The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A = 120 − 2x ∠B = 70 + x ∠C = 105 − x2 ∠D = 40 + 4x
Answers
The value of x from the parallelogram ABCD is 10.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
Given that, ∠A=120-2x, ∠B=70+x, ∠C=105-x² and ∠D=40+4x.
The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary.
Here, ∠A and ∠D are consecutive angles
Now, 120-2x+40+4x=180
⇒ 160+2x=180
⇒ 2x=20
⇒ x=10
So, ∠A=120-2x=100, ∠B=70+x=80, ∠C=160-6x=100 and ∠D=40+4x=80
Therefore, the value of x is 10.
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"Your question is incomplete, probably the complete question/missing part is:"
The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A=120-2x, ∠B=70+x, ∠C=160-6x and ∠D=40+4x.
Related Questions
Use: 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7 to construct a box-and-whisker plot. List the maximum, minimum, and quartiles below. has to be a sentence
Answers
A box-and-whisker plot which represent the given data set is shown in the image attached below.
The five-number summary for the given data set have been listed correctly below.
What is a box-and-whisker plot?In Mathematics, a box-and-whisker plot is sometimes referred to as a box plot and it can be defined as a type of chart that is used for the graphical or visual representation of the five-number summary of a data set with respect to locality, skewness, and spread.
By using an online box-and-whisker plot calculator, the five-number summary for the given data set include the following:
Minimum = 0.First quartile = 4.Median = 7.Third quartile = 9.Maximum = 11.By critically observing the box-and-whisker plots (see attachment), we can logically deduce that all of the five-number summary for the given data set are correctly listed.
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What is the next term in the sequence below?
0.35, 1.05, 3.15, 9.45, …
A. 15.75
B. 27.75
C. 28.35
D. 85.05
Answers
the answer is c because each number is the previous x3
Answer:
Its C
Step-by-step explanation:
What is the quadratic equation??
Plsss reply I’ll mark as brainliest
Answers
Hello !
1. A quadratic equation results in the form: ax² + bx + c
2. Calculate the discriminant: Δ = b² - 4ac
3. Calculate x with the dicriminant: (-b ± √Δ) / 2a
Example:
3x² + 7x - 2 = 0 is a quadratic equation.
x = (-b ± √(b² - 4ac)) / 2a
= (-7 ± √(7² - 4*3*(-2))) / (2*3)
= (-7 ± √73)/6
A cardboard box manufacturing company is building boxes with length represented by x + 1 width by 5-x and height by x-1
Answers
The volume of the cardboard box with given dimensions changes at the fastest average rate over the interval of option c. [1,5].
Length of the cardboard box = x + 1
Width of the cardboard box = 5 - x
Height of the cardboard box = x - 1
Volume of the box V (x) = length × width × height
Substitute the values we have,
V(x) = (x+1)(5-x)(x-1)
Expanding this expression gives,
V(x) = -x³ + 5x² + x - 5
To know where Volume is changing at the fastest average rate,
Find the maximum value of the absolute value of the derivative of V(x) over each of the given intervals.
Taking the derivative of V(x), we get,
V'(x) = -3x²+ 10x + 1
Taking the absolute value of this expression, we get,
|V'(x)| = 3x² - 10x - 1
Now, we can calculate the maximum value of |V'(x)| over each interval,
At [1,2]
|V'(1)| = 8
|V'(2)| = 9
[1,3.5]
|V'(1)| = 8
|V'(3.5)| = 0.75
[1,5]
|V'(1)| = 1
|V'(5)| = 24
[0,3.5]
|V'(0)| = 1
|V'(3.5)| = 0.75
The maximum value of |V'(x)| occurs on interval [1,5].
Therefore, the volume of the box is changing at the fastest average rate over the interval option c . [1,5].
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The above question is incomplete, the complete question is:
A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 − x, and height by x − 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate?
a. [1,2]
b. [1,3.5]
c. [1,5]
d. [0,3.5]
5. Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a
hoodie and a pair of jeans.
c. If the regular price of an item is x dollars, what is the discount price in dollars?
Answers
Answer:
0.7x=discounted price
Step-by-step explanation:
if you have 30% off, you pay 70% of the original price
to get 70% you multiply by 0.7
Find (fog)(x).
f(x) = 6x
g(x) = x + 3
Write your answer as a polynomial in simplest form.
(fog)(x) = ????
Answers
Answer:
\((fog)(x)=6x+18\)
Step-by-step explanation:
We are given:
f(x)=6x
and g(x)=x+3
We need to find (fog)(x)
(fog)(x) =f(g(x)) i.e we will put value of g(x) into f(x) i.e
\((fog)(x)=f(g(x))\\f(g(x))=6(x+3)\\f(g(x))=6x+18\)
So, \((fog)(x)=6x+18\)
(-4x + 5)-( 6x +7)=0
Answers
Answer:
x = -1/5
Step-by-step explanation:
*Steps as a proof*
_________
(-4x + 5)-(6x + 7) = 0
[given]
_____________
1(-4x + 5)-1(6x + 7) = 0 [identity property of multiplication]
1(-4x + 5) + -1(6x + 7) = 0. [additive inverse property]
___________________________________
1(-4x + 5) + -1(6x) + -1(7) = 0 [distributive property]
___________________________________
(-4x + 5) + (-6x - 7) = 0 [multiplying anything by 1 is the same]
___________________________________
(-4x + -6x) + (5 + -7) = 0 [associative property of addition]
_____________________________________
-4x + -6x + (5 + -7) = 0 [subtraction property of equality] - (5 + -7). - (5 + -7)
_______________________
-4x + -6x = -(5 + -7) [simplification]
-4x + 6x = -1(5 + -7) [identity property of multiplication]
-4x + -6x = -1(5) + -1(-7) [distributive property]
-4x + -6x = -5 + 7 [simplification]
-4x + -6x = 2 [simplification]
-10x = 2 [division property of equality]
÷10 ÷10
______
-x = 2/10 [negative one property of multiplication]
×-1 ×-1
x = -2/10 [simplification]
x = -1/5 [simplification]
__________________________
There are 32 chickens and 12 sheep on a farm. The ratio of sheep to horses is 4:1. Write a ratio expressing the relationship between the chicken and the sheep. Then explain what that ratio means. Determine the number of horses on the farm.
Answers
This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:
\(12 * 0.25 = 3\)
What is ratio?Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.
For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.
The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.
To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:
\(chickens : sheep = 32 : 12\)
We can simplify this ratio by dividing both sides by 4:
\(chickens: sheep = 8: 3\)
This means that for every 8 chickens on the farm, there are 3 sheep.
To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:
\(sheep : horses = 4 : 1\)
We can simplify this ratio by dividing both sides by 4:
\(sheep : horses = 1 : 0.25\)
This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:
\(12 * 0.25 = 3\)
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need help converting the point slope form equation to slope intercpt form(y-1)=1/2(x-6)(y+10)=1/3(x+9)
Answers
The standard form of the slope intercept equation is written as
y = mx + b
Where m = slope and b = intercept
\(\begin{gathered} (y\text{ - 1) = }\frac{1}{2}(x\text{ - 6)} \\ \text{Firstly, open the parentheses} \\ y\text{ - 1 = }\frac{1}{2}\cdot\text{ x - }\frac{1}{2}\cdot\text{ 6} \\ y\text{ - 1 = }\frac{1}{2}x\text{ - }\frac{6}{2} \\ y\text{ - 1 = }\frac{1}{2}x\text{ - 3} \\ \text{Isolate y} \\ y\text{ = }\frac{1}{2}x\text{ - 3 + 1} \\ y\text{ = }\frac{1}{2}x\text{ - 2} \end{gathered}\)someone please help with my geometry
Answers
Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.
Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.
You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.
Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.
Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.
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Best describes , whats the best possible answer
Answers
Answer:
D?
Step-by-step explanation:
I'm not completely sure, but there are 2 different 180 degree lines that y falls on. On one line (y+70=180) it is for sure 110 degrees
When measured on the other line it is (y+70+x=180) I'm not too familiar with this??
What Pythagorean triple is made using the Pythagorean identity and the following numbers?
x = 2, y = 1
1. 3, 4, 5
2. 4, 1, 25
3. 2, 1, 2
4. 4, 1, root 5.
Answers
The Pythagorean triples here are; 3, 4, 5. Option 1
What is a Pythagorean triple?We define a Pythagorean triple as a^2+b^2 = c^2 where a, b and c are the three positive integers. Given that we can find the Pythagorean triple from; (x2 - y2)2 + (2xy)2 = (x2 + y2)2
Where; x = 2, y = 1
Substituting values have;
(2^2 - 1^2)^2 + (2*2*1)^2 = (2^2 + 1^2)^2
This results to;
3^2 + 4^2 = 5^2
9 + 16 = 25
25=25
Therefore the Pythagorean triples here are; 3, 4, 5. Option 1
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You pick a marble, roll a die, and pick a card. How many outcomes are possible?
Answers
The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
How to determine How many outcomes are possibleTo determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.
1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.
2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.
3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.
To find the total number of possible outcomes, we multiply the number of outcomes for each event together:
Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)
Total number of outcomes = n × 6 × 52
Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
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what is the e in 2e = 2
Answers
Given data:
The given expression is 2e=2
The given expression can be written as,
\(\begin{gathered} 2e=2 \\ e=\frac{2}{2} \\ =1 \end{gathered}\)Thus, the value of e is 1.
Find the value of angle GFD.
Group of answer choices
24
58
34
122
Answers
Answer:
∠GFD = 58°Step-by-step explanation:
∠F = 180 - 24 - 34
∠F = 122
∠GFD = 180 - 122
∠GFD = 58°
change the decimal to a fraction in simple form.
Answers
Answer:
The answer is 3/4
Answer:
it's 3/4
Step-by-step explanation:
.075 as a fraction is 75/1000 and 75 ÷ 1000 is 0.75 and 0.75 as a fraction is 3/4
When rolling a 6-sided die twice, determine P(sum of 4). three thirty sixths five thirty sixths eight thirty sixths two sixths
Answers
On each roll of a 6-sided die, we have 6 possible outcomes.
Then if we roll it twice, we will have 36 outcomes.
The outcomes where the sum is 4 are:
roll 1 roll 2 sum
1 3 4
3 1 4
2 2 4
Son in 3 out of 36 outcomes the sum can be 4, then the probability opf rolling a sum of 4 is given by the quotient:
P = 3/36
P = 1/12
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help please i rlly need help and if you don't know then don't answer bc i need a right answer ;(
Answers
Answer:
BAD=100° (given)
ADC=105° (180-75)
DCB=50° (vertical angles)
CBA=105° (same as ADC)
If 15+3x=3(2−2x), then x= [blank]
Answers
Answer:
x = -1
Step-by-step explanation:
15+3x=3(2−2x)
Distribute
15+3x = 6 -6x
Add 6x to each side
15+3x+6x = 6-6x+6x
15+9x = 6
Subtract 15 from each side
15-15+9x = 6-15
9x = -9
Divide by 9
9x/9 = -9/9
x = -1
What number can be divided into 2 equal groups without a remainder?
Answers
Answer:
Step-by-step explanation:
When we divide one number by another and there is no remainder, the divisor A the quotient are the of the first number.
8/2=4
A school bus started from the zoo, at point (4, -4), and then traveled 10 units up and 6 units to the left to reach the school. Graph the locations of the zoo and the school.
Answers
Answer: ( -2, 6)
Step-by-step explanation:
Answer:
(-2,6)
Step-by-step explanation:
Hope this helps :)
What is the value of x?
Answers
28% of 2.97 to the nearest hundredth
Answers
Answer:
83.16%
Step-by-step explanation:
Convert 28% into a decimal 0.28 Then multiply 0.28 by 2.97
Which expressions represent a perfect square monomial and its square root? Check all that apply. 121; 11 4x2; 2x 9x2 – 1; 3x - 1 25x; 5x 49x4; 7x2
Answers
Answer:
its 1,2,and 5
Step-by-step explanation:
Answer:
A, B, E
Step-by-step explanation:
Edge
2. At the gym, Alex spends 24 minutes doing
resistance training for every 30 minutes
spent doing cardio exercises, Carisa spends
15 minutes on resistance for every
20 minutes on cardio, and Manuel spends
14 minutes on resistance for every
15 minutes on cardio. Which person has the
greatest ratio of minutes spent on resistance
to minutes spent on cardio? (Example 2)
Alex
Resistance (min)
Cardio (min)
Carisa
Resistance (min)
Cardio (min)
Manuel
Resistance (min)
Cardio (min)
Answers
Answer:
Manuel
Step-by-step explanation:
You should set up a proportion graph first such as r:c where r is the amount of minutes spent on resistance and c is the amount of minutes spent on cardio.
Alex's ratio: 24:30
Carisa's ratio: 15:20
Manuel's ratio: 14:15
Now you have to find the lowest common multiple (lcm) of the cardio minutes. Their lcm is 60. Now the ratios look like this:
Alex's ratio: 48:60
Carisa's ratio: 45:60
Manuel's ratio: 56:60
The ratio with the highest first number is considered larger. In this case its Manuel since he has the number 56.
A pilot flew a jet from City A to City B, a distance of 2400 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 5 h 30 min. What was the speed from City A to City B?
Answers
The speed from City A to City B is 873.33 mi/h.
What is the speed, distance and time?
That is speed = distance ÷ time. Or to put it another way, distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.
Let's call the speed from City A to City B x. The speed on the return trip was 1.2x. The total distance traveled was 2400 + 2400 = 4800 mi. The total time taken was 330 minutes, which is 330/60 = 5.5 hours. The average speed is the total distance traveled divided by the total time taken, so:
4800 mi / 5.5 h = 873.33 mi/h
The total speed for both legs of the trip is 873.33 + 873.33 = 1746.66 mi/h
The speed for just one leg of the trip is half of the total speed, so the speed from City A to City B is 1746.66/2 = 873.33 mi/h.
Hence, the speed from City A to City B is 873.33 mi/h.
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What is (20-(-16))=20+16=36
Answers
Answer:
Step-by-step explanation:
i think its 5/144=0.03472
12 out of 15 randomly selected
students in a class said they would vote
for Kim for class president.
Which is most likely true about all 35
students in the class?
Answers
Answer:
28 students would vote for kim
Step-by-step explanation:
Well first you do 12/15 which would be 0.8
Now to find how many students in that class said they would vote for Kim for class president, we multiply 0.8 by 35 to get that 28 students said they would vote for kim
Emily bought 412 appetizers and she invited 22 people to his party. Use
compatible numbers to estimate the number of appetizers each guest can
have.
OA) 10
OB) 15
OC) 20
OD 25
Answers
If f(x)=x-9 and g(x)=-6x-3 which statement is true
Answers
Answer:
-1 is not in the domain of (f o g)(x)
Step-by-step explanation:
f(x) = sqrt(x - 9)
g(x) = -6x - 3
(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)
(f o g)(x) = sqrt(-6x - 3 - 9)
(f o g)(x) = sqrt(-6x - 12)
Let x = -1:
(f o g)(-1) = sqrt(-6(-1) - 12)
(f o g)(-1) = sqrt(6 - 12)
(f o g)(-1) = sqrt(-6)
Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).