The expression x - 4 is a factor of the polynomial f(x) = 4x³ - 21x² + 26x - 24 as f(4) = 0. And (x - 4)(4x² - 5x + 6) is the product of two factors for f(x).
The factor theorem in polynomialThe factor theorem states that: if f(x) is divisible by x - a if and only if f(a)=0.
We shall evaluate f(4) to know if x - 4 is a factor of the polynomial f(x) as follows;
f(4) = 4(4)³ - 21(4)² +26(4) - 24
f(4) = 256 - 336 + 104 - 24
f(4) = 360 - 360
f(4) = 0
The first row of the synthetic division is derived as follows:
4x³ divided by x equals 4x²
x - 4 multiplied by 4x² equals 4x³ - 16x²
subtract 4x³ - 16x² from 4x³ - 21x² + 26x - 24 will result to -5x² + 26x - 24
Thus x - 4 is a factor and we will divide the polynomial expression 4x³ - 21x² + 26x - 24 exactly to get the quotient 4x² - 5x + 6.
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find the curl of the vector field f. f(x, y, z) = (6y − z)i + ezj + xyzk
B is between A and C.
AB=50 BC=3x AC=6x−25
Find the value of x.
25
65
20
45
The value of x if the point B is between the points A and C is (a) 25
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
B is between A and C.
Also from the question, we have the following parameters:
AB = 50
BC = 3x
AC = 6x−25
The statement "B is between A and C" implies that
AC = AB + BC
Substitute the known values in the above equation, so, we have the following representation
50 + 3x = 6x - 25
Evaluate the like terms
3x = 75
Divide both sides by 3
x = 25
Hence, the solution of x is 25
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Which linear equation shows a proportional relationship? a. y equals two thirds times x
b. y equals negative 3 times x minus one seventh c. y equals three fourths times x minus 5 d. y equals 3 times x plus 7
Answer:
Option a represents a proportional relationship.
Step-by-step explanation:
A proportional relationship is a relationship where two variables are directly related to one another, meaning that their ratio is always the same. In other words, when one variable changes, the other variable also changes in the same ratio.
In the equation y = 2/3 * x, the value of y is directly proportional to the value of x, meaning that for every change in x, the corresponding change in y will always be 2/3 of that change. This is because the coefficient of x is a constant value, in this case 2/3. Therefore, as x increases or decreases, y will also increase or decrease at the same rate in proportion to x.
Option a represents a direct proportion.
Option b, c, and d are not proportional relationships because they include a constant or an operation like subtraction, addition or negative sign.
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What are the 4 rules of congruence?
The 4 rules of Congruence that are used in proving two triangles congruent are (SSS) Side - Side - Side , (SAS) Side - Angle - Side , (ASA) Angle - Side - Angle and (RHS) Right Angle - Hypotnuse - Side .
The Two Triangles are called Congruent if their sides have same length and angles have same measure.
The Four rules by which we can prove 2 triangles as congruent are :
(i) (SSS) Side - Side - Side ,
The 2 triangles are said to be congruent by SSS rule. If all 3 sides of one triangle are equivalent to the corresponding 3 sides of second triangle .
(ii) (SAS) Side - Angle - Side ,
The 2 triangles are said to be congruent by SAS rule if , any 2 sides and the angle included between sides of one triangle is equivalent to corresponding 2 sides and the angle between sides of second triangle .
(iii) (ASA) Angle - Side - Angle ,
The 2 triangles are said to be congruent by SAS rule if any 2 angles and the side included between angles of one triangle is equivalent to corresponding 2 angles and side included between angles of second triangle .
(iv) (RHS) Right Angle - Hypotnuse - Side ,
The 2 triangles are said to be congruent by SAS rule if , hypotenuse and a side of a right- angled triangle is equivalent to hypotenuse and side of second right- angled triangle .
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The 4 rules of congruence
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
SSS (Side-Side-Side) The two triangles are said to be congruent if the three sides of one triangle are equivalent to the corresponding three sides of the second triangle.
According to the SAS (Side-Angle-Side) rule, two triangles are said to be congruent if any two sides and any angle included between the sides of one triangle are comparable to the corresponding two sides and any angle included between the sides of the second triangle.
The two triangles are said to be congruent by the ASA (Angle-Side-Angle) rule if any two angles and the side included between the angles of one triangle are comparable to the corresponding two angles and side included between the angles of the second triangle.
AAS (Angle-Angle-Side) (Angle-Angle-Side)
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
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A cinder block is in the shape of a rectangular prism. the cinder block has two holes shaped like rectangular prisms that are the same size and pass completely through it. what is the volume of the cinder block?
The volume of the cinder block can be calculated as follows: L x W x H) - 2(l x w x h)
To find the volume of the cinder block, you need to know the dimensions of the block and the dimensions of the holes. The volume of a rectangular prism is calculated by multiplying the length, width, and height. If the dimensions of the cinder block are L x W x H, and the dimensions of the holes are l x w x h, the volume of the cinder block can be calculated as follows:
Volume of cinder block = (L x W x H) - 2(l x w x h)
You can use this formula to calculate the volume of the cinder block once you know the dimensions of the block and the holes.
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The volume of the cinder block is 624 cu.in.
Consider the following diagram.
We know the formula for the volume of rectangular prism:
V = length × width × height
First we find the volume of the outer rectangular prism.
Let V1 be the volume of outer rectangular prism.
Let l1 be the length, w1 be the width and h1 be the height of the outer rectangular prism.
l1 = 16 in, w1 = 8 in and h1 = 8 in
So, V1 = l1 × w1 × h1
V1 = 16 × 8 × 8
V1 = 1024 cu. in.
The cinder block has two holes shaped like rectangular prisms.
Let V2 be the volume of one hole.
Let l2 be the length, w2 be the width and h2 be the height of one of the hole.
Dimensions of the hole: l2 = 8 in., w2 = 5 in. and h2 = 5 in.
So, V2 = l2 × w2× h2
V2 = 8 × 5 × 5
V2 = 200 cu.in.
The volume of the cinder block would be,
V = V1 - (2 × V2)
V = 1024 - (2 × 200)
V = 1024 - 400
V = 624 cu. in.
Therefore, the required volume is 624 cu³
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Jahquil makes $35 an hour working as an accounting assistant she works 40 hours each month Jahquil will have made after she worked seven months
Answer: 9,800
Step-by-step explanation: $35 X 40h (hours) = $1,400 x 7m (months) = 9,800
How many times smaller is 1.2 × 106 than 1.47 × 107? 0.82 1.35 2.67 12.25
1.25 times 1.2×106 is smaller than the 1.47×107. Therefore, the correct answer is option D.
Given that, 1.2×106 and 1.47×107.
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Here,
1.2×106 = 127.2
1.47×107 = 157.29
Now, [tex]\frac{157.29}{127.2}[/tex]
= 1.25
Therefore, the correct answer is option D.
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If the sum of the zeroes of the quadratic polynomial kx 2 3 x k 2 + + is equal to their product, then k equals
Which equations are true equations? Select all correct answers. Responses 82−52=42−7 8 squared minus 5 squared equals 4 squared minus 7 56÷8+32=2⋅23 56 divided by 8 plus 3 squared equals 2 times 2 cubed 39−3⋅6=6⋅104+4 39 minus 3 times 6 equals fraction numerator 6 times 10 over denominator 4 end fraction plus 4 2422=50−62−8
The only option that is true about the equations is; Option D: 24/2² = 50 − 6² − 8
How to solve basic mathematical operations?Option A: 8² − 5² = 4² − 7
Simplifying this gives us;
64 - 25 = 16 - 7
39 = 9
Thus, this is not true.
Option B: 56 ÷ 8 + 32 = 2⋅2³
Simplifying this gives us;
(56/8) + 32 = 2⋅2³
7 + 32 = 2⋅8
39 = 16
Thus, this is not true.
Option C: 39 −3⋅6 = 6⋅104 + 4
Simplifying this gives us;
36 - 18 = 624 + 4
18 = 628
Thus, this is not true.
Option D: 24/2² = 50 − 6² − 8
24/4 = 50 − 36 − 8
Apply the division operation,
6 = 55- 44
Apply the subtraction operation,
6 = 6
Thus, this equation is true.
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Thomson directed the beam at an electrometer and tried to separate the evidence of charge from the path of the beam. What connection did thomson find between charge and the cathode rays? was the charge positive or negative?.
Thomson surrounded the cathode ray with two electric plates that were charged in opposition to test the qualities of the particles. The negatively charged electric plate was avoided in favour of the positively charged plate, deflecting the cathode ray. This demonstrated the presence of negatively charged particles in the cathode ray.
The cathode ray tube studies of J.J. Thomson demonstrated that all atoms contain minute, electron-like subatomic particles that are negatively charged.
In Thomson's "plum pudding" atoms theory, a positive electrode "soup" was enclosed by electrons with negative charges.
The most of a molecule is blank space, with a tiny, dense, positively-charged nucleus, as established by Rutherford's gold foil experiment.
Rutherford postulated the nuclear model of the atom in light of these findings.
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The cathode rays were composed of negatively charged particles.
In 1897, J. J. Thomson conducted a famous experiment to determine the charge of the cathode rays. He used an evacuated cathode ray tube, with a small hole in one end that allowed some of the rays to pass through. He then directed the beam at an electrometer, which measures electric current. By adjusting the electric and magnetic fields, he was able to separate the evidence of charge from the path of the beam. By doing so, he determined that the charge of the cathode rays was negative.
To calculate the charge of the cathode rays, Thomson used the following equation: Q = I × t, where Q is the charge, I is the current, and t is the time. He measured the current as I = 0.8 mA and the time as t = 5.0 x 10-3 sec. Thus, he calculated the charge of the cathode rays as Q = 0.8 x 5.0 x 10-3 C = 4.0 x 10-3 C, which is a negative charge. This result was consistent with the idea that the cathode rays were composed of negatively charged particles.
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help please it's eLearning day
The areas of the given problem are:
6. 400 cm².
7. 200 cm².
8. 72 sq. in.
9. 60 sq. in.
How to Find the Area of a Parallelogram and a Triangle?Area of a parallelogram = base (h) * height (h).
Area of a triangle = 1/2(b * h), where h is the height and b is the length of its base.
6. Area of the parallelogram = base (h) * height (h) = 40 * 10
= 400 cm².
7. Area of a triangle = 1/2(b * h) = 1/2(40 * 10)
= 1/2(400)
= 200 cm².
8. Area of the sign = 1/2(b * h) = 1/2(12 * 12)
= 1/2(144)
= 72 sq. in.
9. Amount of fabric she needs for the banner = 1/2(b * h) = 1/2(10 * 12)
= 1/2(120)
= 60 sq. in.
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Amira is d years old.
a) Joshua's age is Amira's age divided by 5. Write
an expression in terms of d for Joshua's age.
b) An expression for Oliver's age is d + 7. Write a
sentence to describe how Oliver's age compares
with Amira's.
Answer:
Oliver is 7 years older than Amira.
Step-by-step explanation:
Amira: d
Joshua: d/5
Oliver: d + 7
if amira's age is "d" and oliver's age is "d + 7," that means you would add 7 to amira's age to get oliver's age. therefore, oliver is 7 years older than amira.
The blue dot is at what value on the number line?
Based on the number line provided, it can be concluded the blue dot is equivalent to 0.
What is a number line?This is a horizontal line with values or numbers on it. Number lines are different from just any other line because the numbers on them follow a sequence and at placed at defined intervals. Most number lines include the number 0,1,2,3, but the sequence might be different.
What value does the blue dot represent?Based on the values provided, it can be concluded the sequence is -10,-6,-8, etc. and this would make the blue dot to be 0.
Note: This question is incomplete, below I attach the missing information.
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Over what interval(s) is the function strictly linear?
(A) -2 < x < 2
(B) -2 < x < 0 and 2 < x < 4
(C) 0 < x < 2
(D) 0 < x < 2 and 2 < x < 4
Th equation is linear at -2 < x < 0 and 2 < x < 4.
What is linear equation?A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. Because of this, it is referred to as a "linear equation."
Given graph,
to find the intervals where function is linear,
for linearity ,
Linearity is the property of a mathematical relationship (function) that can be graphically represented as a straight line. Proportionality and linearity are closely linked concepts.
from graph we find that the intervals at which the function is linear are,
(-2, 0) (0, 2) and (2, -2) (4, 2)
te coordinates of x are
-2 and 0, 2 and 4
-2 < x < 0 and 2 < x < 4
Hence the interval is the function strictly linear are,
-2 < x < 0 and 2 < x < 4
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The scatterplot below shows the relationship between the temperature, in degrees Fahrenheit, at a football game and the number of cups of hot chocolate sold during the game. Number of Cups Sold Hot Chocolate Sales 160 140 120 100 80 60 40 20 0 30 ● 40 50 Temperature (F) -70 80 Which of the following graphs best represents the line of best fit for this data? Tim Atter
The graph that best represents the line of best fit for this data is given below.
What is the line of best fit?A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
Given:
The scatter plot below shows the relationship between the temperature, in degrees Fahrenheit, at a football game and the number of cups of hot chocolate sold during the game.
The table for calculation and plot are given in the attached image.
The line of the best fit for the scatter plot is ŷ = -14.15584X + 1144.93506
Therefore, the line of the best fit is ŷ = -14.15584X + 1144.93506.
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a car is depreciated by 16% each year for 6 years. its value is 8782.45 what the original value
The original value of a car depreciated by 16% annually for 6 years with a depreciated value of $8,782.45 is $21,394.
What is depreciation?Depreciation is accounting terminology that describes the systematic allocation of the cost of a long-term asset over its useful period.
Due to wear, tear, and usage, an asset loses its value over time.
To account for this, accounting provides a method for recognizing the loss (cost).
The depreciated value of a car = $8,782.45
Annual depreciation rate = 16%
Depreciation period = 6 years
Original value = [$8,782.45 x (1.16)^6]
= ($8,782.45 x 2.436)
= $21,394
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What is the exact value of cosine startfraction 7 pi over 12 endfraction? a. startfraction startroot 6 endroot minus startroot 2 endroot over 4 endfraction b. startfraction startroot 6 endroot startroot 2 endroot over 4 endfraction .c startfraction 2 startroot 2 endroot minus startroot 6 endroot over 4 endfraction d. startfraction startroot 2 endroot minus startroot 6 endroot over 4 endfraction
Answer:
StartFraction pi Over 6 EndFraction, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction pi Over 6 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction pi Over 3 EndFraction, negative one-half
StartFraction pi Over 3 EndFraction, one-half
Answer:
StartFraction StartRoot 2 EndRoot minus StartRoot 6 EndRoot Over 4 EndFraction
Step-by-step explanation:
If the sum of two numbers is 6 and the difference is 2 what are the two numbers
Answer: 4 and 2
Step-by-step explanation:
4+2=6
4-2=2
Answer:
4 and 2
Step-by-step explanation:
4+2=6
4-2=2
6-2=4
What is the volume of the figure?
Step-by-step explanation:
The volume of rectangular prism is calculated with the following formula:
V = w×l×h (w: width, l: length, h: height)
The lengths for the figure is given so we can write the following equation and find the volume:
7×5×3 = 105 ft³
Write the equation tor the parent linear value function, f(x)=x, that has been transformed by:
a. reflecting across the -axis, vertical stretch by a scale factor 4, and a translation of 4 units up amd 5 units left
b. vertical shrink by a scale factor of 14 and a horizonta shift O units right.
c. reflection in the x-axis, a vertical shift of 4 units up and a horizontal shift 7 units left
The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, the equation for the parent linear value function, f(x)=x, that has been transformed by,
a) Reflecting across the -axis, vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left :-
Rule for reflection across x-axis = y = f(x) → y = -f(x)
After reflection,
f(x) = -x
And there is a vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left
f(x) = -4(x+4)+5
Therefore, the function will be f(x) = -4(x+4)+5
b) Vertical shrink by a scale factor of 14 and a horizontal shift O units right.
For vertical shrink = f(x)/14 = x/14
For horizontal shift = (x-o)/14
Therefore, the function will be f(x) = (x-o)/14
c) Reflection in the x-axis, a vertical shift of 4 units up and a horizontal shift 7 units left.
Rule for reflection across x-axis = y = f(x) → y = -f(x)
f(x) = -x
For a vertical shift of 4 units up and a horizontal shift 7 units left =
f(x) = (-x-7)+4
Hence, The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4
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Solve the following inequality using both the graphical and algebraic approach: 5 minus x less-than 2 (x minus 3) + 5 Graph A On a coordinate plane, a line goes through (0, 5) and (5, 0). Another line goes through (negative 2, negative 4) and (2, 3). The lines intersect at (2, 3). Graph B On a coordinate plane, a line goes through (0, 0) and (2, negative 6). Another line goes through (0, negative 8) and (2, negative 6). a. x less-than 2 Graph A b. x greater-than 2 Graph A c. x less-than 2 Graph B d. x greater-than 2 Graph B Please select the best answer from the choices provided A B C D
The solution to the inequality in this problem is given as follows:
d. x > 2.
The graphical solution to the inequality is given by the image shown at the end of the answer.
How to solve the inequality?The inequality for this problem is defined as follows:
5 - x < 2(x - 3) + 5.
Applying the distributive property, we have that:
5 - x < 2x - 6 + 5
5 - x < 2x - 1.
Hence the solution set is composed by the region in which the line 2x - 1 is greater than the line 5 - x.
The numerical solution set is obtained as follows:
5 - x < 2x - 1.
-3x < -6
3x > 6. (the leading coefficient is negative, hence the multiplication by -1 also changes the sign).
x > 6/3
x > 2.
Meaning that option d is correct.
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What are the values of x and y*
Based on the given triangles, x is 9/4 and y is 15/4 (B).
To anwer this question, we need to understand that we have 3 different triangles in one picture:
ΔABCΔABDΔBCDFirst, we will focus on the biggest triangle ΔABC. We have 3 sides:
AB = 5BC = yAC = (4 + x)Using the phytagoras theorem, we can get the equation of:
AC² = AB² + BC²
(4 + x)² = 5² + y²
16 + 8x + x² = 25 + y² ... (i)
Next, we will focus on the third triangle, BCD. We have 3 different sides:
BC = yCD = xBD = 3Using the phytagoras theorem, we can get the second equation:
BC² = CD² + BD²
y² = x² + 3²
y² = 9 + x² ... (ii)
We can subtitute the equation (ii) into equation (i) to eliminate y:
16 + 8x + x² = 25 + y²
16 + 8x + x² = 25 + (9 + x²)
16 + 8x + x² = 34 + x²
16 + 8x = 34
8x = 18
x = 9/4 ... (iii)
By subtitute the equation (iii) into equation (ii), we can get the value of y:
y² = 9 + x²
y² = 9 + (9/4)²
y² = 9 + (81/16)
y² = 144 + 81
16
y² = 225/16
y = 15/4
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The net of a right circular cylinder is shown.
net of a cylinder where the radius of each circle is labeled 5 meters and the height of the rectangle is labeled 9 meters
What is the surface area of the cylinder? Use π = 3.14 and round to the nearest whole number.
225 m2
298 m2
440 m2
707 m2
The surface area of the cylinder is equal to: C. 440 m².
How to calculate surface area of a cylinder?Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the surface area of a cylinder formula, we have;
Surface area (SA) of cylinder = (2 × 3.14 × 5 × 9) + 2 × 3.14 × 5²
Surface area (SA) of cylinder = 282.6 + 157
Surface area (SA) of cylinder = 439.6 ≈ 440 square meters.
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Answer:440 m2
Step-by-step explanation:
i took the the test
The treasurer of the student body at a college reported that the receipts from a recent concert totaled $916. Furthermore, he announced that 560 people had attended the concert. Students were charged $1.25 each for admission to the concert, and adults were charged $2.25 each. Solve the systems of equations.
Answer:
300 student tickets and 260 adult tickets.
Step-by-step explanation:
x=number of student tickets, y=number of adult tickets.
1.25x+2.25y=916; x+y=560. x=300; y=260.
I've given up on math. I hate it.
The linear equation representing the data in the table is y = x - 3, therefore;
The slope, m = 1
The y-intercept, c = -3
A linear equation is an equation of the form y = m·x + c, in which the highest index of the variables is 1, and the graph of the ordered pairs obtained using the equation is a straight line.
The first difference of the y-variable is constant and each next value the x-variable increases by 1, therefore, the relationship is a linear relationship.
The slope, m, is therefore;
m = (-3 - (-4))/(0 - (-1)) = 1
The slope of the graph of the data, m = 1The equation of the line that represents the graph of the data in the table using the point (3, 0) is therefore;
y - (0) = 1·(x - 3) = x - 3
Therefore; y = x - 3
The above equation is in the slope-intercept form, y = m·x + c, with the slope, m = 1, and the y-intercept, c = -3
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Select all that are equal to 5^3* 5^-7
. Write a multiplication equation that represents the question:
how many 3/8 are in 5/4?
Answer: hope you got this right
Step-by-step explanation: 3 1/3. divide 5/4 by 3/8. (5/4) / (3/8) = 5/4 * 8/3 = 40/12 = 10/3
Which is the correct order of the steps in bisecting a line segment?
The order of the steps for the bisection of line segment AB will be D, E, B, C, and A.
The first thing we do for bisecting any line segment is to take up a distance of more than the approximate half of the line segment and place the compass on either point of the line.
Hence the first point will be D. Place the compass on point A and open it wider than half the distance of the segment.
Since an arc on both sides of the segment has to be drawn, the next point will be E. Swing an arc above and below the segment.
Since the same thing has to be repeated for the other point, the next point will be B. Keeping the compass the same width, place the compass on point B, and swing an arc above and below the segment.
Now we have got 2 points above and below the line segment, the next point has to be C. Place points C and D on the intersection of the arcs created above and below segment AB.
The line intersecting these points and AB has to be the point that divides AB in half, and the last point will be A. Draw a line from point C to point D.
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Complete Question
What is the correct order of steps for bisecting segment AB?
A. Draw a line from point C to point D.
B. Keeping the compass the same width, place the compass on point B, and swing an arc above and below the segment.
C. Place points C and D on the intersection of the arcs created above and below segment AB.
D. Place the compass on point A, and open it wider than half the distance of the segment.
E. Swing an arc above and below the segment.
which theorem proves congruency. Determine which postulate can be used to pro valid congruency statement. Color the picture according А. B D F X E с ASA AAS SAS 6 4 11 CDE AFDE ADECEAEDF AECD = ADFE Gray Yellow Light Blue
By applying the congruency of triangles, it can be concluded that ΔCDE ≅ ΔFDE by AAS theorem
Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure. The symbol of congruence is ≅.
There are some postulates used to prove congruency:
Angle-Side-Angle (ASA): two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and the side included between the angles of the second triangleAngle-Angle-Side (AAS): two triangles are said to be congruent if two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangleSide-Angle-Side (SAS): two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangleSide-Side-Side (SSS): two triangles are said to be congruent if all three sides of one triangle are equivalent to the corresponding three sides of the second triangleNow we take a look at the given picture, the take some notes:
∠C = ∠F ----> corresponding angles
∠DEC = ∠DEF ----> corresponding angles
DE = DE ----> adjacent sides
Thus ΔCDE ≅ ΔFDE by AAS postulate
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OUR ASSIGNMENT: Wildlife Sanctuary
You are designing a path for traveling to one of the animal habitats in the wildlife sanctuary. Which of the following regions did you choose?
Lion Habitat Hippo Habitat Elephant Habitat
Lion habitats are often designed to mimic their natural environment, with rocky outcroppings, grassy plains, and trees for shade.,
Hippos spend most of their time in the water, and their habitats often include large ponds or rivers, Elephant habitats often include areas for grazing, watering holes, and shaded areas for rest.
what is habitat?
A habitat is a specific environment or place where a particular species of plant or animal lives and thrives. A habitat provides all the essential needs for a species to survive, such as food, water, shelter, and space. The physical characteristics of a habitat, such as temperature, humidity, soil type, and vegetation, determine which species can live there and how they interact with each other.
Habitats can be very diverse, ranging from deserts and forests to wetlands and coral reefs. Different species have different habitat requirements, and some species can adapt to different habitats while others are very specific in their requirements.
The study of habitats is an essential part of ecology, as understanding the habitat requirements of different species is crucial for their conservation and management.
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