if two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplemantary are the lines parallel?
When two lines in a plane are cut by a transversal and a pair of consecutive interior angles is supplementary, the lines are parallel.
Explanation:When two lines in a plane are cut by a transversal and a pair of consecutive interior angles is supplementary, the lines are parallel.
We know that consecutive interior angles are located on the same side of the transversal and are inside the two lines.
Since the consecutive interior angles are supplementary, they add up to 180 degrees. This indicates that the lines are parallel.
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Jay is cutting a roll of biscuit dough into slices that are 3/8 inch thick. If the roll is 10 1/2 inches long, how many slices can he cut?
He can cut 28 slices I have the same homework so I hope this helps much love and your welcome !!
Which expression is equivalent to (3a5 + b4)2
Answer:
The expression [tex]9a^{10}+6a^2b^4+b^8[/tex] is equivalent to the given expression.
Step-by-step explanation:
The given expression is
[tex](3a^5+b^4)^2[/tex]
Use algebraic formula:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](3a^5+b^4)^2=(3a^5)^2+2(3a^5)(b^4)+(b^4)^2[/tex]
[tex](3a^5+b^4)^2=3^2(a^5)^2+6a^5b^4+(b^4)^2[/tex]
Use exponent property:
[tex](a^m)^n=a^{mn}[/tex]
[tex](3a^5+b^4)^2=9a^{10}+6a^5b^4+b^8[/tex]
Therefore expression [tex]9a^{10}+6a^5b^4+b^8[/tex] is equivalent to the given expression.
Graph each equation, Question 5 and 6
There are 32 female performers in a dance recital. The ratio of men to women is 3;8. How may men are in the dance recital?
32 gal/min = what qt/h
32g/m = 32*60 = 1920 gallons per hour
1 gallon = 4 quarts
1920 *4 = 7680 quarts per hour
Answer: 7529.4 qt/hr
Step-by-step explanation:
The conversion used from gal to qt is:
1 gal = 4 qt
32 gal= [tex]\frac{4}{1}\times 32=128[/tex]
The conversion used from min to hr is:
60 min = 1 hr
1 min =[tex]\frac{1}{60}\times 1=0.017hr[/tex]
We are asked: 32 gal/min = ? qt/hr
[tex]32gal/min=\frac{128}{0.017}qt/hr=7529.4qt/hr[/tex]
Therefore, the conversion 32 gal/min = 7529.4 qt/hr
A jar contains 20 yellow marbles, 55 green marbles, and 25 purple marbles. You pick one marble from the jar at random. What is the theoretical probability of picking a green marble
Answer:
The theoretical probability of picking a green marble is 0.55. Step-by-step explanation:
Given : A jar contains 20 yellow marbles, 55 green marbles, and 25 purple marbles. You pick one marble from the jar at random.
To find : What is the theoretical probability of picking a green marble?
Solution :
Theoretical probability is defined as the number of favorable outcome divided by total number of outcome.
Yellow Marble = 20
Green Marble = 55
Purple Marble = 25
Total Number of marble = 20 + 55 + 25 = 100
Let G be the event of getting green marble.
So, Favorable outcome = 55
Theoretical probability of picking a green marble is
[tex]P(G)=\frac{55}{100}[/tex]
[tex]P(G)=\frac{11}{20}[/tex]
[tex]P(G)=0.55[/tex]
Therefore, The theoretical probability of picking a green marble is 0.55.
What is 5 radical 24, times, 2 radical 28? Please explain using steps!! :)
estimate the number of hot dogs sold by rounding each number in the table to the nearest thousand and finding the sum
what is the sum of 4.2x10^5 and 5.3x10^5
Find the domain and range of x + y = 1. Then determine whether it is a function.
The domain and the range of the equation x + y = 1 are both all real numbers. The equation is a function since each x-value corresponds to a unique y-value.
Explanation:The question is asking us to find the domain and range of the equation x + y = 1, and to determine whether it is a function.
The domain of an equation is the set of all possible x values. For this equation, we can substitute any real number for x, therefore, the domain is all real numbers.
The range of an equation is the set of all possible y-values. In this equation, for any given value of x, there will be a corresponding value of y (y = 1 - x). Therefore, the range of the equation is also all real numbers.
Whether an equation defines a function or not depends on whether each x-value corresponds to a unique y-value. For this equation, each x-value does correspond to a unique y-value, so it is indeed a function.
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Write 6.85• 10 to the 8th power in standard form
The cost for a business to make greeting cards can be divided into one-time costs, and repeated costs, suppose the total to make 300 cards is $900.00, and the total to make 650 is 1,600.00. What is the total cost to make 1,000 cards? Round your answer to the nearest dollar
A) 2,100.00
B) 2,300.00
C)2,500.00
D)3,000.00
Use the substitution method to solve the given system of equations. -6y+18=12x and y=3-2x
At one college, GPA's are normally distributed with a mean of 2.7 and a standard deviation of 0.5. What percentage of students at the college have a GPA between 2.2 and 3.2?
Final answer:
About 68.27% of students at the college have a GPA between 2.2 and 3.2 because these values correspond to z-scores of -1 and +1, respectively, in a normal distribution.
Explanation:
To find the percentage of students at the college who have a GPA between 2.2 and 3.2, we will use the properties of the normal distribution. The mean GPA is 2.7 and the standard deviation is 0.5.
First, we calculate the z-scores for the GPAs of 2.2 and 3.2:
z-score for 2.2 = (2.2 - 2.7) / 0.5 = -1
z-score for 3.2 = (3.2 - 2.7) / 0.5 = +1
The z-score represents the number of standard deviations a data point is from the mean. In a standard normal distribution, the percentage of data between z-scores of -1 and +1 is approximately 68.27%.
Therefore, about 68.27% of the students at the college have a GPA between 2.2 and 3.2.
There are two sizes of trucks available: larger truck with a 2.5-ton payload, and smaller trucks with 1.5-ton payload. To unload a freight train 21 larger trucks are needed . How many smaller trucks would be needed for the same job?
Answer:
It’s 35 because my math teacher told me
Step-by-step explanation:
In a recent survey 0.4 of the people surveyed said their favorite food was pizza 25% said it was hot dogs and 3/10 said it was popcorn, which food was favored by the greatest number of people
Answer:
Step-by-step explanation:
It would be pizza since it is 40% of the people
Given A = {18, 6, -3, -12} Determine all elements of set A that are in the solution of the inequality 2/3x + 3 < -2x -7
$14 socks; 15% discount
Pierre has a 15gram bag of cashews. When he examines the nuts, he finds that 4/7 of this amount is whole nuts and 1/3 is only half nuts. The remaining nuts are small pieces. How many grams consist of small pieces?
Please show work.
a. 2.8g b. 2.9g c. 13.5g d. 13.6g
what is the slope intercept form of the linear equation 4x + 2y = 24
drag and drop the appropriate number, symbol, or variable to each box
Kelly formed 7 equal groups out of 4.27 pounds of food find the number of pounds in each group
By noon, the temperature increased 21 from the morning low -13 what was was the tempature noon
In order to paint your bedroom, you buy 2 gallons of paint that cost $10.50 each, 3 paint brushes that cost $2.99 each, and 2 paint rollers that cost $1.25 each. Write an expression to model this situation. Then use the Distributive Property to find the total cost.
4(4x+3)=19x+9-3x+3 what are the steps
The steps of the expression are given below.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 4 (4x + 3) = 19x + 9 - 3x + 3
Now,
Solve the expression as;
The expression is,
⇒ 4 (4x + 3) = 19x + 9 - 3x + 3
⇒ 16x + 12 = 19x + 9 - 3x + 3
⇒ 16x + 12 = 16x + 12
⇒ 16x - 16x = 12 - 12
⇒ 0 = 0
Thus, The steps of the expression are given below.
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Please help!
Which statement best explains the value of 16 − (−3)? (1 point)
The additive inverse of −3 is −3, so 16 − (−3) = 19.
The additive inverse of −3 is −3, so 16 − (−3) = 13.
The additive inverse of −3 is +3, so 16 − (−3) = 19.
The additive inverse of −3 is +3, so 16 − (−3) = 13.
how can you divide larger dividends?
A generator runs for 2 1/2 hand uses 4 3/8 gals of fuel. How many gallons of fuel did the generator use each hour?
divide gallons used by time
4 3/8 = 35/8
2 1/2 = 5/2
35/8 / 5/2 = 35/8 * 2/5 = 70/40 = 7/4 (simplest form) = 1 3/4 gallons per hour
find the value of x. l || m. the diagram is not to scale
The value of x is 32 when l is parallel to m.
What is Angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
In the given figure l is parallel to m.
A transversal is passing through parallel lines hence corresponding angles are formed.
The angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
So 2x=64
Divide 2 on Both sides
x=32
Hence the value of x is 32⁰.
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what is 40÷4-(5-3)??
Answer:
8
Step-by-step explanation:
40/4=10-2=8