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Proving a uadrilateral is a Parallelogram
Assignment Active
Determining Side Lengths in a Parallelogram
In quadrilateral ABCD, AD 1, BC.
3x+7
D
A
B
5x-9
What must the length of segment AD be for the
quadrilateral to be a parallelogram?
O 8 units
O 16 units
O 31 units
O 62 units
Answers
Answer:
31 units
Step-by-step explanation:
If a quadrilateral has a pair of sides that is both parallel and congruent, then the quadrilateral is a parallelogram.
Sides AD and BC are given as parallel.
If they are also congruent, then quadrilateral ABCD is a parallelogram.
3x + 7 = 5x - 9
-2x = -16
x = 8
AD = 3x + 7
AD = 3(8) + 7
AD = 31
Answer: 31 units
Related Questions
Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem
1. One way to calculate the total tax is 0.05(50 + 40). Use the order of operations to evaluate this expression. Show your work. (2 points)
Answers
Answer:
$4.50
Step-by-step explanation:
Okay so, first add both.
50+40 is 90, then multiply 90 by the tax percent which is
90x5%=4.5
If expression then,
x=money that they have to pay.
5%(50+40)=x (the original)
btw there's already a question like this :
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Ram bough some pen for Rs 90. If he paid Rs 1 less for each he would have 3 more pens. How many pens did he buy?
Answers
Based on the fact that Ram bought some pens and they cost Rs.90 but if he had paid Rs.1 less for each he would have 3 more pens, the number of pens he bought is 6 pens.
What number of pens did Ram buy?This can be represented as:
(x + 3) (y - 3) = 90
Where xy = 90
xy - 3x + 3y - 9 = xy
3y - 3x - 9 = 0
y - x - 3 = 0
x - y + 3 = 0
Solving further gives:
x - 90/ x + 3 = 0
x² + 3x - 90 = 0
Remembering that:
90 = 9 x 10
= 3 x 3 x 2 x 5
= 15 x -6
Going back to the formula:
x (x + 15) - 6 (x + 15)
(x + 15) (x - 6) = 0
x - 6 = 0
x = 6 pens
In conclusion, the number of pens bought was 6 pens.
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La nota de Karina en su curso de nivelación matemática es 7 veces la cantidad de factores primos que tiene el siguiente polinomio:
P (a; b; c) =a(a +b-c) +b(a+ b-c) +c(a +b- c)
Hallar la nota que obtuvo.
Answers
Karina obtuvo una nota final de 84 de 100 puntos en su curso de nivelación matemática.
¿Qué nota obtuvo Karina obtuvo en su curso de nivelación matemática?
Antes de comenzar la resolución de este problema, asumimos que la base de calificación del curso de nivelación matemática es 100 y que la nota mínima para pasar es 70. Por otra parte, sabemos que la nota obtenida por Karina es divisible por 7 y que es el producto de aquel número primo y un polinomio formado por una relación de tres números primos, la cual es simplificada a continuación:
p (a, b, c) = a · (a + b - c) + b· (a + b - c) + c · (a + b - c)
p (a, b, c) = a² + a · b - a · c + a · b + b² - b · c + a · c - b · c - c²
p (a, b, c) = a² + 2 · a · b + b² - c²
p (a, b, c) = (a + b)² - c²
p (a, b, c) = (a + b + c) · (a + b - c)
Si asumimos que Karina obtuvo 84, entonces se tiene que 84 = 7 × 12 y 12 = 2 × 6. Tanto el dos como el seis son múltiplos de dos, entonces asumimos a = b = c y encontramos que:
n (2, 2, 2) = 7 · (2 + 2 + 2) · (2 + 2 - 2)
n (2, 2, 2) = 7 · 6 · 2
n (2, 2, 2) = 84
En síntesis, Karina obtuvo una nota final de 84 de 100 puntos en su curso de nivelación matemática.
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In the geometric pattern below, n represents the number of blocks in the bottom row of each figure.
n = 1
n=2
Write a function that models the total number of blocks in terms of n.
OA f(1) = 2; f(n) = f(n-1) + 2n; for n ≥ 2
OB. f(1) = 1; f(n) = f(n-1) + 2n; for n ≥ 2
Oc f(1) = 1; f(n) = f(n-1) + n; for n ≥ 2
OD. f(1) = 2; f(n) = f(n-1) + 4n; for n ≥ 2
n=3
Answers
R = 15 when m = 6 s= 4 inversely when m=24 s =4
Answers
The value of r If r varies directly with the square of m and inversely with s is 240
Variation
Suppose r varies directly with the square of m and inversely with s.
If r varies directly with the square of m and inversely with s, then;
r = km²/s
Given that R = 15 when m = 6 s= 4
15 = k(6)²/4
60 = 36k
k = 60/36
k = 5/3
If the value of m = 24 and s = 4, hence;
r = 5/3*24²/4
r = 240
Hence the value of r If r varies directly with the square of m and inversely with s is 240
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look at the picture
Answers
The interval where the function is increasing is (3, ∞)
Interval of a functionGiven the rational function shown below
g(x) = ∛x-3
For the function to be a positive function, the value in the square root must be positive such that;
x - 3 = 0
Add 3 to both sides
x = 0 + 3
x = 3
Hence the interval where the function is increasing is (3, ∞)
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Rewrite as an exponential equation.
In 5 = y
Answers
The equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]
How to rewrite the expression?The natural logarithm equation is given as:
ln 5 = y
Rewrite as:
ln(5) = y
Take the exponent of both sides
[tex]e^{ln(5)} = e^y[/tex]
Evaluate the expression
[tex]5 = e^y[/tex]
Rewrite as:
[tex]e^y = 5[/tex]
Hence, the equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]
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Rationalize the denominator and simplify
√a+1-2/√a+1+2
Answers
5+a-4√(a+1)/(a-3) is the simplified form of the number. This can be obtained by multiplying numerator and denominator with conjugate of the denominator.
Simplify the number:Given the number,
√a+1-2/√a+1+2
Denominator = √a+1+2
Conjugate of the denominator = √a+1 - 2
Now, (√a+1-2)(√a+1 - 2 )/√(a+1+2)(√a+1 - 2 )
=(√a+1 - 2 )²/(√a+1)² - 4
=(a+1 -4√a+1+5)/(a+1-4)
=5+a-4√(a+1)/(a-3)
Hence 5+a-4√(a+1)/(a-3) is the simplified form of the number.
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Find the area between the two functions
Answers
The area between the two functions is 0
How to determine the area?The functions are given as:
f₁(x)= 1
f₂(x) = |x - 2|
x ∈ [0, 4]
The area between the functions is
A = ∫[f₂(x) - f₁(x) ] dx
The above integral becomes
A = ∫|x - 2| - 1 dx (0 to 4)
When the above is integrated, we have:
A = [(|x - 2|(x - 2))/2 - x] (0 to 4)
Expand the above integral
A = [(|4 - 2|(4 - 2))/2 - 4] - [(|0 - 2|(0 - 2))/2 - 0]
This gives
A = [2 - 4] - [-2- 0]
Evaluate the expression
A = 0
Hence, the area between the two functions is 0
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Instructions: Identify the vertices of the feasible region for the given linear programming constraints.
Optimization Equation: z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Fill in the vertices of the feasible region:
(0, )
(-3, )
(3, )
Answers
The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
How to identify the vertices of the feasible region for the given linear programming constraints?The optimization equation is given as
z=−3x+5y
The constraints are given as:
x+y≥−2
3x−y≤2
x−y≥−4
Next, we plot the constraints on a graph and determine the points of intersections
See attachment for the graph
From the attached graph, the points of intersections are
(-3, 1), (3, 7) and (0, -2)
So, we have:
(0, -2)
(-3, 1)
(3, 7)
Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
So, the complete parameters are:
Optimization Equation:
z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Vertices of the feasible region
(0, -2)
(-3, 1)
(3, 7)
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that any pair of congruent triangles is similar True or false.
Answers
Answer:
yes it's true no problem sir
A ternary string of length n is a sequence of n digits in which only 0, 1, or 2 appear.
For example, (0,1,0,2) and (1,1,2,2) are ternary strings of length 4 and can be seen as: 0102 and 1122.
How many ternary strings of length 2n are there in which the zeros appear only in odd positions?
Answers
dunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunno
dunno
pls need help
ersrsreerre
Answers
The computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.
How to compute the value?It should be noted that from the information given, we are given the information about three salesmen and their sales.
The total earnings for salesman A will be:
= (1300 × 3) + 65 × (11 + 14 + 16)
= 3900 + 2730
= 6630
The total earnings for salesman B will be:
= 300 × 3 + 40 × (14 + 15 + 13)
= 900 + 1680
= 2580
The total earnings for salesman C will be:
= 900 × 3
= 2700
Therefore, the computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.
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The average heart rate of an adult human is 72 beats per minute. For an adult elephant, the average heart rate is 35 beats per minute.
A. Whose heart beats more times in one hour
B. Whose heart makes 1,000,000 beats in less time
Answers
Answer:
A. the adult human
B. the adult human
Step-by-step explanation:
A. There are 60 minutes in an hour, and the human's heart beats 72 bpm (beats per minute). If you multiply 60 by 72, you get 4,320 bpm. If you multiply 60 by 35, you only get 2,100 bpm.
B. If you use the same logic that 72 is greater than 35, than you can assume that the human hear makes 1,000,000 beats in less time. However, if you want to do the math, then simply divide 1,000,000 by 72. Then, divide 1,000,000 by 35. Whichever has the smaller number is the one that can make more heart beats in a faster time.
Simplify the following fractions.
Answer =
[tex] \frac{9}{16 \\ \\ } [/tex]
Show me step by step
Answers
Answer:
Expressions with numerous operators must be simplified in "BODMAS" order only, from left to right. The brackets are solved first, followed by powers or roots,division, or multiplication (whatever comes first from the left side of the formula), and finally subtraction or addition. The BODMAS simplification of fractions is a solution for addressing fractions that include many operations such as addition (+), subtraction (-), multiplication (×),division(÷), and brackets ().[tex] \pink{\maltese{ \text{BODMAS \:Full \: Form \: }}}[/tex]
To make numerical equations easier to understand, operations must be performed according to the BODMAS rule, which involves division, multiplication, addition, and subtraction to be performed in the order brackets.For example,The expression (48-24)÷3×4 as per BODMAS rule.
(48-24)÷3×4
=24÷3×4
=8×4
=32
Now,
The given question is,
Simplify:
[tex] \displaystyle{ \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} }[/tex]
[tex] \displaystyle{ = \frac{7}{8} \div \frac{16}{3} \times \frac{24}{7} }[/tex]
[tex] \displaystyle{ = \frac{ \cancel{7} \times 3 \times \cancel{24} \: {}^{3} }{ \cancel{8 } \times 16 \times \cancel{7}} }[/tex]
[tex] \displaystyle{ = \frac{3 \times 3}{16} }[/tex]
[tex] \displaystyle{} = \frac{9}{16} [/tex]
Thus,the final answer is 9/16.
Solution -:
[tex] \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} [/tex]
Let's begin-
solve,,,
Now,,According to BODMAS rule fist we divide ,
[tex] \frac{7}{8} \times \frac{3}{16} \times \frac{24}{7} \\[/tex]
Now , we multiple
[tex] \frac{3 \times 3}{16} \\ \\ = \frac{9}{16} [/tex]
and this is our final answers
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
Division → Multiplication → Addition → Subtraction
B stand bracket O stand of D stand divisionM stand MultiplicationA stand for additionS stand for subtractionThe price, p, for different size orders of custom printed shirts, n, is given in the table.
Number of shirts ordered (n) 1 5 20 100
Price of order (p) $35 $75 $225 $1025
Can a linear equation be used to model the situation? If it can, what is the slope and the y-intercept of the equation?
linear: slope = 40, y-intercept = 35
linear: slope = 10, y-intercept = 25
A linear equation cannot be used.
linear: slope = 15, y-intercept = 0
Answers
Yes a Linear Equation can be used and the slope and the y-intercept of the equation are respectively; B: slope = 10, y-intercept = 25
How to Write an equation in Slope Intercept Form?
We are given the coordinates;
(n, p) = (1, 35), (5, 75), (20, 225), (100, 1025)
Now, the way to find the slope is;
m = (y2 - y1)/(x2 - x1)
m = (75 - 35)/(5 - 1)
m = 10
The equation that models this is;
(y - 35)/(x - 1) = 10
y - 35 = 10x - 10
y = 10x + 25
Thus, y-intercept is at x = 0.
y = 10(0) + 25
y = 25
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The system of equations is graphed on the coordinate plane.
y=x−1
y=−2x−4
Enter the coordinates of the solution to the system of equations in the boxes.
Answers
Answer:
(-1,-2)
Step-by-step explanation:
Hello!
The solution to the system is at the intersection between the two graphed lines.
Remember that a coordinate is written in (x,y) format, so we take the x-value of the points and the y-value of the point.
The coordinate is (-1, -2).
Step by step
You have two equations
y= x -1 (we will call equation A)
y= -2x-4 (we will call equation B)
Substitute equation A for the “y” value in equation B
x-1 = -2x -4
We need to isolate x to one side of the = so first we will add 1 to both sides
x-1+1 = -2x -4 +1
Combine like terms
x = -2x -3
Now add 2x to both sides
2x + x = -2x +2x -3
Combine like terms
3x = -3
Now solve for x by dividing both sides by 3
3/3x = -3/3
X= -1
Now we can solve for “y” by substituting our “x” value into equation A
y = -1 -1
y = -2
Now you can check your work by substituting your x and y values into with equation
A (-2) = -1 -1
A -2 = -2
B -2 = -2(-1) -4
B -2 = -2
Problem solved and graph is correct - see attached
On a recent trip to the convenience store, you picked up 2 gallons of milk, 6 bottles of water, and 7 snack-size bags of chips. Your total bill (before tax) was $25.65. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.90 more than a bottle of water, how much does each item cost?
Answers
Answer:
The water costs $1.90, the chips are $.95 and the milk is $3.80.
Step-by-step explanation:
Let m = milk
Let w = water
Let c = chips
2m+6w+7c =25.65 w = 2c m = w + 1.90
For the first equation, substitute w for 2C and m for w + 1.90 to get:
2(w+1.90) +6(2c) + 7c = 25.65
2w+3.8+12c+7c=25.65
2w+19c = 21.85
Now substitute 2c for w:
2(2c)+19c =21.85
4c + 19c = 21.85
23c = 21.85
c = .95 Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.
w = 2c
w=2(.95) = 1.90
m = w + 1.90 = 1.90+1.90 = 3.80
Graph line y=-1/5x-5 with y and x points
Answers
Answer:
Please see picture below.
Step-by-step explanation:
PLEASE HELP!!
From the triangle below, if AD=2 and CD=8. Find the Length of side AB
Answers
Evaluate functions from their graph g(−9)=
See the Correct Answer Attached!
Answers
Evaluating the function from the given graph, g(-9) = 1.
How to Evaluate a Function?To find the value of a function for a given x-value using a given graph, trace the x-value against the corresponding y-value on the y-axis.
To evaluate the function from the graph given, for g(-9), find the y-value that corresponds to the x-value of -9.
The graph shows that when x = -9, the corresponding y-value is 1.
Therefore, g(-9) = 1.
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60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER
Answers
1. The solution to the first percent puzzle is as follows:
75% 66²/₃ 11¹/₉
33¹/₃% 25% 22¹/₅% 3⁷/₁₀%
50% 37¹/₂% 33¹/₃% 5¹/₂%
50% 37¹/₂% 33¹/₃% 5¹/₂%
2. The solution to the second percent puzzle is as follows:
10% 90%
50% 5% 45%
50% 5% 45%
What is a percent puzzle?A percent puzzle is a puzzle that engages students to practice working with percentages.
The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.
The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.
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4. In the figure above ABCD is a parallelogram with
mLB = 60°, BC = XC = AZ = 4, XZ BC. What
is the perimeter of parallelogram ABCD?
Answers
Answer:
G. 24
Step-by-step explanation:
The perimeter of the figure is the sum of its side lengths. The given dimensions tell us all of the side lengths.
AnalysisTriangle BCX is given as an isosceles triangle with a base angle of 60° and side lengths of 4. Such a triangle is equilateral, so all side lengths will have a measure of 4.
The given information tells us all sides that appear parallel are parallel, so the figure consists of 4 equilateral triangles. Every short line segment has length 4.
PerimeterThe perimeter is the length of 6 short line segments, so is ...
P = 6×4 = 24
The perimeter of parallelogram ABCD is 24 units.
What is the best approximation of the solution to the system to the nearest integer values?
Answers
Answer:
(-2, 6)
Step-by-step explanation:
3x - 4y = -32
3x + 5y = 24
-9y = -56
y = [tex]\frac{56}{9}[/tex] = 6
3x - 4*[tex]\frac{56}{9}[/tex] = -32
3x - [tex]\frac{224}{9}[/tex] = -32
3x = -32 + [tex]\frac{224}{9}[/tex]
3x = -[tex]\frac{288}{9}[/tex]+ [tex]\frac{224}{9}[/tex]
3x = -[tex]\frac{64}{9}[/tex]
x = -[tex]\frac{64}{27}[/tex] = -2
what is the range if the given function?
Answers
Answer:
Second option
Step-by-step explanation:
The range is the set of output values a function can take. As shown in the table, as x is substituted in, y is the corresponding value.
a map has a scale of 2in: 6mi. if a two twons on a map is 10 in apart then how far apart are the real twons
Answers
Answer: 30 miles
Work Shown:
2 in : 6 mi
5*2 in : 5*6 mi
10 in : 30 mi
Complete the function for this graph.
-5
ertificati...
5
-5
y = |x|+ [?]
Hint: y = |x-h| + v
Answers
Answer:
-5
Step-by-step explanation:
The y coordinate of the vertex is -5.
In the town of Rockville, 3/5 of the students in middle school participate in organized sports after school. If 1/4 of them play basketball, what fraction of the students play basketball?
Answers
The fraction of students that play basketball is [tex]\mathbf{= \dfrac{1}{10}}[/tex].
What is the fraction of students that play basketball?The fraction of students that play basketball from the given information can be determined by assuming that the whole number of students in the middle school is whole i.e. (1)
Let us first determine the number of students that participate in sports, we have:
[tex]\mathbf{=1- \dfrac{3}{5}}[/tex]
[tex]\mathbf{= \dfrac{2}{5}}[/tex]
If 1/4 of these students play basketball, then we have:
[tex]\mathbf{= \dfrac{1}{4}\times (\dfrac{2}{5})}[/tex]
[tex]\mathbf{= \dfrac{1}{10}}[/tex] students play basketball.
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Saca la medida de la pala superior e inferior con respecto a las siguientes medidas
*No son de la misma medida*
Answers
La pala inferior y la pala superior tienen longitudes verticales de 55 y 65 centímetros, respectivamente. No es posible encontrar las longitudes horizontales.
¿Cuáles son las medidas de la pala superior y la pala inferior de un arco compuesto?
En esta pregunta debemos saber interpretar las dimensiones geométricas de un arco compuesto y determinar las longitudes de cada pala. Primero, determinamos las longitudes verticales de cada una:
Pala inferior
i = 65 cm - 10 cm
i = 55 cm
Pala superior
s = 65 cm
La insuficiencia de datos sobre longitudes horizontales no permite obtener las longitudes horizontales de cada pala.
La pala inferior y la pala superior tienen longitudes verticales de 55 y 65 centímetros, respectivamente. No es posible encontrar las longitudes horizontales.
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Solve the following system of equations by elimination. What is the value of x? x = 1.5 x = -1.5 x = 8 x = -8
Answers
Using the elimination method, the value of x in the system of equations is calculated as: 8.
How to Solve a System of Equations by Elimination?To solve a system of equations given using the elimination method, do the following:
Multiply 2x - 5y = 1 by 2 and multiply -3x + 2y = -18 by 5 to get the following:
4x - 10y = 2 --> eqn. 1
-15x + 10y = -90 --> eqn. 2
Add
-11x = -88
Divide both sides by -11
x = 8
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