A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
a
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
b
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
c
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
d
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Answer:
C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step-by-step explanation:
The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)
Hope this helps
Find the measurement of BC.
Need help please- and also explanation.
Answer:
Step-by-step explanation:
Use "Law of sines"
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin B}{b}[/tex] = [tex]\frac{sin C}{c}[/tex]
please help with math!!
Answer:
quadratic
Step-by-step explanation:
You are one of 50 people with an entry into a random drawing for a new bicycle.
What is the probability that you will win the drawing?
The points (p, -2) and (6, 8) fall on a line with a slope of -10. What is the value of p?
Thank you!
Step-by-step explanation:
(8 + 2)/(6 - p)= -10
10/6 - p = -10
-60 + 10p = 10
10p= 70
p= 7
Calculate the value of
x
.
Answer:
25 degrees
Step-by-step explanation:
2x plus 310 degrees add up to a full circle: 360 degrees.
Therefore, 2x = 360 - 310, or 2x = 50, or x = 25 degrees
please help will mark brainliest no links
Answer:
what is this
Step-by-step explanation:
In right triangle abc, altitude cd with length h is drawn to its hypotenuse. we also know ad = 12 and db = 3.
The value of h is 6.
Now, According to the question:
In right triangle, ABC
Given data:
AD = 12 and DB = 3
The equivalent ratio of the triangles is:
h : 12 = 3 : h
Express as fractions
[tex]\frac{h}{12} =\frac{3}{h}[/tex]
Cross Multiply:
[tex]h^2[/tex] = 36
Take positive square roots of both sides
h = 6
Hence, the value of h is 6.
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7.
Choose the linear inequality that describes each graph.
A. y ≥ 2x + 2
B. y ≥ – 2x + 2
C. y ≤ 2x – 2
D. y ≥ 2x – 2
Answer:
D. y ≥ 2x – 2
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
y ≥ 2 x + 2
Graph the inequality by finding the boundary line, then shading the appropriate area.
y ≥ − 2 x + 2
Graph the inequality by finding the boundary line, then shading the appropriate area.
y ≤ 2 x − 2
Graph the inequality by finding the boundary line, then shading the appropriate area.
y ≥ 2 x − 2
pls solve the question (i will mark u the brainliest)
Step-by-step explanation:
May be (p³)³ would be the answer!!!
BRAINLY ME PLEASE IF HELPFUL!!!
Need help asap pleaseeeeeeeeee
Answer:5.7ft
Step-by-step explanation:
sin = opposite/adjacent
sin 35 = x/10
10 * sin 35 = x
x=5.7
What is the quotient (3x2 4x − 15) ÷ (x 3)? 3x 5 3x − 5 3x 1 3x − 1, r = 1
By solving the expression (3x2 +4x − 15) ÷ (x +3) the quotient is 3x-5 and r=0
What do you meant by quotient?When solving a division problem, the quotient is obtained by dividing the dividend by the divisor.
Mathematically, we denote the outcome of this division by separating the quotient and remainder with a capital R. (see below). The entire number that results from simplifying a fraction is known as the quotient.
We can do it by long division method the required quotient is 3x-5 and r=0
not 3x-1 , r=1
multiply the divisor with 3x we will get 3x²+9x to cancel out the first term of dividend.
Now after solving we will get -5x -15
Now, multiply the divisor by -5 we will get -5x-15 which will cancel the entire dividend.
So that the quotient is 3x-5 and r=0
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Which of the following digits could replace the in the ten thousands place to make this statement true? 706,103 rounds to 800,000 if we round to the nearest hundred thousand, Choose all answers that apply (A ) 3 В 5 7 8
4th grade
Answer:
numbers 5-9 could replace the ten thousand place to make the statement true.
5, 7, 8
Step-by-step explanation:
Have a nice day!
You need to put equation signs in between the 6. 1 gross = 144
The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Place the arithmetic symbol between the 6 times 6 to become one. Then we have
⇒ 6 + 6 - 6 - 6 + 6 / 6
⇒ 1
The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.
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Sabreena is playing a card game, and the odds of her winning after drawing the next card are 5:7. What is the probability of her not winning? Enter your answer as a decimal rounded to the nearest thousandth, like this: 0.423
The probability that Sabreena is going to lose is given as 0.5833
How to solve for the probabilityProbability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.
A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.
If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7
In this case, the odds of Sabreena winning are 5:7,
so the probability of winning is 5/(5+7)
the probability of not winning is 1 - 5/12
The probability of not winning is approximately 0.5833
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a wire of radius 6mm and length 400 is melted to sphere.calculate the volume of an irregular solid
Answer:
it's 10 cemetery in a two way too far and far from a lot for
The volume of irregular solid is 45239 mm^3
Given
for cylinder,
radius = 6mm and length = 400 mm
Volume, is defined as the ratio of the mass of object to its density.
since if the cylinder is melted to sphere the volume remains the constant
so.
volume of an irregular solid = volume of cylinder
= πr^2l
= 3.14 x 6^2 x 400
= 45239 mm^3
Thus, the required volume of of irregular solid is 45239 mm^3
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In 6-7, explain whether each graph represents a linear function.
Answer:
In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line.
Step-by-step explanation:
In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line. A linear function is defined as a function of the form y = mx + b, where m and b are constants. The graph of a linear function is a straight line with a constant slope, and so any graph that is not a straight line is not a linear function.
Without the actual graph it's hard to say for sure, but based on the provided information, "The graph does not contain the point (20, –8)" indicates that the graph does not pass through this point (20, -8), and it could be indicating that it's not a straight line, So, The graph does not represent a linear function.
Can some one help me with this question its hard :( down below ill give brainliest
Answer:
A is the answer ...........
[tex]\sqrt{18} +\sqrt{50}[/tex]
Answer:
= 8 (square root of) 2
Step-by-step explanation:
i hope this helps :)
16. A large waffle cone has a diameter of 3 inches and a height of 8 inches. Two scoops of
✓ ice cream have been stacked on top of the cone, after it was filled. The scoops are
completely round and have a diameter the same as the cone.
Find the volume of the two scoops of ice cream combined with the ice cream inside the
cone.
Answer:
(1/3) (44.5)π cm3.
Step-by-step explanation:
The volume of the two scoops of ice cream combined with the ice cream inside the cone can be calculated as follows:
Volume of cone = (1/3) π (3/2)2h = (1/3) π (4.5)8 = (1/3) (35.5)π
Volume of scoop = (1/6) π d3 = (1/6) (3)π
Total volume = (1/3) (35.5)π + 2(1/6) (3)π = (1/3) (44.5)π cm3.
How many numbers lie between the square of 56 and 57
Answer:
Given, two numbers 56 and 57 we need to find out the numbers lie between the squares of the given numbers.
Now, we have numbers lying between the square of n and (n + 1) is 2n
⇒ Numbers between squares of 56 and (56 + 1) = 2 × 56 = 112
Hence, 112 numbers lies between the square of the given numbers.
112
Step-by-step explanation:Given, two numbers 56 and 57 we need to find out the numbers lie between the squares of the given numbers. Now, we have numbers lying between the square of n and (n + 1) is 2n. ⇒ Numbers between squares of 56 and (56 + 1) = 2 × 56 = 112. Hence, 112 numbers lies between the square of the given numbers.
#CarryOnLearning#BrainliestAnswer#BrainliestBautista is planning a vacation to Los Angeles. He already has $42.50 and saves $25.50 each week. If the trip will cost a total of $654.5, how many weeks will it take for him to save for the trip?
Answer:
24 WEEKS
BECAUSE IF U MULTIPLY 24X25.50 U WILL GET 612 ADD 42.50 AND U WILL GET 654.50
Lisa and Jen left home at the same time, only Lisa biked to school at a speed of 10 mph while Jen just walked at a speed of 4 mph.
How far apart are the school and house?
The distance between the school and the house is 1.6 miles.
What is distance?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Let the distance between the school and the house be x miles.
Given that:
Lisa:
Rate = 10mph
Time = t hours
Distance= x
According to distance formula we have:
x = 10 *t [ equation 1]
Jen:
Rate = 4mph
Time = t hours
Distance= x-1 miles
According to the distance formula we have:
x-1 = 4*t [equation 2]
Substitute the value of equation 1 in equation 2 we have:
10t -1 = 4t
6t =1
t = [tex]\frac{1}{6}[/tex]
Now substitute the value of t in equation 1.
[tex]x = 10 * \frac{1}{6}[/tex]
x= 1.6 miles.
Hence the distance between the school and the house is 1.6 miles.
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WILL GIVE BRAINLIEST
PHOTO ATTACHED
Drag each tile to the correct box.
Arrange the solutions of the mathematical expressions from least to greatest according to their values in scientific notation.
(4.3x10^6).(9.8x10^-4)
(2.9x10^7)-(1.6x10^–9)
(4.7 x 10^3). (8.6 x 10^-7)
________________
(3.8 x 10^-4). (6.1 x 10^2)
(4.9x10^3).(74x10^–6)
(3.9 x 10^5). (8.7 x 10^-3)
_________________
(3.7 x 10^-5). (2.9 x 10^8)
Answer:
3,4,2,5,1. youre welcome :)
The arrangement of the solutions of the mathematical expressions from least to greatest according to their values in scientific notation is as follows:
Order Mathematical expressions
1. 3. (4.7 x 10^3). (8.6 x 10^-7)
________________
(3.8 x 10^-4). (6.1 x 10^2)
2. 4. (4.9x10^3).(74x10^–6)
3. 2. (2.9x10^7)-(1.6x10^–9)
4. 5. (3.9 x 10^5). (8.7 x 10^-3)
_________________
(3.7 x 10^-5). (2.9 x 10^8)
5. 1. (4.3x10^6).(9.8x10^-4)
What are mathematical expressions?Mathematical expressions are a combination of numbers, variables, and functions (for example, addition, subtraction, multiplication, or division, etc.) to state complete mathematical thoughts.
Mathematical expressions can be likened to grammatical phrases. In linguistics, a phrase, which may include an action, but it does not make a complete sentence without being combined with other phrases.
Data:1. (4.3x10^6).(9.8x10^-4)
2. (2.9x10^7)-(1.6x10^–9)
3. (4.7 x 10^3). (8.6 x 10^-7)
________________
(3.8 x 10^-4). (6.1 x 10^2)
4. (4.9x10^3).(74x10^–6)
5. (3.9 x 10^5). (8.7 x 10^-3)
_________________
(3.7 x 10^-5). (2.9 x 10^8)
Thus, the arrangement of the solutions of the mathematical expressions from least to greatest according to their values in scientific notation is 3, 4, 2, 5, and 1.
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Write a quadratic function in vertex form whose graph has the vertex (-2, - 13) and passes
through the point (-6,3).
Answer:
f(x) = ⁵/₈(x+2)² - 13Step-by-step explanation:
Vertex form of the equation of a quadratic function with vertex (h,k):
f(x) = a(x - h)² + k
To find a we need to put the point and the vertex into this equation:
3 = a(-6 + 2)² - 13
10 = a(-4)²
16a = 10
a = ⁵/₈
Therefore, vertex form of the quadratic function:
f(x) = ⁵/₈(x+2)² - 13
A rectangle has a length of 2x² + 3x +7 and
width of x^2 +5. What is the perimeter of
the rectangle?
Answer:
[tex]perimeter = ( {2x}^{2} + 3x + 7) + ( {x}^{2} + 5) \\ = (3 {x}^{2} + 3x + 12) \: units[/tex]
Answer:
[tex]P=6x^2+6x+24[/tex]
Step-by-step explanation:
[tex]P=2w+2l\\\\w=x^2+5\\\\l=2x^2+3x+7\\\\P=2(x^2+5)+2(2x^2+3x+7)[/tex]
ASAP please! I have to get this done to get my grades up!
If f(x) = x2 - 3x + 5 and g(x) = 3x. Find the product of the functions.
A) (f · g)(x) = x2 + 5
B) (f · g)(x) = 3x2 - 9x + 15
C) (f · g)(x) = 3x2 - 6x + 15
D) (f · g)(x) = 3x3 - 9x2 + 15x
Answer:B
Step-by-step explanation:
A sequence has a rule to subtract 3/4 from the previous term. Create a sequence using this rule with at least 5 rational numbers.
1, 1/4, -1/2, -5/4, -2
Step-by-step explanation:
Let the first term of the sequence be a;
Since the sequence has a rule to subtract 3/4 from the previous term;
the second term will be a - 3/4
the third term will be (a - 3/4) - 3/4
=> a - 6/4
=> a - 3/2
the fourth term will be (a - 3/2) - 3/4
=> a - 9/4
the fifth term will be (a - 9/4) - 3/4
=> a - 12/4
=> a - 3
We can then create a hypothetical series by setting a = 1.
The first term => a = 1
The second term => a - 3/4 = 1 - 3/4 = 1/4
The third term => a - 3/2 = 1 - 3/2 = -1/2
The fourth term => a - 9/4 = 1 - 9/4 = -5/4
The fifth term => a - 3 = 1 - 3 = -2
The generated sequence is therefore:
1, 1/4, -1/2, -5/4, -2
Note: The numbers in the sequence are rational numbers since they all have a non-zero denominator.
please please please help!!!
Answer:
a = 35, b = 40, c = 17.5
Step-by-step explanation:
The sum of the 3 arcs on the semicircle above the diameter = 180° , that is
65 + 80 + a = 180
145 + a = 180 ( subtract 145 from both sides )
a = 35
The inscribed angles b and c are half the measures of their intercepted arcs
b = [tex]\frac{1}{2}[/tex] × 80 = 40
c = [tex]\frac{1}{2}[/tex] × 35 = 17.5
Find the number of terms and the degree of this polynomial.
Answer:
Terms = 2
Degree = 10
Step-by-step explanation:
Terms are the values appearing separated by the the mathematical sign. for this question we have 2 terms only.
the degree of a polynomial is usually the largest degree of the individual terms. for our question it's degree 10 since it's the highest.