Answer:
Sure! Here's a system of equations we can set up to represent this situation:
Let x be the price of a bag of popcorn and y be the price of a drink.
Then we can set up the following system of equations:
x + 3y = 16.50 (equation for Jack's purchases)
2x + 5y = 29.75 (equation for Jill's purchases)
To solve this system of equations, we can use the substitution method.
First, we can solve for x in equation 1:
x = 16.50 - 3y
Then, we can substitute this expression for x into equation 2:
2(16.50 - 3y) + 5y = 29.75
Simplifying this equation, we get:
33 - 6y + 5y = 29.75
Combining like terms, we get:
33 - y = 29.75
Subtracting 29.75 from both sides, we get:
33 - 29.75 - y = -y
Simplifying, we get:
3.25 - y = 0
Subtracting 3.25 from both sides, we get:
-y = -3.25
Dividing both sides by -1, we get:
y = 3.25
So, the price of a drink is $3.25.
Now we can substitute this value for y back into equation 1 to solve for x:
x + 3(3.25) = 16.50
Simplifying, we get:
x + 9.75 = 16.50
Subtracting 9.75 from both sides, we get:
x = 6.75
So, the price of a bag of popcorn is $6.75.
To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.
Step-by-step explanation:
The angles of a triangle measure 88°, 53°, and 39º. Which of the following could NOT be the measure of an exterior angle of the triangle?
Answer:35° being the smallest interior angle of the triangle, the exterior angle attached to it is the largest. It measures 180° - 35° = 145°.p.
Step-by-step explanation:
What is the value of the 8 in the number 28 451
Answer:
28451= 20000+8000+400+50+1
value of 8 =8000
Step-by-step explanation:
11. On a math test Ryan got 15% of the questions incorrect. If there were 40 questions on the spelling test then how many questions did Ryan get correct?
Answer:
34
Step-by-step explanation:
100-15=85 (15 was the percentage of incorrect so you want the percentage of correct answers)
40*.85=34
oop its just 15% of 40...
15/100 x 40 =6
but these are the ones he got incorrect! he got 40-6 = 34 correct
yw!
An initial deposit of $5,000.00 is made into a savings account that compounds 7.1 % interest annually . How much is in the account at the end of five years ?
Answer:
$7045
Step-by-step explanation:
Given data
Principal= $5,000.00
Rate= 7.1%
Time= 5 years
The expression for the compound interest is
A=P(1+r)^t
Substitute
A= 5000(1+0.071)^5
A= 5000(1.071)^5
A= 5000*1.409
A= $7045
Hence the amount in the account after 5 years is $7045
. Find sin D , sin E , cos D , and cos E . Write each answer as a fraction in simplest form.
The trigonometric functions are sin D = 28/53, sin E = 45/53, cos D =45/53, and cos E = 28/53 as fractions.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric functions are given in the question
Apply the sine ratio on the given right triangle
⇒ sin(θ) = Perpendicular/hypotenuse
sin D = EF/DE
sin D = 28/53
sin E = DF/DE ,
sin E = 45/53
Apply the cosine ratio on the given right triangle
⇒ cos(θ) = Base/hypotenuse
cos D = DF/DE
cos D =45/53
cos E = EF/DE
cos E = 28/53
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Donny is raising money for the school charity drive by mowing lawns for $9.75 per lawn. How much will he raise for the drive?
is this proportional or non proportional and why.
For two numbers to be proportional, they need to be directly increasing or decreasing in a constant ratio.
If Donny makes $9.75 per lawn, we can make a table that looks like this:
1 Lawn = $9.95
2 Lawns = $19.90
3 Lawns = $29.85...
And so on.
You can see this is proportional because it has a constant ratio between both elements.
(1 to 9.95)
So, it is proportional.
Examine the graph of the function. The graph of a line that contains points (negative 1, 7), (0, 5), and (2, 1). © 2017 StrongMind. Created using GeoGebra. What is the initial value of the function? Enter your answer as a number, like this: 42
The initial value of the function is equal to 5.
How to determine the initial value of the function?In order to determine the initial value of the function, we would have to find the slope from line graph and then write the required equation based on the data points contained in the table by using the slope-intercept form.
Mathematically, the slope-intercept form of a line is modeled by this mathematical equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept or initial value.Next, we would determine the slope of the data points as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (5 - 7)/(0 + 1)
Slope, m = -2/1
Slope, m = -2.
At point (0, 5), an equation of this line can be calculated in slope-intercept form as follows:
Note: The y-intercept or initial value is equal to 5.
y = mx + c
y = -2x + 5
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if the curved surface area of a cylinder is two-third of the total surface area and radius of the base is 6cm,find the height of the cylinder
Answer:
Height of cylinder = 12 cm
Step-by-step explanation:
Given:
Radius of cylinder = 6 cm
Curved surface area of cylinder = [2/3][Total surface area of cylinder]
Find:
Height of cylinder
Computation:
Curved surface area of cylinder = [2/3][Total surface area of cylinder]
2πrh = [2/3][2πr(h + r)]
h = 2h/3 +[2/3][6]
h - 2h/3 = 4
[3h - 2h] / 3 = 4
h = 12
Height of cylinder = 12 cm
what is x if 2/6+x=11/18
Answer:
multiply top and bottom of 2/6 to get 6/18, then subtract the answer by 6/18 , you get 5/18
Step-by-step explanation:
Answer:
x = 5/18
Step-by-step explanation:
what is x if 2/6+x=11/18
2/6 + x = 11/18
x = 11/18 - 2/6
x = 5/18
----------------------------
check2/6 + 5/18 = 11/18
11/18 = 11/18
The answer is good
Mr. and Mrs. Nelson hope to send their daughter to college in twelve years. How much money should they invest now at an interest rate of 9.5% per year,
compounded continuously, in order to be able to contribute $8500 to her education?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:$9690
Step-by-step explanation:
P=$8500
T=12 years
R=9.5%
P*T*R/100
8500*12*9.5/100=$9690
Amar and his friends went to a movie at 6:55 P.M. The movie ended at 8:30 P.M.
How long was the movie?
Answer: The movie was 1 hour and 35 minutes long
i need the correct answer only 2 try’s and due in 15 min
The sample space between A to C is A,B,C
What is the probability?The likelihood that a sample point will occur is quantified by its probability.
The likelihood of a sample point
According to tradition, statisticians have adopted the following guidelines.
Any sample point's probability can be between 0 and 1.
The probability of every sample point in a sample space added together is 1.
Let's say we run a straightforward statistical experiment. One coin is flipped. Heads or tails are the possible results of the coin flip. These results taken as a whole serve as our experiment's sample space. Each result stands in for a single sample point in the sample space. What is each sample point's probability?
Solution: the total of all sample points' probability
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Find the median and mean of the data set below:
11,2,44, 49, 33, 41
What is the Median
Mean is 30
Answer:
2 11 33 41 44 49
Step-by-step explanation:
33+41=74 74÷2=37
Answer: The medians the middle, so you put in order to 2, 11, 33, 41, 44, and 49. Then, you just pick the number in the middle and since it's 33 and 41, you add them together then divide by 2 and you answer is 37. I hope this helps you!
If √17 is a side length of a square, what does that mean about the area? Explain.
Answer:
It means the area of the square is 17.
Step-by-step explanation:
To find the area of a square you must multiply the length by the width (A=LxW)
to find area of square you would have to multiply squareroot of 17 by squareroot of 17 (because all 4 sides of a square are equal to each other). That would equal squareroot of 289. When you simplify that further, the answer would be 17.
what is the distance between point A and point B?
Answer: [tex]\sqrt{45}\\[/tex]
Step-by-step explanation:
Use Pythagorean Theorem-
a^2 + b^2= c^2
6^2 + 3^2 = c^2
36+9= c^2
c=[tex]\sqrt{45}\\[/tex]
How do I find the volume?Find the volume?
Answer:hello
Step-by-step explanation:
Answer:
V = 180 [tex]ft^{2}[/tex]
Step-by-step explanation:
What does 5 mean in maths?
5 (five) is a number, numeral, and digit.
It is a prime number and the natural and cardinal number that comes after 4 and before 6. Because most people have five digits on each hand, it has gained significance throughout history.
5 is the second super-prime and third-smallest prime number. It is the first of three known Wilson primes, the first good prime, the first balanced prime, and the first safe prime. The number five is also the third Catalan number, the third Sophie Germain prime, the third exponent of the third Mersenne prime, and the second Fermat prime.
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What is y=-6x+2 in standard form
Jessica earned $16 mowing a neighbor's yard. She bought a craft kit for $7.37. She used $3.75 to buy food for a food drive. She put the rest in her savings account. How much money did Jessica put in her savings account?
Answer:
$4.88
Step-by-step explanation:
Jessica made $16 mowing a neighbors yard
She brought a craft kit for $7.37
16-7.37
= 8.63
She used $3.75 to buy food for a food drive
8.63-3.75
= 4.88
Hence the amount Jessica put in the savings account is $4.88
Answer:$ 4.88
Step-by-step explanation: I hope this is right
Boxes A and B contain some counters.
6y + 2
counters
Box A
Clip A19b
4y + 6
counters
Box B
The number of counters in each box is the same.
Work out the value of y
Find a Clip
106
Please give me the answer it’s really hard no one will help
By simple algebra, The number of counters in each box is 2.
What is Algebra?Algebra is the study of mathematical symbols and the methods for incorporating them into formulas.
Why is algebra so difficult?Since algebra is the first math subject most students take where they must deal with variables, complex concepts, and problem-solving abilities, many find it scary.
Given,
counter in Box A = 6y+2
counter in Box b=4y+6
Since there are the same amount of counters in both boxes.
hence
6y+2=4y+6
6y-4y=6-2
2y=4
y=2
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Which ordered pairs are in the solution set of the system of linear inequalities?
y2-3x+2
y < 2x + 3
-6-5
-3-
(2. 2) (3. 1) (42)
The ordered pairs that are in the solution set of the system of linear inequalities are (2 ,2), (3 , 1) and (4 , 2).
What is system of equations?A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system.
Given the system of linear inequalities:
y > -3x + 2
y< 2x + 3
Substitute the value of x and y for each given ordered pair.
For (2, 2) x=2 and y =2:
y > -3x + 2
2 > -3(2) +2
2> -4 True.
y< 2x + 3
2 < 2(2) +3
2< 7 True
For (3, 1) x=3 and y=1:
1 > -3(3) + 2
1 > -7 True
y< 2x + 3
1 < 2(3) + 3
1< 9 True
For (4 , 2) x=4 and y =2
y > -3x + 2
2 > -3(4) +2
2 > -10 True.
y< 2x + 3
2 < 2(4) + 3
2 < 11 True.
Hence the ordered pairs (2 ,2), (3 , 1) and (4 , 2) are in the solution set of the system of linear inequalities.
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Each side of a square is increasing at a rate of 7 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 81 cm2
At the rate of 126cm/s is the area of the square increasing when the area of the square is 81cm2.
If each side of a square is increasing at a rate of 7 cm/s.
The area of the square increasing rate,
Area, A = s2
each side of the square is increasing at the rate of 7cm / s (= dx / dt).
s is the side length
=> dA/dt = 2s. ds/ dt
ds/dt = 7cm/s
Area of the square = 81 cm2
81 cm2 = s2
s = 9 cm
so, dA /dt = 2. 9. 7
= 126 cm2/s
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Pls help quickly
Needed as soon as possible thank you in advance
a) Bearing from A to B is 253°.
b) Bearing from B to A is 287°.
What is a bearing?
A bearing is an angle measured clockwise from north in mathematics. Typically, bearings are expressed as a three-figure bearing.
a)
The bearing of 73° and the co-interior angle formed must total 180°. The counter-clockwise angle from B to A is 107°.
However a bearing must always be measured clockwise from north. 107° is counter-clockwise from north.
The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.
To work the bearing, subtract 107° from 360°.
360° – 107° = 253° and so, the bearing of A from B is 253°.
b)
The bearing of 107° and the co-interior angle formed must total 180°. The counter-clockwise angle from A to B is 73°.
However a bearing must always be measured clockwise from north. 73° is counter-clockwise from north.
The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.
To work the bearing, subtract 73° from 360°.
360° – 73° = 287° and so, the bearing of B from A is 287°.
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What is the percent change from 15.5 to 70?
Answer:
First, you need to calculate your grade in percentages. The total answers count 70 - it's 100%, so we to get a 1% value, divide 70 by 100 to get 0.70. Next, calculate the percentage of 15: divide 15 by 1% value (0.70), and you get 21.43% - it's your percentage grade.
Step-by-step explanation:
An octagonal prism (shown) has __________ faces and ___________ vertices. Question 20 options: A) 16, 10 B) 10, 16 C) 8, 10 D) 6, 8
With 10 faces and 16 vertices, an octagonal prism is depicted.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.
Do octagonal prisms have eight vertices?An octagonal prism therefore has 10 faces, 24 vertices, and 16 vertices.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape. 16 vertices, 10 faces, and 24 edges make up its surface.Eight of the nine vertices of an octagonal pyramid are found where the triangle faces of the base meet, while the ninth vertex is found where the triangular faces of the pyramid's top meet.There are 8 faces on an octahedron, which is a polyhedron. The octahedron shape of a hexagonal prism is defined by its 8 faces, which include its 2 bases and 6 sides.With 10 faces and 16 vertices, an octagonal prism is depicted. Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.To learn more about octagonal prism refer to:
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Destiny is 56 3 4 inches tall. Glen is 1 1 2 inches taller than Destiny and Jane is 1 1 5 inches taller than Glen. How tall is Jane
By simple algebra, Jane is 57 9/20 inches taller.
In math, what does taller than mean?If one object or person's height exceeds that of another, the taller object or person is said to exist. There is a two-object or two-person limit. Taller is a relative term. For instance: Hoppy stands at 7 feet.
You can begin this issue by first figuring out Dwight's height. At 54 3/4 inches, he would be 1 1/2 inches taller than Chloe:
54 3/4 plus 1 1/2 equals 55 + (3/4 + 1/2) equals 55 + (3/4 + 2/4) equals 55 + 5/4 equals 56 1/4 inches.
Dwight stands at 56 1/4 inches.
Dwight is 1 1/5 inches shorter than Jane, so
56 1/4 plus 1 1/5 is 57 plus (1/4 plus 1/5) is 57 plus (5/20 plus 4/20) is 57 plus 9/20 is 57 9/20 inches.
Jane stands at 57 9/20 inches.
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Can you guys answer the top question thanks?
The required solution are as follows,
(A) Kyra's equation of line, passes through 15 pts.
(B) Liam's equation of line, passes through 20 pts.
(C) the equation of line passes through 30 pts is y = 4/3x + 5.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
here,
Drawing the graph on the graph and evaluating which line pass through which points,
(A)
Kyra's equation of a line is y = 1/2 x
And from the graph, it is seen that the line passes through 15pts
Similarly,
(B) passes through 20 pts
(C)
from the graph, it is seen that equation y = 4/3x + 5 passes through 30 points.
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La derivada de f(x)=3x^2-5x+2
Answer:
6x-5
Step-by-step explanation:
[tex]b^n=nb^{n-1}\\3x^2-5x+2=2*3x^{2-1}-5*1*x^{1-1}+0\\6x-5[/tex]
Answer:
La derivada de la función es: [tex]\bold{f'(x)=6x-5}[/tex]
Step-by-step explanation:
Recordemos que la derivada de
Una suma es igual a la suma de las derivadas: [tex][a + b + c]'=[a]'+[b]'+[c]'[/tex]Una constante es cero: [tex][k]'=0\;\;,\;\;\;\;\text{si}\;\;k=\text{constante}[/tex]Un producto es: [tex][ab]' = [a]'b + a[b]'[/tex]Una potencia: [tex][a^n]'=na^{n-1}[/tex]La derivada de la función [tex]f[/tex] con respecto a [tex]x[/tex] es definida como
[tex]f'(x)=\frac{df}{dx}\\f'(x)=\frac{d}{dx}(3x^2-5x+2)\\f'(x)=\frac{d}{dx}(3x^2)-\frac{d}{dx}(5x)+\frac{d}{dx}(2)[/tex]
donde
[tex]\frac{d}{dx}(3x^2)=\frac{d}{dx}(3)\,x^2+3\,\frac{d}{dx}(x^2)=(0)\,x^2+3\,(2x^{2-1})=0+3\,(2x^1)=6x[/tex][tex]\frac{d}{dx}(5x)=\frac{d}{dx}(5)\,x\;+\;5\,\frac{d}{dx}(x)=(0)\,x+5\,(1x^{1-1})=0+5\,(x^0)=5(1)=5[/tex][tex]\frac{d}{dx}(2)=0[/tex]Por lo tanto,
[tex]f'(x)=\frac{d}{dx}(3x^2)-\frac{d}{dx}(5x)+\frac{d}{dx}(2) \\f'(x)=6x-5+0 \;\;\;\;\;\Rightarrow\;\;\;\;\; \bold{f'(x)=6x-5}[/tex]
seven pounds of fertilizer can cover 1400 square feet can be covered by 2 pounds of fertilizer
The area for 2 pounds of fertilizer is 400 square feet
How to determine the amount of fertilizer for 2 pounds?
From the question, we have the following parameters that can be used in our computation:
seven pounds of fertilizer can cover 1400 square feet
This means that
7 pounds of fertilizer = 1400 square feet
Divide both sides of the equation by 7
So, we have the following representation
1 pounds of fertilizer = 200 square feet
Multiply both sides of the equation by 2
So, we have the following representation
2 pounds of fertilizer = 400 square feet
Hence, the area is 400 square feet
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would this be sin, cos, or tan?
Answer:
tan
Step-by-step explanation:
its the opposite over adjacent
Answer:
tan
Step-by-step explanation:
sinx=Opposite/adjacent
Tanx=8.78/12