Write a complete two-column proof for the following information.
Given: m1 = 62° and lines t and l intersect
Prove: m4 = 62°
Answers
The measure of angle 1 and angle 4 are equal, that is 62°, by vertical angle theorem.
Given that, m∠1=62° and lines t and l intersect.
From the given figure,
m∠1 and m∠4 are vertically opposite angles.
Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
Here, m∠1 =m∠4=62°
Hence, it is proved.
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Related Questions
In the diagram at right, DE is a midsegment of triangle ABC. If the area of triangle ABC is 96 square units, what is the area of triangle ADE? Explain how you know.
Answers
The area of triangle ADE is,
⇒ A = 48 square units
We have to given that,
In the diagram , DE is a midsegment of triangle ABC.
And, The area of triangle ABC is 96 square units
Now, We know that,
Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.
Hence, the area of triangle ADE is half the area of triangle ABC,
That is,
A = 96 / 2
A = 48 square units
Thus, The area of triangle ADE is,
⇒ A = 48 square units
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what is the domain\(y=\sqrt{25-x^{2}\)
Answers
Given equation: y = √25 - x^2
The domain of this equation is all real values of x such that √25 - x^2 is defined.
Step 1: Write the equation in terms of x only so that we can identify the domain:
y = √25 - x^2
=> x^2 = √25 - y
=> x = √(√25 - y)
Step 2: Since "√25-y" must be greater than or equal to 0 for the equation to be defined, we can set the inequality to find the domain for x as:
√25 - y ≥ 0
=> -y ≥ -√25
=> y ≤ √25
Therefore, the domain for the equation y = √25 - x^2 is all real values of x such that y is less than or equal to √25. Represented in the standard form of intervals, this can be written as:
Domain: x ∈ (-∞, +∞) and y ∈ [0, √25]
construct a scatter plot for the data.label your y-axis in increments of 50
Answers
After the graph is labeled and titled, it is complete and ready to be used to represent the relationship between the two variables.
What is data?Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.
A scatter plot is used to represent the relationship between two variables using data points. In this case, the x-axis would represent the data points, while the y-axis would be labeled in increments of 50. To construct a scatter plot, one must first gather the data points and then plot them on a graph. The data points should be connected with a line or points to form the scatter plot.
To begin, the data points must be collected and organized. This can be done by organizing the data points in a table, using two columns to represent the x-axis and y-axis values. Once the data is organized, the x-axis and y-axis values can then be plotted on a graph. The y-axis should then be labeled in increments of 50. Once the data points are plotted, a line or points should be used to connect the data points, forming the scatter plot.
Finally, the scatter plot should be labeled and given a title, if applicable. The x-axis should be labeled with the data points, while the y-axis should be labeled in increments of 50. The title should provide a brief description of what the scatter plot is depicting. After the graph is labeled and titled, it is complete and ready to be used to represent the relationship between the two variables.
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Suppose that of all babies born in a particular hospital are girls. If babies born in the hospital are randomly selected, what is the probability that at most of them are girls
Answers
Answer:
100%
Step-by-step explanation:
If all the babies born in that hospital are girls then if randomly selected they will all be girls because there are no boys even at that hospital.
Select the correct answer. In which direction must the graph of f(x) = x be shifted to produce the graph oSelect the correct answer.
In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = f(x) - 4?
A.
left and down
B.
right and up
C.
down
D.
upf g(x) = f(x) - 4? A. left and down B. right and up C. down D. up
Answers
Answer:
A. down
Step-by-step explanation:
The parent graph is
f(x)=x
If this graph is transformed to obtain
g(x)=f(x)−4
The subtracttion means the graph will shift downward vertically
The graph of g(x) is obtained by shifting f(x) down by 4 unit.
Therefore the direction is down.
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Nate is 2 years younger than Alan and Kai is half Alan's age. The sum of their ages is 63. How old is Kai?
Answers
The ages of Alan, Nate and Kai is 26, 24 and 13 years respectively
AlgebraAlan's age = x yearsNate's age = (x - 2) yearsKai's age = 1/2xTotal ages = 63 years63 = x + (x - 2) + 1/2x
63 = x + x - 2 + 1/2x
63 = 2 1/2x - 2
63 + 2 = 2 1/2x
65 = 5/2x
divide both sides by 5/2x = 65 ÷ 5/2
x = 65 × 2/5
= 130/5
x = 26
Recall,
Alan's age = x years
= 26 years
Nate's age = (x - 2) years
= (26 - 2)
= 24 years
Kai's age = 1/2x
= 1/2(26)
= 13 years
Therefore, the ages of Alan, Nate and Kai is 26, 24 and 13 years respectively
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find the perimeter of the figure
Answers
Answer: \(9 \frac{1}{2} x+5\)
Step-by-step explanation:
In order to find the Perimeter, we add all the segments up.
(2x-1)+(4x+3)+(x+2)+(2x+2)+(1/10x-1)+(2/5x)
=2x-1+4x+3+x+2+2x+2+1/10x-1+2/5x ⇔ Expand Parenthesis
=2x-1+4x+3+x+2+2x+2+1/10x-1+4/10x ⇔ Convert fractions into same
denominator
=(2x+4x+x+2x+1/0x+4/10x)+(3-1+2+2-1) ⇔ Put like terms together
=(9x+1/2x)+5 ⇔ Combine like terms
=9 1/2 x +5
Hope this helps!! :)
Please let me know if you have any questions
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
The mean pulse rate in beats per minute of a certain group of adult males is 76 bpm. The hypothesis test results in a p-value of 0.0075
State a conclusion about the null hypothesis
Answers
The conclusion on the null hypothesis is B. Reject H₀ because the P-value is less than or equal to a.
How to conclude on the null hypothesis ?It is posited that the mean pulse rate for a specific grouping of adult males equals 76 bpm as set forth by the null hypothesis. In its place, an alternative hypothesis suggests this figure does not reflect actuality.
At a given significance level identified by alpha = 0.05, rejection of the null hypothesis requires us to identify a P-value lesser than or equal to 0.05.
The P-value determined within the question happens to be below such a threshold at 0.0075, which results in the rejecting of the null hypothesis.
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how to graph an inequality y<1-2x
Answers
Answer:
Step-by-step explanation:
Explain the inequality -4 C > -9C describes how the temperatures are related
Answers
NO SPEAK ENGLISH SORRYYYY
The inequality explains the value of -4°C is greater than -9°C
What is inequality?It is known as inequality when both sides of a mathematical statement contain mathematical signs that are either less than or larger than one another.
It is given that,
-4°C > -9°C
We utilize the "Greater than or equal to" sign in linear inequalities when the value of a variable is greater than or equal to a certain value. The "greater than" symbol (>), which has a sleeping line beneath it, is used to denote it. It is represented by the character (≥).
Thus, the inequality explains the value of -4°C is greater than -9°C.
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Write the ratio 40.5 to 8.1 as a fraction
Answers
\(\cfrac{40.5}{8.1} ~~ \begin{cases} 40.5\implies \frac{405}{10}\\\\ 8.1\implies \frac{81}{10} \end{cases}\implies \cfrac{ ~~ \frac{405}{10} ~~ }{\frac{81}{10}}\implies \cfrac{405}{10}\cdot \cfrac{10}{81}\implies \cfrac{405}{81}\cdot \cfrac{10}{10} \\\\\\ \cfrac{5\cdot 81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot \cfrac{81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot 1\cdot 1\implies \cfrac{5}{1}\)
Find the coordinates of the point 3/10
of the way from A to B.
Answers
The coordinates of the point 3/10 of the way from a to b is (-0.3, -6.3)
How to determine the coordinates of the point?The given parameters are:
the coordinates of b is (9,7) the coordinates of a is (-4,-6)The position of the point is given as:
Location = 3/10
Express as ratio
m ; n = 3 : 10 - 3
This gives
m ; n = 3 : 7
The coordinates of the point are then calculated as:
Point = Location * (mx2 + nx1, my2 + ny1)
This gives
Point = 3/10 * (3 * 9 + 7 * -4, 3 * 7 + 7 * -6)
Evaluate
Point = 3/10 * (-1, -21)
This gives
Point = (-0.3, -6.3)
Hence, the coordinates of the point 3/10 of the way from a to b is (-0.3, -6.3)
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Complete question
find the coordinates of the point 3/10 of the way from a to b
the coordinates of b is (9,7)
the coordinates of a is (-4,-6)
Find the domain of each expression.
√3 − 6x
√13 − (13 − 2x )
1/√x − 2
Answers
Answer:
To summarize:
√3 - 6x: Domain is all real numbers (-∞, +∞).
√13 - (13 - 2x): Domain is all real numbers (-∞, +∞).
1/√x - 2: Domain is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).
Step-by-step explanation:
To find the domain of each expression, we need to identify any restrictions or limitations on the variables that would result in undefined values.
√3 - 6x:
Since square roots are defined for non-negative numbers, the expression is defined as long as the value inside the square root (√3) is non-negative. The square root of 3 is a positive value, so there are no restrictions on the domain of this expression. Therefore, the domain is all real numbers (-∞, +∞).
√13 - (13 - 2x):
Similar to the previous expression, the square root (√13) is defined for non-negative values. However, we also need to consider the expression (13 - 2x) inside the parentheses. This expression does not have any limitations since it is defined for all real numbers. Therefore, the domain of this expression is all real numbers (-∞, +∞).
1/√x - 2:
For this expression, we need to consider both the square root (√x) and the denominator (1/√x). The square root (√x) is defined for non-negative values of x. However, the denominator 1/√x will become undefined if the value of x is zero because division by zero is undefined. Therefore, we need to exclude x = 0 from the domain. For all other non-zero values of x, the expression is defined. Therefore, the domain of this expression is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).
Help me I’ll mark you brainly!
Answers
−
1
−
6
x
2
−
1
6
x
4
Answer:
- 6x² -x⁴/6 -1 because 6x² is co effectient
82°
118°
95°
X°
Image not to scale
Calculate the missing angle x.
Answers
Answer:
x = 65
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the angles and equate to 360
x + 95 + 118 + 82 = 360
x + 295 = 360 ( subtract 295 from both sides )
x = 65
Why are inequalities like the last two problems graphed on a number line while the ones in the
Set portion of this assignment are graphed on a coordinate plane? What difference is there
between the inequalities in the last two problems and the ones found in problems 13-16?
Answers
It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.
Why some inequalities are graphed on a number line?The type of diagram that we need to use depends on the number of variables that we have.
A single variable ----> number linetwo variahbles ----> a coordinate plane.3 variables ---> a volume.That is the main reason, for example:
x > 2
Is graphed on a number line.
y > 3x + 4
is graphed on a coordinate plane.
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Can somebody please help me and tell me what the error is!! PLEASE I NEED HELP ELSE I WILL FAIL MY CLASS AND GO TO SUMMER SCHOOL SO PLESE HELP ME!
Answers
Answer:
I think that is enlargement
Step-by-step explanation:
i like helping out people oh by the way i'm new will you be my friend
f(x) = 2x - 7
g(x) = 3x² - 5x - 7
Find: f(g(x))
Express in standard form
Answers
The composite function of f(x) and g(x) is given as follows:
f(g(x)) = 6x² - 10x - 21.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The function g(x) in this problem is given as follows:
g(x) = 3x² - 5x - 7.
Hence, for the composite function in this problem, the lone instance of x in f(x) is replaced by 3x² - 5x - 7, as follows:
f(g(x)) = f(3x² - 5x - 7) = 2(3x² - 5x - 7) - 7 = 6x² - 10x - 21.
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-2 (x + 4) – (3x – 8)
What it equals
Answers
Answer:
-2x+-8-3x-8
Step-by-step explanation:
-2 times x =-2x
-2 times 4=-8
Answer:
x
Step-by-step explanation:
-2 (x + 4) – (3x – 8)
-2x-8-3x+8
x+0
x
combine like terms to find the answer.
Answers
Answer: 9m + 5y + 1
Step-by-step explanation:
3 + 6m + -2y - 2 + 3m + 7y
3 + -2 = 1
1 + 6m + -2y + 3m + 7y
-2y + 7y = 5y
1 + 6m + 5y + 3m
6m + 3m = 9m
9m + 5y + 1
Answer:
1+9m+5y
Step-by-step explanation:
which of the following is figure are complementary
Answers
Which of the following functions best describes this graph?
Answers
Answer:
d
Step-by-step explanation:
can you help me with my question n Lucinda Matlock's description of the setting of Spoon River (Lines 15-18), Edgar Lee Masters uses the Modernist writer's convention of A characterization B. dialog C imagery. I will give you brainly
Answer:
THE ANSWER IS D
Step-by-step explanation:
A
P
E
X
How many centiliters are in 0.00005 liters?
0.00005 L = [?] cL in standard form.
Answers
The number of centilitres which is equivalent to 0.00005 liters as required to be expressed in standard form is; 5 × 10-² cL.
What is the number of centilitres in 0.00005 litres?Recall that; it follows from metric systems that;
100 centilitres = 1 litres.
On this note, it follows from proportion that the number of centilitres present in 0.00005 litres as required is;
= 0.00005 × 100 centilitres
= 0.005 centilitres.
Ultimately, when expressed in standard form, it follows that the number of centilitres in 0.00005 liters is; 5 × 10-² cL.
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Write the slope-intercept form of the equation for each line.
Answers
Step-by-step explanation:
points on the line: (4, -2) & (-5, 3)
gradient of the line = -5/9
general equation for all straight lines: y = mx + c
substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c
therefore, c = 2/9
so the general equation is y = (-5/9)x + 2/9
1. In 2023, cities X and Y are nearly the same size and both are growing
rapidly. City X has a population of 100,000 and is growing at a continuous yearly rate
of 2.6%. The population of city Y is 90,000 and is growing at a continuous yearly rate
of 3.1%. Find each of the following.
(a) Assuming continued growth at the same rate, find a formula for the
population of city X at time t years after 2023.
(b) Assuming continued growth at the same rate, find a formula for the
population of city Y at time t years after 2023.
(c) Write and solve an equation that can be used to determine the number of
years it will take for the population of city Y to catch up to city X. Show your work pretty please!!!!
Answers
Answer:
Step-by-step explanation:
(a) To find the population of city X at time t years after 2023, we can use the formula:
P(t) = P(0) * e^(rt)
where P(0) is the initial population, r is the annual growth rate as a decimal, and e is the mathematical constant approximately equal to 2.71828.
Substituting the values given, we get:
P(t) = 100,000 * e^(0.026t)
(b) Similarly, for city Y, we have:
P(t) = 90,000 * e^(0.031t)
(c) To find the number of years it will take for the population of city Y to catch up to city X, we can set the two population formulas equal to each other and solve for t:
100,000 * e^(0.026t) = 90,000 * e^(0.031t)
Dividing both sides by 90,000 and taking the natural logarithm of both sides, we get:
ln(e^(0.026t)) = ln(e^(0.031t)) + ln(9/10)
0.026t = 0.031t + ln(9/10)
0.005t = ln(9/10)
t = ln(9/10) / 0.005
t ≈ 13.9 years
Therefore, it will take approximately 13.9 years for the population of city Y to catch up to city X.
What is mathematics. why is it important?
Answers
Mathematics provides a framework for developing critical thinking, problem-solving, and analytical skills that are valuable in many aspects of life.
What is mathematics?
Mathematics is a fundamental discipline that plays a crucial role in our daily lives and in shaping our understanding of the world.
Mathematics is a field of study that deals with the properties and relationships of numbers, quantities, shapes, and patterns. It involves using logical reasoning, abstraction, and symbolic manipulation to understand and solve problems related to these concepts.
Mathematics is important for many reasons. First and foremost, it is a fundamental tool for understanding and describing the world around us. It plays a crucial role in science, technology, engineering, economics, finance, and many other fields by providing tools for modeling and analyzing complex phenomena.
Mathematics is also essential for making accurate predictions and decisions based on data and evidence, as well as for designing and optimizing systems and processes.
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a 60-hz induction motor is needed to drive a load at approximately 895rpm. part a determine the maximum number of poles required to drive the load at 895 rpm . express your answer as an integer. p
Answers
The maximum number of poles required to drive the load is 8.
full load speed = 120*f/p
850 = 120*60/p
p = 120*60/850
p = 8.47
since no. of poles are even so
p = 8
if number pole p = 8
synchronous speed Ns = 120*f/p = 120*60/8 = 900RPM
SLIP = (Ns - N)/Ns
s = (900-850)/900
s = 0.056
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Find the missing ange:
RPQ =______
Answers
The value of angle RPQ in the circle is 115 degrees.
How to find the angle in the circle?The intersecting chords theorem, also known as the chord theorem, is an elementary geometry statement that describes a relationship between the four line segments formed by two intersecting chords within a circle.
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
∠RPQ = 1 / 2 (arc angle RQ + arc angle SA)
arc angle RQ = 175 degrees
arc angle SA = 55 degrees
Hence,
∠RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115 degrees.
The angle is 115°.
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factor step by step:
x^2+1
Answers
Answer:
(x + i) (x - i)
Step-by-step explanation:
The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.
To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.
We can rewrite x^2 + 1 as:
x^2 + 1 = x^2 - (-1)
Now, we can use the difference of squares formula to factor x^2 - (-1):
x^2 - (-1) = (x + i)(x - i)
Therefore, the factored form of x^2 + 1 is:
(x + i)(x - i)