Answers
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
What is Congruency of triangles?Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".
When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.
Given that,
GH ≅ JH
FH ≅ HI
And,
∠GHF = ∠JHI
Therefore,
ΔGHF ≅ ΔJHI (SAS Congruency)
∴ FG = IJ (CPCT theorem)
Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.
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Related Questions
The geometric sequence LaTeX: a_n=125\left(\frac{1}{5}\right)^{n-1}a n = 125 ( 1 5 ) n − 1 represents the sales of a specific product at a store, where n is the number of years after its release. What is the sum of the first 6 terms?
Answers
The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.
The sum of the first 6 terms of the geometric sequence is calculated as follows:
[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]
[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]
[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]
Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75
The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.
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where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and c are constants.
Find values for a, b and c that will effectively model your motion on the big wheel.
Answers
The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached
The values of the constants in the sinusoidal function, h = a + b·(c·t) are;
a = 30
b = -20
c = π/1.5
What is a sinusoidal function?A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.
The diameter of the Ferris wheel = 40 m
The location of the axle above the ground = 30 m
The time it takes to make a complete a rotation = 3 minutes
The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;
h = a + b·cos(c·t)
The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.
Therefore;
At t = 0, h = 30 - 40/2 = 10
h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b
a + b = 10
Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;
a = 30
a + b = 10, therefore;
b = 10 - a
b = 10 - 30 = -20
b = -20
At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50
50 = a + b·cos(1.5·c)
50 = 30 - 20 × cos(1.5·c)
20 × cos(1.5·c) = 30 - 50 = -20
cos(1.5·c) = -1
cos(π) = -1
Therefore; 1.5·c = π
c = π/1.5
The equation is therefore;
h = 30 - 20·cos((π/1.5)·t)
a = 30, b = -20, c = π/1.5
Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel
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Big Ideas Math:
Q1. The graph of which of the following functions does not belong with the other three?
Answer: f(x) = 3x^2 + 24x - 6
Q2. This is the only function that does not have x-intercepts at x= Response and x= Response and a vertex at (Response, Response).
Answers
Function 3x²+24x-6 does not belong with the other three
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the option we have to simplify each function
a. f(x)=3x²+6x-24
b. f(x)=3x²+24x-6
c. f(x)=3(x-2)(x+4)
=3(x²+4x-2x-8)
=3x²+6x-24
d. f(x)=3(x+1)²-27
3(x²+1+2x)-27
3x²+3+6x-27
3x²+6x-24
So function 3x²+24x-6 does not belong with the other three
Hence, function 3x²+24x-6 does not belong with the other three
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HELPLSPLSPLPSLPSLPSL
Answers
Answer:
25.5
Step-by-step explanation:
first find the area od the rectangle than the triangle.
to find the area count the number of squares and use A=b*h
than do the same for the triangle using A=.5*b*h
15=3*5
10.5=.5*3*7
10.5+15=25.5
hi, can someone please help me
Answers
this is your proper answer
hii, how are you
Answer:
15
Step-by-step explanation:
Let the total number of beads be x[tex]\because\: \frac{3}{8}[/tex] of the beads are blue.& Total number of blue beads = 9[tex]\rightarrow\: \frac{3}{8}\times x= 9[/tex][tex]\rightarrow\: x= \cancel{9}\times\frac{8}{\cancel{3}}[/tex][tex]\rightarrow\: x=3\times 8[/tex][tex]\rightarrow\: x=24[/tex]Number of purple beads = 24 - 9 = 15help? very easy just volume
Answers
Answer:
1920 cubic centimeters
Step-by-step explanation:
FIGURE A:
8 * 10 * 14 = 1120
FIGURE B:
8 * 10 * 10 = 800
So 1120 + 800 = 1920 cubic centimeters!
dat da answer
A rectangle has an area of 16x + 24. What could the length and width of the rectangle be
Answers
The length and width of the rectangle will be 2 and 8x + 12
Area of rectangle = 16x + 24.
A rectangle is a four-sided geometric shape having opposite sides that are equal in length and four right angles. The length and width of the rectangle are its opposing sides.
A rectangle's area is found by multiplying its length and width together, so:
Area = length x width
Calculating the length and width of the rectangle -
Factoring out 2 from the equation -
Therefore -
2 (8x+12)
Since, the area is the length times width, thus -
2 x (8x+12)
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Regular hexagon $ABCDEF$ is the base of right pyramid $\allowbreak PABCDEF$. If $PAD$ is an equilateral triangle with side length 8, then what is the volume of the pyramid
Answers
The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .
The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.
so the height becomes,
√3a/2 = 4√3
The area of the hexagon is calculated using the formula ,
=3√3/2 x a²
=3√3/2 x 64
= 963√3
=332.553 square units.
Volume of a pyramid is calculated as ,
1/3 x base x height
= 1/ 3 x 8 x 8
= 1/3 x 64
=21.33 cubic units answer.
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Maya is saving money to buy a game. So far she has saved $12 , which is three-fourths of the total cost of the game. How much does the game cost?
Answers
Answer:
$16
Step-by-step explanation:
12 = 3/4g
cross-multiply to get:
3g = 48
g = 48/3
g = 16
Suzy randomly picks marbles from a bag containing 13 identical marbles. How many possible outcomes are there if she selects 9 marbles
Answers
Suzy randomly picks marbles from a bag containing 13 identical marbles. The possible outcomes of the given probability if she selects 9 marbles is:
259,459,200.
What is random?Randomness is commonly used to refer to an event's apparent or actual lack of pattern or predictability. Random events, symbols, or steps frequently occur in no particular order and do not adhere to any recognizable pattern or combination.
Germanic in origin, Randon is a name for boys. With a name that means "wolf shield," you can inspire baby Randon to embrace their sense of adventure. something or someone that is suspiciously out of the ordinary, unidentified, or unknown. a peculiar or erratic individual or thing. Something that is random lacks structure, direction, or intent. Like the random selection of lottery numbers or unplanned random events, it occurs entirely by chance.
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y < c - 1 y > x -4
Answers
The graph of the inequality system is attached. The coordinate of a point in the solution set is (-1, 2).
In order to graph the system of inequalities graphically, consider the equation of each inequality.
y = x – 1
y = x - 4
Choosing a few values of x, plot the graph for each equation. Shade the area bounded by the line based on the inequality. If the inequality is less than, shade the area right to the line and if the inequality is greater than, shade the area left to the line. Hence, y < x – 1 is represented by red area and y > x – 4 is represented by blue area. The overlapping shaded area contains the coordinates that represent the solution of the inequality system. The coordinate of a point in the solution set is (-1, 2).
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Evaluate cos(θ) when θ=3π/2?
Answers
Answer:
0
Step-by-step explanation:
What is equivalent to 4 6?
Answers
The fraction which is equivalent to 4/6 is 8/12 as asked in the question.
2 x 4 = 8 and
3 x 4 = 12
Therefore, they satisfies the condition of an equivalent numbers.
Equivalent numbers are those which on reducing to it's lowest terms gives the same number.
Other example , 2/4 is equivalent number to 8/16 .
Equivalent fractions are those fractions which has different numerators and denominators but the same value when reduced to their lowest terms. For, example 2/4 and 3/6 are comparable fractions because they both equal 12.
A fraction is a portion of a number written in terms of numerator and denominator. Equivalent fractions represent the same percentage of the whole.
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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
Answers
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Consequently, it follows that the greatest possible quotient as required is; 25.
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What do I put for question a, b, c and d?
Answers
Answer:
Step-by-step explanation:
a) (52 + 63)/250 = 0,46 = 46%
b) (63+77)/250 = 0,56 = 56%
c) 63/140= 0.45 = 45%
d) vegetarian that exercise: 52/110 = 47%
Compararison with not vegetarian:
63 : 140 = x : 110
50/110
So the answer is the first option
What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?
Answers
The smallest positive integer that is both multiple of 4 and 7 is 2
What are multiples?In mathematics, multiples are the results of multiplying an integer by a given number.
The given numbers for this problem are 4 and 7. The positive multiples of 4 and 7 will be listed and the first number that appeared in the both multiples s the smallest positive integer that is both a multiple of 7 and a multiple of 4.
The multiples of 4
4 8 12 16 20 24 28 32 36 .......
The multiples of 7:
7 14 21 28 35 42 49 56 63 70 77 84 91 98 .....
The smallest common multiple is 28
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Which techniques can be used to evaluate the expression 12. 75÷1. 5? Select all that apply.
Answers
The division technique can be used to evaluate the given expression
12.75÷1. 5
The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are (÷) and (/).
“p divided by q” can be written as: (p÷q) or (p/q).
The method of verification can be expressed as:
Dividend = (Divisor × Quotient) + Remainder.
The given equation is:12.75÷1.5
We'll first write the above decimal numbers in fractional form.
12.75÷1.5
1275/100÷15/10
2. Now we'll divide it further.
⇒1275/100÷15/10
⇒1275/100×15/10
⇒1275/10×15
⇒225/10×3
⇒88/10
3. And finally, we'll write our quotient in decimal form.
⇒88/10
⇒8.8
ㅤ
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Please help I’m going to fail this grade
Answers
The result of the operation between two mixed numbers are listed below:
99 / 104 4 / 3 6 / 5 52 / 25 57 / 53 33 / 100 1 / 2 8 / 5 4 4 / 3How to solve an operation between mixed numbers
Mixed numbers are real numbers with special notation to transform improper fractions into a combination of integers and fractions. That is:
a b / c = a + b / c
Where a, b, c are integers and c is a non-zero number.
The procedure to simplify the operation is described below:
Transform mixed numbers into improper fractions. Divide the resulting two fractions. Simplify the expression.Case 1
1 3 / 8 ÷ 1 4 / 9
(1 + 3 / 8) ÷ (1 + 4 / 9)
(11 / 8) ÷ (13 / 9)
(11 / 8) / (13 / 9)
99 / 104
Case 2
2 1 / 3 ÷ 1 3 / 4
(2 + 1 / 3) ÷ (1 + 3 / 4)
(7 / 3) ÷ (7 / 4)
(7 / 3) / (7 / 4)
28 / 21
4 / 3
Case 3
4 1 / 5 ÷ 3 1 / 2
(4 + 1 / 5) ÷ (3 + 1 / 2)
(21 / 5) ÷ (7 / 2)
42 / 35
6 / 5
Case 4
5 1 / 5 ÷ 2 1 / 2
(5 + 1 / 5) ÷ (2 + 1 / 2)
(26 / 5) ÷ (5 / 2)
(26 / 5) / (5 / 2)
52 / 25
Case 5
9 1 / 2 ÷ 9 4 / 6
(9 + 1 / 2) ÷ (9 + 4 / 6)
(19 / 2) ÷ (58 / 6)
114 / 106
57 / 53
Case 6
2 2 / 10 ÷ 6 2 / 3
(2 + 2 / 10) ÷ (6 + 2 / 3)
(22 / 10) ÷ (20 / 3)
(22 / 10) / (20 / 3)
(66 / 200)
33 / 100
Case 7
2 1 / 4 ÷ 4 1 / 2
(2 + 1 / 4) ÷ (4 + 1 / 2)
(9 / 4) ÷ (9 / 2)
(9 / 4) / (9 / 2)
18 / 36
1 / 2
Case 8
2 2 / 3 ÷ 1 2 / 3
(2 + 2 / 3) ÷ (1 + 2 / 3)
(8 / 3) ÷ (5 / 3)
(8 / 3) / (5 / 3)
8 / 5
Case 9
5 3 / 5 ÷ 1 2 / 5
(5 + 3 / 5) ÷ (1 + 2 / 5)
(28 / 5) ÷ (7 / 5)
(28 / 5) / (7 / 5)
28 / 7
4
Case 10
4 2 / 3 ÷ 3 1 / 2
(4 + 2 / 3) ÷ (3 + 1 / 2)
(14 / 3) ÷ (7 / 2)
(14 / 3) / (7 / 2)
28 / 21
4 / 3
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Find the area of the polygon with the given vertices. N(-2,1), P(3,1), Q(3,-1), R(-2,-1)
Answers
Answer:
10
Step-by-step explanation:
no explanation just math-way
Ten gallons of a sugar solution were mixed with 7 gallons of a 76 percent sugar solution to make a 64 percent sugar solution. Find the percent concentration of the first solution.
answers-
a. 51%
b. 60%
c. 48%
d. 56%
Answers
7 gallons of 76% solution contain 0.76×(7 gal) = 5.32 gal of sugar
10 gal of c% solution (c for concentration) contain c/100×(10 gal) = c/10 gal of sugar
(for example, if you have 10 gal of 50% solution, then it contains 50/10 = 5 gal of sugar)
Mixing the two gives a new solution with a total volume of 17 gal. If its concentration ends up at 64%, then it must contain 0.64×(17 gal) = 10.88 gal of sugar. This means
(sugar in 76% solution) + (sugar in c% solution) = 10.88 gal
5.32 gal + c/10 gal = 10.88 gal
c/10 gal = 5.56 gal
c = 50.56 ≈ 51
which makes the answer A.
Answer:
d. 56
Equation:
Let x = the percent of the 10 gallon sugar solution
10x + 76(7) = 64(10 + 7)
10x + 532 = 1088
10x = 1088 - 532
10x/10 = 556/10
x = 55.6
55.6 is closest to 56, therefore, the answer is 56%
Angle 1 and Angle______ are alternate exterior angles.
Answers
It’s angle 1 and angle 8
The pair of angles that are formed on the other side of the pearl lines, but on the opposite side of the transversal
goodluck
a=___
b=___
c=___
Solve for θ and round your answer to the nearest degree.
θ =___ degrees
Answers
Answer:
a= -2,3*4,-1
b=u
c=w
Step-by-step explanation:
can someone that knows about these problems help me ? i dont think i have the answer right
Answers
Answer:
The equation for the volume of a sphere is [tex]\frac{4}{3}\pi r^{2}[/tex]. Substitute the variables with the given numbers to get [tex]\frac{4}{3}\pi 9^2[/tex]. Simplify the equation to get 3053.63.
A rectangular prism has a length of 2cm, a height of 13cm, and a width of 9cm. What is its volume, in cubic cm?
Answers
Answer:
2 x 13 x 9 = 234 cm3 is your answer.
Step-by-step explanation:
Whenever given 3 side lengths of a rectangular prism you ALWAYS have to multiply those in order to get the volume..
Customary System Units Metric System Units 1 gallon 3.79 liters 1 quart 0.95 liters 1 pint 0.473 liters 1 cup 0.237 liters Approximately how many centiliters are in 3 quarts
Answers
3 quarts is equal to approximately 285 centilitres.
To Calculate this we have:
3 quarts is equal to 3 x 0.95 liters = 2.85 liters.
1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.
Therefore, 3 quarts is equal to approximately 285 centilitres.
In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.
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a) which group has lower mode.
b) what is this mode?
Answers
The easiest way to determine the mode of any data set, is to figure out which number appears most frequently, or most common.
You can take all of the numbers and count how many times each number appears. The number that appears the most is called the mode.
In the first pie chart (Group A), we can see that the orange piece is the biggest, therefore the most common. The orange piece has equal value to 4.
In the next group (Group B), we can determine the mode by looking at the highest bar, which would be 5.
4 is less than 5, which means that the answer to this question would be Group A.
What type of triangle do the points 3 2 (- 2 3 and 2/3 form a right triangle B equilateral triangle C isosceles triangle d none of these?
Answers
Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).
Let the given points be,
A = (3, 2), B = (-2, -3) and C = (2, 3)
The formula for the distance between two points:
The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].
Therefore,
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)
[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex] units
B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex] units
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex] units
By using the Pythagorean theorem:
According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
Now, we can see that,
[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]
[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]
Therefore, the given triangle is a right angled triangle.
Therefore, option(A) s correct.
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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.
A. right triangle
B. equilateral triangle
C. isosceles triangle
D. none of these
Find the value of c that completes the square. Show your work.
First problem included as reference. Use (b/2)^2
Answers
Answer:
26. 16
27. 1
28. 49
29. 169
30. 256
Step-by-step explanation:
26. (b/2)² = (-8/2)² = 16
27. (b/2)² = (-2/2)² = 1
28. (b/2)² = (-14/2)² = 49
29. (b/2)² = (26/2)² = 169
30. (b/2)² = (-32/2)² = 256
What is 35% of 35!!
Answers
Answer:
12.25
Step-by-step explanation:
Solution for What is 35 percent of 35:
35 percent *35 =
( 35:100)*35 =
( 35*35):100 =
1225:100 = 12.25
Now we have: 35 percent of 35 = 12.25
Question: What is 35 percent of 35?
Percentage solution with steps:
Step 1: Our output value is 35.
Step 2: We represent the unknown value with x.
Step 3: From step 1 above, 35 = 100%
Step 4: Similarly, x = 35%
Step 5: This results in a pair of simple equations:
35 = 100% (2)
x = 35% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both equations have the same unit (%); we have
[tex]\frac{35}{x} =\frac{100}{35}[/tex] (with % for 100 and 35)
Step 7: Again, the reciprocal of both sides gives
[tex]\frac{x}{35} =\frac{35}{100}[/tex]
⇒ x=12.25
Therefore, 35% of 35 is 12.25
can someone please help me?