The cost of bag of popcorn is $7.5 and that of one drink is $5.
How to find the general equation of a Straight line?The formula for finding the general equation of a straight line is -
[y] = [m[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have Xochitl who went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50.
Assume that the cost of one popcorn bag is $[x] and one drink is $[y].
Then we can write -
6x + 4y = 65
6x + 4y = 659x + 8y = 107.5
Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. We get x = $7.5 and y = $5.
Therefore, the cost of bag of popcorn is $7.5 and that of one drink is $5.
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Answer:
$7.5 and 5
Step-by-step explanation:
i did this on my assignment
A transformation which results in the pre-image and image having the same shape but not necessarily the same size.
center of dilation
Similarity Transformation
scale factor
dilation
30 points
On solving the provided question, we can say that A dilation is a transformation that yields a different-sized picture with the same general shape as the original.
what is dilation?A dilation in mathematics is a function f from a metric space M to itself that, for any point x, y in M, fulfills the identity d = rd. where r is a positive real integer and d is the separation between x and y. Such extensions are identical in space according to Euclid. Dilation is a transform that modifies an object's size. The process of dilation is used to enlarge or reduce items. The result of this transformation is an image that is a perfect replica of the original shape. However, there is a variation in the shape's size. The initial form ought to be distorted by dilation.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. The scale factor (also known as the dilation constant) and the dilation center are included in the description of a dilation. A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
for example
triangle ABC ≈ triangle A'B'C'
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Given m∠ABC=37°m∠ABC=37°and m∠CBD=165°m∠CBD=165°. According to the Angle Addition Postulate, what is the measure of ∠ABD∠ABD, that contains −−→BCBC→?
According to the Angle Addition Postulate, the measure of m∠ABD = 202°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
The angle measures:
m∠ABC=37°,
and m∠CBD= 165°.
So, according to the angle addition postulate;
m∠ABD = m∠ABC + m∠CBD
Substituting the values,
m∠ABD = 37° + 165°
m∠ABD = 202°
Therefore, the angle measure of m∠ABD = 202°.
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y is inversely proportional to x squared y=8 when x =3.5 find the neagative value of x when =8/9
Since y is inversely proportional to x squared and y = 8 when x = 3.5, the negative value of x when y = 8/9 is equal to -10.5 or -21/2.
What is an inverse variation?In Mathematics, an inverse variation can be modeled by this mathematical expression:
y ∝ 1/x
y = k/x
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Based on the information provided above, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:
y = k/x²
k = yx²
k = 8(3.5)²
k = 98.
Now, we can determine the negative value of x:
x = √(k/y)
x = √(98/(8/9)
x = √110.25
x = 10.5 or 21/2.
x = -10.5 or -21/2.
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Explain why multiplying by 8/3 gives the same result as first multiplying by 8 and then multiplying by 1/3
Because by multiplying by 8/3, you're multiplying by 1/3, 8 times. (8*1/3=8/3)
I need help asap super confused and due in 20 minutes
Step-by-step explanation:
what is so confusing ? let me know, where you need more explanation.
the angle PTS = 96°
that is the angle between the outer left and the outer right line, so the total angle of everything in the graphic.
now we see 2 sub-angles in there :
PTQ = 28°
RTS = 49°
and we are looking for a third sub-angle QTR.
well, we know, all 3 angles together are the same as the one big angle defined at the beginning.
PTS = PTQ + RTS + QTR
96 = 28 + 49 + QTR
96 - 28 - 49 = QTR
QTR = 19°
The function g is defined by g)2+bx, where b is a constant. If the line tangent to the graph of g at x 1 is parallel to the line that contains the points (0, -2) and (3, 4), what is the value of b ? (A) -1
(B) 2
(C) 5/2
(D) 4
Answer:
The cost per hour for renting the boat is $18 per hour.
A function is said to be linear if it is a straight line graph and it can be represented by the equation:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the total cost for renting the boat for x hours.
Given the equation:
y = 18x
Therefore the cost per hour for renting the boat is $18 per hour.
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A landlord plans to take out a $12,000 loan to cover the cost of a new roof for a rental home. If the loan has a 5% annual interest rate compounded continuously and the landowner plans to pay off the loan in 21 months, what is the total amount owed? $34,291.81 $24,600.00 $13,328.53 $13,097.31
Using compound interest formula, the final payment for a principal of $12000 compounded continuously at rate of 5% is $13,097.31
What is Compound InterestCompound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula of compound interest is given as;
A = P(1 + r/n)^nt
A = compound interestP = principalr = rate n = number times t = timeSubstituting the values into the formula
A = Pe^rt
This formula is only for continuously compounded
A = 12000e^(0.05 * 1.75)
A = $13,097.31
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(25 points) find x and y of the heptagon more info in the picture above
Answer:
x = 128.57°
y = 51.43°
Step-by-step explanation:
x = (n - 2) × 180°/n = (7 - 2) × 180°/7 = 900/7° = 128.57°
x + y = 180
y = 180° - 128.57°
y = 51.43°
Given below are descriptions of two lines. Line 1: Goes through ( − 4 , 17 ) ( - 4 , 17 ) and ( 9 , − 9 ) ( 9 , - 9 ) Line 2: Goes through ( 1 , 1 ) ( 1 , 1 ) and ( − 5 , 19 ) ( - 5 , 19 ) The slope of Line 1 is m = m = The slope of Line 2 is m = m = Finally, which of the following is true? Line 1 is parallel to Line 2. Line 1 is perpendicular to Line 2 Line 1 is neither parallel nor perpendicular to Line 2
Based on the descriptions of two lines, a statement which is true include the following: C. Line 1 is neither parallel nor perpendicular to Line 2.
How to calculate the slope of a line?In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following data points on the line:
Points on x-axis of line 1 = (-4, 9).Points on y-axis of line 1 = (17, -9).Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-9 - 17)/(9 - (-4))
Slope, m = -26/(9 + 4)
Slope, m = -26/13
Slope, m = -2
For the slope of line 2, we have:
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (19 - 1)/(-5 - 1)
Slope, m = -18/6
Slope, m = -3
In conclusion, we can logically deduce that both lines are neither parallel nor perpendicular because their slope differs.
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A boy walks 3km from point A on a bearing of 023. He the walks 4km on a bearing of 113 to a point B. what is the bearing of B from A
The bearing of B from A is 76°.
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
Given that, a boy walks 3 km from point A on a bearing of 023°. He the walks 4 km on a bearing of 113° to a point B.
If A is at (0,0) then his first turn is at
X is at A + (3 sin23° , 3 cos23°) = (1.172, 2.761)
and B is at X + (4 cos23° , -4 sin23°) = (4.854, 1.198)
So, the bearing of B from A is θ,
where tanθ = 4.854/1.198 ≈ 76°
Therefore, the bearing of B from A is 76°.
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The tallest tree in the world is in redwood California as of April 2019 if you’re standing on the trail 220 feet from the bottom of the tree you have to look up it is 60° angle to see the top how tall is the tree
Step-by-step explanation:
AB is the height of tree
angle is 60 degree
bc is the bottom of tree
a museum has three rooms, each with a motion sensor (m0,m1, and m2) that outputs 1 when motion is detected. at night, the only person in the museum is one security guard who walks from room to room. create a circuit that sounds an alarm (by setting an output a to 1) if motion is ever detected in more than one room at a time, meaning there must be at least one intruder. start with a truth table.
(a) Truth Table is attached.
(b) In canonical SOP form, A = ∑ m(3,5,6,7)
(c) Minimal form: A = m1m2 + m0m1 + m0m2
(b) Canonical SOP form: The canonical sum-of-products (sop) form of LPP in matrix notation is as follows: Boost Z = CX (objective function) AX b (restrictions) and X 0 (limitations) apply (non-negativity restrictions).
it will be A = ∑ m(3,5,6,7)
(c) Minimal form: The k-map can be defined as a map that provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. The Karnaugh map can also be described as a special arrangement of a truth table.
it will be A = m1m2 + m0m1 + m0m2
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The complete question is:
a museum has three rooms, each with a motion sensor (m0,m1, and m2) that outputs 1 when motion is detected. at night, the only person in the museum is one security guard who walks from room to room. create a circuit that sounds an alarm (by setting an output a to 1) if motion is ever detected in more than one room at a time, meaning there must be at least one intruder.
(a) Specify the truth table
(b) formulate canonical sum of products implementation for A
(c) Minimize A using K-maps and write the minimum implementation of A
Find the removable and non removable discontinuity.
F(x) = 2/x
The function F(x) = 2/x has a removable discontinuity at x = 0, and a non-removable discontinuity at x = 0.
What is the Function?
A function is a mathematical relation between a set of inputs, called the domain, and a set of possible outputs, called the range. The definition of a function is often written as "f: X → Y", where X is the domain and Y is the range, and "f" is the name of the function.
The function F(x) = 2/x has a removable discontinuity at x = 0, and a non-removable discontinuity at x = 0.
At x = 0, the function is not defined, so it has a removable discontinuity at x = 0.
However, since the function is not defined for x = 0, it is also a non-removable discontinuity at x = 0.
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Best Buy and Target are having a Black Friday sale. Best Buy is selling the newest iPad for an original price of $800 with a 10% discount. Target is selling the same iPad for an original price of $875 and is offering a 15% discount. After the discount, which store has the lower price?
Answer:
Best Buy - $720 for the new iPad
Target - $743.75 for the new iPad
Conclusion:
Best Buy has the lowest price for the iPad.
Mason had 30 minutes to do a three-problem quiz. He spent 9 1/4 minutes on question A and 3 4/5 minutes on question B. How much time did he have left for question C?
Answer:
16 57/60 mins
Step-by-step explanation:
9 1/4 = 555 secs
3 4/5 = 228 secs
30.mins = 1800 secs
time for C = 1800 - 555 - 228
= 1017 sec
16 57/60 mins
One red circle of an weighs 12 grams.write an inquality to represent the weight of one blue square
Inequality to represent the weight of one blue square:
s < 12
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given,
One red circle of an weighs 12 grams
By the figure,
Weight of blue square is less than red circle
Let weight of blue square be s.
Then,
s < 12
Hence, s < 12 is the inequality to represent weight of blue square.
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1. How much money would the restaurant take in by selling 100 burritos? (2 points)
Answer:
Multiply price of each burrito by 100
Step-by-step explanation:
I need help with this math
Answer:
what your question tell me I will give you answer and also write down your name and question
BEST ANSWER WILL GET MARKED BRAINIEST!
I am inviting 32 people for my sweet sixteen. Is that considered as a lot of people? Yes or no?
Answer: It depends on how important you think sweet sixteen is, and how much money you have.
Step-by-step explanation:
First, if there is a lot of guests (I consider 32 a lot, but I don't know what you think), you need a lot of birthday cake, a lot of food and drinks, and entertainment. And that costs a lot of money. So, if you want to cross guests off the list to save money, I feel that that would be the more prudent choice.
A river is currently 3 feet deep. Due to rainfall and resulting runoff from the surrounding hills, the depth of the river rises over time. After 2 inches of rainfall, the river is 11 feet deep. Assume that the depth of the river will continue to rise at this same rate with each new inch of rainfall.
Therefore , the solution of equation comes out to be the depth of the river is 5+(6.5/3)*x.
What algebraic fundamentals are there?Algebraic fundamentals include: Algebraic expression addition and subtraction, algebraic expression division and multiplication, figuring out equations, literal formulas and equations, Applying verbal issues
Here,
Given : Let x = amount of rainfall (inches)
Let D = depth of river (feet)
Depth of river increases due to rainfall. Relationship of the depth of increase (in feet) to the amount of rainfall (inches) is:
6.5 feet / 3 inches rainfall
Depth will increase by (6.5/3)*x
Depth of river will be the initial depth plus the amount of increase due to rainfall. So:
D = 5 + (6.5/3)*x
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What is the value of 2+b(a^2+4) when a = 2 and b = 4
[tex]2+b(a^2+4)[/tex] when a is 2 and b is 4
Substitute for variables with given values:
[tex]2+(4)((2)^2+4)[/tex]
[tex]=\fbox{34}[/tex]
Adding several variables to a regression analysis can help do which of the following?
A. Increase the statistical significance of the results
B. Control for several variables at once
C. Increase the construct validity of a study
D. Test for temporal precedence
Regression analysis is mostly used when you want to predict a continuous dependent variable from a several number of independent variables. If the dependent variable is dichotomous, then logistic regression can be used.
If the break between the two levels of the dependent variable is nearly to 50-50%, then we can use both logistic and linear regression will end up giving you similar results.
If you have inserted the data (rather than using an established dataset), it is a nice idea to check the accuracy and the consistence of the data entry.
If you do not want to re-check all the data point, you should at least check the minimum and maximum value for all the variable to ensure that all values for each variable are "valid" or not.
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find the value of x and y
Answer:
Third option
x = 12, y = 20.78
Step-by-step explanation:
This is a 30-60-90 triangle,
In such a triangle the if we are given the length of the hypotenuse, then the perpendicular or the height, which is given as x would half the length of the hypotenuse and the base given by y would be x√3
Calculate x first
x = 24/2 = 12
Looking at the four choices, only fits this value. This is the 3rd choice. So that is the correct one
If you wanted to make sure, find y = x√3 = 12√3 = 20.7846
Answer
Third option
x = 12, y = 20.78
What is the value of x
Answer:
x = 60
Step-by-step explanation:
x and 60 are alternate interior angles and since the lines are parallel, x = 60.
x = 60
Answer:
60°
Step-by-step explanation:
We know that, if two line are parallel, alternate angles are equal.
B D // X Y
Therefore,
x = 60°
Guys I need help with this
14/ 33,120
[tex]\sqrt{144}[/tex]
6) Karishma spends hours of time on watching TV
each day. Calculate the total number of hours she
spends on watching TV in the month of September.
By simple algebra, Karishma spends 12 hours of time on watching TV in September.
Who made algebra famous in India?Mathematical operations are applied on abstract symbols instead of concrete numbers in the field of algebra, which also includes other formal manipulations. The area of mathematics known as geometry is concerned with the qualities of the space that objects are in as well as the shape of the objects themselves.However, many of Leibniz's concepts had already been discovered by the Indian mathematician Bhskara more than 500 years prior. Additionally, Bhskara made significant contributions to geometry, trigonometry, algebra, and arithmetic.
Time spent each day watching TV=2/5 hours
Number of days in September=30
Total number of hours she watched TV in September=(2/5)*30=12 hours
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Question-"Karishma spends ⅖ hours of time on watching TV each day.
Calculate the total number of hours she spends on watching TV in
the month of September."
Graph this on a line please
The last boxplot is the one that displays the values range of the distribution that is given.
What is the range?The range of a function in mathematics can refer to one of two ideas that are connected in some way: Codomain for the function an illustration of the action If there is precisely one y in Y and there are two sets X and Y, then a binary relation f between X and Y is a function that connects x and y.
Here ,Given information:
6,7,9,9,20,22,26,28,29,30
N = 10 observations were made.
The base number is 6. ( least value)
Quartile lower= n+1(0.25)
term = 0.25(13) = 3.25term = 13
Median equals 0.5 (n + 1)
term = 0.5(13) = 6.5 term = (20 + 24) /2 = 22
Upper quartile: 0.75 (13)
A term equals 9.75 a term equals 26.5
Interquartile Range (IQR) is equal to= Q3 - Q1= (26.5 - 13) = 13.5
The highest value is 30. (highest value in the distribution)
As a result, the Last boxplot is the one that shows the distribution that is given.
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3x + 5 =− 7 solve for x
Answer:
x = -4
Step-by-step explanation:
3x + 5= -7
bring the 5 to the other side
3x = -12
divide both sides by 3
x = -4
Answer:
[tex] \sf \: x = - 4[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 3x + 5 = -7
Then the value of x will be,
→ 3x + 5 = -7
→ 3x = -7 - 5
→ 3x = -(7 + 5)
→ 3x = -12
→ x = -12 ÷ 3
→ [ x = -4 ]
Hence, the value of x is -4.
19. Gemma has three less than two-thirds the number of fish that Polly owns, Gemma has 15 fish. How many
does Polly own? Show all work necessary to justify your answer.
Answer:
Polly has 27 fish
Step-by-step explanation:
Polly's Fish= P
Gemma's Fish = G
so the equation to find either's amount of fish is G= [tex]\frac{2}{3}[/tex]P - 3
But since we know Gemmas amount of fish we can change G to be 15
15= 2/3 P- 3
then add 3 to both sides to get 2/3 P by itself
18= 2/3 P
and since P is being multiplied by 2/3 we have to divide both sides by 2/3 and if you want to divide by a fraction then you just multiply by the reciprocal ( flip the numerator and the denominator)
then you have
[tex]\frac{3}{2}[/tex] x [tex]\frac{18}{1}[/tex] = [tex]\frac{2}{3}[/tex] x [tex]\frac{3}{2}[/tex] P
which simplifies to
54/2 = 6/6 P
which further simplifies to
27 = 1P or 27=P
So P=27 which means polly has 27 fish