The two equations are 1.5x+1.25y = 30 and x+y = 22 and values of x and y are 10 and 12 respectively.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Davin is raising money for a school trip by selling candy bars and packs of cookies. The price of each candy bar is $1.50 and the price of each pack of cookies is $1.25. Yesterday, Davin made $30 from selling a total of 22 candy bars and packs of cookies.
Let x represent the number of candy bars sold, and y be the number of pack of cookies sold,
Establishing the equations,
1.5x+1.25y = 30
x+y = 22
Solving the equations, we get.
x = 10 and y = 12
Hence, the number of candy bars sold 10 and the number of pack of cookies sold is 12
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How can you determine if the left end behavior of a polynomial function is rising or falling?
To determine if the left end behavior of a polynomial function is rising or falling, you can look at the sign of the leading coefficient of the polynomial. If the coefficient is positive, the left end behavior is rising, and if the coefficient is negative, the left end behavior is falling.
The left end behavior of a polynomial function can be determined by looking at the sign of the leading coefficient. The leading coefficient is the coefficient of the highest degree term in the polynomial. If the leading coefficient is positive, then the left end behavior of the function is rising, because a positive coefficient will cause the function to increase in value as x increases. On the other hand, if the leading coefficient is negative, then the left end behavior of the function is falling, since a negative coefficient will cause the function to decrease in value as x increases. Knowing the sign of the leading coefficient is therefore a quick and easy way to determine whether a polynomial function is rising or falling on its left end.
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30 points! are the volumes the same? if not which one is greater?
Answer:
i round off to two decimals
LEFT:(solve for radius)circumference = 2ñr
11 = 2(3.14)r
11 = 6.28r
r = 0.57 inches
(solve for volume)
volume = ñr²h
volume = (3.14)(0.57²)(8.5)
volume = (3.14)(0.33)(8.5)
volume = 8.81 inches³
RIGHT:(solve for radius)circumference = 2ñr
8.5 = 2(3.14)r
8.5 = 6.28r
r = 0.74 inches
(solve for volume)
Volume - ñr²h
Volume = (3.14)(0.74²)(11)
Volume = (3.14)(0.55)(11)
Volume = 18 inches
Therefore, the right side cylinder is greater than the left cylinder.
i round off to two decimals
Step-by-step explanation:
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The vertex of the parabola equation is (5, 43) and the parabola standard form is y = 2x² + 20x + 43.
What is Parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed-line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
We have,
The parabola standard from f(x) = a(x-h)² + k
f(x) = 2x² + 20x + 43
The general equation of a parabola is y = a(x - h)² + k or x = a(y - k)² +h, where (h,k) denotes the vertex.
Consider an equation y = 2x² + 20x + 43. For this parabola, a = 2 , b = 20 and c = 43. which is a parabola.
Vertex: (h, k)
h = -b/2a
= 20/(2 × 2)
= 5
k = f(h)
= f(5) = 2(5)² + 20(5) + 43
= 50 + 100 + 43
Thus vertex is (5, 43)
Hence, the vertex of the parabola equation is (5, 43) and the parabola standard form is y = 2x² + 20x + 43.
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What is the prime factorization of 20?
2 x 10 22 x 5 5 x 8 22 x 4
Answer:
the prime factorization of 20 is 2/2 times 5
Step-by-step explanation:
Answer:
2/2 times 5
Step-by-step explanation:
Rahul is deciding between two parking garages. Garage A charges an initial fee of $12 to park plus $4 per hour. Garage B charges an initial fee of $6 to park plus $5 per hour. Let AA represent the amount Garage A would charge if Rahul parks for tt hours, and let BB represent the amount Garage B would charge if Rahul parks for tt hours. Write an equation for each situation, in terms of t,t, and determine which garage would be cheaper if Rahul needs to park for 10 hours.
Answer:
1. AA = 4t + 12
2. BB = 5t + 6
3. Garage A would be cheaper to park for 10 hours.
Step-by-step explanation:
1. Garage A's situation is linear, meaning that there is a constant rate of change, or slope.
A linear function in slope-intercept form is: [tex]y = mx + b[/tex], where m is the rate of change, and b is the y-intercept, or the initial value.
Find m and b:m = 4 because that is the cost per hour, which is additive and constantb = 12 because it is the initial cost Rahul has to pay∴ AA = 4x + 122. Garage B's situation is linear, meaning that there is a constant rate of change, or slope.
A linear function in slope-intercept form is: [tex]y = mx + b[/tex], where m is the rate of change, and b is the y-intercept, or the initial value.
Find m and b:m = 5 because that is the cost per hour, which is additive and constantb = 6 because it is the initial cost Rahul has to pay∴ AA = 5x + 63. To find how much it will cost Rahul to park in Garages A and B for 10 hours, substitute 10 into t, which is the number of hours. Then, determine which cost is lower.
Garage A for 10 hours:AA = 4t + 12AA = 4(10) + 12AA = 40 + 12∴ AA = $52Garage B for 10 hours:BB = 5t + 6BB = 5(10) + 6BB = 50 + 6∴ BB = $56$52 < $56, so Garage A is cheaper for 10 hours.
eight more than five times a number is twenty thirds. find the number.
Answer:
Step-by-step explanation:Charmaine wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (in ) versus the length (in ).
Find the range and the domain of the function shown.
A new patio is in the shape of a square. On a scale drawing, the vertices of the patio's coordinates are (10, 8. 5), (10, 1. 5), (3 ,1. 5 ), and (3, 8. 5). How long is each side of the patio?.
As per the given coordinates, the length of each side is 7
The term coordinate in math refers the pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.
Here we have given that the new patio is in the shape of a square. On a scale drawing, the vertices of the patio's coordinates are (10, 8. 5), (10, 1. 5), (3 ,1. 5 ), and (3, 8. 5).
And we need to find the length of each side of the patio.
While we have given the following points in the given question
=> (10, 8. 5), (10, 1. 5), (3 ,1. 5 ), and (3, 8. 5).
And then we have to plot these values on the graph.
For that we have to label the graph first and then we have to point put the coordinates on the graph.
=> After pointing the values, we have to label the graph with the corresponding coordinates.
Therefore, the resulting graph is look like the following one.
While we looking into the resulting graph, we get the length as 7.
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Are all equilateral triangles congruent Why?
No, All equilateral triangles need not to be always congruent with one another .
Justification of answer:
The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .
Properties of an equilateral triangles:1. All 3 side of an equilateral triangles have same length .
2. All 3 angles of an equilateral triangles have same measure.
3. Each angles of an equilateral triangles is 60 degree .
4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} *a^2[/tex]
5 . Perimeter of an equilateral triangles = 3*a
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How many cans of paint are needed to cover an area of 2000?
The number of cans required to paint an area of 2000 square units is equal to 5 cans.
As given in the question,
Total area to be painted is equal to 2000 square units.
Area covered by one can of paint is equal to 400 square units
400 square units = 1 can of paint
⇒ 1 square units = ( 1 / 400 ) cans of paint
⇒ 2000 square units = ( 2000 / 400 ) cans of paint
⇒ 2000 square units = 5 cans of paint
Therefore, the number of cans required to paint an area of 2000 square units using given can is equal to 5 cans.
The above question is incomplete, the complete question is:
How many cans of paint are needed to cover an area of 2000 square units if one can of paint covers in area 400 square units?
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if B=t+10 and A=3t^2-2 find an expression that equals 2B−3A in standard form.
The expression that equals 2B−3A in standard form is - 9t² + 2t + 14
How to determine the expression that equals 2B−3A in standard form.From the question, we have the following parameters that can be used in our computation:
B = t + 10
Also, we have
A = 3t² - 2
The expression that equals 2B−3A is calculated as
Expression = 2B - 3A
Substitute the known values in the above equation, so, we have the following representation
Expression = 2 * (t + 10) - 3 *(3t² - 2)
So, we have
Expression = 2t + 20 - 9t² - 6
Evaluate the like terms
Expression = - 9t² + 2t + 14
Hence, the expression = - 9t² + 2t + 14
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Can somebody please help me because I don’t understand
Answer: x = 64
Step-by-step explanation:
5/8x = 40
We divided by 5/8 from both sides
40/1 divided by 5/8 is the same as
40/1 times 8/5 = 320/ 5 = 64
x= 64
Solve the system of equations by substitution.
Answer:
x = -6
y = -18
Step-by-step explanation:
6x -2y = 0
x - y = 12
Times the second equation by -2!
6x -2y = 0
-2x + 2y = -24
Now add them together and solve for x first!
4x = -24
x = -6
Now put -6 back in the equation and solve for y
6(-6) -2y = 0
-36 - 2y = 0
-2y = 36
y = -18
So, x= -6
y= -18
What are the 3 methods for finding the inverse of a function?
(1) In general, switching the coordinates x and y is how an inverse is calculated.
(2) The function is a one-to-one function and the inverse is also a function if a horizontal line crosses the original function in a single place.
(3) We can find the inverse in algebra by replacing f(x) by y and then solve for x.
In general, switching the coordinates x and y is how an inverse is calculated. Although not strictly a function, this freshly constructed inverse is a relation.
To ensure that the initial function's inverse will be a function, the major purpose must be a one-to-one function. When every second element matches the first value, a function is said to be a one-to-one function.
To determine whether a function is a one-to-one function, use the horizontal line test. The function is a one-to-one function and the inverse is also a function if a horizontal line crosses the original function in a single place.
When a function's formula has been provided to you, follow these steps to discover its inverse:
(1) Change "f(x)" to "y".
(2) Make an effort to resolve the x= equation.
(3) Switch the xs and ys.
(3) Change y to "f1(x)"
We can find the inverse in algebra by replacing f(x) by y and then solve for x.
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|x-6|=11 solve this equation
Answer:
x = -5 or x = 17
Step-by-step explanation:
The absolute value is the number's distance from 0.
So, we need to write two equations.
x - 6 = 11
x - 6 = -11.
Next, we need to add 6 to both sides of each equations.
11 + 6 = 17
-11 + 6 = -5
So, x = 17 and x = -5.
Answer: It could be -5 or 17
Step-by-step explanation: So, it can be both, but as I see it would most likely be 17 because I see you put x-6 as an absolute value. so, to find the value of x, we could do 11 + 6 (Inverse operations), so 11 + 6 = 17. If it was NOT the absolute value of x-6, we could find it to be -5, by subtracting -6 from 11, to get -5. I hope this helps you understand now, if any questions please comment down below.
How would you write the equation with a slope of 3/5 and a y-intercept of 5?
The equation of the line that has a slope of 3/5 and a y-intercept of 5 will be y = (3/5)x + 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 3/5 and the y-intercept of the line is 5. Then the equation of the line is given as,
y = (3/5) x + 5
The equation of the line that has a slope of 3/5 and a y-intercept of 5 will be y = (3/5)x + 5.
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What do the positive and negative signs mean in limits?
Positive and negative signs in limits indicate whether the limit is approaching from the positive side or the negative side. If a amount is approaching from the positive side, the sign is positive; if it is approaching from the negative side, the sign is negative.
When taking the amount of a function, the positive and negative signs indicate the direction in which the limit is approaching. A positive sign means the limit is approaching from the positive side of the function’s domain, while a negative sign indicates the limit is approaching from the negative side. For example, if a limit is written as[tex]$\lim\limits_{x \to 3^+} f(x)$,[/tex]this means the limit is approaching from the positive side of the domain, when x is approaching 3. Similarly, if the limit is written as [tex]$\lim\limits_{x \to 3^-} f(x)$[/tex] this means the limit is approaching from the negative side of the domain, when x is approaching 3. Thus, the positive and negative signs in limits indicate the direction the limit is approaching from.
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if a rep works eight hours per day and the average length of a call is 30 minutes and the average travel time is 30 minutes and the rep works 250 days per year, then what is the total annual number of calls the rep can make?
Applying basic unitary method and time conversion, The answer is 3750 calls annually.
What is Unitary method?The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Why do we use unitary method?The unitary technique is used practically all the time, from problems involving speed, distance, and time to issues with estimating material costs. The technique is applied to determining a product's pricing. It is used to determine how long it takes a person or vehicle to travel a certain distance in an hour.
average length of call= 30 minutes
average travel time=30 minutes
annual working days=250
per day works 8 hours.
call hour in work = 8*60 - 30 = 450minutes.
number of calls made in those hours= 450/30=15 calls daily.
total annual number of calls= 250 * 15 = 3750
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a local bank needs information concerning the savings account balances of its customers. a random sample of 15 accounts was checked. the mean balance was $686.75 with a standard deviation of $256.20. find a 98% confidence interval for the true mean. assume that the account balances are normally distributed. round to the nearest cent.
Answer:
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What are the 7 types of angles with diagram?
Angles are 7 types.
What are different types of angles?1.Acute Angle: An acute angle is any angle that is less than 90 degrees and is between 0 degrees and 90 degrees.
2.Obtuse Angle: Opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90 degrees and less than 180 degrees. It is the angle that is between 90 degrees and 180 degrees.
3. Right Angle: A right angle is always 90 degrees in length. Acute angles are those that are less than 90 degrees, whereas obtuse angles are those that are higher than 90 degrees.
4. Straight Angle: A straight angle has a measured angle of 180 degrees. Since the angle between its arms is 180 degrees, you can see that it is simply a straight line.
5.Reflex angle: The arms make an acute angle because this measurement is less than 90 degrees. What about the angle on the opposite side, though? What is the name of the larger angle that complements the acute angle? It is referred to as a reflex angle.
A reflex angle is any angle having a dimension higher than 180 degrees but less than 360 degrees (which corresponds to 0 degrees).
6.Complete Rotation: Entire rotation or full angle refers to an angle with a value of 360 degrees. When one of the arms extends completely, it is created.
7.Null angle: Angle of 0 degrees is null angle.
Angles are 7 types.
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gsuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.45. using the empirical rule, what percentage of the students have grade point averages that are greater than 1.66? please do not round your answer.
The percentage of students with GPAs greater than 1.66 is 88.22%.
To answer this question, we need to use the empirical rule, which states that 68% of the data is within one standard deviation of the mean. To calculate the percentage of students with GPAs greater than 1.66, we need to subtract the percentage of students with GPAs less than 1.66 from 100%.
The percentage of students with GPAs less than 1.66 can be calculated by subtracting 1.66 from the mean of 2.56, then dividing by the standard deviation of 0.45. This gives us 2.11 standard deviations below the mean, which corresponds to a percentile of 11.78%.
Therefore, the percentage of students with GPAs greater than 1.66 is 100% - 11.78% = 88.22%.
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A cylinder has a volume of 45 cubic units and a radius of 3 units. What is its height?
Answer:
h = 1.59 (1.6 rounded)
Step-by-step explanation:
A cylinder has a volume of 45 cubic units and a radius of 3 units. What is its height?
A cylinder's volume is π r² h
we use the inverse formula
h=V/πr²
h = 45/π3²
h = 45/3.14 × 9
h = 45 : 28.26
h = 1.59 (1.6 rounded)
How do you describe the graph of x is equal to 2?
The graph of x = 2 is a vertical line parallel to y-axis. Also, the slope of x = 2 is undefined and there is no y-intercept.
In this question we need to describe the graph of x is equal to 2.
To draw the graph of x = 2, firstwe find some coordinates of the points.
Consider the points (2, 1), (2, 0), (2, -1)
[As the x coordinate is fixed, we can take any value of y coordinate]
The graph of x = 2 is as shown below.
The graph of x = 2 is a straight vertical line, which is parallel to y-axis.
There is no y-intercept to the graph of x = 2.
Also the slope of line x = 2 is undefined.
Therefore, the graph of x = 2 is a straight line with Slope = Undefined
and no y-intercept.
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find the area and perimeter of an equilateral triangle whose equal side is 6cm
Answer:
Area = 9√3 cm²
Perimeter = 18 cm
Step-by-step explanation:
Area of equilateral triangle ABC =
(√3/4) × 6²
= (√3/4) × 36
= 9√3 inches2
ABC is an equilateral triangle with side = 6 cm
Perimeter of an equilateral triangle = AB+BC+CA
Perimeter of an equilateral triangle = 6+6+6
Perimeter of an equilateral triangle = 18 cm
Select the reason that best supports Statement 6 in the given proof.
Answer:
B. Distributive Property
Step-by-step explanation:
The equation for the distributive property is
ab+ac = a(b+c)
We, see it similar to statement 6, so it is the correct answer
6. A recipe requires 2 cups of sugar. If Mrs.
Marina is going to make one half of the recipe,
then how much sugar does she need?
Answer:
Step-by-step explanation: 2 cups of sugar divided by 1/2 equals
*can use calculator and type 2 divided by 1 or 2 times 0.5
Ans. One cup of sugar
Answer:
1
Step-by-step explanation:
the recipe requires to cousin sugar if we are only about to Megha of the recipe we should multiply 2 by 0.5
2x0.5
=1
What’s the domain and range of this function?
The domain and range of the given quadratic function are respectively; Domain = -3 < x < 7; Range is; 3 ≤ x ≤ ∞
What is the domain and range of the function?The domain of a function is defined as the set of all possible input values for which the function is possible.
Meanwhile, the range is defined as the set of all possible output values for every possible input value that makes the function possible.
Now, from the graph, the range will be values on the y-axis while the domain will be values on the x-axis.
Now, from the given graph we see that the curve is approaching the lines x = -3 and x = 7. Thus, the domain of this function is;
Domain = -3 < x < 7
Meanwhile the range keeps increasing to positive infinity and as such we can say that;
Range is; 3 ≤ x ≤ ∞
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer: Adult: $20 Child: $9
Step-by-step explanation:
20 + 20 + 20 = 60
9 + 9 + 9 + 9 = 36
60 + 36 =96
Practice & Problem Solving
Identify the domain and range
{(2, 1), (4, 2), (6, 3), (8, 4), (10,5)}
Answer:
It has a constant order in the problem
X (Domain): 2 up every time Y goes up 1
Y (Range): 1 up every time X goes up 2
This is constant and will NOT be broken factor
A realtor leases 180 apartments in a building with 200 apartments. What fraction of the apartments, in tenths, is occupied?
The fraction of the occupied apartments is 9/10.
What is a fraction?In mathematics, a fraction is a symbol for a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total apartments in the building = 200.
Also,
The number of apartments leased by realtor = 180
The fraction of the apartments which is occupied by realtor
= number of apartments leased /Total apartments
= 180 / 200
= 18 / 20
= 9 / 10
The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.
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When two parallel lines cut by a transversal What do you called the four angle formed inside the parallel lines?
When two parallel lines are cut by a transversal, the four angles formed inside the parallel lines are called interior angles.
Interior angles are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. There are always four interior angles formed when two parallel lines are cut by a transversal. These angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior angles is important in geometry, as they can be used to prove the parallelism of lines.
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