What is the missing step in this proof?
Answer:
Option C is correct.
The missing steps in this proof is; [tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex].
Explanation:
Given ΔABC.
Prove that: The sum of the interior angle measures of ΔABC is [tex]180^{\circ}[/tex]
Let A ,B and C forms a triangle [Given]
Parallel lines are those two lines that are always the same distance apart and never touch.
then, by the definition of parallel lines and labeling angles
DE be the line passing through B, parallel to AC, with angles as labelled in the figure as shown below in the attachment.
Alternative Interior Angle theorem states that the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles also this theorem says that when the lines are parallel, then the alternate interior angles are equal.
Then,
[tex]\angle 1 \cong \angle 4[/tex] and
[tex]\angle 3 \cong \angle 5[/tex] [By Alternative Interior angle theorem]
Angles are always congruent if their measures in degrees are equal.
therefore,
[tex]m\angle 1 =m\angle 4[/tex] and
[tex]m\angle 3=m\angle 5[/tex] [By Congruent Angle have equal measure] ......[1]
Straight Angles states that angles on one side of a straight line always add to 180 degrees.
From the given figure;
By the addition angle and definition of straight angle we get;
[tex]m\angle 4 +m\angle 2 +m\angle 5 =180^{\circ}[/tex] ......[2]
Substituting equation [1] in [2] we get;
[tex]m\angle 1 +m\angle 2 +m\angle 3 =180^{\circ}[/tex]
Therefore, the sum of the interior angles measures of triangle ABC is [tex]180^{\circ}[/tex]
Solve by factoring c^2=5c
The solutions to the equation c² = 5c are c = 0 and c = 5.
We have,
To solve the equation c² = 5c by factoring,
we can rearrange it as:
c² - 5c = 0
Then we can factor out the common factor of c, giving:
c(c - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.
So we have:
c = 0 or c - 5 = 0
Solving for c in each case, we get:
c = 0 or c = 5
Therefore,
The solutions to the equation c² = 5c are c = 0 and c = 5.
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What are the amplitude, period, and midline of f(x) = 3 cos(4x − π) + 2?
Answer:
The amplitude of the function is 3, period of the function is [tex]\frac{\pi}{2}[/tex] and midline of the function is 2.
Step-by-step explanation:
The given function is
[tex]f(x)=3\cos(4x-\pi)+2[/tex] .... (1)
The standard form of a Cosine function is
[tex]g(x)=a\cos(bx+c)+d[/tex] ... (2)
where, a is amplitude, period is [tex]\frac{2\pi}{b}[/tex] and d is midline.
From (1) and (2), we get
[tex]a=3,b=4,d=2[/tex]
The amplitude of the function is
[tex]a=3[/tex]
The period of the function is
[tex]\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}[/tex]
The midline of the function is
[tex]d=2[/tex]
Therefore the amplitude of the function is 3, period of the function is [tex]\frac{\pi}{2}[/tex] and midline of the function is 2.
If s is a sequence of consecutive multiples of 3, how many multiples of 9 are there in s? (1) there are 15 terms in s. (2) the greatest term of s is 126.
Pleaseee help. The longer base of an isosceles trapezoid measures 23 ft. The nonparallel sides measure 9ft, and the base angle measure 80 degrees. Find the length of a diagonal.
When college students are asked to solve a puzzle problem independently, only about 10% solve it correctly. then, when students who did not solve the problem were allowed to discuss the problem together, 75% got it right. this illustrates the participants' _____?
The correct answer to fill in the blank is:
“Cognitive flexibility”
Cognitive flexibility refers to a person’s ability to adapt the mental processing strategies to face new and unexpected situations or problems. In this case, some of the students who initially did not solve the problem transformed their way of solving the puzzle after the discussion thus getting it right the next time.
The graph below represents which system of inequalities? graph of two infinite lines that intersect at a point. One line is solid and goes through the points 0, 2, negative 2, 0 and is shaded in below the line. The other line is dashed, and goes through the points 0, 6, 3, 0 and is shaded in below the line.
Answer:
its answer d
Step-by-step explanation:
Simplify the expression
4m+5−3m
I have been stuck on this for a long time >.
Simplified form of the expression 4m+5−3m:
m + 5
Expression : Degree of m is 1 , so the expression is linear.
Given , that expression: 4m+5−3m
Now to simplify the expression,
⇒ 4m + 5 − 3m
Combine like terms,
⇒ (4m - 3m) + 5
⇒ m + 5
Thus the simplified form is m + 5 .
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using the diagram what is the intersection of plane ABCD and gc
can someone help me with this factoring problem? I forgot how to factor.
Factor completely −3x2 + 6x − 9.
−3(x2 − 2x + 3)
−1(x2 − 6x + 9)
−3x(x2 − 2x + 3)
−3(x2 + 2x − 3)
If BC = 4.5, CD = 7.7, and AD = 16.7, find AB to the nearest tenth.
A. 2.1
B. 28.6
C. 9.8
D. 2.2
Express 257.36 multiplied by 10 in scientific notation
Solve the inequality -2x is less than or equal to 3x + 1 is less than or equal to 10
Write 121 raised to the one-half power equals 11 as a logarithmic function
When factored, the trinomials x^2-2x-15 and x^2-9x+20 have one binomial factor in common. What is this factor?
1. x-7
2. x+7
3. x-5
4. x+5
how much would an 185 astronaut weigh on the moon?
Jack is building a deck that is 8 ft by 27.63 ft. He has the base built; he just needs to cover the surface with wood. When he gets to the hardware store he finds sheets of wood that are four ft by eight ft. Use estimation to determine how many sheets of wood he should buy to cover the surface of the deck.
What is the length of the third side of the right triangle?
( Best explained and correct answer gets brainliest. )
6^2 + 3^2 = x^2
36 + 9 = x^2
45=X^2
X= sqrt(45) = 3squareroot5
answer is A
You flip a coin and roll a number cube. What is the probability that you flip tails and roll a number less than five?
The graph of f(x) = x2 is shifted 3 units to the right to obtain the graph of g(x). Which of the following equations best describes g(x)?
a. g(x) = (x + 3)2
b. g(x) = x2 − 3
c. g(x) = x2 + 3
d. g(x) = (x − 3)2
Answer: Option 'd' is correct.
Step-by-step explanation:
Since we have given that
[tex]f(x) = x^2[/tex]
We need to shift the function f(x) 3 units to the right to obtain the graph of g(x).
As we know that shifting right is the horizontal shift.
And f(x-h) = g(x) , here f shift right h units.
so, After shifting 3 units right, we get that
[tex]g(x)=(x-3)^2[/tex]
Hence, Option 'd' is correct.
Find the first six terms of the sequence.
a1 = -1, an = 2 • an-1
Answer:
The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32
Step-by-step explanation:
The sequence is:
[tex]a_1=-1\\a_n=2*a_{n-1}[/tex]
So, for finding the first six terms of the sequence, we need to replace n by the numbers 1 to 6 and we get:
[tex]a_1=-1\\a_2=2*a_{2-1} =2*a_1\\a_3=2*a_{3-1} =2*a_2\\a_4=2*a_{4-1} =2*a_3\\a_5=2*a_{5-1} =2*a_4\\a_6=2*a_{6-1} =2*a_5\\[/tex]
That means that the term n is 2 times the last term. Then, replacing the values of [tex]a_1, a_2, a_3, a_4[/tex] and [tex]a_5[/tex], we get:
[tex]a_1=-1\\a_2=2*(-1)=-2\\a_3=2*(-2)=-4\\a_4=2*(-4)=-8\\a_5=2*(-8)=-16\\a_6=2*(-16)=-32\\[/tex]
So, The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32
Evaluate 9 y 1 − y 0 9y1−y0 if y=−8 y=−8 .
Answer:
Step-by-step explanation:
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 3x + 2y = 6 x - y = 2
In the diagram, which two points are shown to be collinear?
In the given diagram, the points that are shown to be collinear are H and E.
Collinearity in geometry refers to the condition where three or more points lie on the same straight line. In this case, points H and E are collinear as they lie on the same straight line, which is represented by a vertical double-headed arrow passing through them.
The diagram consists of two parallelograms, labeled 'I M' and 'E P', with three points inside each. In the parallelogram 'I M', the points are labeled as I, H, and J from top to bottom. Similarly, in the parallelogram 'E P', the points are labeled as F, E, and G from top to bottom. Among these points, only H and E share the same straight line, making them collinear. The other points do not share this line and hence are not collinear with H and E. This concept is fundamental in understanding geometric relationships and properties.
One week, Katie Hopper earned the following commissions: Monday, $124; Tuesday, $88; Wednesday, $62; Thursday, $137; Friday, $195. Find her total amount of commissions for the week
add them together:
124 + 88 + 62 +137 +195 = $606 total
In triangle def, FE = 13 and angle f equals 34. Find DF to the nearest tenth.
The height of the oversized container is 3 m it's diameter is 2 m what is its area?
to the nearest whole degree, what angle measure has a sine of .9762
How to solve math problems with rules of exponents?
Final answer:
When solving math problems with rules of exponents, it is important to understand key concepts such as multiplication of exponentials, taking square roots of exponentials, and dividing exponentials.
Explanation:
When solving math problems with rules of exponents, there are several key concepts to keep in mind:
Multiplication of Exponentials: Multiply the digit terms in the usual way and add the exponents of the exponential terms.Taking Square Roots of Exponentials: If necessary, decrease or increase the exponential term so that the power of 10 is evenly divisible by 2. Extract the square root of the digit term and divide the exponential term by 2.Dividing Exponentials: Divide the numbers out front and subtract the exponents.It is important to understand these rules and practice applying them to various problems in order to master solving math problems with rules of exponents.
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