Given a parallelogram ABCD with points B and D, we draw two lines such that line BM intersects CD at point M and line DN intersects BC at point N, and BM = DN. The intersection of these lines is point I. Our goal is to prove that IA is a bisector of angle BID.
To prove this, we first note that since ABCD is a parallelogram, AB is parallel to CD and AD is parallel to BC. This means that ∠BAD and ∠CDA are congruent, and ∠BAC and ∠DCB are congruent.
Next, we consider triangle ABM. Since BM is perpendicular to AB, we have ∠BAM = 90°. By the same reasoning, we have ∠BID = 90°. This means that IA is perpendicular to both AB and BD.
Since IA is perpendicular to AB and BD, it follows that IA bisects ∠BAD and ∠BDC. Additionally, we know that AB = BD and ∠BAD = ∠BDC, so it follows that IA bisects ∠BID.
This completes the proof that IA is a bisector of ∠BID. The key idea here is that a line perpendicular to two parallel lines bisects the angles formed by the intersection of the two parallel lines with a third line.
In conclusion, given a parallelogram ABCD with points B and D, the intersection of lines BM and DN, point I, is the bisector of angle BID. This result can be used to prove various geometric theorems and helps to understand the properties of parallelograms and their related figures.
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Which table represents a function?
Answer:
The first table(top row, leftmost) represents a function
Step-by-step explanation:
In a function y = f(x), the value for y must be unique for a value of x
In other words, you cannot have two different values of y for the same x
We see that only the first table(top row, leftmost) satisfies this requirement
So that is the answer
Second table has two values for x = -5
Third table has two values of x = -2
Fourth table has two values for x = -4
In the triangle DEF, the length DX = 3cm, XE = 7cm, and EF = 8cm.
a. Using a pair of compasses only and a ruler, construct the triangle DEF. Leave in your
construction arcs. Be sure to include these for the perpendicular line at X.
b. Measure the length of the side DF.
c. Measure the height of the triangle, XF.
d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.
e. Use compasses to bisect the angle D. You must leave your construction arcs in.
Answer:
This question is asking for a construction problem, which involves using a pair of compasses and a ruler to draw the triangle DEF and then measure certain aspects of the triangle, such as the length of DF, the height of XF, and the locus of a point 2cm from E. It also requires bisecting the angle D.
Step-by-step explanation:
a. To construct the triangle DEF, use the compasses to draw arcs with radii of 3cm and 7cm from points D and E respectively, so that the arcs intersect. Then, connect the points of intersection with a straight line to form the side DE. Next, use the compasses to draw an arc with a radius of 8cm from point F and intersect it with the previous arcs. Connect the points of intersection with a straight line to form the side DF. Finally, use the ruler to connect the points D, E, and F to form the triangle. To draw the perpendicular line at X, draw a line segment parallel to DE passing through the midpoint X, and then use the compasses to draw arcs centered at X and intersecting the sides DE and DF. Connect the points of intersection to form the perpendicular line at X.
b. Measure the length of DF using a ruler.
c. Measure the height of the triangle XF by measuring the distance from X to DF.
d. The locus of the point that is 2cm from E can be found by drawing an arc with a radius of 2cm centered at E and intersecting the sides DE and DF. The points of intersection represent the points that are 2cm from E.
e. To bisect the angle D, use the compasses to draw two arcs centered at D that intersect the sides DE and DF. Connect the points of intersection to form the bisector of angle D.
It is important to note that these steps are only a general guide and may need to be adjusted slightly depending on the specifics of the problem.
Determine whether ABC with vertices A(-3, 6), B(0, 10), and C (3, 8) is similar to XYZ with vertices X(-1, 3), Y(2, 7) , and Z(5, 5) .
Using Pythagorean theorem and the vertices given, the two triangle are similar
What are vertices of a triangleTwo triangles are similar if and only if the ratios of their corresponding sides are equal. So, to determine if triangle ABC is similar to triangle XYZ, we need to compare the ratios of corresponding sides.
One way to do this is to calculate the lengths of the sides in both triangles and compare the ratios. For example, the length of side AB in triangle ABC can be found using the Pythagorean theorem:
AB = √((0-(-3))^2 + (10-6)^2) = √(3^2 + 4^2) = √25 = 5
Similarly, the length of side XY in triangle XYZ can be found:
XY = √((2-(-1))^2 + (7-3)^2) = √(3^2 + 4^2) = √25 = 5
Next, we can compare the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ. If the ratios are equal for all corresponding sides, then the triangles are similar.
In this case, we find that the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ are all equal, so triangles ABC and XYZ are similar.
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The line y= 2x+3 and y=-3x+3 intersect at the point:
The point of intersection of the two equations will be ( 0, 3 ). The correct option is C.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the two equations are y= 2x+3 and y=-3x+3. The value of x and y will be calculated as:-
y= 2x+3
y=-3x+3
Equate the equations and solve,
2x + 3 = - 3x + 3
2x +3x = 0
x = 0
The value of y is,
y = 2x+3
y = 2 x 0 + 3
y = 3
Therefore, the two equations points of intersection will be ( 0, 3 ). The right answer is C.
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There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
The probability of getting 2 same colour balls in a row = 41/81
Probability:The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.
Probability of an event P(E)
= [ No of favorable outcomes ]/ Total No of outcomes
Here we have
There is a bag filled with 5 blue and 4 red marbles.
Number of balls = 5 + 4 = 9
Marble is taken at random from the bag,
The probability of getting the red ball = 4/9
The probability of getting the blue ball = 5/9
The color is noted and then it is replaced.
Another marble is taken at random.
The probability of getting the red ball 2nd time = 4/9
The probability of getting the blue ball 2nd time = 5/9
The probability of getting red ball in 2 attempts = (4/9)(4/9) = 16/81
The probability of getting blue ball in 2 attempts = (5/9)(5/9) = 25/81
Hence the probability of getting 2 of the same color
= 16/81 + 25/81
= 41/81
Therefore,
The probability of getting 2 same colour balls in a row = 41/81
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What is “subtract f from g, then multiply 9 by the result” write it out not answer it.
Step-by-step explanation:
(g–f)
multiply by nine
9(g–f)or 9g–9f
on the basis of your answer to (c), do you think that it is possible to construct a images matrix with linearly independent columns? how about a images matrix with linearly independent rows?
It should be noted that it is possible to construct a matrix with linearly independent columns. This means that no one column can be represented as a linear combination of the other columns. In this case, the columns are said to span the space of the matrix.
How to explain the matrixIt is also possible to construct a matrix with linearly independent rows. This means that no one row can be represented as a linear combination of the other rows.
In this case, the rows are said to span the space of the matrix. In general, the rows and columns of a matrix may or may not be linearly independent, depending on the specific matrix and the basis used to represent it.
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simplify 2m exponent of 0 n exponent of 6 over 3n exponent of 5
The simplified expression is equal to 2/3.
Simplifying Math ExpressionThe expression can be simplified as follows:2m⁰ * n⁶ / (3n⁵)
Since m⁰ is equal to 1, the expression becomes:2 * n⁶ / (3n⁵)
Dividing both numerator and denominator by n⁵ gives:2 * n / (3n) = 2/3
So the simplified expression is equal to 2/3.
The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.
For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.
In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.
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PLEASE HELP ASAP DUE TOMORROW!! IF YOU HELP ME I WILL MARK YOU AS BRAINLIEST AND XTRA POINTS!! PLEASE HELP! LOTS OF LOVE!!!
Answer:
Step-by-step explanation:
To find the speed of a cyclist, divide the distance traveled by the time taken.
In this case, the speed is:
3.75 miles ÷ 0.3 hours = 12.5 miles per hour (mph)
So, the cyclist was traveling at a speed of 12.5 mph.
Answer:
Step-by-step explanation:
Answer should be 12.5 mph.
four numbers; 3, 2, 4 ,7
use all four cards to make smallest number
use all four cards to make the number closest to 5000 as possile
Answer:
To make the smallest number with the cards 3, 2, 4, and 7, you can arrange them as 2, 3, 4, 7 to get the number 237.
To make the number closest to 5000, arrange the cards as 7, 4, 2, 3 to get the number 7243.
Step-by-step explanation:
A bobsled team is practicing runs on a track. Their first run takes 4.85 minutes. On each of the next two runs, the team’s time changes by −512% compared to the previous time.
A photo of a bobsled on a track is shown.
Question 1
Part A
What was the team’s time, rounded to the nearest hundredth of a minute on their final run?
Answer: The team's time on the final run can be found by successively multiplying their first time by (1 - 0.512) twice:
First run time: 4.85 minutes
Second run time: 4.85 * (1 - 0.512) = 2.37 minutes
Third run time: 2.37 * (1 - 0.512) = 1.15 minutes (rounded to the nearest hundredth)
So the team's time on their final run was 1.15 minutes.
Step-by-step explanation:
3y+7=x
Tell whether the equation represents a direct proportion. If so, identify the constant of proportionality.
The equation 3y + 7 = x does not represent a direct proportion.
What is the Constant of Proportionality?The constant of proportionality is a value that describes the relationship between two variables in a proportional relationship. For example, if y is proportional to x, and y = 2 when x = 4, then the constant of proportionality would be 0.5 (since 2/4 = 0.5). The constant of proportionality is often represented by the letter "k".
What is a Direct Proportion?A direct proportion is a relationship between two variables where their ratio is always constant.
In the equation, 3y + 7 = x, the relationship between x and y is not fixed, so it does not represent a direct proportion.
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the students in mr. juarez's homeroom collected more cans than students in ms. wade's homeroom. write an expression that represents how many more cans were collected.
The expression that can represent how many more cans were collected is 8n - 7 > 6n + 3, which is in fact an inequality.
An inequality in math is an algebraic expression that represents, well, inequality. It shows a relationship between two values or expression, which aren't equal to each other. It is used to compare two values/expression, showing if one is greater than, less than, or simply not equal to another. Thus, we would use a mathematical symbol of <, >, ≤, ≥, or ≠ to express an inequality.
Since students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom do, you can use the symbol > in your inequality. The number of cans collected in Mr. Juarez's homeroom is 8n − 7, while the number of cans collected in Ms. Wade's homeroom is 6n + 3. Therefore, your inequality would be 8n - 7 > 6n + 3.
This question is missing some parts, which are most probably these:
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2=e-1 help me I'm stuck it on a math book page 541 question 20
Answer:
[tex]3=e[/tex]
Step-by-step explanation:
I know this might be late but I can help if you still need it
So in the equation [tex]2=e-1[/tex], we need [tex]e[/tex] by itself. To do that we need to add [tex]1[/tex] to each side. We do this because the side that [tex]e[/tex] is on, the [tex]1[/tex] is being subtracted and we need to do the opposite of subtraction which is addition.
[tex]2=e-1[/tex]
[tex]+1[/tex] [tex]+1[/tex]
So the new equation:
[tex]3=e[/tex]
Hope this helped!
Stay safe and have a great day/night! (:
Find the sum of the series. Make sure to use the formula and show your work.
The summation of the series ¹³∑ₙ₎ ₁ (3n - 1) is 260.
What is the sum of the series?Given the summation in the question;
¹³∑ₙ₎ ₁ (3n - 1)
First, we split the summation into smaller summations that fits the summation rule.
¹³∑ₙ₎ ₁ (3n - 1) = 3 ¹³∑ₙ₎ ₁ (n) + ¹³∑ₙ₎ ₁ (- 1)
Now, lets evaluate 3 ¹³∑ₙ₎ ₁ (n).
Using the formula for the summation of a polynomial with degree 1
ⁿ∑ₐ₎ ₁ (a) = n( n + 1 ) / 2
Plug in the values
3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(13+1))/2)
3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(14))/2)
3 ¹³∑ₙ₎ ₁ (n) = (3) (182/2)
3 ¹³∑ₙ₎ ₁ (n) = (3) (91)
3 ¹³∑ₙ₎ ₁ (n) = 273
Next, evaluate ¹³∑ₙ₎ ₁ (- 1)
Using the formula for the summation of a constant
ⁿ∑ₐ₎ ₁ (c) = cn
Plug in the values
¹³∑ₙ₎ ₁ (- 1) = (-1)(13)
¹³∑ₙ₎ ₁ (- 1) = -13
Now, we add the results of the summation.
273 - 13
260
Therefore, the sum of the series is 260.
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Chapter 4 Lesson 3 Solving System of Equations Using Elimination
1) 2x + 5y = 17
+ 6x – 5y = -9
────────
8x = 8
divide both sides by 8 :
Answer : x = 1 (one solution)
2) (3x – y = 0) * 4
(4x + 2y = 14) * 3
12x – 4y = 0
- 12x + 6y = 14
────────
-10y = -14
Divide both sides by -10
Answer : y = 1.4 (one solution)
3) 6x + 5y = 39
- 3x + 5y = 27
────────
3x = 12
Divide both sides by 3
Answer : x = 4 ( one solution )
4) 4x – 7y = 3
+ x – 7y = -15
────────
5x = -12
Divide both sides by 5
Answer : x= -2.4 (one solution)
I NEED HELP PLEASEEE
1) The length of rectangle ABCD is x+3 units and its area is x²+3x units. Find its breadth.
2) A machine fixes 25 stoppers on bottles in a minute. How many hours will it take to fix stoppers on 2250 bottles?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Area of a rectangle is given by :
[tex]\qquad \sf \dashrightarrow \: area = l \times b[/tex]
[ l = Length, and b = width ]
[tex]\qquad \sf \dashrightarrow \: x {}^{2} + 3x = (x + 3)(b)[/tex]
[tex]\qquad \sf \dashrightarrow \: b = \dfrac{ {x}^{2} + 3x }{x + 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: b = \dfrac{ {x(}x^{} + 3) }{x + 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: b = x[/tex]
Next problem ~
[tex] \textsf{Number of stoppers fixed per minute = 25 } [/tex]
[tex] \textsf{1 stopper is fixed in = 1/25 minutes} [/tex]
[tex] \textsf{2250 stoppers are fixed in = 1/25 × 2250 = 90 minutes } [/tex]
Now, convert it into hours~
[tex]\qquad \sf \dashrightarrow \:60 \: \: min = 1 \: \: hr[/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: min = \dfrac{1}{60} \: \: hrs[/tex]
[tex]\qquad \sf \dashrightarrow \: 90 \: \: min = \dfrac{1}{60} \times 90 \: \: hrs[/tex]
[tex]\qquad \sf \dashrightarrow \: 90 \: \: min = \dfrac{3}{2} \: \: hrs[/tex]
[tex]\qquad \sf \dashrightarrow \: 90 \: \: min = 1.5 \: \: hrs[/tex]
So, in total it would take 1.5 hours to fix stoppers on 2250 bottles.
The figure is cut into 12 equal pieces.
Shade 5/6
of the figure.
Answer: that is shading 10/12 of the figure
Step-by-step explanation:
Shading 5/6 of the figure means that 5 out of the 12 equal pieces would be colored or filled in. To visualize this, imagine the figure being divided into 12 equal slices, like a pizza. If 5 of those slices were to be filled in with color, they would represent 5/6 of the total figure.
Write each function in vertex form and identify the vertex.
f(x) = x^2- 16 x + 3
f(x) = 4x^2+24x-7
f(x) = -2x^2- 8x + 9
For the quadratic equations -
1) f(x) = x² - 16x + 3 → Vertex form is y = 3(x - 8)² - 61 and vertex is (8,-61).
2) f(x) = 4x² + 24x - 7 → Vertex form is y = 4(x + 3)² - 43 and vertex is (-3,-43).
3) f(x) = -2x² - 8x + 9 → Vertex form is y = -2(x + 2)² + 17 and vertex is (-2,17).
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The quadratic equation is written in the form ax² + bx + c = 0.
The vertex form of a quadratic equation is -
y = a(x - h)² + k
The first equation is - f(x) = x² - 16x + 3.
Here, a = 1, b = -16 and c = 3
The formula for h is -
h = -b/2a
h = -(-16)/2(1)
h = 16/2
h = 8
The formula for k is -
k = c - (b²/4a)
k = 3 - [(-16)²/4(1)]
k = 3 - (256/4)
k = 3 - 64
k = -61
So, the vertex form is -
y = a(x - h)² + k
y = 3(x - 8)² - 61
The vertex is written as (h,k).
The vertex is (8,-61).
Therefore, the vertex form and vertex is y = 3(x - 8)² - 61 and (8,-61) respectively.
The second equation is - f(x) = 4x² + 24x - 7.
Here, a = 4, b = 24 and c = -7
The formula for h is -
h = -b/2a
h = -(24)/2(4)
h = -24/8
h = -3
The formula for k is -
k = c - (b²/4a)
k = -7 - [(24)²/4(4)]
k = -7 - (576/16)
k = -7 - 36
k = -43
So, the vertex form is -
y = a(x - h)² + k
y = 4(x + 3)² - 43
The vertex is written as (h,k).
The vertex is (-3,-43).
Therefore, the vertex form and vertex is y = 4(x + 3)² - 43 and (-3,-43) respectively.
The third equation is - f(x) = -2x² - 8x + 9.
Here, a = -2, b = -8 and c = 9
The formula for h is -
h = -b/2a
h = -(-8)/2(-2)
h = 8/-4
h = -2
The formula for k is -
k = c - (b²/4a)
k = 9 - [(-8)²/4(-2)]
k = 9 - (64/-8)
k = 9 + 8
k = 17
So, the vertex form is -
y = a(x - h)² + k
y = -2(x + 2)² + 17
The vertex is written as (h,k).
The vertex is (-2,17).
Therefore, the vertex form and vertex is y = -2(x + 2)² + 17 and (-2,17) respectively.
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what shape is the distribution displayed in the following informal histogram? identify the major and minor modes.
The best description is skew right. (the date is missing in this question)
What is Skew right?A distribution is right skewed if it has a “tail” on the right side of the distribution.
here, we have,
The cumulative relative frequency graph shows that
The slope between 0 and 4 is substantially steeper than the curve between 6 and 14.
Then
Because most of the data values are between 0 and 4 (where the histogram's highest bar appears) and relatively few values lie between 6 and 14 the histogram's distribution should be skewed to the right, resulting in low bars tailing to the right side of the highest bars.
Because there are more data values between 0 and 4 than between 6 and 14 we can conclude that skewed right is the best description of the histogram's form. Hence, the it is skewed right.
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Help please 20 points and brainly if picked
Answer:
Below
Step-by-step explanation:
Slope of BLACK line = rise/run = 9 / 3 = m = 3
y intercept = b = 2 Line eq = y = mx+ b y = 3x +2
Slope of BLUE line similarly is 9 / -3 = m = -3
and b = 8
y = mx + b y = -3x + 8
PLS HELP ME!!!
Every year Stafford has a citywide relay and reports the winning times.
Winning relay times
Year║Winning time (minutes)
2015║55
2016║54
2017║50
2018║51
2019║56
According to the table, what was the rate of change between 2015 and 2016?
The rate of change between 2015 and 2016 was 1.
How to find the average rate of change of something?Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
We have been given the data
Year║Winning time (minutes)
2015║55
2016║54
2017║50
2018║51
2019║56
The rate of change = 2016 - 2015 / 55 - 54
= 1/1= 1
Thus, the answer is 1.
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A computer with a manufacturer's suggested list price of $1400 is supplied with trade discounts of 40/10. The invoice is dated october 27th and paid in full on november 15th. Cash terms are 8/10, 2/20, EOM. The computer is priced with a 35% markup based on selling price. What is the total amount due on november 15th?
The total amount due on November 15th would be $1667.81
Let's first calculate the trade discount amount:
Suggested list price: $1400
Trade discount rate: 40/10 = 4%
Trade discount amount: $1400 x 4% = $56
After deducting the trade discount, the price becomes:
$1400 - $56 = $1344
Next, let's calculate the cash discount:
Amount after trade discount: $1344
Cash discount rate: 8/10 = 8%
Cash discount amount: $1344 x 8% = $107.52
After deducting the cash discount, the price becomes:
$1344 - $107.52 = $1236.48
Finally, let's calculate the total amount due:
Amount after cash discount: $1236.48
Markup rate: 35%
Markup amount: $1236.48 x 35% = $431.33
Total amount due: $1236.48 + $431.33 = $1667.81
So, the total amount due on November 15th would be $1667.81.
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how many -digit numbers are there with unique digits from to such that the first five digits form an increasing series and the last five digits form a decreasing series?
The number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.
For the first five digits to form an increasing series, we can choose the first digit in 9 ways (it can't be 0), the second digit in 8 ways, the third digit in 7 ways, the fourth digit in 6 ways, and the fifth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the first five digits.
For the last five digits to form a decreasing series, we can choose the sixth digit in 9 ways (it can't be 0), the seventh digit in 8 ways, the eighth digit in 7 ways, the ninth digit in 6 ways, and the tenth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the last five digits.
Therefore, the number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series, and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.
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Can someone please help me with this question. If you do, you’ll be rewarded with brainliest and extra points!
Answer: NO/MN = QR/PQ
Answer:
[tex]\frac{NO}{MN}[/tex] = [tex]\frac{QR}{FQ}[/tex]
Step-by-step explanation:
∠ 0 ≅ ∠ R and ∠ M ≅∠ F
thus Δ NOM ≅ ∠ QRF ( by the AA postulate )
the ratios of corresponding sides are in proportion, so
[tex]\frac{NO}{MN}[/tex] = [tex]\frac{QR}{FQ}[/tex]
Evaluate 8.3x + 7.5y when x = 3 and y = 4.
8.3( blank) + 7.5( blank) = blank + 30.0= Answer?
The value of the expression is 94.9
How to determine the valueAlgebraic expressions are expression with variables, terms, coefficients, factors and constants.
They are also made up of mathematical operations, such as;
AdditionSubtractionBracketParenthesesSubtraction, etcFrom the information given, we have that;
8.3x + 7.5y
When x = 3 and y = 4
Substitute the values into the formula
8.3(3) + 7.5(4)
expand the bracket
24.9 + 60
Add the values
84. 9
Hence, the value is 84.9
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PLEASE HELP WITH ALGEBRA 1
Complete the square.
4t²-16t+12
The equivalent expression is (t - 2)² - 1
How to complete the square.From the question, we have the following parameters that can be used in our computation:
4t²-16t+12
Divide through the equation by 4
So, we have the following representation
t² - 4t + 3
Take the coefficient of t
k = -4
Divide by 2
k/2 = -2
Square it
(k/2)^2 = 4
So, we have
t² - 4t + 3 + 4 - 4
Rewrite as
t² - 4t + 4 + 3 - 4
Express as squares
(t - 2)² - 1
Hence, the expression is (t - 2)² - 1
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At lake view middle school, there are 2 homeroom teachers assigned to every 48 students. Is the number of students at this school proportional to the number of teachers? Explain your reasoning
Answer:
Step-by-step explanation:
No, the number of students at Lake View Middle School is not proportional to the number of teachers.
Proportionality between two quantities means that they maintain a constant ratio, regardless of their actual values. In this case, if the number of students and teachers were proportional, we would expect the ratio of students to teachers to remain constant as the total number of students or teachers changes.
However, in this scenario, the ratio of students to teachers is not constant. The ratio is 48:2, which simplifies to 24:1. This means that there are 24 students for every 1 teacher. If the number of students at the school were to double to 96, we would expect the number of teachers to double as well if they were proportional. However, this would mean that there would be 4 teachers assigned to the students, which is twice the original number of teachers assigned to the original number of students.
Therefore, the number of students at Lake View Middle School is not proportional to the number of teachers, because the ratio of students to teachers is not constant, and it changes as the total number of students or teachers changes.
superior segway tours gives sightseeing tours around chicago, illinois. it charges a one-time fee of $60, plus $28 per hour. what is the slope of this situation?
So the slope of the scenario is $28 per hour, which indicates that the expense of the tour increases by $28 for every extra hour spent on it.
What is slope?The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, while the y-intercept is (0, 7).
Here,
In this situation, the slope represents the rate of change in the cost of the tour with respect to the time spent on the tour. The slope of the situation can be calculated as the change in cost divided by the change in time.
Since the one-time fee is a fixed cost, it does not change with respect to the time spent on the tour. Therefore, the slope can be calculated as the rate of change in the cost due to the hourly fee of $28.
The slope can be represented as:
slope = Δcost/Δtime = $28/hour
So, the slope of the situation is $28 per hour, which means that for every additional hour spent on the tour, the cost of the tour increases by $28.
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maya earns £3672 each month before tax is taken out . this amount is then split into three parts:She doesnt pay tax on £972 of it. she pays 20% tax on £2665 of it. she pays 40% tax on the rest of it. How much of mayas monthly earnings are left after tax has been taken out? please help
Answer:
£ 3125
Step-by-step explanation:
Tax amount on £ 2665 = 20% of 2665
= 0.2 * 2665
= £ 533
Rest amount = 3672 - (972 + 2665)
= 3672 -3637
= £ 35
Tax amount of £ 35 = 40% * 35
= 0.4 * 35
= 14
Total tax = 533 + 14
= £ 547
Money left after paying tax = 3672 - 547
= £ 3125