[tex]X=3^{y}[/tex]
[tex]Log_{(3)}X=Log_{(3)}3^{y}[/tex]
[tex]Log_{(3)}X=y[/tex]
[tex]f^{-1}(x)=Log_{(3)}X[/tex]
6x4=8xN
how do i solve this equation
Answer:
n = 3
Step-by-step explanation:
find multiples of the product of 24 that comes from 6*4
A 21-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (21 − x) ft. Find the length of the longer rope piece x In ft
Answer:
The length of the longer rope piece is 14 ft
Step-by-step explanation:
Let
x -----> the longer piece
y ----> the shorter piece
we know that
The sum of the longer piece plus the shorter piece must be equal to the length of the original piece
x+y=21
y=(21-x) -----> equation A
3x-7=5y ----> equation B
substitute equation A in equation B and solve for x
[tex]3x-7=5(21-x)\\3x-7=105-5x\\5x+3x=105+7\\8x=112\\x=14\ ft[/tex]
therefore
The length of the longer rope piece is 14 ft
(please answer fast)
can someone write and solve a word problem, while using two key word's for either addition, subtraction, multiplication, or division? thank you.
Answer:
subtraction= Mike is selling 50 apples. Kenny is selling 30 apples,"how many more" apples does mike have than ken?
50- 30 = 20
mike has 20 "more" apples than ken.
there are 15 kindergarteners, "but only" 10 chairs, "how many" chairs would the teachers have to "take away" from the room next door?
15- 10=5
What is the link between steroids and heart disease?
Answer: Steroids Linked to Higher Heart Disease Risk. High Doses May Raise Risk of Heart Attack, Stroke, Study Shows. By Miranda Hitti. Nov. 15, 2004 -- Taking high doses of steroids (glucocorticoids) seems to increase the risk of heart disease including heart attack, heart failure, and stroke, according to new research.
Step-by-step explanation:
Answer:
high dosages of steroids can cause heart disease and increase the risk of heart attack, heart failure, and stroke.
Step-by-step explanation:
Umar has 5 dimes in his right pocket and three dimes in his left pocket how much money does Omar have? What is the hidden question?
Answer:
he has 80 cents
Step-by-step explanation:
dime=10 cents
I'm guessing that the hidden question is how many dimes does Omar have? because this is the first thing I asked myself when solving this equation.
So how many dimes does Omar have?
5 + 3 = 8
Now we know that one dime = 10 cents, so to find the amount of money in cents, all we need to do is multiply 8 * 10
8 * 10 = 80
Omar has 80 cents
How many 2/3-cup servings are in 6 cups of cereal?
Answer: 9
Step-by-step explanation:
6 divided by 2/3 = 9
In 6 cups of cereal, there are 9 servings of 2/3 cup.
Explanation:To find out how many 2/3-cup servings are in 6 cups of cereal, we need to divide the total cups of cereal by the size of each serving. In this case, we divide 6 by 2/3. To divide a whole number by a fraction, we can multiply the whole number by the reciprocal of the fraction. The reciprocal of 2/3 is 3/2, so we have 6×3/2 = 9 cups in total. Therefore, there are 9 servings of 2/3 cup in 6 cups of cereal.
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Please help! Solving polynomial equations with factoring *algebra*
Help please !!!!!!!!!!!!!!!!
Answer:
(12,10)
Step-by-step explanation:
hugo made 100 ounces of lemonade.How many 8 ounce glasses can he fill completely with this amount of lemonade
Answer:
12
Step-by-step explanation:
divide 100 by 8
find the product 3(x + 4 )( x - 5)
Answer:
[tex]3x^2-3x-60[/tex]
Step-by-step explanation:
Given: [tex]3(x+4)(x-5)[/tex]
Let's use the distributive property to multiply [tex](x+4)(x-5)[/tex] together since they are right next to each other. We can use the FOIL method.
[tex](x+4)(x-5)\\x^2-5x+4x-20\\x^2-x-20[/tex]
Now that we simplified that, we still have to multiply everything by the value of [tex]3.[/tex]
[tex]3(x^2-x-20)\\3x^2-3x-60[/tex]
Now, you could have left the answer as [tex]3(x^2-x-20)[/tex] since it is factored, but the problem wants us to find the product, so we need to completely simplify.