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Answers
Answer:
The value of x is 4, and the measure of the four angles are 100°, 80°, 100°, 80°.
Step-by-step explanation:
There is a rule that states the following: when two lines intersect, the verticle/opposite angles formed will have the same degree measure. Using this rule, we can infer that [tex]30x-20=10x+60[/tex]. To solve for x, isolate the variable all on one side of the equation. [tex]30x-10x = 60 + 20[/tex] ⇒ [tex]20x = 80[/tex] ⇒ [tex]x=4[/tex]. Since we now know the value of x, you can use that to figure out a pair of verticle angles, apply the value of x to any equation and you'll get that two of the four angles are all 100°. Since the rotation of a full circle is 360°, you can get that the sum of the remaining two angles is 360° - 100° * 2 = 360° - 200° = 160°. Because we know the remaining pair of verticle angles are equal, we can get that each of the remaining angles is equal to [tex]\frac{160}{2}[/tex] or 80°, so the measure of all four angles are 100°, 80°, 100°, 80°.
Related Questions
which rule must be used to find the number of strings of four decimal digits that have exactly three digits that are 9s?
Answers
The product rule must be used to find the number of strings of four decimal digits, that have exactly three digits that are 9s.
What is product rule ?
The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.
To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the product rule,
In first digit 1 possible way between 0 to 9
In second digit 1 possible way between 0 to 9
In third digit 1 possible way between 0 to 9
In fourth digit 9 possible ways between 0 to 9
That's mean 1 * 1* 1* 9* 4 = 36
Thus 36 possible ways.
The product rule must be used to find the number of strings of four decimal digits.
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Can you use SSA to prove a triangle is congruent?
Answers
Yes, you can use the Side-Side-Angle (SSA) Congruence Theorem to prove that two triangles are congruent.
The SSA Congruence Theorem states that if two sides of one triangle have the same length as two sides of another triangle, and the included angle in the first triangle is congruent to the included angle in the second triangle, then the two triangles are congruent.
Here is an example of how you can use the SSA Congruence Theorem to prove that two triangles are congruent:
Let's say you have two triangles, triangle ABC and triangle DEF. You are given that the length of side AB is equal to the length of side DE, the length of side AC is equal to the length of side DF, and angle A is congruent to angle D.
To prove that triangle ABC is congruent to triangle DEF, you would need to show that all of the corresponding parts of the triangles are congruent. Since the lengths of two sides (AB and DE) and the included angle (angle A and angle D) are congruent, you can use the SSA Congruence Theorem to conclude that triangle ABC is congruent to triangle DEF.
It's worth noting that the SSA Congruence Theorem is not always sufficient to prove that two triangles are congruent. If the conditions of the theorem are not met, you may need to use other methods, such as the ASA Congruence Theorem or the HL Congruence Theorem, to prove congruence.
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Are Mean and median same?
Answers
Mean and Median are not the same.
Mean is the average value of a given dataset. Mean is calculated by adding all the values in the dataset and divided by the number of values.
Median is defined as the number in the middle of the dataset. Median is calculated by arranging the values in ascending order and finding out the middle most term. If there are two middle terms, then we calculate the average of both.
Mean is the arithmetic average, while median is the positional average. There may be various external factors that contribute in defining the mean. So for uneven data, median is the more robust value. Mean defines the central value of data, but median defines the midpoint of data and classify the data points to two sets, higher value or lower value.
So mean is the average of the given dataset and Median is the mid value of the dataset when arranged in ascending order.
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What are the 3 types of solutions when graphing a system of equations?
Answers
Answer:
infinite, no solutions, and uniquely solution
Step-by-step explanation:
• Question 2
In the graph of an inequality, the region below the dashed horizor
What inequality does the graph represent?
Answers
The linear inequality represented by the graph is given as follows:
y < 1/4x + 2.
How to define the inequality?The dashed line is a linear function, hence the slope-intercept format of the inequality is given as follows:
y < mx + b.
(the sign is < because the line is dashed and not solid).
In which the coefficients are given as follows:
m is the slope, representing the rate of change of the linear function.b is the y-intercept, representing the value of y when the graph of the linear function crosses the y-axis.The line crosses the y-axis at y = 2, hence the intercept b is given as follows:
b = 2.
When x = -8, y = 0, thus when x increases by 8, y increases by 2, meaning that the slope is given as follows:
m = 2/8
m = 1/4.
Thus the inequality is given as follows:
y < 1/4x + 2.
Missing InformationThe graph of the linear inequality is given by the image shown at the end of the answer.
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Remember, jed's height is within 3 inches of pablo's height. Describe the solutions in words. Jed can be 67 inches or shorter. At least 67 inches, but at most 73 inches. 73 inches or taller. 67 inches or shorter, or 73 inches or taller.
Answers
at least 67 inches, but at most 73 inches if Jed can be 67 inches or
shorter
The inequality in which involves one or more rational expressions is Rational inequality.
What is inequality?
Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.
An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.
67 ≤ x ≤ 73 are the solutions to the absolute value inequality |x − 70| ≤ 3
the complete question is
What are the solutions to the absolute value inequality |x − 70| ≤ 3? Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3 or as x − 70 ≤ 3 and x − 70 ≥ −3.
Answer: 67 ≤ x ≤ 73
Remember, Jed's height is within 3 inches of Pablo's height.
Describe the solutions in words.
Jed can be
67 inches or shorter.
at least 67 inches, but at most 73 inches.
73 inches or taller.
67 inches or shorter, or 73 inches or taller.
Just found out it's the 2nd choice.
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Answer:
B: at least 67 inches, but at most 73 inches.
Step-by-step explanation:
What are the 4 steps of the 4 step method?
Answers
The steps of the step method are:
1. Analyze the situation: Identify the problem and its causes.2. Plan: Develop a plan of action to address the problem.3. Execute: Implement the plan.4. Evaluate: Monitor and measure the results of the plan.The Benefits of Using the 4-Step Method to Solve ProblemsProblem solving is an essential skill in life. It helps us to find solutions to difficult situations and can be applied to almost any area of life. One effective way to approach problem solving is to use the 4-step method. This method is designed to help you analyze a situation, plan an action, execute the plan, and evaluate the results. In this essay, we will discuss the benefits of using the 4-step method to solve problems.
The first step of the 4-step method is to analyze the situation. This involves identifying the problem and its causes. Taking the time to understand the problem before attempting to solve it can help ensure that the solution is effective. By analyzing the situation, you can determine the most effective solution and avoid wasting time and resources on ineffective solutions.
The second step of the 4-step method is to plan an action. This involves developing a plan of action to address the problem. Taking the time to plan ahead can help ensure that the solution is tailored to the specific situation. It can also help to minimize the risk of unexpected problems or delays during the execution of the plan.
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At 11:45 AM. Jason glanced at the clock. His doctor's appointment was in 2 1/2hours. At what time was his appointment? please help me
Answers
Answer:
14: 15 or 2: 15 pm
Step-by-step explanation:
1/2 times 60 = 30 minutes
2 1/2 hours = 2 hours and 30 minutes
Take
11:45
+ 2:30
13:75
1 hour only has 60 minutes, so 13:75 = 14:15 or 2:15 pm
So, his appointment was at 2:15 pm
Hana i planning a park day for the next month to give her friend ome exercie! The local park open it path for biker every 12 day and open it’ lake for paddling every 8 day. Today, both the biking and paddling option are open. Which two number entence will help Hana pick the next date where both the bike lane and lake padding will be open?
Answers
If a local park is open for biking every 12 day open for paddling every 8 day and if today the park is open for both options, then the next date when the park will be open will be on the 24th day. So Hana should pick 24th day from today next.
Every 12 day the local park is open its path for biking and every 8 day they open their lake or paddling. That is in every multiple of 12 days the biking option is available and every multiple of 8 days the paddling option is available.
If today both the biking and paddling option are open, then the next day where both options will be open can be determined by calculating the least common multiple of 12 and 8.
12 = 2×2×3
8 = 2×2×2
LCM (12, 8) = 2×2×2×3
LCM(12, 8) = 24
LCM of 12 and 8 is 24. So 24 days from today, the park will be open for both options.
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how many permutations of abcde are there in which the first character is abc and the last character is cde
Answers
Total number of permutations of abcde in which the first character is a, b, or c and the last character is c, d, or e is 48 permutations.
Case 1 : First letter is "a", last letter is any of {c, d, e}. Hence there are 3! ways of arranging the remaining three letters
3! * 3 = 18 combinations.
Case 2 : First letter is "b", last letter is any of {c, d, e}. Hence there are 3! ways of arranging the remaining three letters
3! * 3 = 18 combinations.
Case 3 : First letter is "c", last letter is any of {d, e}. Hence there are 3! ways of arranging the remaining two letters
3! * 2 = 12 combinations.
Hence, total number of combinations = 18 +18 + 12 = 48 permutations.
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This problem has a fraction bar. What
operation is the same as a fraction bar?
Division
Addition
Subtraction
Multiplication.
Answers
Answer:
Division
Step-by-step explanation:
Simple, the fraction bar basically represents the operation of division in math!
Is AAA a similarity theorem?
Answers
It is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.
What is the AAA similarity theorem?According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.
Theorem: Two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.
It can also be rephrased as the AAA (angle-angle-angle) similarity theorem.
A triangle is said to be comparable to another triangle if any two of its three angles are equal to any two of its three angles.
Therefore, it is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.
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Identify the number fo zeros for each function. Show your work.
1. P(x)=x³+2x²-12x+1
2.P(x)=2x⁵-5x+10
3.P(x)=3x⁴+2x
Answers
The number of zeros for each function is given as follows:
1. Three zeros.
2. One zero.
3. Two zeros.
How to obtain the number of zeros for each function?The number of zeros for each function is obtained looking at the graph of the function, counting the number of times that the function either touches or crosses the x-axis, which is the horizontal axis.
Thus the graph for each function is plotted, using a graphing calculator, as shown by the image at the end of the answer, and the number of zeros for each of the functions is given by the number of times that the function touches or crosses the x-axis.
The colors of each function are given as follows:
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How many terms are in the binomial expression 2x 3 5?
Answers
A binomial expression is of the form (x + y)ⁿ. The given binomial expression (2x + 3)⁵ has 6 terms in it.
Binomial is said to be the algebraic expression containing exactly two terms.
Examples of binomials are 4x² + 5y², xy² + xy, x + y, x² + 3, etc.
The number of terms in the binomial expression (x + y)ⁿ is given as,
Number of terms = n + 1
where, n is the power of ( x + y )
In the above given binomial expression, (2x + 3)⁵, n = 5.
N = n + 1 = 5 + 1 = 6
Thus, there are a total of 6 terms in the above expansion.
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determine whether an observational or experimental study is appropriate to address the following statement. a car wash operator wants to find out if providing a discount for local residents will generate additional revenue.
Answers
The statement is "a car wash operator wants to see if offering a discount to local residents would create a greater income." This is an observational study.
What is observational or experimental study?A method of study in which participants are observed or certain outcomes are measured. There is no attempt made to change the outcome (for example, no treatment is given).
Experimental investigations include introducing an intervention and observing its results. Experimental investigations are frequently randomized, which means that the individuals are assigned to groups at random. People who qualify are randomly allocated to one of two or more groups in a randomized controlled experiment (RCT).
Cohort studies, case-control studies, and cross-sectional studies are the three different kinds of observational research.
In an observational study, the researchers just observe the participants without interfering with them or attempting to sway the results. In other words, neither the researchers nor the individuals are placed in experimental groups or in charge of the therapies.
Thus, the above mentioned statement is an observational study.
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pls help me im begging you i need a B in this class
Answers
g(x)=-x^2 is the reflection of your function f(x) over the x-axis.
What is function?
The function f(x)=x2 is a parabola facing upward with its vertex at (0,0), and including the points (1,1), (2,4), (-1,1), and (-2,4).
A function that is a reflection across the x-axis compared to f(x) would be the mirror image of f(x). It would have the opposite y-values for each x-value. It would also have its vertex at the same place as f(x).
Therefore, it would be a parabola pointing downward, with the points (1, -1), (2,-4), (-1,-1), and (-2,-4).
To get the opposite values for y, you simply need to place a negative in front of the x2. So the function would be g(x) = - x2.
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What is the 4 type of polynomial?
Answers
Answer:
Binomial,Trinomial,Monomal,Linear equation
Step-by-step explanation:
5+2 x 3². for this question I have put 16 but apparently it’s incorrect
Answers
Answer:
23
Step-by-step explanation:
Given in the picture below (BODMAS rule is applied)
I hope my answer helps you
Answer:
23
Step-by-step explanation:
5 + 2 x 3² = (remember PEMDAS)
5 + 2 x 9 =
5 + 18 =
23
How do you solve a mean table?
Answers
Mean from a frequency table is when we find the mean average from a data set which has been organised into a frequency table.
To calculate the mean we find the total of the values and divide the total by the number of values. The number of values is the total frequency. This can be abbreviated to nn.
[tex]Mean = \frac{total}{number of values} =\frac{total}{n}[/tex]
We can use an extra column to help.
Mean is a measure of central tendency, it is a value that can be used to represent a set of data.
E.g. The frequency table shows the number of people living in 1616 flats.
There are 55 flats with 11 person living there, so we work out 1\times5=51×5=5
There are 66 flats with 22 people living there, so we work out 2\times6=122×6=12
There are 33 flats with 33 people living there, so we work out 3\times3=93×3=9
There are 22 flats with 44 people living there, so we work out 2\times4=82×4=8
The number of values (n)(n) is the total frequency, here n=16n=16
mean = total/n
=34/16
= 2.125
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How do I solve this?
Given h(x)=3x-5,find h(3)
Answers
9-5
Answer 4
Answer:
4 is correct
Step-by-step explanation:
How do you find the value of X step by step?
Answers
Bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Now, According to the question:
The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Standard Equation
The standard form to find the value of X in multiplication operation is
Multiplicand × Multiplier = Product
Let us take Multiplier as x,
Multiplicand × x = Product
Then the formula to find the value of x is
X = product / Multiplicand
Example of how to find the value of x.
Find the value of x for the given expression: 10x = 50
Given: 10x = 50
X = 50/10
X = 5
Therefore, the value of x is 5.
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The graph of y = is translated. The translation is defined by (x + 1, y – 2).
Which is the graph of the translated image?
A B C D
Answers
Answer:
we know that
The rule of the translation is
That means
The translation is units to the right and units down
therefore
the answer in the attached figure
Step-by-step explanation:
please help me with the ratio
Answers
Answer:
total number of votes = 5696
Step-by-step explanation:
the 5 part of the ratio relates to 3560 no votes , then
3560 ÷ 5 = 712 ← value of 1 part of the ratio , then
3 × 712 = 2136 ← number of yes votes
total number of votes = yes + no = 2136 + 3560 = 5696
For what value of A is x 5 a factor of x³ 3x² ax 10?
Answers
The value of a is ( x - 5 ) factor of f (x) = x ³ - 3x² + ax -10 is found to be 8 .
What is a factor of an equation ?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.
Let f (x) = x ³ - 3x² + ax -10 be the given polynomial.
By factor theorem, ( x - 5 ) is the factor of f (x) , if f ( 5 ) = 0
Therefore,
f ( 5 ) = 3 ( 5 )² + a ( 5 ) - 10 = 0
125 - 75 + 5a - 10 = 0
5a = -40
a = -8
Hence, a = -8
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What is a slope grade 11?
Answers
In grade 11 math, the slope is a concept that is typically introduced in the study of linear equations and graphing.
The slope of a line serves as a gauge for its steepness. It is defined as the change in y (the vertical distance) divided by the change in x (the horizontal distance) between two points on the line.
A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope rises as it goes from left to right, while a line with a negative slope falls as it goes from left to right. A line with a slope of zero is horizontal, while a line with an undefined slope is vertical.
The slope is often represented by the letter m in the equation of a line, which is written in the form y = mx + b. The slope of the line is the coefficient of the x term (the m in the equation).
For example, the slope of the line represented by the equation y = 3x + 4 is 3, while the slope of the line represented by the equation y = -2x + 1 is -2.
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Find the height of a standard yield sign when the area is 558 square inches and each side is 36 inches.
Answers
The height of the yield sign is 15.5 inches.
The total amount of space allotted to a triangle's three sides in a two-dimensional plane is known as the area of a triangle. The fundamental formula for a triangle's area is A = [tex]\frac{1}{2}*b*h[/tex], which states that the area of a triangle is equal to half the product of its base and height.
To find the height of the yield sign, we need to use the following formula, which is:
area= length*height
The result of substituting in the data we are aware of is:
558=36*h
h= [tex]\frac{558}{36}[/tex]
h= 15.5
Therefore the height of a standard yield sign when the area is 558 square inches and each side is 36 inches is 15.5 inches.
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How many solutions has the linear equation 3x 2y 5?
Answers
In this given equation, any value of x and y will work, which will cause it to have infinite number solutions
What is an equation?
An equation is a mathematical statement showing that two or more values or mathematical expressions are equal or equivalent.
We represent an equation with the equation symbol (=).
Given the equation:
3x + 2y = 5
The lineear equation has infinitely many solutions
We know the standard form of a linear equation is:
ax + by = C
In this given equation, any value of x and y will work, which will cause it to have infinite number solutions
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what is the smallest sample in the list below that will satisfy the conditions for the use of a normal model to represent the sampling distribution? a. 30 b. 15 c. 25 d. 20
Answers
The smallest sample size that will satisfy the conditions for the use of a normal model to represent the sampling distribution is 30, as stated in option (a).
The smallest sample size that will satisfy the conditions for the use of a normal model to represent the sampling distribution is determined by the Central Limit Theorem, which states that if the sample size is greater than or equal to 30, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
According to this theorem, if the sample size is greater than or equal to 30, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. Therefore, the smallest sample size that will satisfy the conditions for the use of a normal model is 30. The answer is therefore option (a).
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How do you find the square root of a number without a calculator?
Answers
Without using a calculator, the square root of an integer is
1. Use multiplication to calculate the ideal square root.
2. Use division to calculate the ideal square root.
3. Use nearest perfect square number to find the square root of non-perfect squared numbers.
Given that,
We need to figure out how to calculate a number's square root without a calculator.
We know that,
There are some ways to find
First
Use multiplication to calculate the ideal square root.
A number that, when multiplied by itself, equals the first number is the number's square root.
3 is therefore the square root of 9.
Because 3 multiply by 3 is 9
That is 3×3=9
√9=3
Second
To calculate the square root, we use division.
A whole number can also be divided by a number until you get an answer that is the same as the number you used to divide the whole number in order to determine its square root.
For instance: Four is the square root of sixteen.
Because 16 divided by 4 is 4
That is 16÷4=4
√16=4
Third
We must compare the number with a nearly perfect squared number in order to determine the square root of non-perfect squared numbers.
For example: the square root of 63 is not a perfect square.
So,
The closest perfect square integer right now is 64, and its square root value is 8.
So, we can say the square root of 63 as 7.98.
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What are the 2 types of roots and their functions?
Answers
Real roots and distinct roots are the two types of roots of quadratic function.
Given,
Real roots;-
We are aware that anytime we resolve a linear or quadratic equation, we obtain the equation's value variable, or in other words, we identify the equation's solution. We refer to this "solution" as the real roots. For instance, when we solve the equation x27x+12=0, the real roots come out to be 3 and 4.
Distinct roots;-
Whenever the answers to a quadratic equation have two distinct values that may be represented by real numbers on a number line. It is known as distinct roots.
Here,
How do you tell which roots are distinct and real?
The discriminant is the expression b² - 4ac for the quadratic equation ax² + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b² - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b² - 4ac = 0.
That is,
The quadratic function has real roots and distinct roots.
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