A group of students is collecting 16 oz and 28 oz jars of peanut butter to donate to a food bank. At the end of the collection period, they donated 1,876 oz of peanut butter and a total of 82 jars of peanut butter to gre food bank.
a. Write a system of equations that represents the constraints in this situation. Be sure to specify the variables that you use.
b. How many 16 oz jars and how many 28 oz jars of peanut butter were donated to the food bank? Explain or show how you know.
35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation
Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.
The system of equations that represents the constraints in this situation is:
x + y = 82 (total number of jars collected)
16x + 28y = 1876 (total amount of peanut butter collected in ounces)
b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank
we need to solve the system of equations from part (a). One way to do this is to use elimination:
Multiplying the first equation by 16, we get:
16x + 16y = 1312
Subtracting this equation from the second equation, we get:
12y = 564
Dividing both sides by 12, we get:
y = 47
Substituting this value of y into the first equation, we get:
x + 47 = 82
Subtracting 47 from both sides, we get:
x = 35
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What is the value of y in the formula shown when x = 4/5?
y = 4/x
+ √x + 0.2 - 5x
y =
(please look at photo)
Answer:
y = 2
Step-by-step explanation:
substitute x = [tex]\frac{4}{5}[/tex] ( = 0.8) into the formula
y = [tex]\frac{4}{0.8}[/tex] + [tex]\sqrt{0.8+0.2}[/tex] - 5(0.8)
= 5 + [tex]\sqrt{1}[/tex] - 4
= 5 + 1 - 4
= 6 - 4
= 2
(2a³) (3a4) simplify no negative exponents
6a7
Step-by-step explanation:
To simplify the expression (2a³) (3a4), you can use the laws of exponents. First, you can multiply the coefficients 2 and 3 to get 6. Then, you can add the exponents of 'a' which gives you a total of 3+4=7. Therefore, the simplified expression is 6a7. It does not have any negative exponents, and it represents the product of two expressions with the same base 'a' and coefficient multiplication.
Answer: 6a7
Step-by-step explanation: Got this right b4.
Which of the following images shows only a line segment highlighted in red? (3 points)
Figure A has four line segments connected to form a square, with the circle in the upper left corner colored red. Figure B has four line segments connected to form a square, the line segment on the right and the bottom line segment connect at the vertex and are colored red. Figure C has four line segments connected to form a square, with the bottom line segment colored red. Figure D has four line segments connected to form a square, with the top line segment and the bottom line segment colored red.
a
Figure A
b
Figure B
c
Figure C
d
Figure D
Figure C shows only a line segment highlighted in red.
Figure C has four line segments connected to form a square, with the bottom line segment colored red.
The other three line segments in the figure are not colored, and only the bottom line segment is highlighted in red.
This means that only a line segment is shown in red, which is what the question is asking for.
Hence, figure C shows only a line segment highlighted in red.
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what base could be written in the blank to make the exponential function model 15% decay ? y= (____) ^t\12 what answer would I put in the blank?
The exponential function model is y = (0.85[tex])^{t/12[/tex].
We know, The form of the function should be
y= a bˣ
Where, A should be the initial amount and b decrease rate.
Now, y = [tex]b^{t/12}[/tex]
So, the value of base be
= (100 - 15) / 100
= 0.85
Then, the function should be y = (0.85[tex])^{t/12[/tex]
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The current mean weekly wage in a certain industry is 2,117. if the mean weekly wage increases by 4.75% what is the new mean average
The new mean annual wage is; $ 43,149.82.
Given that the initial mean weekly wage is $ 2.117.
The growth rate is 4.75%.
We need to find a new annual wage.
Consider the equation, A be the new annual wage.
Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.
The number of weeks in a year = 52 weeks.
Substitute P= 2,117, R =4.75% = 0.0475and T =52 in the equation.
A = 2.117 x 52(1 + 0.0475)
A = 43,149.82
The new mean annual wage is; $ 43,149.82.
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1.2 grams is how many grains
Robert had 2 2/5 cups of chocolate syrup left in his freezer he used 1/4 cup of Chocolate syrup when he makes a milkshake what is the maximum number of milkshakes that Robert can make with the chocolate syrup
Robert can make a maximum of 8 milkshakes with the remaining chocolate syrup.
How to find the maximum number of milkshakes that Robert can make with the chocolate syrupConverting the mixed number 2 2/5 to an improper fraction: 2 2/5 = 12/5
Subtracting the amount of chocolate syrup used per milkshake from the total amount of chocolate syrup:
12/5 - 1/4 = (48 - 5) / 20 = 43/20
Therefore, Robert has 43/20 cups of chocolate syrup left, which is the maximum amount he can use to make milkshakes.
For maximum number of milkshakes:
(43/20) / (1/4) = (43/20) x (4/1) = 172/20 = 8.6
Since Robert cannot make a fraction of a milkshake, he can make a maximum of 8 milkshakes with the remaining chocolate syrup.
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PLS HELP ASAP!!!!!!!!!
Answer: 4m^5-3m^2+2m+21
Step-by-step explanation: you just have to put the exponents int he right order which we always put the highest first so you put 4m^5-3m^2+2m+21 which is the answer
HELP PPPSKSKFJSJSJSJSJSHDHDDH
Answer:D
Step-by-step explanation:
got it right
Evaluate the following expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3}
We raise the fraction to the power of 4/3.
To evaluate the expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3},
we can simplify each term within the parentheses before multiplying them together.
Let's simplify each term step by step:
\left( \frac{16}{9} \right)^{2/3}:
To simplify this term, we raise the fraction to the power of 2/3.
\left( \frac{16}{9} \right)^{2/3} = \left( \left( \frac{2^4}{3^2} \right)^{1/3} \right)^2 = \left( \frac{2^{4 \cdot 1}}{3^{2 \cdot 1}} \right)^2 = \left( \frac{2^4}{3^2} \right)^2 = \left( \frac{16}{9} \right)^2 = \frac{16^2}{9^2} = \frac{256}{81}
\left( \frac{4}{3} \right)^{4/3}:
Similarly, we raise the fraction to the power of 4/3.
\left( \frac{4}{3} \right)^{4/3} = \left( \left( \frac{2^2}{3^1} \right)^{1/3} \right)^4 = \left( \frac{2^{2 \cdot 1}}{3^{1 \cdot 1}} \right)^4 = \left( \frac{2^2}{3^1} \right)^4 = \left( \frac{4}{3} \right)^4 = \frac{4^4}{3^4} = \frac{256}{81}
\left( \frac{9}{16} \right)^{2/3}:
We raise the fraction to the power of 2/3.
\left( \frac{9}{16} \right)^{2/3} = \left( \left( \frac{3^2}{2^4} \right)^{1/3} \right)^2 = \left( \frac{3^{2 \cdot 1}}{2^{4 \cdot 1}} \right)^2 = \left( \frac{3^2}{2^4} \right)^2 = \left( \frac{9}{16} \right)^2 = \frac{9^2}{16^2} = \frac{81}{256}
\left( \frac{3}{4} \right)^{4/3}:
We raise the fraction to the power of 4/3.
\left( \frac{3}{4} \right)^{4/3} = \left( \left( \frac{3^1}{2^2} \right)^{1/3} \right)^4 = \left( \frac{3^{1 \cdot 1}}{2^{2 \cdot 1}} \right)^4 = \left( \frac{3^1}{2^2} \right)^4 = \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256
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Which is the same length as 65 km
Answer:
65000 metres
Step-by-step explanation:
65*1000=65000
Which set of ordered pairs represents a function?
O {(-5, -9), (-7,-9), (-5, -7), (-8,6)}
O {(-1,6), (0, -3), (5, -9), (-1,3)}
O {(1, 2), (-6, 2), (3,9), (5,3)}
O {(-3,9), (2, 7), (2, -4), (1,5)}
The set of ordered pairs which represents a function among the given answer choices is; {(1, 2), (-6, 2), (3,9), (5,3)}.
Which of.the answer choices represents a function?By definition, a function is a special kind of relation in which case, each input value is assigned not more than one output value.
On this note, by evaluation of the given sets of ordered pairs; the set {(1, 2), (-6, 2), (3,9), (5,3)} represents the relation which is a function.
Ultimately, the answer choice which represents a set of ordered pairs that represents a function is; {(1, 2), (-6, 2), (3,9), (5,3)}.
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HURRY DUE TONIGHT
Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
The percentage of saline solution in brand B is 3%.
Let x be Percentage of saline solution in brand B
We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
Simplifying and solving for x, we get:
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Therefore, the percentage of saline solution in brand B is 3%.
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31. There are two gears that are connected to each other. One gear has 20 teeth and the other gear has 10 teeth. If the bigger gear turns around 5 times, how many times will the smaller gear turn?
10 times will the smaller gear turn.
What is the ratio?
The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Since the smaller gear has 10 teeth and the bigger gear 20, the smaller gear will turn twice for every rotation of the larger gear (20/10=2).
Therefore, if the larger gear rotates five times, the smaller gear will rotate two times five times, or ten times. The smaller gear will thus rotate 10 times.
So, if the bigger gear turns around 5 times, the smaller gear will turn around 5 x 2 = 10 times.
Therefore, the smaller gear will turn 10 times.
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4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z
a.) The value of each angle when 5 is substituted for X would be ;
Y = 55°
Y = 55°W = 75°
Y = 55°W = 75°Z = 45°
b). Chelsea is wrong in her calculation because the total internal angle of a triangle should be 180° and not 175°.
How to calculate the value of the various angles through substitution?For angle Y;
11x = 11(5) = 55°
For angle W;
15x = 15(5) = 75°
For angle Z;
(8x+5) = 8(5) +5
= 45°
The total angles = 55+75+45 = 175°
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Select the statement that best justifies the conclusion based on the given information. If x + 5 = 15, then x = 10.
The Subtraction property of equality justifies the conclusion based on the given information.
Subtraction Property of Equality Definition:The subtraction property of equality states that when the same number is subtracted from both sides of an equality, then the two sides of the equation still remain equal. In simple words, we can say that when a number is subtracted from one side of an equation, the same number must be subtracted from the other side of the equality.
if a = b
then;
a-c = b-c
We have:
If x + 5 = 15
By subtraction property of equality:
Subtract 5 from both sides we have;
x = 10
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Find y.
I will give Brainliest to correct answer !
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 1) + 2
[tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
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Solve 19 × 6 using distributive law.
The solution to the given expression by using distributive law is 114
What is distributive law?The distributive property posits that an expression that is provided in the form of A (B + C) can be further expressed as A × (B + C) = AB + AC. This distributive law is also useful for subtraction and is expressed as, A (B - C) = AB - AC. This implies that operand A is distributed between the other two operands.
From the given information, we are to expand 19 × 6 using the distributive law. The first step would be to expand 19 into two integers.
Let the two integers be 10 and 9.
So, we can have can express this by using the addition distributive law: A(B+ C)
Mathematically, we have:
= 6(10 + 9)
= 6(19)
= 114
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Can someone help me put these in order please!
The order of steps of constructing an inscribed circle of a triangle:
Construct one of the angle bisectors of the triangle. Make sure that it intersects the side opposite of the angle.Construct another angle bisector of the triangle for a different angle. Make sure that it intersects the side opposite of the angle.Identify the point of intersection of the two angle bisectors. This is the incenter and is also the center of the inscribed circle.Construct a circle that has a radius of the length from the incenter to one of the points where an angle bisector intersects a side of the triangle.How to construct the circle ?Commence the process by sketching a line that cuts one angle of the triangle in two and intersects the opposing side at some point. Through this action, a pair of miniature triangles with congruent figures materialize.
Subsequently, draft an additional bisector for another angle of the triangle. The second dividing line needs to meet the side opposite to the situated angle at a specific location.
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What is the area of this figure?
Answer:
142ft^2
Step-by-step explanation:
I hope this picture helps, but if you have any questions about the steps let me know
Please help
A line with a slope of 1/5 passes through the point (-4,-3). What is its equation in point slope form?
A line that includes the point (1,3) has a slope of nine. What is its equation in point slope form?
A line with a slope of -10 passes through the point (-4,-1) what is this equation in point slope form?
There is a line that includes the point (9,3) and has a slope of -1/6 what is its equation in point slope form?
A line passes through the points (1,2) and (2,10). What is its equation in point slope form?
When answering all these questions, you specific points in the equation
What are the polar coordinates of the point A shown below?
A point plotted on a polar coordinate plane.
Select the correct answer below:
(−2,3π4)
(1,−π4)
(1,−7π4)
(2,−π4)
(−2,π4)
(1,3π4)
Answer:(1,−7π/4)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 1, so r=1 or −1. Of the choices available, only an angle of −7π4, drawn from the positive x axis plots at the point A. So θ=−7π4, and r must be positive, as the angle is measured from the positive x axis. Thus, the polar coordinates are (1,−7π4).
finding the inverse of [tex]-(1/2)-log_{3}\sqrt{9-x}[/tex]
The inverse function of the function f(x) is [tex]g(y) = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]
To find the inverse of the given function f(x) = -(1/2) - log₃√(9-x)
we need to solve for x in terms of y, where y = f(x).
Replace f(x) with y
Function y = -(1/2) - log₃√(9-x)
Solve for x
First, isolate the logarithmic term on one side of the equation.
y + (1/2) = -log₃√(9-x)
[tex]3^-^(^y^ +^ 1^/^2^) = 9-x[/tex]
[tex]x = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]
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Anyone else have this question figured out
The equation of line is,
⇒ y = 1/2x + 2
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 4, 0) and (0, 2).
Now,
Since, The equation of line passes through the points (- 4, 0) and (0, 2).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (2 - 0) / (0 + 4)
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - 0 = 1/2 (x + 4)
⇒ y = 1/2x + 2
Therefore, The equation of line is,
⇒ y = 1/2x + 2
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Type the correct answer in the box. Round off your answer to the nearest integer.
Two planes, A and B, start from the same place and move in different directions, making an angle of 50° between them. The speed of plane A is
200 miles per hour, and the speed of plane B is 300 miles per hour.
The two planes are
miles apart after one hour.
what radian measure is equivalent to 300
The equivalent radian to 300 degree is 5π/3.
The given angle measures 300 degree.
We know that, formula used to convert degrees is Radians = Degrees × π / 180
Here, Radians = 300×π/180
= 30 ×π/18
= 10π/6
= 5π/3
Therefore, the equivalent radian to 300 degree is 5π/3.
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what is the relationship between the area of a rectangle and a parallelogram
Answer: The relationship between the area of rectangle and area of parallelogram is that they both are equal in area.
Step-by-step explanation:
parallelogram is formed when two parallel lines intersects other two parallel lines and rectangle is a type of parallelogram in which the intersecting lines intersects at right angle.
rectangle and parallelogram shares the same property and If we consider same base and same parallel lines then the area of parallelograms formed is always equal and as I mentioned above rectangle is also a parallelogram.
hence area of rectangle is equal to the area of parallelogram in same base and same parallel lines.
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Find the x value and explain with reasons for both pls
Applying the triangle sum theorem, the value of x in the image given is:
x = 33°; x = 45°
How to Find the Value of x in the Triangles?Recall that according to the triangle sum theorem, all three interior angles of a triangle is equal to 180 degrees.
a. x + 21 + (180 - 54) = 180 [triangle sum theorem]
x + 147 = 180
x = 180 - 147
x = 33°
b. (180 - 102) + x + 57 = 180 [triangle sum theorem]
x + 135 = 180
x = 180 - 135
x = 45°
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A.solves routine and non-routine problems involving perceentage using appropriate strategies and tools.M5NS-IIIIb-40
Observe the solution to the given problem below.
christmas season is coming and ana is so excited to do her shopping in her list is a pair of shoes that she will wear for their christmas party.what made her more excited was when she saw that her dream pair of shoes is on sale.
from P 4 295, it is now sold with 20%
The sale price of the shoe is given as follows:
P3,436.
How to obtain the sale price of the shoe?The sale price of the shoe is obtained applying the proportions in the context of the problem.
The initial price is of:
P 4,295.
The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:
0.8 x 4295 = P3,436.
Missing InformationThe problem asks for the selling price of the shoe.
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