To find the missing term, we can use the expansion of the square of a binomial, which is given by the formula (a + b)^2 = a^2 + 2ab + b^2. In this case, the binomial is x + 12, so we can use the formula like this:
[tex](x + 12)^2 = x^2 + 2 * x * 12 + 12^2[/tex]
Therefore, the missing term is 144.
You can also find the missing term by expanding the left-hand side of the equation using the same formula:
[tex](x + 12)^2 = (x^2 + 24x) + __[/tex]
When we expand the left-hand side using the formula, we get:
[tex](x + 12)^2 = x^2 + 24x + 144[/tex]
So the missing term is also 144.
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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Matthew made a fruit salad, in which the ratio of blueberries to red grapes is 8:6. Write the ratio of red grapes to blueberries in simplest form. [Type your ratio using a colon and without spaces.]
The ratio of red grapes to blueberries in simplest form is 3/4.
What is ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given:
Matthew made a fruit salad, in which the ratio of blueberries to red grapes is 8:6.
We have to find the ratio of red grapes to blueberries in simplest form.
Let there are 6 red grapes and 8 blueberries.
So, the ratio is
Red grapes / blueberries = 6/ 8
Reduces the ratio,
6 / 8 = (2 x 3) / (2 x 4) = 3 /4
Hence, the ratio of red grapes to blueberries in simplest form is 3/4.
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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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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
What are the 4 types of transformations examples?
The four types of Transformations - Rotation, Translation, Reflection, Dilation.
What is transformation ?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
When we relocate a picture without making any other changes to it, we say that we have translated it.Rotation is the process of slightly rotating a picture.When we flip an image along a line (the mirror line), it is called reflection.Dilation is the process of enlarging or contracting an image's size without altering its form.Transformations may be divided into four categories: translation, rotation, reflection, and expansion. You must be able to carry out each change and recognize which ones have already been done.
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Translation, rotation, reflection, and dilation are the four basic forms of transformations.
What is Transformation?By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made. A fresh viewpoint on geometry known as transformational geometry was put forth by Felix Klein in the 19th century.
The transformation is f: X X, which stands for a function, f, that maps to itself. The transformation causes the pre-image X to change into the picture X. Translation, rotation, reflection, and dilation are only a few examples of the transformations that can be used alone or in combination. A function is translated when it is moved in one direction, rotated when it is spun around a point, reflected when it is turned into the opposite of itself, and dilated when it is scaled. Two-dimensional geometrical figures can move about a coordinate plane via mathematical transformations.
Hence, Translation, rotation, reflection, and dilation are the four basic forms of transformations.
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Given UV, VW and UW are midsegments, if TS
=42, UW=23, and VW=19.
R
RT.
U
T
V
choose your answer...
W
S
Vis the length of
HELP ASAP PLEASE!!!!!!!!!
The required length of the RT is given as 38 units, in the triangle.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
here,
Given figure show is of the triangle where UV, VW, and UW are midsegments,
The property of triangles states that,
The length of the side is half of the line joining the midpoints of the adjacent of the triangle.
2VW = RT
RT = 2[19]
RT = 38
Thus, In the triangle, the required length of the RT is stated as 38 units.
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How will you describe the graph of polynomial functions if the degree is even number and the leading coefficient is negative?
If the degree of the polynomial function is an even number and the leading coefficient is negative, the graph will have an even number of turning points and will be concave down. The graph will also have a single x-intercept at the origin, and the y-intercept will be negative.
A graph of polynomial functions with an even degree and negative leading coefficient will have an even number of turning points and will be concave down. A turning point is the point on a curve where the curve changes direction, and a concave down shape means that the curve is curved down from left to right. The graph will have a single x-intercept at the origin, which is the point where the graph crosses the x-axis. The y-intercept of the graph will also be negative, which is the point where the graph crosses the y-axis. This graph will have a negative slope and will decrease as it moves away from the origin. The graph will approach the x-axis but will not touch it, creating a U-shaped curve. The graph will also have a maximum or minimum value, depending on the specific values of the polynomial function.
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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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somebody help me out
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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How many fair dice are there?
Answer:
Fair Dice. In mathematics we say "fair dice" when we mean that there is an equally likely chance of landing on any face. Most people think of these little cubes. when we say "dice" ... ... but all of the Platonic Solids can make fair dice! Because the faces are all the same, there is an equal chance of landing on any face.
Step-by-step explanation:
Let f be the function given by f (x) = e + cos x - 1. What is the value of
f' (2) ?
Let f be the function given by f (x) = e + cos x - 1. the value of f' (2) is 0.0349
How to find f' (2)The given function is f (x) = e + cos x - 1,
f' is the derivative of the given function, and the derivative is sort for below
f (x) = e + cos x - 1
f' (x) = 0 + -sin x - 0
f' (x) = -sin x
for f' (2) we substitute the x = 2 in the derivative
f' (x) = -sin x
f' (2) = -sin 2
f' (2) = -sin 2
f' (2) = -0.0349
hence f' (2) = -0.0349
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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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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
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:
The tree diagram represents an
experiment consisting of two trials.
P(A and C) = [ ? ]
Answer:
0.2
Step-by-step explanation:
0.5*0.4=0.2
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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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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I need help with this please!! I need this before 2!
Answer:
s=2h
Step-by-step explanation:
it takes 2 hours for 1 inch of snow so 1snow=
How do you prove that an equilateral triangle has equal angles?
So in the traingle PQR shown in the figure below PQ,QR,PR is the side of the traingle .
we have to prove that ∠QPR = ∠PQR = ∠ PRQ.
According to the definition of equilateral triangle all sides length of equilateral traingle are equal.
so PQ=QR=PR
Statement 1:
Angles opposite to equal sides QR and PR are equal so .
=> ∠QPR = ∠PQR
Statement 2:
Angles opposite to equal sides PR and PQ are equal so .
=> ∠PQR = ∠ PRQ.
combining statement 1 and statement 2.
=> ∠QPR = ∠PQR = ∠ PRQ and hence all three angles are same [Proved]
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How is congruence related to rigid motion transformations?
An object is moved rigidly when it is transferred from one location to another without affecting its size or shape.
What is congruence?
A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.
When an object is transferred from one place to another without changing in size or shape, it is said to be moved rigidly. Two shapes can only match if a precise movement results in a correspondence between them.
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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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How many terms are there in the expression 3xy?
Answer:
ur mom
Step-by-step explanation:
haha lol;)
What are whole numbers give 5 examples?
Answer:
whole numbers are numbers including zero, positive and no fractions
Step-by-step explanation:
0, 8, 89, 98, 999999999999, 57, 3, 5
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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What is the length of AC 3 FR?
The AC is 18 feet long.
Triangles are primarily involved in the mid-point theorem. According to this rule, if the midpoints of any two triangle sides are connected, the line formed is parallel to the third side and equal to half of the third side. Contrarily, if a parallel line is drawn from one side's midpoint to any other, it will bisect the third side and be equal to half the side to which it is parallel.
As shown in the diagram,
AM = MB, CN = NB.
The midpoints of the sides AB and CB, respectively, are M and N.
So, according to the midpoint theorem,
MN ║ AC,
The alternative interior angle theorem demonstrates that
∠BMM ≅∠BAC
∠BNM ≅∠BCA
According to the AA similarity postulate,
ΔBMM ≅∠BAC
The characteristic of identical triangles
[tex]\frac{BM}{BA} = \frac{MN}{AC}\\ \frac{BM}{BM+MA} = \frac{MN}{AC}\\ \frac{4}{4+4} = \frac{9}{AC}\\ \frac{4}{8} =\frac{9}{AC} \\[/tex]
4AC=72
AC=18 ft
As a result, AC is 18 feet long.
The complete question is:-
What is the length of the AC?
3 ft
4 ft
9 ft
18 ft
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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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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)
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.