The ratio of the length of each transversal will be [tex]\frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}} =1[/tex]
The ratio of the lines can be compared using Three Parallel Lines Theorem.
What is Three Parallel Lines Theorem?
When two transversals are intersected by three parallel lines, the transversals are proportionally divided.
According to the three parallel lines theorem, the segments created by each transversal and the three parallel lines are proportionate.
The findings are:
The ratio of the lengths of each transversal is equal because the parallel lines divide the transversals in an equal number of halves. [tex]Ratio\ of\ segments: \frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}}[/tex]Reasons:
The question is a four part question
Let the equations of the parallel lines be as follows;
Line, x; y = x
Line, y; y = x + 1
Line z; y = x + 2
The points at which transversal 1 intersect the lines x, y, and z, are;
A(0.4, 0.4), B(0.6, 1.6), and C(0.8, 2.8)
The length of segment [tex]{\overline {AB}}[/tex] = √((0.6 - 0.4)² + (1.6 - 0.4)²) = 0.2·√(37)
The length of segment [tex]{\overline {CB}}[/tex] = √((0.8 - 0.6)² + (2.8 - 1.6)²) = 0.2·√(37)
The ratio of the lengths of the segment formed by transversal 1 is therefore;
[tex]\sqrt{x} \ ratio\ of\ the\ length \ of segments =\frac{\overline {CB}}{ \overline {AB}} = \frac{2.\sqrt{37} }{2.\sqrt{37} } =1[/tex]
The points at which transversal 2 intersect the lines x, y, and z, are;
D(1.1, 3.1), E(1.3, 2.3), and F(1.5, 1.5)
The length of segment [tex]{\overline {DE}}[/tex]= √((1.3 - 1.1)² + (2.3 - 3.1)²) = 0.2·√(17)
The length of segment [tex]{\overline {EF}}[/tex] = √((1.5 - 1.3)² + (1.5 - 2.3)²) = 0.2·√(17)
The ratio of the lengths of the segment formed by transversal 2 is therefore;
[tex]\sqrt{x} \ ratio\ of\ the\ length \ of segments =\frac{\overline {EF}}{ \overline {DE}} = \frac{0.2.\sqrt{17} }{0.2.\sqrt{17} } =1[/tex]
Therefore;
[tex]\frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}} =1[/tex]
Which gives;
The proportion by which the transversals are divided by the parallel lines is equal.Each transversal's length is proportionately equal.The the comparison can also be made with the triangle proportionality theorem.
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Use the linear equations below to answer questions 51 & 52. (HINT: Solve by the
Substitution method - you must first solve for x !!!).
x + 3y = 7
4x-y = 15
a) What is the value of x?
b) What is the value of y?
Answer:
x = 4
y = 1
Step-by-step explanation:
x + 3y = 7 --> Eq1
4x - y = 15 --> Eq2
Find x in term of y using Eq1
x = 7 - 3y
Substitute x in Eq2
4(7-3y) -y = 15
28 - 12y - y = 15
-12y-y = 15 - 28
-13y = -13
y = -13/-13
y = 1
Find x
x = 7-3(1) = 4
If you have to solve for x first
Find y in term of x using Eq 2
y = 4x - 15
Substitute y in Eq 1
x + 3(4x -15) = 7
x + 12x - 45 = 7
x + 12x = 7 + 45
13x = 52
x = 52/13
x = 4
Find y
y = 4(4) -15 = 16 - 15 = 1
Can you find the slope-intercept equation of each line and type the correct code? Please remember to type in ALL CAPS with no spaces. Puzzle 5
The equations are: line 2:- y = 4x-4, line 3:- y = -2x+3 and line 4:- y = 2x+1
What is slope-intercept form?The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given are 4 lines,
For line 1:-
Since, we have only one point of this line and no information about slope, so we can not find its equation.
For line 2:-
Points are - (0, -4) and (1, 0)
Slope = (y2-y1)/(x2-x1)
Slope = 4/1 = 4
Solving for c,
-4 = 4*0 + c
c = -4
Equation will be,
y = 4x-4
Similarly,
For line 3:-
y = -2x+3
For line 4:-
y = 2x+1
Hence, The equations are: line 2:- y = 4x-4, line 3:- y = -2x+3 and line 4:- y = 2x+1
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PLEASE HELP!!!!
At a particular restaurant, each pizza roll has 65 calories and each chicken wing has 50 calories. A combination meal with pizza rolls and chicken wings is shown to have 1015 total calories and 5 more pizza rolls than chicken wings. Determine the number of pizza rolls in the combination meal and the number of chicken wings in the combination meal.
Answer:
11 pizza rolls
6 chicken wings
Answer:
11 pizza Rolls and 6
Step-by-step explanation:
Write this ratio as a fraction in simplest form without any units.
Answer:
change 5 weeks to days(5*7)-35days
then convert the days to seconds
35*86400/10*86400
answer 7/2
what is the equation of yx3 with the given transformations vertical compression by a factor of 17
The transformed equation of is y = x³ is y =-1/7(x+8)³
Given that :
The equation of y=x^3 and Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis
Applying the given transformations, we have:
To have a vertical compression by a factor of 1/7, we need to multiply the function by 1/7. So, we have:
y=1/7x³
We must add 8 to x in order to have a horizontal shift of 8 units to the left. We thus have:
y=1/7(x+8)³
A reflection over the x-axis would be the final step, we need to multiply the function by −1. So, we have:
y= -1/7(x+8)³
Therefore, the transformed equation is y= -1/7(x+8)³
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Divide and write the fraction 1/4 divided by 3/8 =
Answer:3/2
Step-by-step explanation:
3/8 divided by 1/4 is the same as multiplying 3/8 by 4/1
= 12/8
=3/2
What is a paragraph proof of Theorem 3 8?
We prooved the paragraph proof of Theorem 3.8 that if two lines are perpendicular to the same line, then they are parallel to each other.
In the given question we have to explain the a paragraph proof of Theorem 3.8.
Let the lines that cross line a be m and n. Let m be parallel to a. As a result, the intersection of m and a produces four 90° angles.
Let n be parallel to a. This indicates that each of the four angles created by the intersection of n and an is 90 degrees.
The same-side internal angles (between lines m and n) are also congruent because all of the angles are congruent. The lines are parallel if two internal angles on the same side are congruent.
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The right question is:
Write a paragraph proof of theorem 3-8: in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
is x^2+x+1=0 linear?
Answer:
No.
Step-by-step explanation:
Because the equation has an exponent, it is quadratic, and not linear.
Answer:1
Step-by-step explanation:
Solve for x
2 1/2x - 3/4 ( 2x + 5 ) = 3/8
Please explain step by step on how I get this answer to solve x!
Answer:
4 [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
what is the greatest counting number that is a factor of both 96 and 120 but has no common factor with 105 other than 1?
The greatest counting number that is a factor of both 96 and 120 but has no common factor with 105 other than 1 is 2.
The given number are 96 and 120.
What is the greatest common factor?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.
The factors of given number are
The factors for the number 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.
Therefore, the greatest counting number that is a factor of both 96 and 120 but has no common factor with 105 other than 1 is 2.
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A rectangular yard measuring 40 ft by 70 ft is bordered (and surrounded) by a fence. Inside, a walk that is 4 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
The area of the path is 456 square feet
How to determine the areaThe formula for determining area of a rectangle is given as;
A = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values into the formula, we have;
Area of the rectangle = 40 × 70
Area of the rectangle = 2800 square feet (1)
Bordered fence with a 4 ft path so dimensions 44 ft by 74 ft
Area of rectangular garden with Path = 44 × 74
= 3256 square feet (2)
Area of the walk = (2) - (1) = 3256 - 2800 = 456 square feet
Hence, the value is 456 square feet
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How do you find the degree of a polynomial in precalculus?
Answer:
add up the exponents of each term and select the highest sum.
What is the quadrant of 0 6?
Answer:
it depends im pretty sure that you mean y and x cord so answer is 0 x 6 y
Step-by-step explanation:
or 0 X so width or y height 6 Y
what are the missing reasons in the two column proof
Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.
Given that,
We have to find the missing reasons in the two column.
Given
AC bisects ∠DAB and CA bisects ∠DCB
Prove
ΔDAC≅ΔABC
Statement Reasons
1. AC bisects ∠DAB Given
2. ∠DAC≅∠BAC definition of angle bisects
3.AC≅AC reflexive property
4.CA bisects ∠DCB given
5. ∠DCA≅∠BCA definition of angle bisects
6. ΔDAC≅ΔABC ASA postulate
Therefore, Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.
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12. A factory needs to package 2,835 cartons
of orange juice in boxes. How many
more small boxes than large boxes are
needed to package the cartons of orange
juice?
Box Size
Small 15 number of cartons
Large. 35 number of cartons
The total number of cartons needed more to pack small 15 cartons than 35 large cartons is108 cartons.
What is the number of cartons needed?Division is defined as one of the four basic operations of arithmetic in mathematics.
The parameters for this question are:
Total number of cartons =2835
Number of small cartons needed = 15 cartons
Number of large cartons needed = 35 cartons
To package the orange juice in large cartons we need [tex]\frac{2835}{35} =81 cartons[/tex]
Also, to package 15 small cartons we need [tex]\frac{2835}{15} =189 cartons[/tex]
Number of more small cartons than large cartons is
Small cartons -large cartons
=189-81=108 more cartons.
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find the surface area of each of these solid (useπ 22）
__
7
Answer:
156 cm³
Step-by-step explanation:
The solid is a prism with a trapezoid base.
volume = (area of base) × height
V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm
V = 156 cm³
Joseph has $1.45 worth of nickels and dimes. He has a total of 17 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Joseph has.
The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Let the no. of nickels be N and no. of dimes be D.
∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)
Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)
Now multiply (i) by 5 we get 5N + 5D = 85...(iv)
Now subtracting (iv) from (iii) we get,
5D = 60.
D = 12 hence N = 5.
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tic is an isosceles triangle with a vertex angle i if the measure of i90
Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.
An Isosceles triangle has a vertex angle and two equal base angles.
Given that triangle TIC is an isosceles triangle:
angle I is the vertex angle = 90 degrees
angle T is a base angle
angle C is also a base angle
Thus:
angle C and angle T are congruent or equal to each other.
Therefore,
Angle T = (180 - 90)/2
⇒ Angle T = 90/2
⇒ Angle T = 45 degrees.
applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
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A toy maker is putting multicolored sand in transparent cubes. Each cube measures 10 millimeters on each side. A coworker remarks that, for the cubes to be completely filled, each cube will need no more than 30 cubic millimeters of sand. Is the coworker correct? The coworker is correct. The volume of each cube is 20 cubic millimeters. The coworker is correct. The volume of each cube is 30 cubic millimeters. The coworker is not correct. The volume of each cube is 100 cubic millimeters. The coworker is not correct. The volume of each cube is 400 cubic millimeters. The coworker is not correct. The volume of each cube is 1,000 cubic millimeters.
The true statements are
The co-worker is not correct. The volume of each cube is 1,000 cubic millimetresHow to determine the true statement about the volume?The side length of the transparent cube is given as
Length = 10 millimetres
The volume of the cube is calculated as
Volume = Length³
Substitute the known values in the above equation, so, we have the following representation
Volume =10³
Evaluate
Volume = 1000 cubic millimetres
1000 cubic millimetres and 30 cubic millimetres do not have the same value
So, the co-worker is incorrect.
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Write the following using algebraic notation, using the letter x for any unknown numbers:
I think of a number, multiply it by two, then subtract nine.
Answer:
2x - 9
Step-by-step explanation:
x = unknown number
2 * x -9
2x - 9
Which polynomials are in standard form?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
5
−
2
x
5−2x5, minus, 2, x
(Choice B)
B
x
4
−
8
x
2
−
16
x
4
−8x
2
−16x, start superscript, 4, end superscript, minus, 8, x, squared, minus, 16
(Choice C)
C
5
x
3
+
4
x
4
−
3
x
+
1
5x
3
+4x
4
−3x+15, x, cubed, plus, 4, x, start superscript, 4, end superscript, minus, 3, x, plus, 1
(Choice D)
D
None of the above
The polynomial that is in standard form is: B. [tex]x^4 - 8x^2 - 16[/tex].
What is a Polynomial in Standard Form?A polynomial that is expressed in standard form is given in such a way that the terms of the expression are written in ordered from from the term with the highest degree, to the term with the lowest degree. The constant comes last in a polynomial that is expressed in standard form.
5 - 2x is not expressed in standard form because it is not properly ordered. The constant needs to come last.
[tex]x^4 - 8x^2 - 16[/tex] is well ordered, therefore, it is a polynomial that is expressed in standard form.
[tex]5x^3 + 4x^4 - 3x + 1[/tex] is not well ordered. It is not in standard form.
The answer is therefore: B. [tex]x^4 - 8x^2 - 16[/tex].
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Round 0.799 to the nearest hundredth
Answer:
0.80
Step-by-step explanation:
The hundredth is 2 digits after the decimal.
Rounding 0.799, we want 0.xx
Look at the third digit, 9, meaning we round up.
However, since the second digit after the decimal is also a 9, we can make that a 0 by adding 1 to the first digit after the decimal.
We get 0.80
Pls help answer fast rapidly is of khan academy:
Answer:
expanded: 7+0.08
standard: 7.08
Step-by-step explanation:
The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.
This graph shows the relationship between the number of gallons of milk purchased and the cost. Use the ordered pairs from the graph to enter the missing values in the table. Enter your answer by filling in the boxes.
Using the graph of the relationship, the missing values are:
x | y
2 6
4 12
6 18
How to Apply the Graph of a Relationship?Given the graph attached below where:
The number of gallons of water are plotted on the x-axisThe cost in dollars is on the y-axisThe graph shows the relationship between the number of gallons (x) and the cost in dollars (y).
For example, if an ordered pair on the graph is (2, 8), it means it would cost $8 for 2 gallons.
Thus, to find the respective values for each missing pair of values, trace the corresponding value on the graph that is given.
The complete table is therefore:
x | y
2 6
4 12
6 18
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See question in screenshot below:
I only need the compounded continuously amount (the last question marked with an x).
=================================================
Work Shown:
[tex]A = P*e^{rt}\\\\A = 4000*e^{0.07*7}\\\\A \approx 6529.26487982264\\\\A \approx 6529.26[/tex]
-----------
Explanation:
P = deposit amount = 4000 dollarse = special constant equal to roughly 2.718...r = annual interest rate in decimal form = 0.07t = number of years = 7Let your calculator handle the constant 'e's value, rather than typing in the numbers 2.718... so you can get the most accuracy possible. It's like how many calculators have a [tex]\pi[/tex] button for similar reasoning. If your calculator doesn't have an 'e' button, then this should be sufficient
e = 2.71828182846
By the way, it's a bit odd how your teacher didn't require you to round to the nearest cent. Something like 6423.12590591 should round to 6423.13
A line with a slope of 1 passes through the point (5, 3). What is its equation in slope "-intercept" form?
Answer: y=x−2 y = x − 2
Step-by-step explanation:
Please help me find answer
Answer:
I'm not sure but based on my work I would say option 2.
Hope this helps!
Step-by-step explanation:
Which rigid transformation can map triangle ABC onto triangle Fed?
Reflection then translation are rigid transformation can map triangle ABC onto triangle Fed.
What is congruent?
Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’.
Main body:
It has been given in the question that Δ ABC and ΔFED are congruent by SSS congruence theorem.
ΔFED is the picture image of ΔABC and slightly shifted towards left.
Therefore, we can tell about the transformations that if ΔABC is reflected on x-axis and translated towards left, it can map ΔFED.
Hence ,Option B is the answer.
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find the inverse of the function fx 2x 4
The inverse function of the function f(x) = 2x - 4 will be x/2 +2.
What is inverse function?
A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1
Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.
f(x) = 2x - 4
y = 2x - 4
So x = y +4 /2
x = y/2 +2
Now to get the inverse of the function put the x value in y
So [tex]f^{-1}[/tex](x) = x/2 +2
Hence, inverse function will be x/2 +2.
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One integer is 2 times another. If the product of the two integers is 32, then find the integers
Answer:
The integers could be 8 and 4, just checked with a calculator
